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�STJOHN’S
College
ANNAPOLIS ■ SANTA FE
On Faraday
The College (usps 018-750)
ichael Faraday was the Horatio Alger of Victorian Eng
land. His father was a not-especially-successfnl black
smith who had emigrated to London from Westmorland
when the family fell on hard times. Faraday was born
there in 1791. He went to school until he was 13 and at 14
he was apprenticed to a bookbinder. Through reading,
the young man became fascinated with science. By the
time he was 19 he was conducting chemical experiments on his own, with equip
ment and materials he was able to scrounge, and he attended public lectures at
the Royal Institution with tickets provided by one of the bookbinder’s patrons.
In a positive effort at self-improvement, Faraday worked to purge his accent of
Cockney origins. He corresponded with like-minded young men who also sought
to expand their intellectual horizons. He considered science a noble activity and
once wrote: “My desire was to escape from trade, which I thought vicious and
selfish, and to enter into the service of science, which I imagined made its pur
suers amiable and liberal.”
On a long shot, without any introduction, Faraday wrote Sir Humphrey Davy,
the eminent chemist, and enclosed the notes he had taken on Davy’s lectures.
Later, when Davy injured his eyes in an experiment, he sent for Faraday to write
for him and serve as an assistant. From there, Faraday’s rise in the very active
Victorian world of science was swift. By 1813 he had been appointed Chemical
Assistant at the Royal Institution.
By 1835, Faraday was the director of the laboratory at the Royal Institution. He
lived upstairs, having married the daughter of a well-to-do silversmith, and had
his laboratory in the basement. His focus was experimentation and on explaining
to the public the principles governing nature.
In r83i he began research into electromagnetic induction, resulting in a paper
that established his reputation. He published 400 articles and books, including
the monumental Experimental Researches in Electricity.
Scientists in Victorian Britain felt a civic responsibility to use their expertise
for the public good. Faraday made recommendations on railway safety. In his 60s
he traipsed over rocky seacoast terrain to visit lighthouses and study how to
improve their operation. He was called in to investigate a fatal mine explosion.
He tried to improve the quality of steel by making different alloys.
Faraday wasn’t a mathematician, and his experiments did not depend on or
seek to find a mathematical explanation of the world. Faraday belonged to a
strict Christian sect called the Sandemanians. He saw the natural world as
divinely created, and sought the natural laws he felt reflected God’s will.
Maxwell, who later developed the equations that described what Faraday had dis
covered about electromagnetism, called him “The Great Electrical Philosopher.”
M
~BG
is published quarterly by
St. John’s College, Annapolis,
MD and Santa Fe, NM.
Known office of publication:
Public Relations Office
St. John’s College
Box a8oo
Annapolis, MD 21404-2800
Periodicals postage paid
at Annapolis, MD
Send address
changes to The College
Magazine, Public Relations
Office, St. John’s College,
Box a8oo, Annapolis, MD
21404-2800.
postmaster:
Annapolis
410-626-2539
b-goyette@sjca.edu
Barbara Goyette, editor
Sus3an Borden, assistant editor
Jennifer Behrens,
graphic designer
Advisory Board
John Christensen
Harvey Flaumenhaft
Roberta Gable
Katherine Heines
Pamela Kraus
Joseph Macfarland
Eric Salem
Brother Robert Smith
Santa Fe
505-984-6104
classics@mail.sjcsf.edu
Laura J. Mulry, Santa Fe editor
Advisory Board
Alexis Brown
Grant Franks
Robert Glick
David Levine
Margaret Odell
John Rankin
Ginger Roherty
Tahmina Shalizi
Mark St. John
Magazine design by
Claude Skelton Design
�{Contents}
Page Z2i
Commencement 2001
DEPARTMENTS
Elliott Zuckerman delivered a series of
“preludes” for graduates in Annapolis; in
Santa Fe, Cornel West urged graduates to
challenge the assumptions of contempo
rary mass culture.
Page
2, FROM THE BELL towers
•
•
•
•
•
•
•
•
•
z6
Sophomore Seminar
Forever
All Johnnies have wrestled with the
questions about faith, suffering, God,
and mortality. But some alumni, whether
by conviction or vocation, live in a world
where theology is more than a speculative
study.
Faraday, the Experimenter
Balkcom Inauguration invitation
Liberty Tree clones
New dean and GI director appointments
McDowell’s facelift
Poetry Slam highlights
Philanthropia news
The studs of St. John’s
Mortimer Adler, an appreciation
II ALUMNI VOICES
•
Marx Redux
36 ALUMNI NOTES
ALUMNI
PROFILES
38 Barbara Rogan (SF73) is a novelistshe can’t help writing
Page 2/0
31 Robert Bienenfeld (SF80) markets
tomorrow’s cars today
Rousseau and Realpolitik
33 Tia Pausic (A86), a lawyer by training,
works to build democracy in Croatia
Five alumni in the world of politics discuss
how the political philosophy on the pro
gram relates to the issues they deal with in
their professional lives.
36 Catherine Allen (A69), a cultural
anthropologist, focuses on the people
of the Andes
Page 28
40 LETTERS
It Takes Two Villages
41 OBITUARIES
Timothy Miller considers what it means
to learn in a community in his Dean’s
Statement.
•
43 HISTORY
•
Page /j-6
Nick Maistrellis on Leo Raditsa (page 43)
The colorful past of Hunt House
PAGE 46
43 ALUMNI ASSOCIATION
Say It Isn’t So
What happened to St. John’s domination
in croquet?
ON THE COVER
Michael Faraday.
Illustration by DavidJohnson.
•
Finding lost alumni
•
Welcoming new alumni
•
Amendment procedures
48 ST. John’s forever
�2.
{From
the
Bell Towers}
The Experimenter as
Entertainer
Michael Faraday was more than “the great
electricalphilosopher. ”
Who would think the burning of
an ordinary candle a fascinating
subject of study? Michael Faraday
did, and his lecture on the topicoriginally delivered for childrenwas re-created this spring at a
conference on Faraday held in
Annapolis. “There is not a law
under which any part of this uni
verse is governed which does not
come into play, and is not touched
upon, in these phenomena,”
wrote Faraday in the introduction
to his lecture “The Chemical His
tory of the Candle.”
Grant Franks (A78), a tutor in
Santa Fe, donned the garb of a
nineteenth century gentieman
scientist (a suit put together by
his wife, based on a pattern for an
Abe Lincoln Halloween
costume) and grew three
month’s worth of side
burns in order to play
Faraday. His demonstra
tions performed in front of a
crowd of students, faculty, visi
tors, and children kicked off the
three-day conference. Franks-asFaraday showed how a candle
forms a cup for the melted wax,
how capillary attraction occurs as
a candle burns, how a candle’s
vapor is combustible even after
the flame is blown out, why a can
dle flame is brightest at the top
and darker toward the bottom,
and how tongues of flame differ
from a single candle flame,
among other things.
Learn
ing the
hues to the
talk was
the easy
part. More
challeng
ing was
assembling
the props.
“Finding
different
kinds of
candles,
shaping the glass tubes, practic
ing the technique of piping gas
out of a flame, figuring out how
much copper chloride to add to
the alcohol to make a green
flame-it involved a lot of
STUFF,” says Franks. Faraday
dehvered public lectures, not in
an academic setting but at the
Royal Institution. The lab where
he carried out his own experi
ments was in the basement.
“Faraday is important because he
learns about the world by manipu
lating it with his hands, not by
casting it into algebraic forms
that he can play with on a black
board,” says Franks. “Of course,
no scientist is obhvious to experi
mental results, but Faraday is
especially wonderful in the way
his thoughts take physical form in
the apparatus he builds.” Faraday
understood the idea that there
can be some show business in science-“Faraday was, among other
things, the precursor of Mr. Wiz
ard and of Bin Nye the Science
Guy,” says Franks.
The conference (sponsoredby
the Dibner Fund) focused on two
issues: How does experiment lead
one to knowledge of nature, and
how can such knowledge be made
accessible to others, especially to
non-scientists. Faraday is particu
larly apt as a focus for these ques
tions, says Annapolis tutor
Howard Fisher, one of the confer
ence organizers. While Faraday’s
Experimental Researches in Elec-
Santa Fe tutor Grant Franks,
FaRADAY,
PLAYING THE PART OF
demonstrates the characteris
tics OF flames.
{The College. St. John’s College ■ Summer 2001 }
tricity is read in junior lab and
several of his experiments on
electromagnetism and electro
magnetic fields are performed,
his method of thinking and his
approach to experimentation are
themselves worthy of investiga
tion and thought. The confer
ence’s keynote lecture was dehv
ered by tutor emeritus Thomas
Simpson (A50) on the topic “Was
Faraday a Mathematician?” Other
lecturers included David Good
ing, from the University of Bath
(U.K.), Frank James, from the
Royal Institution of Great Britain,
and Ryan Tweney, from Bowling
Green State University. In addi
tion to the lectures and the candle
demonstration, the conference
featured a roundtable discussion
of Faraday’s “Lecture on Mental
Education” and some student
demonstrations of classic Faraday
experiments.
Faraday, whom Maxwell called
“the great electrical philoso
pher,” has been studied at St.
John’s for more than 30 years; a
part of his 7th series on electro
chemical equivalents was done in
senior lab and small segments of
the nth series on induction in
junior lab. About four years ago,
Annapohs adopted the Santa Fe
manual for junior lab electricity
and magnetism, which included
much more generous portions of
both Faraday and Maxwell, who
developed the mathematical
equations for the phenomena of
electromagnetism that Faraday
showed. A book by Howard Fish
er, Faraday’s Experimental
Researches in Electricity: Guide to
a Eirst Reading, has just been
published by Green Lion Press
(run by Bill Donahue, A67, and
Dana Densmore, A65, SFGI93);
Green Lion has also just come out
with a three-volume reprint of
Faraday’s Experimental Research
es in Electricity.
“The conference was a great
delight,” says Fisher. “I saw
again, first hand, how deeply
Faraday’s way of pursuing a ques
tion resonates with ordinary read
ers who respect a natural clarity
in the things around them.”
�{From the Bell Towers}
Balkcom Inauguration
Set for September
All St. John’s College alumni are
invited to attend the inaugura
tion of John E. Balkcom as Santa
Fe’s fifth president. Events will
take place on Friday and Satur
day, September 14 and 15. Dr.
Hanna Holborn Gray, president
emeritus of the University of
Chicago, will give the inaugural
address. Students, faculty, alum
ni, and staff have been working
on committees to organize the
celebration, which wiU include
events for all segments of the
college community. The theme
“Inviting Conversations” was
developed to capture a sense of
Mr. Balkcom’s vision for his
Liberty Tree
Lives On?
When the Liberty Tree suc
cumbed to damage from Hurri
cane Floyd in the fall of 1999,
lovers of the tree took heart in
the fact that there were several
offspring: a seedling planted
across front campus, in front of
what is now the Greenfield
Library, by the Daughters of the
American Revolution in 1889 is
now a very large tree; a Liberty
Tree descendant from a seed
hatching project begun by the
Caritas Society in 1975 thrives
on the grounds of the U.S. Capi
tol; and some crack scientists at
the University of Maryland are
working on cloning the Liberty
Tree using shoots taken from
the tree’s new growth just
months before the hurricane.
Now it seems that the baby
Liberty Tree on the Capitol
grounds may be endangered
itself. A plan to expand the Capi
tol building with the construc
presidency: a commitment to the
program, including his intention
to further relations within the
college community and expand
relationships with those who are
unfamiliar with the college.
On September 14, students,
faculty, and staff will launch the
weekend with a picnic on the
soccer field, followed by an all
college Chicago-style softball
game (an athletic challenge that
resembles “mush ball”). On Fri
day evening, inaugural guests
and college community mem
bers will join with the Santa Fe
community for a performance at
the newly renovated Lensic Per
tion of a visitors cen
ter calls for the Lib
erty offspring, along
with 83 other trees
that have national
significance (some
planted by Congress
men to honor people
or events important
in their state’s histo
ry) to be cut down.
The tree, planted in
1978 by Maryland’s
then-senator,
Charles McC. Math
ias, is now 40 feet
high, with a trunk
that is almost ao
inches in diameter.
Because the tree is
so large, moving it
would be expensive and perhaps
fatal. However, after a couple of
articles in the Washington Post
and the Baltimore Sun reported
on its fate, the Liberty progeny
suddenly appeared on the list of
trees slated to be moved rather
than chopped. Rebecca Wilson,
former public relations director
at St. John’s and the planner of
forming Arts Center in down
town Santa Fe. Students and
alumni, in addition to profes
sional musicians, will perform in
honor of the occasion.
There will be an Inaugural
Breakfast for guests of
the college and dele
gates from distinquished liberal arts
institutions on Satur
day morning, followed
by the official Inaugu
ration at IO a.m. on
Meem Library Placita.
Immediately after the
3
installation of Mr. Balkcom, a
reception will take place on the
Upper Placita. Saturday evening,
the festivities will conclude with
a Student and Alumni Waltz
Party in the Great Hall. 4-
John Balkcom will
BECOME Santa Fe’s fifth
PRESIDENT IN AN INAUGU
RATION THAT CELEBRATES
THE
St. John’s Program.
''The clones
have been
recalcitrant to
rootformation
...bittwehaveni
given up.''
The Liberty Tree, ca. 1955.
WILL ITS OFFSPRING SURVIVE?
the Liberty Tree seedling project
in the 1970s, expressed dismay
about the transplanting. “I don’t
think it can survive the move,”
she told the Baltimore Sun. She
hopes instead that the design of
the visitors center can be
{The College- St. John’s College • Summer 2001 }
modified to save the trees.
As for the clones, Gary Cole
man, a University of Maryland
professor who took cuttings of
Liberty Tree shoots, says in an email that he is still working on
the project. “We have estab
lished tissue cultures and have
managed to increase the number
of cultured shoots through this
process. Although this is good
news, the clones have been very
recalcitrant to root formation,”
he says. “We haven’t given up
and will continue until we suc
ceed.” 4-
�{From the Bell Towers}
New
Appointments
FOR Dean,
GI Directors
Bill Pastille GI Director, Annapolis
What qualifies
a tutor to lead
the Graduate
Institute?
Annapolis
tutor Bill
Pastille has one
idea: “An
advanced sense
of not knowing anything.” As he
begins his three-year term as
Director of the Annapolis Gradu
ate Institute this summer, Pastille
discusses his Socratic take on life:
“Socrates has become more and
more understandable to me, his
repeated refrain: I know that I
don’t know. People either regard
that statement as a sham, false
modesty, or they try to take it seri
ously,” Pastille says. “Socrates
seems to know all the answers,
but the more I live with him, the
more I see it’s just a simple
human truth. We’re constantly
pretending to ourselves that we
know something so that we’U have
something to hang onto.”
Pastille earned a BA in music
from Brown University and an MA
and PhD in musicology from Cor
nell University. He became a tutor
in 1986 and served as assistant
dean from 1994 to 1996.
It’s entirely likely that Gradu
ate Institute students share
Pastille’s sense of not knowing.
Outgoing Director Michael Dink
has recently written that they are
in some sense more self-selected
than undergraduates because
“they have decided that they are
in need of a liberal education
when they had passed the stage of
life when such a need is often con
ceded, if not heartily endorsed, by
common opinion.”
By SusgAN Borden (A87)
Frank Pagano GI Director, Santa Fe
As the newly appointed director
of the Graduate Institute, Frank
Pagano has struggled with the
question: what is an administra
tor? Undoubtedly the title brings
with it a slew of managerial mess
es, loads of paperwork, and tons
of added concerns. But Mr.
Pagano, like many tutors, looks
beyond the trifling details to the
heart of his job. He believes the
role of the administrator is to
“think about how to keep the pro
gram alive,” and to work to main
tain the integrity of the program.
Before joining the faculty at St.
John’s, Mr. Pagano taught at the
University of New England. Class
es geared towards professional
training began to replace the lib
eral arts focus of the college, and
the emphasis placed on grades
reminded him to appreciate the
importance of a liberal education.
It should come as no surprise,
then, that Mr. Pagano views his
move to St. John’s, “where the
grades were not paramount,” as
the beginning of a “second life.”
But this was not his only “sec
ond life.” Along with marrying
tutor Janet Dougherty and father
ing two children, Rachel and Ron,
Mr. Pagano counts his work with
the Eastern Classics among his
life-changing experiences. Teach
ing classes in both Chinese and
Ancient Greek have illustrated for
him the uniqueness of both intel
lectual traditions. Yet, he sees a
startfing similarity between the
Chinese and the Hellenic views of
history, and he understands this
similarity as a “point of contact”
despite their differences. While
on sabbatical, Mr. Pagano pre
pared two lectures on Herodotus’
Histories, and the past fall semes
ter he led a preceptorial on Sima
Qian’s The Records ofthe Grand
Historian. Studying these two
eminent historians has provided
him time to reflect on the nature
of historical thought and how it is
capable of traversing the wide gap
that distinguishes Eastern and
Western culture.
Mr. Pagano sees this sort of
inquiry as crucial to the life of the
graduate program. In his eyes.
Eastern Classics provides an
excellent complement to studies
in Western tradition. It helps stu
dents discover, through another
cultural perspective, “how human
beings choose to live their lives.”
Students in the Graduate Institute
in Liberal Education also apply
themselves to the study of this
question, but within the context
of their own cultural heritage.
Mr. Pagano understands that by
keeping the idea of their “point of
contact” active, he keeps the two
halves of the Graduate Instituteand the study of their distinctive
programs-vigorous and alive.
By John McCarthy (SFoz)
David Levine Dean, Santa Fe
David Levine (A67), appointed
dean in Santa Fe this spring,
brings to the office the experience
of being a Johnnie himself. He
feels he knows what it means to be
on the other side of the desk, and
often tries to view his administra
tive tasks from the perspective of
a student. That knowledge cou
pled with 15 years of teaching
experience, including holding the
positions of assistant dean and the
director of the Graduate Institute,
prepare him for the role of dean.
His academic career was not
always aimed straight for the
office of the dean, or St. John’s
College for that matter. He spent
his first year of undergraduate
work at the University of Pennsyl
vania, and it was not until he
encountered that “sting ray” of a
philosopher, Socrates, that he
made a move for St. John’s. “Plato
(The College ■ St. John's College ■ Summer sooi }
“Should the dean wear jeans?”
GI Director Frank Pagano
(left) and Dean David Levine
(right) address all manner of
QUESTIONS IN THEIR NEW ROLES.
ruined my medical career,” he
says. Mr. Levine also had no idea
when he was a student that he
would ever become a tutor. After
completing his graduate work at
Pennsylvania State University,
and while he was teaching at the
University of Oklahoma, he
received a call from the dean’s
office offering him a position on
the Santa Fe campus. He accepted
because he knew that the interac
tion with colleagues and students
would be of a high caliber at St.
John’s.
He has thoroughly enjoyed the
teaching side of the St. John’s
experience, and is ready to meet
the challenges associated with
being dean. In that role he must
address a variety of questions and
demands, everything from
“Should the dean wear jeans?”
(Mr. Levine sports denim rehgiously) to decisions about faculty
employment. He sees his new role
as an opportunity to become more
involved with student life by meet
ing with organizations such as the
Graduate Institute Council, the
Student Polity, the Student
Review Board, and the MoonTag,
and by eating in the dining hall
more often. In support of stu
dents and the importance of their
opinions in the decisions of the
college, Mr. Levine would like to
see the Student Committee on
Instruction re-instated. 4"
By John McCarthy (SFoi)
�{From
the
Bell Towers}
Of
Bricks
AND
Mortar
Venerable McDow
ell Hall is covered
with a fretwork of
scaffolding this
summer, as the
exterior of the 259year-old building
undergoes a reno
vation. Workers
from the A.J.
Marani Company
and Coastal Exteri
ors in Baltimore
are cleaning the
brick, chipping out
deteriorated grout,
and putting in new grout (22
tons of it) where necessary. The
cupola, whose tin roof had devel
oped several leaks, is being re
roofed with lead-coated copper.
Begun as the governor’s man
sion for the colonial head of the
Maryland colony in 1742, the
building was abandoned before
being completed because of a
dispute between governor
Thomas Bladen and the legisla
ture, which thought his original
plan for the house too
grandiose-£3000 for a house
with a central three stories and
single-story wings extending to
each side, a colonnade of pillars,
and on the inside marble floors
and elaborate woodworking.
When St. John’s was chartered in
1784, the state gave the building
to the college. By 1789, the first
classes were being taught in it.
As late as 179a the college’s
Board was stiU petitioning the
General Assembly for funds to
complete the hall. Until the mid1800S McDowell (named for the
college’s first president) served
every function on campus-it was
the only classroom building,
dormitory, dining hall, and pro
fessors’ quarters (the hbrary
Draped in plastic
sheets and
COVERED WITH A FRETWORK OF
SCAFFOLDING, McDoWELL GETS A
FACELIFT.
hved in the octagon room under
the cupola). During the Civil
War, McDowell became the
headquarters of the Union Army
Medical Corps, which used the
college as a hospital for
exchanged prisoners.
On February 20,1909,
McDowell was gutted by a fire
which began in the cupola and
destroyed much of the front of
the building. At the time
St. John’s had compulsory mili
tary training and ammunition
was stored in the basement, but
students managed to remove it
before fire caused an explosion.
The building was rebuilt accord
ing to its original design. A com
plete interior renovation in 1989
reconfigured former administra
tive offices on the first floor into
classrooms and included modern
heating and air conditioning.
Repointing the brick this sum
mer proved somewhat controver
sial with the Annapolis preserva
tion community, some of whom
felt that grout hke the original
(made from lime and
oyster shells) should
be used, rather than
the cement and lime
compound proposed
by the contractors.
After a review by the
Annapohs Preserva
tion Commission,
the contractors’
methods were
approved. “This
building was con
structed in several
phases over a period
of many years,” notes
John Christensen,
the Annapohs admis
sions director who
has written a book
about the architec
ture and history of
McDowell. “Its brick
and the mortar hold
ing it together are of
different kinds. So
this careful restoration is impor
tant because it will ensure the
building lasts another 250
years.”
Tutor ExtraCURRICULARS
Peter Kalkavage, a tutor in
Annapolis, has a new transla
tion of Plato’s Timeaus out. It’s
published by Focus Press . . .
Annapolis tutor Amirthanayagam David (A86) has a
lecture “ ‘I Know Thee Not, Old
Man’: The Renunciation of Falstaff’ published by the Universi
ty of Chicago Press as a part of
his teacher David Grene’s
festschrift. Literary Imagina
tion, Ancient and Modern:
Essays in Honor ofDavid
Grene.. .Annapolis tutor emeri
tus Curtis Wilson is the author
of a chapter called “Newton on
the Moon’s Variation and Apsidal Motion; The Need for a
Newer ‘New Analysis’” in the
new book, Isaac Newton’s Natur
al Philosophy, published by
MIT.. .Santa Fe tutor emeritus
{The College. St. John's College • Summer 2001 }
5
Charles Bell is featured in two
recently published books by New
York photographer Mariana
Cook. The first. Couples: Speak
ingfrom the Heart, shows Mr.
Bell with his wife, Diana Bell. In
the second. Fathers and Daugh
ters, he is with his daughter Carola. . .Annapolis tutor Andre
Barbera has recently published
articles in The New Grove Dic
tionary ofMusic and Musicians,
Macmillan Publishers; “George
Gershwin and Jazz” in The
Gershwin Style: New Looks at
the Music of George Gershwin,
Oxford University Press; and
biographies of Aaron Thibeaux
(T-bone) Walker and Dianah
(Ruth Lee Jones) Washington in
American National Biography,
Oxford University Press...
Annapolis tutor Adam
Schulman’s book review oIAll
Shook Up by Carson Holloway
appeared in the Wall Street Jour
nal in March. The book’s subject
is the potentially destructive
effects of popular music.. .Santa
Fe tutor William Alba is run
ning the Bard Writing and
Thinking Workshop in Santa Fe
this summer. The workshop,
sponsored by Bard College, is for
high school students interested
in creative writing. Mr. Alba has
also started a publishing compa
ny, Pulley Press, specializing in
small runs of books that are chal
lenging to print. The hrst book
is An Oz Album, a collection of
visual poetry related both to
Dorothy’s journey in Oz in
search of a way home and to a
person’s hfe in Chicago in search
of love.. .Annapohs tutor Eva
Brann’s new book. The Ways of
Naysaying, has been pubhshed
by Rowman & Littlefield. It’s the
third part of a trilogy that
includes The World ofthe Imam
nation: Sum and Substance and
What, Then, Is Time?. ..
Annapolis tutor Jim Beall had
articles pubhshed in Proceedings,
the U.S. Naval Institute, “Tech
nology Policy and Military
Readiness at the Dawn of the
Millennium” and “Restore the
Focus on Technology.”
�6
{From the Bell Towers}
Franz Strum
Slammin’
Stanzas
(SF04) delivers
VERSE AS PERFORMANCE ART IN THE
FIRST ANNUAL POETRY
In celebration of National Poet
ry Month, Meem Library and
the Bookstore in Santa Fe spon
sored the campus’ first annual
poetry slam in April. Poetry
slams make a competitive art of
performance poetry. Partici
pants are judged on both the
content of their poems and the
quality of their performances.
The most exciting performers
interact with their audiences,
and the structure of a slamwith poets advancing in the
rounds according to their judged
scores-depends on the performer-to-audience and audience-to performer relationship.
At the St. John’s slam, a panel of
judges from the college commu
nity that included tutor David
Carl, library staff member Tim
Taylor, and junior Paul Obrecht
rated the 15 high-energy contest
ants on their delivery, content,
form, and style.
The poets exhibited great
variety in form, style, and above
all-content. From haiku to
blank verse to pure rampage,
the contestants never let the
audience’s attention waiver. Not
for a second. The contestants
were students, freshmen to sen
My Lady’s Blancmange
(3poem by winning slammer Mirabai Knight, SF02)
iors, with one lone, brave tutor
(William Alba). The rounds
were fast-paced and fun. The
decisions about who should go
on to the next round and who
should join the audience were
difficult indeed. Mr. Carl said he
was “impressed with the virtu
osity and level of skill” of the
poets. The first place winner
was Mirabai Knight, a junior.
Knight proved herself a true
actress: with each poem she
changed her stance, her accent,
and her tone.
—Marika Brussel
Ye Gods! Her smile, a tender eel
whose spark and sinew strike the fray
of pallid, melancholy meal
awash in jellied consomme.
The ringlets twining ‘twixt her thumbs
along a swathed stretch of brow,
beneath which Thought’s Dark Lantern hums and sput
ters rich, (as per allow)
the treacle-coats of mallow, ripe
until they wither, sweet and spenthut yet they wax, as folds of tripe
unfurl to zaftig firmament!
The pearly spiralling within,
whose snares admit of no escape,
the slumb’ring lips and sinking chin,
the ridge of silk, the sulk of nape...
My bosom fluttersOh, my soul!
Would that her ochre eyes were mine,
and intermittent brilliance
through a patient augure’s agar shine.
Student
ExtraCURRICULARS
On campus, they are united by a
single program. Off campus,
their interests are as numerous
as the entries in the Lidell-Scott
Lexicon. Here’s a quick look at
what Johnnies are doing off-campus these days.
Ellie Kocezela (SF04) and
Erin Hanlon (SF04) traveled to
Nashville, Tenn, to attend the
aooi Amnesty International
Annual General Meeting as rep
resentatives the SJCSF Amnesty
group. They spent three days
attending panel discussions and
participating in breakout ses
{The College- St. John’s College ■ Summer sooi }
SlAM.
sions as they looked for ideas to
make the campus group more
effective.
Adriana de Julio (SFoi) has
won a one-year fellowship with
the National Institutes of Health
to conduct cancer research and
Susannah Daniels (SFoi) has a
conservation internship at El
Malpais National Monument in
Grants, N.M. Philip Bolduc
(SFoi), Brian Ballentine (SFoi),
Karen Gosta (SFoi), and Justin
Kray (SFoi) have internships to
teach English in France through
the French Department of Edu
cation.
Elizabeth Royal (Aoi) will
spend two weeks this summer at
the Claremont Institute, a con
servative think tank, as a Pub
lius Fellow. She will attend semi
nars on political philosophy and
the American political tradition,
contemporary political issues,
and political rhetoric and writ
ing.
Among the 18 Annapolis stu
dents pursuing Hodson Trust
internships this summer are
Randy Pennell (A02), interning
with the Philadelphia ybers;
Hannah Ireland (Aoi), working
with a documentary production
company; Lydia Frewen (Aoa),
learning to make violin bows at
the University of New Hamp
shire; and Peter Heyneman
(A02), attending the Sewanee
Writers’ Conference.
�{From the Bell Towers}
Phoning for Philanthropia
Tuition only covers about 75% of
what it costs to educate students
at St. John’s. The rest comes
from the endowment andfrom
contributions to the Annual
Fund. Phonathons are part of
the story behind those contribu
tions.
Q: You throw a phonathon and
who shows up?
A: In the case of St. John’s, 33
alumni from classes spanning 48
years, from Everett Wilson (A56)
to Hayden Brockett (A04).
Q: And just what does everyone
do (besides making phone calls)?
A: Eat dinner and compete for
prizes for the most donations
and the most new donors (the
phone calls involve chatting with
alumni, outlining the college’s
needs, and asking for $$$).
Q: So where do you throw that
phonathon?
A: In Annapolis, it’s the Conver
sation Room-where else? In
Santa Fe, it’s the Senior Com
mon Room.
Q: And who sits where?
A: Interestingly enough, says
advancement officer Mary Sim
mons, at the Annapolis
phonathon the very youngest
and very oldest choose to sit
right next to each other. It’s a
Alumni phoning alumni;
EFFECTIVE FUNDRAISING AND
SUCCESSFUL FUN.
social event that brings alumni
together for a good cause.
Simmons reports that the
spring phonathon, held May 15,
was a success. In Annapolis, ao
volunteers made 619 calls, rais
ing $r6,arr.5o from 149 donors.
Among the donors, 63 were
making their first gifts to the
Annual Fund. In Santa Fe, 13
volunteers made 38a calls rais
ing over $4aoo (gifts are still
coming in). Of Santa Fe’s 59
phonathon donors, aa were
making their first gifts. These
high proportions of first-time
donors are particularly satisfying
to members of Philanthropia,
the alumni organization dedicat
ed to fundraising among fellow
alumni. While Philanthropia’s
goal is to increase alumni finan
cial support to the college, it’s
not just the number of dollars
they want to increase. The num
ber of donors counts too; foun
dation and corporate support is
often linked to the percentage of
alumni who donate.
Ginger Roherty, Director of
the Annual Fund for the Santa
Fe campus, is a fan of the
phonathon approach. “There is
a tremendous synergy when
phonathons are conducted
around seminar tables and there
is a great sense of everyone
working toward a common
goal,” she says. “Everyone is
truly having a good time and
enjoying each other’s company.”
Phonathons are one tactic
Philanthropia employs to
involve alum
ni in financial
support for
the college.
They also
solicit alumni
with bro
chures and
letters and
they organize
reunion class
es to focus on
social events.
7
cyber-networking,
3,035,763
Dollars given by Alumni
and giving.
FYOl
Annapolis cam
pus vice president
2,083,984*
Jeff Bishop says that
1,953,944
FYOO
Philanthropia
1,520,683 FY99
expects to meet its
FY98
goal of a ten-percent
increase in alumni
participation in the
Annual Fund.
“We’re laying the
groundwork for the
plus $5,000,000 from the estate of Paul Mellon
future of the col
lege,” he says.
2,187
Number of
“More young alum
pYQj
Alumni Gifts
FYOO ■
ni are becoming
1,710
acquainted with
FY99
Philanthropia and
FY98H
recognizing the col
lective power of the
number of gifts
given to St. John’s.”
Before the creation
of Philanthropia,
alumni giving was
around 20%, well
below the median of
other small liberal
arts colleges, which
garet Odell (SGI97), Rachel
is 44%. “Today, we’re up to 25%,
O’Keefe (A82), John Oosterhout
with reunion classes making the
(A5r), John Wood (SFoi), Elaine
biggest improvements, now up to
Coleman Pinkerton (SGI88), and
30%. “While we have a long way
Inga Waite (SF87).
to go,” says Bishop, “we feel
Philanthropia’s leadership
confident that someday we will
recently
changed. Leslie Jump
get there.”
(A84) is the new chair of Philan
Philanthropia wants to thank
thropia. Other members of the
the phonathon volunteers,
Steering Committee are Amber
including Mary Pat Justice
Boydstun
(SFpp-overseeing “spir
(SGI71), Katherine Haas (A60),
it” activities), Eloise Collingwood
Merle Maffei (AGI86), Harry
(A79-overseeing communica
Zolkower (A82), Chris Olson
tions),
Brett Heavner ( ABp-over(A78), Thea DelBalzo (AGIoi),
seeing
the
reunion class leaders),
Rosamond Rice (AGI81), Karen
Marta Lively (A78-at large), Paula
Salem (A76), Everett Wilson
Maynes (SF77-overseeingpoh(A56),Tom Tandaric (A98), Pilar
cy/membership), Becca Michael
Wyman (A86), Tim Pomarole
(A97-overseeing strategy), and
(A98), Steve Wilson (AGI99),
Amy Thurston (A95-overseeing
Jim Heyssel (A84), Hayden
events/phonathons). -ijiBrockett (A04), Isadora Sageng
(A03), Stephen Steim (A03),
Stephanie Porcaro (A03), Brooke
Lee (A03), Gin Behrends
(AGI90), Anne Ferro (A80), Joni
Arends (SF89), Carisa Armen
dariz (SF99), Claiborne Booker
(A84), Kit Brewer (SGI98), Alex
is Brown (SFoo), Peter Dwyer
(A86), Geri Glover (SF80), Mar
{The College -St. John’s College ■ Summer 2001 }
Philanthropia seeks volunteer help
from all alumni who want topar
ticipate, whether in a small or
large role. Ifyou ’re interested,
please call or e-mail Maggie Griffin
in Annapolis: 410-626-2534,
m-griffin@sjca.edu or Ginger
Roherty in Santa Fe: 5O5-g84-6og<).
�8
The Studs of
St. John’s
Ostensibly as a fundraiser (but
primarily for the novelty value)
several juniors in Santa Fe cre
ated the wildly popular “Studs
of St. John’s” calendar. Featur
ing the 15 most macho men per
suaded to pose for a project ini
tially dismissed as a dubious
attempt to raise money, the cal
endar turned out to be a raging
success. While this “success”
was mostly realized in terms of
school-wide interest rather
than fiscal returns (due to con
fused leadership and poor
financial forecasting), the
entire project served Santa Fe
well. It’s not every year that the
campus is hit with a Studs calendar-and despite the lack of a
precedent, the outrageous pic
tures amused all those exposed
to the handsome visages and
physiques displayed in the cal
endar.
The project was conceived to
finance the so-called Junior
Block Party, another first for
Santa Fe. The block party-held
on a pleasant sunny day in
May-featured live music, a bar
becue, outdoor games, much
{From
the
Bell Towers}
lounging in the sun, the third
annual women’s arm wrestling
contest, and kegs of beer to help
facilitate the atmosphere. The
block party, financed by pre-pro
duction sale of the calendars,
treated all to a good time and
lived up to its expectations.
Unfortunately, with a business
plan that drew on the dot-com
legacy, the calendar’s start-up
money got spent on the party
and there were no funds left to
produce the calendar. After
many rounds of creative negoti
ations with several businesses in
Santa Fe and a few helpful mem
bers of the St. John’s adminis
tration, the calendar was pro
duced at a cost far below initial
expectations-with photos of
superb quality and ridiculous
content.
—BY John
Rankin,
SFoa
Greatest Hits (in Russian)
Valery Serdyukov (left),
the governor of Leningrad, recently
LiSA RICHMOND (RIGHT),
PRESENTED A GIFT OF 30 RUSSIAN BOOKS TO
GrEENFIELD LIBRARY AS BuD BiLLUPS, COLLEGE
ThE BOOKS INCLUDED WORKS BY ToLSTOY, DoSTOEVSKi, Chekhov, and Pushkin, The governor was in Annapolis to
SIGN A TRADE AGREEMENT WITH PaRRIS GlENDENING, GOVERNOR OF
Maryland, and expressed an interest in donating books to a local
COLLEGE. The Russian classics found a home with the other
“greats” at the St. John’s library.
LIBRARIAN AT THE
A point of history: As John
Rankin points out, it’s not every
year that the college is hit with a
Studs calendar. But such an
event did happen at least once
before-in Annapolis in 1987,
when Ben Birauss (A88) pro
duced “The Men of St. John’s.”
Drawing on the non-PC transla
tion of the college motto “I
make free men out of boys by
means of books and a balance,”
TREASURER, LOOKED ON.
the calendar featured comely
men posing in St. John’s-esque
situations: Krauss in front of
the pendulum pit mural, Steve
Hulbert (A87) in the King
William Room, Chandran
Madhu (A88) in front of an
Apollonius proof, Mark Shiffman (A89) at the switchboard,
Jeff Kojak (A89) at the plane
tarium, Andre Wakefield (A87)
in a music room, Scott
Vineberg (A88) near the French
Monument, Toby Barlow (SF88)
in a Humphreys bathroom,
Vince Pruden (SF89) in the art
gallery. Matt Krawiec (A88) at
the boat house, John Lavery
(A87) in the weight room, and
John Pronko (A90) in the con
versation room.
La plus qA change;
St. John’s studs in
aooi and 1987.
{The College - Si. John’s College • Summer 2001 }
�9
{From the Bell Towers}
Mutant Gene
Discovery
When Marc Priest (Aoi) began
an internship at the National
Institute of Allergies and Infec
tious Diseases during the sum
mer before his senior year, he
thought he’d be learning some
lab techniques and helping out
with minor projects. Instead, he
discovered a gene mutation that
was causing a i6-month-old
patient to be particularly suscep
tible to common bacterial infec
tions that most people fight off
with no trouble.
Under the direction of Dr.
Steve Holland (A79), Priest set
out to find what was causing the
patient’s interferon gamma
receptor-alpha
deficiency. They
knew that a gene
mutation pre
vented the
receptor from
processing a
chemical that is
essential to the
functioning of
the body’s
immune system.
He isolated the
gene, cloned it,
and then com
pared it to normal genes to
locate the mutation. Priest
found that both the child and his
mother had a deletion on the
gene that acts as a chemical
receptor for the immune sys
tem’s pathway. “After I found
the mutation I met with the
Marc Priest, shown
AT GRADUATION WITH
President Nelson,
LOCATED A GENE MUTA
TION THAT CAN AFFECT
THE IMMUNE SYSTEM.
patient and his mom,” says
Priest. “I explained to her that
the child’s condition was treat
able. This was certainly gratify
ing.” Treatment consisted of
injecting double the amount of
the chemical that cannot be uti-
barred, music-wise)
Annapolis Homecoming 2001 . The
traditional Saturday
Take a handful of Annapolis
alumni and ask them which
building, Mellon or McDowell, is
closer to the heart and soul of the
college. Only the incorrigible
will say Mellon. Yet Mellon’s FSK
lobby has been the site of all
Homecoming registrations in
recent memory as well as the big
Saturday evening cocktail party,
when the acoustically
challenged room
echoes with a din ren
dering individual
words inaudible.
This year we say,
“Enough of this.”
Homecoming (Sep
tember 28-30) will at
last reflect the fond
feehngs of alumni for
McDowell, with regis
tration moved to the
cozy quarters of the
Coffee Shop and the
cocktail party moved
to the Great Hall and
the first and second
floor classrooms.
Other decidedly non-lobby
events will include:
• A career panel, both for cur
rent students and job-chang
ing alumni
• Two rock parties, one Friday
night in the boathouse (all
seventies music, sans disco),
one Saturday night in the
Coffee Shop (no holds
night waltz party in the
Great Hall
Seminars running the gamut
from Plato to Emerson,
from Robert Frost to Chfford Geertz, from Shake
speare to Toni Morrison,
with a seminar on Harry
Potter for children
Reunion dinners, picnics,
croquet games, and
cocktail parties, for
reunion classes 1936,
1941,1946, '95>-1956,
1961,1966,1971,1976,
1981,1986,1991, and
1996
• The Special Meeting
of the Alumni Associa
tion, where Nancy
Lewis, John Moore and
Beate Ruhm Von
Oppen will be made
Honorary Alumni
“Essay Conference” by
Jo Ann Mattson, A(i7
{The College- St. John’s College - Summer 2001 }
lized because of the
missing gene. “This
particular deletion
occurs in only one out
of 200,000 patients,
but it is significant to
study it. Looking at
the few that are with
out the receptors in
their immune system pathways
helps us to understand how the
pathways work. This helps us
understand how to help normal
people who are susceptible to
such bacteria as tuberculosis,”
he says.
• The Saturday night Homecoming banquet, where Tom
Williams (A51) and Warren
Spector (A81) will receive
the Alumni Association
Award of Merit
• The Soccer Classic, with the
alumni rarin’ to avenge last
year’s loss to the students
• The Homecoming auto
graph party, with alumni
and faculty authors signing
books ranging from western
novels to translations of
Aristotle and Plato
• Sunday brunch at the home
of President Christopher B.
Nelson (SF70)
The Homecoming lecture Fri
day night will be dehvered by
Abraham Schoener (A82), who
will speak on “The Biology of the
Fermentation Vessel.” Before
and after the lecture, students,
faculty and alumni will gather,
yes, in the FSK lobby. Some
things never change. 4"
Contact the Annapolis alumni
office at 410-626-2331 or alumni@sjca.edu to registerfor Homecoming.
�IO
{FromtheBellTowers}
Mortimer J. Adler, An Appreciation
ortimer Adler-a teacher,
author of books that
popularized themes in
philosophy, and compil
er of the Great Books
published by Encyclope
dia Brittanica-died on June 28 in San
Mr. Adler played an important role in
Mateo, Calif., at the age of 98.
the establishment of the St. John’s Pro
gram, of which he was a vigorous support
er over many decades. From the earliest
days of the New Program he visited
St. John’s, both in Annapolis and Santa Fe,
many times to lecture and to meet with fac
ulty and students. He was an articulate
spokesman for liberal education and for
the reading and discussion of great books
as central and fundamental to it. Along
with such colleagues as Scott Buchanan,
Stringfellow Barr, Mark Van Doren,
Richard McKeon, and Robert Hutchins,
he made a major contribution to the estab
lishment of great books programs not only
in Annapolis and Santa Fe but also in
New York, in Chicago, and all across the
country.
In the more than three dozen books that
Mortimer Adler wears a crown after being
he wrote, Mr. Adler sought to clarify for a
PROCLAIMED, A LA NaPOLEON, THE HOLY EmPERwide general audience a variety of pro
OR OF THE Western World in the 1992 lec
found philosophic questions illuminated
ture PRANK.
by the study of the greatest authors. His
books included How to Read a Book, How
to Think About War and Peace, The Differ
then went to the University of Chicago as a
ence ofMan and the Difference It Makes,
professor of the philosophy of law.
Aristotlefor Everybody, miHov: to Think
Mortimer Adler did not believe that the
About God.
full exercise of intellect was something for a
Born in New York City, Mr. Adler
small academic elite. In 1946, he joined with
dropped out of De Witt Clinton High
Robert Hutchins to organize a Great Books
School when he was 15, and worked for the
program for the general public and arrange
editor of the New York Sun. Deciding that
for the Encyclopedia Britannica to print a
he wanted to study philosophy, he attended 54-volume set of such books, for which he
Columbia University and completed the
contributed the Syntopicon, a guide to the
course of study, but did not receive a diplo themes, questions, and arguments to be
ma because he refused to take the swim
found in them. In 195a, he organized the
ming test that was a physical education
Institute for Philosophical Research. He was
requirement. Even without his degree,
editor and then chairman of the board of
however, he became an instructor in phi
editors of the Encyclopedia Britannica
losophy, and in 1928 he received his PhD
beginning in the mid-1960s. He organized
(eventually being granted a BA by Colum
and led seminars for executives at the Aspen
bia in 1983.) He did research in psychology
Institute, and initiated the Paideia Project
and taught at Columbia from 1923 to 1930,
to make practice of the liberal arts and dis
M
cussion of great books central to the high
{The College- St. John’s College • Summer 2001 }
school curriculum.
At St. John’s, Mr. Adler is
remembered as an energetic
advocate of studying the great
books and practicing the liberal
arts-one who never stopped ask
ing the big questions, both theo
retical and practical, and who
always relentlessly insisted on
clarity in discussing them. He
showed himself as such a man in
the course of visiting this Col
lege as a lecturer, with undimin
ished vigor, for almost sixty
years. In the early years, his lec
tures were several hours long,
which gave rise to the tradition,
ever since the late 1930s, of
interrupting his talks with a stu
dent prank. Some were simple
like the first, which consisted of
a hall full of alarm clocks which
all began ringing at exactly one
hour into the lecture. Some were
quite elaborate, like the one in
which the curtain opened
behind the lecturer, to reveal a
tableau of students costumed and posi
tioned to resemble the Renaissance painting
“The School of Athens”: there was a Homer
in it, and a Virgil, and a Plato, and the restbut no Aristotle; out came a student, who
placed a wreath on Mr. Adler’s head and
escorted him into the scene, to take the
place of Aristotle. Mr. Adler loved it. He
took the pranks as they were meant to be
taken-as signs of affection and regard for a
man who loved reading hard books, asking
deep questions, clarifying alternative
answers, and making thought make a differ
ence in the world.
Mr. Adler is survived by four sons: Mark,
of Chevy Chase; Michael, of Grand Junc
tion, Colorado; and Douglas and Philip,
both of Chicago.
A memorial will be held for him at 9:00
a.m. on Saturday, September 29, at Homecoming in Annapolis. 4"
—Harvey Flaumenhaft
For a retrospective ofpranks staged during
Mortimer Adler’s lectures, see page 39.
�{Alumni Voices}
MARX REDUX
By Sarah Fridrich, SF99
n the two-year anniversary of my senior oral-on
my essay concerning Karl Marx and his discus
sion of capitalism-I found myself, late at night,
scribbhng a letter in a notebook near my bed
side. It was addressed to Ms. Engel, the chair of
my senior oral committee.
The letter began: “I’ve been
thinking about and slowly sort
ing out what excited me about
Marx’s assessment of capital
ism. Now, I would like to contin
ue the discussion that had only
just begun at the table in Meem
during my oral. You had posed
several questions to me about
my essay. The most troubling
question was about revolution.”
Recent protests at the World
Trade Organization talks in
Quebec, Washington, D.C,, and
Seattle had given me new incen
tive to decipher what Marx was
trying to say about capitalism. The protes
tors questioned whether impacts that world
trade agreements could have on the environ
ment and on the populations and socioeco
nomic stability of developing countries
would be brought to the discussion tables.
Sitting comfortably at my mother’s home
in Annapolis where I grew up, I wondered
why they thought these things. Why did pro
testors believe, even though many of them
had no first-hand proof of it, that certain
issues were not being addressed? Why did
they feel compelled to shout and carry
signs?
It had been five years since I’d participat
ed in similar activities. I’d started a petition
signed by the majority of female students
demanding that the administration permit
us to wear long stockings during the winter
months at our CathoUc high school. I’d
Sarah Fridrich, who currently works in
MARKETING in AnNAPOLIS, WRITES SONGS AND
PERFORMS WITH HER BAND IN HER SPARE TIME.
marched past the White House with a body
of young people shouting to be heard on the
issue of gay rights. I’d made posters and got
petitions signed while shouting for more
culturally diverse faculty and curricula to
serve the needs of a diverse student body at a
small liberal arts college in upstate New
York. Then, in 1994,1 enrolled at St. John’s
and I knew there wouldn’t be shouting, it
wouldn’t be necessary.
I became accustomed to being heard and
having fruitful discussions-in attempts to
figure out what it means to be human-on
topics such as heroism, war, and revenge;
truth, knowledge, and intellect; god, cer
tainty, and morality; rights, givens, and
{The College- St. John’s College ■ Summer 2001 }
assumptions. At times I may have felt like
holding up a sign to get my point across, but
it was never necessary. In silence, I often
learned more. I found that, by listening, I
prepared others to better hear me.
When the discussion turned to Marx’s
essay on alienated labor, I felt compelled to
put some words on paper, but there was still
no need for it to be fluorescent poster board.
In my senior essay, I managed to say a few
things and to clarily what he meant when he
criticized the German Ideologists and when
he talked about the effects of capitalism on
society. But when the hour for the senior
oral was up, it felt like I had just started to
uncover what I needed to know from Marx.
Ms. Engel asked why I thought that non-vio
lent revolution was possible within Marx’s
philosophy. I really didn’t have an answer.
The dilemma highlighted my need to sort
out what Marx said from what Marx had
inspired me to say. This would take much
longer than the weeks we had to write an
essay. Working in the business world after
graduation gave me the opportunity to test
my understanding of the philosophy that
labor in capitalism is a commodity, and that
capital must create more capital.
Two years later, on the couch in my living
room, I wondered if these shouting protes
tors might benefit from a Johnnie-like dis
cussion on Marx’s ideas. Had Marx laid the
foundation for these protests? Did the pro
testors know it? Maybe not. In my letter to
Ms. Engel I submitted: “Much of Marx’s
concern about capitalism was that it dehu
manized common laborers ... Yet in Europe
and America most of those labor issues have
been addressed in the time since Marx
wrote. Might Marx’s insights on capitalism
still shed some light on current issues of
working conditions? Is there a connection
between the globalization of trade and the
nature of capitalism as an ever-expanding
economic system? ... Should I be making
some signs and protesting?” I haven’t felt it
necessary.. .yet.
�{Commencement}
COMMENCEMENT
2001
Ed Moreno (Santa Fe) and
Barbara Goyette (Annapolis)
BY
he
graduating
Mr. Zuckerman attempted to clothe
seniors-95
in
the inevitable graduation bromides in
Annapolis and in
attire appropriate to St. John’s. He said
in Santa Fe-chose
he would present the seniors and mas
as their com
ter’s candidates with seven “preludes,”
mencement
which “have no required form. They may
speakers one each
be perfectly made miniatures; or they
from the two basic
may be mere fragments, famously
pools: tutors at
baffling to the experts.”
the college whose real thoughts they
The subject of the first prelude was the
have been curious about for four years Tutors Peter Pesic and Janet Dougherty
claim that at St John’s, the books are the
CONGRATULATE THE SaNTA Fe GRADUATES.
and “outsiders” who might have
teachers. “It is easy enough for me to
thoughtful words to send them on their
agree with the truism,” he said, “for one
way. In Annapolis, tutor emeritus Elliott
of my own exaggerated opinions about
Zuckerman presented a perfectly constructed, wittily pack
teaching is that all a teacher can do is point to something.
aged set of what he called preludes, while Harvard professor,
Since in the St. John’s seminar the places pointed to are in the
author, and lecturer Cornel West wove the theme of radical
texts... that gives us both a role, the person pointing and the
questioning into his address to the Santa Fe graduates.
page that is pointed to. And this becomes a richly complicat
ed process when, in the course of a seminar or a class discus
Bromideless Preludes in Annapolis
sion, all the participants are doing the didactic pointing.” Mr.
Before the assembled seniors and the a6 master’s degree can
Zuckerman’s second prelude also had to do with his role as
didates and all their families and friends, plus students and
teacher: “Even though I was officially an historian, I never
alumni, Elliott Zuckerman, who’s been a tutor since 1961, was
worried about our not doing official history. I have seen what
introduced on the bright sunny morning of May 13 by Presi
happens elsewhere when lectures on the Greeks intrude upon
dent Chris Nelson. It cannot be said of Mr. Zuckerman that he
Homer, and Machiavelli is crowded out by arguments about
is incapable of uttering a trite remark, but it can certainly be
when the Renaissance began...”
said that he is incapable of uttering a trite remark and not
Third, Mr. Zuckerman related anecdotes from his own stu
identifying it as such. This character trait put him at some
dent days, when he was enrolled in a course at Columbia
thing of a disadvantage in delivering remarks at a graduation,
taught by poet Mark Van Doren on Narrative Art. The course
since, as he said, “Abromide [which is a commonplace] is rec
included works like the Iliad, Don Quixote, and a novel by
ognizable not necessarily by the inevitability of its words but
Kafka. “The exam, as I remember it, consisted of two ques
by the triteness of the very thought behind the words...Bro
tions. The first question was: Which of the books in the
mides are not only the expected material of commencement
course did you like least? The second question was: To what
speeches, but they are the substance of Graduation Day
deficiency in your character do you attribute not liking this
itself.”
book as much as the others?...In classes in cultural history or
{The College. St. John’s College ■ Summer aooi }
�{Commencement}
‘‘‘ Use your intellect to cut though the thicket ofmass tastes
and mass culture...''
Cornel West
{The College- St. John’s College • Summer zoot }
^3
�14
{Commencement}
lost, or known students who have felt lost.
the history of ideas there was one sort of
“Perhaps at such times it might be useful to
final exam that I found particularly vex
remember the grapefruit crate, and to think
ing. I refer to the Imaginary Conversation.
of oneself as not entirely lost, but as in some
One is asked to compare the view of (say)
way
analogous to the stray object that is both
Saint Augustine and Hegel and Jane Austen
lost and found and therefore neither lost nor
on (say) what is the most important pursuit in Elliott Zuckerman in Annapolis (above).
found. Allow oneself to hang poised, like a
life. I was never able to get started on such a Santa Fe Seniors reflect on Cornel West’s
QUESTIONS (below).
character in Henry James who may want to
comparison because I couldn’t decide how
give two contradictory responses at the same
these miscellaneous characters should
time.”
address one another. Does Saint Augustine
Mr. Zuckerman wove the theme of myriad-mindedness versus sin
call Hegel George? Is it in good taste for Jane Austen to ask Augus
gle-mindedness
throughout his address, and concluded with a prel
tine to convey the greetings of Emma Woodhouse to Santa Monica?
ude
on
the
subject.
A fable of La Fontaine, he said, is about a bat who
At St. John’s College the students can engage in the Great Conver
finds himself twice trapped in the nests of different weasels. The first
sation without such stifling problems of entering into it.”
time, he convinced the mouse-hating weasel that he was a bird; the
Prelude number four involved the study of biology at the college.
second time he convinced the bird-hating weasel that he was a
“We used to do a whole year of biology lab in the sophomore year,”
mouse.
“And even though such myriad-minded animals are lovable
said Mr. Zuckerman. “There was a student who, in the seminar, was
enough, it is difficult for people to remain entirely comfortable with
particularly taken with Plotinus, and with a principle called the
mixed natures in these days that still recommend the Romantic
One, which, as you know, is transcendental and undifferentiated. It
virtues
of sincerity and authenticity, virtues that seem to imply one
happened that in the lab that student failed utterly to complete the
ness. So it may not be so bad to take as a model La Fontaine’s inven
fruit fly experiment. It was suggested at his Don Rag that he simply
tive Chauve-souris.”
couldn’t deal with the fruit flies because there were so many of
them.”
Facing the Big Questions in Santa Fe
The fifth prelude included a story about Mr. Zuckerman’s gradu
ate school experience at Cambridge, where he became friends with
An uncommon May rain in Santa Fe marshaled the St. John’s Gollege
Watson and Crick at the time they were discovering the double helix
Glass of 2001, their families and friends across campus and into the
structure of DNA. He and his literary friends had not been open with
Student Activities Genter for commencement exercises on May 19.
Watson because he was a scientist. “Part of our prejudice,” said Mr.
Beneath a soft glow through skylights, in undergraduates received
Zuckerman, “had been owing to the fact that those were the years
the Bachelor of Arts degree, and 26 received the Master of Arts in
when there was a sharp split between the sciences and those pursuits
Liberal Arts degree. Nearly 700 visitors watched as the members of
that were known as the Humanities. They were even called the Two
the largest of the Santa Fe campus’ 34 graduating classes received
Cultures, and there were scandalous revelations about physicists
their degrees.
who had never read Euripides... and
The commencement was the first
poets who didn’t know how many equa
major event in the Student Activities
tions bore the name of Maxwell.”
Center, the new building-opened last
Not all Mr. Zuckerman’s preludes
fall-that overlooks the Atalaya Trail
were from the academic world. The
Arroyo. Although commencement is
sixth told of a boy at a summer camp
usually held outside on Meem Library
who constructed a lost and found box,
Placita, the crowd seemed not to mind
a grapefruit crate that was already
that rain forced the ceremony into the
conveniently divided down the middle
new space. The graduates and many vis
into two sections. For each section he
itors gathered in the gymnasium, while
had a sign, one reading LOST and the
others watched from the mezzanine.
other reading FOUND...Day after day I
The Anasazi Brass and the St. John’s
watched people come up to the box ...
College Chamber Choir performed,
trying to decide which half ...was the
with selections from the Brass includ
more appropriate repository.” Some
ing two trumpet tunes by Henry Purcell
times, noted Mr. Zuckerman, he has felt 5
and from the Choir, “Regina Caeh” by
{The College- St. John’s College • Summer 2001 }
j
�{Commencement}
15
Gioaccino Rossini and “Sicut Cervus” by Gio
to raise the courage to evaluate the evaluations,
to interrogate the most basic presuppositions
vanni Palestrina.
The event was a milestone for the college. In
and prejudgments in the spirit of intellectual
his first commencement as president, John E.
humility-back to the grandpop, eye-pop, potBalkcom revealed fondness and love for his first
belhed, big-lipped, flat-nosed Socrates,” West
ensemble of graduates, recalling numerous
said.
occasions on which students welcomed him into
He continued, “Tradition is not something
you inherit. If you want it, you gain access to it by
the college community. Balkcom had become
president of St. John’s College in Santa Fe just Cornel West in Santa Fe (above).
means not just of hard labor but sacrifice, com
nine months earlier, after a long career in busi Annapolis graduates parry and party
bat. Looking deeply inside of yourself, and
after the ceremony ( below) .
ness and management consulting.
always acknowledging that when you look inside
Commencement speaker Dr. Cornel West, the
yourself you’ll see, in part, the antecedent reali
Alphonse Fletcher Jr. University Professor at
ties, the histories, the social structures that have
Harvard University, called upon the graduates to use their critical
in part shaped us, but never render us captive, because we’re agents.
thinking to challenge and question the seductions and shallowness
We can make choices and commitments and decisions.”
of mass culture and to remain true to their humanistic training. West
In an address filled with references to Leo Strauss, Montaigne,
Nietzsche, Seneca, and St. Paul, West brought a very contemporary
is known for his best-selling book Race Matters, which triggered a
national debate on race issues. Touching on influential traditions in
focus to the age-old question that faces all graduating students: How
religion, philosophy, democracy and populism, he lectures on race
to adopt away of life of “genuine questioning.” That questioning, he
said, “has to go hand-in-hand with the legacy of Athens: the spiritu
issues, education and other subjects. Dr. West Uved part-time in
Santa Fe throughout the academic year. He attended lectures at the
ality of genuine loving, serving, situating oneself in a story bigger
than oneself, being able to locate oneself in a narrative grander than
college and stayed to participate in discussions that followed, which
is how the students got to know him. As in Annapolis, the seniors in
oneself, that tries to tease out the better angels of one’s nature, to
Santa Fe choose who will be invited to give the commencement
get one out of one’s egocentric predicament.”
West said young people might realize the importance of not “sell
address.
West posited the essential question: “The one question that will
ing their souls for a mess of potage,” but they nevertheless must
continue like a drum beat to confront you, the most frightening
somehow confront our market-driven civilization, where the guid
question, the most terrifying question, the question that sits at the
ing principle is “the nth commandment: Thou shalt not get
very center of the humanistic educa
caught.”
West concluded his remarks by urg
tion; What does it really mean to be
human? We will not get out of space and
ing the graduates to continue to use
time alive, and what are you going to do
their “intellectual and existential
armor” acquired at St. John’s to fight
in the meantime?”
West illustrated his point with refer
for justice, “not because you would
somehow create a better world
ences to Socrates’ remark in Plato’s
Apology, that the unexamined life is
overnight, but rather, as my grand
not worth Uving (and to Malcolm X’s
mother used to say going all the way
addition: “the examined life is
back to gut-bucket black churches and
painful”). As Socrates, who was on trial
Jim Grow Mississippi, that ‘if the king
for questioning the “pretenders to wis
dom of God is within you then every
dom” of his day. West challenged the
where you go you ought to leave a little
graduates to use their intellect and to
heaven behind.’ Leave the world just a
“cut through the thicket of mass tastes
little better than how you found it,” he
and mass culture” that dominate socie
said.
ty in the present day.
Both commencement addresses are
“Intelligence is a manipulative facul
ty. It allows us to evaluate immediate
on the web. Elliott Zuckerman’s speech
context. But intellect is about awe and
is at www.sjca.edu, and Cornel West’s
wonder and astonishment. It forces us
is at WWW. sjcsf. edu.
{The College. St. John’s College ■ Summer 2001 }
�{Johnnies on Theology}
SOPHOMORE SEMINAR
FOREVER
Reflections on theoloflcal questions by religious alumni.
BY Sus3AN
Borden, A87
t St. John’s, we come to seminar
seeking answers bnt walk away
with questions. Nowhere is this
more true than in sophomore
seminar, where we read the Bible,
the “A saints” and Martin
Luther, Dante and Chaucer. At
year’s end most of us gather our
thoughts, settle on answers, and
resolve to live with our doubts and difficulties. But some, by
conviction and often vocation, live in a world where theology
is more than a speculative study. They are pastors and can
tors, rabbis and chaplains, ministers and seekers. Their lives
are a permanent search, where the questions of sophomore
seminar are forever open.
Bible ioi
The Bible is the stepping stone in the rushing stream of reli
gion at St. John’s-no matter what their religious upbringing
(or lack of it), sophomores all read and discuss the Bible as a
part of the program rather than as a basis for belief. For some
students, it’s hard to separate past associations and to address
the text directly; for others, reading the Bible opens their
minds to a new world.
The Rev. Janet Hellner-Burris (SF77) remembers her sen
ior enabling oral: “I had boned up on all those seminar books
and I was ready to go,” she says. “The tutor asked me, ‘Ms.
Hellner, do you remember the story of the prodigal son?’ and
I thought, ‘Come on, I grew up on this stuff.’ He said, ‘It’s in
Matthew,’ and I said, “No, it’s Luke 15.’ And then they knew
who they were talking to.” Familiarity with the text, says
Hellner-Burris, did not turn out to be an advantage: “I had a
miserable exam. I could not get beyond a Sunday school
understanding of the story.”
Hazzan (Cantor) Frank Lanzkron-Tamarazo (A95), howev
er, had never read the Bible until sophomore seminar. The
son of a Jewish mother and an Italian-Catholic father, his reli
gious background was fairly limited: “The only Judaism I had
in my family,” he says, “was when my mother got angry at my
father. Then she would say, ‘Frank, don’t forget you’re a
Jew!”’
When Lanzkron-Tamarazo finally arrived at the sophomore
seminar table, he says it was an awakening; in some ways, a
rude awakening. “To hear about a God who destroys an entire
world of people except for Noah, to hear about a God who
would let Abraham sacrifice his son, to learn about David
betraying his soldier, that made me angry,” says LanzkronTamarazo. But, he says, that anger led to some lively discus
sions in the Nick Capozzoli-Wendy Allanbrook seminar and
brought him to study Hebrew with tutor Michael Blaustein
(A74) for a year and a half.
Nine years later (five of them spent studying at the Jewish
Theological Seminary of America), Lanzkron-Tamarazo is
now a cantor. Both his training and his cantorial practice
require the reading of the Talmud and the AfwAraa-biblical
commentaries that inform the Jewish interpretation of the
Torah (the first five books of the Bible). “You can’t read the
Torah just by reading it as a book,” he says. “What makes it a
part of the Jewish tradition is the way the rabbis understood it
in the writings of the Talmud and the MishnaT
Lanzkron-Tamarazo’s problems with stories like the bind
ing of Isaac were put to rest by the commentaries. “I asked,
{The College. St. John’s College • Summer 200 f }
�I?
ing to him because of his work.
“I think there is a tragic char
acter to existence. God, for bet
ter or worse, created the world in
a certain way and we have to deal
with the consequences. That
may be blaming God some, but
that’s all right with me. I think
God knows there’s lots of trouble
in this world and it’s not all our
fault. I guess I’m more involved
now with how to manage the cre
ation as we find it, not so much
asking how it became this way.”
The relationship of God and suf
fering comes up often in Dillard’s
work because of the degree of pain
he encounters and because of the
population of patients he works
with: mostly poor, sometimes
undereducated, and often with a strict religious background
that features a punishing God. “One of the main things patients
here need to believe is that you don’t have schizophrenia
because of sin. It’s a medical thing, not the response of an angry
God,” he says. “That’s a big issue for people here. They think
they’re suffering because of something they did.”
“Why is the universe as it is?” he asks. “The longer I con
tinue with my faith and ministry, I become less and less clear
about issues that were so plainly clear when I was growing up.
I’d like to have God come out looking good, but I think it’s a
process where the universe is emerging and God’s under-
how could God tell Abraham he’s
going to he a father of a multi
tude of nations and then ask him
to destroy his only son?” he says.
“I was bothered that Abraham
would go ahead with it, even if it Outward symbols of religion like a church steeple or meno
rah SERVE AS reminders OF PROFOUND THEOLOGICAL ISSUES.
was God who asked.” As it turns
out, the great rabbis of the ages
have had some of the same prob
lems. “The rabbis weren’t so
troubled by God as by Abraham.
Before this story, Abraham ques
tioned everything and haggled
with God. But when it came to
Isaac, he said okay. He went up
the mountain and lied to his only
son,” says Lanzkron-Tamarazo.
Janet Hellner-Burris (sf 77)
“A hero can be flawed.”
Yhave a deeper understanding
ofthe question ofsuffering than
I did in college, but I don i
have the answer
What About Job?
Reading the Bible as a book, as it’s done in sophomore semi
nar, leads some students to examine the stories in an almost
literary way-the implications for their beliefs recede into the
background as the stories’ universality is considered.
Rev. David Dillard (A89), a psychiatric chaplain at a state
mental hospital in Kentucky, wrote his sophomore essay on
Job and says that, in the context of his current work, the ques
tions of that book remain. “Why are people born with mental
illnesses? Why should they suffer the way they do? How is a
righteous God involved in all of that?” he asks. The questions
he first dealt with on a theoretical level now have more mean-
{The College - St John’s College ■ Summer 2001 }
�i8
{JohnniesonTheology}
Y think ofinterfaith work as an opportunity to share
our glimpses ofGod. None ofus, by assumption,
has seen Godface toface, but each ofus has
experienced God in a variety ofways.""
Clark Lobenstine (A67)
standing is emerging too. I think God is struggling with cre
ation as much as any of us are.
“There’s a theology called ‘God Wins’ theology, where we
do everything we can to make sure that God comes out look
ing good. If there’s a problem, it’s not God’s fault, it’s some
thing else’s fault. I don’t think God respects that frame of
thought any more than a free-thinking individual would.”
Dillard knows there are objections to his point of view: “One
criticism of this kind of thinking is that I’m anthropomor
phizing God, but I can’t bring the other kind of theology into
a room with a patient.”
Rev. Hellner-Burris, pastor of an urban church facing urban prob
lems (violence, addiction, poverty, racism), also struggles with the
question of suffering. “I have seen so much suffering in my workthat question doesn’t go away,” she says. “I would say that I have a
deeper understanding of the question [than I did in college], but I
don’t have the answer. All I know is that I would rather live with God
and all of those questions than without God.”
The Rev. Dr. Glark Lobenstine (A67), director of an interfaith
organization, tells the story of William Sloan Coffin, a former chap
lain at Yale: “His son was killed and someone gave him the tradi
tional line about it being God’s will, and Coffin lashed out and said,
‘To Hell it was! God was the first to cry!’”
As for Lobenstine’s understanding of God’s relation to suffering,
he says that for him, it isn’t a question of how to understand suffer
ing but a challenge of how to remain faithful in the face of suffering.
“I am very clear that God never promised us a rose garden. There are
joys that are part of the spiritual journey, some of which come in the
midst of pain and suffering and some of which come in what appear
to be much easier ways.”
Glimpses of God
When Lobenstine was in high school, he asked God to make clear
His personal love for him. “I never doubted the existence of God,”
says Lobenstine. “But I wanted something more personal.”
The summer before his senior year, Lobenstine was in a car acci
dent. “It was my fault. I broke the windshield and they had to pull the
glass out of my mouth, but no one was injured,” he says. “I was very
struck by this being the answer to my prayer. God didn’t cause the
accident, but I felt he protected me in it. I responded to that experi
ence, a revelation to me of God’s love, as a calling to my ministry. I
was God’s to do with as he wanted.”
Lobenstine’s ministry is an unusual one. As director of the Inter
Faith Conference of Metropolitan Washington, D.C., he works with
people of many faiths and representatives of many communities on a
host of social issues from housing and child welfare to racial toler
ance and interfaith understanding. Through his work, Lobenstine
says, God is revealed to him in many ways: “I see a great variety and
depth of God’s love. Although I’m profoundly grateful to be a Chris
tian, I know from Sana the Muslim and Jan the Baha’i and D.C. the
Hindu the great joy they have in their own relationship with God and
the depth of that relationship with God.
“I think of interfaith work as an opportunity to share our glimpses
of God. None of us, I assume, has seen God face to face, but each of
us has experienced God in a variety of ways. By sharing ghmpses,
whether we are all Presbyterians or all Muslims or all Catholics or of
diverse faiths, we deepen our understanding of God while we grow in
our appreciation of our own traditions and our understanding of
others’.”
In her own spiritual journey, Vicki Manchester (SF71) has seen
glimpses of God through different religions, from her Episcopalian
childhood to a time when she attended a Jewish temple to now, when
she has found what she was searching for in Tibetan Buddhism.
Manchester says that faith does not demand understanding. Rein
carnation, for example, is an important idea in Tibetan Buddhism,
and although it doesn’t make sense to her, she has faith that it will.
“I keep listening to my teachers and seeing that everything else they
say makes sense. My respect for the dharma, the teachings, has
steadily built up, mainly because it works. Being kinder to people
really did increase my own happiness. That’s kind of a law of karma
which is connected to the idea of reincarnation,” she says. “A lot of
the teachings are mysterious to me. I can’t understand all of them,
but I have faith that someday, maybe, I will.”
The Rev. Rachel Frey (Agi), an associate minister at a suburban
parish, agrees that questions of doubt can live within a faithful per
son. “I wrote my senior essay about doubt,” she says. “I asked if you
could be both faithful and doubtful, something I was thinking about
and wanted affirmed.” Now, after seven years as a minister, she says
she no longer looks for answers in theological readings. “I have
more life experience that affirms my faith,” she says. “When I was at
St. John’s, I thought about God in an academic way. Being a minis
ter, my experience with congregations of faithful people has led me
to believe in having a relationship with God, as opposed to thinking
philosophically about a concept of God. I used to believe because it
was logical, but now I believe because of the things I see in people’s
lives.”
Frey, who works part-time at the University Christian Church, in
Hyattsville, Md., says she set out to find a position at a church with
more than one minister so she could continue learning from some
one with more experience. “I’m at U.C.C. because my senior minis
ter, Marshall Dunn, is the kind of minister I wanted to be with and
work with and learn from. He’s an excellent pastor. He loves his
{The College. St. John’s College ■ Summer soot }
�{Johnnies on Theology}
19
''When I was at St. Johns, I thought about God in an
academic way. Being a minister, my experience...has led
me to believe in having a relationship with God.''
Rachel Frey [A91]
church and he’s beloved by his church. He loves people and he loves
being a minister, which sometimes seems kind of rare. There are a
lot of disheartened ministers out there.”
Keeping the Faith
As a pastor at an active and diverse church near Pittsburgh, Rev.
Hellner-Burris has sought to avoid the disheartened minister syn
drome by focusing on her prayer life. She recalls a time early in her
ministry when she saw she was heading for burnout. “I became com
mitted to daily prayer,” she says. “For me the inner journey is what
feeds the outer journey. The inner focus of my prayer life has been
crucial to my outward expression of ministry. I can’t do one without
the other.”
For Dillard, the psychiatric hospital chaplain, the difficult cir
cumstances of his work keep him from burnout-an irony not lost on
him. “This is a place where there’s a lot of suffering and mental
anguish, but we’re able to do some good and help people out.
Patients really give us the greatest affirmation.” As an example, Dil
lard describes a group he leads in geriatric music: “These folks can’t
remember what they had for lunch, but they remember all the words
to the a3rd Psalm or ‘Your Cheatin’ Heart’ or ‘The Old Rugged
Cross.’ We’ll use these songs to access memories and emotions.
We’ll sing the old church song ‘Break into the Garden,’ and it’ll
bring somebody back to a little country church in Kentucky.
“It’s a gift to worship with people who really want to be in a wor
ship environment, a gift to be in a service with people who aren’t
driving up to the church in a Jaguar. They come with a rawness you
rarely see out in the real world where people put on their church
clothes and church personas and don’t show their true selves.” -#■
Theology Bookshelf
David Dillard (A89) is a psychiatric chaplain at Central State Hos
pital in Louisville, Kentucky. He is a member of the Alliance of
Baptists. He recommends:
The Brothers Karamazov by Fyodor Dostoevsky
Tragic Vision and Divine Compassion: A Contemporary
Theodicyiyj'^&aAy^sAey
Either/Or by Soren Kierkegaard
The Crucified Godby Jurgen Moltmann
Rachel Frey (Agi) is associate minister at University Christian
Church in Hyattsville, Maryland. She is a member of the Christian
Church (Disciples of Christ). She recommends:
Desiring God: Meditations ofa Christian Hedonist
by John Piper
Walk in the Light and Twenty-Three Tales by Leo Tolstoy
The Christ-Centered Woman: Finding Balance in a World of
Extremes by Kimberly Dunnam Reisman
Janet Hellner-Burris (SF77) is pastor at the Christian Church of
Wilkinsburg in Wilkinsburg, Pennsylvania. She is a member of the
Christian Church (Disciples of Christ). She recommends:
Jesus and the Disinheritedby Howard Thurman
Open Mind, Open Heart by Thomas Keating
Pedagogy ofthe Oppressedby Paolo Frieire
Frank Lanzkron-Tamarazo (A95) is hazzan (cantor) and education
director at Temple Beth-El Mekor Chayim in Cranford, New Jer
sey. He is a member of the conservative movement. He recom
mends:
The Guidefor the Perplexed by Moses Maimonides
The Talmud over 500 years of rabbinical commentaries
The Jewish IFtzz-by Josephus (around 37 c.e.)
Clark Lobenstine (A67) is director of the Interfaith Conference of
Metropolitan Washington in Washington, D.C. He is a member of
the Presbyterian Church (U.S.A.). He recommends:
The Illustrated World’s Religions: A Guide to our Wisdom
Traditions by Huston Smith
A New Religious America by Dr. Diana Eck
Vicki Manchester (SF71) has taken refuge vows as a Tibetan Bud
dhist. She recommends:
The Dhammapada (teachings of the Buddha)
Liberation in the Palm p/’FoMr/ZazztZby Pabongka Rimpoche
Ethicsfor a New Millennium by His Holiness The Dalai Lama
The Art ofHappiness by His Holiness The Dalai Lama
The Four Noble TFiztAj by Venerable Lobsang Gyatso
What the Buddha Taught by Walpola Rahula
{The College - St. John’s College ■ Summer aoot }
�ao
{Politics}
ROUSSEAU
AM) HKAI.I'OI I I IK
How alumni in the world ofpolitics are influenced
by their St. Johns background.
By John Rankin, SF03
rom a C-SPAN production studio
to
the diplomatic negotiating table in
F
Cyprus, St. John’s graduates have
found their calling in the field of
While the alumni
interviewed
for this article
politics
and government.
Could
express a great appreciation
for
their
education,
they
this array of positions held by alum
see the value moreniinindicate
the mental
tools and skills
they
a connection
between
picked up at St. John
than in the
content ofread
the pro
the’spolitical
philosophy
at St.
gram. Reading political
careersphilosophy
chosen? was not particu
larly persuasive for any of them in terms of choosing a
career; they felt a desire to get involved and pursue
the causes important to them. However, all the alum
ni profiled value the fact that they have read the
majority of the political texts that played a role in the
evolution of western political thought, and they cite
this as an indispensable background for a thoughtful,
substantive take on the political world of today.
The stories of five alumni follow: an ambassador, a
television producer, a writer and television panelist,
and two who work at think tanks.
Donald Bandler (sfgi 73)
“Getting things done-that’s what it’s about,” quips Donald Ban
dler, American Ambassador to Cyprus. Appointed to the post by
former President Bill Clinton in May 1999, Bandler faces the
complex and delicate issues concerning this small island nation
off the southern coast of Turkey. As ambassador, Bandler’s pri
mary mission is to represent American interests in Cyprus. This
involves everything from providing political analysis to the U.S.
State Department, to managing the 200-employee embassy in
Nicosia.
Recently,
John’s and
the he played a role in facilitating a major sale of
Boeing planes to the commercial fleet of Cyprus Air. The issues
facing any diplomat in Cyprus demand thoughtful analysis and
careful handling. Divided since 1974 by a Turkish invasion, the
status of the island as a whole, and potential unification, remains
uncertain. Tensions run high, and lives have been lost in demon
strations and uprisings.
Bandler came to this post with a solid background in interna
tional diplomacy. After j oining the State Department in 1976, his
career took him to posts in Africa, the Middle East, and Europe,
where he participated in the negotiations leading to the
unification of Germany.
Consistent with the practice of political appointees, Bandler
submitted a letter of resignation to President Bush when he took
office. The Bush administration, however, has given no indica
tion it would like him to leave, and Ambassador Bandler expects
to stay at his post.
Bandler’s connection with St. John’s began during his under
graduate years at Kenyon College, where he met several profes
sors who had studied with Leo Strauss and other academics
involved in the Great Books movement. Bandler married Jane
Goldwin (A71, daughter of former Annapolis Dean Robert A.
Goldwin, A50) and completed the Graduate Institute in Santa Fe
several years after graduating from Kenyon.
{The College- St. John’s College • Summer sooi }
�{The College* St. John’s College • Summer 2001 }
�{Politics}
^...the conceptualfoundation acquired
from studyingpoliticalphilosophy can be
very helpful in thepolicy debate.
Donald Bandler [SFGI73]
Philosophy Meets Politics
Bandler discusses the role that his political philosophy background
hasplayed in the world ofRealpolitik in ‘"Philosophy Meets Politics. ”
Talking with John Rankin caused me to reflect on whether and how polit
ical philosophy, my academic concentration at Kenyon College and St.
John’s College, was a good background for a career in international rela
tions. The short answer: a resounding yes.
Early in my career I had the privilege of working as Special Assistant
to Dr. Paul Wolfowitz, currently the Deputy Secretary of Defense. As
Director of the Secretary of State’s Policy Planning Staff, Paul assembled
a group of 20 or so policy thinkers-many grounded in political philoso
phy, some taught by students of Leo Strauss-with a mandate to provide
an independent judgment on policies developed largely by career
experts. The policy debate often turned on issues that would appeal to
the student of political philosophy: What are the necessary conditions
for security of human rights? What deters hostile human behavior?
Fear? Hope? And why are so many people so desperately poor, i.e., what
causes poverty? Or the better question: what causes prosperity?
Later, I had two assignments in Paris, six years in all, ending up as
Charge d’Affaires at our embassy. The ambience alone was a political
philosopher’s daydream: Ben Franklin’s statue in the courtyard. Jeffer
son’s name carved at the top of the list of U.S. Envoys. Rousseau and
Lafayette memorabilia to explore. Even the pervasive reek of Gauloise
cigarettes did not dent the pleasure of a bistro lunch with Jean-Francois
Revel, a visiting Alan Bloom or Robert Goldwin. But Paris was not all
atmospherics. France wields considerable international influence and
enjoys playing her role as a counterweight to America. Although the
French Revolution and U.S. Constitution emerged at a common
moment, 1789, France had a string of different regimes and the U.S. only
one. Understanding the similarities and differences is important in
striving for good relations and cooperation. For its part, the French
“classe politique” is steeped in history and political theory that rein
forces its self-image as a competing pole of civilization. This comes out
in foreign policy seminars (“colloques”), which are often contentious
and are taken seriously. So too, are our discussions with French leaders
in the Elysee Palace, the Prime Minister’s office, and the Foreign Min
istry. Realpolitik generally prevails in those sessions, but the conceptu
al foundation acquired from studying political philosophy can be very
helpful in the policy debate. And when the U.S. and France agree, it is
usually a lot easier to build an international consensus.
Political philosophy also figured large in my work in Germany on its
reunification and on Israel’s peace negotiations with the Palestinians
and Jordan-and it is at the heart of my current ambassadorship. “The
Cyprus Problem” revolves around whether and how to negotiate a set
tlement to reunify this island that has been divided along ethnic lines
since 1974. Debate centers on “political equality” and whether the set
tlement should be a federation, confederation or some hybrid. The
issues parallel those in the Federalist Papers, especially debate over the
respective powers of the states and central government. I maintain an
intensive dialogue on these subjects with the Greek-Cypriot and Thrkish-Cypriot leaders on the island, in UN-led talks, and in unofficial study
groups led by U.S. academic experts.
I would hasten to add that political philosophy is only one of many
fields that provide a good background for a career in diplomacy. In fact,
the best preparation is probably a good liberal arts education, one that
dwells on books of lasting value, leads students to grapple with funda
mental ideas, values inquiry, and cultivates the art of serious conversa
tion.
Seth Cropsey (spya)
A Visiting Fellow at the American Enterprise Institute in Wash
ington, D.C. (a public policy think tank generally labeled con
servative), Seth Cropsey studies national security and defense.
Newt Gingrich, Lynne Cheney, and former Annapolis dean
Robert A. Goldwin are just a few of his well-known colleagues.
Cropsey analyzes how the United States military may best take
advantage of new technology. He studies the questions raised by
the increased accuracy and range of new weapons systems. As
history has demonstrated, technological advances such as the
longbow in medieval times and the Tomahawk cruise missile of
today can render old strategies and plans useless or even deadly.
Cropsey’s work creates new methods the military can use to keep
their tactics resonant with their technological capabilities.
Cropsey also studies the implications raised by the “kinder
and gentler” military of today. In recent years, the American mil
itary has undergone serious structural changes and adopted new
training methods. American military personnel often find them
selves in foreign countries as “peacemakers”-an ambiguous
type of policemen far from the typical (and expected) role of a
soldier. This often frustrates individuals in the armed services,
as few enrolled in order to police the streets of an unfamiliar
land. Furthermore, the character type the military has tradition
ally rehed on to excel-those interested in taking risks and test
ing themselves in combat-is put off by the style of the modern
military and less inclined to enlist.
Cropsey began his career in national security in 1981 as a
recent St. John’s graduate concerned with the relationship
between the United States and Russia. He has served as a profes
sor at the Marshall European Center in Germany, run jointly by
the governments of the United States and Germany. There,
Cropsey taught military personnel from former Warsaw Pact
countries principles of modern liberal democratic governments
{The College - St. John’s College ■ Summer 2001 }
�{Politics}
^3
''Because I work in politics, lam especially
grateful to have read works related to societies
organizing themselvespolitically, from Plato
andAristotle to the Federalist Papers. ”
Eloise Collingwood [A8o]
and related national security issues. He also worked with Ronald
Reagan and George Bush, Sr. as the Deputy Undersecretary of
the Navy from 1984 to 1990.
Cropsey values his St. John’s education for enabling him to
deal with a wide range of material and understand the fundamen
tal issues at stake. He suggests one change to the program, which
should not come as much of a surprise considering the path of his
career. “Edward Gihhon \Decline and Fall of the Roman Empire\
is no longer on the program, and he should he,” says Cropsey.
Eloise Collingwood (A80)
C-SPAN producer Eloise Collingwood uses the problems of
Washington, D.C., as the raw material for a television show.
Collingwood is responsible for getting C-SPAN’s national morn
ing call-in show, “The Washington Journal,” on the air. This is no
small task. Each day begins at 4 a.m. Collingwood thinks up seg
ment topics for the show, finds guests, determines the leads for
each segment, and works with the director and technicians to
ensure a seamless program. Collingwood reviews scores of arti
cles from newspapers, magazines, and the Internet to stay on top
of the issues and find new material for the daily show; under
standably, she values St. John’s for helping her learn how to get to
the gist of an argument and relate ideas to one another.
Like many Johnnies in politics, Collingwood finds the pohtical
books she read in seminar valuable in her professional life.
“Because I work in politics, I am especially grateful to have read
works related to societies organizing themselves pohtically, from
Plato and Aristotle to the Federalist Papers.”
Tom G. Palmer (A82)
Palmer is a Fellow in Social Thought at the
Cato Institute, a public policy research
institute in Washington, D.C. He publishes
papers, lectures at universities and insti
tutes around the world, and edits book man
uscripts and policy papers, determining
whether they meet Cato’s standards. He is
also director of Cato University, which gives
seminars on the principles of free markets,
limited government, the rule of law, and
other issues central to modern classical liberalism.
The libertarian Cato Institute suits Palmer’s interests well.
“My life work has been dedicated to advancing individual liber
ty,” he says. The Cato Institute has allowed him to immerse him
self in the study of the ideas he loves. In his work. Palmer fre
quently revisits texts he read at St. John’s. However, he feels that
books do not always hold the answer. “I learned at St. John’s that
there are lots of people who read a lot, but who have no wisdom
or who are bad people, and many more who don’t read much, but
who are wise and good,” he says.
Palmer does suggest some improvements to the program. He
argues that St. John’s “seriously underestimates the importance
of economics” and cuts off the study of economics with “one of
the most disastrous dead ends in the history of thought: Karl
Marx.” Palmer would like to see inclusion of the work from the
Marginahst Revolution of 1871, in which economists Karl Menger,
W.S. Jevons, and Leon Walras independently solved several prob
lems facing the classical economics of Marx and Adam Smith.
Will of the People?
In January 2001, Palmer and two colleagues, John Samples and
Patrick Basham, released a paper titled '"Lessons ofElection 2000. ”
Among other contrarian views ofthe election, the authors argue that
the electoral college should not be discarded, high campaign spending
did not discourage voters but actually increased voter turnout, and
the misguided appeals to the "will of the people ” by politicians on
both sides of the debate represent a confused claim to a concept
opposed to the nature ofAmerican representative democracy.
The United States is a constitutional republic, not a regime intended to
embody “the will of the people.”
Talk of the will of the people is profoundly misleading. Indeed, the
idea of the will of the people is a deeply authoritarian idea completely at
odds with the idea of government under law. It derives, not from the
American Founders or from any “Whiggish” antecedents in Britain’s
constitutional history, but from the radical authoritarian and anti-liber
al philosopher Jean-Jacques Rousseau, who postulated a “general will”
of the people as the foundation of the state. According to Rousseau in
The Social Contract-. “The general will is always right, and always tends
to the public good; but it does not foUow that the deliberations of the
people will always have the same rectitude. We always desire our own
good, but we do not always recognize it. You cannot corrupt the people,
but you can often deceive it; and it is then only that it seems to will some
thing bad.”
As political historian J. L. Talmon noted in his classic study of the play
ing out of Rousseauian politics, “The very idea of an assumed preor
dained will, which has not yet become the actual will of the nation . . .
gives those who claim to know and to represent the real and ultimate will
of the nation-the party of the vanguard-a blank cheque to act on behalf
of the people, without reference to the people’s actual will.”
{The College. St. John’s College ■ Summer zoot }
�{Politics}
24
''Thepersonal is the universal [in America]. Each
individual experience is a chapter in the larger
drama called the American Story.
Robert George [A86]
The United States is not based on some grand notion of the will of
the people. American government depends on the more modest idea
that the people may delegate certain limited powers to a representative
government operating on principles and procedures set out in our
Constitution.
If by “will of the people” pundits have in mind the Constitution, that
is closer to the occasional use of the term by the American founders. But
current debate indicates that what they have in mind is, instead, whatev
er the will of the people is (should be) about particular matters ofpolicy,
or who should be president. If the Constitution is the abiding will of the
people, then it sets the terms within which policies and officers will be
selected, and continual recourse to the “will of the people” is otiose.
The phrase “the will of the people”-along with “dimpled chad”-has
no place in a system of equal liberty under law. Instead of confusing our
selves with airy metaphysical talk about the will of the people, we
should, with Jefferson, “with courage and confidence pursue our own
federal and republican principles, our attachment to our union and rep
resentative government.”
Robert George (a86)
As an editorial writer for the New York
Post, Robert George writes five or six
unsigned pieces for the newspaper each
week, covering issues from the national
level to the local concerns of New York
ers. Where George really lets loose,
though, is in his regular columns for
National Review Online. Favorite topics
of recent months are Bill Clinton’s par
don fiasco and the early stages of Hillary Clinton’s senate
term. George’s columns feature slick appeals to his view of the
issues and a rhetorical flair unmistakably his own. Although at
heart a thoughtful commentator, his columns often leave the
reader more impressed by his brazen style than his cunning
erudition.
Before working at the Post and National Review, George
helped staff the communications office of former Speaker of
the House Newt Gingrich, writing speeches and press releases
and formulating public relations strategy. He then went on to
coordinate the efforts of grassroots organizers with the
Republican National Committee. His latest project is serving
as a regular panelist on the Saturday evening CNN show “Take
5.” On the show, he discusses topics from politics to popular
culture -with two co-hosts and guest panelists.
My Independence Days
Last year, Robert George took a breakfrom his clever and combative
style to write a sentimentalJuly 4th columnfor Salon, com, “My Inde
pendence Days. ”
Here we celebrate the Fourth of July. For this writer, everything that the
dream called America represents can also be found in two personal
“independence days.”
The first is January ai, 1971. It was the day an eight-year-old boy first
landed in the United States at JFK International Airport. At the time,
U.S. hospitals were experiencing a nursing shortage, so the boy’s moth
er responded to an inquiry from New York City’s Mt. Sinai Hospital. The
boy wasn’t happy about leaving his island home. It was only later that the
lesson of taking advantage of an opportunity when presented sunk in.
Fortunately, a volatile case of air-sickness endured by the young boy on
the flight over did not prove to be a portent for future experience in the
United States.
Living in a country for close to three decades, there are any number of
days and experiences that might stick out that also symbolize America.
But this writer selects November 3, 1989....the swearing-in ceremony
[for my citizenship]. The event itself was rather low-key; ultimately, it
seemed somewhat prosaic. The poetry was supplied moments later as
the new American emerged into a crisp Maryland morning and looked
up in the sky. There, fully unfurled over a government building, was Old
Glory flapping in the wind. Couldn’t have been more perfect if Spielberg
had directed it.
Many people consider the passage of the first 18 years as the initial
step from childhood into adulthood. This particular r8-year passage
marked a period separating arrival and “Americanization.” Other
opportunities followed. Less than three years later, a few of the writer’s
words ended up in the last speech Ronald Reagan delivered at a RepubUcan Convention. Just a short phrase, but for a young island immigrant, it
was certainly a thrilling, awe-inspiring moment. And then, a few years
after that, the immigrant found himself writing for the first Republican
Speaker of the House in 40 years.
As we celebrate the nation’s birth, it’s not a bad idea to pause and con
sider our own personal “independence days.” These are the moments in
our lives that stand out as uniquely American. At one time, for many, it
was the Ellis Island arrival. For others, it’s starting a business, beginning
the novel or casting the first vote. These are the days that connect each
of us intimately with the opportunity that is America. The personal is
the universal here. Each individual experience is a chapter in the larger
drama called the American Story. The opportunity to excel within the
story is the connection we all share, regardless of race, gender, or any
other superficial attribute.
{The College -St John’s College • Summer 2oot }
�as
{The Program}
It Takes Two Villages
In his Dean s Statement, Timothy Miller considers
what it means to learn in a community
By Barbara Goyette, A73
very year the chairman of the
Instruction Committee
(which alternates hetween
the dean in Annapolis and
the dean in Santa Fe) submits
a Dean’s Statement of Educa
tional Policy and Program. Topics for the
Dean’s Statement vary from the hroad to
the more specific; sometimes the Statement
serves as an institutional don rag or propos
es major changes to the program. This year,
Timothy Miller, acting dean in Santa Fe,
characterized his topic as “the intrinsic
fundamentals that make this small college
precious to its memhers and also a precious
resource within the larger educational
sphere.”
The Statement begins, “For St. John’s
College it takes two villages-one in Santa
Fe and one in Annapolis. Even in an age of
spin the notion of a village has an appeal
Timothy Miller (right) included passages
that is not merely sentimental. Reaching
FROM Simone Weil and William James in his
more deeply into our souls, it suggests
Dean’s Statement.
mutual care and nurture, the daily support
of family and neighbors, help in emergen
cies, the sharing of rituals . . ., recurring
celebrations . . ., and ceremonies by which,
often recedes to some vanishing point in
as thinking animals, we mark the stages of
the future.” Tenured tutors are more likely
our growth, maturity and decline.”
to be granted partial or full leave from
Mr. Miller discusses the primary goal of
teaching, and they are more likely to have
the college as the education of young peo
added responsibilities such as administra
ple who are emerging from adolescence to
tive posts that free them from the class
early maturity. The college must meet their
room. A result is that on the Santa Fe cam
educational needs and see to their personal
pus, throughout the 1990s, “approximately
needs and interests as well. That American
60 percent of tutors have been tenured, but
colleges and universities operate on a fourtenured tutors have taught only about 40
year cycle to bring students to this desired
percent of the classes. . . Clearly a majority
maturity makes for some difficult decisions
of our classes depend on the energy and dis
along the way.
tinction of our newer tutors.”
He expands on some of the problems this
Mr. Miller also discusses the perennial
compressed schedule creates for tutors,
problem of there being too many books to
whose primary responsibility is to “teach
read in too little time. The Statement sug
and make ourselves as competent as possi
gests alternatives for dealing with the music
ble in all parts of the St. John’s program.”
and visual art tutorials-including a sugges
In their early years, faculty must spend
tion to move the visual arts tutorial to soph
much time and effort to learn the parts of
omore year and to focus more time in lan
the program they are teaching. Even after
guage tutorials on writing. He also
receiving tenure, tutors find that the goal of considers a larger question: “We intend our
teaching at all levels in all areas of the pro
program of studies to have a wholeness that
gram is still elusive-“achieving that goal
does not exist in the typical college curricu
E
{The College. St. John’s College ■ Summer 2001 }
lum. Whatever our judgment
about the incompleteness and
inadequacy of specific parts of our
program most of us believe that
the program as a whole is greater
than the sum of its parts.
Whether this wholeness may be a
reflection of a wholeness existing
in the world is worth our atten
tion...”
Passages from William James
and from Simone Weil illustrate
some approaches to this question
of how it’s possible to pay atten
tion to the most important things.
In a passage from Psychology,
James lays out an approach to
learning that demands “willful
attention in study,” while Weil
denies the effectiveness of will
power and posits that leaving our
selves open works better: “Attention con
sists of suspending our thought, leaving it
detached, empty, and ready to be penetrat
ed by the object,” she writes.
Mr. Miller cites a passage in Weil’s
“Human Personality” that addresses “the
proper balance between the individual
intellect and the collective in which an indi
vidual has its natural origins”: “When sci
ence, art, literature, and philosophy are
simply the manifestation of personality they
are on a level where glorious and dazzling
achievements are possible...But above this
level...is the level where the highest things
are achieved. These things are essentially
anonymous...The human being can only
escape from the collective by raising him
self above the personal and entering into
the impersonal...” This passage serves as a
source for his final question: “Are we over
weening in the hope that our lives as stu
dents and faculty at St. John’s College are
directed toward the sacred realm of the
impersonal?”
Thefull text ofthe Dean’s Statement is
online at www.sjcsf.edu/academic/
deanoi. htm, or is availablefrom the Dean’s
Office in Santa Fe (505-g84-6o7o).
�{Alumni Notes}
1935
Richard Woodman writes: “Glad
to read the article on St. John’s in
the Smithsonian^ February aoor
issue. Those prior to the 1937 class
did get a good liberal education
with a chance to see the Maryland
legislature and U.S. Congress in
session without having to wait in
line and go through metal detector
systems. It was a poorer but it
seemed a kinder world in some
respects. I wonder how many of the
class of 1935 are stiU alive and
working as I am.”
1936
Gilbert Crandall, a Civil War
buff, recently had articles on that
subject published in the Washing
ton Times and the North Georgia
Journal.
1938
Frank Townsend reports that he is
still alive and thriving.
1942
Ernest Heinmuller writes about
two classmates: “Bill Ruhl died in
January. As a community leader in
Salisbury, Maryland, he was prop
erly honored by a large gathering of
friends and officials at the funeral.
Some of you 4aers might like to
send a note of encouragement to
Al Poppitti (use the register
address). Al suffered a severe heart
attack but is showing improvement
daily. I have been busy working for
World Vision, a ‘feed the hungry’
effort for Rwanda and other Third
World peoples.”
1949
Oscar Lord reports that his son,
Lt. General Lance W. Lord, USAF,
is Commandant of the U.S. Air Uni
versity Maxwell Field, in Mont
gomery Alabama.
copal parish in Palm Springs, Calif.
“This Sunday ‘work’ and a variety
of physical problems keep me from
attending Sunday alumni seminars
in Los Angeles. Health problems
hit us hard from Christmas into
January. Son David broke his left
leg and is in a wheelchair, and wife
Rita is on oxygen 24 hours a day
due to emphysema. So I get food
and run errands until we get David
on his feet and Ruth free of oxygen
tanks.”
1950
“I regret not being able to attend
the 50th reunion of my class this
last fall,” writes Tom Meyers. “My
health is generally quite good, but
that of my widowed sister is not.
Perhaps I will be able to make the
next one. It will not be quite the
same, but one does what one must.
Amazingly, I will be 80 years old
this coming October-both
astounding and amusing.”
stayed in pubs, B&Bs, and resort
hotels. “It was a blast!” he says.
“Great scenery, great people.”
Jennefer Ellingston is active in
1953
Charles Powleske reports: “My
fourth year of retirement finds me
at work on ‘The History of BCIU
(The Business Council for Interna
tional Understanding)’ where I
began working in i960.1 also con
tinue to be active with BCIU’s
working group that brings about its
annual benefit at the Metropolitan
Opera (since 1984); also still active
in the affairs of The Princess Mar
garita of Romania Foundation as a
member of its board. I still ‘rest up’
in Mexico when I can (Puerto Vallarta, mainly) and, in 2000,
enjoyed April, May, and October
there.”
1955
Priscilla Bender-Shore and
Merle Shore (class of ’54) write
1951
Alfred Franklin sends a message
to classmates; “Our 50th reunion is
this year. Myself, Ray Stark, and
Herman Small are starting togeth
er a committee for setting up the
agenda. We would like to expand
the committee to establish what the
class gift should be, who we can get
to tutor, and choose the reading.”
from California. Priscilla curated
and juried an art exhibition,
“Susan B. Anthony on Mt. Rush
more,” for the Santa Barbara Coun
ty Arts Commission. The exhibit
ran from February through April
and celebrated Women’s History
Month. Eighteen artists were repre
sented. Priscilla gave two lectures
in connection with the exhibit.
William Roberts writes that he
spent last March bumbling around
England, Wales, and Scotland. He
A Happy Accident
ARL Hammen
(A44) sent in the following contribution:
“I was a Maryland scholarship student, class of 1944.
Going to St. John’s was a happy accident for me. I last
Mostly I studied visited
oyster metabolism
taught cellular
and
comparative
the campus and
in October
1999, and
enjoyed
seeing
physiology courses.
Also
ran the Boston
Marathon
times.
Sinceand
a few
classmates.
Most of
my career12was
teaching
retirement in 1993
I have in
taught
freshman
biology at of
a community
col
research
biology
at the University
Rhode Island.
lege several times and have held other part-time jobs, the most interest
ing: enumerator for the 2000 census. I became so good at obtaining
information that I was promoted to denominator. Beginning in August I
C
Richard Frank was made an hon
orary member of the Societe Asiatique.
The Rev, Frederick Davis says
that he is still assisting at an Epis
1956
plan to teach math review at the Ringling School of Art and Design, one
of the best art schools in the U.S. I remember that Jacob Klein said that
if you have a mind at all, it is a mathematical mind. My running career
continues. In 2000 I was ranked number one M75 in Florida for both
5 km and 15 km.”
{The College. 5t. John’s College ■ Summer 2001 }
the Green party and reports that it
now has 84 elected officials. “Yes,
we are small, but everyone is grow
ing green or withering away. Global
warming continues and the Arctic
ice cap loses four inches a year.”
1957
Arianne Laidlaw writes that she is
going to Vietnam as the guest of
people she and her husband spon
sored in 1975. She will spend three
weeks there, from Ho Chi Minh
City to Hanoi. She also plans a few
days in Hong Kong and Bangkok.
1959
John McDevitt says that he con
tinues to teach part time at the
community college and to make
dulcimers and harps. His daughter,
Gianna, has joined with his wife in
the operation of a country general
store and trailer park.
“ISI Books of Wilmington,
Delaware, has just brought out my
newest (of nine) books,” reports
Hugh Curtler. “It is entitled
Recalling Education and it propos
es a traditionalist approach to high
er education that is counter to the
major trends today (except, of
course, St. John’s) where the liberal
arts are in serious jeopardy.”
i960
“I am in the third year of a fouryear great books program at the
University of Chicago downtown
campus,” writes Peter Ruel. “We
meet once a week for three hours
(one and a half seminar and one
and a half tutorial) for three iiweek semesters. Forty years makes
a difference in how one reads a
book. It is definitely worthwhile to
return to what we all loved as young
people, and breezed through ivith
little understanding.”
1962
Lenke Vietorisz reports a new
web site address: members.net/
rrrepasy.
�{AlumniNotes}
Jon Cohen retired last summer
after ai years as a social worker for
the State of New Jersey.
David Schiller writes that he is
planning to deliver another paper
for the International Society of Chi
nese Philosophers in Beijing in July
2001.
David Benfield has enjoyed elec
tronic correspondence with various
classmates and suggests that the
class of 1962 plan an electronic
reunion to coincide with Homecoming 2001. “At this reunion we
can make plans for a real face-toface reunion in 2002 to celebrate
40 years of reality. Write to me at
david.benfield@montclair.edu.”
1964
Judith Laws Wood has moved to
Visalia in the San Joaquin Valley of
California. She is a reference librar
ian at the county public Ubrary.
1966
Constance Baring-Gould writes:
“Congratulations on the Smithson
ian article! My sister wrote to me
about it and I really enjoyed reading
it. I still protect my books rather
than my hair-I’llbet we all do!”
1967
Meredith Burke continues to
publish editorials on the subjects of
AIDS control and negative popula
tion growth. Her pieces have
appeared in the San Francisco
Chronicle, the San Francisco Exam
iner, the San Diego Union-Tribune,
and the Philadelphia Inquirer.
Hope Zoss has been appointed
Associate Director of Development
at the Chemical Heritage Founda
tion in Philadelphia.
1968
Ellin Barret (SF) writes that
there are several St. Johnnies in the
San Francisco Bay Area who are
involved with a winter production
called the California Christmas
Revels. Revels uses a unique form
of music theater to dramatize the
celebratory traditions of diverse
cultures and eras. Both profession
als and amateurs perform, and
there are carefully planned
moments of audience participa
tion. The 2001 show will focus on
music as a force for ethnic and reli
gious reconciliation, drawing espe
cially on Irish-Celtic heritage, to
portray some of the unifying
themes underlying the on-going
struggles that beset warring fac
tions over generations. This year’s
script is built on the story of the
greatest Irish harper of all times,
the blind O’Carolan, who, against
great opposition, steadily dedicated
his life to using music to heal enmi
ty among peoples.
Antigone Phalares (SF) has been
a part of the Sacramento alumni
seminar group for over 20 years.
“Our crown jewels are Marion and
Tom Slakey,” she writes. “How
lucky it is to have our very own
St. John’s tutor and tutoress to con
tinue those enriching conversa
tions we began long ago, in
Annapolis and Santa Fe. This
is life lived to the full.”
“Our daughter has joined the Peace
Corps. We are planning to visit her
in the Dominican Republic this
spring,” writes Carol Neitzey
Dale (A).
tour the ancient Temples in Noa
(Japan’s first capital), and see
Kabuke. He is a professor of Pedi
atrics, Physiology, and Biophysics
at the University of Southern Cali
fornia and Children’s Hospital Los
Angeles.
1969
“Got caught in the dotty-com melt
down. An interesting experience
but one I don’t want to repeat,”
writes Frances Burns (A).
Joseph Baratta (A) will be teach
ing the history of math at Worces
ter State College in Worcester,
Mass., in 2002.
Carl Severance (SF) is now living
in Lexington, Ky., teaching adult
education (GED Preparation). His
wife Deanna is Director of Ken
tucky’s historic Frontier Nursing
Service. His son Alex is in his sec
ond year at Boston College Law
School, and his daughter Sarah
Sebestyen is pursuing a singing and
song writing career in New York.
Greetings may be sent to
carlsev@aol.com
1970
Allison Karslake Lemons (SF)
Steven Hanft (A) says, “In nine
reports: “I am currently teaching
French part-time at Wichita State
University and at East High School
in Wichita. My husband, Don
(SFGI), teaches physics at Bethel
College, in North Nevrton Kansas,
and my oldest son, Nathan, is a
freshman at (dare I admit it?) Ober
lin College, studying piano (among
other things). I’m afraid making
money just isn’t in the genes; but
we’re leading enjoyable lives (and
possibly even somewhat virtuous
ones) all the same.”
years I can retire.”
Thomas Keens (SF) received a fel
lowship for Foreign Scientists to
Japanese Institutions from the
Japanese Foundation for Emer
gency Medicine. He spent nearly
two weeks at the National Chil
dren’s Hospital in Tokyo. He gave
two major presentations on his
research on sudden infant death
syndrome (SIDS) and discussed
SIDS and respiratory research with
Japanese colleagues. He also had a
chance to walk in the East Gardens
of the Imperial Palace in Tokyo,
Catherine Carroll (A)
announces her marriage to Gilbert
T. Lusero on January 6, 2001, at
their home in Portland, Oregon.
She continues to practice law, spe
cializing in domestic relations;
Gilbert is semi-retired. They will be
traveling to Spain and would like to
hear from any St. John’s people
who are there now or who have
travel suggestions, recommenda
tions, or reminiscences they’d like
to share. Their address is 8100 SW
68th Place, Portland, OR 97223.
Maya Hasegawa (A) and Bor
Wycoff (A) were sorry they missed
the 30th class reunion in 1999.
Maya’s father Ichiro had become
very ill and they went to Richmond
several times that autumn to visit
before he passed away Christmas
Eve morning. Maya continues to
work at the Boston Housing
Authority, overseeing compliance
with civil rights requirements man
dated by HUD. Bob, working for
{The College. Sr. John^s College ■ Summer 2001 }
ay
Data Dimensions as a systems con
sultant, survived Y2K and now
looks forward to at least several
more years of steady employment
dealing with the changes required
by the 1996 HIRPA legislation.
“This January we detoured into
Annapolis for a few hours on the
way back to Boston from Richmond
and strolled around the campus,
stopping in to see the new library,”
they tvrite. “We had the sensation
of being ‘ghosts,’ invisible or nearly
so, to the students there, as doubt
less past alumni were invisible to us
when they stopped to gather mem
ories as we lolled around on a donothing Sunday afternoon in 1967,”
Hudi (Schneider) Podolsky (SF)
reports: “I’m now the executive
director of the National Coalition
of Essential Schools-back to the
world of teaching and learning that
I love so much. It has taken me a
long time to come back to this
great work, but my sojourn in the
profit-making world has given me
skills and perspectives that I can
now put to good use. You can see
what we’re up to at www.essentialschools.org.”
1971
Vicki Manchester (SF) is teaching
English and drama at the CIUA
Charter School in Colorado
Springs. “I helped to start the
school four year ago and after three
years of incipient chaos the school
is stabilizing and even has a waiting
list. I get to seminar lots with the
seniors. On the non-professional
side I took refuge vows as a Tibetan
Buddhist in 1998.”
Jane Goldwin Bandler (A) and
Donald Keith Bandler (SFGI73)
are currently living in Cyprus
where Don is serving as the Ameri
can Ambassador at the U.S.
Embassy. Jane is a psychological
counselor with a specialty in par
enting skills. They have three chil
dren: Lara (25), a PR account exec
utive in New York City, Jillian (23),
beginning University of Maryland
Medical School in 8/01, and Jeff
(24), in eighth grade in Nicosia,
Cyprus.
�a8
{Alumni Notes}
The Writer as Addict
Praising a writerfor writing is likepraising a crack addictfor
assiduous smoking. Writing is an addiction, and like all addictive
substances, it stokes thepleasure centers ofthe brain.
Emma Roth in Suspicion by Barbara Rogan
BY Sus3AN Borden, A87
mma Roth, the main charac
ter in Barbara Rogan’s (SF74)
novel Suspicion, is, like
Rogan, a full-time writer and
part-time soccer mom. Like
Rogan, she’s Jewish, has a
love of jazz, and lives on Long Island. But,
Rogan says, Emma is not her. “The main
thing about Emma is that she’s very vulnera
ble, emotionally fragile,” says Rogan,
“whereas I, despite my share of occasional
woes, am as healthy as the proverbial horse.”
Still, even without knowing Rogan, you
get the feeling that the two have a lot in
common, especially when it comes to writ
ing. Rogan agrees with Emma’s comparison
of writing and addiction. “That speaks for
me very accurately. Writing has always been
the thing I do that gives me the most pleas
ure and the fact that I can make a living at it
is great. That reinforces it: when you get
published and get paid and get all the
stroking that goes with it.”
Rogan says she always wanted to be a
writer. “I always could write, even as a kid I
had a talent for writing, a great love for
words. I was a huge reader. That’s what led
me to St. John’s in the first place,” she says.
At St. John’s, Rogan wrote several good
essays, but was nearly silent in class. This
led, temporarily, to an interesting problem:
“There was one essay that was so good and
so out of line with my participation in class,
that I was accused of plagiarizing it. It was a
Jungian analysis oiDon Quixote. I was into
Jung that year and it kind of clicked for me
in one essay,” she says. “There was a great
One of Barbara Rogan’s St. John’s essays
brouhaha, a lot of fuss made in the attempt
WAS so good, she was accused of plagia
to find my ‘source.’” When the smoke finally
rism. She took that as encouragement to
cleared and it was acknowledged that Rogan
BECOME A WRITER.
had written the essay, many of the tutors
involved in the investigation told her that
in 1974 after she graduated from St. John’s
she should be a writer.
and moved to Israel. There she worked as a
Though an accusation of plagiarism is an
production director and English editor for a
unusual source for encouragement, Rogan
Tel Aviv publishing house while she wrote
took it as such and started writing seriously
E
{The College- St. John’s College • Summer 2001 }
her first book, which she describes as a prac
tice book. The following year she opened her
own literary agency, which eventually
became the largest in Israel, supplying over
50 percent of the Israeli market for translat
ed books. In 1980, Rogan met and married
Ben Kadishson, an Israeli musician. Their
first son (they have two: Jonathan, 18, and
Daniel, 14) was born during the 1982 war in
Lebanon. During the same year Rogan’s first
novel. Changing States, was published
simultaneously in England, the U.S., and
Israel.
“Getting my first book published was a
huge thrill and it was published in three
countries. I was so new to the business I
didn’t realize what a terrific piece of luck I’d
had,” she says. Rogan’s good fortune has
continued. She now has seven novels to her
credit and is co-author of a non-fiction book
about the Middle East. Two of her books- A
Heartbeat Away and Rowing in Eden-wcxc
Literary Guild selections. Her 1999 book.
Suspicion, was a Book-of-the-Month Club
featured selection.
“Every book is a thrill. And a heartbreak
usually. It’s a tough career; not the easiest
business to be in. You never really feel suc
cessful entirely,” she says. Rogan explains
the trials that come with a book’s publica
tion: “Very rarely do things just click and go
the way you want them to. I’ve seen it from a
lot of angles: as an agent, as an editor, and as
a writer. There’s always a lot of expectation
built up around publication and it doesn’t
always pan out.” She discusses the econom
ics of book distribution, advertising, and dis
play: “Most books that are published have
little or no advertising budget. They’re just
shoved out the door with the hope that
someone will pick them up. The advertising
budgets go to Nora Roberts and Stephen
King-a guaranteed return on investment.
But publishers do this for sound business
reasons. I have maybe the misfortune of
understanding their point of view; neverthe-
�{Alumni Notes}
less, it is often frustrating for the writer.”
On the whole, Rogan has heen among the
more fortunate writers. Her hooks have
been reviewed in the New York Times and
the San Francisco Chronicle. They have been
released as audio books and published in
eight languages. The movie rights to Rowing
in Eden were optioned and the movie rights
to A Heartbreak Away were sold to MGM.
Rogan says that A Heartbeat Away is a
favorite among her books, combining sever
al subjects important to her: a hospital set
ting, which grew to interest her after her son
dragged her to a number of emergency
rooms when he was little; jazz, an interest
she shares with her husband, a jazz musician
when they met; and Jane Austen-Rogan bor
rowed the plot for the book from Pride and
Prejudice.
Rogan doesn’t always turn to the Great
Books for story lines, but program works are
often present in her books. Whether a char
acter is compared to Don Quixote, shudders
when she thinks of Medea, or hides a piece
of evidence in her copy of Kant’s Critique of
Pure Reason, Rogan’s ease with the great
books will seem familiar to Johnnies.
Not that she feels at ease with all of St.
John’s. “I still have nightmares about
Greek,” she says. “I dream that I took a year
off and came back and couldn’t remember a
single word.”
Although she has long since left Monte
Sol behind, Rogan remains in the classroom.
1972
JuanHovey (SF) reports: “My wife
EUse Cassel and I, being now empty
nesters, have bought a lovely town
house at the far northern end of
Topanga Canyon Road in the San
Fernando Valley, up on a hilltop
among huge stone outcroppings and
oak trees that formed the back
grounds for the Tom Mix movies, for
the Lone Ranger TV series and, it is
said, for one or two scenes from the
John Ford classic ‘Stagecoach.’
There are bobcats up here plus at
least one mountain lion and plenty
of coyotes, of course; people tell us
there is also a small herd of wild
goats in these mountains. I continue
to write a weekly column on business
finance and insurance for the Los
Angeles Times and contribute to a
number of other publications on the
same subjects. Life is sweet!”
She writes quickly,
notpausing to
think, just letting
the words spill out.
Later she will cut
and edit ruthlessly,
hut not now.
First drafts are
playgrounds where
anything goes.
FROM
Suspicion
now as a continuing education writing
teacher. She encourages her students to
write quickly, the way she describes Emma
as writing, but she doesn’t practice what she
preaches, Rogan approaches her first drafts
with a bit more deliberation. “I plan more
carefully and have to rewrite less than I used
to,” she says. “I’m trying to be a httle bit
more efficient. I try to plan out my themes
James Burress (A) notes that his
son, Toby Burress, is entering the St.
John’s class of 2005.
Louise Romanow (SF) sends this
report: “I find it amazing how busy
one can be and not be earning any
money! Bill’s and my son Curt is now
14 and cycles to school every day, a
rare event today. I continue to push
the catbriar back, planting indige
nous shrubs and perennials under
the forest canopy around our house.
I’m active in the League of Women
Voters, a bunch of opinionated
women-always lively discussion, and
I produce our newsletter and do a bit
on our web site. Keeping up with
technology keeps me learning new
stuff every day.”
1973
A medical journalist for more than
20years, Nancy Plese (SF) is cur
29
more and let the story drift less.” Before she
starts a chapter, Rogan writes a list of goals
and makes notes on the interweaving plot
lines she has to work with. She then thinks
up ways to dramatize her goals and invents
incidents that do so.
Rogan says that her new approach to writ
ing might be related to the fact that she’s
now working on her second mystery. “Mys
teries have to be plotted more succinctly,”
she says. “With a character-driven novel,
you can meander a little bit more.” Her new
mystery, to be published by Simon & Schus
ter sometime in aooa, is centered on a
reunion of old school friends who vowed to
get together again after ao years. When the
time comes, one of them is missing-mur
dered by one of the friends.
The idea for the book, Rogan explains,
grew out of real life, when she and a group of
classmates vowed to meet on the eve of
aooo. “For some bizarre reason a lot of us
did remember and six months before the
night we started reaching out and contacting
each other,” she says. “It was a pretty amaz
ing experience and the book grew out of
that.” Any chance that some of her SF74
classmates will recognize themselves in the
book? Unfortunately not. The group that
inspired the mystery was from Rogan’s high
school in Westbury, New York.
rently Executive Editor of The Pfizer
Journal, a bimonthly health policy
publication with an audience of sen
ior health policymakers. She is also
the mother of two, Andrew (17) and
Katelyn (7), and recently celebrated
the 22nd anniversary of her mar
riage to George Lewert. She lives in
Brooklyn, having moved to New York
in 1973, shortly after graduation.
“My son’s search for the right col
lege brought back memories of the
decision to go to St John’s, which
was one of the best decisions I have
made in my life,” she said. “On a
daily basis, I draw on the knowledge
and experiences gained there.”
“A bill has just been introduced in
the Michigan legislature to require
the teaching of ‘creationism’ in our
public schools, which is, of course,
the starter’s gun to revisit Origin of
Species,” writes JoN Ferrier (A).
“Jane Spear (A) and I both begin
our sixth decades this year, hoping
{The College. St. John’s College ■ Summer 2001 }
that the owl of Minerva truly does fly
at dusk. Tuesday’s New York Times
reported on the launching of scien
tific studies to assess the medicinal
properties of hallucinogenic drugs
such as LSD, mescaline, and psilocy
bin in treating alcoholism, phobias,
and other illnesses. Is there no limit
to the powerful strangeness of life?
Let’s hope not. May chaos find us
ready.”
1974
Virginia Newlin (SFGI) is retired
but teaching autobiography, working
as a poet, and volunteering as an
environmental activist.
“I’m a family practice physician
working at Lovelace,” writes Anne
Ashbrook Fitzpatrick (SF). “For
fun I sing with the Albuquerque
Women’s Choral Ensemble and the
Harmony Project.”
�{AlumniNotes}
3°
1975
John A. White (SFGI) has had his
book Kevvy published by Xlibris of
Philadelphia. “Set in future time, it’s
an epic novel with twin themes, a
society that has abolished marriage,
and which has made scientific dis
coveries which are too successful. It
provides ideas and value exploration
for the thoughtful, and adventure,
science fiction, sex, and romance for
folks looking for a good yarn. It’s the
culmination of many years’ work.
Further information is at www.Xlibris.com/Kewy.html.”
Howard Meister (A), having suc
cessfully defended his very cool the
sis, “Media and Metaphor,’’ has
received the MA in media studies
from The New School in New York
City. He is currently looking for suit
able employment as a teacher,
writer, exhibit designer, or curator,
following 20 years as an internation
ally exhibited visual artist. Howard
can be reached at
HMMeister@aol.com.
Jim Jarvis (A) says, “I enjoyed see
ing so many classmates at reunion
time last year. Hope we can have as
good a turnout for #30.”
G. Kay Bishop (A) is commissioning
a “musical commentary” from com
posers Chris Turner and Rich Robe
son. Text for the pieces will be drawn
from her poetry, including poems
from the collections Zero and The
Book ofLillith. Plans are to combine
the five performance and text pres
entation on a CD to appear next
year.
1976
Victoria Hanley (SF) has written
The Seer and the Sword, a fantasy
novel for young adults. Published in
December 3000 by Holiday House,
it is also being published in Britain,
Denmark, Holland, Germany, Spain,
Finland, and Japan. Hanley is a
Montessori teacher and massage
therapist; she says that although she
didn’t finish St. John’s, “the experi
ence of daily dialectic during that
time has influenced my life ever
since.” The novel, which garnered
praise from reviewers, is about a
princess who discovers she has the
power to see the future but must
confront the issues of greed and
revenge and perhaps fight to save
her kingdom.
1977
Ann Worth (SF) writes; “I am an
active member of the Local 510,
Sign, Display, and AUied Crafts. We
set up tradeshows and conventions
in the greater Bay Area and I am fre
quently the steward. Anyone want a
new job?”
Susan Holton (A) reports: “For the
last four years I’ve worked as a senior
designer for Tribune Media Services,
one of the companies, along with the
Chicago Tribune, of the Tribune
Company. I design everything from
sales collateral for our properties,
which include columnists, editorial
cartoonists, and comic strip cre
ators, to corporate brochures and
web sites. Through it all I’ve also
maintained a freelance illustration
and graphic design business. Cur
rently I’m one of the artists on the
Millennium campaign for posters for
the Northwest Indiana Forum.”
Jon is still enraging DAs as he suc
cessfully defends ‘innocent citizens
wrongfully accused of heinous
crimes.’ I am in the lower profile job
of engineering manager at Zairmailsee what my team is doing at
www.zairmail.com.”
1980
Liz Pollard Jenny (SF) was the
organizer of the first Alumni Art
Show, held in July in Santa Fe at the
campus gallery.
Nancy Jene Cline Wright (SF)
writes: “No major changes; still
teaching, still married to the same
fine fellow, still in Richmond, Vir
ginia. I do have a computer now,
with an e-mail address: cornishogre@earthlink.net. I have not
figured out how to forward things to
multiple addresses, and probably
won’t anyway, but enjoy watching
the way things end up moving about
to multiple groups of people with a
few button clicks-a different sort of
‘Great Discussion,’ I guess. I’d enjoy
hearing from fellow Johnnies.”
David Pex (SF) is the director of
finance for RuleSpace, an Internet
infrastructure start-up company. He
got certified as a scuba diver fast
year, dove in the Cayman Islands,
and is off this summer to St. Vincent
and Tobago for more diving and
snorkeling with his family.
1978
Larry Ostrovsky (A) writes: “I
have been living back in Anchorage
for the past seven years. If you can
look beyond the typical western
sprawl, it’s really kind of an undis
covered gem of a city. There’s excel
lent hiking and skiing, long summer
days and crisp winters. There’s even
some big economic scheme every
five or ten years to keep everyone
excited. If anyone comes through
this way. I’d love to hear from them.
My e-mail is Larryostrovsky@h<itmail.com.”
1981
Mary Filardo (A) wrote an editorial
in the May i edition of the Washing
ton Post. As the executive director of
the nonprofit 31st Century School
Fund, she outlined the phght of the
physical facihties at the D.C. public
schools. Her editorial stressed the
importance of planning for the
future and of keeping a good handle
on current design and construction
needs and services.
James Schamus (A) co-wrote and
was producer for “Crouching Tiger,
Hidden Dragon.” He’s worked with
Ang Lee on other films in addition to
the Oscar-nominated surprise hit
about Chinese warriors, such as
“The Ice Storm” and “Eat Drink
Man Woman.” Schamus also wrote
the lyrics for Crouching Tiger’s
theme song, “A Love Before Time.”
Marilynn Smith (SFGI) reports:
1979
Marie Toler Raney (A) and Jon
Raney (A74) report that they are
“still happy in Portland, Oregon in
our house ‘Wits End.’ Soon to be
empty nesters, we expect to find it
easier to come east to see friends.
“I’m still working at Coachella Val
ley High School in the Southern Cal
ifornia desert-and looking forward
to retirement (or is it re-focusing) in
about a year and a half. Teaching
composition and literature at the
College of the Desert is a great joy.
So are my four grandchildren!”
{The College. St. John^s College . Summer 2001 }
1982
Lemuel Martinez (AGI) ran on the
Democratic ticket for the 13th Judi
cial District Attorney post in Albu
querque. He’s an assistant district
attorney and an instructor at the
University of New Mexico who was
formerly a public school teacher for
ten years.
Eileen M. Renno (A) is living in
beautiful southern Oregon on the
east fork of the Illinois River. “I am
the proud mother of two daughters,
Molly (17) and Katy (6). I am work
ing in Human Services as a Job
Coach for The Job Council. I work
with ‘hard-to-serve,’ long-term wel
fare recipients, supporting them in
their efforts toward self-sufficiency.
It’s a challenging and rewarding
position with never a sometimeslonged-for dull moment. I miss the
Chesapeake Bay and look forward to
visiting family in Shady Side and
Frederick, Md., this summer. It’s a
happy thought that I’ll be visiting
Annapolis and St. John’s again, too.”
1984
John L. Bush (SF) says that he has a
new place of employment-he’s work
ing in the office of the university
architect at Virginia Tech in Blacks
burg, Va. “I’m enjoying walking to
and from work every day. Elizabeth
is finishing her masters degree at
Virginia Tech in plant pathology.
Salem is finishing his senior year of
high school at Blacksburg High and
looking at colleges to attend. He is
hoping for an athletic scholarship for
track and cross-country. Loran is
finishing his freshman year of high
school and enjoys playing soccer and
basketball. Hope everyone is well
and prospering.”
Karl and Lisa Walling (both A)
write that Karl is now a professor of
strategy at the Naval War College in
Newport, R.I. Lisa is now the direc
tor of the Tiverton Public Library
system.
Barry and Cynthia Hellman (both
A) have a new daughter, born 11-700, named Abigail Faith Hellman.
They now have three children, Barry
III (14), Joel (7), and the new baby.
Tracy Mendham (A) e-mails: “After
living in Brooklyn, N.Y., for nine
�31
{Alumni Notes}
Thinking in the Future Tense
BY
Barbara Goyette, A73
A
yjobistothink
/I about the
! I future,” says
/ I Robert Bienenfeld(SF8o).As
senior manager
of alternative-fuel vehicle marketing for
Honda, Bienenfeld works to promote the use
of cars that run on fuels other than gasohne.
The present is rapidly approaching the future
as far as internal combustion engine technolo
gy is concerned. What with the energy crunch
in California (and elsewhere), the high price of
gasohne, the arguments about the best ways to
deal with environmental problems like pollu
tion and misuse of non-renewable resources,
hybrid automobiles-which are fueled by gaso
line and electricity-are in the news today.
Bush has proposed a tax incentive to encour
age sales of hybrids. The American auto com
panies are working to develop hybrid versions
of their top-selling SUVs. Honda and Toyota
promote their small hybrids in hip ads in
major magazines like Time and the New York
er. Movie stars, gear-heads, and environmentally-sensitive politicians are buying the Hon
das and Toyotas currently on the market.
“Technology is changing all the time, and
I’m optimistic about how social priorities are
changing, too,” says Bienenfeld. “We’re con
suming way too much petroleum and we need
to be really concerned about that. There’s
been progress, but we need to go further.”
Alternative-fueled cars are one factor in the
mix of regulations, proposals, and products
that aim to help us deal with these current
problems and prepare us for the future.
Bienenfeld has worked for Honda since
right after he graduated. “I knew I wanted to
go into business, and I didn’t want to go to
graduate school right away to do it. I thought
my St. John’s education was great for any
W I
years, my partner Dana Chenier and
I are moving back to Massachusettswe’ll be relocating to Natick in May.
In July, I’ll be graduating from the
MFA in Writing Program at Vermont
College. For the time being, my
e-mail address will be
tmendham@nish.pair.com.”
Sue (Price) Gavrich (A) e-mails:
“My husband Bob and I joyfully
career,” he says.
“At St. John’s I was
used to picking up
a new, difficult
book every week
and then applying
myself to under
stand it. I thought
about the business
world; ‘How hard
could it be?’”
After a threeyear stint as a con
tractworker, Bienen Robert Bienenfeld
WITH the Insight,
feld was hired
Honda’s hybrid.
full-time. He worked
in parts inventory
management and then spent a year and a half
in Japan. In 1993 he was assigned to the alter
native fuel task force. Over the past decade
Honda has developed cars that are fueled by
natural gas, battery electric power, and a
combination of gas and electricity (the
hybrid). The Insight, a hybrid, uses its gaso
line engine for most driving but has an elec
tric motor as a supplement. When the driver
brakes, the battery recharges. “It’s a huge
challenge to provide alternatives to gas-pow
ered vehicles,” Bienenfeld says. “However,
the social and environmental benefits are
great, like reduced dependence on imported
oil and reduced emissions.”
Bienefeld helped Honda launch a battery
electric car in California in 1997. Although
the car was very advanced, battery electric
cars are not new. It turns out that electricity is
a very old method of powering cars. At first,
electric cars outsold aU others. Other fuels
had their drawbacks: steam was dangerous,
and gas engines were smelly and noisy. How
ever, when demand grew for travel between
cities, the battery-powered electric cars fell
announce the birth of our daughter,
Anna Lucy Gavrich on October 18,
2000. You can see pictures of Lucy
on her web site, www.annalucy.com.
We recently moved to a Craftsman
bungalow in Alameda, Calif., which
is basically Mayberry with good
sushi. I’m working from home as a
self-employed fee-only financial
planner. You can e-mail me at
sue_gavTich@moneywell.com.”
into disfavor with the
public, who instead
bought gas-powered
cars that could travel
farther. Now, the
almost perfect infrastructure-with a gas
station every corner
makes introduction of
alternative-fuel cars
difficult. The supply of
natural gas is in the
hundreds of years, says
Bienenfeld, and Honda has developed a car
that runs on natural gas. But there are only
about 1,500 places around the country to
refuel such a car, as opposed to 200,000
places that sell gasoline. Bienenfeld is work
ing with another company to develop a home
refueling appliance for natural gas vehicles.
“The answer to the marketing challenge is
in education,” says Bienenfeld. “We have to
look at innovative advertising, reach key opin
ion makers. A variety of people have to throw
their support behind these new cars-the
automobile magazines, the environmental
groups, even government.”
Bienenfeld is also busy with the next step
in the consideration of the future: product
planning for Honda-thinking about what the
next generation of Accords, Civics, and
Odysseys will be like. He’s been pondering
the difference between speculating and plan
ning. “I read Paul Erlich’s The Population
Bomb while I was in junior high,” he says. “I
was really influenced by that book-what he
thought was going to happen. Yet every pre
diction he made was wrong...In 20 years we’ll
still be planning for the future-after all, we
never really get there. The principles will be
the same: you need to have a really clear
understanding of your goals and mission.”
John Wright (A) has published
short stories in Isaac Asimov’s SF
magazine and in Year’s Best Annual
(David Hartwell, ed.) His two
novels, Golden Age (sf) andLa.st
Guardian ofEverness (fantasy), are
due for publication in aooi and
2,002, by Tor Books. John is a retired
attorney, newspaperman and news
paper editor. He presently lives in
fairy-tale-like happiness with his
{The College .St John’s College ■ Summer 2001 }
wife, the authoress L. JAGI LAMP
LIGHTER (A85), and their two chil
dren, Orville and Wilbur Wright.
1985
Sarah (A) and Dan Knight (A84)
write that they had a wonderful time
at Homecoming weekend. “It was
great to see everyone and we were
�{AlumniNotes}
3^
surprised by how relaxed and ‘at
home’ we felt on campus.”
Robert George (A) is going to be a
regular on a new talking head show
on CNN, airing Saturdays at 8:30
p.m. The show, called “Take 5,” pre
miered on March 17.
Karen Bell-Andrews (A85, also
AGI93) is married to Ben Andrews, a
singer very popular in England and
currently on tour there. She is an athome mom working on her PhD.
With their three children, Amelia,
Eliza, and Ian, they live on a historic
old farm in Fairplay, Md. (near
Hagerstown). Karen raises cows and
chickens as well as bees.
1986
Debbie Jones Humphries (SF) is
stiU teaching part-time. She loves
working with graduate students. She
has also started homeschooling her
two sons, Ranier (5) and CameronJack (3), “and that’s keeping me
busy,” she says.
Julie (Spencer) Moser (SF) sends
this request: “Would anyone who has
experience teaching in a Paideia
high school please contact me? I’m
helping found a new high school and
I need your advice. My e-mail is
rainyday@taosnet.com.”
1987
is so much fun and we love him so
much we can hardly stand it,” says
Claudia. “I would love to hear from
classmates-it seems like just yester
day we were at Homecoming for our
loth reunion. Please e-mail me
stackc@uncwil.edu.”
1989
Pamela Jeffcoat (SF) writes: “I
finally got a job as a Russian inter
preter, and now I’m starting to learn
Turkish. I play ping pong with a lot
of Chinese guys but so far, I haven’t
learned a word of Chinese.”
Koko Ives (A) writes that she now
has two beautiful daughters, Zoe and
Cate.
1988
Alden Joseph Stack was born to
Claudia Probst Stack (A’88) and
Joe Stack on October 29, 2000. “He
Roberta Faux (A91) live
in downtown Baltimore where they are restoring a historic
building that functioned as a pharmacy with living quarters
above. Roberta received her MA in classics in 1999. After
receiving his doctorate in composition from Boston Universi
ty and teaching for several years in Colorado, Travis now
operates a music production studio. The Apothecary, with Frank A
(Ago). “We love doing this stuff and are always looking to work with
on interesting film and video projects. Music from some of our recent proj
ects can be heard at our web site www.mp3.com/TheAp0thecary.”
T
Marion Gunn Jenkins (SFGI) is still
in retirement, living in New Haven
next door to her only grandchild and
her daughter and son-in-law. “I’m
active observing local and regional
government for the League of
Women Voters of New Haven. I hope
to take up my study of Greek which
gives me great pleasure despite the
obstacle of age.”
“Young Adam Pittman was born
April ig, 2000,” writes Clinton
Pittman (SF). “Thought about a
Homerian name, but then decided
against such a radical step-not
everyone gets all those Odyssey ref
erences in Oh Brother, Where Art
Thour
“I am leaving my job as an attorney
in the Antitrust Division of the U.S.
Department of Justice to take up a
one-year Visiting Assistant Professor
post at the Northwestern University
Law School, where I received my JD
in 1994,” writes JOE MILLER (A). “I
will be teaching intellectual property
law courses. My residence at the Law
School starts June 4, 2001. One
thing will not change-namely, my
permanent e-mail address at
findjoemiller@hotmail.com.”
Amanda Dalton (A) played the
parts of Delightful and Nadine in a
Colonial Players production of Dear
ly Departed this spring in Annapolis.
A professional clown who graduated
from Ringling Brothers’ Clown Col
lege, she has appeared in summer
theater productions for the past sev
eral years.
Charlotte Glover (SF) reports:
“I’m living with my husband David
Kiffer in beautiful, wet Ketchikan,
Ala., and we are enjoying our first
child, a darling boy named Liam
Benjamin Kiffer, born December ii,
2,000. So far, his favorite ‘great
book’ is Bugs in Spaced
ravis Hardaway (A91) and his wife
our four-year-old daughter, Imogen,
loves her Montessori pre-school.
Hope all is well with the many
friends I’ve lost touch with.”
Margaret (Meg) Lewis (A) is work
ing at the Academy of Natural Sci
ences in Philadelphia as a Ubrary
specialist. She invites alums and stu
dents to visit.
The MP3 Scene
1990
Margo Maganias Thomas (A)
writes: “What a difference 12 years
makes! My husband Bill and I are
still living in Arlington, Va., and
appreciate its village/urban charac
ter. We’re planning on renovating
and expanding our Cape Cod which
over the past four years has become
too small for our family. Our oldest.
August, is enjoying kindergarten and
GenevaMacDonand Pulgham (SF)
co-authored a book with her sister; it
was published in igg? by Texas A&M
Press- Women Pioneers in Texas
Medicine.
Fritz Hinrichs (A) writes; “I am
very pleased to announce two great
gifts of God to me. On March 25,1
had the privilege of marrying
Christy Hass of Rocklin, Calif. On
January 4, we were blessed with the
birth of a beautiful girl-Annabelle
Faith Hinrichs. With great grief, but
also trust in God’s loving provi
dence, I must also relay that after let
ting forth a short, beautiful cry, she
mysteriously passed into the land of
the living (Job 1:21). We would love
to hear from you all-contact us
through our web site, www.gbt.org.”
Sundance Metelsky (AGI) and Tom
Oehser, her partner of nine years,
were married on May 7 in Luray Cav
erns. More than go people attended,
including their children, Bela Wolf
gang Zoltan Seaton Williams Metel
sky Oehser (son, age 5 ) and Zina
Xena Metelsky Oehser (daughter,
age 14 months). Johnnies in atten
dance included Johnny Metelsky
(Ag4) and Lydia Rolita Metelsky
(Ag6) and honorary Johnnies, John
Metelslcy and Ethan Billotte. Also on
hand was a film crew from the cable
TV show, “A Wedding Story.” The
episode will air sometime in Septem
{The College. St. John’s College ■ Summer 2001 }
ber or October on The Learning
Channel. Sundance says, “The wed
ding was a unique celebration, fea
turing the casting of the circle and
calling of spirits, a hearty group
singing of‘Yellow Submarine,’
humorous legal proceedings featur
ing Tom’s cousin, Tina Oehser, who
asperged the couple with water from
the sacred springs near the Oracle of
Delphi, Tom and Sundance being
wrapped in a blanket held up by four
friends (one doing the holding in
spirit) and time in total darkness in
the cave, a talking stick in which
each attendee had a chance to offer a
blessing, and closing with the Grate
ful Dead song ‘Ripple.’ If you want to
know when the episode airs (or just
want to say hi!), please e-mail me at
sundance@toms.net.”
1991
Nate Downey (SF) is helping to
organize the tenth reunion in Santa
Fe this summer and would like to
gather e-mail addresses for any and
all classmates. E-mail him at
nate@sfpermaculture.com with
“Hegel rocks! ” in the subject line.
Elliott Tullock (SF) writes: “In
December I will complete training at
the Texas Maritime Academy and
receive a third mate unlimited ton
nage any oceans license. Upon
receiving my license I will sail on a
general cargo steamship trading
from the U.S. Gulf to Europe and
Africa. Wife Diana and son James (3)
are doing well. We expect to return
to Belize next year and take up
ranching and tropical fruit cultiva
tion when 1 am home from sea.”
Karen Andrews (SF) recently par
ticipated in a group theme show fea
turing “functional/dysfunctional”
art at the Flux Gallery in Denver.
�{AlUMNiPrOFILE}
33
Democracy Brokering
IN THE Balkans
BY Roberta Gable, A78
hat moment after you graduate
election systems (our
forte!) and party-building
from law school (in the case of
Tia Pausic, A86, Harvard Law
to commercial legal
School) can be one of the most
reform and economicfree moments in life. The rig
related issues like pension
reform, the creation of
ors of the academic world are
small and medium enterprise, and the devel
behind you, and the long grind towards
opment
of trade unions. The CDP opened the
becoming a partner somewhere looms
ahead;
Zagreb office in May of ’92, and Pausic was
but in the meantime, Sisyphus can take a
the first executive director.
couple of weeks off and relax. Pausic cele
She had been back to Croatia three times
brated her freedom by going with her father
on CDP business but now we’re talking
on the Croatian Fraternal Union of Pitts
immersion. There was the language to be
burgh’s more or less annual trip to Croatia
reckoned with (“I tried not to be afraid of
(her father is Croatian and her mother is
speaking”), the lack of consumer goods (“I
Romanian). They had a swell i8-day trip,
including a weeklong cruise on the Adriatic.
developed a scavenger mentality that has
been hard to shake! ”), the toilet paper (“like
Then, back to reality, and Pausic moved to
tree bark”), and her living situation. She had
D. C., where she had a typical entry-level j ob
a small one-bedroom apartment, which was
as an associate at a fairly large law firm. They
did government contract work and also some
not only her home, but also the CDP office
and the crash pad for any CDP visitors.
international and immigration work, which
Pausic set to work developing projects to
was Pausic’s area of interest.
In the meantime, as a result of the Croat
submit to funding agencies, both public and
private. For example, the Children’s Hospital
ian vacation, she became involved with the
in Zagreb was in need of a mobile medical
Croatian American community in D.C.
clinic, since they were basically the only pedi
Young professionals, mostly children of
atric hospital in the country and also tasked
recent emigres, would get together and talk
with health care for refugee children
politics: it was 1989, and change, with the
throughout Croatia. She found funding with
prospect of multi-party elections in Hungary,
the Soros Foundation to purchase and equip
Poland, and Czechoslovakia, was sweeping
the vehicle, and in 1993 they were then able
Europe. And then they did more than talk:
to help children in remote places. (By 1999
they started to host visits from democratic
the local hospitals were enough recovered
political leaders in Croatia, hoping to get
U.S. governmental support for free elections
that the vehicle was then donated to the mili
tary unit in charge of mine-clearing opera
there.
tions.)
Finally they decided they needed to form a
By 1994 she had to face reality once again.
non-profit organization to support this work,
She was making next to nothing working for
and the Croatian Democracy Project (CDP)
a non-profit, and had deferred her law
was born. As the situation in Croatia heated
school loans for two years, but now had to
up, Pausic’s interest in government contract
think about shouldering that burden again.
work cooled down-her pro bono work for the
“I left in December ’93, thinking I was
CDP became her focus.
never going back. I cried on the plane to
In 1991 war broke out in Croatia. The CDP
Frankfurt.”
(and Pausic, the president thereof) realized
Back in Washington, she camped on her
that the only way they would succeed in
sister’s couch and continued to help out at
bringing democracy-building resources from
the U.S. to Croatia would be to open an office
the CDP while she looked for a job. She
talked to the president of America’s Develop
in Zagreb. And what exactly are “democracy
ment Foundation (ADF) about possibly get
building resources,” do you ask? In response
ting involved with their projects. In March
to the democratic changes in eastern Europe
in the eighties, an industry of support grew
1994 he called her and told her that USAID
had issued an RFA (Request for Applications)
up in the United States, for everything from
T
{ T H E C o L L E G E . St. John’s College ■ Summernoot }
Tia Pausic (bottom row, far left) poses with
Croatian friends and co-workers.
for a human rights project in Croatia, and
asked her if she would help write it and be the
Chief of Party (basically, be the person who
would be in charge if the grant were given).
She would, she did, and ADF, a non-profit in
Alexandria, Virginia, was awarded the con
tract for a project to strengthen the abilities
of the human rights organizations in Croatia.
So, having left Croatia expecting never to
return, she moved back in October ’94 to
provide training, give technical assistance,
and bring grant funding to the Croatian
groups. This time her set-up in Zagreb was a
lot different. The grant was for $2.5 million
over a three-year period. She had her own
apartment, and in her office she had actual
equipment, actual staff, and an actual salary;
and she had become fluent in Croatian, fluent
enough even to be a Croatian/English inter
preter. She designed a grant program, but
when they were about to give their first
grants in ’95 the government initiated a mili
tary operation to seize occupied territory
from the Serbs, and Zagreb was bombed,
making for a certain amount of, shall we say,
uncertainty in her life. Nonetheless, they
stayed, the occupied territory was liberated,
and life got back to more or less normal.
A pleasant influx of additional funding
turned the three-year $2.5 million project
into a six-year, $10 miUion project, which
from mid-1996 focussed on displaced persons
and repatriation issues. The pursuit of happi
ness continues abroad for Pausic. She left this
June for her next posting with ADF-Sarajevo,
Bosnia-Herzegovina, where she will be
directing a $4 million, three-year project cre
ated to provide training, technical assistance,
and grants to local nonprofits to encourage
more civic participation, advocacy, public
private partnerships, and coalition-building
among the local groups.
�{AlumniNotes}
34
Christopher Johnson (SF) says: “I
Dianne Cowan (A) is still in Boston,
recently completed my PhD in com
parative literature at New York Uni
versity. My dissertation, ‘Hyper
boles: Exemplary Excess in Early
Modern English and Spanish Poetry,
and its Origins in Classical Epic and
Rhetoric,’ won the Outstanding Dis
sertation Prize in the Humanities for
2000-01 at NYU. Currently, I am
also teaching at New York University
and City College, but this summer
I’m off to a friend’s organic farm in
the Pacific Northwest to clear the
head and get the hands dirty.”
still working for the same software
company. Her e-mail address is diannecowan@mindspring.com.
1992
Kate (Griehs) Sullivan (SF) and
her husband John Sullivan (SF94)
live in Austin, Tex., where John is a
project manager for 7-24 Solutions
and Kate homeschools their four
children, Madeline (7), Jack (5), Lily
(3), and Claire (i). John’s e-mail is
Jsullivan@724.com and Kate’s is
Kate@willdev.com.
Boaz Roth (AGI) recounts his
recent life: 1999, marriage; 2000,
baby #1; 2001, home ownership. He
asks: “Will I ever get a chance to
read Proust again?”
“The charter school I’ve been work
ing on for the last two and a half
years finally got chartered, so we’ll
be opening in September,” says
Taeko Onishi (SF). “It will be a
multi-aged, project-based K-5 school
targeting low income families in
Troy, N.Y. It is an outgrowth of a
community learning space for K-12
in a local public housing neighbor
hood where I work now. I’d love to
hear from any and all Johnnies.
Come for a visit or just get in touch,
ktaeko@hotmail.com.”
Amy Elizabeth Parton (A) says, ‘I
am working as a clinical research
monitor in the pharmaceutical
industry. Still enjoying life in Austin,
Tex., and would love to hear from old
friends. The rest of the world knows
me by my middle name so I can
reached by e-mail at elizabeth.parton@austin.ppdi.com.”
Elyette (Block) Kirby (SF)
reports: “I’m having a baby in May
and soon after will be transferring
from The Netherlands to the UK
with my job at Amazon.co.uk. I enjoy
working at Amazon where every
interview situation seems to fit in a
discussion on who one’s favorite
authors are. I am what’s called a
‘communications specialist,’ which
means I write a lot. My husband I
hope to be settled in the London
area by June and would love to hear
from anyone close by-or far away!
My e-mail is elyette@hotmail.com.”
Trish Dougherty (A) reports that
Sean Donald Dougherty was born
5/5/01; he joins his big brother
Owen and his mom and dad in
Orwell, Vermont.
Simon Bone (SF) sent in a photo of
himself in front of Kant’s grave in
Kaliningrad. “He is still dead,”
notes Simon.
J. Elizabeth Huebert (SF) received
her MD from University of Nebraska
Medical Center, May 5, 2001. She
will do a one-year internship at
Broadlawns Hospital in Des Moines,
Iowa, and then return to Omaha for
three years of specialty training in
anesthesia.
Alec Berlin (SF) released an album
of original jazz in October 2000,
“Crossing Paths.” It is available at
www.cdbaby.com/alecberlin. Since
then he’s been composing a lot and
working in the new media world, all
the while freelancing in bands
around New York City.
1993
Jennifer Council Jones (A) moved
to Newport Beach, Calif., where she
is opening an office for an ad agency
and having a great time learning to
surf.
Nereos Gunther (A) writes, “I am
completing my period of indenture
in the City of Baltimore and plan to
begin an entertainment web site and
educational association for vivisectionists.”
Valerie Duff (SF) is currently
teaching at Boston University and at
Harvard Extension. She plans to
take a year off to attend Trinity Col
lege in Dublin, Ireland. While there,
she will be in an MA program in cre
ative writing. Valerie received an MA
in creative writing from Boston Uni
versity, and has since published
extensively in Agni, Salamander,
Verse, and other literary magazines.
She was managing editor of Agni
(the literary magazine of Boston
University ) for two years.
Aaron Mason (SF) works as a mar
keting writer/editor in the NYC
offices of STV Inc., as an architectur
al consultant; most projects involve
public transportation planning.
Aaron and Nick Gray (SF97) were
both involved with a theatrical per
formance in New York City in
March-Mercury Retrograde: An
Evening of 4 Original Short Plays @
the Sanford Meisner Theatre. Aaron
wrote a lo-minute play called “Mr.
Oedipus,” which is, he says, “artful
ly directed by goddess-on-wheels,
Elysa Marden. Appearing with the
hilarious Laura Agudelo (roles of
Hillary and God), I play the title role
of a man trapped between two
conflicting identities. One personali
ty is an angry white rap star (sound
familiar?), and the other side of him
remains a reclusive author of chil
dren’s books. It is VERY loosely
based on the original Oedipus.” In
another lo-minute play, “Bye Bye
Love” by Milton Johnson, Aaron
plays the proud owner of a trailer
home, a Trans-Am, and a hidden
past... “‘Bye Bye Love’ is directed
with zen-like poise by the
unflappable Beth Ouradnik. And
Nicholas Gray has written a 20minute play, ‘Coat Room,’ directed
by the wise and wooly Sean McGlynn.
‘Coat Room’ is a romantic farce that
takes place (where else!) in the bed
room/coat room of a party. Mr. Gray
plays a lovelorn twentysomething lad
in the midst of a messy separation.”
Anna Vaserstein (A) writes that she
and Warren Ellison announce the
birth of Daniel Vaserstein Ellison on
May 6, 2001 at their house in Jeri
cho, Vt.
Jenna Palmer (SF) and James
Michel (SF92) send word that Jenna
received her MA in literature at San
Francisco State University with a
thesis on Jane Eyre, as well as
certificates in the teaching of com
position and reading. She is current
ly teaching at San Francisco State
and the College of San Mateo and
hoping to hook a permanent posi
tion. Jim’s law practice is in its fifth
year and has recently moved to
downtown San Francisco. You can
{The College. St John’s College ■ Summer aooi }
contact them at jpalmer@sfsu.edu
and jamich@pacbell.net.
Jeff Natterman (AGI) is currently
involved with the Johns Hopkins
Urban Health Council and Baltimore
City Schools. He says, “I could spend
an hour at least describing the
deplorable conditions of the elemen
tary schools in the city. In particular,
their books are in some cases 20
years old (history books with
Richard Nixon as the current presi
dent); their libraries in disrepair and
mostly empty of books of any kind.
The city pleads for more funding
from the state; the state attempts to
meets the needs, but fails...badly! I
have developed a program called
‘Great Books for Great Kids: The
Tench Tilghman Project.’ This pro
gram targets just one elementary
school in Baltimore City. I am hop
ing to solicit either funding or ele
mentary school age resource books
for the school by August 2001.1
believe these children will never rise
above a ‘mediocre at best’ environ
ment without the best possible
resources for learning starting with
books. Please contact me if you’d
like to help out;
jnatterm@jhmi.edu.”
Special greetings to the class of ’93
from Amalia Uribe (SF). She writes,
“I have two pieces of good news to
report. First: Graduated with honors
from Massage Therapy school in
October 2000. Since November I
have been a full time certified Mas
sage Therapist, and I absolutely love
my new career. I work at a chiroprac
tic clinic and at a small day spa, both
in the East Bay of California. Sec
ond; On July 14, 2000,1 eloped!!! I
am now happily married. My hus
band is Mustapha Moutri; he is 28, a
2nd degree black belt in Tae Kwon
Do, and is from Rabat, Morocco. We
are quite happy big smile, and NO,
there are no plans for little ones just
yet. I would love to hear from any of
you, but especially from my class
mates: My e-mail is
amaliacmt@yahoo.com (this is a
new address). If any of you have tried
to get in touch at the old address, I
have not had that for a few months,
so please try again. I would also very
much like to hear from: Jonathan
Bricke Rowan (SF96) Will and
Amy Glusman (A93)
Julie (Girone) Martin (A) and her
husband Eric announce the birth of
their second daughter, Josephine
�35
{Alumni Notes}
April. She was born on April 24.
Says Julie, “I’ve been a housewife
since Charlotte, our first child, was
born three and a half years ago. At
the moment, we’re still in
Somerville, N.J., although we’re
moving to a house on an organic
farm in Hopewell, New Jersey, this
fall, where my husband is the care
taker. He’s still the executive chef
and manager of a fine-dining
restaurant in Hamilton as well. Any
Johnnies interested in either line of
work (especially the farming
apprentices are always wanted),
give a call.”
Matthew Wright (A) writes:
“Hello to everyone. Michelle, Anne,
Emily, John and I are still living in
Philly. We are homeschooling and
living in a small intentional commu
nity we helped get started last
August. I would love to hear from
people at matthew.wright@wholefoods.com.”
1994
Sarah Liversidge (A) and Mike
Afflerbach (A) were married Sept
16, 2000 in the Great Hall. Their
reception was held on the back lawn
of the house of President Chris Nel
son and Joyce Olin. Many Johnnies
were in attendance. The Afflerbachs
are still living in New Bern, N.C. and
are enjoying racing sailboats. Sarah
will be taking her architectural
exams this year and Mike is loving
the radio biz.
Peter Bezanson (SF) has been
appointed tutor at the College of the
Humanities and Sciences in
Phoenix, Arizona. The College of
the Humanities and Sciences is a
great books distance learning col
lege established in 1997; it offers
undergraduate and graduate educa
tion in the humanities with concen
trations in imaginative literature,
natural science, philosophy and reli
gion, and social science.
Kenneth Wolfe (SF) is spending
this year as a visiting assistant pro
fessor at Reed College. He received
his PhD in classics from UC Berkeley
in May 2000.
Paul Barker (AGI) will be moving
back to Maryland from Ohio. He has
been appointed principal of John
Carroll School in Bel Air.
Antique Information Systems
Tracy Whitcomb (A) says she is still
enjoying life in Burlington, Vt.
Michael ViLLACRUsis (AGI) writes
n article about Randolph Stakk (A98) called “Under
that he and his wife Jennifer had
ground Mail Road” appeared on the front page of the New
their first child on February 15,
York Times metro section in May. Stark, identified in the
Emily Rose.
article as an entrepreneur, is interested in the under
ground pneumatic tubes installed in the 1890s to carry
Sarah (Van Deusen) Flynn (A) says:
mail throughout the city. He wants to use them to hold
“We are enjoying Guam. It’s a very
fiber optic cable which would connect with telecommunications nice
systems
place for young families. Ethan
that already exist. The pneumatic system was state-of-the-art in several
is stationed here at the Naval Hospi
East Coast cities until about rgrS, Stark discovered, until it was phased out
tal until September 2002.”
by a quicker and less expensive form of transport that could also carry a
greater volume-motor wagons. It was not until 1953 that the tube system
Thea Agnew (SF) is still living in
was closed. Stark is quoted in the article as saying it would cost “about
Alaska. She’s working for herself
$roo million a mile to repUcate the conduits today...making even five miles
writing grants, particularly working
of them a worthwhile resource.” He’s currently searching for the original
with rural development in Alaska
blueprints for the system.
Native communities. She completed
an MA in history in May 2000 focus
ing on 19th century encounters
and coordinate the distribution of
Patricia Greer (AGI) wiU be a tutor
between Yupik Eskimos and Russian
marketing materials for the various
at the Santa Fe campus next year.
Orthodox and American Protestant
FtvS products. She will be responsi
missionaries.
ble for sales materials and press kits
Dan Farley and Elizabeth Rhodes
on projects as diverse as the upcom
Farley (both A) write: “In addition
ing local Fox World Productions ver
to our daughter, Hannah (now three
sions of “Temptation Island” and
years old), we have a son, Dylan,
the movie based on popular chil
born May rq, 2000 (Mother’s
“John and I are busy planning our
dren’s author R.L. Stine’s story enti
Day!).”
house-to be built this summer on
tled “When Good Ghouls Go Bad.”
our II acres of slightly wet paradise
A
1996
1995
Emily Murphy (A) was one of four
Pennsylvania graduate students to
receive the Outstanding Graduate
Student award from the Pennsylva
nia Association of Graduate Schools.
Of course, she says, “around here
it’s ‘for the Glory of Old State,’ but I
think that a lot of the credit goes to
St. John’s as well.”
Susan Talkington (SFGI) is cur
rently working as a software engi
neer for the Seattle offices of Mer
rill Lynch. She married Ian
MacGillivray of Santa Fe in March
2oor, and the two are currently
residing in Eldorado.
Rontt Koren (SFGI) has been pro
moted to Manager, Marketing, Fox
Television Studios. Ms. Koren will
continue to develop marketing
opportunities for Fox Television Stu
dios, including top series suppliers
Regency Television and the Greenblatt-JanoUari Studio, alternative
studio Fox TV Studios Productions,
international production specialist
Fox World Productions, Fox Televi
sion Pictures and non-fiction pro
duction companies Foxstar and Nat
ural History New Zealand. Ms.
Koren will continue to help design
icksT
in central Maine,” writes Allison
Eddyblouin (SF). “The girls (Mary
Catherine and Thalia) are great
homeschooling is a blast. It was
great to have Jason Voigt come visit.
He will be doing the same boat build
ing program that John did four years
ago! Any other Johnnies want to
come visit? If so, drop us a line.”
Mara Giles (SF) writes, “Just read
Geoff Marslett (SF) currently has
the Spring 2oor The College and
enjoyed reading about a distant and
not-so-distant past of my own. I rem
inisced about my years on both the
Santa Fe and Annapolis campuses. I
am enjoying my life very much with
my non-Johnnie husband, a biology
professor, and our wonderful daugh
ter in Nebraska. I work for a comput
er software company located in New
Mexico and feel quite lucky to be
able to telecommute. I still enjoy the
academic life, can’t seem to get away
from it (married into it), and am pur
suing more (yea!) degrees in litera
ture and philosophy with hopes
of...??? Well, let’s just say it’ll ruin
the surprise if I tell you now. Best of
luck and regards to each of you.”
an animated short film out called
“Monkey vs. Robot.” For more infor
mation, check out his website at
WWW. swervepictures. com.
Rosemary Ingham (AGI) writes: “I
retired from teaching at Mary Wash
ington College in May and am spend
ing the summer at the Utah Shake
spearean Festival where I will be
designing costumes for Two Gentle
men of Verona and The Fantask-
Nada Khader (SFEC) is teaching
French and private tutoring students
at the United National International
School in Manhattan. She’s also a
Girl Scout troop leader.
{The College. St. John ’5 College ■ Summer 2001 }
Jon Stephen Pearson (SF) is com
pleting requirements for an MFA
degree in comparative literature
while teaching literature under an
assistantship at the University of
Georgia in Athens.
Amy (Norman) Morgan (A)
reports: “I was married in June
1998. During the ‘99-00 school year
my husband (Bill) and I taught Eng
lish and methodology to secondary
school English teachers in
Ovorkhangai, Mongolia. Now, we
live in the Cincinnati area where
Bill teaches elementary school
music and I teach English to foreign
business people and their spouses. I
am applying to study applied lin
guistics at Indiana University or
�{AlumniProfile}
Cultural Jam Session
Anthropologist Catherine Allen explores the culture ofthe Andes.
BY SUS3AN
Borden, A87
cattered
throughout
Catherine
Allen’s
(A6g) office
are Andean
textiles-woven pieces in
reds, black, and white
with patterns marching
down one side and up
the other. Allen nods
towards one, a woman’s
shawl, and points out
the seam down its cen
ter. “You’d think that
they’ve just taken two
complete pieces and
sewn them together, but
it’s really a single pat
tern,” she says. “The
two halves are part of
the design. In the
Andes, everything needs
a companion.”
Allen’s knowledge of
Andean culture goes
well beyond textiles. An
anthropologist, she did
her fieldwork with the
Quechua-speaking people in the Peruvian
region of Cuzco, where she lived and partici
pated in community life by harvesting and
planting potatoes, cooking, learning to spin,
and helping to herd animals. She has written
many articles, a book, and a play that draw
on her fieldwork in the Andes. And she has
just won a Guggenheim Fellowship to write a
book examining Andean expressive media
(such as storytelling and weaving) and write
another play.
Allen didn’t start out as an anthropologist.
She was originally interested in classical
archaeology, an interest that led her first to
St. John’s and then to the University of Illi
nois to study archaeology at the graduate
level. It wasn’t long, however, before Allen
found herself frustrated with the narrow
focus of archaeology. “I was interested in
questions of meaning, questions that needed
Catherine Allen (second from left)
SWITCHED from IMAGINARY TO REAL FRIENDS
THROUGH THE STUDY OF QEROS, ARTIFACTS FROM
THE
Andes.
a living context” she says, “but all the peo
ple I was studying were dead.”
In pursuit of her master’s degree in the
iconography of ceramics from the southern
coast of Peru, Allen spent hours staring at
museum collections and studying pictures of
ceramics. She learned plenty about the
ceramics themselves, but little about what
they were used for. “It was like having the
grammar of a language, but not knowing
what any of the words mean,” she says.
When she considered questions of meaning,
she had only her own mind to consult: “I felt
like I was making up my imaginary friends.”
Allen moved from imaginary to real
friends during her dissertation research.
{ The C o llege-St. John’s College • Summer 2001 }
which began with the
study of lacquered
wooden cups called
qeros. Although the
first part of her project
brought her back to
museum work, the sec
ond part sent her into
the world of people,
meaning, and anthro
pology.
Qeros date back to
the 17th century, but
they are still used for
drinking rituals in
some communities in
the Peruvian highlands.
Allen decided to study
one of these communi
ties, Sonqu, hoping
that current drinking
rituals would shed light
on past qero uses and
answer the questions of
meaning she had been
formulating. Allen went
to Sonqu and immersed
herself in the communi
ty’s way of life. While
her academic interests centered on the per
formative aspects of life (storytelling, cere
monies, and rituals), Allen found herself
focusing on the community’s everyday
modes of interaction.
“What I studied was a kind of etiquette,
really,” she says. “Ritual is an intensified
expression of everyday courtesies.” Among
the people of Sonqu, the basic vehicle of rit
ual is the coca leaf, always chewed in a cere
monial context. And so her dissertation
moved away from the qeros that had brought
her to Sonqu. “I ended up writing on coca
chewing,” she says. “Coca is the bare bones
of their ritual life.”
Allen completed her dissertation. Coca,
Chicha, and Trago: Private and Communal
Rituals in a Quechua Community, in 1978.
Ten years later she published The Hold Life
Has: Coca and Cultural Identity in an
�{AlumniProfile}
37
''When Ifirst studied culture, I thought
ofit more as a symphony: each person
has apart to play and the culture gives
you a score. But the class made me realize
there isn i any score; culture is something
that is always emerging ''
Andean Community,
the book that devel
oped out of her disser
tation. It is still in
print today, read pri
marily by anthropology
students; a second edi
tion is in the works.
And as her book is a
perennial at universi
ties, Allen is now a
perennial at George
Washington University in Washington, D.C.
Hired 20 years ago as a newly-minted PhD,
she is surprised to find herself still teaching
there. “I never expected to stay,” she says. “I
thought I would go on to a small experimen
tal college, but I began teaching in an era
when experimental programs were folding
or contracting.”
Allen says her longevity at George Wash
ington is primarily due to the congenial
atmosphere of the anthropology department
and the university’s Division of Experimen
tal Programs. Through this division, Allen
has collaborated with colleagues from the
school’s religion, art, literature, history, and
political science departments. In 1993 and
1994 she wrote a play. Condor Qatay, with a
colleague in the theater department and the
two teach a class together: “Anthropology in
Performance.”
She describes a typical exercise from one
of their classes: “Rather than explore a situ
ation intellectually and analytically, we do
an improvisation. We set up situations like
waking up or harvesting, assign participants
kinship and household roles, and have them
play out these situations without speaking
English.” It is through negotiating these
improvisational roles that students gain
insight into the rituals of another culture.
But Allen says that it’s not just the students
who benefit from the exercises: “I’ve
learned a lot from teaching and watching
the improvs,” she says. “I get flashes,
moments that show me how cultural prac-
Catherine Allen
tices grow out of the dynamics of the inter
action of a group.
“When I first studied culture, I thought of
it more as a symphony: each person has a
part to play and the culture gives you a score.
But the class made me realize there isn’t any
score; culture is something that is always
emerging,” she says. “Culture is more like
jazz. You have some basic sequences in your
head and general expectations of other peo
ple, but the jam session never comes out the
same way twice.”
Starting this Septem
ber, Allen will have the
chance to further her
studies of the cultural
jam session. As the recip
ient of a Guggenheim fel
lowship, she’ll have a year
off to work on two proj
ects. The first is a book
on Andean aesthetic
strategies. It will include
examinations of story
telling, weaving, and ceramics. “It draws on
my original interests,” Allen says. “I’m finally
going to include a chapter on qeros."
The other project is a second play. “My
first play. Condor Qatay, means the Condor
Son-in-Law. The condor carries off the Indi
an maiden and becomes the son-in-law,”
Allen explains. “This play is the converse:
the star woman who marries an Indian man.”
Like the textiles in her office, the two stories
form a single design: they are reflections of
each other, companions.
Catherine Allen’s FAVORITE BOOKS IN
CULTURAL ANTHROPOLOGY
Argonauts ofthe Western Pacific by Bronislaw Malinowski
The Nuer by E. E. Evans-Pritchard
Tristes Tropique (or The Savage Mind) by Claude Levi-Strauss
The Ritual Process by Victor Turner
The Interpretation of Cultures by Clifford Geertz
Purity and Danger by Mary Douglas
Pigsfor the Ancestors by Roy Rappaport
The Spoken Word and the Work ofInterpretation
by Dennis Tedlock
Unnatural Emotions by Catherine Lutz
Andean Lives by Valderrama, Escalante, Gelles, and Martinez
{The College- St. John’s College ■ Summer 2001 }
�{AlumniNotes}
38
TESOL at the University of Cincin
nati in the fall.”
“I am completing study for my mas
sage therapist certificate and plan to
eventually specialize in maternity
care and rape recovery treatment,”
writes Erin (Hearn) Furry (A).
She’s heen married to William C.
Furhy tV for a year. Erin has plans to
start an Alaska alumni chapter after
this summer. “If anyone is interested
in helping, I can be reached at celebrinthol@usa.net.”
Loreen McRea Keller (AGI)
writes that she and her husband
Greg are expecting their third child
in May-“maybe a third girl? We
can’t wait to find out! ”
Jennifer (Wamser) Deslongchamps (AGI) writes: “The
year after graduation, having just
returned from a year studying
medieval philosophy in Pisa, I met
my future husband in a laundromat
in Fairfield, Conn. Paul Deslongchamps and I were married in
January 1999 and this October we
were blessed by the birth of Thomas
Robert. While I’ve been taking this
year off. I’m currently ‘all but dis
sertation’ at Yale, where I’m work
ing on the notion of infinity in the
work of Meister Eckhard and
Nicholas of Cusa.”
Scott Field (SFGI) and his wife Jes
sica will celebrate their fifth anniver
sary this summer, and they will have
their son Henry (born September 33,
3000) along. “I’m still teaching fifth
grade, although I now have senior
elective psychology and a philosophy
course to teach as well,” says Scott.
“Finally, I’m putting all of that liber
al arts background into my perform
ances each weekend at ImprovBoston, the improvisational comedy
troupe I’ve been performing with for
over three years now.”
Erica Maria Ginsberg-Klennt
(SFGI) writes: “We sailed away from
Annapolis in 1997 and stayed in the
Bahamas for a year before crossing
Panama to French Polynesia. I’ve
been writing articles on technomodism (the use of technology to make
your location irrelevant) for French,
German and Italian magazines. Our
daughter Antonia Tahia was born in
Hawaii in August r999 and we are all
moving to the south of France this
summer with the ‘Pangaea Nui.’
Check out our web site, www.pangaea.to for more stories.”
1997
Ryan ViGUERlE (SF) writes: “Shortly
after graduating from some college
no one’s ever heard of, I moved out
to LA to try and make it as a writer.
Then, after floundering about for a
few years, I decided to go back to
school and am now studying at the
American Film Institute. A swell
place. Greetings maybe sent to
raoulduke@mediaone.net.”
Rebecca Michael reports that she
and Mike Gaffney (A95) are getting
married in Annapolis on June 39,
3003. They are living in Jack
sonville, N.C., where Mike is sta
tioned for the Marine Corps. Rebec
ca is finishing her master’s thesis.
Kit Linton (A) and Sonya Schiff
Linton (Aoo) were married last
September and are living in
Washington, D.C.
Romance novelist HiLLARY FIELDS
(SF97) had an article in Cosmopoli
tan (April 3001) called “The Tough
Girl Trap.” She offers advice to
“strong women” whose independ
ence is seen as a threat by men. She’s
the author of two books. The Maid
en ’s Revenge and Marrying Jezebel.
“I finally got my dream job-working
in the ‘new’ field of agri-tourism,”
writes Mary Beth Stevenson (AGI).
“I am the assistant manager of a site
in Grafton, Wise, called the Family
Farm. It is a 135-year-old, 46-acre
farmsite. I five on site, too, in a stone
farmhouse built in 1890. Any Wis
consin alumni should check it out.”
Postcard from Panama
Luke and Rachel Trares (both A)
have moved to Fort Worth, Tex.,
where Luke is attending Southwest
ern Baptist Theological Seminary in
the hope of becoming a church
planting missionary, probably some
where on this continent. “I am really
enjoying school,” he says. “Please
don’t hesitate to contact us with
questions about Christian ministry
(ltrares@yahoo.com).”
Genevieve Goodrow (A) writes:
“Hooray! I passed the bar exam and
started work, and while it’s nice to get
paid I’m beginning to fantasize about
school again. At least I have plenty of
time to read while commuting.”
Christopher English (SFGI) and
Diane Shires (SFGI98) are getting
married on December 37, 3001 on
Catalina Island, Calif., 170 years to
the day Darwin set sail on the Beagle.
1998
“Lest anyone is interested, I am cur
rently working as a flight instructor
for Swissair at the Flight Safety
International Academy in Vero
Beach, Fla.,” e-mails Ariel Szabo.
“Through the Swissair Aviation
ow I’ve been in Panama with the Peace Corps for
School (SRAS), I train pilots for both
almost four months. I spent three of these months
Swissair and Austrian Airlines. If
in training, in a suburb of a suburb of Panama City.
anyone is interested in information
Had a great host family (whom I visited and partied
concerning airline careers or flight
with for my birthday), and made good friends, both
training under the new European
Panamanian and American. There were 17 other
regulations (JAR/JAA), please feel
free to contact me at Thesmophopeople in training with me. The best of training? Los Carnavales”
they rivaled Brazil and definitely beat Mardi Gras in Newria@mac.com.
Orleans!
Recent graduate Valerie Whiting (Aoo) writes
aboni her assignment in the Peace Corps.
N
Now I live in La Raya de Santa Maria, in the province of Veraguas, almost in the middle of the country. It’s hot, dry, about 800
people. We have TV, water, and some houses have indoor toilets,
but the house I’m renting has a latrine. As an environmental edu
cation volunteer, I work in the school (K-6) doing projects and
teaching English (oh joy!). More so, this community needs organi
zation. I’m a hit because my town meeting actually had 100 people
(out of 800). Trying to end the family feuds, religious clashes
(Catholic vs. evangelical), and pohtical partisanship seems to be
my main goal.
I love Panama-the music’s loud and tacky, the food’s greasy (and
sometimes unrecognizable as to which animal it came from), we all
paint our toenails hot pink and wear tight jeans and tank tops. It’s
my kind of country.
I’m still feeling out the Peace Corps and its effectiveness here.
I’ve only got one month in site, so we’ll see how that goes. If any
one would like to reach me, my mailing address is: Entrega Gener
al, Santiago, Veraguas, Republica de Panama, or
valeriewhiting@yahoo.com.
David Braden (SFGI) teaches fifth
grade math at Casady School, a pri
vate Episcopal day school for grades
K through 13. He and his wife have
three children: Hannah (almost5
years old), John Henry (3), and Paul
(i), and they are expecting their
fourth in October.
Kristina Rodriguez (SF) writes:
“We had another baby boy in Sep
tember 3000. We named him
Matthew. I’m currently living in
Alamogordo, N.Mex., where my hus
band manages an Applebee’s. I’m
fortunate enough to stay at home
with my boys.” Greetings may be
sent to brianandtina@tularosa.net,
or 1454 Columbia Ave., Alamogor
do, NM 88310.
Nathan and Heather Greenslit
(both A) five in Worcester, Mass.
{The College. St. John's College ■ Summer aoot }
�39
{Alumni Notes}
Summa Adlerologica
dler goes with Prank the way
that Reality goes with Week
end.when
Andhis
thetalk
Adler
Prank
has
John’s was in 1937,
lasted
over
a longer pedigree
than Reali
two hours. The following
year, students
were
tysomething
Weekend. Mortimer
determined to do
about the over
Adler
’s first
lecture
at St.
whelming length. They
gathered
every
alarm
A
clock on campus, brought them to the bal
cony of the Great HaU (where lectures were
then held), and timed them to ring one hour
into the lecture. In Adler’s biography.
Philosopher at Large, he recounted his reac
tion to that first prank: “I stood my ground,
waited for the din to subside, and then, with a
smile and bow to acknowledge their ingenu
ity, completed the lecture. The students plot
ted another way to defeat me.”
Such a plot was executed the following year
when, again an hour into the talk, someone
cut the power to the Great HaU. “Utter darkness-and silence-reigned for a moment,”
wrote Adler. “I knew they expected me to rise
to the chaUenge, so I took matches out of my
pocket and continued the lecture by matchlight for the brief interval it took for a mem
ber of the faculty to restore the electricity.”
They were married in June 1998 and
have a beautiful daughter, Emily
Ruth, who is now a year old. Heather
taught middle school math and sci
ence until Emily was born. She now
tutors and sells Discovery toys. Nate
got his master’s degree in cognitive
science from Johns Hopkins last year
and is now in a doctoral program at
MIT called “The History and Social
Study of Science and Technology.”
They are expecting another baby
sometime in August.
Lorna Anderson (A) is engaged to
be married on May 25, 2002, to
Aaron Johnson, a classical pianist,
and they are both living and working
in Chicago. Lorna flirted briefly with
a career in journalism, was accepted
into Northwestern University’s
Medill School of Journalism, and
after two months decided she’d leave
the hot pursuit of the ephemeral up
to someone else. She is now working
part-time and writing poetry, which
she has come to admit was her voca
While the records
of decades of Adler
pranks have been lost
to the coUege, the
pubhc relations
office still maintains
a hefty file stuffed
with reports of lec
ture high jinks.
According to a
igUr clipping, prank
ing seniors scattered
throughout the audi
Adler — named Holy
ence interrupted the
lecture with their own Roman Emperor
DURING A PRANK —
conversation. They
COMPLETES HIS LEC
imphcated Adler in
TURE WITH CROWN IN
some of the world’s
PLACE.
most significant works
and deeds, including
Adler Grossing the Delaware, Adler the
Great, Adler’s Last Stand, The Critique of
Pure Adler, Thus Spake Adlerthustra, Summa
Adlerologica, Cain and Adler, E Pluribus
Adler, Huckleberry Adler, and Wealth of
Adlers.
The 1984 prank featured a “This Is Your
Life” segment where Adler’s parents were
interviewed. Mrs. Adler, played by Nancy
tion all along. She also volunteers for
a great books organization in the city
and has been leading poetry discus
sions at venues throughout Chicago.
She welcomes a visit from anyone
passing through.
Mease (A84), spoke of her son’s early
years: “Even as a baby he had this annoy
ing habit of going on and on, and we
sometimes thought he’d never stop! He
would latch onto some topic. I think it was
the forms first, and ethics later, and he
would just keep talking.”
In 1987, television journalist Bill Moy
ers filmed Adler’s lecture for a series on
the Gonstitution. WeU before the event,
then-president WiUiam Dyal (HA89)
assembled the ringleaders of the senior
class and swore them to a prank moratori
um. When junior class members heard of
their oath, they decided to take matters into
their own hands. They went to Maria’s Pizze
ria, bought a pepperoni pizza, and wrote in
large letters on the box, “From the Junior
Class.” Midway through the lecture Thomas
Burke (SF91), dressed as a delivery boy,
brought the pizza onstage to Adler. Adler
reached into his pocket, pulled out a ten, and
gave it to Burke, who propped up the box on
the front of the lectern to remind the audi
ence who had delivered the pizza-and the
prank.
Moyers declared it fine television. “A little
prank at St. John’s probably keeps the mind
awake,” he said.
Ruth Busko (SF) is currently living
in Columbia, Md., pursuing a mas
ter’s degree in acupuncture at the
Traditional Acupuncture Institute
there.
Tilman Jacobs (SF) has been living
1999
From Scott Larson: “I am writing
this note just to let you know some
recent events in my life. On March
18, 2000,1 married my long-term
girlfriend Jennifer (nee Rodgers)
(AGI99). On December 7th 2000,
we had a son, Oliver Scott Larson,
weighing 6 pounds 15 ounces. We are
both (my wife and I, not our son)
working at Thomas Jefferson School
in St. Louis.”
Kelly O’Malley (A) is pursuing a
master’s degree program in forestry
and ecosystem management at Duke
University’s School of the Environ
ment.
in Sweden since last August and
plans to stay for another year in
Europe.
2000
Andre Rodriguez (SFGI) is cur
rently teaching eighth grade Ameri
can history; he’s applying to law
school.
Stacy Allen (AGI) reports that
she had a son, John Brady Allen,
9 lbs., 5 oz., born one month after
graduation.
“I am now a student in the psycholo
gy department at New School Uni
versity in Manhattan,” reports James
Lewis (SFGI).
{The College .St John's College . Summer 2001 }
Calling All Alumni
The College wants to hear from you.
Call us, write us, e-mail us. Let your
classmates know what you’re doing.
The next issue will be published in
November; copy deadline is
September 20.
In Annapolis:
The College Magazine, St. John’s
College, Box 2800, Annapolis, MD
21404; b-goyette@sjca.edu.
In Santa Fe:
The CoUege Magazine, St. John’s
College, Public Relations Office,
1160 Camino Cruz Blanca,
Santa Fe, NM 87505-4599;
classics@mail.sjcsf.edu.
Alumni Notes on the Web:
Read Alumni Notes and contact
The College on the web at:
www.sjca.edu - click on “Alumni.”
�{Letters}
On The College
Whether it is a work slowdown
from the world of writing ency
clopedia articles, anticipation of
Jon Ferrier’s 50th birthday this
coming Wednesday, or my own
youthful longings, I do not know.
But my week has been full of
dreams of Prince George Street,
Thucydides, (never really TOO
far from my psyche, I confess) the
scent of boxwood, and the glories
of an Annapolis spring.
When I opened my mailbox
this Saturday morning, I found
the new issue of The College. On
this Saturday afternoon when I
would rather be enjoying Reality
weekend than cleaning house,
please know what a joy and com
fort this brilliantly-conceived,
marvelously-executed “new”
magazine brought to my soul, my
heart, and, ah, my mind!
Some mail days are better than
others. Thank you for being such
an integral piece of a pretty good
mail day.
—Jane E. Spear, A73
I have just completed The College
cover to cover and take my
(proverbial) hat off to you all for
the obvious work and resulting
high quality. My wife graduated
from the Graduate Institute in
1991 and I only completed half
the program before 1 went on to
(gasp) make money! The one
regret of my life is not complet
ing the, G1 program. The concept
and the execution of The College
is wonderful! Please keep up the
hard but great work!
—Sean P. Scally, AGI89
In your introduction to the new
alumni periodical, you asked
readers to “Let us know what you
think.”
Here’s what I think.
I think the new format is excel
lent. It allows for lengthier and
more serious treatment of issues
than The Reporter. The content
of the first issue was excellent
and thought-provoking. It invites
alums to reflect on how they
might interpret their current
lives in light of the program. The
professional format is appealing.
I hope to see wonderful things in
the future.
“This hath offended; oh, this
unworthy hand! ”
-James A. Cockey, A71
—Michael Ciea, A78
I’d like to commend the staff of
The College for a wonderful new
format for your publication. It’s
much more enjoyable to read. In
fact, for once, I read every arti
cle.
—Lisa Lashley, SF80
Good show-big improvementexcellent start. And only
St. John’s could offer a wrestling
bout with Aristotle and then deal
with the technicalities of dehcate
training of the very, very young a
few pages later.
Go to it. St. John’s ranks near
the top (or at the top) of Ameri
can educational institutions. And
I’m glad that at least one of my
children had the benefit of it.
—Donald Harriss
Historical Accuracy
I enjoyed your article about the
r95i St. John’s production of
Thomas Cranmer ofCanterbury
[“St. John’s Forever”], but I must
point out the obvious error,
about which I suspect you have
already heard many times.
Archbishop Thomas Cranmer
did not “suffer martyrdom as a
result of his stance on the king’s
divorce from Catherine of
Aragon.” His stance on the
divorce actually made his career
with Henry VIII, and led to his
appointment as the first Protes
tant archbishop of Canterbury.
He continued in his position
under Henry VIII and Edward VI,
and only got into trouble under
Queen Mary. She imprisoned
him because of his Protestant
involvement, and coerced him to
a recantation of his Protestant
views before his execution. He
then dramatically reversed his
position again before he was
burned at the stake, asserting
that his only sin was his previous
recantation of his Protestant
position. Before dying, he put the
hand which had signed the recan
tations into the fire, saying.
More Great Books on
Parenting
I loved the parenthood piece in
the spring issue [“The Education
That Is Parenthood”]. The Pro
gram is surely an excellent prepa
ration for parenthood, since,
whatever the great books may be
about, it trains you in open and
respectful dialogue, the proper
relationship with one’s child. Of
books about parenting, I have
fond memories of Children the
Challenge, by Rudolph Dreikers,
Hawthorn Books, New York,
1964. It too fosters such dialogue.
And for little children of course
Dr. Spock. With reference to
Janette Fischer’s letter on
Galileo’s talents, it’s evident
from Dava Sobel’s recent
Galileo’s Daughter that he was an
attentive and loving father too.
—John A. White, SFGI75
I am breaking a 25-year silence to
share this one thought with the
St. John’s community. The best
book on parenting I have ever
read, in fact the best book I have
ever read, the book I would keep
if I had to give away every other
book I own, the book I have
bought ao copies of over my life
and given away to troubled par
ents and been thanked again and
again for the gift.. .was not
included in the list. From the
first time I read it 15 years ago, I
said if there ever was a book writ
ten about parenting for a mem
ber of the St. John’s community,
it is Whole Child/Whole Parent
by Polly Berrien Berends.
—George Kiberd, A7a
I read your recent article on par
enthood with enjoyment. I am a
mother of two, a La Leche
League leader and something of
a “birth junkie,” and I’d like to
recommend a few more books.
For birth. Dr. Bill and Martha
Sears’s The Birth Book, and
Birthing From UY'zAzzibyPam
England and Rob Horowitz.
{The College- St. John's College • Summer 2001 }
La Leche League’s The Woman
ly Art ofBreastfeeding is essen
tial for nursing moms, and
Dr. Sears’s The Baby Book is a
wonderful book on parenting
and baby care. The Sears books
promote attachment parenting
breastfeeding and holding the
baby whenever he wants it, carry
ing him in a sling, co-sleeping.
This produces secure, independ
ent children, contrary to what
advocates of the old “don’t pick
that baby up or you’ll spoil him”
school might say.
I also wanted to mention the
large part that breastfeeding can
play in the first year or more of a
baby’s life, since it wasn’t dis
cussed in your article. Breastfed
babies are smarter, have stronger
immune systems, and have a
lower risk of leukemia, MS, obe
sity and heart disease later in life.
Breastfeeding moms have a lower
risk of breast, ovarian, and cervi
cal cancer, as well as a lower risk
of osteoporosis. In addition to its
many, many health benefits for
mother and baby, breastfeeding
helps to forge a stronger bond
between them, and gives the
mother a wonderful parenting
tool as the baby gets older. Nurs
ing is a wonderful way to soothe
the bumps, bruises, hurt feelings
and tantrums of toddlerhood,
and I didn’t think it should be left
out of a discussion on parenting!
For more information on breast
feeding, check out www.lalecheleague.org and www.breastfeeding.com.
—Tamara Steblez Ashley Aga/gs
Hurray for Planning
I was excited to read in “One Col
lege-How to Make it Really
Work” (Springissue) that “...the
Management Committee pre
pared a framework for a college
wide strategic plan that considers
needs and resources well into the
future.” What a great idea!
—James Laws, SF86
Corrections
Probably due to my somewhat
illegible scrawl/penmanship
�{Obituaries}
C. Thomas Clagett Jr.
Class ofiQsg
C. Thomas Clagett Jr., a retired business
executive who graduated from St. John’s in
1939, died on June 18. Mr. Clagett served in
the Navy during World War II and became a
lieutenant commander. He worked for the
Zeigler Coal Company beginning in 1947; he
was board vice chairman and head of the
board’s executive committee when the com
pany was bought by Houston Natural Gas in
1973. Mr. Clagett continued to serve on the
board of the new company until he retired in
1985A lifelong resident of Washington, D.C.,
Mr. Clagett was involved with many civic and
church groups, including Decatur House,
the Navy League, the Masons, the Sons of
the American Revolution, Washington Hos
pital Center, Washington National Cathe
dral, and the Chesapeake Bay Maritime
Museum. He was also a yachtsman and sailor
who established the Leiter Trophy, in honor
of his wife, who died in 1977.
He is survived by a son, a daughter, and
four grandchildren.
Constance Darkey
Constance H. Darkey, who was known to
every generation of New Program students
and tutors, died May a6 at her Santa Fe
home of a cerebral hemorrhage at the age of
eighty-four.
She is survived by her husband, tutor
emeritus William Darkey; a son by a previ
ous marriage, Peter Nabokov, professor of
anthropology at UCLA; by a daughter,
Catharine Darcy, who works with a real
estate firm in San Bernadino, Calif; by a sis
ter, Sally G. Holladay of Schroon Lake, NY;
and by a number of grandchildren.
Mrs. Darkey was born and grew up in Min
neapolis, Minn.; she graduated in 1938 from
more letters
there were a number of typos in
the Alumni Notes for a listing I
submitted which appeared in the
1986 section in the Spring 2001
issue:
Firstly, I married Graham Gar
ner, not Grant as listed once in
the note. I work for the Friends
General Conference of the Reli
gious Society of Friends (not the
Religions of Friends) and my email address is lucyd@fgcquak-
Wells College in Aurora, NY, where she
majored in Engbsh literature and drama and
then did graduate study in literature with
Professor Lane Cooper at Cornell University.
In Annapolis she became deeply persuad
ed of the rightness of the St. John’s curricu
lum, a conviction which never waned. For
several years she was manager of the College
Bookstore in Annapolis, resigning in 1944 to
take an editorial position in New York with a
trade publication.
Returning to Annapolis in 1947 she, with a
group of other parents of young children,
became involved in an enterprise which
resulted in the Key School. She was first the
librarian and had great fun buying books and
then devised the school’s history program,
which she taught delightedly.
She understood and was an enthusiastic
supporter of and participant in both the
intellectual and social life of St. John’s, well
understanding that these were not separable
provinces.
She favored the idea of the western cam
pus and once in Santa Fe took up her resi
dency with all of her considerable energies,
making new friends, reading widely and
deeply in the literature and history of the
Southwest, and traveling throughout the
entire region. She put her new knowledge to
work first as a docent in local museums, and
then became the librarian of the Wheel
wright Museum of the American Indian.
When her husband became the dean of the
Santa Fe campus, she again turned her ener
gies to the social life of the college, acting
for five years as hostess to visiting lecturers
and to generations of students.
She was a regular and excellent partici
pant in Gommunity Seminars, and for one
year she was happily a co-leader of an under
graduate seminar.
er.org not lucyd@fgquaker.org.
The wedding was really beautiful
by the way-a really perfect day.
—Lucy Duncan, SF86
Editor’s Note
Due to a computer software
glitch, many households received
multiple copies of the first issue
of The College. We hope the soft
ware problem is corrected and
apologize for loading up your
Donald S. Elliott
Class oftg48
Donald S. Elliott, who taught at Garrison
Forest School for 30 years, died on March 13.
Mr. Elliott also wrote children books devoted
to teaching about music, “Alligators and
Music,” “Frogs and Ballet,” and “Lamb’s
Tales from Great Operas.” At the private
school in Owings Mills, Md., where he
taught, his favorite course was an interdisci
plinary one that combined art, literature,
history, and music.
Mr. Elliott was born and raised in
Lutherville, Md., and entered St. John’s
when he was 14. He received his degree in
1948 and went to work for the Baltimore Life
Insurance Company in the actuarial depart
ment. He left to become a teacher at Garri
son Forest School. He is remembered as a
Renaissance man who taught himself to play
the piano, read philosophy and literature
constantly, and built his own swimming
pool.
He is survived by his wife, Cielito Obina,
and by three sons, two daughters, and four
grandchildren.
ALSO NOTED:
Elizareth D. Hatch, A76, died in Decem
ber 1998
John A. Joh, Class of 193a, died in March
2000
Craig Allen Johnston, A95
Kenneth Lenihan, AGI88, died in May
2001
Jesse Elhert Morgan, Class of 1954
F. Scott Seegers, Class of 1967, died in
February 2001
Tad Sanwick, Class of 1938, died in May
2001
George F. Wohlgemuth, Class of 1919,
died in June 2001
mailboxes unnecessarily.
Contacting The College
The College welcomes letters on
issues of interest to readers. Let
ters may be edited for clarity
and/or length. Those under 500
words have a better chance of
being printed in their entirety.
Please address letters to; The
College Magazine, St. John’s
College, Box 2800, Annapolis,
MD 21404 or The College Maga
{The College- St. John’s College . Summer soot }
zine, Public Relations Office,
St. John’s College, 1160 Camino
Cruz Blanca, Santa Fe, nm
87505-4599-
Letters can also be sent via email to:
b-goyette@sjca.edu, or via the
form for letters on the web site
at www.sjca.edu - click on
“Alumni,” then on “Contact
The College Magazine.”
�{Obituaries}
42,
In Memory of Leo Raditsa
emarks delivered by tutor
Nick Maistrellis at a
memorial service for Leo
Raditsa, tutor in Annapo
lis from 1973 to aoor. Mr.
Raditsa died in January.
R
I first met Leo in the mid-yos when we
shared a sophomore seminar-the first of
three seminars we shared over the next
35 years. We may have a record. I liked him
immediately although we disagreed, almost
from the beginning, about many things; poli
tics, the college, the purpose of seminar. I
thought of him as a political conservative
because of the passion with which he
believed in the inherent evil of the Soviet
empire. But he himself rejected that label.
He thought of himself as a partisan of free
dom and humaneness. He was also deeply
skeptical about the college’s approach to the
books. He did not believe they could be read
without the context of the struggles which
surrounded their birth, and without the con
stant guidance of a teacher.
At bottom, Leo believed that the task of
the tutor is to show students what is impor
tant in the extraordinary books we read
together. I, being more conservative,
thought that no such thing can be done in
seminar, and that all we can do is to allow
students the occasion to examine their own
insights into the books. For me, the main job
of the seminar leader is to wait and listen,
whereas for Leo it was to assert and provoke.
What he cherished most in seminar was oneon-one exchanges between himself and a stu
dent who was responding to something he
had said. He told me that he didn’t believe
students could sustain an important conver
sation just among themselves. This made for
seminars in which there was always at least
the possibility of tension between the tutors.
I found being in seminar with Leo difficult
and wearing, but also very exciting. If we had
not been in seminar together, I do not know
if I would have ever allowed myself to know
and care for this extraordinary man.
Many people one meets are interesting for
what they know or for what they have done. It
is much rarer to meet one who is interesting
in himself. Leo was one of these. I have
often, over the
past many
years, experi
enced a lack
which on
reflection
turned out to
be a need to
have lunch
with Leo, just
to be with him.
In every
encounter with
him you knew
you were in the
presence of
someone.
Every opinion he expressed had that in it
which marked it as one of Leo’s utterances.
In this way he had of always being truly pres
ent in every conversation, Leo was one of the
most intimate human beings I have known.
Leo always said what he thought, and what
he thought was never ordinary. His thinking
had for me the following quality; he seemed
to be the conduit for opinions coming from a
deeper source, rather than the originator of
them. His own awareness of this quality of
his thinking is probably reflected in his
respect for the discovery of the unconscious
by classical psychoanalysis, and especially for
the work of Freud and Wilhelm Reich. I
remember so many occasions when he said
things I could not possibly have expected, or
expressed opinions I could not imagine any
one holding, that I could spend hours relat
ing them. One in particular happened 25
years ago in the sophomore seminar we
shared. In those days we read John Calvin’s
Institutes ofthe Christian Religion, a formi
dable book best known for its austere teach
ing on the predestination of souls for salva
tion. Leo had never read it before, and came
to the seminar very excited. It was his open
ing question. He looked at the class and said,
“Isn’t this the sweetest, the warmest, the
most humane author you have ever read?” Of
all the things I could have imagined being
said about Calvin, this was the least expect
ed, and yet, it became the beginning of a very
good discussion, for it challenged us to
reassess our own first opinions. What Leo
saw was that the doctrine of predestination
{The College. St. John’s College ■ Summer noot }
removed an unbearable burden of
responsibility from human beings.
This story also has its own irony, for
it shows Leo being a seminar stu
dent in the best St. John’s tradition
in spite of his own doubts about
being a seminar leader.
Leo cared about his students.
His manner was often abrupt and
challenging. He was sometimes
grumpy. It is hard to know how
much of this was from the chronic
pain in his leg, for he never com
plained. He could be unfairly criti
cal, and judgmental. He often mis
judged students. But, he cared
deeply both for their learning and
for their personal welfare. He didn’t talk
about students very often, but when he did
he surprised me by how much he knew about
them. He was impatient with what he saw as
phoniness, and much of his harshness was
directed against perceived laziness, or what
he thought was the mere parroting of fash
ionable opinions for effect. But if he thought
a student was doing his best Leo could be
extraordinarily gracious and encouraging. I
remember two occasions when he saved me
from unfairly undervaluing the written work
of students, when I had allowed myself to be
too critical of superficial defects. He was
often more generous in formal evaluations
than in oral exams. We were together on
more than one occasion on senior essay com
mittees when he was very harsh in person to
a student to whom he gave a good grade on
the essay itself. His response to this apparent
discrepancy was to say that he thought the
student was too pleased with himself, and
needed to be woken up.
My favorite times with Leo were outside
class, and especially when we were not talk
ing about college matters where he was usu
ally furious about a decision that had just
been made by some officer of the college in
which, all to often, I was implicated. I loved
to hear him talk about Italy. He cared deeply
about the world, and in his presence I cared
about it more too. We had both adopted chil
dren at about the same time, and it was with
him that I shared my feelings about the spe
cial joys and challenges of being an adoptive
parent. He gave the best dinner parties.
�43
{History}
HUNT HOUSE
The sprawling Santa Fe-style adobe home with the courtyard
perfectfor viewing sunsets once belonged to a colorfulpoet.
BY Alexis Brown, SFoo
new president for the Santa Fe campus travels to Asia, Bynner had a newfound love
and appreciation for poetry. He settled down
occupies the Hunt House, and as he and his in the hills of Santa Fe and began to expand
on his poetic expression, using the simple,
wife begin planning for their future there, elegant styles of Asian poetry.
is it, exactly, that the house named
one wonders about the house’s history. Not forHow
Robert Hunt, Witter Bynner’s partner, is
much is known about the house in the hills now being used by the college as a home for
president? This isn’t the house Bynner
across from campus, even less of our con its
lived in on Santa Fe Trail-the house where
famous parties
were held. Instead, it’s a
nection with the man who donated it to thethecollege,
poet
sprawling set of buildings, a main house with
Witter Bynner (1881-1968).
two guest houses surrounding a courtyard.
A
In 1922, Witter Bynner moved to Santa Fe, a
place he would call home the rest of his life.
For decades, Bynner was a prominent citizen
in Santa Fe and an active participant in the
cultural and political life of the city. He had
no official affiliation with the “new” college
that was built in Santa Fe in the mid-sixties.
His association with St. John’s was a result of
his appreciation and respect for the college
and its program.
Bynner and Robert Hunt, his companion
of more than 30 years, lived in a house on
Old Santa Fe Trail. There they held parties
that attracted artists, literary figures, and
celebrities who lived in or were visiting
Santa Fe-people like D.H. Lawrence, Ansel
Adams, Errol Flynn, Robert Oppenheimer,
and Georgia O’Keefe.
In his 87 years Witter Bynner produced
many volumes of poetry, translated Greek
and Chinese works into English, taught
poetry classes at Stanford and Berkeley, trav
eled throughout the world, and made numer
ous friends. Yet despite his achievements few
Americans recognize his name. Bynner’s
obscurity is mostly due to the 1916 “Spectra
Hoax,” in which Bynner and Arthur Davison
Ficke, writing under pseudonyms which they
later revealed, established “Spectrism,” a
supposedly new school of poetry that attract
ed many advocates. When Bynner and Ficke
revealed this “new” type of poetry as a hoax.
and their
identities,
they offended
many of their
peers, and
thus lost
respect in the
literary
world.
Despite lack
of recogni
tion from his
contempo
raries, Byn
ner contin
ued to
Santa Fe president John
produce many Balkcom and his wife carol
excellent writ are new residents of the
Hunt House.
ten works
throughout his
lifetime. He also translated Iphigenia in Tauris from the original Greek to English in
1915. During these years, he lectured
throughout the United States on poetry and
women’s suffrage.
In 1917, soon after the Spectra Hoax, Byn
ner visited Japan and China, spending
approximately two months in each country.
He wished to explore Asia and to escape
America’s involvement in World War I. A
staunch pacifist, he loathed Europe’s war
and strongly denounced violence. After his
{The College -5f. John’s College ■ Summer 2001 }
Up in the hills, it affords wonderous views of
Santa Fe sunsets.
The story goes like this:
Hunt and Bynner were travel
ing south to sell a house they
owned in Chiapas, Mexico,
because they were planning
to move into a new house in
Santa Fe designed andbuUt
by Hunt. On the way, though.
Hunt died suddenly. Bynner
was so grief-stricken that,
although Hunt left the house
to him, Bynner could neither
move into the house by him
self, and nor could he sell it.
A year later, Bynner had his
first stroke, and was confined
to living in his own house, the one that had
been site to so many parties.
Neither Hunt nor Bynner ever lived in the
house Hunt built, but they are now both
buried near there, in a spot marked by a
bronze statue of a dog once loved by Hunt.
When Hunt died, Bynner acquired the titles
to both houses. Bynner himself died in 1968,
leaving both houses to St. John’s, presum
ably because he admired something about its
philosophy of education. The college sold
the Witter Bynner House on Old Santa Fe
Trail because it was too expensive to main
tain. But, luckily, the Hunt House still
stands strong, home to a new president.
�44
{Alumni Association News}
From the Alumni
Association President
Senior Dinners:
Welcoming the
Newest Alumni
Dear Johnnies,
St. John’s may have you for four years, but the
Alumni Association has you forever after. That’s
the message alumni pass along to their newest fel
low alums—the soon-to-be-graduated seniors-during Senior Dinners. These dinners, which take
place in Santa Fe in January and Annapohs in
April, have become an important tradition for the
seniors and for their alumni hosts alike. It’s a
chance for Johnnies who’ve been out in the “real
world” to welcome students into the Association.
The hosts, the college, and the Association all
work together to make the evening a success. The
Alumni Directors, Tahmina Shalizi and Roberta
Gable, choose the local restaurants (with input
from participating alumni). The students choose
the friends they want to go out with. And the
alumni hosts put their social skills to good use in
bringing the evening together.
Leo Vladimirsky, a member of the Annapolis
class of 2001, says he enjoyed his dinner at North
woods with Mark Middlebrook (A82) and Robert
Bienenfeld (SF80). “The food was great-Northwoods being one of the best places to eat around
Have you received your copy of the St. John’s College Alumni Register aooi? Have
you checked to make sure your own info is right? Have you seen who’s lost and
who’s found? (More about that later.) Have you scanned your
class to see who’s married or divorced? Who’s moved or
changed johs? Have you used the new e-mail section to send ehellos to old friends? I certainly have, especially because I’m
getting ready for the 25th reunion of my class!
Glenda Eoyang
We owe a note of resounding thanks to Roberta Gable, Direc
tor of Alumni Activities in Annapolis, and her team for the
tremendous work they did preparing the Register. Every five
years, the Alumni Association and the college fund the effort to collect data about
alumni and to publish that information for all of us to share. The Register is an
excellent tool to help us stay connected with each other and with the college.
Many thanks to all!
Now, about those lost alumni.... As you browse the new Register, you’ll note that
some names are marked with an asterisk for “address unknown.” These are alum
ni who have lost contact with the community. The Alumni Association and the col
lege will be making an effort over the next few months to rebuild connections with
these missing persons. You can help! If you’re in touch with ones who are “address
unknown,” please contact them and encourage them to get in touch with the col
lege (or call or e-mail the Alumni Office so that they can follow up). A phone call, a
note, or an e-mail will provide the information tie that hinds us.
I hope your summer is joyous and rewarding and that you have a chance to partici
pate in some of the summer’s alumni activities: Homecoming in SF, Summer
Alumni Weeks, GI graduation, various chapter gatherings, listserve conversa
tions, or a private visit to one of the campuses.
For the past, the present, and the future,
Glenda Holladay Eoyang, SF76
ST. JOHN’S COLLEGE
ALUMNI ASSOCIATION
Whether from Annapolis or Santa Fe,
undergraduate or Graduate Institute,
Old Program or New, graduated or not,
all alumni have automatic membership in
the St. John’s College Alumni Association.
The Alumni Association is an independent
organization, with a Board of Directors
elected by and from the alumni body.
The Board meets four times a year, twice
on each campus, to plan programs and
coordinate the affairs of the Association.
This newsletter within The College
magazine is sponsored by the Alumni
Association and communicates Alumni
Association news and events of interest.
President - Glenda Eoyang, SF76
Vice President - Jason Walsh, A85
Secretary-Barbara Lauer, SF76
Treasurer - Bill Fant, A79
Getting-the-Word-Out Action Team ChairTom Geyer, A68
Web site - www.sjca.edu/aassoc/main.phtml
eoyang@chaos-hmited. com
Mailing address - Alumni Association,
St. John’s College, Box 2800, Annapohs,
MD 21404 or 1160 Camino Cruz Blanca,
Santa Fe, NM 87505-4599.
{The College- St. John's College ■ Summer 2001 }
�{Alumni Association News}
Annapolis. It was a nice conversation among
people who didn’t know each other,” he says.
The students knew each other, he hastens to
add-“we all decided to list each other on the
forms the Alumni Office sends out, to be sure
we’d be with our friends.”
After an initial discussion in which each sen
ior talked about his or her future plans, the con
versation turned to more general matters about
college life, graduate school, the business world,
working as an engineer, and other matters, says
Vladimirsky. There wasn’t any purposeful net
working, but the students all got the feeling that
their alumni hosts cared about what happened
to them and would be willing to help out in job
searches or with graduate school advice. They
also learned a fife skill-how to “taste” wine.
Mark Middlebrook, who lives near the Napa Val
ley wine region, demonstrated how to swirl the
wines around in their glasses before smelling
and tasting.
“AU around, it was a nice evening, and it’s
great of the Alumni Association to do this for
seniors,” says Vladimirsky. Himself, he’s not
sure what he’ll be doing come fall. After some
rest from academic matters, he’ll probably go to
graduate school. He knows he can count on
alumni for advice or networking once he has an
idea of where he’d like to study. One thing for
sure, though, “the chocolate cheesecake at
Northwoods was great.”
Amending the
Amendment
Mechanism
In order to make it easier to explain proposed
changes in the Alumni Association By-Laws to
the alumni ofthe college, the Alumni Association
Board isproposing thefollowing amendment to
the By-Laws:
In accordance with Article XIII, Section I of the
By-Laws of the St. John’s CoUege Alumni Associ
ation, notice is hereby given that the following
by-laws amendment has been proposed by the
Alumni Association Board of Directors. This
amendment will be voted upon at the Special
Meeting, September 29, 2001, 2:00 p.m. in the
Conversation Room in Annapolis.
The amendment to Article XIII is indicated in
capitals.
ARTICLE XIII
AMENDMENTS
SECTION I. Any and all provisions of these ByLaws may be altered, amended, added to, or
repealed by a majority of the membership of the
Association, present in person or by proxy, at
any regular or special meeting of the member
ship, provided that a copy of any proposed
amendment shall have been mailed to each
member at least six weeks prior to that meeting
OR PROVIDED THAT A NOTICE, AS SPECI
FIED HEREUNDER, SHALL HAVE BEEN
MAILED TO EACH MEMBER AT LEAST SIX
WEEKS PRIOR TO THAT MEETING. THE
NOTICE SHALL INDICATE THE ARTICLE(S)
AND SECTION(S) PROPOSED TO BE AMEND
ED; AWEB SITE ADDRESS DETERMINED BY
THE BOARD OF DIRECTORS AT WHICH A
MEMBER MAY ACCESS THE COMPLETE
TEXT OF THE PROPOSED AMENDMENT;
AND A STATEMENT INFORMING EACH
MEMBER HOW THEY MAY RECEIVE A COPY
OF THE PROPOSED AMENDMENT BY MAIL
OR FAX.
Amendments to these By-Laws shall be sub
mitted to the membership upon the vote of the
Board of Directors, or by Petition of at least fifty
members in good standing which is received at
least ten weeks prior to the date of the meeting.
SECTION IL Unless so stated, any amend
ment to these By-Laws shall take effect immedi
ately foUowing its adoption.
The Croquet Match is a favorite gathering
SPOT FOR 1980s AND I99OS ALUMNI (lEFt).
At the Match Alumni Association Board
MEMBERS sported SHADES PRINTED WITH
“Beat Navy” — in Greek, of course.
CHAPTER CONTACTS
Call the alumni listed belowfor information
about chapter, reading group, or other alumni
activities in each area.
ALBUQUERQUE
PHILADELPHIA
Bob & Vicki Morgan
505-880-2134
Bart Kaplan
215-465-0244
ANNAPOLIS
PORTLAND
Valerie Garvin
410-280-6119
Dale Mortimer
360-882-9058
AUSTIN
SACRAMENTO
Jennifer Chenoweth
512-482-0747
Helen Hobart
916-452-1082
BALTIMORE
SAN DIEGO
Roberta Gable
410-295-6926
Stephanie Rico
619-423-4252
BOSTON
SAN Francisco/
NORTHERN CALIFORNIA
Ginger Kenney
617-964-4794
CHICAGO
Lorna Anderson
847-467-3069
DENVER
Elizabeth Pollard Jenny
303-330-3373
LOS ANGELES
Elizabeth Eastman
562-426-1934
MINNEAPOLIS/ST. PAUL
Carol Freeman
612-822-3216
NEW YORK
Fielding Dupuy
212-974-2922
NORTH CAROLINA
Susan Eversole
919-968-4856
{The College- St. John’s College ■ Summer soot }
45
Jon Hodapp
831-393-9496
SANTA FE
John Pollak
505-983-2144
SEATTLE
Kyle Kinsey
206-715-1081
WASHINGTON, DC
Jean Dickason
301-699-6207
ISRAEL
Emi Geiger Leslau
15 Aminadav Street
Jerusalem 93549
Israel
972-2-6717608
boazl@cc.huji.ac.il
�{Campus Life}
Say It Isn’t So
What happened to St. Johns domination in croquet?
VI Sus3AN
Borden, A87
e were, perhaps, a bit smug. We
were, you might say, a tad over
confident. And we were, no doubt,
somewhat drunk. But still, it doesn’t
add up. When did smugness become
an obstacle for a Johnny? What good
is a croquet team that’s not overconfident? And why would a
martini or two ever keep us from the Annapolis Cup?
And yet it happened. After a nine-year win
ning streak and a 15-3 series record, St.
John’s lost the 19th croquet match against
the Naval Academy, held the last Saturday in
April on the front campus.
While we were unahle to contact Imperial
Wicket Paige Postlewait (Aoi) for this story,
her teammate and next year’s Imperial
Wicket, Jonathan Polk {A02), has some
insight into the loss. “We might have heen a
little overconfident,” he says, “but I’m
tempted to think of it as just a combination
of bad luck-lots of people’s different bad
luck in combination.”
“It’s been a pretty rough year for us,” Polk
says. “We didn’t compete in the National
Championships and we didn’t start practic
ing until about a month beforehand.” (Why
the team didn’t go to the Nationals, where
they were three-time champions, is another
story-involving a change in the game from
traditional nine-wicket to something called
“golf croquet.”) Still, he says, even with the
late start the team logged so much playing
time they felt they were ready to play and
prepared to win.
An article in the Trident, the Naval Acade
my’s newspaper, suggests that the win may
be a result of strategy, the players’ lucky ties
and lucky mallets, or brainpower-the team
included two Trident Scholars and a Pownall
Scholar. Word around town is that the Acad
emy brought in a croquet coach from Yale to
beef up the middies’ strategy and skills.
Whatever the reason, says former Imperi
al Wicket Bob DeMajistre (A88), the mid
shipmen deserved to win. DeMajistre attend
ed this year’s match, as he does most years.
One of the college’s four losing Imperial
Wickets {1987), DeMajistre is well qualified
to analyze the play. “I watched the court
where we played the first lost game and the
mids were shooting very well, they were dead
on. They were making long shots, they were
hitting balls. And we weren’t.”
Johnnies, as usual, were a bit more fla
grantly OUTFITTED THAN THEIR OPPONENTS.
{The College. St John’s College ■ Summer zooi }
�47
Steven Werlin (A85), St. John’s first
defeated Wicket, recalls that losing was no
surprise to him in 1985. “Two separate cro
quet things were happening at St. John’s that
year,” he says. “There were serious croquet
players and then there was the croquet team.
The only person who fell into both groups
was James Hapner (A85).” Only later, Werlin
says, did croquet play become more serious
and practice become intense.
Once practice did take hold, it became St.
John’s secret weapon. Or perhaps not so
secret, as it was revealed in a Sports Illustrat
ed article, “The Best of Everything” ( April
28,1997, special issue on college sports).
Citing the croquet match as the Most
Obscure Rivalry, the article quotes a Naval
Academy plebe explaining St. John’s strate
gy: “They’re out practicing croquet every
afternoon! Alabama should take football this
seriously.”
Louis Elias {A91), another former Imperi
al Wicket, recalls the year his team lost the
match (i99r). “I sort of knew we were going
to lose all along,” Elias says. “I lost heart
Jonathon Polk lines up a long shot (top).
Polk AND Imperial Wicket Paige PostleWAIT WAIT THEIR TURN (BOTTOM LEFT) WHILE
CURRENT Johnnies enjoy the festivities
(bottom Right).
{The College -St John’s College ■ Summer 2001 }
that year. The hype and media attention [G<2
covered the event] and the reaction to the
attention seemed, to me, to detract’from the
spirit of the event.” Still he says, the loss was
not without a silver lining: “I figured we
were due for a loss if only to keep the Acade
my interested.”
DeMajistre agrees that an occasional loss
can serve a strategic purpose: “The main
reason to lose is so that the mids will come
back. You got to throw them a bone every
once in awhile. ” *
�48
{St. John’s Forever}
These photos of student desks were
TAKEN BY EdWARD GrAY, CLASS OF I934.
The date on the photos is 1933.
From the 1933 yearbook,
THE Rat Tat, describing the
TENOR OE COLLEGE LIFE AT
St. John’s:
...Like all other freshman classes we gave lit
tle evidence of ability, although we did study a
bit between building bonfires, attending rat
meetings and football, basketball and lacrosse
games...One of the outstanding features this
year was the inauguration of the new presi
dent of the college [Amos W. Woodcock].
Another was the coming of Hopkins. What a
fight! If you don’t believe me, ask the
Annapolis police, the Annapolis firemen or
the jail keeper...By the time we were juniors,
we had forgotten most of our high school and
prep school training and were beginning to
realize that it takes a smart man to admit
there is plenty he doesn’t know...Each one of
us came here with ideals and aims. Some of us
have done things we set out to do, others have
done more, others have met with disappoint
ments. Most of us brought little to St. John’s
with us. The amount of knowledge and the
number of friends we take away with us
depends on the individual. Everything the
school could offer us was placed at our feet.
Who picked it up and who trampled it is
another question.
{The College. St. John’s College ■ Summer zoot }
�{Alumni Events Calendar}
Homecoming 2001 - Annapolis
Friday, septemDcrau-siwflay, September 30
Reunion Classes: 1936,1941,1951,1956,
1961,1966,1971,1976,1981,1986,1991,
and 1996
Homecoming Highlights
Friday, September 28
• Homecoming Lecture by Abraham
Schoener (A82): “The Biology of the
Fermentation Vehicle”
• Wine and Cheese Party in the
Dining HaU
• Rock Party in the Boathouse
Saturday, September 29
• Memorial Service for Mortimer Adler
• Saturday Morning Seminars
• Children of alumni seminar on Harry
Potter (followed by croquet)
• Freshman Chorus Revisited led by
Elliott Zuckerman
• West Street Story, a reprise of the Class
of 1981’s senior prank show
• Alumni-Student Soccer Classic
• Autograph Party
• Cocktail party in the Great Hall and
McDowell classrooms
• Homecoming Banquet: Tom Williams
(A51) and Warren Spector ( A81) will
receive the Alumni Association Award
of Merit; Nancy Lewis, John Moore,
and Beate Ruhm Von Oppen will be
recognized as new Honorary Alumni
• Waltz Party in the Great Hall
Sunday, September 30
I
• Rock Party in the Coffee Shop: Robert ■
George (A85) will make a cameo DJ 3
appearance
i
• Champagne Brunch at the President’s
House
-
?
‘
I
t
A Johnnie is a Johnnie—no matter if their
GRADUATION YEAR WAS IN THE 1950’s OR THE
1990’s.
Inauguration of John Balktom as
Santa Fe President _____ - '
-1
Friday, September 14 and Saturday;
September 15
“Inviting Conversations” is the theme of
this inaugural weekend where festivities
will include:
Friday, September 14
• Picnic on the soccer field
• All-college Chicago-style softball game
• Performance at the newly renovated
Lensic Performing Arts Center
Saturday, September 15
• Inauguration at 10 a.m. on Meem
Library Placita
• Reception for all in attendance will
take place on the Upper Placita
• Waltz Party in the Great Hall
For information on events, contact the
Offices of Alumni Activities:
Tahmina Shalizi,
Director of Alumni and Parent Activities
Santa Fe - 505-984-6103;
alumni@maiLsjcsf.edu
Roberta Gable,
Director of Alumni Activities
Annapolis - 4io-6a6-253i;
alumni@sjca.edu
�STJOHN’S COLLEGE
ANNAPOLIS • SANTA PE
Published by the
Public Relations Office
Box a8oo
Annapolis, Maryland 21404
ADDRESS service REQUESTED
Periodicals
Postage Paid
�
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The St. John's College Communications Office published <em>The College </em>magazine for alumni. It began publication in 2001, continuing the <em>St. John's Reporter</em>, and ceased with the Fall 2017 issue.<br /><br />Click on <strong><a title="The College" href="http://digitalarchives.sjc.edu/items/browse?collection=56">Items in The College (2001-2017) Collection</a></strong> to view and sort all items in the collection.
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Santa Fe, NM
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48
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The College, Summer 2001
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Volume 27, Issue 3 of The College Magazine. Published in Summer 2001.
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St. John's College
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St. John's College
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Annapolis, MD
Santa Fe, NM
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2001
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pdf
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The College Vol. 27, Issue 3 Summer 2001
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Goyette, Barbara (editor)
Mulry, Laura J. (Santa Fe editor)
Borden, Sus3an (assistant editor)
Behrens, Jennifer (graphic designer)
Johnson, David
Harvey, Keith
Eoyang, Glenda Holladay
Brown, Alexis
Maistrellis, Nicholas
Hellner-Burris, Janet
Goyette, Barbara
Moreno, Ed
Fridrich, Sarah
Flaumenhaft, Harvey
Rankin, John
Knight, Mirabai
-
https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/45709523ddccdeb799588a8848abb06e.pdf
35c2cecd076ac303d83387b733342e0d
PDF Text
Text
The St. John’s Review
Volume XLVIII, number one (2004)
Editor
Pamela Kraus
Editorial Board
Eva T. H. Brann
Frank Hunt
Joe Sachs
John Van Doren
Robert B. Williamson
Elliott Zuckerman
Subscriptions and Editorial Assistant
Audra Price
The St. John’s Review is published by the Office of the Dean,
St. John’s College, Annapolis: Christopher B. Nelson,
President; Harvey Flaumenhaft, Dean. For those not on the
distribution list, subscriptions are $10.00 for one year.
Unsolicited essays, reviews, and reasoned letters are welcome.
Address correspondence to the Review, St. John’s College,
P Box 2800, Annapolis, MD 21404-2800. Back issues are
.O.
available, at $5.00 per issue, from the St. John’s College
Bookstore.
©2004 St. John’s College. All rights reserved; reproduction
in whole or in part without permission is prohibited.
ISSN 0277-4720
Desktop Publishing and Printing
The St. John’s Public Relations Office and the St. John’s College Print Shop
�2
THE ST. JOHN’S REVIEW
3
Contents
Classical Mathematics and Its Transformation
St. John’s College, Annapolis
June 5-6, 2004
Foreword.......................................................................5
Harvey Flaumenhaft
Why We Won’t Let You Speak Of the Square
Root of Two..................................................................7
Harvey Flaumenhaft
The Husserlian Context of Klein’s
Mathematical Work.....................................................43
Burt C. Hopkins
Words, Diagrams, and Symbols: Greek and
Modern Mathematics or “On the Need to Rewrite
the History Of Greek Mathematics” Revisited............71
Sabetai Unguru
A Note on the Opposite Sections and Conjugate
Sections In Apollonius of Perga’s Conica.....................91
Michael N. Fried
Viète on the Solution of Equations and the
Construction Of Problems.........................................115
Richard Ferrier
�4
THE ST. JOHN’S REVIEW
5
Foreword
Harvey Flaumenhaft
On the weekend of June 5-6, 2004, the Annapolis campus of
St. John’s College hosted a conference on the topic of classical mathematics and its transformation. This is a pivotal topic
in the program of instruction here at St. John’s, where classes
consist in the discussion of great books ancient and modern,
and where approximately half of the entirely prescribed curriculum may be classified as either mathematics or heavily
mathematical natural science.
The topic was made truly pivotal at St. John’s by Jacob
Klein, who joined the faculty in the second year of the New
Program (1938-39) and became Dean eleven years later. Just
a few years before arriving at St. John’s, Klein had published
Die Griechische Logistik und die Entstehung der Algebra (later
translated by another Dean—Eva Brann—as Greek
Mathematical Thought and the Origin of Algebra). In a letter
written just a few weeks after arriving at the College, Klein
said, “It is almost unbelievable to me that all the things that
occupied me for years, that is, the whole theme of my work,
are realized here. The people don’t do quite right, very much
is superficial and they are not quite right about certain fundamentals. But it….is clear that I am in the right spot.”
Klein’s presence, and his book because of his presence, had a
deepening and correcting effect on the life of this college, and
through this college, on intellectual life far beyond our halls.
The effects of his work pervade the conference papers, which
are printed as this issue of The St. John’s Review.
The conference took place through the generosity of the
Andrew W Mellon Foundation, as the culminating event
.
under a large grant supporting faculty study groups led by
me, over several years, on the topic of the conference. The
Harvey Flaumenhaft is Dean at the Annapolis Campus of St. John’s College.
�6
THE ST. JOHN’S REVIEW
grant also supported groups on the same topic on the Santa
Fe campus, with participation by faculty members from
Thomas Aquinas College. Grateful acknowledgment is due to
Sus3an Borden, the college’s Manager of Foundation
Relations in Annapolis, who did a great deal of work, under
very severe time constraints, to set up the conference.
7
Why We Won’t Let You Speak
of the Square Root of Two
Harvey Flaumenhaft
Part One
Progress and Preservation in Science
We often take for granted the terms, the methods, and the
premises that prevail in our own time and place. We take for
granted, as the starting-points for our own thinking, the outcomes of a process of thinking by our predecessors.
What happens is something like this: Questions are asked,
and answers are given. These answers in turn provoke new
questions, with their own answers. The new questions are
built from the answers that were given to the old questions,
but the old questions are now no longer asked. Foundations
get covered over by what is built upon them.
Progress can thus lead to a kind of forgetfulness, making
us less thoughtful in some ways than the people whom we go
beyond. We can become more thoughtful, though, by attending to the thinking that is out of sight but still at work in the
achievements it has generated. To be thoughtful human
beings—to be thoughtful about what it is that makes us
Harvey Flaumenhaft is Dean at the Annapolis campus of St. John’s College. This
paper was delivered in the form of a Friday-night formal lecture at St. John’s
College in Annapolis on 27 August 1999.
The first part of it is adapted from the “Series Editor’s Preface” in the
volumes of Masterworks of Discovery: Guided Studies of Great Texts in Science
(New Brunswick, NJ: Rutgers University Press, 1993-1997).
The last part is adapted from the “Introductory Note on Apollonius” in
Apollonius of Perga, Conics: Books I-III, new revised edition, Dana Densmore,
ed. (Santa Fe, NM: Green Lion Press, 1998).
The three parts placed between them are adapted from the manuscript
How Much and How Many: The Euclidean Foundation for Comparisons of Size
in Classical Geometry (forthcoming from Green Lion Press), which is part of the
larger manuscript Insights and Manipulations: Classical Geometry and Its
Transformation—A Guidebook: Volume I, Starting up with Apollonius; Volume
II, From Apollonius to Descartes (also forthcoming).
�8
THE ST. JOHN’S REVIEW
human—we need to read the record of the thinking that has
shaped the world around us, and still shapes our minds.
Scientific thinking is a fundamental part of that record,
but it is a part that is read even less than the rest, largely. That
is often held to be because of the opinion that books in science, unlike those in the humanities, simply become outdated: in science, the past is held to be passé.
Now science is indeed progressive, and progress is a good
thing; but so is preservation. Progress even requires preservation: unless there is keeping, our getting is little but losing—
and keeping takes plenty of work.
Precisely if science is essentially progressive, we can truly
understand it only by seeing its progress as progress. This
means that our minds must move through its progressive
stages. We ourselves must think through the process of
thought that has given us what we would otherwise thoughtlessly accept as given. By refusing to be the passive recipients
of ready-made presuppositions and approaches, we can avoid
becoming their prisoners. Only by actively taking part in discovery—only by engaging in re-discovery ourselves—can we
avoid both blind reaction against the scientific enterprise and
blind submission to it.
We and our world are products of a process of thinking,
and truly thoughtful thinking is peculiar: it cannot simply
outgrow the thinking it grows out of. When we utter deceptively simple phrases that in fact are the outcome of a complex development of thought—phrases like “the square root
of two”—we may work wonders as we use them in building
vast and intricate structures from the labors of millions of
people, but we do not truly know what we are doing unless
we at some time ask the questions which the words employed
so casually now were once an attempt to answer.
The education of a human being requires learning about
the process by which the human race gets its education, and
there is no better way to do that than to read the writings of
those master-students who have been the master-teachers.
FLAUMENHAFT
9
Part Two
Manyness: The Classical Notion of Number
The first great teachers of the West, and subsequently the rest
of the world, were the classical teachers who wrote in Greek
some two-and-a-half millennia ago. In their language the
word for things that are learned or learnable is mathêmata,
and the art that deals with the mathêmata is mathêmatikê—
the English for which is “mathematics.”
In mathematics, the first and fundamental classic work is
the Elements of Euclid. From its Seventh Book we learn that
a number is a number of things of some kind. When there are
more than one of something, their number is the “multitude”
of them. It tells how many of them there are. Suppose, for
example, that in a field there are seven cows, four goats, and
one dog. If we count cows, then the cow is our unit, the cow
being that according to which any being in the field will count
as one item; and there is a multitude of seven such units in
the field. If we count animals, however, then the animal is our
unit; and now there is a multitude of twelve units. Of cows,
there are seven; but of animals, there are twelve.
Of dogs as dogs, there is no reason to make a count (as
distinguished from including them in the count of animals).
There is no reason to count dogs, for the field does not contain dogs. It contains only one dog, and one dog alone does
not constitute any multitude of dogs. If what we were thinking was “There is only one dog in the field,” we might say
“There is one dog in the field”; but if we were not thinking
of that single dog in relation to some possible multitude of
dogs, we would simply say “There is a dog in the field.” Of
pigs, there is no reason to make a count, for the field does not
contain a single pig, let alone a multitude of pigs.
If there had earlier been six horses in the field, which
were then lent out, the field might now be said to lack six
horses; but while six is the multitude of horses that are lacking from the field, there is not any multitude of horses in the
field.
�10
THE ST. JOHN’S REVIEW
If we chop up one of the cows, arranging to divide its
remains into four equal pieces, and we take three of them,
then we have not taken any multitude of cows. We have taken
merely three pieces that are each a fourth part in the equal
division of what is a heap of the makings for beef stew.
And so when we have several items, each of which counts
as one of what we are counting, then what we obtain by
counting is a number. The numbers, in order, are these: two
units, three units, four units, and so on. The numbers, we
might even say, are these: a duo, a trio, a quartet, and so on.
To us, nowadays, that seems strange: a lot seems to be lacking.
“One” does not name a multitude of units: although a
unit can be combined with, or be compared with, any number of units, a unit is not itself a number—so “one” does not
name a number. “Zero” also does not name a number, for
there is no multitude of units when there are no units for a
multitude to be composed of. Neither does “negative-six”
name any multitude, although “six” does; “six” names a number, but there is no number named “negative-six”—and hence
there is no number named “positive-six” either.
Although “three” names a number of units, and so does
“four,” “three-fourths” does not name a number of units—
for if the unit is broken up, then, being no longer unitary, it
ceases to be a unit. The Latin word for breaking is “fraction.”
A fraction is not a number. (Of course we can, if we wish,
take a new unit—say, a fourth part of a cow’s equally divided
carcass—and then take three of these new units.)
As for “the square root of two,” it is not a number;
indeed, as we shall soon see, it is not even a fraction. And neither is “pi” a number.
To say it again, the numbers are: two units, three units,
four units, and so on—taking as many units as we please.
That is what Euclid tells us; and, after telling us, Euclid goes
on to speak of the relations among different numbers.
We learn, for example, that because fifteen “measures”
sixty—that is to say, because a multitude of fifteen units taken
FLAUMENHAFT
11
four times is equal to a multitude of sixty units—fifteen is
called “part” of sixty, and sixty is called a “multiple” of fifteen.
But fifteen is not “part” of forty, because you cannot get
a multitude of forty units by taking a multitude of fifteen
units some number of times. That is to say: the multitude of
fifteen units does not “measure” forty units. Both fifteen units
and forty units are, however, measured by five units; and five
units, which is the eighth part of forty units (the part obtained
by dividing forty units into eight equal parts), is also the third
part of fifteen units, so fifteen units is three of the eighth parts
of forty units. This is to say that fifteen units, which is not a
“part” of forty units, is “parts” of it. Indeed, a smaller number, if it is not part of a larger number, must be parts of it,
since both numbers must—just because they are numbers—be
measured by the unit.
After that, Euclid goes on to tell us about sorts of numbers, and the ways in which they are related, numbers such as
those that are “even,” or “odd,” or “even-times-even,” or
“even-times-odd,” or “odd-times-odd,” or “prime,” and so
on.
Numbers are thus of interest not only with respect to
their relations of size, but also with respect to their relations
of kind. Even and odd are distinguished by divisibility into
two equal parts (or by odd’s differing from even by a unit),
and the more complex terms here are distinguished with
respect to “measuring by a number according to another
number”—which nowadays would be stated thus: “dividing
by an integer so as to yield another integer as quotient without a remainder.”
Euclid thus defines some kinds of numbers by employing
notions such as being greater than or equal to or having a certain difference in size. However, he also sorts numbers into
kinds by referring to shape. What might lead to doing that?
We might use a dot to represent a unit, and then represent a number by dots in a line. For example, four would be
represented as it is at the top of Chart 1. We might then rep-
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THE ST. JOHN’S REVIEW
resent in a shape the number produced by taking a number
some number of times. For example, the number produced
when four is taken three times would be represented as it is
in the middle of the chart, where we see that the numbers
four and three are “sides” of the “plane” number twelve; and
similarly, six and four are “sides” of the “plane” number
twenty-four. But the number twenty-four can also be represented as a solid, as it is at the bottom of the chart: the numbers four and three and two are “sides” of the “solid” number twenty-four.
So Euclid speaks of numbers that are “sides,” “plane,”
and “solid,” and also of the multiplication of a number by a
number, and then of the sorts of numerical products of such
multiplication—such as the numbers called “square” and
“cube,” whose factors are called “sides.”
But he does not represent numbers by dots in lines. To use
dots would force us to pick this or that number. To signify not
this or that number, but rather any number at all, it is more
convenient to use bare lines, without indicating how many
dots are carried on each line, although it might be confusing
that we then also have to represent by a line the unit.
FLAUMENHAFT
13
On the other hand, since the unit does have a ratio to any
number, as does any number to any other number, and since
the product of multiplying any number by any other number
is also a number, it might make everything more convenient
if we represent as lines not just the numbers that are “sides,”
as well as any “side” that is a unit, but also all the figurate
numbers that we can produce. After all, though the sort of
number called a “square” number may be somehow different
from the sort of number called a “cube,” it is nonetheless true
that any “square” number has a ratio to any “cube” number
(since any number has a ratio to any other number), whereas
a square cannot have a ratio to a cube (since they are not magnitudes of the same kind). If we go along with speaking in this
way, however, we must take care to keep in mind that when
it is numbers that are called “sides” or “squares” or “cubes”
we are not engaged in speech about figures; we are using figures of speech. Several of the books of Euclid’s Elements deal
with what would nowadays be called “number theory” rather
than “geometry.”
The numbers in the classical sense—the multitudes two,
three, four, and so on—tell us the result of a count, and
nowadays we often speak as if those numbers, the countingnumbers, are merely some of the items contained in an
expanded system that we call “the real numbers.”
Whenever we put numbers of things together we get
some number of things, and whenever we take a number of
things a number of times we get some number of things; but
only sometimes can we take a given number of things away
from a given number of things, and even when we can, only
sometimes can we get some number of things by doing so. For
example, we cannot take seven things away from five things;
and although we can take six things away from seven things,
we will not have a number of things left if we do, but only a
single thing. It is also only sometimes that we can divide a
given number of things into a given number of equal parts. A
multitude of ten things can be divided into five equal parts,
but a multitude of eight things cannot. In dividing a many-
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THE ST. JOHN’S REVIEW
ness, there is constraint from which we are free in dividing a
muchness.
We often measure a muchness to say just how much of it
there is compared with some other muchness: having chosen
some unit of muchness, we count how many times such a unit
must be taken in order to be equal to the muchness that we
are measuring. A line, for example, is a kind of a muchness:
there is more line in a longer line than in a shorter line. If two
lines are not of equal size, one of them is greater than the
other. Lines are magnitudes. If we measure them, we obtain
multitudes that tell their sizes—their lengths. But magnitudes
are not multitudes. Whereas the size of a magnitude has to do
with how much of it there is, the size of a multitude has to do
with how many units it is composed of.
Not only magnitudes, but multitudes as well are often
measured: we measure these by using other multitudes to
measure them. Thus, we say that twelve is six taken two
times, or is twice six. We say, moreover, that eight is twice the
third part of twelve, or—to abbreviate—that eight is twothirds of twelve. “Two-thirds” does not name a multitude
(unless we say that we are merely treating a third part of
twelve as a new unit) but “two-thirds” is nonetheless a
numerical expression. If we therefore begin to treat it like the
name of a number, we are on the road to devising a system of
fractions. “Two-thirds” of something is less than one such
something, but it is not fewer. Two-thirds are fewer than
three-thirds—but to say this, we must have broken the unit
into three new and smaller units. The numerator of a fraction
is a number or else it is “one.” The denominator is also a
number: it is the number of parts that result from a division
(although we will allow a denominator as well as a numerator to be “one.”) With a fraction, we divide into equal parts
and then we count them. A fraction is not itself a number (a
multitude), but it may be the counterpart of a number.
“Twelve-sixths” is not the number “two”; but it is a counterpart, among the fractions, of the item “two” among the numbers. Another counterpart of the number “two” is the fraction
FLAUMENHAFT
15
“eight-fourths.” Those counterparts are really the same counterpart differently expressed, since they are both equal to the
fraction whose numerator is the number “two” and whose
denominator is “one.”
As with division, so with subtraction. In taking things
away, we may get a numerical expression that we can treat
like a number in certain respects. When we have twelve
horses and eight of them are taken away, there is a remainder
of four horses. But if eleven are taken away, then there are
not horses left; only a single horse remains. And if twelve
horses are taken away, then not even a single horse is left:
none remain. But twelve horses can be compared with a single horse: the twelve are to the one as twenty-four are to two.
“Twenty-four” and “two” are numbers, and “twelve” is also a
number—so “one” is like a number in being comparable with
a number as a number is. Moreover, “one” can be added to a
number as a number can be, and “one” is sometimes what we
reply when asked how many of some kind of thing there are.
“One” is therefore a numerical word even if it is not a number. But in that case, so is “none”: if twelve horses are taken
away, leaving not a single horse, and we are asked how many
remain, we can then say “none.” Now suppose that Farmer
Brown owes fourteen horses to Farmer Gray, but has in his
possession only ten horses. Farmer Gray takes away the ten.
How many horses does Farmer Brown now own? None. But
he might be said in some sense to own even less than none,
for he still owes four. If we did say that, then we would have
to say that he owns four less than no horses, or that fourteen
less than ten is four less than none. But then we would be
counting, not horses-owned, but horses-either-owned-orowed. We would be letting the payment of four-horses-owed
count as wealth equal to no-horses-either-owed-or-owned.
Again, as with the fractions, we have numerical expressions
that we are beginning to treat like numbers. We are on the
road to devising a system of so-called “rational numbers,”
which includes “negative” items as well as such non-negative
items as “zero” and “one” in addition to fractions (which
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include the counterparts of those multitudes that were first
called “numbers”—namely, two, three, four, and so on).
We must say “counterparts” because the multitude
“three,” for example, while it corresponds to, is not the same
as “the positive fraction nine-thirds” or “the positive integer
three.” We have not brought about an expansion of a number
system by merely introducing additional new items alongside
old ones; rather, we have made a new system which contains
some items that correspond to the items in the old system, but
that differ from the old items in being items of the very same
new sort as are the new items that do not have correspondents in the old system. For example: although the number
“three” is a multitude, “positive three” is not a multitude; it
is an item defined by its place in a system where, among other
things, “positive six” takes the place belonging to the item
that is the outcome of such operations as multiplying “negative two” by “negative three.”
We have just taken a look at part of the road that leads
from numbers in the classical sense to what we nowadays are
used to thinking of as numbers. We have looked at some steps
on the road to the so-called “rational numbers,” the so-called
numbers that have something to do with ratios. But the system of what we nowadays are used to thinking of as numbers
is the system of “real numbers,” only some of which are items
that have counterparts among the items in the system of
“rational numbers.” The system of what we nowadays are
used to thinking of as numbers is replete with “irrational
numbers,” some of them “algebraic” (such as “the square root
of two”) and some of them “transcendental” (such as “pi”).
Classically, numbers are multitudes, and there may be
some number-ratio that is the same as the relation in size of
some one magnitude to another. But there does not have to
be a number-ratio that is the same. If there did have to be
such a ratio of numbers for every ratio of magnitudes, then
there would not have been a reason for devising a system of
“real numbers.” The reason for taking the step from “rational
FLAUMENHAFT
17
numbers” to “real numbers” has to do with the difference
between multitudes and magnitudes.
The difference between how we can speak about multitudes (that is, numbers in the classical sense) and how we can
speak about magnitudes classically manifests itself in the
statements with which Euclid begins his treatment of magnitudes in the Fifth Book of the Elements and his treatment
afterwards of numbers in the Seventh Book.
Although Euclid says what number is, he does not say
what magnitude is. Examples of magnitudes can be found in
his propositions, however. After the Fifth Book of the
Elements demonstrates many propositions about the ratios of
magnitudes as such, these are used by later books of the
Elements to demonstrate propositions about such magnitudes
as straight lines, triangles, rectangles, circles, pyramids, cubes,
and spheres. Such magnitudes correspond to what we nowadays call lengths, areas, and volumes. Weight is yet another
sort of magnitude. Though weights are not mentioned in the
Elements, what Euclid says there about magnitudes generally
is applied by Archimedes to weights in particular.
At the beginning of the Fifth Book, Euclid defines ratio
for magnitudes; but at the beginning of the Seventh Book he
does not define ratio for numbers. There in the Fifth Book he
also defines magnitudes’ being in the same ratio, and only
after doing that does he define magnitudes’ being proportional. But here in the Seventh Book he does not define numbers’ being in the same ratio: he goes directly into defining
numbers’ being proportional, which he needs to do in order
to define the similarity of numbers that are of the sorts called
“plane” or “solid.”
The Greek term translated as “proportional” is analogon.
After a prefix (ana) meaning “up; again,” the term contains a
form of the word logos. This is the Greek term translated as
“ratio.” Logos is derived from the same root from which we
get “collect” (which is what the root means); and in most
contexts, it can be translated as “speech” or as “reason.”
Proportionality is, in Greek, analogia (from which we get
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THE ST. JOHN’S REVIEW
“analogy”), a condition in which terms that are different may
be said to carry or hold up again the same articulable relationship.
Later in the Elements, in the enunciation of the fifth
proposition of the Tenth Book, for example, Euclid does use
the term “same ratio” in speaking of ratios that are numerical. In the definitions with which the Tenth Book begins,
Euclid says that lines which have no numerical ratios to a
given straight line are called “logos-less”—that is, alogoi. This
Greek term for lines lacking any articulable ratios to a given
line is translated (through the Latin) as “irrational.”
Such a line and the given line to which it is referred cannot both be measured by the same unit, no matter how small
a unit we may use to try to measure them together. They are
“without a measurement together”—that is, asymmetra. This
Greek term is translated (through the Latin) as “incommensurable.” Because magnitudes of the same kind can be incommensurable, magnitudes are radically different from multitudes, and so we must speak of them differently.
Part Three
Muchness Not Related Like Manyness: Incommensurability
Let us turn now to the classic example of incommensurability: let us consider the relation between the side of a square
and its diagonal.
If a square’s diagonal were in fact commensurable with its
side, then the ratio of the diagonal to the side would be the
ratio of some number to some other number. But it cannot be
that. Why not? Because if it were, then it would have two
incompatible properties: one property belongs to any ratio
whatever which a number has to a number, and the other
property follows from that particular ratio which a square’s
diagonal has to its side. Let us convince ourselves that there is
such a contradiction.
First, let us look at that property which belongs to any
ratio whatever that is numerical. It is this: any numerical ratio
whatever must either be in lowest terms already, or be
FLAUMENHAFT
19
reducible to them eventually. Consider, for example, the ratio
that thirty has to seventy. Those two numbers have in common the factors two and five; so, dividing each of them by
ten, we see that the ratio that thirty has to seventy is the same
as the ratio that three has to seven. The ratio of three to seven
is the ratio of thirty to seventy reduced to lowest terms. If a
ratio of one number to another number were not reducible to
lowest terms, then the two original numbers would have to
contain an endless supply of common factors, which is impossible: any number must sooner or later run out of factors if
you keep canceling them out by division.
This property of every ratio that a number has to a number cannot belong to the special ratio that a square’s diagonal
has to its side. To see why this is so, consider a given square.
If you make a new square using as the side of the new square
the diagonal of the given square, then the new square will be
double the size of the original square.
Chart 2 shows that doubling. In the left-hand portion of
the chart, the diagonal of a square divides it into two triangles, and it takes four of these triangles to fill up a new square
which has as its own side that diagonal. In the right-hand portion, the chart also shows what happens if we now make
another new square, using as this newest square’s own side a
half of the diagonal of the original square. The original
square, now being itself a square on the newest square’s diagonal, will itself be double the size of this newest square—
since this newest square is made up of two triangles, and it
takes four of these triangles to make up the original square.
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THE ST. JOHN’S REVIEW
Let us suppose that it were in fact possible to divide a
square’s diagonal as well as its side into pieces that are all of
the same size. Let us count the pieces and say that K is the
number of pieces into which we have divided the diagonal,
and that L is the number of pieces into which we have divided
the side. By taking as a unit any of those equal pieces into
which we have supposedly divided the diagonal and the side,
we have measured the two lines together: the ratio which the
number K has to the number L would be the same as the ratio
which the square’s diagonal has to its side.
Now, disregarding for a moment just what ratio the number K has to the number L, but considering only that it is supposed to be a ratio of numbers—which, as such, must be
reducible to lowest terms—we can say that there would have
to be two numbers (let us call them P and Q) such that (1) P
and Q do not have a single factor in common and (2) the ratio
that P has to Q is the same ratio that K has to L. Since the
ratio that K has to L is supposed to be a ratio of numbers,
there cannot be any such pair of numbers as K and L unless
there is also such a pair of numbers as P and Q. (If the ratio
of K to L is already in lowest terms, then we will just let K
and L themselves be called by the names P and Q.) So now we
have P being the number of equal pieces into which the
square’s diagonal is divided, and Q being the number of such
pieces into which the square’s side is divided. And now we
will see that there just cannot be any such numbers as P and
Q because this pair of numbers would have to satisfy contradictory requirements.
The first requirement results from the necessities of numbers; the second, from the consequences of configuring lines.
Because (as has been said) the ratio of P to Q is a ratio of
numbers reduced to lowest terms, P and Q are numbers that
cannot have a single common factor; but (as will be shown)
because the ratio of P to Q is the same ratio that a square’s
diagonal has to its side, P and Q must both be numbers divisible by the number two. That is to say, P and Q are such that
they cannot both be divisible by the same number, and yet
FLAUMENHAFT
21
they also must both be divisible by the number two—a direct
contradiction.
Now we must see just why the latter claim is true. We ask:
why is it, that if any pair of numbers are in that special ratio
which a square’s diagonal has to its side, then both numbers
must be divisible by the number two?
In order to see why, we must first take note of another
fact about numbers: if some number has been multiplied by
itself and the product is an even number, then the number
that was multiplied by itself must itself have been a number
that is even. (The reason is simple. A number cannot be both
odd and even—it must be one or the other—and when two
even numbers are multiplied together, then the number that
is the product is also even; however, when two odd numbers
are multiplied together, then the number that is the product
is not even but odd.) That said, we are now ready to see why
it is that if any two numbers are in that special ratio which a
square’s diagonal has to its side, then they must have the factor two in common.
The numbers P and Q have the factor two in common
because both of them must be even. They must both be even
because each of them when multiplied by itself will give a
product that must be double another number—and therefore
each must itself be double some number. Why?
Look at the left-hand portion of Chart 3, and consider
why P must be an even number. Because the square on the
diagonal is double the square on the side, the number produced when P is taken P times is double the number produced
when Q is taken Q times. Hence (since any number which is
double some other number must itself be even) the multiplication of P by itself produces an even number, and hence the
number P itself must be even.
And now look at the right-hand portion of the chart, and
consider why Q also must be an even number. Since it has
already been shown that P must be an even number, it follows
that there must be another number that is half of P—call this
number H. But because the square on the side is double the
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THE ST. JOHN’S REVIEW
square on the half-diagonal, it follows that the number produced when Q is taken Q times is double the number produced when H is taken H times. Hence (since, as we said
before, any number which is double some other number must
itself be even) the multiplication of Q by itself produces a
number that is even, and hence the number Q itself must be
even.
Since both P and Q must therefore be even numbers, they
must have the number two as a common factor, even though
they cannot have any number as a common factor. It is therefore absurd to say that there is a pair of numbers like P and
Q. And hence there cannot be a pair of numbers like that K
and L which we supposed that there could be.
If a pair of numbers did in fact have the same ratio that
the square’s diagonal has to its side, then no matter how
many times we halved both numerical terms in the ratio, both
terms that we got would have to remain even. But no pair of
numbers can be like that. Each number of the pair would
have to contain the number two as a factor in endless supply.
Such a ratio would be irreducible to lowest terms, because no
matter how many common two’s we were to strike as factors
from the terms of the ratio, there would still have to be yet
FLAUMENHAFT
23
another two in each. No number, however, can contain an
endless supply of factors.
It is therefore self-contradictory to say that any ratio can
be a ratio of one number to another and also be the ratio of a
square’s diagonal to its side. To avoid being led into absurdity,
we must say that a square’s diagonal and its side are incommensurable.
The diagonal of a square and its side are not the only pair
of lines that are incommensurable. In the tenth proposition of
the Tenth Book of the Elements, Euclid begins to show us
how to find many incommensurable lines. After presenting
thirteen sorts of them, he concludes the Tenth Book by saying that from what he has presented, there arise innumerably
many others.
That makes it hard to say what we mean when we say that
one pair of lines is in the same ratio as another pair of lines.
Even if we could somehow ignore the difficulty with the ratio
of a square’s diagonal to its side, other ones like it would still
keep popping up all over the place, since the ratio of a
square’s diagonal to its side is only one of innumerably many
ratios of incommensurable lines. And it is not only with lines
that the difficulty arises. Whatever the kind of magnitudes
that are being compared, whatever it is with respect to which
they are greater or smaller, comparisons of muchness are not
as such reducible to comparisons of manyness. The sizes of
magnitudes cannot always be compared by comparing counts
obtained by measuring. Magnitudes of any kind can be
incommensurable. It is true that one cube may have to
another, or one weight may have to another, the same ratio
that three has to five, for example; but the one cube may have
to the other, or the one weight may have to the other, the
same ratio that a square’s diagonal has to its side.
Magnitudes are called “incommensurable”—incapable of
being measured together—not when they are of different
kinds, but rather when they are not measurable by the same
unit even though they are of the very same kind. Two magnitudes may be of the very same kind and yet it may be true that
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THE ST. JOHN’S REVIEW
whatever unit measures either one of them will not measure
the other one too. By a unit’s “measuring” a magnitude, we
mean that when the unit is multiplied (that is, when it is taken
some number of times), it can equal that magnitude.
Therefore, when magnitudes of the same kind are incommensurable, one of them has to the other a ratio that is not
the same as any numerical ratio.
The demonstrable existence of incommensurability
means that comparisons of size can only be approximated by
using numbers. We can, to be sure, be ever more exact—even
as exact as we please—but if we wish to speak with absolute
exactness, numbers fail us.
For the ancient Pythagoreans, who were the first to conceive of the world as thoroughly mathematical, knowledge of
the world was knowledge of numerical relationships. In the
world stretching out around us, the Pythagoreans saw correlations between shapes and numbers, such as we encountered
when we considered kinds of numbers, “square” numbers
and “cube” numbers, for example.
The Pythagoreans noted also that the movements of the
heavenly bodies take place in cycles. Their changes in position, and their returns to the same configuration, have
rhythms related by recurring numbers that we get by watching the skies and counting the times. With numbers, the
world goes round. We are surrounded by a cosmos. (Cosmos
is the Greek word for a “beautiful adornment.”) The beauty
on high appears to us down here in numbers.
But even the qualitative features of the world of nature
show a wondrous correlation with numbers: numbers make
the world sing. It is not merely that rhythm is numerical, it is
that tone or at least pitch, is too. If a string stretched by a
weight is plucked, it gives off some sound. The pitch of the
sound will be lowered as the string is lengthened. If another
string is plucked (a string of the same material and thickness,
and stretched by the same weight) then the longer the string
the lower will be the pitch of the sound produced by plucking it. Now, what set the Pythagoreans thinking was the rela-
FLAUMENHAFT
25
tion between numbers and harmony. (Harmonia is the Greek
word for “the condition in which one thing fits another”; a
word from carpentry thus is used to describe music.) When
the lengths of two strings of the sort just mentioned are
adjusted so that one of them has to the other the same ratio
that one small number has to another, or to the unit, then
there is music. With the Pythagoreans’ mathematicization of
music, mathematical physics begins.
Thus not only were the sights on high seen to be an
expression of mathematical relationships, so were the sounds
down here that enter our souls and powerfully move what
lies deep down within us. Thinking that nature is a display of
numerical relationships, and that human souls are gotten into
order by attending to those relationships, the Pythagoreans
formed societies that sought to shape the thinking of the
political societies of their time by being the givers of their
laws. It is said that when the discovery of incommensurability was first revealed to outsiders, thus making public the
insufficiency of number, the man who thus had undermined
the Pythagorean enterprise was murdered.
But never mind the whole wide world; even the relationships of size in mere geometrical figures cannot be understood simply in terms of multitudes. If geometry could in fact
be simply arithmeticized; if we could just measure lines
together, getting numbers which we could then just multiply
together, and thus simply express as equations all the relationships that we have to handle, then much in Euclid, in
Apollonius, and in the other classical mathematicians that is
difficult to handle could be handled much more easily—and
Descartes in the seventeenth century would not have had to
undertake a radical transformation of geometry. Instead of
manipulating equations, however, we must in the study of
classical mathematics learn to deal with non-numerical ratios
of magnitudes, and with boxes that are built from lines
devised to exhibit those ratios.
However, before we can freely deal with ratios, we must
learn what can be meant by calling two ratios the same—even
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THE ST. JOHN’S REVIEW
when they are not the same as some numerical ratio. Euclid
tells us that in the Fifth Book of the Elements. That is long
before his discussion of number, which does not take place
until the Seventh Book, thus raising a question about what
kind of a teacher he is: after all, is it not a principle of good
teaching that questions should be raised before answers are
presented?
Incommensurability is responsible for the difficulty of
Euclid’s definition of sameness of ratio for magnitudes, as
well as for the difficulty that modern readers encounter in the
classical presentation of relationships of size generally. Let us
now look at that definition.
Part Four
Muchness Related After All: Euclid’s Definition of Same
Ratio
We insist that even when two magnitudes are incommensurable, their ratio can be the same as the ratio of two other
incommensurable magnitudes. For example, we insist that the
ratio which one square’s diagonal has to its side is the same
ratio which another square’s diagonal has to its own side.
Sameness of ratio for magnitudes is therefore not to be
defined in terms of measuring magnitudes: we could so define
it only if we could divide each of the magnitudes into pieces,
each equal to some magnitude that is small enough to be a
suitable unit, and then, when we counted up all of those small
equal pieces, we found no left-over unaccounted-for evensmaller piece of either of the magnitudes; but we cannot do
that with magnitudes that are incommensurable. Although we
can say that two ratios of magnitudes are the same as each
other if they are both the same as the same ratio of numbers,
we will not say that they are the same as each other only if
they are both the same as the same ratio of numbers.
What, then, is to be said instead? According to Euclid,
this: “Magnitudes are said to be in the same ratio, the first to
the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equi-
FLAUMENHAFT
27
multiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of,
the latter equimultiples respectively taken in corresponding
order.”
When Euclid says for ratios of magnitudes, what sameness is, it is very difficult at first to understand just what he
means. While his definition may be the proper departure
point on a road that we need to travel, for a beginner it seems
to constitute a locked gate.
A key to open that locked gate, however, is this fact:
while there is no ratio of numbers that is the same as a ratio
of incommensurable straight lines, nonetheless every ratio of
numbers is either greater or less than such a ratio of straight
lines. That is to say: whatever ratio of numbers we may take,
we can decide whether the ratio of one line to another is
greater or less than it.
For example, we might ask: which is greater—the ratio of
the one line to the other, or the ratio of seven to twelve? We
would divide the second line into twelve equal parts, and
then take one of those pieces in order to measure the first
line. Suppose that this first line, although it may be longer
than six of these pieces put together, turns out to be shorter
than seven of them. We would conclude that the first line has
to the other line a ratio that is less than the numerical ratio of
seven to twelve.
Let us consider the ratio of lines that has been of such
concern to us, the ratio which a square’s diagonal has to its
side. And let us take the following ratio of numbers: the ratio
which that three has to two. As we have seen, the ratio of
lines that we are considering cannot be the same as any ratio
of numbers whatever; so it must be either greater or else less
than that ratio of numbers which we have taken. Which is it?
It must be less—because if it were greater (that is: if the
diagonal were greater than three-halves of the side), then the
diagonal taken two times would have to be greater than the
side taken three times. But if that were so, then a new square
whose side was the diagonal of the original square would
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have to be more than double the original square, as is shown
in Chart 4.
Having thus shown that the ratio of a square’s diagonal to
its side is less than the ratio which three has to two, we could
in like manner also show that the ratio of those two lines is
greater than the ratio that, say, four has to three. And we
could go on showing, for the ratio of any pair of numbers
which we choose, that the ratio of a square’s diagonal to its
side is greater or is less than the ratio of the pair of numbers
chosen.
Indeed, although no ratio of numbers is the same as the
ratio of a square’s diagonal to its side, we can nonetheless
confine this ratio of lines as closely as we please by using pairs
FLAUMENHAFT
29
of ratios of numbers, as follows. (The results are shown in
Chart 5.) Let us divide the square’s side into ten equal parts,
and take such a tenth part as the unit; then the diagonal will
be longer than fourteen of these units but shorter than fifteen
of them; then let us consider what we get when we take as the
unit the side’s hundredth part, and then its thousandth. We
can go on and on in that way, eventually reaching numbers
large enough to give us a pair of number-ratios that differ
from each other as little as we please; we can show it to be
greater than the ever-so-slightly-smaller number-ratio, and
smaller than the ever-so-slightly-greater number-ratio. So,
although the ratio of a square’s diagonal to its side cannot be
the same as any number-ratio, it can be confined between a
pair of number-ratios that differ from each other as little as
we please.
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The question that we want to answer, however, is not
when it is that ratios of magnitudes are almost the same, but
rather when it is that they are the very same—even when they
are not both the same as the same ratio of numbers. The key
to the answer, restating what we said, is this: given any ratio
of magnitudes, any ratio of numbers that is not the same as it
must be either greater than it or smaller.
That gives us the following answer: given two ratios of
magnitudes, they will be the same as each other (whether or
not they are the same as some ratio of numbers) whenever it
is true that—taking any ratio of numbers whatever—if this
ratio of numbers is greater than the one ratio of magnitudes,
then it is also greater than the other; and if it is less than the
one, then it is also less than the other.
Euclid’s definition seems much more complicated than
that, however, because it emphasizes “equimultiples.” Why
does it do that? Because that makes it simpler to compare
ratios of magnitudes with ratios of numbers: taking multiples
is a way to make the comparisons without performing any
divisions. We could in fact get a definition by using division,
but the definition would be clumsier if we did.
Let us put the notion of equi-multiples aside for a
moment, and consider multiples simply, in contradistinction
to divisions into parts.
Suppose, for example, that the ratio of some magnitude
(A) to another magnitude (B) is greater than the ratio of nine
to seven but less than the ratio of ten to seven. This means
that if we divide B into seven equal parts and we use as a unit
(for trying to measure A) one of those seventh parts of B, then
A will turn out to be greater than nine of those parts of B, but
less than ten of them. If A and B happen to be incommensurable, then, no matter how many equal parts into which we
divide B—that is, no matter how small we make the B-measuring unit with which we try to measure A, we will find that
we cannot divide A into pieces of that size without having a
smaller piece left over.
FLAUMENHAFT
31
So, in comparing the ratio of A to B with the numerical
ratio of some multitude m to some multitude n, it is less awkward to speak of A-taken-n-times and of B-taken-m-times
than to speak of the little piece of A that may be left over
when we divide A into m pieces that are each equal to the nth
part of B—or, in other words, the little piece that may be left
over in A, no matter how small are the equal parts into which
we divide B. To make the requisite comparisons, we must
consider multiples of magnitudes, but we need not consider
parts of them; we have to multiply, but we do not also have
to divide. Instead of trying to measure magnitudes together,
by dividing them and counting the parts, we can speak merely
of multiples of the magnitudes.
What we have just now seen is this: to say that the ratio
of magnitude A to magnitude B is either the same as the
numerical ratio of m to n, or is greater or less than it, is to say
that A-taken-n-times is either equal to B-taken-m-times, or is
greater or less than it. Let us take that and put it together with
what we saw earlier—which was this: to say that the ratio of
A to B is the same as the ratio of C to D is to say that whatever numerical ratio you may take (say, of m to n) this ratio
of numbers will not be the same as, or greater than, or less
than one of the ratios of magnitudes unless it is likewise so
with respect to the other one.
All that remains is for multiples of a certain sort to be
brought in—namely, “equi-multiples.” Equimultiples of two
magnitudes are two other magnitudes that are obtained by
multiplying the two original magnitudes an equal number of
times. Here, as Chart 5 shows, both ratios’ antecedent terms
(namely, A and C) are each taken n times, and their consequent terms (namely, B and D) are each taken m times. In
other words, equimultiples (nA and nC) are taken of the first
and third magnitudes (A and C); and also equimultiples (mB
and mD) are taken of the second and fourth magnitudes (B
and D). And m and n are any numbers at all: we are interested
in all the equimultiples of the first and third magnitudes, and
also of the second and fourth ones.
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Now at last we are in a position to see that Euclid’s definition is not so bewildering as might have seemed at first
glance. There are several ways of saying what we can do with
what we have seen. In abbreviated form, they are exhibited in
Chart 7.
FLAUMENHAFT
33
Now in interpreting the chart, just remember that whenever we say “IF something, THEN something else,” that is
equivalent to saying “NOT something UNLESS something
else.” So, the ways laid out in the chart are these:
First way: Staying with ratios, we can say that two ratios
of magnitudes (call them the ratios of A to B, and of C to D)
are the same if, and only if, whatever numerical ratio we may
take (say the ratio that some number called m has to some
other number called n) the following is true: that numerical
ratio which m has to n will not be the same as, or greater
than, or less than one of the two ratios of magnitudes, unless
it is likewise so with respect to the other one.
Second way: We might want to get more explicit by making divisions into equal parts—that is, divide B into n equal
parts and do the same to D (these, B and D, being the conse-
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THE ST. JOHN’S REVIEW
quent terms of the two ratios). Then the ratios would be the
same if the following is true: antecedent term A will not be
greater than, or less than, or equal to m of those nth parts of
its consequent term B unless the other antecedent term C is
likewise so with respect to that same number m of those nth
parts of its own consequent term D.
Third way: Someone who was willing to do all that
(namely, willing to divide magnitudes into equal parts and
then count them up and compare sizes) might insist on using
fractions to restate that as follows: A will not be greater than,
or less than, or equal to m/nths of B unless C is likewise so
with respect to that same fraction (m/nths) of D.
Fourth, and final way: Rather than getting into the complicated business of dividing, counting divisions, and comparing sizes, even though we can briefly restate it all by using
fractions, we might simply take multiples alone; and then we
would say that the ratios are the same if the following is true:
A-taken-n-times will not be greater than, or less than, or
equal to B-taken-m-times unless C-taken-exactly-as-manytimes-as-A is likewise so with respect to D-taken-exactly-asmany-times-as-B.
Those are several ways to determine, despite incommensurability, when we may say that the ratio of one magnitude
to another is the same as the ratio of a third magnitude to a
fourth one. The first way formulates our initial insight, and
the final way formulates Euclid’s definition of same ratio for
magnitudes. Euclid’s definition, like the others, covers all
ratios of magnitudes, whether or not they are the same as
ratios of multitudes; but, unlike the others, it manages to do
so by speaking simply of multitudes of magnitudes.
Magnitudes and multitudes are not the same as each
other, nor is either of them the same as ratios of them, but
magnitudes and multitudes and their ratios are all, in a way,
alike. How?
In the first place, any two magnitudes of the same kind
are equal, or else one of them is greater than the other; and
likewise, any two multitudes are equal, or else one of them is
FLAUMENHAFT
35
greater than the other. Moreover, any magnitude has a ratio
to any other magnitude of the same kind, just as any multitude has a ratio to another multitude. Finally, any two ratios
(whatever it may be that they are ratios of, whether magnitudes or multitudes) are the same as each other, or else one of
them is greater than the other. This last fact supplies the
insight that enabled Euclid to define same ratio for magnitudes regardless of whether the magnitudes are commensurable.
Euclid’s definition can help us to understand what
enabled Dedekind several thousand years afterward to define
“the real numbers” in terms of “the rational numbers.”
Dedekind found himself in the following situation. In modern times, after proportions containing magnitudes and multitudes had given way to equations containing “real numbers,” there was still some difficulty in saying just what “real
numbers” were. To say much about the matter, it seemed necessary to refer not only to multitudes to which we come by
counting (that is, numbers in the strict sense) but also to magnitudes that we visualize (namely, lines). If we place the
counting numbers along a line (as in the top portion of Chart
8), it is then clear not only where to put all the “rational numbers,” including those which are fractional and those which
are non-positive (as in the middle portion of the chart)—but
also where to put such “irrationals” as “the square root of
two.” To put “the square root of two” in its place, for example, (as in the bottom portion of the chart) just erect a square
that has a side that is a unit long, and swing its diagonal
down.
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But if “the square root of two” is a number, it should be
definable without appealing to visualization. After all, we
need not visualize in order to count, or even to go on to think
up fractions and negatives. That thought troubled Dedekind
as he taught calculus in the nineteenth century, relying upon
appeals to a number-line. He finally saw how to treat “real
numbers” (the modern counterpart of Euclidean ratios of linear magnitudes) in terms of collections of “rational numbers”
(the modern counterpart of Euclidean ratios of numbers),
thus making it more plausible to speak of the “real numbers”
as really numbers.
Reading Dedekind is one way to think about what it
means to rely on a system of “real numbers.” Unless we do
think through the meaning of relying on a system of real
numbers, many of the things we take for granted in the modern world are without foundation.
But does Dedekind’s work simply represent progress
beyond Euclid’s, or are very important differences covered
over by the important similarities between what Dedekind
had his mind on and Euclid his?
Ratios relate multitudes, or magnitudes. Ratios (like multitudes) have homogeneity, and also (like magnitudes) have
continuity; but magnitudes do not have homogeneity, and
multitudes do not have continuity. Ratios themselves are
FLAUMENHAFT
37
therefore not things of the very same sort as the things that
they relate.
Ratios are not things of the same sort as quotients either.
To be sure, ratios are like quotients in that they are quantitative. Like any two magnitudes of the same sort, or any two
multitudes—or any two quotients—any two ratios (whether
of magnitudes or of multitudes) have an order of size. But
quotients, unlike ratios, are like what they are quotients of: a
quotient is itself a “real number” that is obtained through the
operation of dividing a “real number” by a “real number”; if
A and B are “real numbers,” then the quotient A/B is a “real
number” also.
Yet, although ratios and “real numbers” are things of different sorts, they do have a similarity—and not merely that
they are both quantitative. Although the magnitudes are not
homogeneous, and the multitudes are not continuous, the
ratios are both homogeneous and continuous—and so also
are “the real numbers.”
Part Five
Mathematics and the Modern Mind
In all this, we have been considering the classical handling of
numbers and lines in its difference from modern notions
which conflate the two, but we have not considered what it
was that led to the conflation. That is, indeed, an immensely
important matter, but it is too long a story to be told now. To
tell that tangled tale, one must traverse much of the road that
constitutes the Mathematics Tutorial at St. John’s College.
Along that arduous road, it is easy to be overwhelmed, however, and thus to lose sight of why it is worth our while to traverse it at all—so perhaps at least something should be said
about it now.
Euclid’s Elements prepares us for a higher study in geometry, the Conics of Apollonius. This was, for almost two-anda-half millenia, the classic text on the curves which—following the innovative terminology of Apollonius—came to be
called the “parabola,” the “hyperbola,” and the “ellipse.”
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Apollonius’ conic sections were lines first obtained upon a
plane by cutting a cone in various ways; they were then characterized by relative sizes and shapes of certain boxes formed
by associated straight lines standing in certain ratios. After
Descartes, although the names of those curves persisted, and
they continued to be called collectively “the conic sections,”
they nonetheless eventually ceased to be studied as such: they
came to be studied algebraically. But although Descartes’
Geometry may be in fact what it has been called—the greatest single step in the progress of the exact sciences—no one
could clearly see it as that without studying Apollonius, for
Cartesian mathematics has shaped the world we live in and
shapes our minds as well.
Apollonius tells his tale obliquely. He does not give us
questions, but rather gives us only answers that are too hard
to sort out and remember unless we ourselves figure out what
questions to ask. About Apollonius as a teacher we must ask
whether his work is informed by wisdom and benevolence.
Descartes did not think so. In his own Geometry, and in his
sketch of rules for giving direction to the native wit,
Descartes found fault with the ancient mathematicians.
Descartes severely criticizes them—for being show-offs.
He says that they made analyses in the course of figuring
things out, but then, instead of being helpful teachers who
show their students how to do what they themselves had
done, they behaved like builders who get rid of the scaffolding that has made construction possible. Thus they sought to
be admired for conjuring up one spectacular thing to look at
after another, without a sign of how they might have found
and put together what they present.
Descartes also suggests, however, that they did not fully
know what they were doing. They did not see that what they
had could be a universal method. They operated differently
for different sorts of materials because they treated materials
for operation as simply objects to be viewed. Hence they
learned haphazardly, rather than methodically, and therefore
they did not learn much. Mathematics for them was a matter
FLAUMENHAFT
39
of wonderful spectacle rather than material for methodical
operation. The characteristic activity of the ancient mathematicians was the presentation of theorems, not the transmission and application of the ability to solve problems.
They had not discovered the first and most important
thing to be discovered: the significance of discovery. They
had not discovered the power that leads to discovery and the
power that comes from discovery. They were not aware that
the first tools to build are tools for making tools. They were
too clever to be properly simple, and too simple to be truly
clever. They were blinded by a petty ambition. Too overcome
by their ambition, they could not be ambitious on the greatest scale.
Were the ancient mathematicians as teachers guilty of the
charges set out in that Cartesian critique? Were they guilty of
the obtuseness of which Descartes in his Geometry accused
them—were they guilty of the desultory fooling-around and
disingenuous showing-off of which Descartes had accused
them earlier, in his Rules? You cannot know unless you study
them.
In any case, the study of Euclid and Apollonius gives
access to the sources of the tremendous transformation in
thought whose outcome has been the mathematicization of
the world around us and the primacy of mathematical physics
in the life of the mind. Scientific technology and technological science have depended upon a transformation in mathematics which made it possible for the sciences as such to be
mathematicized, so that the exact sciences became knowledge
par excellence. The modern project for mastering nature has
relied upon the use of equations, often represented by graphs,
to solve problems. When the equation replaced the proportion as the heart of mathematics, and geometric theoremdemonstration lost its primacy to algebraic problem-solving,
an immense power was generated. It was because of this that
Descartes’ Geometry received that accolade of being called
the greatest single step in the progress of the exact sciences.
To determine whether it was indeed such a step, we need to
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know what it was a step from as well as what it was a step
toward. We cannot understand what Descartes did to transform mathematics unless we understand what it was that
underwent the transformation. By studying classical mathematics on its own terms, we prepare ourselves to consider
Descartes’ critique of classical mathematics and his transformation not only of mathematics but of the world of learning
generally—and therewith his work in transforming the whole
wide world.
It is in the study of Apollonius on the conic sections that
the modern reader who has been properly prepared by reading Euclid can most easily see both the achievement of classical mathematics and the difficulty that led Descartes and his
followers to turn away from it.
It all has to do with ratio, and with notions of number
and of magnitude. For Apollonius, as for Euclid before him,
the handling of ratios is founded upon a certain view of the
relation between numbers and magnitudes. When Descartes
made his new beginning, almost two millenia later, he said
that the ancients were handicapped by their having a scruple
against using the terms of arithmetic in geometry. Descartes
attributed this to their not seeing clearly enough the relation
between the two mathematical sciences. Before modern readers can appreciate why Descartes wanted to overcome the
scruple, and what he saw that enabled him to do it, they must
be clear about just what that scruple was. Readers must, at
least for a while, make themselves at home in a world where
how-much and how-many are kept distinct, a world which
gives an account of shapes in terms of geometric proportions
rather than in terms of the equations of algebra. For a while,
readers must stop saying “AB-squared,” and must speak
instead of “the square arising from the line AB”; they must
learn to put ratios together instead of multiplying fractions;
they must not speak of “the square root of two.”
Mathematical modernity gets under way with Descartes’
Geometry. By homogenizing what is studied, and by making
the central activity the manipulative working of the mind,
FLAUMENHAFT
41
rather than its visualizing of form and its insight into what
informs the act of vision, Descartes transformed mathematics
into a tool with which physics can master nature. He went
public with his project in a cunning discourse about the
method of well conducting one’s reason and seeking the truth
in the sciences; and this discourse introduced a collection of
scientific try-outs of this method, the third and last of which
was his Geometry.
For those who study Euclid and Apollonius in a world
transformed by Descartes, many questions arise: What is the
relation between the demonstration of theorems and the solving of problems? What separates the notions of how-much
and how-many? Why try to overcome that separation by the
notion of quantity as represented by a number-line? What is
the difference between a mathematics of proportions, which
arises to provide images for viewing being, and a mathematics of equations, which arises to provide tools for mastering
nature? How does mathematics get transformed into what
can be taken as a system of signs that refer to signs—as a symbolism which is meaningless until applied, when it becomes a
source of immense power? What is mathematics, and why
study it? What is learning, and what promotes it?
With minds that are shaped by the thinking of yesterday
and of the days before it, we struggle to answer the questions
of today, in a world transformed by the minds that did the
thinking. We will proceed more thoughtfully in the days
ahead if we have thought through that thinking for ourselves.
Our scientific past is not passé.
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43
The Husserlian Context of
Klein’s Mathematical Work
Burt C. Hopkins
I have to begin my remarks with the admission of my ignorance about their ultimate topic, which is neither Edmund
Husserl’s nor Jacob Klein’s philosophy of mathematics nor,
for that matter mathematics itself, but numbers. I do not
know what numbers are. To be sure, I can say and read, usually with great accuracy, the numerals that indicate the prices
of things, street addresses, what time it is, the totals on my
pay stubs, the typically negative balance in my checkbook at
the end of each month, and so on. Moreover, I know how to
count and calculate with them, though usually with less accuracy no matter how much I try to concentrate on what I am
doing.
But if I am asked or try to think about what they are
when, for instance, I say my address is six hundred fifty-three
Bell Street, or that my house has two bedrooms, or that I only
have twenty bottles of wine left, it is obvious to me that I do
not know what I am talking about. Of course, I know that my
address refers to my abode, that my bedrooms are the rooms
in the house with beds, and that my wine is something I drink
solely for its medicinal purposes. But the six hundred fiftythree, the two, or the twenty, what are they? I do not know.
Likewise, if I am asked or try to think about what the
numbers are with which I calculate, when for instance I think
that because I need one-half pound of steak per person to
feed each of my dinner guests, that I expect five guests, and
that therefore I need two and a half pounds to feed my guests,
Burt Hopkins is Professor of Philosophy at Seattle University, and is Secretary
of the International Circle of Husserl scholars. He is the author of a book,
forthcoming from the University of Wisconsin Press, entitled Edmund Husserl
and Jacob Klein on the Origination of the Logic of Symbolic Mathematics:
An Inquiry into the Historicity of Meaning.
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THE ST. JOHN’S REVIEW
or when I think that the price of two and a half pounds of
steak, at eight ninety-nine per pound is twenty-two dollars
and forty-seven and a half cents, I know well enough what
dinner guests, steak, and dollars and cents are. But the one
half and the eight ninety-nine with which I calculate, and the
two and a half and twenty-two and forty-seven and a half that
are the results of my calculations, what are they? I do notknow.
Some among us will say and, indeed have already said for
a long time, that numbers, any numbers, are amounts of
things, specifically, amounts of whatever it is that we count in
order to answer the question how many of the things in question there are. In my examples above, to talk or think about
two as the amount of my bedrooms, twenty as the amount of
my bottles of wine, five as the amount of my dinner guests,
eight ninety-nine as the amount of money it takes to buy a
pound of steak, twenty-two and forty-seven and a half as the
amount of money it takes to buy two and a half pounds of
steak, certainly does seem to make sense. But what about my
house address? Is six hundred fifty-three the answer to the
question of how many of my house? Or is the one half pound
of steak needed to feed each dinner guest the answer to the
question how many of pounds of steak? The numbers here do
not straight away appear to be telling us how many houses my
house is, since the answer to that question is that it is not
many at all but one; neither do numbers tell us how many
pounds of steak are needed to feed each dinner guest because
each does not need many pounds at all but only a half a
pound. And, to complicate things deliberately, let us consider
what it means, numerically speaking, if I have a negative balance in my checkbook at the end of the month. Whatever the
amount of the negative number, let us hypothetically say it is
an even negative one hundred six dollars, that certainly does
not seem to provide the answer to the question of how many
dollars and cents I have.
For the moment, however, let us push these concerns
aside and assume that a number really is the amount of some-
HOPKINS
45
thing. Moreover, let us suppose that the amount of something
or its number first makes sense to us when we count more
than one of something. Finally, let us suppose that any group,
that is, any collection of more than one of something, no matter how big, has a number, which is to say, an exact or definite amount that answers the question how many with
respect to the things in the group, and that this can be arrived
at by counting. Does this really answer the question what a
number is? Or, more precisely, does this really answer the
question what numbers are? I say numbers because when we
count we always use more than one number to arrive at the
exact amount of something, even though once we arrive there
we conclude the count by saying a single number.
What, then, are the numbers two, three, seven, or, if I
have a lot of enumerative stamina, five hundred eighteen, that
I say when, having nothing better to do, I count the grains of
sand I have decided to put into separate piles? Or, what are
the numbers two, three, seven, five hundred eighteen, that I
say when I count the crystals of salt that I use to duplicate the
numbers of grains of sand I previously put into piles? The
things counted and therefore their amounts are not the same;
that is to say, an amount of grains of sand and an amount of
salt crystals are different things. But are their numbers the
same? Is the two that is the amount of grains of sand the same
two that is the amount of crystals of salt?
If number is supposed really to be the amount of something, and if the stress is placed on the of something, then
number, as its (the something’s) amount, would be nothing
more or less than the two grains of sand, or, the two crystals
of salt, both of which, being different somethings, would also
be different numbers. This situation would be illustrated were
I to say that there are a number of people I do not know in
the room. If I proceeded to count them, whatever number I
came up with would be not just an exact amount of anything
whatever, but precisely the exact amount of people I do not
know in the room.
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On the other hand, if the stress were placed on the how
many of the amounts in question, then two would indeed be
how many grains of sand and crystals of salt there are in my
smallest piles of each, and therefore their amounts and hence
numbers would indeed be the same. This situation would be
illustrated were I to say all dogs, if they are naturally formed,
have the same number of legs, namely, four. The exact number is the same, though the legs are not, because, silly as it
sounds to say this, different dogs have different legs.
Now some might want to put an end to this whole line of
inquiry, but especially to my last question about whether
numbers of different things are different or the same, by saying that the obvious answer is that what numbers are are
abstract concepts. Hence they are really ideas, ideas that we
can relate to different things when we want to count or want
to apply the results of our calculations. But we do not have
to. Thus I can add 4 to 6 and get 10. I can multiply 10 times
10 and get 100, and so on, without having to think or answer
anybody’s question about 4 of what, or 6 of what, or 10 of
what, and so on. Just as it makes perfect sense to say that 2
plus 2 is 4, it does not make any sense to say 2 plus 3 is 4,
because everybody who can count knows 2 plus 3 is 5.
Perhaps. But perhaps not. And this is where Husserl and
then eventually Klein come in. But first Husserl. It is generally known that Edmund Husserl, the German philosopher
who, as the founder of the so-called phenomenological movement in philosophy, was responsible for one of the two dominant approaches to philosophy in the last century (the other
being so-called analytic philosophy), was originally a mathematician. Known likewise is that his first book, published in
1891, is titled Philosophy of Arithmetic.1 However, the contents of this book are not so well known, because, among
other reasons, soon after its publication both its author and
Gottlob Frege had some very critical things to say about
them.
For our purposes, however, the contents of the book are
more important than their criticism of them. From beginning
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47
to end, the book concerns the answer to the question whether
numbers are really abstract concepts that make perfect sense
without saying or thinking what they are numbers of; or
whether to make sense as numbers, numbers have to be spoken or thought about as being numbers of something. Husserl
began his answer to this question by first distinguishing
between two kinds of numbers, one of which he called
“authentic” and the other “symbolic.” We will discuss the latter first, because even though, as its name suggests, it is the
less authoritative kind of number, it is also the one with
which we are usually more familiar. A number is symbolic in
Husserl’s understanding when the number and the sign used
to designate it are indistinguishable. For example: 3. Most of
us have no doubt been taught or learned that this is the number three rather than what it really is, which is a number sign
or numeral. Indeed, even though most of us are also aware of
other numerals, for instance, Roman numerals, my suspicion
is that when we see such numerals we immediately interpret
what they really mean in terms of our numeral system, a system that was actually invented by the Arabs. A symbolic number, then, is a number that most of us—with or without thinking about it—identify with the sign that we either write or
read.
Most of us, that is, unless we have thought about the fact
that the signs used to designate numerals, and therefore these
numerals themselves, are based on what were originally and
still remain conventions, even if they are no longer recognized as such. Different conventions mean different numerals, as we have just seen. But what about the numbers? Do
different numerals mean different numbers? Many when
faced with this question conclude no. Their thinking here is
that numbers remain the same, however different the numerals that express them, because numbers are really concepts.
Hence, no matter what numeral or word is used to express
the number three, ‘three’ is a concept that remains the same
because it is not identical with some numeral (which is subject to change) or with a word from some language (which is
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subject to variability). Moreover, for just this reason number
is a properly abstract concept: it remains identical with itself
no matter what sign or word is used to express it.
Despite the sophistication of this view of number, it is
dead wrong according to Husserl, because if numbers were
really abstract concepts in this sense, then the most basic
operation of arithmetic—addition—becomes unintelligible.
For instance, if in adding the number two to the number two,
what we are really adding is the abstract concept of the number two to another (!) abstract concept of the number two,
then arriving at their putative sum, the abstract concept
‘four’, becomes a great mystery. Most obviously, there is the
problem of how a concept that is supposed to remain identical can nevertheless change into another concept that is also
supposed to remain identical. That is, the abstract concept
‘two’ is not supposed to be able to change as words and signs
can and do, but to remain what it is, namely, the number two.
Yet precisely this supposition has to be abandoned if talk of
adding the concept of two to the concept of two to get the
concept of four is to make sense, since when the number two
is added to the number two the sum is not two number twos
but the number four.
Indeed, it is precisely this consideration that led Husserl
to the realization that authentic numbers are not abstract concepts. This is, admittedly, a difficult thought. What, then, are
they, these authentic numbers, if they are not abstract concepts? Husserl’s answer is that they are the definite amounts
of definite things that have been grouped together by the
mind. What kind of things? Literally any kind. What definite
amounts? Pretty much the first ten, namely two, three, four,
five, six, seven, eight, nine, ten. Why are zero and one not
among these? Because they are not definite amounts, which in
the case of zero is obvious, while in the case of one is less so
but still fairly obvious, since one is not an amount; it is not
many. What has the mind to do with authentic numbers?
Plenty for Husserl, since not only do authentic numbers first
show up in counting, but also, only those definite things can
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49
be counted that have been grouped together by it to compose
what Husserl, and as we shall also see, ancient Greek philosophers and mathematicians, called a multiplicity. Moreover—
and this is the most important consideration for our purposes—an authentic number really is something that manifestly cannot be found in either the reality of the definite
things that are counted or in any relationship among them.
This last point requires closer scrutiny. If we ask how is it
that the first authentic number, two, is able to register a definite amount of definite things as ‘two’, in the sense that in
saying or thinking the number two, the things in question are
recognized as being exactly two with regard to their number,
we are then asking about something that is different from the
things that this number numbers as two. Husserl, following a
long philosophical and mathematical tradition, refers to what
is asked about in this question as the unity of this number. In
asking it, we are asking how it is that distinct things, in this
case two of them, can nevertheless be brought together as
precisely this, namely, the two that is articulated by the number two. This all-important question about the unity of
authentic numbers becomes more explicit when we consider
Husserl’s reason for thinking that only the first ten or so definite amounts can be authentic numbers. Husserl’s reason is
deceptively simple: the mind can only apprehend—all at
once—each of the definite items that are numbered in a number when these things do not exceed ten. When the amount
of definite things in a multiplicity of things exceeds ten, each
one of them cannot be apprehended all at once by the mind
as when, for instance, it counts thirty of them.
These considerations, do not provide us yet with
Husserl’s answer to the question of the unity of authentic
numbers, but only address what is at stake in it. What is at
stake is that in registering the definite amount of definite
things, an authentic number is bringing them together in a
way that cannot be explained by each of the things so brought
together, no matter whether these are considered by themselves or as each relates to the other things. Each considered
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by itself cannot explain it for the simple reason that authentic numbers are always amounts of something that is more
than one. Considering the relations among things cannot
explain it either—they may be side by side, or on top of, or
bigger and smaller than one another, and so on, because none
of these relations is even remotely numerical. Each definite
thing, as one thing, can only be registered as having a number by being brought together with other definite things, each
of which is also one, a bringing together which does not
apprehend the things brought together singly but precisely as
all together.
Husserl’s explanation of how the mind does this is as simple as it is remarkable. The mind combines things into groups
or collections in such a way that what is grouped or collected
forms a whole that is different from the group members or
collected items, even though as the whole of just these members or items, it is clearly related to them. For example, in a
row of trees, a gaggle of geese, or a flock of birds, what is
named by the row, gaggle, and flock is the whole Husserl has
in mind, a whole that cannot be separated from what it is a
whole of any more than it can be identified totally with it.
Authentic numbers for Husserl are also comprised of wholes
like this, so that the whole of the number three is clearly
related to each of the things it registers as three, without,
however, its being totally identical with them. Two distinct
but related things are involved for Husserl here. One is the
fact that there are groups and collections of this kind, and the
other is that they have their origin in the mind. The talk
about the mind’s involvement in originating groups and collections of things does not mean that these things are only figments of the mind. Husserl only mentions the mind to
explain something very specific, the fact that the unity, the
whole of authentic numbers that we have been talking about,
is neither an abstract concept nor something that can be
explained by the definite things it registers as to their exact
number. Once this is recognized, and only once it is recognized, are we then in a position to understand why Husserl
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51
tried to explain this unity—this being a whole—of authentic
numbers by the way the mind organizes and grasps things as
groups and collections.
Husserl is very specific about this. The mind considers
each thing that it groups or collects as something that belongs
to the whole of whatever it is grouping and collecting. In the
case of authentic numbers, it considers each as something, a
certain one, without attending in the slightest to any other
qualities that belong to what it collects. This is the case
because unlike other groups and collections, which are
groups of something specific, for example, geese or trees,
authentic numbers are wholes of quite literally anything
whatever. The moons of Jupiter, Homer’s psyche, the city of
Annapolis, etc., can be collected together and the collection
registered as an authentic number—so long, of course, as the
amount in the collection does not get too big. The process of
forming authentic numbers, as well as other kinds of groups
and collections, is expressed in language according to Husserl
by the word “and,” although both this process and the wholes
it generates are for him most decidedly not anything linguistic. Hence the formation of a group, such as the group or
whole of students in a room, comes about when one student
and one student and one student and one student, and so on,
are collected by the mind. Note well, however, that in this
example not just anything can be grouped together, but only
what belongs to the whole that is being grouped, namely, students. Likewise, the formation of a collection, the whole of
which is the red objects in a room, comes about when one of
any kind of red object and one of any kind of red object and
one of any kind of red object, and so on, are collected by the
mind. Again, as in the whole that is a group, not just anything
can be collected. Finally, the formation of a collection, the
whole of which is its number, comes about when something
and something are collected, and then the process is stopped.
More precisely, when the process of collecting is stopped
after something and something are collected, the first authentic number, two, is the result. Likewise, when something and
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something, and something are collected, the authentic number three is the result, and so on, until the limit of authentic
numbers, ten, comes about.
Authentic numbers, then, are just such collections of
something, which is to say, of anything that can be considered
as simply one thing, without any other qualities or determinations of it being relevant to its belonging to a collection
that is numbered. Since its being just one is the only thing relevant here, Husserl follows a long tradition and refers to
these collected ones as “units.” Because authentic numbers
are amounts of units, Husserl can explain on their basis what
the understanding of numbers as abstract concepts cannot,
namely, addition. Adding two and two involves the combination of ‘one unit and one unit’ with ‘one unit and one unit’,
and hence, there is no mystery here, since ‘one unit and one
unit, added to ‘one unit and one unit’, yields ‘one unit and
one unit, and one unit, and one unit’, which is the authentic
number four.
Before considering what Husserl thinks happens to numbers when their number exceeds ten and they are no longer
authentic, let us step back for a minute. I have been talking
now for some time about something I have acknowledged my
ignorance of, namely, what numbers are. After considering
two common views of them—one that considers them to be
amounts of something and the other that considers them to
be abstract concepts—I have turned our attention to the contents of Husserl’s book on the philosophy of arithmetic. The
very question it attempts to answer is which of these two
views of number is correct. So far I have pointed out that
Husserl begins this investigation by distinguishing between
authentic and symbolic numbers, both of which we have now
discussed in some detail. Indeed, at this point it might seem
that Husserl’s answer to the question of whether numbers are
amounts of something or abstract concepts is pretty obvious,
since authentic numbers can explain what abstract conceptual
numbers cannot, namely, the basic operations of arithmetic.
However, things are not that simple because when we con-
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53
sider numbers greater than ten, Husserl thinks that they
become inauthentic, as they cannot be authentic. They cannot
be authentic, it will be recalled, because the mind cannot
grasp more than ten things all at once. Symbolic numbers on
Husserl’s understanding are therefore also in this sense inauthentic.
Even though they are inauthentic, however, symbolic
numbers are not inferior, mathematically speaking, to authentic ones for Husserl. On the contrary, because they deal with
numbers larger than ten, they come in handy any time calculation with large numbers is required, since without them, we
would be reduced to counting units when we calculate with
such numbers, which no doubt would be both tedious and
time consuming. At the time Husserl wrote his first book,
mathematicians and philosophers wanted an explanation
how it was possible to do what no one denies can be done: to
calculate with inauthentic numbers, which are symbolic and
so in some sense are abstract concepts. In the first ten chapters of The Philosophy of Arithmetic, Husserl attempted to
prove that authentic numbers and symbolic numbers are logically equivalent because each refers to the same objects,
specifically, the collections of more than one unit that authentic numbers register the first ten amounts of. He argued that
authentic numbers do this directly and symbolic numbers
indirectly. When Husserl reached chapter eleven, however, he
realized something that shook him to his depths, quite literally. (He later recounted a decade-long depression that
ensued as a result.) He realized not only that symbolic numbers did not refer to the same objects as authentic ones—to
collections of units—but also that the basic operations with
quantities that are known, what he called general arithmetic,
could only be explained on the basis of the very opposite of
what he had argued in the first ten chapters. General arithmetic only makes sense if the numbers it uses are symbolic in
the sense I discussed above, wherein the sign and the numerical concept are identical so that a number is interpreted to be
the sign that we write or read—what Husserl called “sense-
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perceptible” signs. Husserl also realized he had no idea of
how this is possible. As he described it some two decades
later, “how symbolic thinking is ‘possible’, how...mathematical...relations constitute themselves in the mind...and can be
objectively valid, all this remained mysterious.”2
Thus we can say that, while recognizing that some numbers are clearly definite amounts of units and others are
abstract, symbolic concepts because they do not refer to such
units, Husserl came to see that he did not know what either
of them really is. Husserl eventually thought he could solve
this mystery by explaining the manipulation of symbolic
numbers, or, more precisely, number symbols, as well as all
mathematical symbols, in terms of what he called “the rules
of a game,” rules that were invented not by mathematics but
by logic. Mathematics thus came to be understood by Husserl
as a branch of logic. Moreover, Husserl thought that all the
rules invented by logic have their foundation in concepts that
are true of other concepts, these other concepts, in turn,
being true of anything whatever, that is, anything that can be
experienced and therefore thought of as an individual object.
As a consequence, Husserl’s eventual explanation of how
symbolic mathematics is possible, in The Crisis of European
Sciences, was really not so far from his failed first attempt at
explanation. To be sure, his later explanation does not characterize number symbols as referring to the same objects that
authentic numbers do, namely to units, but it did trace the
truth of the logic that invented the rules for manipulating
them to a basis in individual objects. This, we shall soon see,
is a problem if we follow Jacob Klein’s mathematical investigations, which I am going to suggest can best be followed by
first considering their Husserlian context.
The bulk of Klein’s mathematical investigations are contained in his Greek Mathematical Thought and the Origin of
Algebra, which as many of you know was originally published
in German as two long articles in 1934 and 1936 and translated into English in 1968 by St. John’s tutor and former
Dean of the College, Eva Brann.3 The historical nature of the
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55
topic announced by its title might initially seem to be far
removed from what we now know is the systematic nature of
Husserl’s topic in Philosophy of Arithmetic. However, one
does not need to read very far in Klein’s book to discover that
he understands the key to the historical investigation of his
topic to lie precisely in the distinction between symbolic and
non-symbolic numbers. Specifically, he expresses the view
from the start not only that the symbolic number concept is
something that makes modern, algebraic mathematics possible, but also, that symbolic numbers were entirely unknown
to ancient Greek mathematicians and philosophers. The very
point of departure for Klein’s investigation of the origin of
algebra is therefore informed by his view that unless the nonequivalence of ancient Greek numbers and modern symbolic
numbers is recognized, the change in the nature of the very
concept of number that took place with the transformation of
classical mathematics into modern mathematics in the sixteenth century will go unrecognized.
Klein’s thought here can be made clearer by closely considering precisely how he characterizes the difference
between the ancient Greek numbers and the modern symbolic ones. Ancient Greek numbers or arithmoi are manifestly
not abstract concepts, but rather beings that determine definite amounts of definite things. In contrast, symbolic numbers
are characterized by him to be abstract concepts that do not
refer to anything definite except that which is referred to by
their sense-perceptible signs. When we consider the fact that
Husserl articulated the difference between authentic and
symbolic numbers in precisely these terms, the resemblance
between Klein’s and Husserl’s view of the distinction between
symbolic and non-symbolic numbers is striking. So striking is
it in fact that some have drawn the conclusion that Husserl
should be given precedence in this matter, as either the source
or the major influence on Klein’s formulation of the distinction in question.4 These matters, however, are not so simple.
To begin, it is important to keep in mind that Husserl
sought in Philosophy of Arithmetic to demonstrate the logical
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equivalence of non-symbolic and symbolic numbers, whereas
Klein’s book begins with the insight that this is impossible, an
insight, as we have seen, Husserl arrived at only reluctantly.
Moreover, subsequent to his first book Husserl explains the
relationship between symbolic and authentic numbers as a
matter of logic. In his Logical Investigations (1900) and
Formal and Transcendental Logic (1927), the relationship is
explained as a matter of the translation of logical truths into
rules for the manipulation of symbols. Logical truths for
Husserl are rooted in concepts that are true of other concepts, other concepts that, in turn, can be traced back to
truths that are rooted in individual objects. Husserl calls the
rules established on the basis of this logic the “rules of a
game,” because even though they permit calculational operations on symbols that yield mathematically correct results,
these operations and hence the very process of symbolic calculation have nothing to do with insight into concepts that
pertain to the objects to which they are ultimately related,
and therefore nothing to do with real knowledge. In a word,
Husserl thought he resolved the issue of symbolic and
authentic numbers by exposing symbolic calculation to be a
“technique” whose cognitive justification can only be provided on the basis of the conceptual knowledge of individual
objects that logic provides.
Klein, however, thought otherwise. He thought that it is
impossible to explain the sharp distinction between non-symbolic and symbolic numbers on the basis of the knowledge—
logical or any other kind—of individual objects. He conducted an historical investigation into how an aspect proper
to ancient Greek arithmoi was transformed into modern symbolical numbers and concluded that the objects referred to by
each kind of number are fundamentally different. The objects
referred to by arithmoi are definite, which is to say, individual. The objects referred to by symbolic numbers are indefinite. They refer neither to individuals nor to their qualities
and are therefore indeterminate. Individual objects, both
Husserl and Klein agree, are objects that we encounter in our
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57
experience of the world and thus, they can be pointed to.
Moreover, their qualities, which either some (general qualities) or all (universal qualities) individual objects share, are
qualities that, even though they are not individual, can nevertheless be spoken about in connection with the individual
objects that we do encounter in the world. For instance, we
can point to dogs and cats, each one of which is therefore
individual. We can also talk about their general or universal
qualities and relate these to the individual dogs and cats that
we encounter in the world. Indeterminate objects, on the
contrary, can never be encountered in our experience of the
world, and therefore they cannnot be pointed to. Husserl and
Klein also agree that because their objects are not determinate
in this very precise sense, symbolic numbers cannot have a
direct relationship to any individual objects in the world or to
their qualities. Finally, both Husserl and Klein agree that symbolic numbers themselves, and not their indeterminate
objects, are nevertheless encountered in the world: namely,
they are encountered as the sense-perceptible signs that, we
mentioned earlier, many of us interpret as numbers.
Where Husserl and Klein disagree, or more accurately,
where Klein would have had to express his departure from
Husserl’s understanding of the relationship between symbolic
and non-symbolic numbers, had he chosen to do so, has to do
with the possibility of theoretically clarifying the philosophical meaning of symbolic numbers. Husserl thought this could
be done—indeed, he thought he did it in his two books on
logic. Klein did not think it could be done. In fact, as we shall
see, Klein’s mathematics book explains why the very attempt
to clarify theoretically the philosophical meaning of symbolic
numbers and mathematical symbolism generally is doomed to
failure. It is so doomed because all the concepts available to
provide such a theoretical clarification, without exception,
only make sense when the philosophers or anyone else using
them are talking about individual objects and their qualities.
Klein explains why this is the case by establishing a fundamental difference in what he calls the “conceptuality”5 of
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the concepts that belong to ancient Greek and modern science. He uses this term to articulate both the way in which
the concepts proper to these respective sciences are structured and the status of their relationship to the non-conceptual realities of both the mind and the world. Klein thinks
that despite the continuity discernable in the technical vocabulary of ancient Greek mathematics and philosophy and their
modern counterparts, the mathematical and philosophical
significance of each of the words in it is nevertheless radically
divergent for the ancients and moderns. Thus in his view the
fundamental significance of words like knowledge, truth,
concept, form, matter, nature, energy, number, and so on is
completely different for the ancient Greeks and the moderns
because of the differences in the respective conceptualities of
each. In other words, Klein thinks that these conceptualities
shape the meaning of words, rather than the other way
around, that is, rather than the significance of words shaping
the structure of the conceptualities.
Klein locates the key example of the shift from the
ancient Greek to the modern conceptuality in the transformation the concept of number undergoes in the sixteenth
century. Prior to Viète’s invention of the mathematical symbol, the concept of number according to Klein always only
meant a definite amount of definite things, a meaning that
was established by the ancient Greeks and that remained
operative in both European mathematics and the Europeans’
everyday praxis of counting and calculation until the invention of algebra. Klein claimed in his book—but did not elaborate—that this transformation is paradigmatic for the conceptuality that structures the modern consciousness of the
world.
Before considering in more detail Klein’s account of this
exemplary transformation of the conceptuality of number, a
few words about the potentially misleading talk of the “concept” of number are in order. Klein engages in such talk when
his investigation is comparing what he refers to as the different “number concepts” of ancient Greek and modern mathe-
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matics. It is potentially misleading because for Klein the most
salient difference between in these number concepts is
located in the fact that the ancient Greek “concept” of number is precisely something that is not at all a concept, but a
being, while the modern “concept” of number is precisely
something that is not a being but a concept. The object of the
word “concept” in these comparative contexts is, I think,
clearly the “conceptuality” of ancient Greek and modern
numbers, which means it would be a mistake to attribute to
Klein in such contexts the thought that in ancient Greek and
modern mathematics numbers are concepts, albeit different
in kind. Klein, however, also talks about the ancient Greek
“arithmos-concept” (arithmos-Begriff or Anzahl-Begriff) and
the modern “number-concept” (Zahl-Begriff), which again is
potentially misleading, for the same reasons. Yet here, too,
careful consideration again discloses that such talk always
occurs within the context of his comparison of what he presents as the different ancient Greek and modern characterizations of numbers, only one of which formulated them as concepts.
Before elaborating Klein’s account of these different characterizations, I want to raise and then answer one more question. From what perspective was Klein able to compare the
ancient Greek and modern numbers? Klein, after all, was neither ancient nor Greek but, by his own admission, thoroughly
modern. How, then, was he able nevertheless to get sufficient
distance from the presuppositions that inform his modernity,
from his modern outlook and consciousness, such that he
could encounter and investigate what, again by his own
admission, are the radically different presuppositions of the
ancient Greeks?
I think the answer to this question can be found in the single reference in Klein’s published work to Husserl’s
Philosophy of Arithmetic.6 It occurs in “Phenomenology and
the History of Science,” an article Klein wrote for a memorial
volume of essays on Husserl’s phenomenology published in
1940, two years after Husserl’s death. In this article Klein did
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not at all hesitate to articulate the philosophical significance
of his 1934 and 1936 investigations of ancient Greek mathematics and the origin of modern algebra in terms of Husserl’s
last writings, which were published in 1936 and1939.7 In
these writings Husserl traces the cause of the crisis of
European sciences to their failure to grasp properly the scope
and limits of scientific methods that are rooted in modern
mathematics for understanding the non-physical, which is to
say human spiritual reality together with the world of its
immediate concerns. I will come back to this theme at the end
of my remarks. I want to focus for now on Klein’s reference
to what he characterizes in this article as Husserl’s “earliest
philosophical problem,” namely “the ‘logic’ of symbolic
mathematics.” He asserts, “The paramount importance of
this problem can be easily grasped, if we think of the role that
symbolic mathematics has played in the development of modern science since the end of the sixteenth century.” Klein concludes his remarks on “Husserl’s logical researches” by saying
that these researches “amount in fact to a reproduction and
precise understanding of the ‘formalization’ which took place
in mathematics (and philosophy) ever since Viète and
Descartes paved the way for modern science.”
Klein’s qualification that Husserl’s logical researches
“amount . . . to” both a “reproduction” and “precise understanding” of the “formalization” in mathematics initiated by
Viète contains the key to my answer to the question. It indicates that Klein, but not Husserl, was aware of the historical
significance of these researches. The result of the “formalization” in mathematics referred to here by Klein concerns the
“indeterminacy” of the object of mathematical symbols that I
called attention to earlier, the absence of any direct reference
to both individual objects and their general and universal
qualities that is the mathematical symbols’ most salient characteristic. Because Klein thought Husserl’s logical researches
in Philosophy of Arithmetic amount in fact to the reproduction and precise understanding of the historical genesis of this
formalization, it would follow from this that Klein under-
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61
stood that work’s investigation of the relationship between
authentic and symbolic numbers to mirror what his own
research presents as the relationship between the ancient
Greek arithmos and the modern symbolic number.
This being the case, the question of image and original
suggested by my mirror metaphor arises, namely, did
Husserl’s investigations mirror Klein’s or Klein’s Husserl’s?
Here I think chronology is relevant, which would suggest that
what enabled Klein to encounter the presuppositions of both
his own modern as well as the ancient Greek conceptuality
was Husserl’s reluctant discovery in Philosophy of Arithmetic
that the formal conceptual status of symbolic numbers cannot
be rendered intelligible in terms of authentic numbers. By
saying this, however, I want to emphasize in the strongest
terms possible that I am not suggesting what some others
have suggested, namely, that what makes Klein’s comparison
of the conceptuality of the ancient Greek and modern numbers possible is his projection of Husserl’s “concepts” of
authentic and symbolic numbers back into the history of
mathematics.8 On the contrary, I want to suggest and then
develop a much more subtle and more radical claim.
Husserl’s failure provided Klein with the guiding clue that
enabled him to trace and illuminate certain historical dimensions of that very failure. Klein detected an historical transformation of non-symbolic numbers: an aspect of their conceptuality was transformed into symbolic numbers. This discovery resulted in a more definitive philosophical account of
both kinds of numbers. Moreover, Klein discovered something of which Husserl had not the slightest inkling, namely,
that the formal conceptuality of symbolic numbers, and symbolic conceptuality in general, cannot be made intelligible on
the basis of theoretical concepts traceable to ancient Greek
science. And that discovery highlighted something more ominous: built into symbolic cognition is the misguided selfunderstanding that evaluates its own cognitive status as the
ever-increasing perfection of ancient Greek science’s theoretical aspirations.
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Klein’s account of the origination of algebra is really the
story of the simultaneous invention of the mathematical symbol, the symbolic formulae it makes possible, and the resultant novel art of symbolic calculation. It is a story with a such
a complex array of intricate subplots and such a diverse cast
of characters that it is not always easy to follow the action,
especially given its approximately two-thousand-year time
span. It is also a difficult story to follow, since not only are
there really no good and bad guys to identify with or to dislike, but its beginning as well as its ending is obscure. The
action takes place, for the most part, in the realm of pure
beings and pure concepts, a realm that is invisible to the eyes
and in which all the actors are likewise invisible and therefore, with some justification, referred to by many as
“abstract.” Despite its otherworldly aura, it is a story well
worth trying to follow because what it is about is the origin
of the mistaken identity of the very technique that has
enabled mathematical physics and the technology spawned
from it quite literally to transform the world. Unraveling the
plot is an exercise in discovering the true identity of this technique and, in the process, rediscovering something essential
about our relation to the world that the events surrounding
the technique’s origination continue to make it easy for us to
forget.
Turning now to the story: we have already seen that nonsymbolic and symbolic numbers are key players in Klein’s
tale. Guided by our discussion of Husserl’s account of them,
we are in a position to see what it means to say with Klein
that the non-symbolic numbers of the ancient Greeks are not
concepts, let alone abstract concepts: being definite amounts
of definite things, arithmoi were initially understood not only
to be inseparable from things but also to be what is responsible for the well-ordered arrangement proper to all their parts
and qualities. In other words, they were understood by the
Pythagoreans as the very being of everything that is. To be is
to be countable, and because to be countable each thing has
to be one, the one was very important, as was the odd and the
HOPKINS
63
even, since whatever is counted ends up being odd or even.
The one or the unit (monas), as something without which
counting is impossible, is therefore the most basic principle
(archê) of arithmos. The odd and the even, which order the
arithmos of everything countable, insofar as it has to be one
or the other, manifest the first two kinds (eidê) of arithmoi.
Moreover, since the even can be divided without ever arriving at a final arithmos, while the odd cannot be divided
evenly at all, because a one is always left over, these two kinds
are understood, respectively, as unlimited and limit.
It is important to note here three things, according to
Klein: (1) the arithmoi are inseparable from that which is
countable; (2) the most basic principle as well as the kinds of
arithmoi are not themselves arithmoi. In other words, they
are not numerical if by numerical we understand, as the
ancient Greeks did, number to be a definite amount of definite things; and (3) the arithmoi, being inseparable from what
is countable, are not abstract entities, and because they are
different from both their most basic principle and their kinds,
they are not even remotely “conceptual,” assuming for the
moment that it is even appropriate to use this adjective to
refer to the archê and eidê of arithmoi. It is important to note
these three things because, on Klein’s telling, no matter how
much the ancient Greek characterization of the mode of
being of arithmoi changes in what become, in Plato and
Aristotle, the two paradigmatic ways of its understanding it,
these three things about the arithmoi remain constant. In
Klein’s words, “All these characterizations stem from one and
the same original intuition [Anschauung], one oriented to the
phenomenon of counting.”9
While the discovery of incommensurable magnitudes
brought to an end the Pythagorean dream of a world in which
being counted was identical with being measured, Plato’s
positing of the invisible, indivisible, and therefore sensibly
pure mode of being of the archê of arithmoi brought into
being another dream, the dream of what Klein calls an arithmological ordering of the eidê responsible for arithmoi as
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well as anything else that is a being. As Klein relates it, Plato
realized that the Pythagorean account of the archê of arithmoi, the one or the unit, as something that is quite literally
inseparable from the sensible things that are countable on its
basis, presented an obstacle to understanding the true relation
of arithmoi to the soul when it counts. This is the case
because Plato must have noticed that even before, the soul
counts each one of the definite things that it perceives, it
already has some understanding of the arithmoi it employs in
arriving at the arithmos of such things. According to Klein,
Plato must have thought this possible because prior to counting sensible things the soul has available to it arithmoi that are
definite amounts of intelligible (noêta) units, intelligible in the
sense that they cannot be seen with the eyes, cannot be
divided like the things seen with the eyes, and cannot be
unequal like the things seen by the eyes. Just like the
Pythagoreans’ sensible arithmoi, these intelligible arithmoi
are either odd or even, though unlike the Pythagorean eidê,
those belonging to intelligible arithmoi are likewise intelligible, and thus cannot be seen with the eyes.
Now it has to be stressed here that absolutely nothing is
either abstract or general about Plato’s intelligible arithmoi.
They are not abstract because they are not lifted off anything.
They are not general because they are precisely definite
amounts of definite things, albeit in this case the things are
noeta. Moreover, they are not general because, just like the
Pythagorean arithmoi, they are not concepts: each arithmos is
a definite whole, the unity of which is exactly so and so many
intelligible units. What allows intelligible numbers to be used
in the counting of anything whatever is what Plato’s Socrates
never tired of pointing out to his interlocutors, namely, that
the true referents of our speech, in counting off amounts of
things or in anything else, are not sensible but intelligible
beings. Thus in counting what the soul is really aiming at
when it counts off in speech, the definite amounts of definite
sensible things, things that in being counted are treated as sensible units, are definite amounts of intelligible units. Indeed, it
HOPKINS
65
is precisely this state of affairs that allows the soul to count
anything that happens to be before it, since the true units of
its counting are not those that can be seen but precisely those
that can only be thought.
Plato’s way of explaining how the availability of intelligible arithmoi to the soul enables it to count anything whatever
means that these intelligible units are manifestly unlike the
units in Husserl’s authentic numbers. Plato’s intelligible units
explain the ability of arithmoi to count anything whatever
because they, and not the “whatever,” are each arithmos’ true
referent. In other words, for Plato—and for that matter, for
all the ancient Greeks including Aristotle10—there is no such
concept of any thing, or any object, or any being whatever.
Such a concept, as we have seen, is explained by Husserl in
terms of an abstracting activity of the mind that is so powerful it is powerful enough to create a concept so general that
literally anything whatever (Etwas überhaupt) can “fall under
it.” This is to say, for Husserl the mind is able to create a formal concept that has absolutely no determinate reference to
any individual thing in the world or to the general and universal qualities of such things. Klein’s point, and in my judgment the point is the fulcrum upon which the story told in his
math book pivots, is that until Viète invented algebra, the
power behind this abstraction—what Klein calls a symbol
generating abstraction—was something that the world had
never seen before.
Husserl’s concept of the units in authentic numbers is
therefore modern, which is something Klein was not only no
doubt aware of, but it is also no doubt the reason why Klein
silently passed over in silence Husserl’s investigations of the
logic of symbolic mathematics. Indeed, Klein’s book also
bypassed any reference to Husserl’s concept of intentionality
when he articulated the difference between the conceptuality
of non-symbolic and symbolic numbers in terms of the mediaeval concept of intentionality, and, again, no doubt it was for
the same reason: a part of the composition of Husserl’s concept of intentionality was already determined by the very for-
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mality that Klein was investigating the origin of, in the shift
from non-symbolic to symbolic numbers. Once this is realized, Klein’s use of the medieval concepts of first and second
intentional objects, rather than Husserl’s concepts of straightforward and categorial intentional objects, to talk about the
difference in the mode of being of non-symbolic and symbolic numbers makes perfect sense.
The transformation of an aspect of the ancient Greek
arithmoi into the modern, symbolic numbers, however, does
not make perfect sense. That is, Klein’s account of the shift in
the referent of ancient Greek and modern symbolic numbers
is something that does not, and indeed cannot, render theoretically transparent the philosophical meaning of either the
shift or the different numbers in question. The characterization of ancient Greek arithmoi in terms of their direct
encounter with either sense perceptible objects encountered
in the world or with intelligible objects encountered in the
soul—what Klein reports the medievals called first-intentional objects—does not explain what such arithmoi are, in
the precise sense of how it is that the different arithmoi render intelligible the different definite amount that characterizes each arithmos. Indeed, Klein never suggests that the concept of a first-intentional object can do this. Likewise, the
characterization of symbolic numbers as having their referent
in the mind’s conception, a conception the medievals called
the object of a second intention, does not render theoretically
perspicuous what symbolic numbers are, either. To characterize symbolic numbers as pertaining to that aspect of arithmoi
that concerns the “how many” of something, while at the
same time no longer pertaining to its exact determination that
each arithmos brings about, does not clarify theoretically
what a symbolic number is. In other words, pointing out that
the conceptuality of symbolic numbers disregards both the
units of the something whose definite amount it is the
province of arithmoi to determine and the exact amount of
these units that each arithmos registers, does not explain
what a symbolic number is—and neither does Klein’s account
HOPKINS
67
of how more than this shift is involved in its conceptuality.
Klein affirms that what is required in order for us to be dealing with a symbolic number is that the second-intentional
mode of being of the “how many,” which brings into the
world for the first time a formal concept because it is now
shorn of any connection to either first-intentional objects or
the exact determination of their amount, be expressed in a
sense-perceptible sign that is grasped by the mind as the object
of a first intention.
What Klein’s talk of objects of first and second intentions
accomplishes is to call attention to something that nobody
else in the twentieth century had seen, namely, that the invention of symbolic cognition represents nothing less than a
reversal of the pre-modern relationship between concepts
and objects: what were concepts for the ancient Greeks are
now objects and what were objects for them are now concepts. Modern “theoretical thinking,” being symbolical, is
thus necessarily blind to this reversal. Ancient “theoretical
thinking,” not being symbolical, is likewise necessarily blind
to it. It does not follow from this, however, that thinking per
se must remain blind to it. On the contrary, for a thinking that
is on its guard against falling victim to the most shameful
ignorance, that is, to thinking it knows what, in truth, no
mortal can know, not only is the shift in conceptuality articulated by Klein something that can be seen, but once seen, it
is something that the soul’s phronesis can never forget.
If we had more time, I would continue my remarks by
calling attention to what I think is the key to Klein’s account
of how something like a symbol generating abstraction was
able to come into the world, namely on the basis of Viète’s,
Stevin’s, Descartes’s, and Wallis’s formulating the method of
an art that permits calculation with what the ancient Greeks
characterized not as arithmoi but as their eidê. And, indeed, I
would call attention to the fact that, for Klein, with this not
only do the true objects of mathematics become conceptual,
that is, formal, but also, such concepts at the same time
become numerical. Finally, I would call attention to the par-
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THE ST. JOHN’S REVIEW
allel Klein draws between the breaking of the bounds of the
intelligibility proper to the logos that is the result of Plato’s
formulation of the eidê of beings as having an arithmological
structure and the similar breaking of these bounds by Viète’s
numerical formulation of the symbolic calculation with the
species of numbers in symbolic cognition,11 and then ask the
following question: Do both of these attempts to comprehend beings theoretically transcend the limits of what can be
spoken of intelligibly for the same simple reason, namely, that
their theories presuppose a knowledge of what no mortal can
claim in truth really to know, namely that most wondrous gift
of the gods to humans—one and number?
Before I conclude, I would like to return very briefly to
Klein’s memorial essay on Husserl that I mentioned earlier
and to the matter of his articulation in that essay of the philosophical meaning of his mathematical investigations in terms
of Husserl’s of last writings, the so-called crisis texts. It is
important to draw attention here to the chronology of Klein’s
mathematical investigations and Husserl’s last writings,
because it is only in these writings that Husserl connects the
two themes that had already informed Klein’s earlier investigations of the history of mathematical concepts. Prior to
1936, when the second part of Klein’s investigations were
published, Husserl therefore had not yet recognized what
Klein had already recognized, and indeed investigated extensively, guided as I have suggested by Husserl’s first—and
failed—investigation of the relationship between non-symbolic and symbolic numbers. Klein recognized the connection
between the philosophical meaning of mathematical concepts
and the history of their origination.
Notes
Edmund Husserl, Philosophie der Arithmetik, ed. Lothar Eley,
Husserliana XII (The Hague: Nijhoff, 1970), 245; English translation: The Philosophy of Arithmetic, trans. Dallas Willard
(Dordrecht: Kluwer, 2003).
1
HOPKINS
69
Edmund Husserl, Introductions to the Logical Investigations, ed.
Eugen Fink, trans. Philip J. Bossert and Curtis H. Peters (The
Hague: Martinus Nijhoff, 1975), 35. German text, “Entwurf einer
‘Vorrede’ zu den ‘Logischen Untersuchungen’ (1913),” Tijdschrift
voor Philosophie (1939): 106-133, here 127.
2
Jacob Klein, Greek Mathematical Thought and the Origin of
Algebra, trans. Eva Brann (Cambridge, Mass.: M.I.T. Press, 1969;
reprint: New York: Dover, 1992). This work was originally published in German as “Die griechische Logistik und die Entstehung
der Algebra” in Quellen und Studien zur Geschichte der
Mathematik, Astronomie und Physik, Abteilung B: Studien, vol. 3,
no. 1 (Berlin, 1934), pp. 18–105 (Part I); no. 2 (1936), pp.
122–235 (Part II). Hereinafter referred to as GMTOA.
3
See the following: Hiram Caton, who claims that “Klein projects
Husserl back upon Viète and Descartes,” (Studi International Di
Filosophia, Vol 3 (Autumn, 1971): 222-226, here 225; J. Phillip
Miller, who writes “Although Husserl’s own analyses move on the
level of a priori possibility, Klein’s work shows how fruitful these
analyses can be when the categories they generate are used in studying the actual history of mathematical thought,” (Numbers in
Presence and Absence [The Hague: Martinus Nijhoff, 1982], 132;
Joshua Kates’ account is more circumspect, as he notes “[i]t is difficult to capture adequately . . . how much of Klein’s understanding
of Greek number is already to be found in Husserl, despite the
important differences between them,” (“Philosophy First, Last, and
Counting: Edmund Husserl, Jacob Klein, and Plato’s
Arithmological Eidê,” (Graduate Faculty Philosophy Journal, Vol.
25, Number 1 (2004), 65-97, here 94.
4
This is the literal translation of the word in question here,
“Begrifflichkeit,” which is rendered for the most part as “intentionality” in the English translation GMTOA. Because of this, the point
I make below about the “concept of number” and “number concepts” will be more familiar to readers of Klein’s original German
text.
5
Jacob Klein, “Phenomenology and the History of Science,” in
Philosophical Essays in Memory of Edmund Husserl, ed. Marvin
Farber (Cambridge, Mass.: Harvard University Press, 1940),
143–163; reprinted in Jacob Klein, Lectures and Essays, ed. Robert
6
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B. Williamson and Elliott Zuckerman (Annapolis, Md.: St. John’s
Press, 1985), 65–84, here 70.
Edmund Husserl, “The Origin of Geometry,” in The Crisis of
European Sciences and Transcendental Phenomenology, trans. David
Carr (Evanston, Ill.: Northwestern University Press, 1970). The
German text was originally published in a heavily edited form by
Eugen Fink as “Die Frage nach dem Ursprung der Geometrie als
intentional-historisches Problem,” Revue internationale de
Philosophie I (1939). Fink’s typescript of Husserl’s original, and significantly different, 1936 text (which is the text translated by Carr)
was published as Beilage III in Die Krisis der europäischen
Wissenschaften und die transzendentale Phänomenologie. Eine
Einleitung in die phänomenologische Philosophie, ed. Walter
Biemel, Husserliana VI (The Hague: Nijhoff, 11954, 21976).
Edmund Husserl, “Die Krisis der europäischen Wissenschaften und
die transzendentale Phänomenologie. Eine Einleitung in die
phänomenologische Philosophie,” Philosophia I (1936), (the text of
this article is reprinted as §§ 1–27 of the text edited by Biemel).
7
8
See note 4 above.
9
GMOT, 54.
Aristotle’s dispute with Plato over the mode of being of the arithmoi studied by the discipline of mathematics was about the origin
of the units that they are the definite amounts of, and not whether
theoretical arithmoi are definite amounts of units.
10
“As Plato had once tried to grasp the highest science ‘arithmologically’ and therewith exceeded the bounds set for the logos (cf.
Part I, Section 7C), so here [in Viète’s invention of symbolic calculation] the ‘arithmetical’ interpretation leads to . . . the conception
of a symbolic mathematics,” the implication being, of course, that
such a conception exceeds the same bounds as did Plato’s attempt
to grasp dialectic in terms of the arithmoi eidetikoi (GMOT, 184).
11
71
Words, Diagrams, and Symbols:
Greek and Modern
Mathematics or “On the Need
To Rewrite The History of
Greek Mathematics” Revisited
Sabetai Unguru
Mademoiselle de Sommery, as Stendhal tells us in De
l’Amour, was caught “en flagrant delit,” i.e., in flagranti, by
her lover, who was shaken seeing his “amante” bedding down
another man. Mademoiselle was surprised by her lover’s
angry reaction and denied brazenly the event. When he
protested, she cried out: “Oh, well, I can see that you no
longer love me, you would rather trust your eyes than what I
tell you.”
The historian of mathematics should behave like
Mademoiselle’s lover: believe his eyes and not what mathematicians-turned-historians tell him about the texts he studies. There are optical illusions, it is true, but they are to be
preferred to the illusionary mental constructs of the mathematical historians. A text is a text is a text. Moreover,
metaphors aside, not everything is a text and it behooves the
cultural critic, and surely the historian, to relate only to written records as texts. Furthermore, texts are about something
definite and not every conceivable interpretation suits them
all. The Conica is about conic sections not about women. It
deals with three (or four) kinds of lines obtained by cutting a
Sabetai Unguru is Professor Emeritus and former Director of the Cohen
Institute for the History and Philosophy of Science and Ideas at the
University of Tel-Aviv. He is the author of a controversial study with the title
“On the Need to Rewrite the History of Greek Mathematics,” as well as of a
two-volume introduction to the history of mathematics. He is (with Michael
Fried) the co-author of Apollonius of Perga’s Conica: Text, Context, Subtext.
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THE ST. JOHN’S REVIEW
conic surface with a plane, lines baptized by Apollonius as
parabolas, ellipses, hyperbolas, and opposite sections. It does
not deal with a classification of women according to their
degree of perfection, as seen by a male chauvinist pig, hiding
his true intentions behind the cloud of mathematical jargon.
Texts are made of words, sometimes accompanied by
illustrations; in the case of Greek geometry, the texts are
made of words and diagrams, C’est tout. And the diagram is,
in a very definite sense, the proposition. The words accompanying it serve to show how the diagram is obtained; they
provide us the diagram in statu nascendi. But in principle it
would be possible to supply the absent words to an extant
diagram, though I doubt the possibility of understanding a
reasonably sophisticated geometrical text in the absence of
diagrams. If there is a manipulative aspect to Greek geometry,
and I think there is, it resides in the construction, the bringing into being of the diagram, while the steps of the process
are supplied by the words accompanying the diagram, typically in the kataskeue (construction).
There are no true symbols in a Greek mathematical text.
What looks like symbols to the untrained modern eye are
actually proper names for identifying mathematical objects.
They are not symbols, and cannot be manipulated, as algebraic symbols are. Even in Diophantus, which is a late and
special case, his so-called symbols are actually verbal abbreviations, making his Arithmetica an instance of syncopated, not
symbolic, algebra, in Nesselmann’s tripartite division (Die
Algebra der Griechen).
In modern, post-Cartesian mathematical texts, on the
other hand, there are words and diagrams and symbols, but
the actual necessity of the first two ingredients is minimal,
serving heuristic, pedagogical, and rhetorical needs that can
be dispensed with, leaving the text in its symbolic nakedness.
It is no exaggeration to see modern mathematics as symbolic,
while ancient mathematics cannot be seen historically in symbolic terms. This being the case, interpretations of ancient
mathematical texts relying on their symbolic transmogrifica-
UNGURU
73
tion are inadequate and distorting. They are ahistorical and
anachronistic, making them unacceptable for an understanding of ancient mathematics in its own right.
An ancient text—mathematical, philosophical, literary, or
whatever—is the product of a culture foreign to ours, whose
concerns, values, aims, standards, ideals, etc., are, as a rule, as
alien to ours as can be. Though, inescapably, all history is retrospective history, the approach described and decried by
Detlef D. Spalt, in his Vom Mythos der mathematischen
Vernunft (1981), as Resultatismus, or, “Orwellsche 1984Geschichtsschreibung für den grossen Bruder Vernunft,” that
takes its bearings and criteria from what it sees as the modern
outcome of a lengthy, linear, and necessary evolution of concepts and operations, looking always back at the past in light
of its modern offspring, is necessarily a highly distorting
approach, since it adopts unashamedly the perspective of the
present to (in this order) judge and understand the past.
Taken at face value, Percy W Bridgman’s statement that the
.
past has meaning only in terms of the present is simply not
true. The historian’s stance is rather the opposite: the present
has meaning only in terms of the past. Prima facie and on
principled grounds therefore, an interpretation of any written, reasonably extensive document belonging to an ancient
culture that results in its totally unproblematic and absolute
assimilation to our own is suspect. That this is so is, more or
less, acceptable when it comes to cultural artifacts other than
mathematical ones, which seem to enjoy the privilege of perdurablility and universality. The immunity from cultural
specificity that mathematical truths command stems from the
prevailing view that their outward appearance—their packaging, as it were—and their purely mathematical content—the
packaged merchandise, as it were—are neutral, unrelated,
and mutually independent items. It is a calamitous view and
the root of all evil in the historiography of mathematics.
But there is another entrance into an ancient text, mathematical or not, one that does no violence to it, that does not
break the inviolable unity of form and content and then enter
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THE ST. JOHN’S REVIEW
victoriously through the shambles it created, with the claim
that the text is now understood; it is rather an ingress that
accepts willingly and respectfully the unity of the text without pulverizing its inseparable aspects, bringing to its understanding both critical acumen and full acceptance of its outward appearance. This is the historical approach. The mathematical and historical approaches are antagonistic. Whoever
breaks and enters typically returns from his escapades with
other spoils than the peaceful and courteous caller.
Let me be more specific. Faced with an ancient mathematical text, the modern interpreter has an initial choice.
First is the mathematical approach. It consists of two steps:
(1) try to find out how one would do it (solve the problem,
prove the proposition, perform the construction, etc.) and
then (2) attempt to understand the ancient procedure in light
of the answer to step (1). Instead of this preeminently mathematical approach, however, the modern interpreter can
refuse to decipher the text by appealing to modern methods,
using for its understanding only ancient methods available to
the text’s author. This is the historical approach. Needless to
repeat, the spoils of interpretation differ according to the two
approaches followed. The longstanding traditional approach
has been the mathematical, though in the last three decades
or so the historical approach is gaining increasingly more and
more ground and, at least in the domain of ancient Greek
mathematics, seems to be now the prevailing one. What
seems certain is that in practice no compromise is possible
between the mathematical and historical methodological
principles. Adopting one or the other has fateful consequences for one’s research, effectively determining the nature
of the results reached and the tenor of the inferences used in
reaching them.
What I am saying, then, is that despite the numerous and
varied styles of writing the history of mathematics throughout the centuries, it is possible to group all histories of mathematics into two broad categories, the “mathematical” and
the “historical.” The former sees mathematics as eternal, its
UNGURU
75
truths unchanging and unaffected by their formal appearance,
and sees the mathematical kernel of those truths as being
independent of their outward mode of expression; the latter
denies this independence and looks upon past mathematics as
an unbreakable unity between form and content, a unity,
moreover, that enables one to grasp mathematics as a historical discipline, the truths of which are indelibly embedded in
changing linguistic structures. It is only this approach that is
apt to avoid anachronism in the study of the mathematics of
other eras.
To make this a historical talk, what is needed are specific,
historical examples, supporting the preceding generalizations. I have offered numerous such examples in my published work, most recently in the book I published with
Michael Fried, Apollonius of Perga’s Conica: Text, Context,
Subtext (2001). However, I would like now to enrich my
offerings by drawing illustrations from historical sources less
drawn upon in the past. One such source is Euclid’s Data.
In one of the attacks launched against a notorious article
of 1975, “On the Need to Rewrite the History of Greek
Mathematics,” Hans Freudenthal argues that, had its author
been aware of the existence of the Data, he “would never
have claimed there were no equations in Greek geometry.”
For Freudenthal, and not only for him, the Data is a “textbook on solving equations.” He summarizes the 94 propositions contained therein in a succinctly and strikingly epigrammatic statement: “Given certain magnitudes a, b, c and
a relation F(a, b, c, x), then x, too, is given.” But the fact
remains that Greek geometry contained no equations. One
cannot find even one equation in the entire text of the Data.
Proof (as the Hindu mathematician would say): “Look!”
Unless one has at his disposal the algebraic language and the
capacity to translate into it, it is impossible to sum up this little treatise of rather varied content as offhandedly as
Freudenthal has done, Indeed, had Euclid at his disposal
Freudenthal’s functional notation, it is rather easy to infer
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THE ST. JOHN’S REVIEW
that he would not have needed 94 propositions to get his
point across.
Each case in Euclid’s Data is unique, having its own
method of analysis, and none is subsumable under or
reducible to other cases, though, of course, later propositions
rely on earlier ones. Thus, “The ratio of given magnitudes to
one another is given” (proposition 1) and “If a given magnitude have a given ratio to some other magnitude, the other is
also given in magnitude” (proposition 2)—to use perhaps the
simplest illustration possible—are not for Euclid both
instances of “Given a, b, c and y=F(a, b, c, x), x is also given,”
but are two different problems, interesting in their own right,
having their own solutions. Of course, Freudenthal’s description is mathematically correct. Historically, however, it is
wanting. Heath is much more to the point when he says:
The Data…are still concerned with elementary
geometry [my italics], though forming part of the
introduction to higher analysis. Their form is that
of propositions proving that, if certain things in a
figure [my italics] are given (in magnitude, in
species, etc.), something else is given. The subjectmatter is much the same as that of the planimetrical books of the Elements, to which the Data are
often supplementary.
This is what the Data is, not a textbook on solving equations, but a treatise presenting another approach to elementary geometry—other than that of the Elements, that is.
As an example of this characterization of the Data, I shall
present proposition 16, in the new translation of C. M.
Taisbak [Euclid’s Data or The Importance of Being Given,
(Copenhagen, 2003)]:
If two magnitudes have a given ratio to one
another, and from the one a given magnitude be
subtracted, while to the other a given magnitude
be added, the whole will be greater than in ratio to
the remainder by a given magnitude (p. 75).
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UNGURU
First we must clarify the meaning of the expression “greater
than in ratio...by a given.” Definition 11 of the Data reads:
A magnitude is by a given greater than in ratio to a
magnitude if, when the given magnitude be subtracted, the remainder has a given ratio to the
same. (p. 35)
The meaning of this definition is, according to Taisbak, as follows (p. 57): “M is by the given G greater than the magnitude
L which has to N a given ratio;” in other words, M=L+G
and L:N is a given ratio.
Back to the proof of prop. 16:
Let two magnitudes AB, CD have a given ratio to one
another. From CD let the given magnitude CE be subtracted
and to AB let the given magnitude ZA be added.
Then, the whole ZB is greater than in ratio to the remainder
DE by a given magnitude.
Z
C
A
E
H
D
B
Now, since the ratio AB:CD is given and AH can be obtained,
by Dt. 4, from AH:CE::AB:CD, i.e., AH:CE is also given, it
follows that CE is also given. Hence, AH is given (by Dt. 2).
But AZ is given; therefore the whole ZH is given (by Dt. 3).
Since AH:CE::AB:CD, the ratio HB:ED of the remainders is
also given, by V 19 and Def. 2, i.e., HB:ED::AB:CD. But HZ
.
is given; therefore, ZB is by a given greater than in ratio to
ED (Def. 11), Q.E.D.
No algebra appears here, and although the language of
givens, the idiosyncratic concept “by a given greater than in
ratio” and the sui generis concatenation of inferences burden
the understanding, the proposition is clear and rather simple.
It is graspable as it stands, without any appeal to foreign
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THE ST. JOHN’S REVIEW
tools. And yet, Clemens Thaer, in his Die Data von Euklid
(1962), proceeds as follows to its clarification:
Let a:b=k , then the proposition claims that if x=ky, then
(x+c)=k(y-d)+(c+kd), which is, of course, correct mathematically, but this blatantly algebraic procedure betrays the
Data. It is a betrayal since ratios in Greek mathematics are
not real numbers, i.e., the initial substitution a:b=k is not
kosher. Though there is some controversy about the status of
ratios in the Elements, with respect to their being two, or
four-place relations, their status in the Data is uncontroversial: a ratio P:Q is an individual item “however impalpable. A
and B are magnitudes, most often (and least problematically)
understood to be line segments; one may think of them as
positive real numbers, that is as lengths of line segments, while
remembering that the Greek geometers could not think like
that, for want of such numbers” (Taisbak, Euclid’s
Dedomena, p. 32). Taisbak claims that distorting “clarifications” like the one above characterize all of Thaer’s algebraizations. He goes on to say:
About the following four theorems (Dt 17-20) he
maintains that they prove that all linear transformations, {ax+b a, b ℜ} form a group (‘dass die
ganzen linearen Substitutionen einer
Veraenderlichen eine Gruppe bilden’). I am not sure
I understand what he means to say, and the Data
certainly does not help me,—so probably Euclid
would not understand either. (p. 77)
Let us take our next example from Archimedes. Against
Freudenthal’s assertion, Archimedes’ works are not
“instances of algebraic procedure in Greek mathematics.”
Heath’s edition of The Works of Archimedes (1897) is “in
modern notation.” It is faithful only to the disembodied
mathematical content of the Archimedean text, but not to its
form. And this is crucial. If one abandons Archimedes’ form
and transcribes his rhetorical statements by means of algebraic symbols, manipulating and transforming the latter, then
UNGURU
79
clearly “the algebraic procedure” appears. But this procedure
itself is not “in Greek mathematics.” It is a result, as
Freudenthal himself states it, of “replacing vernacular by artificial language, and numbering variables by cardinals, a quite
recent mathematical tool.” Indeed! Archimedes’ text is
anchored securely in the terra firma of Greek geometry. If one
is not willing to compress wording, to replace “vernacular”
by artificial language, to introduce variables and number
them by cardinals, and to apply all the other technical tricks
which are “quite recent mathematical tools,” then
Archimedes’ proof of Proposition 10 of Peri Helikon is geometric, not algebraic. This was discerned in a curious way
even by Heath, who justified his algebraic procedure and the
use of the symbols , “in order to exhibit the geometrical character of the proof” (p. 109, my italics).
Dijksterhuis himself in his Archimedes said: “In a representation of Greek proofs in the symbolism of modern algebra it is often precisely the most characteristic qualities of the
classical argument which are lost, so that the reader is not sufficiently obliged to enter into the train of thought of the original.” So let us oblige ourselves to enter into the train of
thought of the original by having a look at the 10th proposition of Peri Helikon.
I shall give you the full enunciation and then set at its side
Heath’s algebraic variant:
If any number of lines, exceeding one another by
the same magnitude, are set one after the other,
the excess being equal to the smallest, and if one
takes other lines in the same number, each of
which is equal to the magnitude of the greatest of
the first lines, [then] the squares on the lines equal
to the greatest, augmented by the square on the
greatest, and by the rectangle the sides of which
are the smallest line and the sum of all lines
exceeding one another by the same magnitude are
equivalent to thrice the sum of the squares on the
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80
lines which exceed one another by the same
amount.
The enunciation is geometrical and it is accompanied by simple, linear diagrams.
And here is Heath’s enunciation:
If A1, A2, A3, ..., An be n lines forming and ascending
arithemetical progression in which the common
difference is equal to A1, the least term, then
(n+1) An2+A1 (A1+A2+...+An)=3(A12+A22+...+An2)........
…the result is equivalent to
12+22+32+...+n2=n(n=1)(2n+1)
6
The proof is not difficult, but very long (more than three
pages in Mugler’s edition of Archimedes’ works, if one
includes the porism), and I think we can dispense with it, but
not before pointing out the fact that it lies squarely within the
realm of traditional Greek geometry, relying on Elements 2.4,
it is true, which, as is well known, belongs to the so-called
geometric algebra, but which, as I have argued elsewhere, is
strictly geometric; additionally, the porism relies on Elements
6.20.
As in the enunciation, Archimedes formulates consistently
his statements in terms of lines squares, and rectangles, which
he manipulates à la Grecque, and his diagrammatic notation
is not at all perspicuous to a modern eye, making his transformations opaque, or at least cloudy, to a mind spoiled by
the easy mechanics of algebraic manipulations and their
immediate visual transparency. This makes following his elementary inferences quite difficult and almost forces upon the
reader recourse to algebraic notation. Such a procedure, how-
UNGURU
81
ever, easy, pellucid, and revealing as it is, is not legitimate historically.
What I have said about the proposition applies in its
entirety to the porism following it, out of which Heath makes
two corollaries!
Let us, again, limit ourselves to the enunciations of
Archimedes and Heath, which substantiate our characterization. Archimedes first:
It is manifest from the preceding that the sum of
the squares on the lines equal to the greatest is
inferior to the triple of the sum of the squares on
the lines exceeding one another by the same
magnitude, because, if one adds to it [the former]
some [magnitudes], it becomes that triple, but
that it is superior to the triple of the second sum
diminished by the square on the greatest line,
since what is added [to the first sum] is inferior
to the triple square of the greatest line. It is for
this [very] reason that, when one describes similar
figures on all the lines, both on those exceeding
one another by the same magnitude, as well as
on those which are equal to the greatest line, the
sum of the figures described on the lines which
are equal to the greatest line is inferior to the
triple of the sum of the figures described on the
lines exceeding one another by the same magnitude, but it is superior to the triple of the second
sum, which is diminished by the figure constructed
on the greatest line, because similar figures are in
the same ratio as the squares [on their sides].
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82
Now Heath:
Cor. 1. It follows from this proposition that
nAn2<3(A12+ A22+...+An2), and also that
nAn2<3(A12+ A22+...+An-12).
Cor. 2. All the results will equally hold if similar
figures are substituted for squares.
The differences between Archimedes and Heath are blatant.
Faithfulness to the Archimedean way of doing things
demands, therefore, the rejection of an edition of his works
“edited in modern notation.” There is no escape for the historian but to take texts at their face value.
One last example I shall draw from Diophantus’s
Arithmetica. Diophantus is an exception in the long tradition
of Greek mathematics, which is largely geometric. Living
probably in the third century A.D., his preserved work is an
instance, the only one of its kind in Greek mathematics, of
what we call algebra. It is a sui generis algebra, however, in
which the notations are properly nonexistent, except for the
unknown, arithmos, which is itself most likely an abbreviation, and a few abbreviations for powers of the unknown and
for the unit, monas. That is all. This is what makes his rhetorical algebra syncopated, according to Nesselmann’s classification. It is an algebra in which there is a total lack of true,
operative symbols, including symbols for operations, relations, and the exponential notation, with the exception of a
symbol for subtraction, in which the exceptional skill of
Diophantus enables him somehow to overcome with great
dexterity the built-in drawbacks of his Arithmetica. This
Greek algebra, however, is most emphatically not geometric
algebra. If anything, it is conceptually a far away relation to
what has been traditionally called Babylonian algebra, perhaps not even this, in light of the recent researches of Jens
UNGURU
83
Hoyrup, who identifies the geometrical roots of the
Babylonian recipes [Lengths,Widths, Surfaces, (Springer,
2002)].
Whatever it is, it is largely a collection of problems, to be
solved by means of skilful guesses and less by systematic
methods (though one also finds methods, for example, a general method for the solution of what we call determinate
equations of the second degree and another for double equations of the second degree), involving specific known numbers. It is not a book of propositions to be proved, but rather
of exercises to be solved, leading mostly to simple determinate and indeterminate equations, by means of which one
finds the required numbers, which are always rational, quite
often non-integral. Still, despite what I just said, one finds in
the treatise also some “porisms” and other propositions in the
theory of numbers, which proved themselves influential in
the history of the theory of numbers, especially in Fermat’s
work. Thus, Diophantus knew that no number of the form
8n+7 can be the sum of three squares, and that for an odd
number, 2n+1, to be the sum of two squares, n itself must not
be odd, which means that no number of the form 4n+3 or
4n-1 can be the sum of two squares.
Now, some simple illustrations from the Arithmetica, to
get the flavor of the true Algebra der Griechen:
Problem 1. To divide a given number into two
numbers, the difference of which is known.
Let the given number be 100, and let the difference be 40 monads; to find the numbers.
Let us assume that the smaller number is 1 arithmos; hence, the greater number is 1 arithmos and
40 units. Therefore, the sum of the two numbers
becomes 2 arithmoi and 40 units. But the given
sum is 100 units; hence, 100 units are equal to 2
arithmoi and 40 units. Let us subtract the like
from the like, that is, 40 units from 100 and, also,
�THE ST. JOHN’S REVIEW
84
the same 40 units from the 2 arithmoi and 40
units. The two remaining arithmoi equal 60 units
and each arithmos becomes 30 units.
Let us return to what we assumed: the smaller
number will be 30 units, while the greater will be
70 units, and the validation is obvious.
And here is Heath’s faithful version of the solution:
Given number is 100, given difference 40.
Lesser number required x. Therefore
2x+40=100
x=30.
The required numbers are 70, 30.
Problem 2. Diophantus:
It is necessary to divide a given number into two
numbers having a given ratio.
Let us require to divide 60 into two numbers in
triplicate ratio.
Let us assume that the smaller number is 1 arithmos; hence, the greater number will be 3 arithmoi,
and thus the greater number is thrice the smaller
number. It is also necessary that the sum of the
two numbers be 60 units. But the sum of the two
numbers is 4 arithmoi; hence 4 arithmoi are equal
to 60 units, and the arithmos is therefore 15 units.
Hence, the smaller number will be 15 units, and
the greater 45 units.
Heath:
Given number 60, given ratio 3:1.
Two numbers x, 3x. Therefore x=15.
The numbers are 45, 15.
UNGURU
85
Finally, an example of what is called indeterminate analysis of
the third degree:
Problem 4.8. Diophantus:
To add the same number to a cube and its side and
make the same.
Let the number to be added be 1 arithmos and the
side of the cube be a certain amount of arithmoi.
Let this amount be 2 arithmoi and it follows that
the cube is 8 cubic arithmoi.
Now if one adds 1 arithmos to 2 arithmoi, they
become 3 arithmoi, while if one adds it to the 8
cubic arithmoi, they become 8 cubic arithmoi and
1 arithmos, which are equal to 27 cubic arithmoi.
Let us subtract 8 cubic arithmoi, and it follows
that the remaining 19 cubic arithmoi will become
equal to 1 arithmos. Let us divide all by the arithmos, and 19 squared arithmoi will be equal to
1 unit.
But 1 unit is a square, and if 19, the amount of
square arithmoi, were a square, the problem would
be solved. But the 19 squares find their origin in
the excess by which 27 cubic arithmoi exceed 8
cubic arithmoi; and 27 cubic arithmoi are the cube
of 3 arithmoi, while 8 cubic arithmoi are the cube
of 2 arithmoi. But the two arithmoi are taken by
hypothesis, and 3 arithmoi exceed by one the
amount taken arbitrarily as the side. Therefore, we
are led to finding two numbers which exceed one
another by one unit, and the cubes of which
exceed one another by a square.
Let one of those numbers be 1 arithmos, and the
other 1 arithmos plus 1 unit. Hence the excess of
their cubes is 3 square arithmoi plus 3 arithmoi
plus 1 unit. Let us set this excess equal to the
square the side of which is 1 unit less 2 arithmoi,
�THE ST. JOHN’S REVIEW
86
and the arithmos becomes 7 units. Let us return to
what we supposed, and one of the numbers will be
7 and the other 8.
Let us now return to the original question and
assume the number to be added to be 1 arithmos,
and the side of the cube to be 7 arithmoi. This
cube will be then 343 cubic arithmoi. Hence, if
one adds the arithmos to each of these last numbers, one will become 8 arithmoi and the other
343 cubic arithmoi plus 1 arithmos. But we
wanted this last expression to be a cube the side of
which is 8 arithmoi; hence 512 cubic arithmoi are
equal to 343 cubic arithmoi plus 1 arithmos, and
1
the arithmos becomes 13.
Returning to the things we assumed, the cube will
343
7
1
be 2197, the side 13, and the number to be added 13.
I assume you could follow, at least in outline,
Diophantus’s solution procedure, though this is not essential
for my main purpose. (For those of you who could not follow
after all the details, which, as I said, is not really necessary, a
glance at Heath’s, or Ver Eecke’s, Diophantus would clarify
matters.) My purpose is to compare Diophantus to his modern editors. This time, instead of Heath, I shall take, however,
Nesselmann.
Nesselmann:
It is necessary that x3+y=(x+y)3, i.e., 3x2+3xy+y2=1.
Solving for y, we get y=
1
2
2
[-3x±√4-3x ].
4mn
Putting 4-3x2=(2-=m x)2, one gets x= 3n2+m2.
n
Hence, y=
-6mn±(m2-3n2)
3n2+m2
. Taking only the + sign,
87
UNGURU
for y to be positive, it is necessary that m2-3n2>6mn,
or,
m2 -6 m
n
n2
>3, or, ( m -3)2>12, or ( m >3+√12.
n
n
Diophantus’s solution corresponds to m=7, n=1.
Now this is historical faithfulness!
Time to conclude. Historians must take the past seriously.
For historians of science and mathematics, this means taking
texts seriously. How does one do this? By reading them as
they are, in their nakedness, as it were, in the language in
which they were written, without shortcuts and transmogrification, resulting in their translation into scientific and mathematical languages which became historically available only
long after they were written. It is, therefore, crucial that the
form of those texts remain inviolable. Without this, anachronism, i.e., historical misunderstanding, becomes rampant and
the resulting interpretation is misinterpretation. As Benjamin
Farrington put it,
History is the most fundamental science, for there
is no human knowledge which cannot lose its scientific character when men forget the conditions
under which it originated, the questions which it
answered, and the function it was created to serve.
A great part of the mysticism and superstition of
educated men consists of knowledge which has
broken loose from its historical moorings.
In 1975 an article appeared in the Archive for History of
Exact Sciences, arguing for the need to rewrite the history of
Greek mathematics. In one of its many footnotes, namely the
one numbered 126, attention is called to an important book,
Greek Mathematical Thought and the Origin of Algebra. The
footnote in question contains a parenthesis, saying:
[L]et me urge those readers who have a choice and
wish to read [this] highly interesting study to refer
back to the original German articles: somehow the
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THE ST. JOHN’S REVIEW
pomposity, stuffiness, and turgidity of the author’s
style are better accommodated by the Teutonic
cadences than by the more friendly sounds of the
perfidious Albion.
This was a nasty and uncalled for remark, attributable to the
author’s hubris.
How pleasantly and embarrassingly surprised must he
have been, then, when, a few weeks after the article’s appearance in the Archive, a postcard from the slighted author of the
book (to whom no reprint was sent!) arrived, saying: “Dear
Dr.,… Thank you very much for your important article in the
Archive.…” In character, you may say. Indeed.
As a belated, and highly inappropriate atonement for that
unsavory footnote, its author would like to finish this lecture
with a highly pertinent and lengthy quotation from an article
written by the great scholar he so carelessly slighted:
[T]he relation between ancient and modern
mathematics has increasingly become the focus
of historical investigation… Two general lines of
interpretation can be distinguished here. One—
the prevailing view—sees in the history of science
a continuous forward progress interrupted, at
most, by periods of stagnation. On this view, forward progress takes place with ‘logical necessity,’
accordingly, writing the history of a mathematical
theorem or of a physical principle basically means
analyzing its logic. The usual presentations,
especially of the history of mathematics, picture
a rectilinear course; all of its accidents and
irregularities disappear behind the logical
straightness of the whole path.
The second interpretation emphasizes that the
different stages along this path are incomparable.…it sees in Greek mathematics a science totally
distict from modern mathematics.…Both interpretations, however, start from the present-day
UNGURU
condition of science. The first measures ancient by
the standard of modern science and pursues the
individual threads leading back from the valid theorems of contemporary science to the anticipatory
steps taken towards them in antiquity.… The
second interpretation strives to bring into relief,
not what is common, but what divides ancient and
modern science. It too, however, interprets the
otherness of ancient mathematics...in terms of the
results of contemporary science. Consequently, it
recognizes only a counter-image of itself in ancient
science, a counter-image which still stands on its
own conceptual level.
Both interpretations fail to do justice to the true
state of the case. There can be no doubt that the
science of the seventeenth century represents a
direct continuation of ancient science. On the
other hand, neither can we deny their differences…above all, in their basic initiatives, in
their whole disposition (habitus). The difficulty is
precisely to avoid interpreting their differences
and their affinity one-sidedly in terms of the new
science. The issues at stake cannot be divorced
from the specific conceptual framework within
which they are interpreted.…
We need to approach ancient science on a basis
appropriate to it, a basis provided by that science
itself. Only on this basis can we measure the
transformation ancient science underwent in the
seventeenth century—a transformation unique
and unparalleled in the history of man.…
This modern consciousness is to be understood
not simply as a linear continuation of ancient
επιστημη, but as the result of a fundamental
conceptual shift which took place in the modern
era, a shift we can nowadays scarcely grasp.
89
�THE ST. JOHN’S REVIEW
91
The name of the man who wrote these lines is, as I am sure
you know, Jacob Klein. Yehi Zichro Baruch! May his memory
be blessed!
A Note on the Opposite
Sections and Conjugate Sections
in Apollonius of Perga’s Conica
90
Michael N. Fried
Introduction
To a careful reader of Apollonius of Perga’s Conica, the difference between Apollonius’ view of conic sections and ours
ought to be evident on nearly every page of the work. Yet this
has not always been the case. Indeed, it has not always been
easy to persuade readers that there really is something Greek
about Apollonius’ mathematics. Partly to blame is the seductive power of the algebraic framework in which we study
conic sections today and in which historians of mathematics
have interpreted the book in past years.1 Viewed algebraically,
for example, all of Book 4 of the Conica—the book concerning the number of points at which conic sections can meet—
can be reduced to a single proposition, namely, that a system
of two quadratic equations in two unknowns can have at
most four solutions. This tremendous power allowing one to
obtain results corresponding to ones in the Conica makes it
all too easy to think that Apollonius’ own text, in effect, can
be bypassed and replaced by an updated algebraic version of
it. However, there are things in the Conica that are refractory
to this kind of modernization of the text and show its essentially geometric character. One of these, surely, is that most
peculiar entity in the Conica, the opposite sections; it is they
that I shall turn my attention to in this note. In particular, I
want to show something about status of the opposite sections
in the Conica and show, among other things, why their status,
Michael Fried teaches mathematics education at Ben-Gurion University of the
Negev. He is the author of a translation, with introduction, of Book Four of
the Conics of Apollonius, and is the co-author (with Sabetai Unguru) of
Apollonius of Perga’s Conica: Text, Context, and Subtext.
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92
why their place in the Conica, is different from that of the
conjugate sections.
The Absence of the Opposite Sections from the Modern View
The reason why looking at the opposite sections is a good
way to re-focus on Apollonius’ text, rather than on an algebraic reconstruction of it, is simply that the opposite sections
do not exist in modern mathematics. For us, there is only the
hyperbola. Our view of the hyperbola, on the other hand, is
that it is a curve consisting “of two open branches extending
to infinity.”2 That we are not bothered by one curve consisting of two is directly related to our defining the hyperbola, as
we do the other conics, by means of an equation. Defining it
this way, the hyperbola becomes merely a set of points given
by coordinates, say the Cartesian coordinates (x, y), satisfying
an equation such as this:
x2 - y2
=1
a2 b2
Hence, there is nothing shocking when we discover that this
set of points consists of two disjoint subsets, one containing
points whose x coordinates are less than or equal to –a
(where a is taken to be a positive real number) and one containing points whose x coordinates are greater than or equal
to +a; the only relevant question to ask is whether the coordinates of a given point satisfy or do not satisfy the given
algebraic relation.3 The equation, in this view, tells all; it contains all the essential information about the object; in a sense,
the equation of the hyperbola is the hyperbola (see Fried &
Unguru, 2001, pp. 102-103; Klein, 1981, pp. 28-29). To
speak about opposite sections in addition to the hyperbola is
unnecessary because they are not distinguished by different
equations.
FRIED
93
The Opposite Sections in the Conica
The point of view above has also been the point of departure
for an older, but still much listened to, generation of historians of mathematics. Zeuthen (1886) and Heath (1921,
1896), leaders of that generation, had no doubt that
Apollonius’ achievement was in the uncovering and elucidation of the equations of the conic sections and that
Apollonius understood the conic sections in an algebraic
spirit. For them, Apollonius’ view was the modern view. Thus
Zeuthen writes:
An ellipse, parabola or hyperbola is here [in Book
1] planimetrically determined as a curve which is
represented by the equation (3), (1) or (2) [the
Cartesian equations for the ellipse, parabola, and
hyperbola, respectively] in a system of parallel
coordinates with any angle between the axes.
Thus, apart from the determination of the position
of these curves, they seem to depend on three constants, namely, that angle [between the axes, or,
equivalently, the ordinate angle], p [latus rectum],
and a [the length of the diameter] (Zeuthen, 1886,
p. 67).
And Heath, echoing Zeuthen, writes:
Apollonius, in deriving the three conics from any
cone cut in the most general manner, seeks to find
the relation between the coordinates of any point
on the curve referred to the original diameter and
the tangent at its extremity as axes (in general
oblique), and proceeds to deduce from the relation, when found, the other properties of the
curves. His method does not essentially differ from
that of modern analytical geometry except that in
Apollonius geometrical operations take the place
of algebraic calculations (Heath, 1896, p. cxvi)
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THE ST. JOHN’S REVIEW
As for why Apollonius notwithstanding referred to both
opposite sections and hyperbolas, Heath remarks that, “Since
[Apollonius] was the first to treat the double-branch hyperbola fully [emphasis added], he generally discusses the hyperbola (i.e., the single branch) [Heath’s emphasis] along with
the ellipse, and the opposites [Heath’s emphasis], as he calls
the double-branch hyperbola, separately” (Heath, 1921,
p.139). Zeuthen simply says that, as a matter of terminology,
“What [Apollonius] calls an hyperbola is always only a hyperbola-branch” (Zeuthen, 1886, p. 67). But these remarks are
hardly satisfying. First, while it is most likely that Apollonius
was truly the first to treat the “‘double-branch hyperbola”’—
that is, the opposite sections—fully, the opposite sections
were not so completely unfamiliar to his contemporaries that
he had to continually remind them of their existence; indeed,
in the preface to Book 4 he refers to the opposite sections as
if they were known and discussed, at least by Conon of Samos
and Nicoteles of Cyrene. Second, although Zeuthen’s remark
is not meant to explain Apollonius’ use of both terms, it still
begs the question: if what Apollonius called the hyperbola is
truly represented by the Cartesian equation and therefore, is
the modern double-branched hyperbola (as Zeuthen unambiguously implies throughout his book), why cause confusion
by referring to a branch of the hyperbola as the hyperbola
and the two branches together as something else, namely, the
opposite sections? Zeuthen himself never speaks of “opposite
sections” but only of the “two (or “corresponding”) branches
of the hyperbola” the “whole hyperbola” (vollständige
Hyperbel), and, most often, simply the “hyperbola.” In this
way, he and his followers, including Heath, merely push aside
as if nugatory the obvious fact that in the Conica, from start
to finish, there are hyperbolas and there are opposite sections.
The opposite sections (hai tomai antikeimenai) are quite
prominent in the work. They figure in 24 of the 53 propositions in Book 2; 41 of the 56 propositions in Book 3, and 38
of the 57 propositions in Book 4. In all these propositions,
Apollonius treats opposite sections as something apart from
FRIED
95
hyperbolas. A sign of this is that the opposite sections are separated from the hyperbola in the enunciations of propositions. For example, the statement of proposition 3.42 is: “If
in an hyperbola or ellipse or circumference of a circle or opposite sections [emphasis added] straight lines are drawn from
the vertices of the diameter parallel to an ordinate, and some
other straight line at random is drawn tangent, it will cut off
from them straight lines containing a rectangle equal to the
fourth part of the figure to the same diameter.” 3.44 reads, “If
two straight lines touching an hyperbola or opposite sections
[emphasis added] meet the asymptotes, then the straight lines
drawn to the sections will be parallel to the straight line joining the points of contact.” If one knew nothing about the
opposite sections, these statements would suggest that the
hyperbola and the opposite sections were as different from
one another as the hyperbola is different from the ellipse.5
The proofs of these two particular propositions make little
distinction between the hyperbola and opposite sections. In
3.44 a separate diagram for the opposite sections is needed to
bring out a case that applies to the two sections together, but
in 3.42 not even that is needed, despite Heiberg’s insistence
on adding an extra diagram for the opposite sections anyway
(fig. 1). Nothing from the logical rigor would be lost if
Apollonius referred only to the opposite sections in these
propositions. So even where the logic does not require it,
Apollonius makes a point to separate, in words verbally, the
hyperbola from the opposite sections.
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Fig. 1: Conica 3.42 (Heiberg)
Α
Ζ
Μ
Η
Θ
97
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Fig. 2: Diagram for Conica 1.14
H
Ε
N
Ξ
Δ
Κ
P
O
Θ
Γ
Α
Y
K
Λ
Β
T
Μ
Η
Ζ
Θ
Ε
Δ
Κ
Β
A
Λ
Γ
Of course this is not to say there is no connection
between the opposite sections and the hyperbola, for the central property of the opposite sections is that they are composed of two hyperbolas. Apollonius proves this in the
proposition that introduces the opposite sections, proposition 1.14:
If the vertically opposite surfaces are cut by a
plane not through the vertex [see fig. 2], the section on each of the two surfaces will be that which
is called the hyperbola [emphasis added]; and the
diameter of the two sections will be the same
straight line; and the straight lines, to which the
straight lines drawn to the diameter parallel to the
straight line in the cone’s base are applied in
square, are equal; and the transverse side of the
figure, that between the vertices of the sections, is
common. And let such sections be called opposite
(kaleisthôsan de hai toiautai tomai antikeimenai)
Π
E
Z
B
M
Λ
Σ
Γ
Δ
This is also the way he refers to the opposite sections
later, especially in Book 4, where he consistently speaks of
“an hyperbola and its opposite section.”7 The genitive in
those phrases suggests that the opposite section belongs to the
given hyperbola, that is, every hyperbola has its very own
opposite section.
The most striking instance in which Apollonius refers to
the opposite sections as two hyperbolas is in his construction
of the opposite sections in 1.59. It is worth reviewing how
this construction is carried out. Apollonius asks, specifically,
for the following:
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98
Fig. 3: Diagram for Conica, 1.59
Δ
A
E
B
H
Γ
K
Z
Θ
Given two straight lines perpendicular to one
another, find opposite [sections], whose diameter
is one of the given straight lines and whose vertices are the ends of the straight line, and the lines
dropped in a given angle in each of the sections
will [equal] in square [the rectangles] applied to
the other [straight line] and exceeding by a [rectangle] similar to that contained by the given
straight lines.8
Let BE and BΘ be the given lines and let H be the given
angle (see fig. 3). Choosing BE to be the transverse diameter
(plagia) and BΘ to be the upright side of the figure (orthia),
Apollonius says to construct an hyperbola ABΓ, adding, that
“This is to be done as has been set out before (prosgegraptai).” For the latter, he has in mind 1.54-55 where he shows
how an hyperbola is constructed having a given diameter,
upright side, and ordinate angle. Next he says: let EK have
been drawn through E perpendicular to BE and equal to BΘ,
and draw an hyperbola ΔEZ having BE as its diameter, EK its
upright side, and H its ordinate angle, again, presumably,
relying on 1.54-55. With that, he concludes: “It is evident
(phaneron dê) that B and E [i.e., ABΓ and ΔEZ] are opposite
[sections] and they have one diameter and equal upright
sides.” I shall return to the question whether it truly is evident
that B and E are opposite sections, but for now what is
important to understand is that Apollonius constructs the
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opposite sections by constructing one hyperbola and then
another.
Hence the opposite sections are two hyperbolas but not
any two hyperbolas; they are two hyperbolas somehow
linked together; they belong to one another the way identical
twins do.9 In a sense, then, Apollonius, as I understand him
and as Zeuthen understands him, begins with the hyperbola;
however, we disagree about the direction in which he proceeds. Whereas Zeuthen begins with the hyperbola as the
two-branched curve given by the Cartesian equation and then
focuses on the single branch, which Apollonius calls the
hyperbola, my view is that Apollonius begins with the single
connected curve, which he calls the hyperbola, and then
investigates the opposite sections in terms of it. Although
Ockham’s razor would probably fall on the side of the latter
view, we need to get a better grasp of this peculiar situation
wherein two well-defined curves, the two hyperbolas, become
together a distinct geometrical entity, the opposite sections.
To do this, let us consider the ways in which two conic sections are juxtaposed in the Conica, that is to say, let us consider how Apollonius treats pluralities of curves.
Pluralities of Curves
Surely, the juxtapositions of conic sections are to be found in
Book 4 of the Conica. The very point of that book is to investigate the ways in which conic sections can come together—
whether they touch, whether they intersect, at how many
points can they touch, at how many they can intersect, and so
on. The variety of configurations Apollonius considers can be
seen in the diagram for, say, 4.56:
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Fig.4: Diagram for Conica 4.56
Δ
Δ
Γ
Γ
Γ
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straight lines drawn to either of the curved lines parallel to
some straight line…and I call that straight line the upright
diameter which, lying between the two curved lines, bisects
all the straight lines intercepted between the curved lines and
drawn parallel to some straight line.” An illustration for the
upright and transverse diameter can be seen in fig. 5 below,
which is not a diagram from Apollonius’ text.
Δ
Fig. 5 The upright and transverse diameters
Δ
Γ
Δ
Δ
Γ
Γ
As discussed elsewhere,10 one of the fundamental facts
explored in Book 4 is the ability of conic sections to be placed
arbitrarily in the plane, as Euclid postulates for circles and
lines—a fact partially justifying Book 4’s inclusion into what
Apollonius terms a “course in the elements of conics.” But it
is this arbitrariness that makes the question of the plurality of
conic sections in Book 4 the exact opposite of the one we are
trying answer about the opposite sections; for the opposite
sections are not thrown together; they belong together.
The first indication that a pair of curves may be associated
with one another as the opposite sections is given by
Apollonius in the definitions at the start of Book 1. Among
these definitions are those for the transverse and upright
diameters (diametros plagia and diametros orthia). Having
defined the diameter of a curved line, Apollonius continues,
“Likewise, of any two curved lines (duo kampulôn grammôn)
lying in one plane, I call that straight line the transverse diameter which cuts the two curved lines and bisects all the
These definitions prepare us for the transverse diameter
of the opposite sections introduced in the same proposition
in which the opposite sections themselves are defined, 1.14;
that the two hyperbolas making up the opposite sections have
a common diameter is one of the things that links them
together. Interestingly enough, the upright diameter, which is
the diameter explicitly defined for two curves and that which
is most clearly applicable to the opposite sections,11 is rarely
used by Apollonius: it is used twice in Book 2 (2.37, 38) and
once in Book 7 (7.6); and even in those cases Apollonius is
quick to identify it as one of a pair of conjugate diameters
(suzugeis diametroi), which are good for both two curves and
one. So while Apollonius provides for the possibility of distinct curves linked together, he seems almost to avoid the
idea, at least with regards to the opposite sections.
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The Conjugate Sections
But the opposite sections are not the only curves linked
together in the Conica. What Apollonius calls the conjugate
sections (hai tomai suzugeis) consist of four hyperbolas, or, to
be precise, two pairs of opposite sections.12 The very word
Fig.6: Conjugate Sections
K
H
Γ
B
A
Δ
Λ
Θ
suzugeis refers to a couple yoked together, a married pair.13
What links them together? First, by the definition given them
in 1.60, the diameter of the one pair is the conjugate diameter of the other, that is, if the diameters of AB and ΓΔ are D
and d, respectively, then lines drawn in AB parallel to d will
be bisected by D, and vice versa; moreover, D is equal in
square to the rectangle contained by d and the latus rectum
with respect to d (this rectangle being the “figure” or eidos of
the opposite sections), while d is equal in square to the rectangle contained by D and the latus rectum with respect to D.
Second, as Apollonius shows in 2.17, “The asymptotes [lines
HΘ and ΛΚ in fig. 6] of conjugate opposite sections are common.” This is also shown for the opposite sections in 2.15;
these shared asymptotes are certainly a crucial unifier not
only of the conjugate sections but also of the two opposite
sections themselves.14
Compared to the arbitrary juxtapositions of conic sections presented in Book 4, the opposite sections and the conjugate sections seem to be quite similar in that their component curves are bound by means of asymptotes and diameters.
Indeed, Apollonius often treats the opposite sections and conjugate sections in analogous propositions for instance: 2.41
states, “If in opposite sections two straight lines not through
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the center cut each other, then they do not bisect each other”;
and 2.42, states that “If in conjugate opposite sections two
straight lines not through the center cut each other, they do
not bisect each other.” Yet this close connection between the
opposite sections and conjugate sections raises the question
about why the opposite sections nevertheless enjoy a status in
the Conica that the conjugate sections do not? Why, in particular, are the conjugate sections never mentioned in conjunction with the other conic sections as are the opposite sections? Why are only the opposite sections included in the
clique, parabola, hyperbola, ellipse, and opposite sections?15
For this, we must return to the beginning of the Conica, for
the answer has very much to do with beginnings.
The Genesis of the Opposite Sections
The Conica opens not with the definition of the conic sections, but with the definition of the conic surface (kônikê
epiphaneia) from which arises the figure of the cone. Here is
Apollonius’ definition:
If from a point a straight line is joined to the circumference of a circle which is not in the same
plane with the point, and the line is produced in
both directions, and if, with the point remaining
fixed, the straight line being rotated about the circumference of the circle returns to the same place
from which it began, then the generated surface
composed of the two surfaces lying vertically
opposite one another, each of which increases
indefinitely as the generating straight line is produced indefinitely, I call a conic surface, and I call
the fixed point the vertex…..And the figure contained by the circle and by the conic surface
between the vertex and the circumference of the
circle I call a cone.
The definition is vivid and visual owing in large part to its
motion-imbued language. Motion, as is well known, is
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THE ST. JOHN’S REVIEW
avoided in Greek mathematics. Thus, much has been made of
the hints of motion in Elements, 1.4. But avoiding motion
seems to be a desideratum chiefly for propositions and
demonstrations, for motion in definitions is not all that
unusual. Besides this one from the Conica, Archimedes gives
similar kinematic definitions for conoids and spheroids in the
letter opening On Conoids and Spheroids, and Euclid himself
defines the cone, sphere, and cylinder in Book 11 of the
Elements by means of rotating a triangle, semicircle, and rectangle, respectively. The presence of motion in these definitions gives one the sense that one is witnessing the very coming to be of the objects being defined. In this way, such definitions take on a mythic quality; one almost wants to see the
demiourgos turning the generating line about the circumference of the base circle.
Fig.7: The Conic Surface
Following the definitions, Apollonius proceeds in ten
propositions to develop the basic properties of sections of
cones and, in particular, to show (in 1.7) how a cone may be
cut so that the section produced will be endowed with a
diameter. When the reader arrives at 1.11, which begins the
series of four propositions defining the parabola, hyperbola,
ellipse, and opposite sections, one is ready to see how these
sections arise within the cone. I do not use the word “see”
lightly. In these propositions, Apollonius dedicates considerable space both in the enunciation and in the body of the
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proof to describe the sequence of geometrical operations
undertaken to produce the particular sections; just as one witnesses the coming to be of the conical surface and cone, now
one witnesses the coming to be of the conic sections.
Of all the sections presented in 1.11-14, the one that is
most obviously related to Apollonius’ cone is in fact the
opposite sections. The reason is clear when one considers
Apollonius’ definition of the conical surface and cone. When
Euclid, by contrast, defines a cone in Book 11 of the
Elements, he does it by describing the rotation of a right triangle about one of its legs. Hence, Euclid begins by defining
the figure of the cone; moreover, Euclid’s cone, from the
start, is right, that is, its axis is perpendicular to its base, and
it is bounded. Apollonius begins by defining a conic surface,
which is generally oblique (since the line from the fixed point
to the center of the circle about whose circumference the generating line turns is not necessarily perpendicular to the plane
of the circle), unbounded, and, significantly, double. The cone
arises from this surface as the figure (schema) contained by
the base circle and the vertex. Later, in proposition 1.4,
Apollonius shows that by cutting the conic surface with
planes parallel to that of the base circle any number of cones
may be produced from the conical surface. In this way, the
two vertically opposite surfaces (hai kata koruphên
epiphaneiae) of the conic surfaces give rise to cones on either
side of the vertex.
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106
Fig. 8: Conica 1.4
Η
Δ
Ε
Θ
A
A
Α
Θ
Δ
Κ
Β
E
H
K
B
Z
Γ
Z
Κ
Θ
Γ
Δ
H
Β
Ε
Ζ
Γ
The doubleness of the conic surface and the double set of
cones that arise from it is (together with its obliqueness)
surely one of the most striking aspects of Apollonius’ definition. So, when Apollonius defines the opposite sections in
1.14, the definition is not entirely unexpected; it has been
prefigured in the definition of the conic surface itself. Indeed,
while the hyperbola is defined in terms of the figure of the
cone, which is defined by means of the conic surface, the
opposite sections are defined in terms of the conic surface,
and in this sense, the opposite sections are prior to the hyperbola. It is worth observing in this connection that 1.14 is the
last proposition in the book in which the conic surface
appears, as if to say that it no longer has to appear, having
served its purpose.
But here a little more needs to be said. For while it is true
that the conic surface does not appear again in the Conica,
the cone does: it reappears in Book 6, where it is used to
carry out various constructions connected with similar and
equal conic sections, and, most importantly, at the end of
Book 1, where Apollonius constructs conic sections in a plane
having given diameters, latera recta, and ordinate angles. In
the latter constructions, Apollonius generally proceeds by
taking the given plane as the cutting plane and then constructing the cone cut by that plane so that the section pro-
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duced is the section required. One might expect, therefore,
that when in 1.59 he set out to construct opposite sections,
he would similarly have constructed the conic surface cut by
the given plane to produce opposite sections. But, as we saw
above, this is not what he does. Applying 1.54-55 in the same
sequence, he constructs one hyperbola and then another.
Furthermore, if one follows 1.54-55 to the letter in constructing the hyperbolas on both sides of BE, which involves
constructing cones as I have remarked, one does not arrive at
the two vertical opposite surfaces composing the conic surface without significantly altering the construction in 1.5455. Can Apollonius truly say, then, as he does, that “it is evident” (phaneron de) that opposite sections are produced in
1.59? I think he can. For when he produces the first hyperbola in 1.59, he does so by producing a cone, in accordance
with 1.54-55; but the cone is only a figure cut off from a
conic surface, and we know from 1.14 that when the plane of
the first hyperbola cuts the opposite surface of the conic surface it will produce the opposite section of the first hyperbola. What remains for Apollonius is only to produce that
second hyperbola so that it has the right diameter, latus rectum, and ordinate direction, which is precisely what he
does.16 So, although the conic surface does not appear explicitly in 1.59, it is still there implicitly. In fact, this is the case
with all the constructions at the end of Book 1: the initial
construction of the parabola, ellipse, and hyperbola, in which
the ordinate direction is right, is carried out by explicitly constructing a cone, but in the continuation of the constructions,
that is, in the cases in which the ordinate directions are not
right, the cone does not appear. In this way, I think it is wrong
to think Apollonius is trying to break away from the cone; the
conic sections are rooted in the cone. Indeed, it is like the
roots of a tree: although the roots are unseen, the leaves, even
those at the very summit of the tree, will not survive without
them.
Thus we can still say with confidence that the opposite
sections have the special status that they do because of their
immediate origin in the double conic surface. They inherit
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THE ST. JOHN’S REVIEW
their doubleness directly from the doubleness of the conic
surface; their unity they obtain from the single plane that cuts
the surface. This geometric birth of the opposite sections sets
them apart from the conjugate sections and puts them in the
same class as the parabola, ellipse, and hyperbola.
Summary and Concluding Remarks
Apollonius’ treatment of the opposite sections tells us much
about his mathematical world—mostly because these sections
are not found outside of it. In modern mathematics there is
only the hyperbola, and the hyperbola has two branches. In
Apollonius’ geometry there is an hyperbola and there are
opposite sections. The hyperbola is produced by cutting a
cone; it has an opposite section since the conic surface from
which the cone arises extends not only below but also above
the vertex of the cone. The opposite sections are linked by
their common asymptotes and common diameter. The conjugate sections are linked similarly by common asymptotes and,
though not a common diameter, by conjugate diameters.
However, this kind of linkage seems to be less compelling for
Apollonius than the linkage arising from the single plane cutting the conic surface, for only the opposite sections, and not
the conjugate sections, are spoken of in conjunction with the
other conic sections.
Earlier I referred to Apollonius’ definition of the conic
surface as having a mythic quality. This was to give some
explanation of the motion-filled description constituting the
definition and to highlight the possibility that the development of the conic sections from the conic surface and the figure of the cone was, for Apollonius, nothing short of a spectacle of mathematical genesis. The use of the word “myth” in
a mathematical context is jarring for modern ears; mathematics, if to anything, should be related to logos not muthos.
But in the Greek world, it must be recalled, muthos and logos
overlapped as well as being opposed (Peters, 1967, pp. 120121), so that relationship between the two was one of tension
rather than exclusion. Cassirer has gone far to show that the
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myth-making function is fundamental to human experience,
and I rather agree with him when he says:
The mythical form of conception is not something
superadded to certain definite elements of empirical existence; instead, the primary “experience”
itself is steeped in the imagery of myth and saturated with its atmosphere. Man lives with objects
only in so far as he lives with these forms; he
reveals reality to himself, and himself to reality in
that he lets himself and the environment enter into
this plastic medium, in which the two do not
merely make contact, but fuse with each other.
(Cassirer, 1946, p. 10)
Be that as it may, the use of the word “myth” in the context
of the Conica does suggest a view of Apollonius as one very
much engaged with the being of his objects and where they
come from; indeed, the distance we feel between myth and
mathematics is partly the result of an overly pragmatic view
of mathematics in which properties take precedence over origins, a view which is characteristically modern. In this paper,
I have tried to show that if we disregard visible geometrical
origins and focus only on abstract relations, such as are captured in an algebraic equation, it becomes difficult to understand why the opposite sections enjoy the status they do in
the Conica as conic sections different from the hyperbola,
and why their status is different from that of the conjugate
sections—and, conversely, I have tried to show that the opposite sections bring us back to the importance of geometrical
origins in the Conica and, in so doing, allow us one key to the
character of classical mathematics.
Bibliography
Apollonius. (1891, 1893). Apollonii Pergaei quae Graece exstant
cum commentariis antiquis. Edited by I. L. Heiberg. 2 volumes.
Leipzig: Teubner.
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Apollonius. (1998). Apollonius of Perga Conics Books I-III.
Translated by R. Catesby Taliaferro. Santa Fe: Green Lion Press.
Apollonius. (2002). Apollonius of Perga Conics Book IV. Translated
with introduction and notes by Michael N. Fried. Santa Fe: Green
Lion Press.
Cassirer, E. (1946). Language and Myth. New York: Harper and
Brothers.
Fried, Michael N. and Unguru, Sabetai. (2001). Apollonius of
Perga’s Conica: Text, Context, Subtext. Leiden: Brill.
Goodwin, W W & Gulick, C. B. (1992). Greek Grammar. New
. .
Rochelle: Aristide D. Caratzas.
Heath, Thomas L. (1896). Apollonius of Perga, Treatise on Conic
Sections. Cambridge: At the University Press.
Heath, Sir Thomas L. (1921). A History of Greek Mathematics,
2 vols., Oxford: At the Clarendon Press (repr., New York: Dover
Publications, Inc., 1981).
Klein, Jacob (1981). “The World of Physics and the Natural
World.” The St. John’s Review, 33 (1): 22-34
Peters, F. E. (1967). Greek Philosophical Terms. New York: New
York University Press.
Sommerville, D. M. Y. (1946). Analytic Conics. London: G. Bell
and Sons, Ltd.
Toomer, G. J. (1990). Apollonius Conics Books V to VII: The Arabic
Translation of the Lost Greek Original in the Version of the Banu
Musa. 2 vols. (Sources in the History of Mathematics and Physical
Sciences, 9), New York: Springer-Verlag
Toomer, G. J. (1970). Apollonius of Perga, in DSB, 1, 179-193.
Youschkevitch, A. P (1976). The Concept of Function up to the
.
Middle of the 19th Century. Archive for History of Exact Sciences
16, pp. 37-88.
Zeuthen, H. G. (1886). Die Lehre von den Kegelschnitten im
Altertum, Kopenhagen, (repr., Hildesheim:Georg Olms
Verlagsbuchhandlung, 1966).
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Notes
The algebraic reading of the Conica as an historical interpretation
has, of course, Zeuthen (1886) as its greatest representative;
indeed, Zeuthen’s view of the Conica was completely adopted by
Heath (1896) and, to some extent, by Toomer as well (Toomer,
1990, 1970).
1
From Sommerville (1946), but, needless to say, a similar description can be found in any other textbook of analytic geometry.
2
In this connection, it is worth recalling that the sense in which
functions such as f(x) = a/x (whose graph, of course, is also an
hyperbola) are to be considered continuous or not has itself an
interesting history, one that shows again how history rarely moves
in straight lines. For Euler, “continuity” referred to the rule, so that
a function, like f(x) = a/x, governed by a single analytic equation
should called “continuous.” Although this view still echoes in our
calling the hyperbola one curve with two branches, Euler’s
approach to the continuity of functions gave away to a more geometrical view of continuity, that is, where continuity has much to
do with connectedness in the work Cauchy and Bolzano (For a
detailed discussion of these shifts in the meaning of continuity in
the history of the function concept, see Youschkevitch, 1976).
3
They are less prominent, however, in the extant later books,
Books 5-7 and in Book 1, where they appear in only 9 propositions.
4
The same argument also shows the difficulty in maintaining that,
for Apollonius, the circle was a kind of ellipse. The relationship
between the ellipse and the circle has been discussed extensively in
Michael N. Fried & Sabetai Unguru, Apollonius of Perga’s Conica:
Text, Context, Subtext, chap. 7.
5
Unless stated otherwise, all translations from Books 1-3 are from
R. Catesby Taliaferro in Apollonius of Perga Conics: Books I-III
(Green Lion edition).
6
For example in 4.48 (although any proposition from among 4.4154 could be taken as an example) we have in the ekthesis: estôsan
antikeimenai hai ABΓ, Δ, kai huperbole tis he AHΓ...kai tês AHΓ
antikeimene estô he E.
7
8
My translation.
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THE ST. JOHN’S REVIEW
For this reason, one might expect the dual to be used in referring
to the opposite sections instead of the simple plural. The dual was
used for denoting “natural pairs” (see W W Goodwin & C. B.
. .
Gulick, Greek Grammar, §§ 170, 838, 914). But, as Christian
Marinus Taisbak has pointed out to me, it seems that by Hellenistic
times “the dual had become more or less obsolete.”
9
Fried & Unguru, op. cit., chap. 3; Fried, M. N., Apollonius of
Perga: Conics Book IV, pp. xxi-xxvii.
10
Thus, it is not at all surprising that the figure Eutocius uses to
illustrate Apollonius’ general definition of the transverse diameter is
evidently a pair of opposite sections (Heiberg, 2.201), and not, say,
a pair of circles, which would have served as well and which I have
used above.
11
12
The conjugate sections are introduced in the last proposition of
Book 1, proposition 60. Besides 1.60, the conjugate sections appear
also in propositions 2.17-23,42-43; 3.13-15,23-26,28-29, as well
as in a very striking proposition in Book 7, 7.31.
For the verb suzeugnumi, from which suzugeis is derived, Liddell
and Scott give the definitions, “to yoke together, couple or
pair…esp. in marriage.” It is worth noting that in 4.49, 50, 51
Apollonius uses the same adjective suzugeis to refer to opposite sections.
13
14
See Fried & Unguru, op.cit., pp. 123-124.
In Book 4, particularly in 4.25 (which is the central theorem of
the book: “A section of a cone does not cut a section of a cone or
circumference of a circle at more than four points”) the opposite do
seem to be separated from the other conic sections. In this specific
case, however, Heath’s argument above might be correct, namely,
that the cases involving the opposite sections, as Apollonius stresses
in the preface, were new and needed to be highlighted. It may also
be that 4.25 does actually intend the opposite sections, even though
the proof for the opposite sections comes latter; that kind of nexus
is not unusual in the Conica. Whatever the case, it still remains that,
unlike the opposite sections, the conjugate sections do not appear at
all in Book 4.
15
One might argue here that he is using a result here from Book 6,
namely, that two hyperbolas having the equal and similar figures are
16
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113
equal (6.2), but this could be argued regarding all the constructions
at the end of Book 1.
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THE ST. JOHN’S REVIEW
115
Viète on the Solution of
Equations and the Construction
of Problems
Richard Ferrier
Introduction
I wish to do two things in this paper, first to review the
grounds for taking François Viète as a pivotal figure in the
history of thought, and second to clarify an interesting technical aspect of his work, namely, what he called the “exegetical art.” This clarification will show Viète to be a traditional
thinker as well as a revolutionary one, by showing how he
stops short of writing symbolic formulae or solutions to problems in geometry.
The second part is much longer, and will take us through
some proofs, none terribly difficult, I hope. The mathematical climax is the analysis of the inscription of a regular heptagon in a circle, an example of the exegetical art in action
taken from Viète’s work.
The Importance of Viète
According to Jacob Klein, the man chiefly responsible for
interest in Viète in the last 70 years, “The very nature of
man’s understanding of the world is henceforth, (that is to
say, after Viète’s work), governed by the symbolic number
concept. In Viète’s ‘general analytic’ this symbolic concept of
number appears for the first time, namely in the form of the
species.” Now this last remark needs clarification, particularly
in its use of the term “species,” that is “form” or “eidos,” but
also, perhaps, in the notion of symbolic mathematics that Mr.
Richard Ferrier teaches at Thomas Aquinas College. He has written, but not
yet published, a study of Viète’s transformative work on the analytic art.
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Klein is drawing upon (Greek Mathematical Thought and the
Origin of Algebra, p. 185). I will give a very brief account of
what I think he means.
It comes to something like this. The letters upon which
we operate when we do algebra are not signs of the same
order as the words of common speech. They do not immediately intend or signify anything. They are ciphers related to
each other by rules of connection analogous to syntax in a
spoken language. It is by those rules alone that they acquire
what “meaning” they have. That meaning is now called “syntactic” as opposed to “semantic” meaning. The equals symbol
in an equation does not mean, “is the same in magnitude or
number.” It is rather a relation between two other terms, say
A and B, which happens to be a convertible relation, so if the
first relation holds, A = B, so also the second, B = A holds.
If you give this symbol enough of the behaviors or of the
characteristics that ordinary equality has, then what will be
valid for its use, that is, what will be consistent to say of it
once you have posited the suitable rules governing its role in
a system of such symbols, will also be true of arithmetic or
geometry. This presumes, of course, that you interpret all the
symbols as the kind of beings that arithmetic considers, relations of inequality and equality, numbers themselves, and so
forth. But prior to this interpretation, the set of symbols does
not signify numbers, magnitudes, equalities, additions, divisions, or any other determinate kind of mathematical being.
Moreover, the indetermination in the single letter symbols
gives rise to the notion of a variable, which in turn underlies
modern mathematical or formal logic. Such mathematics is
symbolic mathematics. Mr. Klein claims that the symbolic
concept of number originates in the work of François Viète,
and that this concept comes to dominate modern mathematical thought and to influence modern conceptuality altogether.
Now I do not intend to demonstrate these larger claims
or to argue for them, but rather to look into some particulars
connected with Klein’s view of Viète. First let us note this
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aspect of his view: Klein says, “The symbolic concept of number appears for the first time . . . in the form of the species.”
How can that be? How is it that the term “species” can be the
entry point for the modern notion of number, and in general
for a mode of cognition, symbolic cognition, to enter mathematics?
This is what I understand Mr. Klein to mean, and I think
he is correct: Viète found a use of the word “eidos” in a text
of solutions to number problems, an ancient text, the
Arithmetica of Diophantus, where the word is used for the
unknown number. That is, Diophantus calls the unknown a
“species.” Viète conjoined this use to a discussion of a
method of finding unknown magnitudes in geometry. This
method is called analysis. In geometrical analysis, authors
such as Archimedes and Apollonius operate on unknown or
not actually given lines and figures as though they were given.
Viète, then, brought these two together: (1) the name
“species” or “eidos” for the unknown or, as we would say,
variable; and (2) operating or calculating without making any
distinction between unknown and known quantities. But he
went further. He replaced the given quantities, numbers, or
magnitudes with more species, and so produced the first
modern literal or non-numerical algebra, which he called
“species logistic,” that is, computation in forms.
A very elementary example may serve to clarify this idea
somewhat. You are familiar with the problem of finding a
fourth proportional. Now if you express that in algebra you
would come up with something like this: let ‘x’ stand for the
unknown. x is to a as b is to c. In that expression the letter ‘x’
does not stand for something you now have or know. It is not
clear how you should add or multiply or in any way deal with
something that you do not yet have.
Let us ignore this mystery of operating on what is not
there for you, what is not given. Writing x is to a as b is to c,
you take the product of means and extremes, and you wind
up with x times c = a times b. Then you divide both products
by c and you have x = a times b divided by c, where a, b, and
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c are the givens that will determine x, and when you have that
you have a formula for making x be given to you. Of course,
you cannot compute x unless a, b, and c are actual numbers,
say 4, 5, and 10. If these are the given numbers, then x is
given as well, and it is the number 2. Neither can you construct x, unless you have determinate magnitudes, say straight
lines, as the three givens.
If you keep the letters a, b, and c and you allow a, b, and
c to be equally indeterminate with x, then you no longer have
a definite x so much as a kind of relation between a, b, c, and
x. In algebra, we stop with this relation, calling it both the
formula and the solution to our problem. That is what happens when the particular numbers of an ordinary problem—
to find the fourth proportional—are replaced by signs for the
possibility of finding such a number. You no longer can take
a times b and divide it by c, because a, b, and c are just as
indeterminate as the original unknown. This is what I mean
when I say that Viète used Diophantus’ term species to designate not only the unknowns but also the knowns. He called
the resulting field of calculations and operations, and the consequences of performing them according to laws set out,
“species logistic,” that is, calculation in species.
If we take two easy steps beyond what Viète did, writing
a formula for quadratics and using two unknowns as axes in
a plane, his work leads directly to negative, irrational and
complex numbers, to the idea of a variable, and to analytic
geometry. All this stems from letting the symbol, the
“species,” stand in for the determinate number or magnitude
of classical mathematics.
Viète himself puts it this way, (he uses the term “zetetic,”
which I will discuss later). “The zetetic art does not employ
its logic on numbers, which was the tediousness of ancient
analysts, but uses its logic through a logistic which in a new
way has to do with species. This logistic is much more successful and powerful than the numerical one.” So Viète commands our attention as the originator of the modern algebraic
number concept, and the notion of mathematics as a symbolic
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science not immediately about anything but the arrangements
of its own terms into systems. I say Viète commands our
attention as the originator. Now it is of course the case that
however revolutionary Viète thought he was and however
proud he was of his accomplishment, he did not see all the
things that came from it, for example, imaginary numbers, or
co-ordinate geometry. How did he think of his work? He considered his work largely a restoration of a way of seeking that
went back to Plato. I say he considered it largely a restoration
because there is an addition to the restored analysis that Viète
expressly claims as his own, which he calls exegetic, and it is
this part that I would like to set out next.
The principal ancient text from which Viète formed his
view of analysis is the Seventh book of the Collectio of
Pappus. Pappus distinguishes between seeking, or “zetetic,”
and providing, or “poristic” analyses. This difference answers
to the difference between the propositions in the Elements
that end “Q.E.D” and those that end “Q.E.F.,” that is,
between theorems and problems. There are two types of
analysis, since there are two types of propositions with which
geometers are ordinarily concerned. Viète, for reasons too
subtle to lay out here, read Pappus in another way, making
zetetic and poristic parts of one procedure, a procedure ordinarily applied to a problem, not a theorem. Still, he conceived
of his work as a restoration of the lost art—or perhaps the
partially lost art—of analysis, that is, as a renovation, not an
innovation. That is a striking characteristic of Viète and his
contemporaries. You find in them a preference for the lost or
partially recovered sources in antiquity, for Democritus over
Aristotle, and when Plato is not fully available, for Plato over
Aristotle, for Archimedes over Euclid, and in general for
whatever the schoolmen did not hand on over what the
schoolmen did hand on. They sought the key to the deepest
truths in the arts and sciences in a correct restoration of the
faultily preserved sources of antiquity in preference to accepting the ones that they had received more perfectly intact from
their teachers.
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This is what Viète says: “And although the ancients had
set forth a two-fold analysis, the zetetic and the poristic, it is
nevertheless fitting that there be established also a third kind,
which may be called ‘rhetic’, [telling] or ‘exegetic’, [showing
or exhibiting], so that there is a zetetic art by which is found
the equation or proportion between the magnitude that is
being sought, and those that are given, a poristic art, by which
from the equation or proportion the truth of the theorem set
up is examined, and an exegetic art, by which from the equation set up or the proportion there is exhibited the magnitude
itself which is being sought.” As if to emphasize his own
achievement in completing the method of analysis, he says,
“And thus the whole threefold analytical art, claiming for
itself this office may be defined as the science of right finding
in mathematics.” As to the importance of the third part,
rhetic or exegetic, he says in another place, “Rhetic and
exegetic must be considered to be most powerfully pertinent
to the establishment of the art, since the two remaining provide examples rather than rules.” He emphasizes the importance of the third part in the remarkable concluding words of
the introduction to the analytic art: “Finally, the analytical
art, having at last been put into the threefold form of zetetic,
poristic, and exegetic, appropriates to itself by rights the
proud problem of problems: To leave no problem unsolved.”
What exactly is the third part of the analytic art, the
showing or exegetic part, the part that Viète himself emphasized and considered his own invention? One way to proceed
to answer would be to read or re-read the parts of Viète’s
Isagoge that touch on exegetics. If your experience is like
mine, though, you know that it is one thing to have someone
describe a procedure, especially a mathematical procedure,
another to know it from having carried it out. Accordingly, I
propose to explicate Viète’s notion of exegesis by doing some
geometry. To prepare for the example of exegetics taken from
Viète, we will look at a problem of my own.
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Viète’s Exegetic Art
Analysis Bootcamp
Our practice will be the analysis of the construction of a regular polygon, the pentagon.
Problem: to inscribe a regular pentagon in a circle.
Figure 1 Inscription of a regular pentagon in a circle
Now the analysis of a construction always starts this way:
suppose you already have what you want to make.
Let it be done, or rather as they say, “let it have been
done.” Our figure is, then, given not really but hypothetically.
ABXCY is supposed to be a regular pentagon in a circle. All
the sides are equal, equal sides subtend equal arcs, equal arcs
subtend equal angles at the circumference, and therefore
angle ACB is precisely half the angle ABC, and is also half the
angle CAB.
The triangle CAB is therefore an isosceles triangle, CA
equaling BC, with the vertex angle half the angles at the base.
Next let the angle at A be bisected by AD. The two half
angles then will each be equal to the angle ACD and the triangle ADC will also be an isosceles triangle.
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Since the angle BAD is equal to the angle ACD, if a circle
be described through the three points A, D, C, the line AB
will be tangent to that circle, for the angle that a tangent
makes with a chord is equal to the angle subtended by the
same arc at the circumference. But the square on a tangent is
equal to the rectangle contained by the whole secant and the
part outside the circle, that is BC and BD, i.e., the square on
AB = rectangle BD, BC. But inasmuch as AB = AD = DC,
then the square on DC = the rectangle BD, BC.
Well, then, if I had this pentagon in this circle, I would
have this line BC cut at a point D so that the square on DC,
the greater segment, is equal to the rectangle contained by the
whole line and the lesser segment. But there is a proposition
that tells me how to do that, the eleventh proposition in the
second book of the Elements. So, let it be done and then
prove “forwards,” or synthetically, all the connections that I
just established “backwards,” or analytically, and at the end
we will really have our pentagon in a circle.
Now, that is a classical geometrical analysis and synthesis
of the sort you would find in the second book of Apollonius,
numerous places in Archimedes, and in Pappus. I have not
used anything algebraic. But, let us indulge ourselves in some
algebra, and look at the equation here: the square on DC =
BD, BC. Calling BC ‘a’, and DC ‘x’, the equation is x2 = a(ax). “And,” you could say to yourself, “if I could only solve for
x, then I would know how long to make DC, and if I could
make DC then I could do the problem. But this is a quadratic
equation, and I can solve it.”
That is the method of analysis. I include here what came
to be called the ‘resolution.’ We began in the classical mode
by looking at the angles and finding a proportion, which we
resolved into an equality between a square and a rectangle.
When we reach this point, we can either continue in the classical mode by thinking of the equality in geometrical terms,
and do the synthesis as a construction, which would be the
answer to the problem. Or we can examine the equality alge-
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braically and work with it in that mode to reach a formula for
x, and consider the formula the solution of the problem.
Recall what Viète said about exegetics: it is supposed to
provide the unknown magnitude itself, to exhibit or construct
it. One would expect exegetics to provide the way for finding
such an unknown as we had in the present problem, that is,
it would seem to be some sort of procedure for cutting the
line BD at a point like D that will produce the requisite properties. One is tempted to think that the procedure intended is
to use the quadratic formula to solve for x, and then interpret
the right hand side as a series of simple geometric constructions. As we shall see later, though, this is an error. Viète’s
exegetic art is not the mechanical exploitation of the formulae of solved equations.
Analysis with Live Ammunition
Next, we will see what Viète does in a real problem that is
considerably more complex but of greater interest.
The problem is to inscribe a regular seven-sided polygon,
a heptagon, in a circle. It is taken from Viète’s published work
and is a real instance of the kind of solution Viète promises in
the introduction, that is, it is a real instance, I think, of
exegetics. To solve it we will need a postulate and two lemmas.
Postulate: To draw a straight line from any point to any two
lines so that they cut off on it any possible predetermined
interval. (I have illustrated this in the next figure. See figure 2.)
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Figure 2 Postulate
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Figure 3 First Lemma: Trisection of an angle:
First Lemma: To trisect a given angle.
Let the given angle be DCE.
The point called the pole is the “any point” of the postulate. “To draw a straight line from any point”: so the straight
line must pass through the pole. “To draw it to any two
lines”—those two lines are the curved line and the straight
line below—“so that they cut off on it any possible predetermined interval”—the interval is up there above; it is given in
advance, predetermined, and what I would like you to grant
me in this postulate is the power to put a line through that
pole so that between those two other lines, that interval is cut
off. Now I must say, “Any possible predetermined interval”
because as is obvious to the eye, I guess, in this figure, if I
made that interval too short, I could not fit the line through
the pole so as to have that interval cut off on it no matter
what. If the two given lines were, for another example, concentric circles, and if the pole were the center of the circle,
then this postulate would be of no use at all because the only
distance between those two lines on lines drawn from the
center of the circle is the difference between their radii; that
is all I could have. So I must say, “any possible predetermined
interval.” If it is possible, I would like the right to place that
line passing through the pole so as to have that distance intercepted on it. This postulate is mentioned in the Isagoge. To
the reader who has not read more of Viète than the Isagoge,
it is not clear why that is in there at all—but he asks for that
postulate for certain purposes, and I ask for it, too.
Let a circle be described with C as center and radius CD.
With pole D and interval = CD we use the postulate to insert
line ABD, so that the interval falls between the circle and the
line CE extended.
I say that angle BAC is 1/3 of angle DCE.
Since AB = BC = CD, the triangle BCD is isosceles, with
equal angles at B and D. But each of these is double the angle
at A. And the one at D together with A is equal to angle DCE.
In the case where the angle to be trisected is greater than 135
degrees, we use the equal exterior angles at B and D, which
are again each twice the angle at A, as in the second figure.
Q.E.F.
Second Lemma: In the first figure for Lemma 1, if we construct DE=CD, the following equality holds:
The cube on AC, minus three times the solid contained by
AC and the square on AB, is equal to the solid contained by
CE and the square on AB.
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Figure 4 Lemma 2: cube AC - 3 times solid (AC, sq. AB) = solid (CE, sq. AB)
Looking at the figure (figure 4), if I drop perpendiculars
BI, DK, and erect a perpendicular CH and extend it, on the
vertical line FHCG I have the situation presented in the
Elements 2.5, that is, I have a straight line bisected and cut
somewhere else, and therefore the square on the half will
equal the sum of the rectangle contained by the unequal segments and the square on the segment between the bisection
point and the point making the unequal cut. And looking at
the straight lines BHD and FHG, I have the situation of 3.35,
namely two lines in a circle cutting each other. When two
lines in a circle cut each other, the rectangles contained by the
segments are equal. I will use those properties and the
Pythagorean Theorem and a few other elementary truths to
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demonstrate the lemma, but the key ones are the ones I just
indicated.
The proof is given next to the figure. The square on AB,
which, since AB = BC is the same as the square on CG, is
equal by that proposition in the second book of the Elements
to the square on CH and the rectangle contained by the
unequal segments FH, HG. But the square on AB minus the
square on CH will be the rectangle which is in turn equal to
the rectangle BH, HD by the other proposition from the third
book, namely that rectangles made of the segments of two
intersecting lines in a circle are equal. Now the square on
CH, by the Pythagorean Theorem, will be equal to the difference between the square on the hypotenuse AH and the
square on AC. But since BI is a perpendicular drawn from the
vertex of an isosceles triangle, it will bisect the base AC, and,
BI being parallel to HC, the line AH will also be bisected at
B, so that the square on AH is four times the square on its
half, AB. Then the square on CH is the difference between
four times the square on AB and the square on AC. Next,
from that and the line above, namely, that the difference
between the square on AB and the square on CH is equal to
the rectangle BH HD, the square on AC minus 3 times the
square on AB will be equal to the rectangle BH HD. Now that
is almost where I want to be because I am interested in the
cube on AC, and the difference between that and—I am looking at the conclusion now—three times the solid contained by
AC and the square on AB. I have those solids with the height
removed, as it were, I just need the height AC and I have
those solids. That is my next goal.
Then BH is to HD as IC is to CK, since any two lines cut
by parallel lines are cut proportionally. And if BH is to HD as
IC is to CK, then it is also in the same ratio as their doubles
AC and CE. So that BH is to HD as AC is to CE. Then, taking the common height, BH, the square on BH is to the rectangle BH, HD as AC is to CE. But BH is equal to AB so that
the square on AB is to the difference between the square on
AC and three times the square on AB—that was what we
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found equal to the rectangle BH, HD—in the same ratio,
namely as AC is to CE.
Then taking means and extremes, the solid contained by
the means is equal to the solid contained by the extremes,
namely the cube on AC, minus three times the solid contained
by AC and the square on AB is equal to the solid contained
by CE and the square on AB. Q.E.D.
I would note at this point that everything we have gone
through in these preliminaries is strictly classical, synthetic
geometry. It could all have been done by Archimedes or
Apollonius, and some of it, in fact, was done by them.
Now let us see what interest this second lemma might
hold. It seems to me the easiest thing would be to look at this
figure given below (figure 5) which removes all the middle
steps and just looks at the result.
Figure 5
If you have two isosceles triangles with equal sides p and
unequal sides q and x, then you get an equation answering to
the equality that I gave in the geometrical mode namely that
x3 – 3xp2 = qp2 or, in short, this is a geometrical configuration that answers to a cubic equation. If you have ever gone
back and looked at things in Euclid, trying to express them in
equations, you will know that cubics are unusual. You almost
always get squares. This theorem answers to a cubic equation.
And that is why Viète proves it. He proves this theorem in
order to give a geometrical counterpart to that cubic equation.
If the terms in the equations are interpreted as the sides
and bases of the triangles in this theorem, then the solution
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of the interpreted equation would reduce to the construction
of this figure. That is, if you could construct the triangles set
up this way, and in particular if you could give yourself x,
then you would have solved this equation, this interpreted
equation, as I would like to speak of it. To put this another
way, if x3-3xp2+qp2, then x can be found as the base of an
isosceles triangle whose equal sides are p and whose base
angle is 1/3 the base angle of an isosceles triangle with sides
p and base q. Now the angles of such a triangle, namely the
one with two sides p and a base q, are given. Why? Because
the whole triangle is given. If you have three sides you have
a determinate triangle, and so the angles are given. And given
two equal sides and any one angle in an isosceles triangle, the
remaining side and the remaining angles are also given.
Consequently the base of the flatter triangle would be given.
Thus all we need to do to solve for x is to trisect a given
angle. This is easily done by means of our first lemma.
To review: we have a postulate that allows us to insert a
rotating line through a given point across two lines so as to
have cut off on it any interval. We have found a figure that
answers to a certain cubic equation, namely, paired isosceles
triangles with a 3:1 base angle ratio, that answers to a certain
cubic equation, and we obtained this figure by trisecting an
angle. Those are the preliminaries.
Last, let us see how Viète inscribes a regular seven-sided
polygon in a circle. This problem, incidentally, is Viète’s own
final problem in his Supplementum Geometriae, his completion of geometry. I have chosen it not only for its intrinsic
interest but also because I think Viète, who calls the
Supplementum a work in exegetics, gave this problem as a
specimen of the workings of his exegetic art.
Problem: To inscribe a regular heptagon in a circle.
Let it have been done. (See figure 6.)
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Figure 6 Inscription of a regular heptagon in a circle
And let BE be one side of the heptagon; then the angle ECB
will be 1/7 of two right angles. Then the angle at E, CEA, will
also be 1/7 because that is an isosceles triangle, EAC. Then
the angle EAB will be 2/7 because it is the sum of those. Now
from the point E let ED be drawn equal to the radius of the
circle, and where it cuts the circle at F let the line FA be
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drawn to the center. Then we have two isosceles triangles of
the sort in the trisection lemma from which it follows that the
angle FAC is three times angle EDA. It is the same figure that
we had in the trisection lemma. In the triangle EAC the two
smaller angles each being 1/7 of two right angles, the remaining angle at A is 5/7 of two right angles, but the whole angle
FAC being triple the angle at D, which is itself 2/7, will be
6/7. The remaining angle FAE will be 1/7 of two right angles.
It will be equal then to the angle AEC, so that the lines FA and
EC will be parallel.
Since those two lines are parallel they cut the sides of the
triangles DEC and DFA proportionately, so DE is to DC as
DF is to DA. But, by another proposition from book 3 of the
Elements, the book of circles, the rectangle contained by the
segments of a secant, that is, the whole secant and the part
outside, DF, DE, is equal to the rectangle contained by the
segments of any other secant drawn from the same point outside. So DB, DC equals DE, DF. Then, turning that equality
into a proportion: DE is to DC as DB is to DF, but as DE is
to DC as DF is to DA, therefore DB, DF, DA are continuously
proportional. Then, in a continuous proportion the first is to
the third in the duplicate ratio, or as the squares, on any
terms in the ratios and also any terms having the same ratio
as those terms. So DB is to DA as square DE is to square DC.
But DE was by construction made equal to the radius so DB
is to DA as square AB is to square DC. Here we stop.
How does one know when to stop in an analysis? Well,
here is one way I know in this one. You stop when you have
projected the ratios you know in various parts of the figure
down to ratios on one line. It happens in the synthetic proofs
of Apollonius, too. You take a number of ratios in the figure
and when you transform them into a proportion all on a single line, that tells you how the lengths in that line are related.
That is where we are now. We have taken the ratios that exist
through the figure because of its shape and we have turned
them into a proportion among the parts of one line. That is
also beautifully adapted for conversion into an equation.
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That line, of course, is the diameter extended, DBAC, and
our proportion is DB is to DA as square AB is to square DC.
Let us turn this into species logistic, or algebra. What do
we need to construct the heptagon that we do not know? Is
it not clear that we need to know DB? If we knew DB, we
could locate point D and since DE is equal to a radius, we
could just swing a radius out from D and cut off the other end
of the side of the heptagon, and we would be done. So DB is
the unknown, and that is the only term we need to find on
this line, on the diameter extended. So call DB ‘x’, and the
radius ‘r’. DA will then be (r+x), and DC will be (2r+x). The
proportion then may be written: x: (r+x) :: r:(2r+x). Means
and extremes can be taken, yielding the equation: x3 + 4rx2
+ 3r2x = r3.
This does not look very promising. It is a cubic, and we
have a pattern for solving a cubic, but not this cubic. Happily,
there is an algebraic gimmick that Viète invented called
“plasma,” which will do the trick. (Almost none of Viète’s
technical terms passed into common use, by the way.
Accordingly, it is like reading ancient law-books to read him
talking about his procedure. One of the few Viètean terms
that did last was “coefficient,” but “plasma” did not.)
“Plasma” is the technique of getting rid of an unwanted term
in an algebraic expression by taking a substitute variable. In a
way you might say that is what you do when you complete
the square in solving a quadratic. You find the right thing to
remove the middle term, the term that is just an x, and then
it is just a simple square; it is no longer a three-term expression. Now in cubics if you could remove two terms at once,
then all you would have to do is take cube roots and you can
solve them in much the same way you solve quadratics.
Plasma gets rid of one term, a term in x or x squared, but
unfortunately only one. The substitution that you make to do
it is y = x + 4/3r, or x = y – 4/3r. Let that substitution have
7
been made, and you get the equation in y:y3 – 7 r2y= 27r3.
3
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Now if we let p = r √7/3, and r/3 be q, this equation
transforms into our pattern y3 – 3yp2 = qp2. Point D gives x
and y, and hence one side of our heptagon. Since we have the
side, we can just go around the circle six more times and the
problem is done.
I omit a slight digression in Viète’s analysis here. It is
done for reasons of elegance and does not substantially
change the argument. This is the pivot point of the argument,
where we move from analysis to synthesis. Viète’s synthesis
runs through the analysis backwards: first the analysis in the
equations and proportions, and then the analysis in the
angles, until he has a proof that the figure that he had made
in the circle is a regular seven-sided figure. I will omit the synthesis.
It must be noted, however, that not only would every
ancient geometer have provided a synthesis, but that Viète,
too, gives it in the Supplementum Geometria, the text from
which this all comes. Indeed, it is all that he gives. What I
have laid out here is a reconstructed analysis following his
remarks on how to do these sorts of problems. That is, he
says that the proof will be the reverse of the analysis and that
the analyst dissimulates and does not show you everything he
did. This seems to me to be a kind of challenge to readers of
those texts to find out what he did do. Descartes says just that
in his Géométrie. So that is what I have given you: it is a
reconstructed analysis of his problem. Like Descartes, Viète
complains that the Ancients covered their tracks and then
does the same himself!
Conclusion
A survey of our procedure is now in order. First, we did
not do something that the discussion of exegetics in the
Isagoge might suggest. I think also it is what Mr. Klein’s book
suggests, and I know it is what I thought when I first read the
Isagoge myself. We did not, using algebra, or as Viète calls it,
species logistic, solve the equation to which we had reduced
our problem. That equation would be the first one that had
�134
THE ST. JOHN’S REVIEW
the fours in it, and that we later on reduced by plasma to
another equation. At no point in working with that equation
did we solve for the unknown in the shape of a formula.
There is not an algebraic or analytic solution to that equation;
it is not to be found. You perhaps may wonder if I misspoke
my thought there: absolutely not. In fact, the cubic equation
involved here is the so-called “irreducible cubic,” which
means that it cannot be solved by algebra. If you try to solve
it by algebra, you involve yourself with imaginary quantities,
and every attempt you make to get rid of them is like stepping on the bump in the rug: they pop up again elsewhere.
They cannot be gotten rid of. So it is not just that he failed to
do it. He cannot do it; no one can do it.
Exegetics, then, does not mean performing the geometric
counterpart of an algebraic solution as it is laid out in a formula. It does not mean getting -b±√b2-4ac
for example, and then
2a
going through the squaring,
adding, subtracting, and so on in geometry, with the formula
laid out for you as a kind of blueprint. This is something to
which the opening pages of Descartes’ Géométrie point. I say
“point” because I am not sure even Descartes does it; you
have to think for awhile to see whether he intends his figures
to be the simple exploitation of his operation or not. Perhaps
they are not exploitations of the quadratic formula, but independently given geometrical constructions. As is so often the
case with the foxy Descartes, he does not say enough to help
us be sure what he has in mind. It is defensible, though, in the
light of what he does say, that he intends you to have a geometric counterpart for each algebraic operation, and just to
exploit the formula directly. That is at least defensible in
Descartes. In Viète it is not so.
So what did we do if we did not do that? Well, first we
performed an ordinary geometrical analysis of the sort
Archimedes might have done. This ended in a proportion.
That proportion was then treated as an item in logistic. We
forgot that it was about lines and just regarded it as a number
of items in a logistic relation. It was transformed until it
FERRIER
135
reached a certain form. What form? A form we knew in
advance from our first lemma to have its geometrical counterpart in a constructable figure—that is, constructable if you
grant our postulate. Then, after we had noted certain proper
elegances pertaining to this particular problem, we proceeded
synthetically (or rather, we would have if we had gone
through all of the steps), first constructing the requisite line
and then the whole polygon, and then, via the resulting equation and other relations, proving that it is indeed a regular
seven-sided figure in a given circle. Zetetic is Viète’s name for
the first two parts of this procedure, both the geometrical
part terminating in the proportion and the algebraic analysis
in which we reach an equation in standard form.
Zetetic ended when the equation to which the problem
had been reduced fit one of a number of standard forms, our
lemma for cubics being one such form. This lemma provides
the principal exegetical part. By means of this lemma, we can
now find the unknown, in this case the line DB. Exegetics as
a procedure is regular and synthetic. I mean those terms
strictly, that is, the construction is a standard, mechanical
exploitation of the equation that can be given by a standard
construction. The complete synthesis simply runs through the
zetetics in reverse order. If your problem reduces to a cubic
of another form (this is the same with the one we have been
examining, but with the signs on the left side of the equation
switched: 3p2x – x3 = p2q) there is, in the Supplementum,
another, similar exegetical lemma you can use to start your
construction, and the situation is quite the same for problems
such as inscribing the pentagon, reducing to quadratic equations.
Viète treats quadratics in another treatise, and it is an
extraordinarily puzzling little work. Almost everything in it is
painfully obvious, at least the first 14 or so propositions are,
and it has the rather odd and stuffy title, which I think should
now make sense, “The Standard Enumeration of Geometrical
Results.” It is a handbook; it is like a carpenter’s manual.
When you have one of these, build in this order that, etc. He
�136
THE ST. JOHN’S REVIEW
does this for quadratic equations and for certain biquadratic
equations. Moreover, in all these cases, the proof, which follows the construction, as in Euclid, is a straightforward reversal of the geometrical and logistic analyses that preceded—
now that, I think, fits Viète’s language in his introduction; it
makes sense of his language.
So exegetics in practice comes to this. It is the provision
and employment of a series of standard constructions for
finding unknown quantities when such quantities are
enmeshed in equations of various degrees, without solving
the equations. This is important, since it manifests the way
Viète stands in two camps, modern or symbolic, and ancient
or constructive. Though species logistic is of profound value
to him, he never rests in the fully analytical or symbolic solution to his equations. They must always be perfected by realization in construction or computation, artful synthetic and
non-symbolic procedures.
I hope we may now see why Viète wrote, “Exegetic comprises a series of rules, and is therefore to be considered the
most important part of analytic, for these rules first confer on
the analytic art its character as an art, while zetetic and poristic consist essentially of examples.” The analyst who knows
exegetics will know what the standard constructable forms in
each degree are, and he will accordingly know what to aim at
in his zetesis, in his analysis. This will in turn inform his
development of the techniques of species logistic, and finally,
if he believes, as Viète came to believe, that he has all the
exegetics that can be, he may well boast that, “The analytical
art, having at last been put into the threeform form of zetetic,
poristic, and exegetic, appropriates to itself by right the
proud problem of problems, which is to leave no problem
unsolved.”
�
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Kraus, Pamela
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Sachs, Joe
Flaumenhaft, Harvey
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Fried, Michael N.
Ferrier, Richard
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The St. John's Review
Volume XLV, number three (2000)
Editor
Pamela Kraus
Editorial Board
Eva T. H. Brann
James Carey
Beate Rubm V<in Oppen
Joe Sachs
John Van Doren
Robert B. Williamson
Elliott Zuckerman
Subscriptions and Editorial Assistant
Blakely Phillips
The St. John's Review is published by the Office of the Dean, St. John's
College, Annapolis: Christopher B. Nelson, President; Harvey Flaumenhaft,
Dean. For those not on the distribution list, subscriptions are $15.00 for
three issues, even though the magazine may sometimes appear semiannually
rather than three times a year. Unsolicited essays, stories, poems, and reasoned
letters are welc?me. Address correspondence to the Review, St. John's ·College,
P.O. Box 2800, Annapolis, MD 21404-2800. Back issues are available, at
$5.00 per issue, from the St. John's College Bookstore.
©2000 St. John's College. All rights reserved; reproduction in whole or in
part without permission is prohibited.
ISSN 0277-4720
Desktop Publishing and Printing
The St. John's Public Relations Qffiu and the St. John's College Print Shop
��Contents
The Liberty Tree: A Memorial
What's In a Name? Why Should We Remember?
The Liberry Tree on St. John's College Campus
Annapolis, Maryland, June 3, I999 ................................................ 5
Dr. Edward C Papa!fuse
The Liberry Tree Ceremony............................................................ I I
October 25, I 999
Christopher B. Nelson
Essays and Lectures
What Was New About the New Republic? ................................ I9
Harvey Flaumenhift
What, Then, is Time? .......................................................................47
Eva T.H. Brann
The Taking of Time ......................................................................... 67
Douglas Allanbrook
Nature and Creativity in Goethe's Elective AJfinities............•••••..85
Astrida Orle Tantillo
Three Poems
Pears
Preparation
While You Are In The Hospital .................................................. IOJ
Laune Cooper
Review
Mind in the 04Yssey.......................••......................••.....•.....•........... !07
Seth Benardete's The Bow and the Lyre
Paul Ludwig
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�-.:f What's In a Name?
fj- Why Should We Remember?
The Liberty Tree on
St. John's College Campus
Annapolis, Maryland
Dr. Edward C. Papenfuse
President O'Brien, Governor Glendening, Comptroller Schaefer, ladies
and gentlemen:
Today,* we not only pay tribute to the largest known Tulip tree in
America as a Maryland Treasure well worth saving, but also, through the
miracle of modern genetics, we ~ommence its cloning as a living memorial to those who have struggled over the years since its birth to define the
meaning of Liberty. Indeed, there is no greater symbol of resistance to
arbitrary rule and of the advocacy of representative government than a
Liberty Tree. One historian, John Higham, has even suggested that the
Liberty Tree replace Uncle Sam as "a compelling symbol of American
identity:'
The idea of Liberty embodied in a living tree comes from Boston in
1765, when the Sons of Liberty chose a stately elm under which to voice
their opposition to the Stamp Act, a British-imposed tax on newspapers
and official documents. They also commissioned Paul Revere to design a
medal that each member wore that bore the image and the caption "Liberty
Tree:' The best known and most articulate critic of the Stamp Act was a
resident of Annapolis, Daniel Dulany, whose stirring words helped marshal all of the colonies to resist taxation without representation.
• Dr. EJwan.J C. Papenfuse is State Archivist of Maryland. He delivered these remarks on the occasion
of designating the Liberty Tree a Maryland Treasure by the Maryland Commission for Celebration
2000 on June 3, 1999.
�6
THE ST. JOHN'S REVIEW
Undoubtedly, Dulany and the Sons of Liberty also supplemented their
words with such protest songs as the popular "Liberty;' first widely published in 1763, which begins
Hearts of oak are we still, for we're sons of those men
who always were ready,
steady boys, steady,
to fight for our freedom again and again.
and has a chorus
Come, chear up, my lads, to our country be firm,
As kings of the ocean, we'll weather each storm,
Integrity calls out, uFair Liberty;' see,
Waves our flag o'er our heads, and her words, are, BE FREE
The Stamp Act was repealed, but in its place carne ever more repugnant
and repressive laws passed by a Padiarnent in which Americans had no vote.
By September 1775, the citizens of Annapolis, like their counterparts in
the other twelve colonies, returned to their Liberty Trees to condemn the
oppression and launch a resistance that would end in independence. This
time a new song was composed by Thomas Paine, the author of Common
Sense, which again was instandy popular. Called 'The Liberty Tree;' one
verse in particular resonates the meaning of liberty as succeeding generations of Americans have come to define it:
The celestial exotic struck deep in the ground,
Like a native it flourish'd and bore;
The fame of its fruit, drew the nations around,
To seek out its peaceable shore.
Unmindful of names or distinction they carne,
For freemen like brothers agree:
With one spirit endow'd they one friendship pursued,
And their temple was Liberty Tree.
�PAPENFUSE
7
The British so hated Liberty Trees that when they occupied the seaports of Boston and Charleston they cut the Liberty Trees down. The
Boston Liberty Elm became fourteen cords of wood to fuel the British
campfires, while the stump of the Charleston Liberty Oak was burned to
remove
any trace of its existence, only to have its roots made into heads of
canes, one of which was presented to Thomas Jefferson.
Annapolis was never occupied and its Liberty Tree would become the
town's oldest living survivor of the Revolutionary era, ultimately playing a
role in our nation's history, not unlike that of Annapolitan Charles Carroll
of Carrollton, who became the revered last surviving signer of the
Declaration of Independence.
As a symbol and shelter to Liberty, the history of this Liberty Tree did
not end with Washington's resignation as Commander-in-Chief, nor with
the ratification of the Treaty of Peace, both of which occurred but a short
distance away in the historic Old Senate Chamber of the State House. Over
time, it was visited by a number of distinguished citizens and became the
site of celebration, including the 4th of July.
In December I 824, the Marquis de Lafayette returned from his horne
in France to speak in its shadow, having witnessed a revolution in his own
country in which over 60,000 Liberty Trees were planted, and in which the
Liberty Tree became a general symbol of adherence to its principles.
Lafayette came to Annapolis to thank Maryland for the citizenship
bestowed upon him some forty years before, and to receive, once again, the
accolades of a grateful people for the part he had played at Washington's
side during the Revolution.
One hundred and four years later, in I 928, even President Calvin
Coolidge would speak here in tribute to the principles for which this tree
stands.
Beginning its life as a sapling 400 orso yeats ago, and now nearly IOO
feet tall with branches spreading 60 feet wide, this magnificent tree proudly symbolizes the constant struggle to define and defend what is meant by
�THE ST. JOHN'S REVIEW
8
'Liberty'. It has weathered debilitating storms that cast its limbs on the
sleeping Civil War soldiers encamped beneath it. A fire in its trunk renewed
its life but required tons of concrete and reinforcement bars to keep it
standing. To keep it alive requires careful and constant care. An offspring
today flourishes on English soil at Kew Gardens. Soon each of the original
I3 states will have a genetic duplicate, fulfilling in fact the historic motto
of the Maryland General Assembly which dates back to the time of the
Revolution: Crescite et Multiplicamini, Grow and Multiply.
In its most recent history, however, lies the most meaningful testimony
to this tree's distinguished past. Under its branches, successive generations
of St. John's students have debated and discussed the great books of the
world, held their commencements, and, for recreation, have battled the
Navy with croquet mallets and wooden balls.
As Clemenceau, France's World War I Premier, is thought to have said,
"Liberty is the right to discipline oneself so as not to be disciplined by others:' Today we too often take liberty for granted. Like the students of St.
John's, we should stop and think of how we got where we are, how much
pain and travail we went though to get here, and how so many people &om
so many different nations have managed to come together here to live in
relative peace.
We live in a great nation in which liberty carries with it a great deal of
responsibility. It is most important that we pause now and then, perhaps in
the shade of a great tree such as this, to reflect on what Liberty is all about
and to recall the words of Thomas Paine in I775:
From the east to the west blow the trumpet to arms,
Thro' the land let the sound of it flee,
Let the far and the near,-all unite with a cheer,
In defense of our Liberty Tree.
Thank you.
�PAPENFUSE
9
Sources:
Documentation for these remarks ts available at the Museum
Without Walls on the Maryland State Archives web site:
http://www.mdsa.net
��-..:f Liberty Tree Ceremony
fj:- Christopher B. Nelson
Introduction
I don't quite know how to greet you this cool brisk morning, as we
all feel such a deep sense of sadness over the duty we must perform today.
So we will do our best to celebrate the great life of the Liberty Tree and
the good things that it stands for.
I am Christopher Nelson, president of St. John's College. I want to
start by setting out the protocol for this morning's ceremony, providing
you with an explanation for our action, and telling you what we will be
doing with the wood and leaves once the Liberty Tree is down and what
the college will be doing for an appropriate memorial and commemora-
tion.
First, let me thank all of you for being with us to pay tribute to this
venerable old friend, this symbol of America's most treasured prize: the
independence and liberty of our people.
I want especially to thank:
• Governor Glendening for joining us
• Janet Owens, our county executive
• Dean Johnson, mayor of the city of Annapolis
• Louise Hayman, executive director of
Maryland 2000
• The several members of the Maryland
legislature who are here, including our own
representative, Richard D'Amato
• And most of all, the many, many friends of the
Liberty Tree gathered here today.
Christopher B. Nelson is President at the Annapolis Campus of St. John's College. These remarks
were delivered on Octobrr 25, 1999,
�12
THE ST. JOHN'S REVIEW
When I have completed these introductory remarks, we will hear a
few words from the Governor, from Louise Hayman of Maryland 2000,
county executive Janet Owens and Mayor Dean Johnson. I will speak for
the college. We will then have a presentation of colors by the U.S. Marine
Corps Color Guard, followed by a moment of silence during which the
bell in McDowell Hall will toll thirteen times, once for each of the thirteen original colonies.
Mayor Dean Johnson will present a commemorative wreath to be laid
at the foot of the Liberty Tree.
We will then dedicate an offspring of the Liberty Tree as a monument
to its natural parent. This is the tree now standing just opposite the Liberty
Tree on the front of our campus, grown from a seedling of the Liberty
Tree planted IIO years ago, and now a majestic tree in its own right.
After that dedication, I will introduce a special guest who will place
a bouquet of flowers at the foot of the new Liberty Tree. This will be followed by the singing of the national anthem, authored by one of our
alumni, Francis Scott Key, and sung by one of our faculty members, Peter
Kalkavage.
That will conclude the ceremony.
Following the ceremony, workmen from The Care of Trees will begin
the difficult work of raking down the tree. The college will save all the
wood from the tree that can be preserved. We will haul it off campus to
a site where the wood can be cured for use at a later date. Mementos of
the tree will then be made available to all who want a piece of the Liberty
Tree. We are still determining what form those mementos should take.
In the meantime, we have already removed a few low hanging branches and plan to distribute to everyone present this morning commemorative leaves from the tree. College representatives staffing the reception
table will distribute leaves to everyone following the ceremony. We also
have at those tables copies of summaries from the lengthy report of
arborist Russell Carlson, the last in a succession of tree experts the college consulted in an effort to save the tree.
�NELSON
13
At those tables, we have two books available for written comments by
members of the public. Some of you may wish to express your sadness
over the loss of the tree, others to share a story about it, and some to suggest what we might do with the wood. I invite all of you to take the time
to sign the books and add your thoughts and comments.
The Decision to Take Down the Tree
Almost six weeks ago, on September sixteenth, hurricane Floyd hit
the area, bringing high winds and dumping over twelve inches of rain on
the city of Annapolis. Area work crews are still cleaning up the damage
caused and clearing the countless trees downed by the hurricane. The
Liberty Tree suffered a fifteen-foot crack extending from the split at the
first huge branch off the stem and well down into the trunk itsel£ A second crack has developed along the main stem. The cracks indicate both
that the tree has decayed and that the wood is brittle. Because the trunk
is filled with concrete, stress from the wind has been causing the tree to
pivot. The tree was deemed a safety hazard and a fence was erected. The
college gave notice to all that the area within was unsafe.
During the first several days afi:er the storm, the college called in several experts to examine the damage to the tree. The local tree company
that has been under contract to rake care of the tree since 1959 advised
that it be taken down, saying that it posed "an imminent risk of failure"
and that it was already "in the process of failing:' Other private firms, the
state Department of General Services, the National Arboretum and other
sources were consulted, and all reported to the college that the Liberty
Tree could not be saved. College officials sought help from the governor
and comptroller of Maryland. The governor and the Department of
General Services arranged for the arborist who cares for many of the
state's large trees to take a look at the Liberty Tree.
On October fifteenth, we received the twenty-seven-page report of
this arborist, Russell Carlson. He found that the tree was "now structurally weakened to a degree that it poses a hazard to any person or object
�14
THE ST. JOHN'S REVIEW
within reach of its branches:' He declared it to be "at great risk of massive structural failure:'
He further found that the decay in the tree was progressing at an
increasing pace and that the decline in the tree's structural integrity could
not be reversed. The uentire tree now consists of a hollow shell of wood,
sometimes only two or three inches thick ... much below the safe threshold level:' Afi:er examining the alternatives including pruning and
mechanical supports, he concluded that even the "process of installing
these support mechanisms and shortening the canopy would be detrimental to the tree, and would result in a more rapid decline of its vitality:' He concluded, 'The only prudent course of action ... is to remove
the tree now. It is inherently unsafe, and at a high risk of failure:'
The tree has lived a long and valiant life and has already been on life
support for the last century. Notwithstanding the health and beauty of its
canopy, its structural support is no longer sufficient to carry its weightany weight-and its hollow shell is too fi:agile to support external means
of reinforcement. The crack has widened in the weeks since hurricane
Floyd and the tree is now standing only because of the cables already
strung through the tree. The pressure on those cables too is growing.
Tulip trees grow rapidly and typically die early, usually within their
first 100 years. Their wood is soft and brittle. Well-maintained, longlived, protected and healthy trees may survive to 250 years. None other
we know of has lived past 400 years as the Liberty Tree has. In other
words, this may be not only the last surviving Liberty Tree fi:om the days
of the Revolution, but the oldest known tulip tree, too--and it now is in
the process of dying.
It is with a heavy heart that we take the tree down now before it does
damage to others. We hope to leave a stump at the base and surround it
with a protective iron fence. When the stump has produced new suckers
in the spring, suitable stock for cloning, we will remove the remainder of
the stump and its concrete interior, and make room for a clone or seedling
to take its place in the same spot. A cloning project is now underway in
�NELSON
15
laboratories at tbe University of Maryland, part of a project undertaken
by the Maryland Commission for Celebration 2000. [It was not possible
to preserve tbe stump of tbe tree, Ed.]
I want to thank the governor, his staff and tbe Department of General
Services for tbeir support in helping us tty to find a way to save tbe tree,
tbe controller, too, and his staf£ and tbe Maryland Commission for
Celebration 2000 for tbeir prescience in starting a cloning project four
months before tbe hurricane hit. I tbank also the many friends who offered
advice and financial support as we agonized over tbis decision.
The Liberty Tree at St. John's College
St. John's College is the tbird oldest college in the United States, tracing its origins to I696. Yet tbe Liberty Tree was a mature tree back tben.
It began irs life long before Isaac Newton ever gave tbought to tbe notion
of universal gravitation to explain why tbe tree's broken boughs might fall
down toward tbe eartb ratber tban away to the heavens. Back to tbe days
of Cervantes, before the dawn of modern science, before classical music
was ever conceived-this tree's birtb predates tbe majority of the great
books on tbe St. John's College classical program of education. It stood
tall and majestic in tbe years before tbe Revolution to serve as a popular
public meeting place in colonial times. And, of course, it was here tbat
Annapolis residents planned tbeir own tea party before burning tbe vessel Peggy Stewart in I 774. Francis Scott Key, a graduate of tbe college, was
an admirer of tbe tree, and one of his classmates, John Shaw, penned a
poem entitled "The Ancient Tree;' one of many poems written about tbe
tree by students of tbe college over tbe centuries. In tbose days, two hundred years ago, when irs age was tbought to be approaching 400 years, irs
condition was even tben described as fragile. Hear tbe opening lines of
John Shaw's I 797 poem:
The ancient tree, autumnal storms assail,
tby shattered branches spread tbe sound afar;
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THE ST. JOHN'S REVIEW
thy tall head bows before ·the rising gale,
thy pale leaf flits along the troubled air.
General Lafayette was greeted beneath its boughs in I824 and Civil
War soldiers camped here too. It has suffered through wind and storm,
lightning strikes and hurricanes, even fire and a gunpowder explosion in
its hollow trunk.
For the past seventeen years, students &om the college and midshipmen from the Naval Academy have fought their annual battle on the croquet field of honor beneath this tree.
And for as many years as memory can serve, seniors have received
their diplomas beneath the tree during the college's annual commencement ceremonies.
The Liberty Tree has served generations of students as a symbol of
the world they would enter upon leaving these halls-a world touched
deeply by the idea of individual political freedom under the rule of law,
in a nation rooted deeply in these principles with the perennial promise
of renewal.
But this tree has also served these students as a symbol for the kind
of education they began at St. John's College. I am speaking of a liberal
education. This word "liberal" is related to the word "liberty;' and the
college's own motto is built on a Latin pun over the root word for liberty. It goes like this:
Facio liberos ex libecis libris libraque
I make free men from children by means of books and a balance
These two things, government by the people under law ... and liberal education, ought always to be linked together in the minds of our
students and in the minds of all thoughtful Americans if we wish to
remain a free society dedicated to preserving life, liberty and the pursuit of happiness.
�NELSON
17
Let me see if I can be more clear about this relationship. Consider
this formulation for education: I go to school to learn a trade so that I
can get a job and earn a living.
Now, there is nothing wrong with wanting this much &om an education. It is really quite useful. But there is something terribly wrong with
wanting nothing more. After all, does that formulation sound like "the
pursuit of happiness?" No; it may be a necessary condition for life, but it
is not sufficient for living a good life--a life concerned with happiness. You
must ask more of your education than how to make a living if you care about
living a good life. Liberal education is concerned less with the means-the
"how-to"--of achieving your desires, and more with the ends themselves.
A liberal education frees the individual &om the limitations of thinking
about means, and helps him to think about life's purposes. To distinguish
good &om evil, you must free yourselves &om the prison of ignorance, the
constraints of convention, and the bonds of prejudice and popular opinion. Liberal education has to do with that kind of liberation.
The health of the nation depends on its citizens experiencing that kind
of liberation. The power to choose one's own ends in a government <if the
people and by the people carries with it the awesome responsibility of
knowing something about what the purposes of government ought to
be-which ends are good and which are bad, which ones are conducive to
the management of private affairs alone, and which are concerned with
the public good-those purposes that ask what it means to have a government for the people.
These then are the principles of liberty to which we dedicate ourselves at St. John's College, and it will behoove us to recall these purposes with other symbols once this dear tree is gone.
The closing refrain &om another srudent's poem &om I896, dedicated to this tree, now seems appropriate:
Farewell, thou noble Poplar Tree!
Each rising sun but hastens our advent
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THE ST. JOHN'S REVIEW
Upon the stage of life, when we must leave
Thee, Poplar, Yea, how soon; but sun ne'er shed
A brighter glow in human heart than doth
Thine image, Poplar: and although decades
Have rolled away, and Fortune kind called
To us position with the foremost, still
Unquenched will be the spark of love which draws
Us to thee, Poplar
And now we turn to the next generation. 1;, 1889, a seedling of the
Liberty Tree was planted on the opposite side of the front campus near
the Greenfield Library. We will, at St. John's College, begin a new tradition next May, weather permitting, by celebrating commencement under
its limbs.
We hereby dedicate it to that purpose and to carry with it the memory of its parent and the symbol of political freedom for which it stood
Thank you all for joining us this morning. Please feel free to stay to
sign the comment books, take your Liberty lea£ and observe the beginning of what promises to be a long and difficult tree removal project.
Farewell, dear Friend. Farewell, thou noble poplar.
�--:g What Was New about
fj- the New Republic?
Harvey Flaumenhaft
Practical people ofi:en have a certain disdain for theory, since theory
does not tell you what to do here and now, about this or that particular.
Be glad that it doesn't-since, afi:er all, if theory did tell you what to do,
there would then be no need for you. The decisions that you are called
upon to make could be made instead by a computer program. The very
value of theory for the man or woman of affairs depends upon the difference between theory and practice. Theory does not determine practice;
it informs practice. What I mean by that is not that theory supplies practice with its information; I mean, rather, that theory gives practice its
form. The terminology, the premises and the methods that are now in use
by practical people as they go about their business are all the outcometo a surprising degree--of theoretical reflections that arose unexpectedly and controversially but eventually carne to be taken for granted.
Unless much of what we think were taken for granted much of the
time, we would not be able to cope with the complex and ever-changing
world, and so we usually do not worry much about theoretical questions.
We do not keep wondering what ultimate standard of success to use in
judging what we do. We do not relenrlessly pursue the question of what
questions are the best to ask, or try to fi:nd an answer to the question of
what makes answers adequate or even relevant.
Sometimes, however, in unprecedented or in critical moments, we
cannot take such things for granted. And even in quiet times, amid circumstances that do not seem momentous, we sometimes get the feeling
Harvey Flaumenhaft is Jean at the Annapolis campus of St. John's College. This lecture was
delivered there on August 28, 1998. Earlier versions were delivered at Anne Arundel Community
College, Arnold, Maryland, on May 5, 1987, and at the National Defense University: Industrial
College of the Armed Forces, Washington, DC, August 27, 1990.
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THE ST. JOHN'S REVIEW
that unless we reassess prevailing modes of thought we shall miss out on
hidden opportunities, or else drift gradually downward to disaster.
In order to make ourselves more thoughtful about the fundamental
things we take for granted-to get some perspective on our handling of
the urgent particulars of the here and now-there is nothing better than
considering the thinking of first-rate minds of other times or places. For
doing this, we Americans have a ready resource of our own, one guaranteed to be not only somewhat distant but at the same time also especially relevant to our needs. The United States was, after all, the first "new
nation"-the first country that attempted to make fundamental innovations by reflection and choice, an effort that requires hard thinking. The
records left to us by the American founders can help us to rethink for ourselves a very serious effort by some very thoughrfUI practical men to consider the foundations of politics.
Those who laid the foundations of the new American nation were
raised on the classics of Greek and Roman antiquity. They admired the
virtue that sprouted from the soil of the ancient republic, and they sought
to revive republican government, which had fallen into disrepute. They
sought to revive it, however, on a new foundation and in a new form. They
rejected the classical philosophy that articulated the foundation of the
classical city, and they rejected the classical city as a model of political
organization. Under the influence of modern philosophers, they believed
that the understanding of nature (including human nature) had recently
taken some great steps forward, and had thus made it possible for even
greater progress to be made-if only those who led the way saw dearly
what they were trying to do, and could articulate it dearly enough, and
promote it courageously enough, to gain and keep a following in a country so fOrtunately endowed with natural and with human resources as was
America.
The attempt of the American founders to progress beyond the classics cannot be understood without understanding what it was that they
sought to go beyond, and why. Among other things, it is not easy to
�FLAUMENHAFT
21
understand how to fit together, on the one hand, the rejection of classical philosophy and the classical city, and, on the other hand, the admiration for classical virtue. To understand those things requires theoretical
reflection.
Among the American founders was Alexander Hamilton-a man
admired, even by his enemies, for penetrating to the foundations of practical questions, for relentlessly pursuing a line of thought to the end, and
for expressing his thinking with extraordinary clarity. 1 During the
Revolutionary War, Hamilton was aide-de-camp to George Washington,
the Commander-in-Chief of the American army. He was a prime mover
in the effort that produced the new Constitution of the United States,
and he was responsible for the classic account of its meaning, The Federalist
Papers, the writing of parts of which he assigned to collaborators. When
Washington became the first President of the new republic, Hamilton
acted as a kind of prime minister in his capacity as Secretary of the
Treasury, creating the financial basis for national security and prosperity.
And when Washington was called from retirement to preside over the creation of an army during America's quasi-war with France, Hamilton was
placed in charge as second-in-command to the aged chie£ There can be
no doubt that Hamilton was a most practical man of affairs. It was
nonetheless his belief that, however much the practice of government
might differ from the activity of theory, no one could be a statesman who
did not engage in theory. His theoretical reflections informed the words
by means of which he accomplished his deeds--deeds that did much to
shape the world around us and also to shape the minds with which we,
even now, observe and deal with that world.
That is why I propose to consider Alexander Hamilton's account of
the problem of popular government and its solution. It raises questions
about how to relate the classical political thought of our tradition to the
world that we inhabit as Americans. So, let me turn now to my subject. It
might be called "the effective republic:'
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THE ST. JOHN'S REVIEW
The New Foundation
When the new Constitution was first proposed, its opponents argued
that it would not be safe. So much power should not be placed in any government over a country so extensive as the United States of America, they
said. Alexander Hamilton replied that this argument wandered from the
real question. It is absurd, he said, to give a government the job of directing the most essential interests of the nation, while not daring to entrust it
with the powers that it needs for doing the job effectively. The people, he
agreed, should be vigilant and carefUl to see that their government is so
formed as to be safely vested with the requisite powers. But the question
that he thought the critics should address was this. did the structure of the
proposed government render it worthy of the people's confidence? It was
beside the point to attack the proposal for giving the government too much
power. If there was to be a government extending over the entire United
States--if the states were to remain united-then the powers of the Union
would have to be at least as great as those proposed, said Hamilton.
Without the powers proposed to make it a more perfect union, the very
incompletely united Union would fall apart. The extent of the country, far
from arguing against the powers proposed, was itself the strongest argument
in Javor of a powerfUl government-for no weaker government could preserve the union of so large a country.
But the adversaries of the Constitution wished to keep the Union, even
though it required what they were unwilling to accept--effective government of the Union. HLet us not attempt to reconcile contradictions;' insist-
ed Hamilton, "but firmly embrace a rational alternative:' The question of
the extent of the Union's powers could not be the real question, because the
alternative to the Union was not a real alternative for choice. It could
become such an alternative only
if there were a reconsideration of the spir-
it of modern life, and of the modern view that derives civil society from an
equality of natural rights. From the principles of modern government came
the foundation that supports the structure of modern government.
Modern government is, fundamentally, representative popular government;
and the representative republic when perfected is extensive. Only a rejection
�FLAUMENHAIT
23
of the large republic could justifY the refusal to generate an effective government of the Union, which might become ever more completely the government of the nation. Hamilton therefore had to discuss why the large
republic is, in principle, better than the small.
The only serious republican alternative to the extended republic is the
very small republic. The opponents of the proposed Constitution, said
Hamilton, keep referring to Montesquieu, who wrote that a republican government must have a small territory. But they have not drawn the right conclusion from the principle with which they so readily agree. They have not
noticed that when Montesquieu recommended a small extent for republics,
the size that he had in view was far smaller than the limits of almost every
one of the American states. If the opponents of the Constitution were
right that the liberties of the United States would probably be easily subverted under a government having the powers proposed, then there ought
at once to be an end of all delegated authority. The people should resolve
to recall all the powers which they have previously let go out of their own
hands, and, in order to be able to manage their own concerns in person,
they should divide themselves into very many, very little republics--into as
many states as there are counties.
Hamilton insisted that if Americans refused to the government of the
Union those extensive powers which are needed to maintain an extensive
republic, then limited monarchy is what they would eventually get, at best.
More likely, they would end up living under several little despotisms.
America's best hope for effective government in a republican form was the
Constitution that had been proposed.
Hamilton gave several reasons why the small republic is undesirable.
One reason is the overwhelming urgency of mere safety from external danger. It overwhelms, afrer a time, even the ardent love of liberty. An independent small republic, unable to withstand the power of a great enemy, is
in a terrible situation; so is an independent small republic continually at war
with neighbors as small as itsel£ And mere confederation is no solution to
the problem of external defense.
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THE ST. JOHN'S REVIEW
The requirements of external defense, moreover, do not conflict with
considerations of internal welfare. The extensive republic is better than the
small one, not only because it is safer from external danger, but also because
it is safer within. It is also more prosperous within. Let us examine these
reasons more closely.
The public councils of a large jurisdiction are more likely to act impartially than are the public councils of a smaller one, which does not contain
so great a variety of interests. Councils with jurisdiction over a more exten-
sive territory, containing a greater variety of interests, are less apt to be
tainted by the spirit of faction. They are more out of the reach of those
occasional ill humors or temporary prejudices and propensities which frequently contaminate the public deliberations in smaller societies that are
less diverse. These evils beget injustice toward and oppression of a part of
the community; and they engender schemes that gratifY a momentary inclination or desire but terminate in distress, dissatisfaction, and disgust. It is
harder for these evils to produce an effect when a variety of interests must
get together on a large scale--as they must before they can do much harm
in an extensive republic. Extensiveness, moreover, not only presents an
obstacle to the predominance of partiality in the public councils of the
whole; it also helps to repress fuction in local councils, as well as local insurrection against public authority. When a country is extensive, local disorders
are disorders merely in a part, and hence may be overcome by those other
parts that remain sound.
Consider the ancient history of the small republic. In the republics of
old, the people's true condition was that of a nation of soldiers. In those
barbarous times, war was the principal business of man. The people of
antiquity were poor, and the maxims they lived by were ferocious. The
classical republics were inflated with the love of glory. The assembled people, jealous of authority, were an ungovernable mob.When not fighting
against other peoples, they clashed tumultuously among themselves.
Among themselves, they alternated between anarchy and despotism; with
others, between despotism and servitude.
�FLAUMENHAFT
25
But eventually came those humane innovations of later times which
accord with the pronouncements of enlightened reason. Not heroic display
but profitable business, it came to be acknowledged, is the business of government. The industrious habits of a modern people, absorbed in gainful
pursuits and devoted to productive improvements, are incompatible with
the condition of a nation of soldiers, where civic life centers on an assem-
bly of warriors whose delight is domination. The industrious habits of a
modern people are incompatible with the condition of a nation of citizens
absorbed in being citizens; for if merely the power of appointing officers
of government were ordinarily exercised by the people at large, the people
would have little time for anything else. If those who might otherwise go
about their business, with enterprise and industry, instead were busy where
the action is, the citizenry would be impoverished-unless the action were
that collective piracy which supported the armed splendor of antiquity. But
modern humanity discountenances fierce rapacity; modern enlightenment
looks not to dominion and to plunder, but to commerce and to industry.
The common good, the good that is common to common men,
requires that participation in government be uncommon. Government
by
the people cannot secure popular safety and prosperity. A people's liberty is
not a stage or an arena for displaying popular action. It is rather a protective fence, which, properly erected by popular fear and desire, and prudently managed by wise and energetic leadership, may become a productive
force. Liberty is that security for life and property which is provided by
checks and controls on government.
It was want of safety against the power of their governors that first led
ancient men to popular government, said Hamilton. The interests of the
people required government intimately connected with the people. In the
first, crude attempts to institutionalize this connection, government for the
people was identified with government by the people. Modern enlightenment, in founding government on the equal right of every man to secure his
safety and prosperity, had revived the ancient prejudice against establishing
power far from the hands of the people who are to be affected by the exer-
�26
THE ST. JOHN'S REVIEW
cise of that power. The modern doctrine of equality had, however, also generated a modern improvement which permitted government to be popular
while freeing it from the defects of government by the collective body of
the people. This principle of popular representation, said Hamilton, gave
to modern republics the decisive advantage over ancient republics.
Only in the small republic was it possible to have direct democracy, government conducted directly by the assembled people. But the very good reasons for having popular government at all are reasons that argue in favor of
representative democracy, and against government conducted directly by the
assembled people of a small republic. It is sometimes said that a direct
democracy would be the most perfect government if only it were practicable. Experience had proved, said Hamilton, that there is no political observation more false than that.
Small commonwealths are jealous, clashing, and tumultuous--the
wretched nurseries of unceasing discord, and the miserable objects of universal pity or contempt. Unceasing agitations and frequent revolutions are
the continual scourges of small republics. In the ancient democracies, where
the people themselves assembled, the field of debate presented an
ungovernable mob, which was incapable of deliberation and was capable of
every enormity. In these assemblies, the enemies of the people systematically brought forward their plans of ambition; they were opposed by their
enemies of another party; and it became a matter of contingency whether
the people subjected themselves to be led blindly by one tyrant or by another. Thus no &iend to order or to rational liberty can read without pain and
disgust the history of the commonwealths of ancient Greece. They were a
constant scene of the alternate tyranny of one part of the people over the
other, or of a few, usurping demagogues over the whole. This, together with
the lack of a solid federal union to restrain the ambition and rivalry of the
different cities, ended-afi:er a rapid succession of bloody wars-in their
total loss of liberty and their subjection to foreign powers.
It is impossible to read the history of the small republics of ancient
Greece and Italy without feeling horror and disgust at the distractions
�FLAUMENHAFT
27
which continually agitated them, and at the rapid succession of revolutions
which kept them perpetually in vibration between tyranny and anarchy,
enjoying only brief and occasional felicity amid the furious storms of sedition and party-rage that repeatedly and frequently overwhelmed them.
The original government of most had been monarchy, which had sucetunbed to its natural disease, despotism. In reaction, those communities
had established popular governments in which (except for Sparta) the jealousy of power hindered the people from trusting out of their own hands
an authority competent to maintain the repose and stability of the commonwealth. Thus they had erected government to keep them safe from each
other and from strangers; then, finding themselves not safe from their government, they exchanged it for one which lefr them even less safe from each
other and from strangers.
But a government framed for durable liberty must pay as much regard
to giving the magistrates a proper degree of authority to make and execute
the laws with vigor, as to guarding against encroachments by the magistrates
upon the rights of the community. Just as too much power leads to despotism, so also too litde power leads to anarchy, and both lead eventually to the
min of the people. These well-known maxims had never been given
sufficient attention in adjusting governmental frameworks, and so the advocates of despotism had been able to draw arguments not only against the
forms of republican government, but even against the very principles of civil
liberty, from the disorders that disfigure the annals of the small ancient
republics.
America, however, was the beneficiary of progress. If it had been found
impracticable to devise models of a structure more perfect than that of the
small ancient republic, then the enlightened friends to liberty would have
had to abandon the cause of republican government as indefensible. But it
did not have to come to that, for the science of politics--like most other
sciences--has been greatly improved. Now well understood is the effectiveness of various principles, which the ancients either did not know at all, or
only knew imperfectly. These principles are powerful means for retaining
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THE ST. JOHN'S REVIEW
the excellencies of republican government while lessening or even avoiding
its imperfections. Hamilton gives a catalogue of things that tend to the
amelioration of popular systems of civil government-things that he says
are either totally new discoveries or else have progressed towards their perfection principally in modern times. After listing the regular distriburion of
power into distinct departments, the introduction of legislative balances
and checks, and the institurion of courts composed of judges who hold
their offices during good behavior, he comes to the representation of the
people in the legislature by deputies of their own elecrion; then he says that
he
will venture, however novel it may appear to some, to add one more, on
a principle which has been made the foundarion of an objection to the new
constitution: the enlargement of the orbit within which such systems are to
revolve.
In comparing our governments with those of the ancient republics, we
must not hesitate to prefer our own, because every power with us is exer-
cised by representarion, not in tumultuous assemblies of the collective body
of the people, where what almost always has to govern is the art or impudence of the orator, rather than the utility or justice of the measure.
However, it is only by enlarging the orbit within which popular systems are
to revolve that full effect can be given to the principle which makes the
modern American republic superior to the ancient republic-the principle
of representation. And, with reciprocal action, it is only by representation
that republican government can be made extensive. The celebrated principle
that no government
but a despotism
can exist in a very extensive country
has been misunderstood. It relates only to democtacies where the whole
body of the people meet to transact business, and where representation is
unknown.
The New Problem
We must, said Hamilton, prefer our own governments to those of the
ancient republics, because every power with us is exercised
by representa-
tion. But jealousy of power has prevented our reaping all the advantages
�FLAUMENHAFT
29
which we ought to have obtained from the example of other nations. This
jealousy of power has rendered the constitutions of the American governments in many respects feeble and imperfect.
Americans threw off the British monarchy, not because a free people
cannot have a prince, but because the British monarch refused to recognize that a free people must have its own representatives. Great Britain is
a free country because its inhabitants have a share in the legislature
through representation. In no government is consent safely given once for
all time: a people not represented will be a people oppressed, and representation requires an intimate connection of interest between the representative and those he represents. The requisite intimate connection of
interest does not, however, require that the
body of representatives mirror
the citizenry in all its multitudinous socio-economic variety. Indeed, the
true and strong bonds of sympathy between the representative and the
constituent are polirical-the twofold requirement that the representative
depend upon the constituent for continuance in office, and that the representative and his posterity be bound by the laws to which he assents.
The end of government is to secure the safety and prosperity of the
people, who are its source. Government by the collective body of the people endangers and impoverishes the people. Popular representation, while
securing the people against themselves (by removing government from the
hands of the collective body of the people), also secures the people
against the government. Only, however, if things are properly arranged.
The body of representatives is different from the body of the people.
The representative body is superior to the people in its ability to serve the
people's interests. The representatives' interests, however, are not superior
to the people's interests. Representatives might nonetheless come to think
that they are. Safety requires, therefOre, that the members of the representative assembly be numerous, and also be frequently elected.
That is not enough, however. Government flowing from the people
must be divided to work for the people. Some partition of governmental
power is essential to free government-indeed, the very definition of des-
�30
potism is: a government in which
THE ST. JOHN'S REVIEW
all
power is concentrated in a single
body. Absolute monarchy is its most obvious form, but no single body, not
even a representative assembly, is a safe depository of ample unchecked
power.
In a nation itself made up of states, the particular state governments
may contribute to safety against the general government of the whole by
their multiplying the depositories of power. From one point of view, the
state governments are the parts of the whole. But there is something problematic in a multiplicity of depositories of power that are wholes of a
sort similar to the whole of which they are parts. The government of such
a whole (the parts of which themselves are wholes) verges on being a mere
league of governments or a government over governments-that is to say,
no government at all. If the whole is not to be an anarchy, the parts must
lose their similarity to the whole, thus leaving the government of the
whole a great mass of power deposited in a single representative body.
However urgent may be the question of the partition of power among
the component parts of a compound republic (that is, a nation of states),
the central question is that of the partition of power among the several
departments in a single government.
There is a sense in which good government is thoroughly representative. Under the proposed Constitution, Hamilton pointed out, the
President of the United States himself would be a representative of the
people. He would act to protect the people against an unfaithfUl
Congress. Nonetheless, the proper name "The House of
Representatives" belongs most properly to that one of the several governmental branches which is the representative body. By means of representation, the people obtain public servants, whom the people hire to free
themselves for business other than the public business, and whom they
can fire for acting as if free to neglect their tie to the people. The ends of
representative government are served by government conducted according
to law-legislation is the most manifestly public of acts--and legislation
by a numerous assembly most represents the multitudinous people. The
�FLAUMENHAFT
31
legislature seems to represent the immediate being of the society. There
is no question that free government requires a freely elected popular
assembly. The question is what else it needs.
Though representative government is perfected by the partitioning of
governmental power, it is diffirult to maintain such partition in a government that is thoroughly representative. Insofar as the parts do not
approach being whole governments themselves, the parts must be differentiated organs. But one of them, the popular legislative assembly, the
part most properly called representative, tends to primacy and even hegemony. The partitioning of power, and even the intermixture of the powers of the parts, are partly explained by the need for checks upon power,
and for balance to preserve the system of checks. But the partitioning of
power cannot be understood unless one understands the parts as differentiations of power, each with its own peculiar property. Representation
is necessary to the foundation of good government, but representation is
not the whole of it.
Popular representation freed the populace from continual contention
and for productive industry, while safeguarding them against their governors. Americans had accepted this governing principle, Hamilton
thought, but imperfectly. Representative popular government could succeed as an alternative to the discredited participatory popular government
only by developing administrative effectiveness. By itsel£ representation
did not suffice to protect the people against turmoil and invasion, and to
manage their prosperity. The people had to choose: government by the
people, affecting democratic workings-or government from and for the
people, effecting popular works. The proper end of government is popular, as also is its source. Popular representation is the fimdamenral
reliance for keeping the ends of government popular. According to
Hamilton, while the Chief Executive is in a sense a representative, the representatives in the most precise signification are those officials who are
most numerous and have the shortest duration in office of all the men
publicly elected. On the other hand, Hamilton also thought that while
�THE ST. JOHN'S REVIEW
32
uthe administration of government" (the actual business of governing)
is in its "largest sense" the work of
all the parts of the government11
legislative, executive, and judicial-yet in its most precise signification"
the administration of government is the work of the executive part. The
most popular part of government, the numerous assembly of representatives with short duration in office, cannot itself do the actual detailed
work of governing.
Government flowing &om the people must be divided to work for
the people. Partition prevents bad deeds by multiplying the agencies which
must cooperate to act. The powers needed to do much of anything are
separated, on the presumption that although the several depositories of
power will have difficulty coming together, and staying together, in order
to do bad things, they will nonetheless come together, and stay together, in order to do good. But the fear that leads to precautions against government's doing bad may lead to arrangements that keep government
&om doing much good. In a government amply arranged for safety
against government, adequately arranging for effectiveness of government is a problem.
The problem is twofold: to concentrate power sufficiently for many
wills to act as one, at one time, soon enough; and to stabilize policy
sufficiently for many actions to be in concert during a long time, for constant purposes. Unless the powers of government are apportioned to
promote effectiveness, those who take part in the mutable affairs of the
multitudes of men massed in political society will be uncooperative and
improvident. Good government--a system of liberty that is effective for
protection and prosperity-must concentrate power and keep policy
constant. America's new order of the ages would not last for ages if the
founders could not &nd a way to make the means of safety also
efficacious.
The man who most sharply posed the problem rried to show the way
to a solution. It was Alexander Hamilton who taught what it takes to
administer a republic. The people are the beginning and the end of good
�FLAUMENHAFT
33
government, he thought, but between the source and the outcome operates that organization of means which is administration. Popular representation is of little avail without effective administration. Republican
statesmanship required that American principles be restated.
Government flowing &om the people must be divided to work for the
people. Partition can promote good deeds by differentiating agencies so that
different sorts of work are done. The very device for diminishing danger
from government can be employed as well for promoting effectiveness of
government. Effectiveness of government had two ingredients fur
Hamilton: unity and duration. Neither of these is characteristic of the
numerous and short-lived popular representative body that is both characteristic of free government and fundamental to good government.
Nonetheless, both ingredients of effectiveness could be infused into parts
of a popular government properly partitioned.
To see how, let us consider the Presidency and the Senate. Both institutions were attacked by opponents of the Constitution. From the
Presidency, they said, monarchy would arise; &om the Senate, aristocracy.
Hamilton defended the constitutional provisions for both Presidency and
Senate, as necessary to the success of popular government. Let us first
consider some of Hamilton's arguments concerning unity in the
Presidency, and then some others that he made concerning duration in
the Senate.
The One Ingredient of the Solution
The true test of a good government is irs aptitude and tendency to
produce a good administration, said Hamilton, and rorms of government
differ in their aptitude and tendency to produce a good administration.
Hamilton presented himself as someone who is able to estimate the share
that the executive in every government must have in its good or bad
administration.
The single-minded attention to security &om abuse of power, he said,
does not attend with due care to the mischief that may occur when the
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THE ST. JOHN'S REVIEW
public business cannot go forward at critical seasons. Whenever two or
more persons are engaged in any common enterprise, there is always a
danger of difference of opinion, and there is peculiar danger of personal emulation and even of animosity if it be a public trust or oflice clothing them with equal dignity and authority. Men often oppose a thing
merely because they have had no agency in planning it, or because it may
have been planned by those whom they dislike, or because they had once
been consulted and happened to disapprove.
The principles of a free government require submitting to the inconveniences of dissension in the formation of the legislature. In the legislature, moreover, prompt decision is more often bad than good. There,
deliberation and moderation are often promoted by the differences of
opinion and the jarring of parties that may sometimes obstruct salutary
plans. In the executive department, however, dissension does no good that
counterbalances the harm which it does to what should be the characteristic features of the executive: vigor and expedition.
A numerous legislature is best adapted to deliberation and wisdom,
and is also best calculated to conciliate the confidence of the people and
to secure their privileges and interests, whereas a single executive is best
because the proceedings of one man are most eminently characterized by
decision, activity, secrecy, and dispatch.
Hamilton presented a list of the sorts of "executive details" that constitute what seems to be most properly understood by the administration
of government: "the actual conduct of foreign negotiations, the preparatory plans of fi:nance, the application and disbursement of the public
monies, in conformity to the general appropriations of the legislature, the
arrangement of the army and navy, the direction of the operations of
war; these and other matters of a like nature:'
The apportiomnent of power into several depositories is not an itemby-item distribution guided only by the wish to prevent abuse by equilibrating the capacity for abuse: there are sorts of work into which the various powers of government have a natural tendency to be sorted. The
�FLAUM EN HAFT
35
executive power has an inherent nature: it is not a convention produced by
the Constitutional Convention. What our Constitution does is to vest the
executive power, with certain expressed exceptions and qualifications, in
an official called the President, and the executive powers which it enumerates are not exhaustive of the President's powers. There is unanimous
agreement that the vesting of the executive power in the President ought
to be interpreted in conformity with other parts of the Constitution
which express exceptions and qualifications. There is also unanimous
agreement that it ought to be interpreted in conformity with the principles of free government. About the meaning of the latter, however, there
is antagonistic disagreement. According to Hamilton, free government
must not only be free, it must also be government. Free government need
not simply be popular; it may also be monarchical.
The idea that a vigorous executive is inconsistent with the spirit of
republican government is, to say the least; not without its advocates; but
Hamilton places them in a dilemma: those who are unfriendly to the proposed Constitution because its executive is energetic must choose between
government that is republican but bad, and government that is good but
non-republican.
Opposition to the energetic executive must be abandoned by enlightened well-wishers to republican government, for energy in the executive
is a leading characteristic in the definition of good government. Energy
in the executive is essential to the protection of the community against
foreign attacks, and it is just as essential internally. Internally, it is essential to the steady administration of the laws, and it is also essential to the
protection of property against those irregular combinations which
sometimes interrupt the ordinary course of justice, as well as to the secu-
rity of liberty against the enterprises and assaults of ambition, faction,
and anarchy.
Whatever may be our theory about the preferability of republican
over monarchical government, practice shows the necessity of an energetic
executive. Hamilton's problem is to persuade enthusiastic defenders of
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THE ST. JOHN'S REVIEW
republicanism that a due dependence on the people, and a due responsibility-the two things which constitute safety in the republican sensecan consist with an executive attacked as monarchical because of its ener-
gy. The chief or central difficulty with which Hamilton must contend is
the fear that a concentration of governmental power in one man, the chief
executive, is not safe. Americans' habits and opinions impede the effort to
protect their rights and promote their interests. They resist being governed, because they fear being oppressed.
It is often best in a monarchy for the prince to relinquish part of an
excessive prerogative in order to establish a more moderate government,
better adapted to the happiness or temper of his people. A government
characterized by the absolutely unqualified monarchical principle is less
truly energetic than is its antithesis, free government. But, although freedom has this tendency to energize government through the extensive feelings that identifY public and private, it also has a tendency to enfeeble government, through the fear and the fear-manipulating envy which resist the
concentration of power in men elevated above their fellows to exercise
public authority. Freedom is not identical with energy: fi:eedom energizes
when the requirements of energy are not ignored. A country like Great
Britain, in which the principle of freedom has been joined to the monarchical principle, may have both governmental energy and popular enthusiasm. Early in the American Revolution, Hamilton declared himself in
favor of what he ca!Ied "representative democracy;' and also urged an
arrangement for administration by single men that he said would "blend
the advantages of a monarchy and republic in our constitution:'
Executive energy is essential to good government, however much it
may be thought to be not republican, said Hamilton, and unity is the first
ingredient of executive energy. This argument-that an executive authority lacking unity would be exercised with a spirit habitua!Iy feeble and
dilatory-applies with principal weight to the first of two methods that
destroys the unity of the executive: the arrangement for a plurality of
magistrates of equal clignity and authority. That feeble arrangement is also
�FLAUMENHAFT
37
unsafe, owing to the danger of differences that might split the community
into the most violent and irreconcilable factions. Thus there are not likely
to be many advocates of this arrangement.
More numerous were the advocates of the other method that destroys
executive unity. This second method-the method more popular in
America--ostensibly vests executive power
in one man, but subjects him
wholly or partly to the control and cooperation of others who are the
members of his council. To this arrangement, which makes a council's conrurrence constitutionally necessary to the operations of the ostensible exec-
utive, the argument that a plural executive is an executive lacking energy does
not apply with equal weight, Hamilton concedes; but he says that it does
apply with a weight which is considerable. Harniltoris argument then goes
on to turn against
itself the argument for an executive council. Not only is
the executive in this method still quite feeble (even if not so feeble as in that
other plan), an executive with a council is also in fact unsafe. The method
of an executive council, as much as the other method for plurality in the
executive, tends to conceal faults and destroy responsibility, thus depriving
the people of their securities against infidelity in elected officials. Those
securities are the removal and punishment of wrongdoers, and (even more
important in an elective government, because more commonly required) the
censure of public opinion.
The council in the British monarchy helps keep Britain free: it increases responsibility-from no responsibility whatever, to responsibility in
some degree (though only in some degree, for the King of England is not
bound to do what they say). But the American executive with a council
would be less responsible, and would therefore be more dangerous to
republican liberty. To recognize that many cannot exercise executive authority well, but to stop short of vesting that authority in one, is in fact to
reduce the security against infidelity to the people. A few may combine
more easily than many, but are harder to watch than one.
The state government of Hamilton's immediate audience, he points
out, has no council except for the single purpose of appointing to offices.
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THE ST. JOHN'S REVIEW
The republican fear of unity in the executive seems to make its last stand
on this ground of appointments: even if there is only one chief magistrate,
there must be many other magistrates; to allow him to name them all by
himself would make him a lone magistrate, followed by his friends and servants. Hamilton therefore takes note of how the President, while making
appointments under the proposed Constitution, will be subject to the control of a branch of the legislative body.
What sort of arrangement is best calculated to promote a choice of the
right men to fill executive offices? The legislators themselves are not to be
the holders of executive office-they themselves are not to constitute the
administtation. If the power of appointment is to be placed in a body of
men, that body must be not the people at large, but a select body of a moderate number. Men in a select body of a moderate number, however, unlike
a numerous and dispersed people collectively, are regulated in their movements by a systematic spirit of cabal and intrigue; which spirit of cabal and
intrigue is the chief objection against reposing the power of appointment
in such a body. The resolutions of a collective body are frequently distracted and warped by a diversity of views, feelings, and interests; and nothing
ls so apt to agitate men's passions as personal considerations, whether relat-
ing to themselves or to others whom they are to choose or prefer. Hence,
the process of appointing to office when an assembly of men exercises the
power will be a display of attachments and animosities that will result in a
choice, not for merit, but for what gives to one party a victory or to many
parties a bargain.
One man, by contrast, will have fewer personal attachments to gratifY
than will a body of men, each of whom may be supposed to have as many
as does that one man. Moreover, a single man with the sole and undivided
responsibility will have a livelier sense of duty and a more exact regard for
reputation. He will be led by the concentration of obligation and interest
to investigate with care what qualities merit appointment, and to prefer with
impartiality men who have those qualities. Hence, to analyze and to estimate the peculiar qualities adapted to particular offices, one man of dis-
�FLAUMENHAFT
39
cernment is better fitted than a body of men of equal or perhaps even of
superior discernment.
However, to reduce the danger of evils from one man's uncontrolled
agency in appointments, it would be well to restrain him by making it dangerous to his reputation, or even to his political existence, fOr him to play
favorites or to follow popularity. An effective check will be the requirement
of the Senate's cooperation for appointment to office. Such a check would
not impair executive energy: the Senate restrains only by the power to concur or not; the President retains the initiative.
The Other Ingredient of the Solution
Hamilton argued that there would be more constancy under the proposed Constitution because the Presidency would be a seat of resistance to
harmful change, and of persistence in beneficial action. But the feature most
characteristic of the Presidency was unity, not duration. Another part of
government received a name that suggested lasting a long time-namely,
the Senate. With respect to number, the few Senators are more than one but
less than many; with respect to number, the Senate and the House of
Representatives differ from each other only in degree, while both differ in
kind from the President: bodies of men are more or less numerous, but
unity is not numerous at all. The Senate is distinguished by duration: the
body, for at no time can its membership change
for the most part; and its members remain in office longer
Senate is a continuing
entirely, or even
than any other officials elected in the republic. As the President is the incarnation of nnity, so the embodiment of duration is the Senate.
When the New York RatifYing Convention discussed the provisions
for the Senate, an amendment was proposed: no person should be eligible
as Senator for more than six years in any period of twelve years, and the legislatures of the several states should have power to recall their Senators and
to elect others to serve for the remainder of the time for which those
recalled had been appointed. Hamilton spoke against the amendment.
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THE ST. JOHN'S REVIEW
He began by speaking of the noncontroversial end, We all are eager to
establish a republican government on a safe and solid basis, he said. We
must therefore mix the ingredients that make for safety with those that
make for solidity; we must not think that we have established good government when we have provided only for republican safety. The choice of
means to the noncontroversial end is most controversial.
Nothing was more natural than that, in the commencement of a revo-
lution which received its birth from the usurpations of tyranny, the public
mind should be influenced by an extreme spirit of jealousy. To resist these
tyrannical encroachments and to nourish this jealous spirit was the great
object of all our institutions--and it was certainly a valuable object, he said.
But the zeal for liberty became excessive. In forming our confederation, this
passion alone seemed to actuate us, and we appear to have had no other
view than to secure ourselves from despotism. Safety from despotism is certainly one important object of good government. But there is another
object, equally important, which enthusiasm kept us from attending to. Our
exclusive attention to tying the representative to the people has kept us from
seeing the need also to embody in our government another principle, a principle of strength and stability in the organization of government, and vigor
in its operations.
In every republic, he said, there should be some permanent body to
correct the prejudices, check the intemperate passions, and regulate the
fluctuations of a popular assembly. A body instituted for these purposes
must be so formed as to exclude as much as possible from its own character those infirmities and that mutability which it is designed to remedy.
It is therefore necessary that it should be small, and that it should hold
its authority during a considerable period. We shall never have an effective government unless our government has within it some stable body
which will pursue a system, will guard against innovations that lead to
instability, and will have the opportunity to know what must be known
for directing public affairs.
�FLAUMENHAFT
41
The people do not possess the discernment and stability necessary
for systematic government. To deny this would be flattery, which their
own good sense must despise. Yet these ttuths are not ofi:en held up in
public assemblies-although they cannot be unknown to any who hear
me, said Hamilton. The reason for this seems to be that the people are
not only lacking in information but are also misled by artful men or by
men of influence whose views are partial. The body of the people in every
countty intend the good end; it almost goes without saying that the populace desires public prosperity. The people's leaders in America, however,
need to be told that the people's deficiencies do not include an incapacity to bear being told that they have deficiencies. The people are capable
of recognizing that it is misleading flattery to tell them that they need not
provide against their deficiencies. A part of the misleaders are misled by
partial views that can be enlarged; a part of them, artful and ambitious,
may be overcome by leadership that holds up in public assemblies the
ttuths not ofi:en publicized in enthusiastically republican America.
Because two objects need to be conciliated, there ought to be two distinct
bodies in our government. One of the two bodies is to be immediately
constituted by, and peculiarly to represent the people. Being dependent on
the people and possessing all the popular features, it will have a quick sensibility of the ideas of the people; this body, being made up of representatives elected for a short term who shall be closely united to the people,
is the representative body. In addition to the representative body, there is
to be another body: a permanent body with the firnrness to stand against
popular fluctuations and to pursue the public interest, the ttue interest of
the people, as the arts of demagogues and designing men play upon and
generate popular dissatisfactions.
The next day, Hamilton spoke again. He began by pointing out the
source of the difficulty: ttuth in the matter under debate resided not in a
single principle, but in a judicious combination of principles. There is a
double object in forming systems of government-safety for the people,
and energy in the administration. But one element in administrative ener-
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THE ST. JOHN'S REVIEW
gy or governmental strength is stability: without stability as well as security for the rights of the people, government is not government, The principle of stability in government and the principle of safety for the people
are best combined by instituting one branch peculiarly endowed with sensibility, and another with knowledge and firmness, Through the opposition and mutual control of these bodies, the government in its regular
operations will perfectly combine individual liberty with governmental
strength. The principle of caution, of a laudable anxiety for the safety of
the people, is the principle justly applied in reasoning about the representative house. However, we constantly have it held up to us that, as it is
our chief duty to guard against tyranny, it is our best policy to form all
the branches of government for this purpose, But, replied Hamilton,
experience shows that when the people act by their representatives, they
are commonly irresistible; when the people have an organized will that
pursues measures, they will always prevail. And the principle that justly
applies to the representative body would destroy tl1e essential qualities of
that which is senatorial. We should not impose the same principles upon
branches of government designed for different operations. The two houses were built for different kinds of work. The differences laid down in
building them were meant to be embodiments of differences in nature.
The House of Representatives was designed primarily to keep the people
safe; the Senate, to keep the government steady.
The Status of the Solution
Hamilton's two themes of unity and duration are the two aspects of
his one problem: to give effectiveness to the American constitution of
republican liberty. Hamilton presented himself as the great friend of
republican government, not-as his opponents charged -its secret foe.
He said that what he sought was this: by the establishment of properly
differentiated parts within governmental machinery founded upon popular representation, to give to the republic the effectiveness without which
it would be discredited and destroyed.
�FLAUM EN HAFT
43
It was not simply to get things done that Hamilton was a proponent
of constitutional arrangements for energizing and stabilizing the exercise
of governmental power. Things may get done, soon and so as to last a
long time, even when a constitution makes for fragmented and mutable
government. If the machinery of government provided by the constitution is lacking in effectiveness, then a political machine unknown to the
constitution may be improvised to do the job: effective decisions can be
made and enforced by a boss sitting in the back room, and then sent up
front for dignified promulgation by those who formally preside; or the
man who presides up front with a popular air of republican humility may
himself do the effective work, operating his own machine in the back
room. But constitutional arrangements that necessitate such extraconsti-
tutional arrangements so that the public business may in some way go
forward are dangerous and demeaning.
Hamilton repeatedly declared himself "iiffectionately attached to the
Republican theory:' He said that he had "strong hopes of the success of
that theory;' but in candor ought to add that he was "far &om being
without doubts:"
ul consider its success as yet a problem;' he said. As
yet, successful republican government was not an accomplished fact but
a project to be accomplished-for "it is yet to be determined by experience whether it be consistent with that stability and order in Government
which are essential to public strength & private security and happiness:'
In the circumstances, he said, republican theory ought to govern governmental practice.
11
1n the abstract:' or neglecting the circumstances
here and now, the nonrepublican theory may seem to be better.
"Permanent or hereditary distinctions" of political rights are an essen-
tial part of the British constitution, a constitution that is good, as well
as being the best that there yet has been. Experience thus shows that the
nonrepublican theory can be successful in practice. Experience, moreover,
gives cause to doubt whether the republican theory can be successful in
practice. But "every good man" ought to have "good wishes" for the
republican theory's essential idea, the "idea of a perfect equality of
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THE ST. JOHN'S REVIEW
political rights among the citizens:' The republican theory has a more
desirable constitutive principle than does the nonrepublican theory. The
nonrepublican theory would seem to be better only because the republican theory would seem to be less practicable. The republican theory
11
merits "the best efforts to give success to it in practice." It has hither-
to from an incompetent structure of the Government ... not had a fair
trial, and ... the endeavor ought then to be to secure to it a better chance
of success by a government more capable of energy and order:'
Hamilton had repeatedly "declared in strong terms;' he insisted, "that
the republican theory ought to be adhered to in this Country as long as
there was any chance of its success:'
The republican problem could be solved only by the development of
a republican form of government that did not lack the aptitude and tendency to produce a good administration. If such a form were not developed, warned Hamilton, if popular prejudices against being governed
were flattered to the point of inciting those popular propensities which
bring on the self-destruction of popular government, then monarchy
would after all prevail. Proclaiming long and loudly the merits of the
British constitution, Hamilton tried to teach emphatically what he
thought Americans needed most to learn-the lesson that government
cannot be good unless it joins to private safety public strength• In rejecting the hereditary principle in government, a British inheritance from less
enlightened times, Americans had not cast off their unenlightened
parochial prejudice against executive energy. But the necessity of executive energy was rooted in the nature of things: in some way or other it
would return; and if refused a stately republican admission, it would
break violently through the front door-or enter by stealth through the
back. In some way or other, Hamilton thought, the public business would
go forward, or the government would cease to be. His wish was that the
public business might go forward in a way not &tal to liberty and to
honor. Monarchy under the free British constitution produced a good
administration, but the independent Americans did not have the materi-
�FLAUMENHAFr
45
als for a constitution of the British sort: their failure to solve the republican problem would produce a tyrant or a boss.
Previous experience had shown the republican theory to be doubtful.
But republican government might succeed if "so constructed as to have all
the energy and stability reconcilable with the principles of that theory:'
Not only would Americans "endure nothing but a republican government;' but it was "in itself right and proper that the republican theory
should have a fair and full trial:' Considerate and good Americans should
wish for a true test of the republican theory in America, said Hamilton,
and should therefore advocate republican institutions of the greatest possible energy and stability. Republican government would be vindicated as
a good form of government only if it could thus be formed for durable
liberty--only, that is to say, if it could thus be made effective.
1
Citations for the passages here paraphrased and quoted from Alexander Hamilton will be found
in my book The EJftctivt Republic: Admirristraticm and Constitution in tbt Thought of Alexaudrr Hamilton
(Durham: Duke University Press, 1992).
��-;f What, then, is Time?
!j:- Eva Brann
When our dean asked me to lecture this September it was because I've
just completed a book on time, and I'm happy to have the opportunity
to talk about it. There seemed to be three possible kinds of profit that I
figured might come to you and to me if I gave what one might call a book
report.
First, even if the writing of books is a few decades off for most of
you here tonight, it turns out that writing papers and annual essays is not
so different from writing books, and I thought I might be able to tell you
something useful. In fact I'll do it right now. When the time comes to
write, whether it's a small paper or a long annual essay, never think: 'Tve
got to write this thing! Help! I need a paper!" Instead, search your soul
for a question you have nursed for quite a while, whether articulately or
inarticulately, something that bothered and puzzled you, something that
might be very intimate but is capable of public expression. Then flip mentally through the books you've studied, or the music you've sung, or the
theorems you've proved, or the experiments you've reenacted, and ask
yourself which have a bearing, taken in the largest sense, on your issue.
What will happen next is the result of a mixture of concentration and
luck: some paradox or analogy or some other significant array will jump
out at you. Seize that and slowly pummel, stroke, and shape it into an
articulate order. Of course, none of that can happen at the last minute.
For looking into yourself, for calling on your studies, for finding a crystallizing moment, for working all of it into a well-shaped whole, time is
of the essence.
Eva Brann is a tutor and former dean at the Annapolis Campus of StJohn's College. Her book is
entitled: What, Thm, Is Timt (Lanham, MJ: Rowman & Littlefield, 1999). This lecture was delivered
at the Annapolis campus, September 4, 1998.
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THE ST. JOHN'S REVIEW
My second thought was that time is one subject concerning which it
does not matter whether one is a freshman finishing the second week at
the college or a senior beginning the fourth year, or even a tutor who has
taught most of the program. Stormy love is not a pressing issue to all
ages, nor is looming death, but there is, I think, no one, at any time of
life, for whom time does not become a problem in some way or other. I
know this &om experience, Of the things that have urgently interested me
&om time to time, the mention of Being and Nonbeing, for example,
provokes mostly stupefied noninterest, the mention of the imagination
elicits an account of people's favorite fantasy-series, but the mention of
time gives rise to intelligently companionable puzzlement. People have a
different relation to the question concerning time than to other deep matters, which they are either willing to bypass as too obscure for their taste
or to treat with the most unreflective but familiar particularity.
The title of this lecture-and of my book-is "What, then, is
Time?" It is a quotation from the most famous sentence ever written on
time by the man who was most deeply immersed in its elusive familiarity,
St. Augustine. It comes &om the eleventh book of his Confessions, which
we read in the sophomore year. Here is the whole sentence:
What, then, is time? If no one asks me, I know; if I
want to explain it to the questioner, I do not know.
My own concern with time started -&om two ends at once, intellectual puzzlement and deep-felt irritation, and it developed, as really good
questions do, from annoyed fascination to serious interest. The intellec-
tual puzzlement was just that expressed by Augustine: What sort of a
being, if it was a being, could be so handily familiar in daily usage and so
fugitive to the grasp of thought? Here I did as all my fellow humans do:
I make time, kill time, manage my time, waste time. To be sure, I've never
"done" time, though but for the grace of God I might have. I know that
time heals all wounds and ravages all the beauties of the world. But if I
�BRANN
49
ask myself what it is that does this, I see and touch nothing and think of
less. That is at first just a puzzling and then an engaging state of affairs.
The irritation I experienced had a superficially different source. In all
the departments of life people talk of time as a force or a power, not just
in the sort of dead metaphor that makes up the unconscious poetry of
popular usage, as in all the phrases cited above. No, they mean it literally, especially when they are talking of the so-called "phases" of time.
"Phase" will be the most important word in this lecture. It is my worddifferent authors use different words-for the three parts of time, past,
present, future. Perhaps I should have said the three parts of human time,
for I will argue that only human, or human-like, beings have pasts and
presents and futures.
It is the future with which these people mostly play infuriating havoc.
They say and they mean that there is a future coming and our business is
to form a reception committee for it. Some see this Future with a capital
F as a doom, as in Yeats's great poem, uThe Second Coming":
And what rough beast, its hour come round at last,
Slouches towards Bethlehem to be born?
Far more of our contemporaries see it cheerfully as a benefactor,
though a totally manipulative one: it is the Information Age or the Global
Age or the Age of Megacorporations, you name it, and our duty is to be
ready or to be run over by time. They engage in what I call to myself
"proactive passivity:' This time-mode-the adjective, incidentally, is
"temporal;' so I will say, this temporal mode-strikes me as paralyzing
the human will, and that is one form of immorality.
So besides the intellectual desire to understand the nature of time and
whether it is a being or a nothing, I also began to think about time in its
human effects. Almost everyone who has lived for some time has neat
observations about these effects. For example, I have been at St. John's
College forty-one years or almost IS,OOO days. Sometimes it seems like
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THE ST. JOHN'S REVIEW
forever and sometimes it seems like a day. What accounts for this mad
elasticity of time? But besides these time-ruminations there is also that
sense I have of the important moral consequences of not thinking about
the nature of time, about accepting what seem to be abuses of our phasenature. In fact, a new hero of mine, Octavio Paz, whom I discovered
through an alumnus of St. John's, Juan Villasenor, put my thought much
more expansively than I would have had the courage to do. He says in his
book on India:
I believe that the reformation of our civilization must
begin with a reflection on time,
Recall that I am still laying out the possible profit of telling you about
my book, and here is the last one, chiefly to mysel£ Imagine what a pleas"
ure it will be to come on campus and to be able to fall easily into a conversation about this magical subject with some proportion of the people
that live and learn here-with the more virtuous part, I might add, those
who come to Friday night lectures,
Now let me tell you of two discoveries or devices--it's always hard to
tell whether it's one or the other-about which the book crystallized, One
was the discovery-and I became persuaded that it was a discovery, was
really there to be _founJ.-that writers on time who lived millennia apart in
time and who were wodds apart in thought were at crucial moments driven into the same understanding, or at least the same problem, Once I had
discovered one such pair of time-twins I came upon three others. And
finally I came to believe that amongst them they pretty well established the
perennial possibilities and the pertinent problems concerning time. In a
moment I will tell who these writers are and what deep notion each pair
shares, But let me say here that it was a blessing to find such a principle of
selection. For it is hard for most of us to think about these enigmas without help. The trouble is, there is too much help on offer. I own a bibliography of time which tells of nearly 200,000 books and articles written
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51
between I 900 and now. Of course, much of it is piffling, but much of it
is, I am sure, thoughtful. I chose four great writers, and they paired quite
naturally with four more, and by good luck these are the eight among the
ancient and modern writers generally agreed to have the deepest theories.
The pairs, then, are Plato and Einstein, Aristotle and Kant, Plotinus and
Heidegger, Augustine and Husser!. Since many of you will not have read
them, though all are on the Program, I'll present their time-theories as simply and as unencumbered by terminology as possible. But I'll omit completely telling you about one pair, Plotinus and Heidegger, because it is too
tricky to do, although their similarity on the point of time is most spectacular in view of their diametric opposition on everything else that mat-
ters.
The other discovery was that a human effect which never ceases to
enchant me, namely the images that arise before the mind's eye in our imagination, had a certain remarkable similarity
with our sense of time, a for-
mal sort of similarity. Images are absent presences or present absences; they
are not what they are, they are made of Being and Nonbeing. What I mean
is that any image, but particularly a mental image, presents someone or
something not actually present. To imagine an absent friend is to have him
there, but not really. Time as well, it turns out, has this curious character of
being and not-being, of being there but not really, of being present only in
its absence. My all-time favorite time-saying is by the inimitable Yogi Berra.
When someone asked him: fiWhat time is it?" he replied: You mean
11
now?" It is the wisest of answers, because you can't tell time, and yet we do.
It is always and never Now.
So the book began to have two parts. One part was a study of these
eight philosophers for the purpose of seeing what kinds of answers could
be given to the question "What is time?" and what problems were inherent
in the answers. But studying, while a help to thinking, and fur most of us
an indispensable help, is not thinking, since to understand what others
think is simply a different activity &om the thinking that goes directly, with-
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THE ST. JOHN'S REVIEW
out intermediary, to the question, So in a second part I tried to go directly
to the question, having absorbed all the help I could.
Therefore in this lecture, too, after telling what some of the best writers I could find have thought about time, I will try to tell what I think. I
should say right now, lest you be disappointed, that what I conclude first
and last is that it is a true mystery. I mean a potent effect whose characteristics are poignantly clear but whose nature is finally unfathomable. You
can specify a mystery but you can't resolve it.
If you have a huge field of apparently possible answers to a question,
it clears the decks somewhat to begin by removing the answers that are
simply unacceptable. In thinking about the ways time is spoken of. it
seemed to me that whatever else is said, time is spoken of either as occurring in nature or as being within. the human being. Time is either external
or internal, or perhaps both.
External time has attracted by far the greater interest. Time is written
of in religion, where it is a great question how an eternal God acts in created time. Time is treated in history, where it is a great question whether
the times make history or people do. But, above all, time is a great subject in physics, where the best-grounded and most remarkable theories of
time are developed.
Without question, the physicist who has done most to make other
physicists and people in general think about time is Einstein. The work I
chose to examine is his I 905 paper on what came to be known as the
Special Theory of Relativity. What struck me first was that every mention
of time was in quotation marks. This habit conveyed to me that I was dealing with the most careful and thoughtful of writers, one who knew that
time in physics is a most problematic notion. Einstein says tight away:
It might appear possible to overcome all rhe difficulties
attending the definition of "time" by substituting "the
position of the small hand of my watch" for "time:' And
in fact such a definition is satisfactory ...
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At least it is satisfactory when we are talking only of time here and
now. Before Einstein, physicists had believed what everyone believes: that
it is the same time throughout the world, that every other Here simply has
the same Now as my Here. This situation was called simultaneity and was
regarded as a chief feature of external, I mean narural, time. Einstein goes
on to show that for any stationary Here far away &om my own, it takes
some calculating to synchronize our watches. And, when we are moving
relative to each other, one of our most entrenched senses about time is
overthrown, namely that what time it is is independent of our state of rest
or motion. Einstein's theory rums out to have to do entirely with the
measurement of time-what my local clock and your local clock tell
under different physical conditions. That is why Einstein puts "time" in
quotations: he is warning us that not the nature of time but its measurement is at issue.
Now I'll jump back rwo and a half millennia and quote to you what
is the most famous, most o&en cited definition of time. It comes &om
Plato's dialogue called Timaeus. Timaeus is a made-up character, a visiting
physicist. He and some of Socrates' friends have planned an amusement
for him. On the day before, Socrates had produced for them a picrure in
words of the ideal political community-some people think it is the one
set out in the dialogue called The Republic. Now Timaeus will reciprocate
by painting for Socrates' entertainment the cosmos, the ordered world
within which such an ideal city might fit. In the course of giving a mathematical account of such a cosmos, Timaeus says this about the way the
maker of the world introduced time into it:
He planned to make a movable image of eternity, and as
he ordered heaven into a cosmos, he made an image of
that eternity which stays one and the same, an eternal
image moving according to number. And that is what we
call time.
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THE S"I JOHN'S REVIEW
What Timaeus is saying is that the heavens move like a great cosmic
dial and that this motion allows us to tell time.
So the mythical early physicist and the greatest of modern physicists
are saying the same thing: Time is what the clock tells, in one case the
cosmic clock, in the other a local watch. And so say all working physicists
in between, It is a working, a so-called operational definition of time, and
it works just fine-until you begin to think about it. That time is what
the clock tells is what one might call a dispositive definition. It disposes
of time as an issue. But if you turn it around and try to say that the clock
tells time you're in trouble. Time never appears on the face of a clock. Nor
does it appear anywhere else in nature, ever. All other natural phenomena
appear somehow to sight or hearing or touch. Of time not a trace.
What does appear is motion, An analog clock is a standard cyclical
motion, A digital clock is a standard progressive motion, Clocks are calibrated motions. There is no time actually used in physics and none that
actually appears in nature. There is much more to be said about this
shocking claim, and I'll be happy to hear any arguments you might have.
Among other points then to be made, some, who have read Newton,
might want to point out that Newton, at least, does stipulate true natural time, an equable flux that comes before motion. And I would answer
that it is not only as physicist but also as theologian that Newton puts
time into nature. For this so-called absolute time, which has no observable features, is probably not so much in nature as in God's mind, in that
part of God's mind, called his "sensorium;' with which he is receptive to
all of nature, irs infinite spaces, irs primary forces, irs ultimate bodies. My
point at the moment is, however, only to reinforce a conclusion I came to:
Wherever time is seriously considered, mind, soul, consciousness and sen-
sibility come on the scene. Time can only be internal, meaning within a
mind, possibly God's mind.
So I disposed to my own satisfaction of the vast majority of theories
of time. Intricate and interesting as they are, they are really theories of
motion, not of time, and they don't tell what time is. But time is the sort
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55
of subject for which every settling of the mind in one respect is punished
by a complementary problem popping up in another. You can, and I think
you have to, take time out of nature, but I am not so perverse as to claim
that the outside world isn't full of variations: locomotions, processes,
alterations. The mystery that has now popped up is that we have no idea
what is really going on in this time-deprived world. Let me show you what
I mean.
Human time, internal time, will be distinguished by its phases, past,
present, future. But nothing in nature; except perhaps the near-human
mammals, apes and dolphins, has a past or a present or a fUture. Edwin
Muir says in a poem called "The Animals":
But these have never ttod
Twice the familiar ttack,
Never turned back
Into the memoried day.
All is new and near
In the unchanging Here...
Animals and sticks and stones do not have a past, though they might
be said to be their past. But I, for one, just cannot imagine what it is like
to live in the unchanging Here and not have memory, how such a being
gets itself into and out of existence, in short, how anything can change
without having phases of time. But then again the effort is love's labor
lost: How could I have empathy with, feel my way into, that which has no
inside? So the outer world becomes in this respect opaque, and this is the
price to be paid for making a philosophical choice. In coming to conclusions in philosophical inquiries, I want to say as an aside, it is always a
matter of what we can best live with for the time being-which is why all
philosophy as carried on by human beings is ultimately moral philosophy.
There is perhaps a solution to the timelessness of nature. It is a commonplace for writers on time that there are two kinds of time. They
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THE ST. JOHN'S REVIEW
might be called succession-time and phase-time. Phase-time is dynamic in
the sense that the human present, about which time breaks into past and
future, continually shifts-as Yogi Berra's counter-question, You mean
now?" makes clear in its unavoidable absurdity. Succession-time, on the
other hand, is static. It is merely the endless chain of before-and-afi:er,
established once and for all. It is time all by itself, no one's time, the time
of all events taken only with relation to their succession and to nothing
and nobody else, Perhaps nature does have its time, succession-time, But
11
even the successions of nature turn out to be more intelligible as causal
than as temporal sequences,
This is the moment to introduce Aristotle, who produced the first
extensive treatment of time ever, in Book Four of his Physics. Here is what
he says time is:
Time, then, is not motion but that by which motion
has number.
Aristotle seems to be making spectacularly short shrifi: of that mysterious power, time. It is nothing but an attribute of motion. Then he says
what sort of attribute:
Time . , , is the number of motion with respect to
before and after.
What the deep meaning of all this is can't come out unless we follow
up what Aristotle means by motion, number, before-and-afi:er. But we
might guess at two problematic elements of this understanding of time.
The first, which is by far the less deep of the two but is endlessly discussed, is this: if time is the number of motion as a progression in which
the parts come before and afi:er, if it is in fact the succession-time I just
introduced, it must somehow share in a chief feature of motion, namely
continuity. Physical motion borrows this feature fi:om the fact that it takes
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place over distance. Distances are representable as mathematical lines, and
these lines must be continuous-no elements can be missing. So time, as
Aristotle himself emphasizes, is continuous, like a line. Wherever you cut
the line you get a point that belongs to both parts of the cut. This point is
the Now. Time is in every way like a line of geometry: It lies upon its points,
each of which is a Now. The only difference is that the geometric points are
static, whereas the Now moves forward, ever the same in its features, ever
different in temporal location. But as you know by now, a point is that
which has no parts, so the Now has no parts. Therefore it has no extent, no
bulk, no force, no presence. Therefore the point-Now of the mathematical
model of time is as far removed as anything can be from the humanly experienced present, which is vivid, full, and altogether the most impressive
phase of time. Insofar as time is continuous it is not very human.
But then Aristotle has also said that which will make time totally discontinuous. For time is a number by which motion is counted, and anum-
ber is a collection of completely discontinuous units-there is no way one
unit can be tangent to another. Motion, locomotion at least, is bound to
distance and borrows from that fact its continuity. But number is bound
to something else which reinforces its discontinuity. Many things in the
world are collections of items. Aristotle mentions herds of horses and
flocks of sheep. Other things, such as distances of all sorts, can be marked
off into artificial units. All these things have a number that belongs to
them. But nothing in nature gets its number unless someone is counting.
Aristotle says that it is the soul that counts. So time, in order to be the
number of motion, requires a wide-awake counting soul. Now comes the
critical question: When the soul is counting, does it take time to do it?
Does it get its numbering from some motion? What distance does that
psychic motion cover?
Aristotle is in big-and I must say unacknowledged-trouble. Time
in nature is only the number of motion, but what is the counting that
announces that number? I don't think he knew, but perhaps in the question period someone will make his case.
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58
Now let me leap 2000 plus years ahead. For Aristotle, time originates
with the counting soul. To
my mind, Aristotle's true modern successor,
the one who takes Aristotle's thought and turns it thoroughly and precisely upside down, is Kant. Here is an aside: This kind of inversion of
thought, so that it is the same in name but utterly different in significance,
is the chief moving force of the philosophical tradition we study at this
college. By "force" I don't mean some magical attribute of the passage of
time, but the way of proceeding that is congenial to those immersed in
this tradition. At any rate, whatever time is, if it has power it has it only
as an aspect of human consciousness.
Back to Kant. You will be relieved to hear that I do not plan to tell
you what is in the Critique of Pure Reason, Kant's founding book, although
everything in there is sooner or later related to time. Instead I will focus
on a few sentences which show what it is that brings Kant so very close
to Aristotle in the letter, though he is worlds apart in meaning.
Kant regards time as a constitutional part of our receptive capacity,
our ability to take in what is given to us. Such a capacity is called "sensibility;' and we are so made that whatever comes to us, the world of nature
especially, comes in the form of temporal sensibility. The Critique is a great
work of philosophical art, and I omit the many factors that feed beautifully into rounding this notion out, in order to concentrate on just one
thing: When we ask what it means that nature comes to us in the form of
time, the answer is that whenever we think about nature we begin by
noticing quantities, and we do that first of all by numbering-not topof-the-head counting, but a deeply interior kind of beating out of units
that add up into a number. Here is Kant's word on what is happening in
this counting: ul generate time itself ... "
So Aristotle and Kant agree that time is a kind of psychic beating or
counting. It does not save Kant from the question I asked of Aristotle
that he calls time a form of the sensibility. Is this form, I now ask, itself
static or is it fluid? If it is static, how does it produce the psychic flow of
pulses? If it is fluid, is there yet another time behind Kant's deep consti-
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tutional time? Let me say right now that all the authors who put time
within the soul run into this trouble. And those who put the origin or
ground of time outside of the soul run into other and worse troubles.
Both Aristotle and Kant have been primarily interested in what I have
called succession-time, the steady chain of before-and-afi:ers found in
nature, though apprehended by our counting. Now is the time to speak
of human time, phase-time.
To my mind, Augustine is the greatest writer on time-and the most
beautifUl one. Here's another aside: very broadly speaking, philosophers
come in rwo kinds, those who inquire serenely and hopefUlly into a subject they long to know and believe they can approach and those who question severely and disenchantedly a matter they think is ultimately hopeless. Augustine certainly has travails of the soul, and I would not be unfair
to call Husser!, who takes up rwo millennia later exactly where Augustine
had !eli: off. a fi.tsspot. But both are not so much driven as led by faith in
their subject, and I want to say that these are the philosophers I trust and
prefer to be with.
Augustine wants to know what time is because it is the human counterpart of God's eternity, the eternity of the God he has just found and
acknowledged. But there is nothing exalted about his questioning-it is
very down-to-earth. He loves to sing hymns, and the question is: How do
I measure times, the long and short syllables, the lengths of the stanzas?
Distances are easy to measure. They stay put while you lay a measuring
stick alongside them. But the moment slips away, the past is no longer, the
fUture not yet, and there is no way to lay a time-stick along an elapsed
time. Lengths measure lengths, motions measure motions-what measures time? Here is his answer, as I said, to
my mind the most illuminating
thing ever uttered about time, a new discovery, as he himself says:
Time is nothing else but a stretching out, though of what
I do not know. Yet I marvel if it be not of the mind itself.
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THE ST. JOHN'S REVIEW
Our mind or soul is distended and that makes it capable of holding
time, so to speak. How distended, how stretched? Here is Augustine
agam:
This then is clear and plain, that neither things to come
nor things past are, nor should we properly say: 'There
are three times, past, present, and future:' But probably
we should say: "There are three times, a present of things
past, a present of things present, and a present of things
future:' ... The present of things past is memory, the
present of things present is sight [or perception), the
present of things future is expectation.
So we can measure times gone
by and times
to come because
they are
now present to us. But the solution of the measuring problem is the least
of it. What Augustine has done is to tell what makes a human being temporal, how time is in us.
To be human is to be present and to have things present before or within. Yet another aside: certain so-called postrnodern writers, taking their
departure &om Heidegger, think that this is a very derivative way of
approaching human Being and that to think of human beings as containing presences within and confronting things present without demeans the
originality of existence. But Augustine does think that to exist is both to be
in the present and to be in the presence of things.
Augustine's book on time in the Confessions is preceded by a book on
memory, and this book is the indispensable preparation for his understanding of time. For there he shows how we can also be in the presence of
absent things: we have the whole spacious world, its fields and palaces,
within us, not, however, the things themselves but their images. Here you
can see how the imagination, as a power for making the absent present, is
essential to our inner sense of time. For with it we can have memory of past
times and also expectation of future things, since expectation is a forward-
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61
directed imagination. And since much of what has happened to us is now
present to us or is now recoverable, we can not only measure time somewhat as we do space, which is all there simultaneously. We can also see how
our mind is a temporal image of God's mind, who holds all creation
together there at once, in the eternal Now.
To be human, then, is to have a mind so stretched that it encompasses
in its present both memory and foresight. One way to depict that condition is in a diagram like a coordinate system. The horizontal axis is the time
of the world, of Creation; it is succession-time. God knows how it works;
we don't. Astride of this horizontal coordinate sits a vertical stretch of line,
our mind. Where the two intersect is the moment of sight, of perception,
our point of intake for the world. The segment below represents remembered events, dropped out of sight but not out of mind. The part above
represents the dreams and plans we now have for the future-and that is
all the future that actually exists. As the world passes by, our memory line
grows longer and our expectation line shortens. Then one day it ends.
Husser!, who actually draws diagrams of this sort, in fact marks one of
his lines as the "tug towards death:' It is not, however, one of the axes he is
marking in this way, but one of the oblique lines with which he connects
the horizontal axis of succession-time and the vertical axis of phase-time.
These oblique lines show how each perception offered by the horizontal
succession-line sinks away into vertical memory
in an orderly and continu-
ous manner, without any scrambling or dislocation. Husserl's time-diagrams are clever and complex, and I had a lot of fun-fun bordering on
agony, that is--working them out.
Husser! is the founder of a way of inquiry called Phenomenology. Its
chief feature is that it excludes all questions of existence and realiry, such as
whether time is real. Instead a Phenomenologist pays attention to the
appearances within consciousness, articulating and ordering them. Our
sense of time is a perfect subject fur Phenomenology and Husserl's lectureseries known as The Phenomenology '!f lnternalTime-Consciousntss is the great firstfruit of his method.
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THE ST. JOHN'S REVIEW
Husser! makes hundreds of acute observations, but his main advance
on Augustine is to puzzle seriously over the extent of the present. Recall
that the point-Now of mathematics is too skimpy to live in, but consider also that an extended present is going to be part past, part future.
Husser! finds a way, fairly technical, to show that there is a discernible
immediate past and an immediate future that are so bound in with the
present as to give room, so to speak, for perception, so that there is time
for a time-sequence, say a melody, to be taken in. He shows how the present has time for the world to impress itself on us.
One last word about Husser!, The horizontal axis, which represented
the world's time for Augustine, represents an internal time-flux, a contin-
uous sort of subjective succession-time, for Husserl. For he is withholding all claims about the reality of the world and its time, and attending
only to our inner experience, to our internal time-consciousness. In trying to understand this internal flow, Husser! is drawn into questions
beyond Phenomenology. The question that finally preoccupies him is the
familiar one: how can this flux, which is one aspect of our sense of time
and for him the deepest, be spoken of? Are we fluid through and through,
or is this flux grounded in a stable form? But how can a fixed form be the
source of a flow? Husser!, a man who is willing to admit ultimate perplexity without losing faith in the worth of his problem, says:
For these things we have no names.
Now is the time for me to say what I think time is-maybe it would
be more sensible to say "how time works:'
I think that phase-time is the fountain and origin of all time. Every
phenomenon of time is derivative from the fuct that we have past, present and future. To me the most astounding circumstance of our temporal life, surpassingly strange but apparenrly unavoidable, is the crux and
center of the three phases: the present. All that is ever real for us, all that
is really there, really present, occurs in these point-by-point moments of
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presence. This is the instant of perception when we see and hear and
touch the world. The rest, the long stretches behind and before, is
absence-what has gone by and what is yet to come.
Human life would therefore be very pointillistic and poor if present
existence were all we had. Happily there are ways of being that are even
more potent rhan present reality and momentary existence. There is the
actuality of imaginative memory and of imaginative expectation. The
present of perception is the point of intake for the novelties that the
world offers to our senses, but the past and the future are also present to
us as images, as memories of things past and plans for things to come.
These are the present actualities, the powerfully present absences that give
coherence and resonance and significance to the moment. They also make
it possible for us to measure time directly, not by observing external
motions as of the hands of the clock, which never displays time at all, but
by the thickness of the image-pictures we flip through or leap over to get
to the past moment from which we want to estimate a stretch of time.
Our memory is like a laminate of transparencies or a carousel of slides,
and my claim is that this accumulation we call the past and this projection we call the future is what produces our inner sense of time. And this
thickening of the present by past and future is what Augustine calls "the
stretching of the mind:'
Now note that I have described the present as punctual, instantaneous, momentary. And this description seems to be supported by the
observations of all kinds of people, perhaps poets above all. The Nows
that matter are somewhat isolated-instants of recognition, moments of
meaning. In his book The Labyrinth '!f Solitude Octavio Paz calls the Now
"explosive and orgiastic" and wonders how it fits into ordinary historical
passage.
But much of the time of our lives passes in seeming continuity, and
this sort of time, the time that seems like a continuous passage, usual-
ly called duration, has to be accounted for as well. I think it works as
follows.
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THE ST. JOHN'S REVIEW
Our present appears punctuated by the ever-varying world and our
perception of it, Now we see our friends, now they've disappeared around
the corner; now we hear one note, now another. But there is another time
experience that we become conscious of when we are deprived of most
external sensation or when our inner images are pushed out of sight by
fear and anxiety. Or we can deliberately close off our senses and empty
our minds to concentrate simply on our inner duration. What then comes
to the fore is a sort of inner pulsing, the very beat of our mere consciousness, empty life itself. I am trying to describe the soul's aboriginal
counting that both Aristotle and Kant discovered. This inner beat then is
the origin of that succession-time that is mirrored in the before-and-a&er
of physical motion and that plays so large a role in our practical life.
Now most of the time we are not taking note of this pulse, or paying much attention to our inner life at all The beats recede and merge as
in a long perspective; time's passage appears continuous and acquires all
the characteristics and problems of a line in space. Then, retrospectively,
time is thought of--not felt-as a continuum that is continuously cut by
a point-like Now, the kind of Now in which nothing can happen,
So my description of time, which leaves time as what I call "a wellspecified mystery;' ends with the point-Now. And that is where a review
of the various pathologies people attach to the phases of time begins.
I'll give the sketchiest summary of our time-troubles, partly because
time is short, partly because every one of us has a lot of personal experience with this aspect of time, and it will make a good subject for
future conversation.
One way, then, to think of the way people wreak havoc with the perceptual present is that they treat it as a mere, point-like Now, monotonously empty and featureless, while racing unrestrainably forward. To/try
to live in this Now is to long to fill it with strong stimulation and increasing novelty. Now-life is the pathological counterpart of present-life.
Similarly, some people deprive themselves of the image-filled memory that gives the present its anchor of significance by rushing to keep up
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with novelty and trashing not only their own past but that past which
their communities have in common, their external memories.
And finally, some people are so dominated by a future that is supposedly coming at them that they give up what they really care about to
make themselves into ready servants of this oncoming power. But according to my understanding the future is nothing but the dreams and plans
we currently have, and as far as the humanly-made world is concerned,
nothing is coming but what we actively or passively agree to. It is that passivity which is, to my mind, the greatest time-pathology.
��--:f The Taking Of Time
fj- by Douglas Allanbrook
Part One
Consider the short Latin verse: Deus creator omnium:' St. Augustine
examines this verse towards the end of his chapter on time in The Co'!frssions,
a chapter which comes at the end of his autobiographical examination. Try
to memorize it, to inscribe it permanently on your minds: Deus creator
omnium." Consider its aspect on the written page. Read it out loud It is now
11
11
present to you in space as you take the time to read it-as convention pre-
scribes-from left to right, though it could be written &om right to le&. It
would take the same time to read : "muinmo rotaerc sueD:' Once I have the
verse in mind, however, and utter the syllable De, the whole of the verse's
future begins to pass through my present utterance into the past. If I have
the verse memorized it is--of course-all of it present in some unspeak-
able manner in my memory. If I recite it, give life and breath to it, its direction is by no means reversible: it has a beginning, a middle, and an end It
is in this sense analogous to God's relation to his creation, except for the
fact that our verse was made, not created, and has an earthly author, the
estimable Bishop of Milan, St. Ambrose--a formidable rhetorician.
The time it takes to recite our verse may be longer or shorter depending on the speed with which it is read. By paying attention to the motion
of the second-hand on your wrist watch, you can tell you how long it took
for you to recite it. You count as the second hand sweeps past and, if in one
recitation you count up to ten and in a second recitation you count to seven,
you say the second recitation is faster than the first and that the first is slower than the second. When you have done this you have not done very much,
though it is your attentive mind which has done it. It has numbered a
motion and compared it nmnerically with another motion. It's not, howevDouglas Allanbrook is tutor emeritus at St. John's College. This lecture was delivered at Annapolis
on February 17, 1995, and at Santa Fe, November 12, 1993.
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THE ST. JOHN'S REVIEW
er, as if you had taken rhe true measure of rhe verse. If, experimentally, you
slow up rhe recitation excessively, you will run out of brearh. If you speed
it up too murh, it will sound breathless. Your lungs and your brearh are now
fixing limits to rhe rime taken for rhe performance of rhe verse, Our bodily organs and our senses do provide a mean for us; they guide us into a
pleasing lengrh of time ("Deus creator omnium"). The senses also judge of
anorher relation, a fimdamental relation which obtains between syllables of
our verse. While rhis ratio may be roughly numerable, its presence is signalled to us--and is immediately present to us--via our bodily senses, You
may develop a notation for rhis which might seem to be completely numerical or metrical (quarter note; half note), but such a notation does not hit
rhe mark. All of the traditional names which attempt to label what is going
on catch rhe essence of rhe ratio more correctly. Here are just a few of
rhem: rhe eloquent Latin terms, elevatio and deposition; rheir Greek equivalents,
arsis and thesis; or simply our English upbeat and downbeat. How does rhe measuring of rhe second syllable by rhe first syllable occur physically; how is us
measured by De in rhe word Deus in our Latin verse? What has transpired?
When rhe second syllable has been uttered it is compared physically
wirh rhe first syllable; our body's attention is directed to a happening in
time, directed not by our ability to compare 2 to I, but by rhe physical force
of our feet and the motion of our brearh as it is inhaled and exhaled. It is
an event, not a cognition, though we are well aware of it. (It is not unlike
our primitive sensing of same and other, and rhe connection this has wirh our
ability to compare I to 2.) Once rhe first pairing is established, future rime
seizes us: we suspect rhat the next syllables will be like rhe opening ones,
rhat rhere will be a knowable and sensed double: DeuS gives tise to c;:,;;,
anorher iamb. 1 We will be able to dance or at least walk steadily to what is
awaiting us, and we are not disappointed Our pulses adjust to it and our
feet can so easily give us a down beat. The meaning of rhe words now has
its soul, its brearh, its animus; our hope for rhe future becomes realized as
rhe verse moves rhyrhmically rhrough rhe present moment of sense, on into
rhe past. God becomes rhe creator of everything, starting from ground zero,
�ALLANBROOK
69
as we prepare to say the word Deus, and ending as ending with the very thing
itself as we say the word omnium---everything.
Consider now a verse that may be more familiar. It is in the English language, though it has a Scotch accent. "My love is like a red, red Rose:' My
and is are up-beats even though My has a lot more weight than the innocent
little copula is. When "my love" is safely tucked into the past, my anticipation of the future is rhythmically capped when is is notched with like. A marvel occurs when, with the memory of the past two iambs ("My love is like")
firm in our memory, we get a simple little article, a, followed by two reds and
a rose: My love is like a red, red Rose:' Of course the first iamb, My love"
11
11
has not the gravity, at least to the general public, of
11
Deus our Latin verse,
11
;
however, has not the excitement that is generated by a simile. The future
awaits us when a simile is broached. What will it be like? A red, red, Rose.
What a happy consummation! Think about the second red. The first one
comes as the downbeat of an iamb--a red, the second one as the first word
in a pair that ends with rose. Consider the force of the three ri.
Now for a verse much closer to us than that of Robert Burns, though
it may be that only to certain rather aging Americans does it seem so irrunediate. This generation's rhythmic habits may well be different. Here goes: "I
can't give you anything but love 2 3 4 Baby!" Read it out loud: it starts with
a jolt on I, foot down, first person singular. Once we have heard it with its
catchy tune and rattling snares we tap our feet. Can't help it. After its slamdunk into love on the first down beat of the third measure you can't help but
begin counting empty time (2, 3, 4!) so that Balry!, in all its sweet fecklessness, gives us a double jolt on the fourth down-beat of the piece. There's an
endearing insouciance, a sophisticated sappiness in the whole verse. Its con-
struction pulls us into the act, making us both witty and sexy as the 1--the
(g<>--<lances through its slice of time, deprecating itself and fi:nessing us
into the universal seduction game!
The "My love.. in the verse My love is like a red, red Rose" is more
mysterious than the 'T' in "I can't give you anything but love,-Baby!" My
points to its down beat love; but that is something that can't be pointed to,
11
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THE ST. JOHN'S REVIEW
let alone defined. In reciting the verse we could, if we wish, imitate the longs
and shorts of our Latin verse: uDeus creator omnium"-"My love is like a
red, red Rose"-but there's no necessity for it. English verse depends on
stress, not length. In either performance, however, the foot comes down on
the important words kve and like, The rest of the quatrain takes off from
the like and plunges the rose first into spring-time, June, and then, in the next
two verses, into a simile that is the heart of this essay. Here is the quatrain:
My love is like a red, red, Rose
That's newly sprung in June.
My love is like a melodie
That's sweetly played in tune.
A melody has a beginning, a middle, and an end. It is a wordless and
memorable piece of time, coiled up in our mind's winter like a tulip bulb
ever ready to unfold when spring arrives, Is love like a melody? Love is a
hope, an anticipation, looking ever forward to a consummation that
would mark its demise. All similes are double-edged: they are both like
and unlike what they refer us to. That is the pathos of all similes and in
particular of this simile:
My love is like a melodie
That's sweetly played in tune
A melody can be repeated over and over again, Its very reality lies in
its not being real! Love is not like that.
We must look back at the first verse we examined, which is by now
firmly stored up in your memory: uDeus creator onmium." St. Augustine
places his discussion of this verse, as you may recall, at the very end on
his chapter on time, a chapter which in its turn is placed at the completion of the autobiographical section of his Co'!fessions. The unfolding of
his life's time has led him-almost of necessity-into both a meditation
�ALLANBROOK
71
and an explication centered upon the word time. It is only with this in
mind that the sense and meaning of his analysis of the verse gets its full
import. Let it be stated hypothetically: if God created everything, then
time is indeed part of that creation and accompanies every created thing
in the course of its life here in this created world. That world has a beginning, a middle and an end, as does the life of a man and the history of
the world. A melody or a psalm in such a world might well then be a true
image of creation, and not merely a construct that taunts us with both its
likeness and its pathetic difference: not a simile, not a metaphor.
Just as at this moment in his life he both looks forward with anticipation and backwards into the halls of his memory, so when Augustine is
about to recite our verse his expectation extends fotward into the future over
the whole extent of the psalm. Once he begins reciting, whatever he plucks
from the future and lets fall into the past enters his memory, what he calls
his faculty of "looking back at:' The life of this activity is both backwards
to memory and forward in expectation of what he is about to recite. In
other words his--and our-present attention is what the future passes
through on its way to the past. As I progress, expectation lessens and memory increases. Here are his exact words:
And what is true of the whole psalm is also true of every
part of the psalm and of every syllable in it. The same
holds good for any longer action, of which the psalm may
be only a part. It is true also of the whole of a man's life,
of which all of his actions are parts. And it's true of the
whole history of humanity of which the lives of all men
are parts.
This tremendous conclusion completes his discussion of time and
memory, and the verse chosen- Deus creator omnium, C'God the creator
11
of everything")--substantiates in its words what the action of his attention
performs. The moments, weeks, months and years of our life, the totality
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THE ST. JOHN'S REVIEW
of such parts, the very ages of man, are not one damned thing afi:er another, mere perturbations in the sea of becoming-tomorrow and tomorrow
and tomorrow-; they have a true beginning, a true middle, and a true end
because and only because they were created by God. Given this understanding, our psahns and our speeches reflect this: they are true images, not
the paltry work of our so-called creativity with its games of simile and
metaphor, When we give voice to them we lend them the life of our breath
and of our movements which serve to measure their lengths and to round
out their periods. Genesis tells us our breath was the breath of life, our
"inspiration;' breathed into us by the Diviniry, that very breath which measures our syllables and our feet. This is the literal meaning of both the
famous word psyche and its Latin twin animus. Our enlivening, our first aspi-
ration, was from God, our first inspiration.
For most of us such statements seem to issue from the mouths of
either saints or madmen; we are not, like St. Augustine, rhetoricians seized
by the blinding, ever-present moment of ultimate attention, Grace. Our
poems are not the Psahns or the Bible and our lifetimes are opaque. We take
our time differently, and the perennial memorability of our constructs, of
our cherished lyrics, of our caged nightingales, are--of necessity-fraught
with pathos as we cottfront the tricky sea of self-love, and swim like drunken boats in a medium which sets no limits, which has no port of arrival,
nor any hope of one!
Part Two
All poems are time-pieces-always constructed, always formal. The best
of them are like an excellent Swiss watch, unswervingly acrurate. They make
us catch our breath as we are paced through their matchless lengths. I propose now to get down to brass tacks, to present to you three marvelous sonnets, one Italian, one English, and one American. All three of them, being
Italian or Pettarchan sonnets, follow a pattern of eight lines followed by six
lines: an octet followed by a sextet, as you can readily observe if you glance
at your scores. (They are scores, as this is an essay whose subject is music.)
�ALLANBROOK
73
Read carefiilly to yourself the first and by far the earliest of these sonnets
so as to have something in your ears before any discussion of them ensues.
Que! rosignuol, che si soave piagne
Forse suoi figli o sua cara consorte
Di dolcezza empie il cielo e le campagne
Con tante note si pietose e scorte;
E tutta notte par che rn' accornpagne
E mi rammente la mia dura sorte;
Ch' altri che me non o di ch'i' rni lagne,
Che'n dee non credev'io regnasse Morte.
0 che lieve inganar chi s' assecura!
Que' duo be'lurni, assai piu che'l sol chiari,
Chi penso rnai veder fra terra oscura?
Or cognosco io che rnia fera ventura
Vuol che vivendo e lagrimando impari
Corne nulla qua giu diletta e dura.
e
There were sonnets around the literary landscape before Pettarch; he,
however, firmly established the form with his many, many sonnets to the
Lady Laura: one set was written ~~In Vita di Madonna Laura'1-"In the
life of Lady Laura"-and another set written "In Morte di Madonna
I.aura"-"In the death of Lady Laura:' To those of you who do not know
Italian the reading of the sonnet may be somewhat irksome as it could
only have be a musical experience for you if you can mouth the proper
sounds of the words, and for those who are not acquainted with Italian
they are merely words. If you examine closely the scores you will note that
the separate lines, the measures as it were, all contain eleven syllables, the
famous undecasillabe employed throughout the Commedia by Dante. There is
also a rhyme scheme which is in the octet,
abba abba
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THE ST. JOHN'S REVIEW
and in the sextet,
cdc cdc,
rhyme being a rhythmic device which chimes like sounds at the ends of
measures, underlining the last downbeat. As all Italian words end in vowels it strains less the Italian poet to rhyme than his English brother,
though the rhymes in this particular sonnet are all double: compagne-m'accompagne-lagne, consorte-sorte-Morle. In the sextet: s'assecura-oscura-duraJ chiariimpari. Once we are accustomed to Italian sonnets, whether they be in
English or Italian, our anticipation of what is to come is specific, and
pleasure results as we see the fUture slipping past us with the lengths and
accents we expected, but with the actuality of the sounds-that is the
words-brand new. If we are acquainted with Italian the particular meaning of the rhymed words reaches a climax at both the end of the octet
and at the end of the sextet: sorte, Morte--fate, death-, and at the end of
the sextet oscura, dura--dark, harsh.
Here is a rough but adequate translation:
That nightingale that is weeping so smoothly, perhaps
for his little ones or for his dear consort, with sweetness
fills the night with so many notes both pitiful and
accomplished. It is also my companion all night long,
and reminds me of my own hard fate: I cannot blame
anyone but myself for believing that she was a goddess
and not subject to Death. Oh how easy it is to be secure
in one's self-deceit! Who ever thought to see beneath the
dark earth those two eyes dearer than the sun? But I recognize that my bitter path means living and crying at the
same time, bitter and harsh as anything here below.
�ALLANBROOK
75
The nightingale is famous. Its very name is beautiful in many languages: Nachtingal, Nightingale, Rossignol, Usignuolo, Bulbul. We are told constantly that its chirpings are beautiful and without fUrther thought we
apply our human word song to its nocturnal emissions.
What has the nightingale to do with the life and death of Laura?
Some have gone as far as doubting that the Lady Laura existed. Others,
who enjoy a mixture of philosophy and criticism, would admit that while
Petrarch may have met her during the years he lived in Avignon, he "idealized" her. She is, without a doubt, nearly immortal in the countless
songs and sonnets written to her by Petrarch, just as he himself has gained
immortal fame as the author of her praise. The fourteen-line form,
known forever after as the Petrarchan sonnet, has a most particular sub-
ject matter, a subject matter which is inseparable from its formal structure. In its first eight lines, the octet, the sonnet pays attention to something in nature. In its concluding six lines, the sextet,
it takes a look,_ as in
a mirror, at the author, or at all of us, in contradistinction to nature. This
is the artifice or the nature of a sonnet.
In one important use of the word nature we are all of us as natural as
the nightingale. But the nightingale is not self-conscious, and we are. In
this our natures differ. Is it a fallacy to feel sympathy with nature, and to
feel that it, in its turn, is sympathetic to us? If, as seems to be the case,
modern biological science demonstrates that we share DNA with the
humblest of one-celled creatures and worms, that we are in fact akin to
them, what follows for us? Does the fact that all life is akin induce sympathy or even empathy in us or in them? We can't soar like the gimlet-eyed
eagle, though we are remarkably like the sluggish worm both spatially and
temporally: food in the front end, digest in the middle, and out at the
other end. Beginning, middle, and end. As it is so wittily put by Gilbert
and Sullivan in a song addressed to a grieving tit-willow: '"Is it weakness
of intellect, birdie' I cried, 'or a rather tough worm in your little inside?"'
Nature is a slippery word. It so easily becomes a red herring, a deception designed to lead us on some defiantly theoretical trip. In so many
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THE ST. JOHN'S REVIEW
books and in so many arguments this word is employed as a pawn in some
artful game. We, almost all of us, also say commonly that nature has its
ways of taking time: summer and winter, spring and fall, generation and
corruption. The sun and the moon have their periods as do our physical
bodies. Analogically our very sentences are periodic (as are our melodies)
and the entrancing completions of our rhythmic verses are a musical
device which enhances this "natural" phenomenon.
Does great nature mock our symmetries or are we imitating her tak-
ings of time, her comings to be and her passings away? If she eternally
returns as the seasons roll by and the great sphere rotates, then indeed
Laura's death is not consonant with her, and the nightingale's courtship is
indistinguishable fi:om lament.
Look over the sextet of the Petrarch sonnet again:
Oh how easy it is to be secure in one's self-deceit. Who
ever thought to see beneath the dark earth those two eyes
clearer than the sun? But I recognize that ·my bitter path
means living and crying at the same time, bitter and harsh
as anything here below.
When Augustine at the end of his dissertation on time analyzed for
us Ambrose's verse "Deus creator omnium;' he, as a trained rhetorician, one
might even say as the ultimate rhetorician, was well aware of the full
meaning of the words he was looking at. If God is the creator of every-
thing, he is creator of time. God's time it is and not our time, or nature's
time. The creator's time has a true beginning, middle, and end as do our
days and years, as do our lives. as do our syllables, our phrases, and our
periods. All of these aforementioned things are true images of God's
time, a tracing of his reality, and the ever present now, the ultimate
moment of attention, is indeed the moving finger of eternity.
Let us now take up Augustine's analysis again. This time we will operate upon it; it will suffer a violent sea change in the process. Instead of
�ALLANBROOK
77
11
1
employing his verse Deus creator omnium" ( God the creator of everything")
we will substitute the sonnet of Petrarch we have been examining.
For what is true of the whole sonnet is also true of every
part of the sonnet and of every syllable in it. The same
holds true for any longer action of which the sonnet is only
a part. It is also true of the whole of a man's life, of which
all of his ,actions are only parts. And it is true of the whole
history of humanity, of which the lives of men are only
parts.
Time is now the locus of pathos; it is in truth our time, our brief span,
our transient moments and days which find their image in our syllables and
in our phrases and in our periods. History's great paragraphs pass befOre our
eyes in all their awful sameness. We seek solace in the crystallizing moments
of present attention, moments which seek to memorialize our lives by fixing
rime within our human constructs with the aid of words and with the aid
of music.
A priest wrote the next sonnet and he speaks of a priest's business--the
administration of the sacraments.
It is, nevertheless, a true sonnet both in
form and in content. if indeed it is proper to separate the two.
Felix Randal the furier, 0 he is dead then? my duty all ended,
Who have watched his mould of man, big-boned and hardyhandsome
Pining, pining, rill time when reason rambled in it and some
Fatal four disorders, fleshed there, all contended?
Sickness broke him. Impatient he rursed at first. but mended
Being anointed and all; though a heavenlier heart began some
Months earlier, since I had our sweet reprieve and ransom
Tendered to him. Ah, well, God rest him all road ever he
offendedl
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THE ST. JOHN'S REVIEW
This seeing the sick endears them to us, us too
it endears
My tongue had taught thee comfort, touch had quenched thy
tears,
Thy tears that touched my heart. Child, Felix, poor Felix
Randal
How far from then forethought of. all thy more boisterous
years,
When thou at the random grim forge, powerful amidst peers,
Didst fettle for the great grey drayhorse his bright and
battering sandal!
On reading the score, note the rhyme scheme: in the octet,
abba abba
-all ended, -handsome, --and som~ --all contended; --mended, --began som~ ransom, --offended. In the sextet,
ccd ccd
--endears, -tears, -Randal; --years, -peers, -sandaL There is not a fixed
syllable count but rather an astonishing, fulsome line whose rhythm lopes
along with a prose-like spring.
While the Petrarch sonnet begins with "Q.<el rosignor' ('That nightingale"), this sonnet begins with a proper name, Felix Randal, and then
names his profession. He is a farrier, or blacksmith. The natural event
reported is the reception of the news of his death. "Oh he is dead then?"
It is cast in the vivid present and immediately followed by "My duty all
ended;' a completed perfect tense. The rest of the octet takes past time as
it progresses: "pining, pining, till time when reason rambled in it.'' A single past event-"Sickness broke him"-and what transpired afi:er-"he
�ALLANBROOK
79
cursed at first, but mended I being anointed and all; though a heavenlier
heart began some I months earlier, since I had our sweet reprieve and ransom I tendered to him"-a past perfect moment. The octet ends with a
third person imperative, a prayer for all future time in reference to what
is past: ''Ah, well, God rest him all road ever he offended:' With hope and
prayer the blacksmith's time will be consonant with God's time.
The sextet then proceeds to pack a wallop, but not until its last three
lines. It begins with a present general statement: ''This seeing the sick
endears them to us, us too it endears." Then we are thrust back to past
time as bearing witness to the general statement. "My tongue had taught
thee comfort, touch had quelled thy tears, thy tears that touched my heart,
child, Felix, poor Felix Randal:'
A mere priest might have stopped here, but the time-artist, the poet,
seizes the moment of compassion, his memory and imagination placing
it against the blacksmith as he was in his prime, working at his forge.
How far from then forethought of, all thy more boisterous
years
When thou at the random grim forge, powerful amidst peers,
Didst fetter for the great grey drayhorse his bright and
battering sandal!
The extraordinary phrase "How far from then forethought of" crams
time into a capsule. The regular iambs concentrate our attention; the reit-
erated consonantsf and th give added intensity: "How far from then forethought o£'We could-though we needn't-recite it with long and short
syllables as was done in our Latin verse: uDeus creator omnium,-~~how
far from then forethought o£'The last two verses of the sextet and of the
sonnet stamp an image so vividly upon the mind's eye that the very conceit of the poem loses its feeling of artifice as the poem clangs into its last
rhyme of sandal with Randal and the figure of the man, the blacksmith
Felix Randal, resounds in our ears.
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THE ST. JOHN'S REVIEW
When thou at the random grim forge, powerful amidst peers,
Didst fettle for the great grey drayhorse his bright and batter
ing sandal!
The then in "How far from then forethought of" has become a now,
present to us in all its pathos if we pause to think back at the opening of
the sonnet: "Felix Randal the farrier. Oh, he is dead then?"
The last sonnet, by Robert Frost, begins, not with a nightingale or
with the death of a man, but with an anonymous bird singing in its sleep.
We are not told whether it is a robin or a lark or a whippoorwilL It is a
plain sounding sonnet, its sophistication arising out of its seeming simplicity. It employs, with three notable exceptions, short Anglo-Saxon
words.
A bird half wakened in the lunar noon
Sang halfWay through its little inborn tune.
Partly because it sang but once all night
And that from no especial bush's height,
Partly because it sang ventriloquist
And had the inspiration to desist
Almost before the prick of hostile ears,
It ventured less in peril than appears.
It could not have come down to us so far,
Through the interstices of things ajar
On the long bead chain of repeated birth,
To be a bird while we are men on earth,
If singing out of sleep and dream that way
Had made it much more easily a prey.
The octet reports an event in nature; the sextet-as is traditionalcomments on the natural event, bringing in not so much the poet as all
of us "men on earth" as the focus of attention. The metric structure
�ALLANBROOK
81
adheres strictly to the rules of the game: there is a ten syllable count. It
is written in iambic pentameter, the bread and butter of English
versification.
Unlike Shakespeare's habits with the pentameter, there are no caesuras
after the first two feet, however. The rhyme scheme differs from that of
the other two sonnets and sounds with the close clang of rhyming couplets: noon-tune, night-height, vmtriloquist-desist, ears-appears, Jar-ajar, birth-earth,
way-prry. When a Latinate word crops up in the fifth line it sticks out, the
sound of it and its placement having everything to do with its meaning:
vmtriloquist. The poet himself is a ventriloquist in this sonnet. He's a plain
old bird using plain old words. You can't put your finger on him. Where
is he? The next line delivers over to us the most famous of all Latinate
words having to do with poesy: inspiration. We have one more Latinate
word in the sextet: interstices, a crabbed and fussy word. With these simple
observations in mind, peruse the poem once again:
A bird half wakened in the lunar noon
Sang halfway through its little inborn tune.
Partly because it sang but once all night
And that from no especial bush's height,
Partly because it sang ventriloquist
And had the inspiration to desist
Ahnost before the prick of hostile ears
It ventured less in peril than appears.
It could not have come down to us so far,
Through the interstices of things ajar
On the long bead chain of repeated birth,
To be a bird while we are men on earth,
If singing out of sleep and dream that way
Had made it much more easily a prey.
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THE ST. JOHN'S REVIEW
It's part of the pleasure of the piece that it is not a nightingale singing
for its mate; it's some plain feathered creature. It is not singing in some
imagined garden, some sylvan grove reminiscent of our ancestral Eden, It
is happening in some plain old woods. To be sure, the moon is out as the
bird is "half wakened in the lunar noon:' The singer's Hinspiration" is not
the source of his singing, quite the contrary: his "inspiration, is a cautionary impulse to desist from singing before danger appears. There is no
snake that will imperil him in this non-Eden. He must be alert for a fox
or a marauding owl which could silently swoop from below or above and
consume him utterly. Very much a report on nature and certainly intended as a palliative for the "pathetic fallacy:'
In addition to being most "American;' this sonnet is decidedly a
11
modern" sonnet. It is, as we would expect, this aspect and reflection
which comes to the fore in the sextet, The word nature, if we dare employ
it any longer-and many are the writers and lecturers who brandish it
about with equanimity-is now part of a new bali game, a game in which
time and distance leap far beyond the limits of imagination. We are nowadays beyond even the old "modern" view of Pascal, who was aghast when
faced with the infinity of space: 'The eternal silence of those infinite
spaces terrifies me;' he wrote. We cannot, as he could not, conceive of the
cosmos as a glorious ornament. How consoling it would be to have a
crystalline sphere with a proper, finite diameter! Our mathematical
artifices in this century have plunged us far beyond Pascal into a numbing beginning of an explosion emanating from a near infinitesimal point,
an explosion that coagulates into something that is no longer matter, as
if we had ever known what that was! Black negativity reigns at the center
of our galaxies, and there are simply too many of them either to imagine
or to conceive. Vision ceases. It is almost with a sense of relief that we
turn from such matters and consider our men on the moon and their view
of our home, our blue and cloud-shrouded sphere, enveloped in its
gaseous life preserver. Back down on earth we take time as evolution presents it to us. We have no choice but to accept being's timetable as estab-
�ALLANBROOK
83
lished by Darwin, and our reading of the geological record, rhe long bead
chain of repeated birrh, as Mr. Frost states so succinctly. Benearh our
gaseous envelope, in our little corner of the universe, something remark-
able confronts us, something more wondrous than a miracle. We men on
earth hear a bird singing in its sleep and pay attention to it. Borh man and
bird have emerged from evolution's long and solidified game of chance.
We are both of us, bird and man, the residue of evolution's random but
ordered production of all of our dear and memorable species. What a
coincidence; we are aware of each other. It cannot have been planned! It
did occur, however. Frost's sonnet is full of this wonder;
it calls attention
to a simple event and rhe poem itself becomes a memorial, an artifice that
escapes from time by fixing our attention upon a moment in time.
It is also a cautionary sonnet. God is not looking at rhe bird nor looking afrer him. The bird could well be dead if he were not a ventriloquist,
cunningly throwing his voice, singing from a certain undetectable height,
and having rhe inspiration to stop singing before the onslaught of a
marauding fox or a cruising owl.
All of our songs and sonnets are constructions, cages in which we
place our nightingales. They are made out of our breathing, our walking,
and our heartbeats: the physical lumber of our existence from day to day.
They are all cautionary tales in which we celebrate and lament our timeridden lives, and in which we preserve for future generations our bestcrafted observations, like insects preserved over millennia in Baltic amber.
What we do when we are wide awake is
pay attention to our existence, to
its duration, and to our place: what, where, and when. These celebratory
constructs are our perennial poems;
they fix us with fUll self-conscious-
ness in that moment of observation and parhos. They are rhe nearest we
have to a definition of ourselves as we peer forth from rhis obscure corner of an unimaginable universe, observing, wondering, and preserving.
Some of you may be wondering, remembering rhe opening of this
essay, if St. Augustine has been lefr far behind, if I have not insisted that
all our poems are either pagan or secular. Perhaps so. It is perfectly clear
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THE ST. JOHN'S REVIEW
that there can be no music in Paradise: that ultimate construct is out of
time, eternal. ("Is there no change of death in Paradise;' begins a canto of
Wallace Stevens.) When we recite--or even better, sing-and intend to
ourselves the meaning of "Deus creator omnium;' we assent that God, the
creator of everything, made the world and established its time as having
a beginning, a middle, and an end. We make of the history of the world
a celebratory hymn of praise, a psalm, an ultimate period. We can quote
Augustine backwards and try it on for size:
What is true of the whole history of humaniry, of which
the lives of men are parts is true also of the whole of a
man's life, of which all his actions are parts. The same
also holds good for any action of which the psalm is a
part and what is true of the whole psalm is also true of
every part of the psalm and of every syllable in it.
There is another psalm which sings so eloquently of this same thing:
"Let everything that has breath, Praise the Lord;' a psalm set with per-.
fection by Stravinsky at the end of his "Symphony of Psalms:'
Bear in mind however that when our priest played at poet he took
time as a true time-keeper. The last lines of his incomparable sonnet
speak in never-to-be-forgotten words the pathos of self-conscious human
existence when face to face with death, time's end.
How far from then forethought o£ all thy more boisterous
years.
When thou at the random grim forge, powerful amidst peers
Didst fettle for the great grey drayhorse his bright and
battering sandal.
I. In Latin, meter is quantitative.
�~
fj-
Nature and Creativity in Goethe's
Elective Affinities
Astrida Orle Tantillo
Both in his literary and personal life, Goethe has the reputation of
being a lover. Yet, it is difficult to pin down his views of love from his literary texts. Werther is a great romantic who refuses to give up his love for
Lotte, while Faust is so caught up in his own sphere of enjoyment that he
cruelly forgets about Gretchen. The poet who uses the naked back of his
mistress to tap out hexameters 1 is the same novelist who preaches the
virtues of renunciation in Wilhelm Meister.
In his autobiography, Poetry and Truth (Dichtung und W.hrheit), Goethe
provides us with sketches of his views on love. He describes in great detail
his first and youthful loves-Frederica, Charlotte, and Lili-and how he
literally runs away in order to escape romantic attachments with them. He
then describes how these flights become intimately entwined with his art.
His powers of creativity exist symbiotically with his capacity to love: his
artistty stems from his ability to turn the reality of his romantic experiences into poetty. He tells us, for example, that he himself was Werther,
but instead of actually shooting himself, he does it on paper and thereby
escapes Werther's fate (HA 9:588). Love inspires the young Goethe to
write a novel about suicide, but art makes possible his own escape (HA
9:588).
For Goethe, art becomes a means of overcoming limits in order to
gain new freedoms and insights. This relationship in itself is perhaps not
at all unusual when speaking of writers and their work. Goethe, however,
extends this view of creativity into the natural realm. According to his
natural philosophy, nature is not limited to the procreative in its expressiveness, but finds other creative avenues as well. Both organic and inorAstrida Orlc Tantillo is Assistant Professor in the German Department at University of 1Ilinois at
Chicago.
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THE ST. JOHN'S REVIEW
ganic natural entities are capable of overcoming regular Hlaws" of nature
in order to create new entities and forms.
This essay examines the relationship between love, nature, and creativity in Goethe's most scientific novel, Elective Affinities. During the course
of his novel, Goethe compares natural and human artistry. The characters
in the novel are successful to the extent that they are able to be creative.
Their creativity, however, is not limited to innovative endeavors, but is
closely linked to their ability (and inability) to find creative solutions in
the face of personal obstacles. Similarly, throughout Goethe's scientific
works, plants, animals, and inanimate colors strive to be creative in the
face of struggles or obstacles, And like human artists, plants and animals
are capable of creation beyond and apart from sexual reproduction. Even
colors possess a myriad of creative possibilities in their various interactions with the world around them, Moreover, time and time again,
Goethe draws parallels between nature's works and his own, whether he
likens the process of writing an essay to the growth of a plant' or applies
Aristotle's principle of compensation' to both organic forms and literary
works (HA 1:201-203). Goethe's scientific works therefore provide a
philosophical and non-literary context for the importance and role of
creativity in Elective Affinities.
A generation before Darwin! Goethe hints in some of his scientific
works at how plants and animals may break out of a necessitous gene
pool through eros and create a new species. In other words, Goethe suggests that animals are not limited to procreativity in their creative endeavors, but that they may have the ability to evolve and change their forms as
their environment or other conditions warrant. For example, in a review
essay' on the anatomist d'Alton's works on sloths and pachyderms,
Goethe describes how an animal may, through an exertion of its will,
change its own form and its way of life. In the middle of this scientific
commentary, Goethe asks for our indulgence. He wishes to deviate &om
scientific prose for a moment in order to use more poetic expression. He
then begins a kind of tale or fable about a monstrous spirit, which we
�TANTILLO
87
could well recognize as a whale in the ocean. Goethe's fable, as we shall
see, is an evolutionary one. This monstrous spirit attempts to live on land.
At first this creature feels constrained by its new environment. Soon, however, it sprouts monstrous or enormous limbs to help him carry his mon-
strous body around on land. This whale goes through a period of experimentation as it tries to find the correct balance for its limbs in its new
environment. The first creative attempt of this creature backfires-it
grows disproportionately large gangly limbs out of an "impatience" to
gain freedom on land (GA 17:350). Goethe, however, describes another
attempt of a monstrous spirit which is more successfUl in its endeavors to
produce a new form for itself. He writes of a later cousin of the first creature, an Unau (a type of sloth), which forges a more balanced approach
to the limitations of a new environment. This cousin, which successfully
challenges some limits, while accepting others, creates a new body for
itself which approaches the "mobile ape genus:'
Goethe similarly examines the mobility and the creativity of particular species, in a less fancifUl manner, in several other scientific works. In
his review essay6 on d' Alton's works on rodents, Goethe discusses a vari-
ety of different kinds of rodents and describes how their particular
method of balancing their wills against necessitous limirs leads to deliberate artistry, warfare, and even the creation of new creatures.
In this essay, Goethe describes teeth generally for all animals as a
"shackle of nature;' a shackle which determines their development. He
links the clumsy state of cows to their "incompleteness of chewing" and
explains that their teeth keep their development close to the ground and
occupied with food. His examination of the rodent family, however,
shows how nature's very shackle leads to creativity not only in the animal's
activity, but also in the formation of new animals.
Goethe's description of the main characteristic trait of rodents,
incessant gnawing, illustrates how this activity has far-reaching creative
implications. This gnawing may be regarded as a kind of almost convulsive passion (GA 17:355) or as a Hcontinuous exercise, a restless drive to
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THE ST. JOHN'S REVIEW
be occupied" (GA 17:357) which finally escalates into a "destructive fit"
(GA 17:357). Afi:er satisfying their needs, the rodents still would like to
live in more secure plenty. They exert their passionate energy toward the
gathering or collecting drive as well as toward other activities, which
leads, according to Goethe, to some deeds that at first appear to be very
similar to
II
deliberate artistry". 7 For example, the obsessive gnawing of
beavers enables them to build elaborate dwelling spaces for themselves,
Whereas many of Goethe's contemporaries, such as d'Alton, believed
that animals create their dwellings out of "dumb instinct," Goethe
argues the opposite. In d' Alton's mind, there is no great difference
between a beaver's dwelling and a snail's shell. Both are created out of an
animal's unconscious instinct for shelter. 8 Goethe, in contrast, argues
that a rodent's passionate drive leads to highly creative acts-acts that
appear to be more closely related to human artistic activities than to
determined natural ones.
A rodent's creativity, however, is not limited to its collection of nuts
or to its building of elaborate housing structures, but has far greater possibilities. In discussing the various members of the rodent family, Goethe
further illustrates how limitless the variations of the structure of these
creatures can be. He suggests in this essay that species may evolve and
change over time. While he admits on the one hand that animal forms are
in part determined and static, he also argues on the other hand that the
forms can change and transform themselves into infinite varieties over the
generations (GA I7:354). In other words, an animal is not limited simply to reproduction in its ability to create, but it may change its very form
from one generation to the next, He stresses the versatility of the rodents
and describes how their capricious will (Willkiir) leads to the creation of
so many different forms that a close observation of them may cause us to
fall into a kind of insanity (W..hnsinn). He then points to the variety of
different rodents, including beavers, flying squirrels, and rabbits, and
describes how different environments led to the formation of each rodent
type. He further explains how these rodents are very similar to very dif-
�TANTILLO
89
ferent animal groups. He describes how rhe rodent species "leans as much
toward the carnivores as toward the ruminants, as much toward the apes
as toward the bats, and resembles still orhers which lie between these genera" (my translation). If any doubt is left about the creative heights the
rodents can achieve, Goerhe links upright posture in squirrels and in
human beings, contending rhat borh stem from the same desire (GA
I7:355-56). This tendency, which Cornell calls "Faustian excess;' is a
striving to break free of limits imposed upon rhis creature (485).
Goethe's account of passionate striving extends into the inanimate
world. He demands in his Theory of Colors (a work which he thought
eclipsed all of his poetry") that we analyze colors according to their
actions and passions. He explains that we can only understand colors if
we study them as we would rhe behavior of human beings. Notably,
some colors are more active (e.g. yellow), while others are more passionate (e.g. blue). Their interactions
an4 unions, moreover, are seen as acts
of procreation. Goerhe characterizes the entire Theory of Colors as a kind
of play in which the individual stories of various colors form the plot of
an intricate drama. And like any play, it must be experienced visually if
one is to experience its full effect:
A good play is only half present in the written text. The
greater portion of it draws on rhe glitter of the stage, the
personality of rhe actor, the power of his voice, the distinctiveness of his gestures, even the intelligence and
favorable mood of the audience. This applies all the more
to a work on natural phenomena. If rhe reader is to enjoy
and make use of it, he must actually have nature before
him, either in fact or in the activity of is imagination. 10
This scientific work becomes a drama in every sense of rhe word as
we witness colors that act in various ways. The main plot of this play is
a kind of love story between yellow and blue and rhe dilemma they face.
They can eirher choose an earthly marriage and meld into the color green
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THE ST. JOHN'S REVIEW
or they can aspire towards heavenly heights and meet through
intensification in the ideal color pure red (HA I3:478-79, 52I).
Although both green and pure red are formed by the union of two
opposing colors, red is the more perfect union because it is able to reconcile, without destroying, the characteristics of each opposing color
(HA 13:499-500). [Notably, the drama here echoes that work which
critics tend to think of as Goethe's best-Faust. Faust has a double nature
and laments that the two souls in his breast are not at peace (HA 3:4 I,
lines I I I 0-22). He, too has a choice in the direction he may take. Faust
is successfUl in his gamble, and in the end, we literally see a unified soul
ascending towards heaven.)
Goethe does not, however, speak of love and creativity in nature sim-
ply metaphorically. Like the natural philosopher Lucretius, Goethe
believes that animate and inanimate nature act similarly, 11 and that the
human and the non-human realms are in some way a reflection of each
other. Goethe's world is an active and interactive one, in which colors,
chemicals, plants and people-all have characters and all influence one
another. He therefore believed that human beings stand to learn about
themselves from the inanimate world.
As we now turn to Goethe's novel Elective Affinities, we can begin to
trace the theme of creativity and necessity in the human realm. Having an
overtly natural scientific premise, this novel gives us an opportunity to
witness the successfUl and unsuccessful human attempts to overcome limitations through creativity, especially those limitations presented by love.
Elective Affinities, on many levels mirrors the themes of his scientific works.
However, where nature often seems human in his scientific works, the
characters in the novel see their own actions in light of natural principles,12 Moreover, where Goethe's example of the rodents demonstrates
how one can use desire to strive to reach beyond one's self-whether to
create collections, build intricate structures, or create entirely new physical forms--the characters in the novel illustrate how limiting natural
desire may be when not accompanied by creative striving.
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91
One of the main themes of the novel is marriageY Two of the main
characters, Charlotte and Eduard, have recently wed after the death of
their respective first spouses. Although they were childhood sweethearts,
both initially married for money and position. Their current relationship
to each other drastically changes with the arrival of the Captain, Eduard's
close friend, and Ottilie, Charlotte's young and beautiful niece. The novel
takes its title from an eighteenth-century chemical principle of attraction,
"Wahlverwandtschtiften;' translated as "elective affinities" or telations by
11
choice:' 14 This conveniently ambiguous name, suggesting both marriages
and chemical bonds, asks us to examine not only the actions of human
beings but also the actions of nature in matters of love. Is love at first
sight, in essence, at all different from the reaction between limestone and
sulfuric acid? Conversely, if even the elements are viewed as possessing a
kind of will and choice in their actions and interactions, should not
human beings, too, be able to free themselves from "fatal" attractions? In
the novel, the characters themselves discuss the theory and make analogies
to their own lives. The focal point of the discussion is what happens to a
pair of united elements once a third party is introduced.
As in Goethe's characterization of passionate squirrels and colors, the
chemical formula within the novel is also described in passionate terms:
tender elements unite, flee from one another, search for one another, and
show marked inclinations for particular partners. Where the Theory if
Colors presents a love story between blue and yellow in which we study
their actions and passions, the chemical theory of elective affinities portrays a love-story among the inanimate elements. One of the main characters, the Captain, even echoes Goethe's instructions from the Theory if
Colors. he lectures another character that one can only understand these
natural elements
(with
their various unions or marriages, divorces, and
reunions) if one is an active observer and has these elements before one's
very eyes (HA 6: 275-76).
The basic premise of the principle of "elective affinities" is rather
straightforward: opposites will attract and form a new union. Charlotte and
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THE ST. JOHN'S REVIEW
the Captain, however, see completely different dynamics at work behind the
theory. Charlotte, responding to her husband's fascination with the
udivorces" or the separations of the elements, cannot abide the word
"divorce:' even when merely referring to chemicals. She laments: HDoes this
sad word, which unfortunately we hear so often in society now, also occur
in the natural sciences?" (36; HA 6:273) She then denies the term "elective" or "choice" either to the elements or htunan beings. Instead, she
stresses the power of necessity and opportunity: "I would never see a choice
here, but rather a necessity of nature, and possibly not even this; for after
all it may be perhaps only a matter of opportunity. Opportunity occasions
relationships, just as it makes thieves" (37; HA 6:274). Strikingly, in her
own life, fi:ee will has litrle to do with her choices, Her first marriage was
arranged. Her second, to Eduard, comes about because both of their
spouses die unexpectedly, giving Charlotte and Eduard the opportunity to
marry.
In contrast to Charlotte's rather deterministic interpretation of the
theory, the scientific-minded Captain believes, in a manner reminiscent of
Lucretius, 15 that both human beings and the elements operate under the
rubric of fi:eedom, In observing the interactions between various chemical elements, the Captain believes "that it is justifiable to apply the word
elective affinity, because it really does look as if one kinship was preferred
to the other and chosen before it" (36; HA 6:274). His interpretation
emphasizes that nature's most simple elements do not act in a predetermined or mechanistic way, but are to a certain degree free to choose their
own partners, During the course of the novel, the Captain, like his view
of the elements in the theory, will fi:eely move fi:om place to place (HA
6:258; 479) and be willing to go fi:om partner to partner. 16
Given that each of the characters sees a radically different dynamic at
work within the theory, a question for us becomes whether the events in
the novel validate either of these character's views-Charlotte's deterministic view of nature or the Captain's opposing one of free will--or
whether they point to another possibility.
�TANTILLO
93
Many critics side with Charlotte, claiming that nature represents
necessiry and that Goethe is illustrating our unsuccessful battle against
nature and necessity. 17 Such interpretations revolve around a mistaken
impression of Goethe's natural philosophy and do not take his creative
view of nature into account. Nowhere in his scientific writings does
nature seem simply determined or for that matter simply &ee. Nature, as
the examples of the rodent species and evolving whale demonstrate, may
at times be highly creative. Indeed, that we are to view colors as characters with actions and passions (or elements as passionate beings), further
demonstrates how creative Goethe believes nature may be. Even Charlotte
does not see nature acting differently &om human beings. If she views
nature as determined, it is because she believes human beings to be so.
Similarly, the Captain thinks the elements are free because human beings
are. Strikingly, although these two characters have diametrically opposed
opinions on love and freedom, they agree with Goethe's basic tenet that
human beings and nature are similar.
One of the difficulties in trying to interpret the role of nature is that
the tone of the novel is never consistent. Occasionally it is ominously serious: one child goes insane, another drowns, and both Ottilie and Eduard
die. At other times, however, it is playfully, even maliciously, ironic.
Charlotte, the character who most defends societal norms, also rearranges
tombstones for aesthetic reasons. The institution of marriage is vehemently defended, but its champion is the eccentric bachelor, Mittler. The
greatest critic of marriage, the unhappily married Count, cannot wait to
marry agam.
Nor are Goethe's own comments on the book very elucidating. He
hints to one friend that the novel contains an all-pervasive theme (GA
24:636). He also claims, much as he did about Werther, that the novel is
highly autobiographical-that he experienced every line within it (GA
24:395). When accused of being a heathen, he defends himself by saying
that he killed off Ottilie (presumably for her sins), 18 yet in his autobiography he tells us her character was based upon a Christian saint. At one
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THE ST. JOHN'S REVIEW
time he claims to hate Eduard (GA 24:219), while at another he admits
to admiring his capacity to love.I''
If we return to text and examine the main relationships in the novel,
then Ottilie and Eduard's relationship seems to support Charlotte's deterministic interpretation of the chemical theory. Eduard and Ottilie act
very much as if no freedom of choice exists for their lives. Opportunity
has brought them together and once it has, no force seems strong
enough-whether societal customs, paternal emotions, or duty to one's
guardian or spouse-to pull them apart. At the end of the novel, the narrator even characterizes them as representing not two human beings, but
one (HA 6:478). Ottilie and Eduard, in their love for each other, do not
appear to have any freedom to refuse their affinity. Their passion for each
other appears to be too strong for rational choice to play a role in their
relationship.
Conversely, Charlotte and the Captain's relationship seems to support
the Captain's view of nature. They seem so free from lasting attachments
that they unite and separate at wilL Charlotte marries rwice without love
and therefore cannot understand why Eduard and Ottilie cannot renounce
each other. After she first is widowed, she does not think of Eduard, the
love of her youth, for hersel£ but attempts to unite him with Orrilie. When
her attempts fail, she marries Eduard primarily because he is so persistent
in wooing her (HA 6:246). Although Charlotte eventually falls in love
with the Captain, it does not stop her &om either encouraging him to
accept a promotion that includes an arranged marriage, or when that falls
through, from trying to play match-maker berween Ottilie and the
Captain. Similarly, the Captain spends most of the novel drifting in and
out of romantic alliances, whether to the neighbor girl in the "Novella" or
to Charlotte.
Given that events in the novel support both Charlotte's and the
Captain's opposing natural views, how then are we to interpret the novel?
Perhaps the most important issue within the chemical theory and its rei-
�TANTILLO
95
evance for human beings is not whether nature is free or determined; at
times it may be free while at others determined. Neither extreme view
(that love is a necessitous force or that we may freely choose it) seems an
adequate explanation for the events in the novel. If we return to
Charlotte's and the Captain's discussion of the chemical theory, we discover that an important aspect is missing from both of their interpretations: both fail to address in any detail the creative function of the theory. Neither discusses the consequences of chemical unions, i.e. the creation of new entities. Charlotte appears to be more concerned about
avoiding divorces, while the Captain is fascinated by the elements' ability
to move from one partner to the next. The characters' inability to focus
upon or understand the creative aspects of nature within the chemical
theory becomes reflected within their own creative endeavors throughout
the novel. Their limited and often failed artistic attempts come to reflect
their personal limitations. Unlike the creative beavers, the evolving whale,
or the procreating colors, the characters do not seek creative options.
When we first meet Charlotte, she is putting the finishing touches
on a "moss hut:' The irony of this moss covered hut is heightened by
the way Charlotte treats the windows. To her, the windows are frames,
the view is a painting she has created by landscape gardening (HA
6:243). Charlotte's relationship with nature is analogous to her relationship with human beings. Like her efforts to tame and cultivate nature,
she hopes to restrain and civilize others. She believes that since she can
control her emotions and renounce the Captain, Eduard and Ottilie
should be able to renounce each other. But as her landscaping techniques
are faulty, and only make nature a greater adversary to the inhabitants of
the manor, so too does her plan of control backfire in the human sphere:
had she agreed to a divorce earlier, neither her baby nor Ottilie would
have died (HA 6:460).
Similarly, the Captain believes he has a great deal of control over
nature. His naesthetic" endeavors involve many mathematical calculations.
He believes that by carefully measuring and mapping nature one will have
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THE ST. JOHN'S REVIEW
mastery over it. For example, he calculates the exact number of stones
that need to be taken away from a cliff in order to build a better paththe exact number, moreover, that will then be needed to build a new wall.
So too, he believes he has a solution to get rid of beggars: they are to
receive money, not upon entering the town, but upon leaving it. His
rational calculations, however, fail to take the powers of nature into
account. His newly created shores crumble beneath the spectators' feet,
and beggars are not daunted in trying to receive money both within town
and while leaving it.
Eduard also attempts to practice art on nature. The first time we
encounter him, he is grafting shoots onto fruit trees (HA 6:242).
Eduard's efforts here, as in music and love, are sterile. The trees do not
produce fruit as they did before. This metaphor of grafting is used
throughout the novel. Charlotte hopes that her baby will act as a grafTed
shoot (HA 6:4 19), uniting the family, but Eduard has his eye on another young shoot: Ottilie. The middle-aged Eduard hopes to rejuvenate
himself and produce new fruit through Ottilie, but both nature and society reject such forced and artificial attempts at creativity. In his own
attempts to unite himself with Ottilie, Eduard stubbornly insists on getting his own way, but will not trouble himself with the details (HA
6:447-51). He believes that love itself is his talent and that he is already
a master of it (HA 6:355).
Similarly, the more Ottilie falls in love with Eduard, the more she
abandons her own creativity to become like him. She proves her love to
Eduard by adopting his handwriting to the extent that one can no longer
distinguish his handwriting &om her own. She eventually gives up her
own domestic pursuits and takes up Eduard's of gardening. Ottilie's and
Eduard's artistic attempts mirror their personal failures. Eduard plays the
violin abominably but insists that the others listen to him. Ottilie intentionally learns to play pieces, not as they are composed, but in accordance
with Eduard's mistakes. In consciously mimicking Eduard's unconscious
mistakes, Ottilie rejects art to choose mediocre conformity.
�TANTILLO
97
In this novel, art generally reflects the characters' limitations. Even the
minor characters do not attempt to be creative when they practice art, but
remain largely imitative. For instance, when a large party is bored, they put
on tableaux vivants. They search through copperplates and tty to imitate,
through elaborate stagings, selected pictures (HA 6:392-94). In essence,
they imitate imitations of art. The fact that the characters are trapped in
imitation is closely linked to their failures in love. Indeed, the only dilettante who is praised in the novel is an architect whose love for Ottilie
makes his paintings come to life (HA 6:370).
One of central Cteative" events in the novel is the conception of the
baby, Otto. On the night the child is conceived, the biological parents
engage in spiritual adultery, with very strange consequences. While making love to each other, each spouse thinks of another: Charlotte of the
Captain and Eduard of Ottilie. "And so the absent and the present were
interwoven-miraculously enough--seductively and blissfully each with
the other" (HA 6:32I). The result of this nocturnal indiscretion? A baby
who bears a resemblance to Eduard (HA 6:420), has Ottilie's eyes, and is
otherwise the spitting image of the Captain (HA 6:42I). As the baby
grows older, his resemblance to Eduard drops out of the account, and he
becomes more and more like Ottilie and the Captain (HA 6:455; 459).
The baby's procreation is symbolic of the artistic limitations of the
individual characters. Charlotte and Eduard, on their own, had not yet
been able to conceive a child. Otto is only conceived with the participation of ali four of the main characters. His existence, moreover, further
demonstrates that nature is both necessitous and capricious. Biology plays
a role in that he is born of Charlotte and resembles Eduard. However, his
resemblance to the other characters indicates that nature can break free of
its regular laws to create this being. We witness the triumph of love, not
mind, over matter. Love demands its rights and creates a ttue representational picture of the facts. This triumph of spiritual love, however, comes
at the expense of natural love. The maternal instinct appears to be
destroyed. The baby is largely ignored by its biological mother. Ottilie, the
11
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THE ST. JOHN'S REVIEW
spiritual mother, is a careless guardian, She simultaneously reads, walks
and carries the baby. Due to her carelessness, the baby dies in a boating
accident. Once again Goethe's irony comes into full play as Ottilie loses
her balance in the boat while carrying the baby and the book in the same
hand. Afi:er the baby dies, one would expect someone to mourn his death.
Again, Goethe appears to tease: the mother has no reaction, while the biological father is pleased. Almost everyone is relieved as this little being
dies. His death is not tragic because no one has chosen to love him. Here
the parents are even free to refuse an aflinity.
If the baby demonstrates, albeit in a very bizarre way, the creative
powers of love,20 the relations between the pairs, demonstrate the limitations of love. One might reasonably ask what alternatives these characters
really had. In the novel, two characters, the Count and the Baroness, have
situations similar to Ottilie and Eduard's: their marriage is delayed
because the Count's wife will not grant him a divorce. Unlike Eduard and
Ottilie or Charlotte and the Captain, however, this couple creatively work
around the obstacles, They meet whenever possible, but they also attempt
to keep up some appearances for the sake of society. Although not immediately, they eventually find togetherness afi:er the death of his wife. And
once again, they do not immediately marry, but wait for the time of
mourning to pass (HA 6:390).
Goethe explored even more radical relationships in an earlier play,
Stella. In a scenario similar to Elective Affinities, a man is torn between duty
to his wife and child, and love for a younger woman. Tragedy is averted in
the play because the women agree to a rather unconventional solution.
They agree to share the husband and occupy "one house, one bed, and
one grave"(HA 4:346). Afi:er the play was banned, Goethe rewrote the
ending which parallels that of the novel: the husband and the lover kill
themselves,
In Stella, Goethe openly explores the most radical of solutions
through art, By so doing, he presents both sides of the coin. We see the
mistakes which lead to tragedy, but we also see radical, partly ironic, solu-
�TANTILLO
99
tions. As a novelist, Goethe is able to explore and weigh, and at the same
time ask that we too explore and weigh, intricate moral questions. Certain
situations cannot be understood in terms of a simple opposition between
good and bad. The novel, as the two different endings to StelL., forces us
to consider anew society's standards.
Goethe, however, is not a nihilist or a relativist, even in matters of love.
He acknowledges and respects limits, partly because as an artist and scientist, he realizes that if one is to advance and create new and higher
forms, one requires limits and obstacles if only to overcome them. When
he describes an organism's attempt to flourish and strive towards beauty
and creativity, he stresses that superfluity of resources is just as damaging
to an organism as scarcity. In a conversation with Eckermann, Goethe
turns to the example of an oak tree in order to discuss how beauty arises
in nature. He suggests that an oak tree is beautifUl only if it has struggled
with opposition and competition as it has grown. Harsh conditions may
be "favorable" as long as they are balanced against good ones. If, however,
the oak tree grows in a moist marshy place, and the earth is too nourishing, it will, with proper space, prematurely shoot forth many branches and
twigs on all sides; but it will still want the opposing, retarding influences:
it will not show itself gnarled, stubborn, and indented; and, seen from a
distance, it will appear a weak tree of the lime species; it will not be beautiful-at least, not as an oak. (IS April I827; GA 24:618-19)
Like an indulged or spoiled child, the oak tree that never has to face
adversity will never have a beautiful character. It will not have grown at a
measured pace, but will grow disproportionately. Goethe spoke also of a
plant that is over-watered in his "Metamorphosis of Plants:' Although
such a plant will grow continuously, it will never intensity its form to
reach its greatest articulation of form. Similarly, while the conditions for
the oak tree's growth ensure survival, they do not enable it to reach the
height of its potential.
The most ideal conditions for the oak are mixed ones. The oak must
have enough nourishment to grow, while it must also engage in some
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THE ST. JOHN'S REVIEW
struggles: "a century's struggle with the elements makes it strong and
powerful, so that, at its full· growth, its presence inspires us with astonishment and admiration" (GA 24:6I9). Beauty arises only if the tree has
faced some adversity that acts as a check upon its desire to thrive. And
while numerous different circumstances influence the development of the
tree outside of its control (the conditions of the soil, the climate, the
proximity of its other neighbors, etc.), the individual tree actively participates in the entire process as well. It has a will that expresses a tendency
(Tendenz), drive (Trieb), and striving (Bestreben).
Goethe's natural world is comprised of entities which are always
struggling to achieve new kinds of perfection and new ways of flourishing as they attempt to overcome the limits presented to them either by the
outside environment or by their own forms. And just as nature oversteps
its own boundaries to create a new kind of perfection (GA 17:106), so
too Goethe describes how a master artist intentionally deviates from the
norm in his works to create a masterpiece (HA 12:169).
In the end, the failure of the main characters of Elective Affinities in their
artistic endeavors is a reflection of their failures in their personal lives.
They never attempt to use their love to reach beyond their passions and
attempt innovative solutions to their problems. Charlotte and the
Captain, despite their feelings for each other, remain largely wedded to the
laws of society. Neither initiates creative options until it is too late. Ottilie
and Eduard, the most passionate of the characters, similarly do not try to
use creativity to channel the destructive nature of love. When Charlotte
buries them together as the last act in the novel, they, like the color green,
are finally joined together at the expense of their individual lives;
NOTES
!.Goethe, "Romische Elegien" (Y), vol. I, GJtthts Wtrkt: Hamburger Ausgabe
(Hamburg: Christian Wegner Verlag, I960) I 60. References to this edition will be
hencefOrth cited in text as "HA:'
2. See my article, "Goethe's Botany and His Philosophy of Gender;' Eighterntb~Crntury
Life 22 (!998):128-31.
�TANTILLO
101
3. Aristotle, PariS of Animals 655a I8-34, 657b 5-35, 664a I-I4, 674a 32-6I8;
Cmrmtian of Animals 749b 5-750b5; 750a2I,35.
4. The extent to which Goethe was a precursor to Darwin is a debated point. See
John F. Cornell "Faustian Phenomena: Teleology in Goethe's Interpretation of
Plants and Animals;' Journal cf Medicine and Philosoplry 15:489; George A. Wells, Goethe
and the Development cf the Sciences 17 50-1900 ( Alpen aan den Rijn: Sijthoff and
Noordhoff, 1978) 28; Timothy Lenoir Goethe and the Sciences: A Re-Appraisal, cd. by
Frederick Amrine, J. Zucker and Harvey Wheeler (Boston: D. Reidel Publishing
Co., I986) 27.
5. Goethe, "Die Faulticre und die Dickhautigen," vol. 17, Gedenkausgabe drr Hirke, Briife
und Gespriirhe (Zurich: Artemis-Verlag, 1949) 347-54. This edition will be henceforth cited in text as "GA."
6. "Die Skelette der Nagetiere, abgebildet und verglichen von d'Alton:'
7. For further discussion, see Cornell (286ff).
8. Eduard Joseph d' Alton, Die Skelete der Nagethiere, abgebildet tmd verglichen (Bonn: In
Commission bei Eduard Weber, I 823) I -2.
9. Conversations with Eckermann, February 19, 1829, John Oxenford translation (San
Francisco: North Point Press reprint, I984). [(GA 24:328)]
10. Translated by Douglas Miller, CcetM Scirntifir Studie; (New York: Suhrkamp, I988)
I62. (HA I3:32I).
I I. Goethe was quite familiar with Lucretius' De Rerum Natura. He even planned to
write a poem similar in scope to Lucretius' poem. See Grete Schaeder, Gott und Welt:
Drei Kapitel Goetbescber Wrltanscbauung (Hameln: Fritz Seifert, 1947) 286.
12. Many commentators have noted the importance of The Theory if Colors in interpreting Elective Affinities. See, for example, Loisa Nygaard, "'Bild' and 'Sinnbild' ;•
Crnnanic &virw, 63 (I988):58-76; John Milfull, "The Idea of Goethe's
Wahlverwandtscbajten,"Germanic Review, 47 (1972): 83-84; Alfred G. Steer, Goethe~
'iflective Aifinities:"Tbe Robe o/ Nessus (Heidelberg: Carl Winter, 1990), 4 I; Hans Reiss,
CortbrJ Navrls (Coral Gables: Univ. of Miami Press, I969), 206-7.
13. Walter Benjamin is the most notable critic who takes exception to this statement
in his essay "Goethes Wahlverwandtscbciften," Gesammelte Schrijten, ed. by Rolf
Tiedermann & Hermann Schweppenhauser (Frankfurt Suhrkamp, 1978) I3Iff.
I 4. Goethe takes the terms "Wahlvetwandtschaften" from the translated title of the
chemical treatise "De attractionibus electivas."The treatise was written in 1775 by the
Swedish chemist Torbern Bergman and was translated into German by Heinrich
Tabor in I 782.
I 5. Specifically, the Captain's opinion of elective affinities seems to mirror Lucretius's
claim that since "nothing comes from nothing;' animal and human will must find
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THE ST. JOHN'S REVIEW
its origins in the most basic unit: the atom. See De Rerum Natura, trans. by W.H.D.
Rouse (Cambridge: Harvard University Press, 1975), lines 2.220-23; 253-60.
I 6. He begins the novel as Eduard's second self (HA 6:267). He then joins briefly
with Charlotte, but then leaves the manor when offered a job promotion which
includes an arranged marriage. Moreover, during the story of the neighbor children,
we discover that he was in all likelihood engaged as a young man to another woman.
Towards the end of the novel, he once again hopes to be united with Charlotte.
I 7. Marita Gilli, "Das Verschweigen der Geschichte in Goethes WablvtrWandtschtiften
oder Wie man der Geschichte nicht enftlichen kann;' Sie, und nicbt Wt'r, ed. by Arno
Herzig, lnge Stephan, and Hans G. Winter (Hamburg: Dolling and Ga!itz, !989)
553-65; Milfitll, 94; Albert Biclschowsky, Guth" Srin Leben und srine I#rke (New York:
G.P. Putnam's Sons, !907), 2:383; Emil Staiger, Goethe (Zurich: Artemis Verlag,
!956), 2:495; Reiss, 209; Friedrich Gundolf. Goethe (Berlin: Bondi, 1920) 553.
18. Varnhagen von Ense, Tagebuch vom 28. Juni 1843. Cited in HA 6:623. Thomas
Mann explores the possible Christian implications die to this remark in
Gesamrnelte Werke, Band IX, Rcden und Aufsiitze, "Zu Goethes
Wahlverwandtschaften;' Frankfurt, I 974.
19. Letter to Karl Friedrich von Reinhard. Weimar, Feb. 21, 1810, GA 19:597.
20. Other commentators, such as Steer (54), believe that the baby represents a criticism of loose Romantic practices in love and marriage. Atkins attempts to explain
away the baby's appearance by pointing to possibility of intermarriage among the
families in the past ("Die Wahlverwandtschaften: Novel of German Classicism;'
Gennan Qu'fterly, 53 (!980) n.29, p.35).
�-.:f Three Poems
fj:- Laurie Cooper
Pears
All summer long on a I2.5-horsepower John Deere
I cut grass in 43-inch swaths, each week
holding back the jungle that would otherwise begin,
the wildness that waits just below surfaces for an opening.
I cut grass in 43-inch swaths, each week
vigilant, keeping safe the gardens, the house, our lives
from the wildness that waits just below surftces for an opening.
The days grow shorter. My shadow spreads across the lawn.
Vigilant, I keep safe the gardens, the house, our lives.
Now it is November, the last mowing of the year.
The days are short. My shadow spreads across the lawn.
Soon winter's white palms will try to press the chaos down.
It is November, the very last mowing of the year
and there are fallen pears, at least 200 on the ground
daring winter's white palms to press their chaos down,
unyielding to my tractor's slow, insistent blade.
Fallen pears, at least 200 on the ground. They are
silent, sunned breasts or low, harvest moons
that will not yield to my slow insistent blade.
Or they are a gathering of golden, swollen wombs.
Laurie Cooper lives in Chaplin, Connecticut, and is a 1988 graduate of St. John's College,
Annapolis.
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THE ST. JOHN'S REVIEW
Silent, sunned breasts and low, harvest moons
hold their gaze though I turn quickly away.
Even a golden gathering of lost, swollen wombs
cannot distract me from
my essential task.
They hold their gaze, though I keep turning away.
Time slithers past. The grass has not yet grown to haybecause I will not be distracted from my task.
But when you come outside to kiss me, you've grown old.
Somehow time has passed. The grass is not a tangle of hay
but your hair is gray and your lips purple from the cold
as you come outside to kiss me. I see that you are old.
On your breath is a fuint scent of fermented pears.
Though your hair is gray and your lips purple from the cold,
I must keep cutting the grass in 43-inch swaths.
Your breath's scent of fermented pears is lost to the wind
as I ride past on my I2.5-horsepower John Deere.
�COOPER
Preparation
If sometimes I find myself imagining
the thick unmoving whiteness of your hands
lying properly at your sides or nicely folded
on your chest, the heavy scent of a gardenia
fastened there, an organ softly swirling tones
through a darkened vestibule,
If sometimes I imagine all of this, it is because
I am stunned by the life that moves in every grain
of us, how when we embrace it is only the beginning,
and never enough. It is also the end: there will be
a last time that our skins will touch. One of us
will be cold, the other warm and dying.
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�THE ST. JOHN'S REVIEW
106
While You Are In The Hospital
At home, I think I see small pools of blood
forming in corners of the bathroom ceiling,
but they are clumps of ladybugs, having found
their way in through the old wood of this leaning
house. They are slow and silent as they mount
each other, wrap their spindly legs around, cling.
In the hospital, beneath the syncopation
of intercoms and monitoring machines,
there is a silence: a woman in a room down
the hall contemplating her amputation, snowstooped trees through your window, fear.
Here, mail arrives daily: merchandise
sales, conference announcements, friends
sending cheer. I sort it into piles to keep,
recycle, discard. I think of love I've left,
and lost, and never known.
If I could really love, I would take away
these tubes dripping lipids and glucose
into your blood. I would liquefY the things
you love and Rood them through your veins:
our sleeping dogs' rhythmic breathing, huge
orange trumpets of the amaryllis we thought
would never bloom, the crunch of the gravel
road coming home. If I could really love,
I would climb onto your narrow back
and wrap myself around, guarding like
a ladybug, or Achilles' mighty shield.
�--:£ Mind in the Odyssey
!j- Paul Ludwig
Veteran readers of Homer will find Seth Benardete's book The Bow and
the Lyre to be an exciting and at times disturbing meditation on the Odyssey.
For those wary of the maddening difficulty of Benardete's oracular style
of writing, the present volume is more readable than some of his previous works. Benardete's explications of texts rarely fail to strike a nerve.
Beginning readers of the Odyssey who use The Bow and the Lyre as a companion volume may be so overwhehned by the ingenuity of his interpretations that they lose the inclination to interpret the Odyssey in any other
way. At the same time, many readers with firm prior interpretations of the
Odyssey will be repelled by Benardete's conclusions. Among them:
Odysseus on his return commits gross injustice against the suitors;
Penelope and Odysseus, when finally reunited, fail to achieve love or intimacy.
Before we come to grips with these substantive issues, Benardete's
method of reading Homer merits considerable attention. He tteats poetry as proto-philosophy. The Bow and the Lyre is intended to explore the
extent to which Homer anticipated Plato's thought, hence the subtitle "A
Platonic Reading of the Odyssey:' Those who hold that poetry asserts
nothing will lay aside the bopk as useless to them. When, for example,
Menelaus keeps his grip on Proteus- despite the latter's shape-shifting,
does this story of a god who is one thing despite becoming many things
mean that Homer is wrestling with the philosophical problem of being
vs. becoming? Many readers would be loath to say so. Benardete recognizes that his interpretations may seem "forced and willful" (p. xi) if he
repeatedly discovers Platonic thoughts in earlier Greek poetry. But readers who fear that Benardete is merely digging up what he himself has
Seth Benardete. The Bi.Jw and tbt Lyrt: A Platonic Reading of tbr Odyssey. Lanham, Md: Rowman and
Littlefield, 1997. Paul Ludwig is a tutor at St. John's College.
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THE ST. JOHN'S REVIEW
buried are, he suggests, like people who would question their luck if. wandering in a dark wood, they came across a clearing in which they could
take their bearings.
One problematic method of reading is the principle of logographic
necessity &om the Phaedrus, i.e. the assumption that the placement of
every detail in a piece of writing has a purpose and contributes to the
overall meaning if only the reader can find out how (a principle Benardete
elsewhere admits is mythical). Homer never seems to nod in The Bow and
the Lyre; the slightest commission or omission can be seized upon and have
meaning wrung out of it. An amazing assertion early on highlights the
difficulty inherent in this method: "No one in the Iliad dies in pain;'
meaning that Homer never explicitly says that X died "in pain:' Teeth can
grip the dirt in the paroxysm of death, but if Homer does not say it is
painfUl, it is not painfUl. Reading Benardete can be infuriating because of
such claims, even though they are often adduced in support of a larger
argument
which Benardete can and does sustain on other, more substan-
tial grounds. The principle of logographic necessity implicitly contradicts
longstanding trends in classical philology, in which apparent inconsistencies in Homeric epic are typically explained away as the result of diverse
sources knitted into a motley whole. Benardete, by contrast, is able to
make his principle pay high returns when he provides alternative explanations for such problems as the unsatisfactory ending of the Odyssey, where
the jarring quality of the final scenes--e.g. the dismemberment of
Melanthius, the strangeness of hearing conversations in Hades a second
time, Odysseus's cruel teasing of his father Laertes, and the falseness of
the forced reconciliation between Odysseus and the relatives of the dead
suitors-all scenes which most readers would prefer to ignore, are fUlly
integrated into his troubling interpretation.
The substantive issue of greatest concern is Odysseus's choice
between immortality and mortality. he refUses the immortality offered
him by Calypso, choosing to remain a man. The treatment of this theme
is among the most fruitfUl in The Bow and the Lyre. What good does
�LUDWIG
109
Odysseus see in mortality? On the one hand, the questing of Odysseus's
mind, his desire to see the cities of many men and know their minds,
would not be possible or even necessary if he stayed with Calypso, since
Odysseus presumably would have access to divine knowledge once he
became a god. This implication merely puts a fine point on the problem
since seeking knowledge entails the desire to find it why would Odysseus,
of all people, turn down divine knowledge?
The answer comes at the "peak of the Odyssey;' when Odysseus goes
to rescue his men from Circe,- who has turned them into swine. On the
way, Hermes shows him that things have natures. The nature of the moly,
a plant with black root but white blossom, enables Odysseus to resist the
magic of Circe, who transforms men such that their bodies become pigs
but their minds remain human, Just as nature teaches that, in a plant, blossom goes together with root, no matter whether they are as different as
white from black, so Odysseus learns that, in man, mind goes together
with body. This knowledge is proof against a magic which would claim
to separate body from mind.
For such a reading to work, Circe's magic cannot be taken literally.
Since mind and body always go together, Circe cannot truly have changed
the men's bodies into pigs while leaving their minds human. Later, Circe
admits it was the mind (not body) of Odysseus that was proof against her
enchantment. But her statement is odd because the men's minds were not
supposed to be enchanted any more than Odysseus's: only their bodies
were said to have undergone change. This problem was recognized in
antiquity: the two descriptions of enchantment contradict one another
(I 0.329 with 239-40). If Circe's version is accepted, then the men's
minds were affected: they believed an illusion about their bodies being
changed into pigs. The men were superstitious because they lacked knowledge of nature; hence their "bestiality" was not literal. The
moly/enchantment episode becomes a symbol of the emergence of philosophy. By contrast, a conservative reading might say that the efficacy of
the moly's nature lies in its being (at most) an herbal antidote to Circe's
�110
drugs
THE ST. JOHN'S REVIEW
11
(if not mere medicine" in the sense of a magical talisman). On
the conservative reading, Homer would not have understood the full
implications of his word physis (nature). For Benardete, it is the revelation
of physis which is at stake. Lest we suspect that such an interpretation is
wholly his own invention, Benardete quotes a scholiast to the effect that
taking the moly meant taking the complete logos.
A god (Hermes) thus gives Odysseus access to knowledge which,
apparently, was hitherto a divine preserve. Knowledge of nature allows
Odysseus to share the gods' knowledge without becoming a god himsel£
Calypso's later offer to make Odysseus immortal thus appears ungenuine:
in the light of nature, Odysseus sees that a transformation in which his
body became deathless and ageless would also destroy the unity of body
and mind which makes him Odysseus. Belief in the separation of mind
from body, at least in the case of Circe's enchantment, produces only bestiality. By refusing immortality, Odysseus seems to achieve a humanity
which Benardete regards as the peak of humanity, not open to everyone,
since man's being, the inseparability of mind and body, is not complete
unless he has knowledge of that being, i.e. unless he knows about the
inseparability.
Benardete's chief preoccupation is that Odysseus may achieve this
knowledge only to forget or reject it. Odysseus seems subject to two
temptations, which arise from his given name and his punning nom de
guerre. In the cave of the Cyclops, he puns on the two Greek words of
negation, ou and mf, when he tells the Cyclops his name is Outis, No-one.
This clever idea keeps the other Cyclopes from coming to Polyphemous's
aid when he cries out after his blinding. Odysseus's heart laughs when he
comprehends that his name Outis and his metis (cleverness or mind but
also No-one) fOoled the Cyclops. Mind is no-one. The universal applicability of mind means that mind is the property of no one in particular:
pure mind is sheer anonymity. If Odysseus comes to think of himself as
pure mind, then he believes in his own unconditionality, a type of godhead. But this is a paradox because anonymity means being a nobody, a
�LUDWIG
111
person without fame, the opposite of a god. No sooner does Odysseus
think himself beyond the Cyclops's reach than he vaunts himself and his
victory: he wishes Polyphemous to know his real name, so that
Polyphemous may know whose mind got the better of him. Odysseus's
mind is thus not disembodied but conditioned by the emotions of pride
and anger. Driving Odysseus to assert his triumphant mentality, his
unconditionality, is an emotionalism which belies it, and which arises
from his true name, the origin of which Homer reveals shortly before the
slaughter of the suitors: his grandfather named him Odysseus with a pun
on odyssamenos, angry or hateful. Anger such as he expresses against the
Cyclops who threatened his life, and whom he taunts, is related to pride,
the desire to be somebody, to be famous. Eventually the suitors, whose
consumption of Odysseus's household would reduce him to a nobody,
must bear the brunt of his pride, even though their crimes do not rise to
the level of capital punishment. Benardete regards this pride as an inadequate view of death, an attempt to escape death through glory, as though
in a shade existence one could continue basking in one's fame (contrast
I 1.482-91 with 24.80-94), a belief which entails a forgetfulness of the
humanizing knowledge of the inseparability of body and mind.
Odysseus's quest for justice against the suitors is thus characterized by
the most gross injustice, which in turn implies a lack of self-knowledge.
Readers who always thought that the suitors got what they deserved and
that Odysseus was both wily and good will experience constant annoyance with The Bow and the Lyre as Benardete again and again exculpates enemies and minor characters in the Odyssey solely with a view to inculpating
Odysseus's own behavior. From the Cyclops (who punishes liars and, his
cannibalism notwithstanding, is a vegetarian) to the Lotus-eaters (if
Odysseus had not used force to drag aboard ship the ones who partook,
they would at least have remained alive, unlike the rest of his crew), to the
crewmen who ate the cattle of the Sun (Odysseus's imploring them not
to put in at that shore and then making them swear an oath not to touch
the cattle was insufficient warning), to the suitors themselves (self-defense
�112
THE ~1. JOHN'S REVIEW
forced them to plot Telemachus's murder), Benardete tries radical readings
on for size, None should perhaps be taken as his final word, but the interpretive license can be breathtaking: angry at the crew for opening the bag
of winds, Odysseus puts in at the harbor of the Laestrygonians and loses
his men on purpose.
The issue of Odysseus's injustice is set up as a contrast between justice and necessity: getting rid of Ithaca's disaffected princes is politically
necessary to secure the throne for Telemachus, Odysseus's self-righteous
anger may render him incapable of distinguishing when he is acting out
of Machiavellian expediency and when he is exacting justice, The
Cyclops's cave exemplifies the problem in microcosm. After Polyphemus
has eaten two of his men, Odysseus's first thought is to draw sword and
run him through. Then he realizes that they would all be trapped in the
cave, unable to move the huge stone blocking the entrance, They need
Polyphemus alive to remove it; hence the plan of blinding him. For
Benardete, the heroic but vain act of killing the Cyclops while trapping
oneself in the cave would have been justice. When the practical question
of escape comes to the fore, necessity overwhelms justice, The blinding is
therefore technically non-just or even unjust, since it is administered in a
spirit of selfish expediency. Odysseus's anger then reinterprets expediency as justice,
As with the Cyclops, so with the suitors: the political expediency
which necessitates their removal effectually empties their punishment of
justice. When the suitors see death staring them in the face, they make an
eleventh-hour promise to pay back the property they have used up. Why,
Benardete asks, could not Odysseus have accepted the suitors' promise?
He knows one answer: because there is no means of holding the suitors
to that promise, and they could just as easily return in force after they
have been let off the hook. Practicality necessitates their deaths. For
Benardete, nothing practical is allowed to interfere with justice, which
must be perfect and spotless if it is to be justice at all. It is worth noting
the narrowness of the choice he offers us. The only way Odysseus could
�LUDWIG
113
have fulfilled justice was to act in a naive, hopeful and self-wounding fashion. Similarly in the Cyclops's cave, the only course Benardete considers
just was for Odysseus to cut off his nose to spite his face. These alternatives seem parodies of justice. Would not conventional justice prescribe
that the Cyclops deserved death for his cannibalism but also concede that
necessity allowed only a lesser sentence to be carried out? Benardete offers
no argument other than an implicit one: maiming the Cyclops was too
happily coincident with Odysseus's selfish interest for us to believe that
the maiming in any way was just. That an action was motivated by selfish
interest is a popular criterion for judging actions, but it is also a notori-
ously broad criterion. Conventional justice has seldom proscribed one
person's injuring another who threatens him, in order to defend his own
life. Some stronger critique of Odysseus's violence against the Cyclops is
surely needed before we can accept Benardete's conclusion. Likewise if the
suitors do not deserve death (a big assumption), their own willfulness has
nevertheless put them in a situation in which, for them to receive any punishment at all, the punishment must be death. Their crime has only two
possible rewards: death or ruling Ithaca. Surely the latter is the less just of
the two alternatives.
The Bow and the Lyre at various points suggests the alternative punishments of a beating for the suitors and a "stinging rebuke" for the disloyal slaves. But it is unclear on whar grounds Benardete could ever argue in
favor of inflicting punitive justice on another human being. His Homer,
looking on from a "perspective beyond justice," does not condone the
anger of Odysseus but rather, in the title sentence of the book, distinguishes the bow from the lyre, i.e. the life of action from the life of observation and thought. There is something too easy about making the theoretical life the only just life if said justice is achieved only because the theoretical man does not have to act in the world. To cite a Platonic example: when the Thirty tyrants tried to deputize Socrates to help round up
Leon of Salamis for what was to be an extrajudicial killing, Socrates
"justly" did not obey. Instead, he went home. He did not warn Leon, he
�114
THE ST. JOHN'S REVIEW
did not try to restrain his fellow deputies, he did not raise a rebellion in
the streets. Justice conventionally understood would have required a more
fUll-blooded action, If this is the way in which the Homeric perspective
is beyond justice and injUstice, then no man of action, no Odysseus, can
ever be righteous. Why then does Benardete recur constantly to justice,
particularly justice with an impossibly high standard? What he must mean
is that Homer deprecates punishments such as the slaughter of the suitors, the hanging of the slave girls, and the dismemberment of Melanthius
without reference to their justice. Homer would deprecate the bloodshed
because it is inhumane, and Benardete would have moved to a standard
different from justice, a standard such as "humanity" (the term he used
to describe Odysseus' knowledge of mortality).
Penelope and Odysseus's failure to achieve intimacy is a crucial interpretation which clarifies Benardete's assumptions. Why are husband and
wife so distrustfUl that they must test each another instead of falling into
one another's arms? Benardete signals that he knows but is unimpressed
by Penelope's reason for testing Odysseus, She has long feared that an
impostor might deceive her into giving hersel£ only to find that she has
been hopelessly compromised. As Benardete also points out, Penelope's
erotic longing is so powerful that she mistrusts her own strength to resist
seduction, and she has thrown up high walls to guard against its ever happening, even while she simultaneously uses sexual charm to gain time for
Telemachus, a beautifUl example of love allied to intelligence, For
Benardete, however, caution and prudence imply the absence of love. Just
as practical necessity compromises justice irretrievably, so mind hardens
heart. The same assumption underlies both pairs, justice/necessity and
love/prudence, since Benardete characterizes the expediency which drives
out the blind emotional wish for justice as the insight of cold calculation.
Mind and heart seem simply incompatible. Here again, the strictness of
the dichotomy which Benardete brings to the text makes it unclear how
Penelope and Odysseus could ever have fUlfilled his high standard of
emotional love except by becoming mindless. Readers who had thought
�LUDWIG
115
that the Odyssey taught how to love wisely will find no Jane Austen in this
pantheon. As should be clear, Benardete deprecates choosing a heartless
mind. What prevents Odysseus from being dehumanized by Circe, who
like Calypso wishes to keep him, is his heart or manliness, a strength of
soul "that can be lost or diminished regardless of knowledge" and which
responds to the call of justice when she offers him food and drink before
his comrades have been set free.
The theme most difficult to assess is the withdrawal of the gods &om
contact with man at the close of the age of heroes. Teiresias prophesies
that Odysseus must undertake a second journey to carry Poseidon's fame
so far inland that the people he meets will mistake an oar for a winnowing fan, i.e. he must act as missionary to people who have never heard of
the sea nor of its patron deity. His mission symbolizes a new religious
dispensation which will obtain not only between Poseidon and landsmen
·but between god and man everywhere: the aloofness of the gods will
inevitably give rise to misunderstanding and the need for intermediaries.
Ignorance, superstition and dependence upon priestcraft will characterize
the new age. Benardete compares it variously to quasi-Biblical prophethood, to the pity and fear of Greek tragedy, and to Plato's Cave. The
moral aspect of this religiosity implicates the guest-host relationship:
kindness toward strangers and beggars will no longer arise out of generosity but out of fear that a beggar may prove to be a god in disguise.
Mistaken identity, the mistaking of a somebody for a nobody, is the crime
of the suitors when Odysseus comes disguised as a beggar. Their punishment can only be proportional to their crime if they have, in fact, insulted a god in disguise. For Benardete, this is a morality of "entrapment;'
characteristic of the human type who will flourish in the new regime:
slaves elevated beyond their desert such as the swineherd Eumaeus who
resents Melanthius's insults and the extra labor the suitors imposed upon
him and who takes out his resentment on Melanthius by helping to dismember him Homer's frequent direct address of Eumaeus would otherwise be odd if it did not signifY that he is the addressee of the Odyssey and
�116
THE ST. JOHN'S REVIEW
the low type who will hereafter interpret the poem as the vindication of
justice,
In this reconstruction of Homer's rhetorical project, Benardete is ret-
icent about the intended reception of the poem among other categories
of its audience. Since an age of heroes is always perceived as pre-existing
whatever age one happens to be in, it follows that Homer is not ushering
in a new age but fabricating a mythical transition to explain how his audience arrived in its current, unheroic age. His audience will enter a new age
only to the extent that this new explanation succeeds in bringing about a
revolution in their thought, For Benardete, the majority of us, like the
swineherd, are intended to misconstrue even this new lie about how the
heroic age ended, and to be confirmed in our low morality: one wonders
to what good end. Presumably the grandeur as well as the shortcomings
of Homer's Olympians will give students of nature a hand up toward
appreciating the grandeur of the cosmos and man's place in it Would a
third category of Homer's audience have been intended to ennoble themselves by taking, however ignorantly, Penelope and Odysseus (and
Achilles) as paradigms for their own morality, or is the revolution intended to eradicate the last vestiges of heroism?
The contribution of The Bow and the Lyre is to have opened up a vista
on Homer's story, and the book constantly forces engagement with the
original, The strong reactions it provokes serve to lay bare the assumptions which each of us brings to the text. Though the reader may disagree
with the relative weight assigned to certain premises, the awareness of
alternative possibilities is always present in the book. Readers who strike
-out on their own will tend to meet Benardere coming back from wherever they were headed.-
�LUDWIG
117
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The St. John's Review
Volume XLV, number two
Editor
Pamela Kraus
Editorial Board
Eva T.H. Brann
james Carry
Beale Ruhm von oppen
joe Sachs
john Van Doren
Robert B. Williamson
Elliott Zuckerman
Subscriptions and Editorial Assistant
Anne McShane
Special Advisors for this Issue
Howard Fisher
Curtis Wilson
The St. John's Review is published by the Office of the Dean, St.
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© 1999 St. John's College. All rights reserved; reproduction in whole
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��Contents
Beyond Hypothesis:
Newton's Experimental Philosophy
St. John's College, Annapolis
March 19-21, 1999
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Harvey Flaumenhaft
Newton's Nature:
Does Newton's Science Disclose
Actual Knowledge of Nature? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Franr;:ois De Gandt
Newton's Theory of Light and Colors ......................... 20
William H. Donahue
How Did Newton Discover Universal Gravity? .................. 32
George E. Smith
Redoing Newton's Experiment for Establishing
The Proportionality of Mass and Weight . . . . . . . . . . . . . . . . . . . . . .. 64
Curtis Wilson
The First Six Propositions in Newton's Argument
For Universal Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
William Harper
Cause and Hypothesis:
Newton's Speculation About the Cause of Universal Gravitation ..... 94
Dana Densmore
��I
Foreword
Harvey Flaumenhaft
Newton's work, one of the greatest enterprises of the human spirit, has
shaped our minds and transformed the world we live in, yet only a very
small portion of humanity has ever read what Newton wrote. It seems that a
large part of that very small portion of humanity must consist of people who
have passed through the halls of St. John's College. Every junior at this
college spends a large part of the year pondering long and difficult passages
in Newton's Principia, presenting in class the fruits of that study, and
discussing other great thinkers who were trying to come to terms with
Newton's work. That is not business as usual in American higher education
-nor, for that matter, in higher education anywhere else.
Some years ago, I wrote to a number of historians of science in order
to call attention to a series of guidebooks to the study of great texts in
mathematical and natural science. One of those historians was a worldfamous scholar who at the time was the leading American authority on
Newton; he replied with praise for the enterprise, but with a sad warning:
willingness to read serious books, he said, may be too much to expect of
students; after all, when you can hardly get people to look at authors like
Shakespeare, it would seem hopeless to try to get them to study authors like
Newton. On the occasion of the three-hundredth anniversary of the
Principia, therefore, when I read a newspaper article that mentioned how
many copies of the book were sold each year, the thought that struck me on
examining the numbers was that most of those copies of Newton's Principia
had to have been sold to Johnnies in the St. John's College Bookstore.
So, I'm happy to say that the study of Isaac Newton's work flourishes
uniquely at St. John's College. Our nondepartmentalized faculty regards it as
among their most important tasks to equip themselves to study Newton and
to help our students to do so. To help us in that endeavor, the College held
a conference on the work of Isaac Newton the weekend of March 19-21,
1999. The conference provided an opportunity to share with guests the
delight and the instruction to be gained from the distinguished scholars
Harvey Flaumenhaft is Dean at the Annapolis Campus of St. Jolm's College.
�6
TilE ST. JOHN'S REVIEW
whom we invited to speak on the subject; and collecting the papers in this
issue of the St. John's Review provides us with the opportunity to share what
we gained with even more people.
It is a pleasure to acknowledge with gratitude the support of the
Dibner Fund, whose generosity made the conference possible. It's also a
pleasure to acknowledge the gracious loan of various sorts of Newtoniana books and equipment that were on exhibit during the conference in our
Greenfield Library-from the Burndy Library of the Dibner Institute for the
History of Science and Technology at MIT, and from the Smithsonian
Institution's National Museum of American History. A great deal of work in
setting it all up was done by several tutors: Howard Fisher, chairman of the
planning committee, and its other members, Adam Schulman and Curtis
Wilson. The person who set it all in motion was the alumnus for whom our
new Library is named, Stuart Greenfield, a member of our Board of Visitors
and Governors who is also a member of the board of the Dibner Fund.
�~
Newton's Nature:
) Does Newton's Science Disclose
~ Actual Knowledge of Nature?
~
Fran\=ois de Gandt
The question posed to me was: Does Newton's science disclose actual
knowledge of Nature? The question was not mine; it was posed to me, but I
accepted it. I found it interesting and challenging and rich. And also, in this
question I feel several smells or moods. For instance, I feel some postmodern suspicion about the value of science. Does it disclose actual
knowledge of nature? I feel also some nostalgic mood: maybe we have lost
contact with nature through our modern science. Such a question for me was
an occasion to sum up, to tighten various things, to envisage things in a
unified view, and to tighten some knots that were loose in my own mind. So
my lecture will not be a part of the book that Mr. Wilson has so well
translated into English;' (or, if you consider it, it could be a development of
the last page of the book). But the book mostly deals with the mathematics
of Book I of the Principia/ and some aspects around that, I mean
mathematics at the time of Newton or before Newton. And here I shall deal
more with the presence or absence of Nature, and that means especially
Book III of the Principia, Tbe System of the World.
I shall put this in the context of 18th-century science, because this is a
domain in which I am at work now. I work particularly in a group, a large
group of people who are preparing the complete critical edition of the works
of Jean le Rand d'Alembert-d'Alembert the friend of Diderot. There are
many manuscripts left in Paris, Berlin, and elsewhere, manuscripts which
have never been edited, and we want to give a complete, critical edition of
the works of d'Alembert. It is a huge task, and we are just in the beginning
of that enterprise. Probably I shall not see the end of it myself, but, well,
that's the intellectual life.
This has also been the occasion for me to pose certain philosophical
questions, and as I grow older I think the time has come to philosophize,
especially concerning the place of science in culture, the place of science in
Franr;;:ois de Gandt is Professor of Philosophy at Universite de IJlle. This keynote address, given
to students and tutors at St. Jolm's College, Annapolis, on 19 March 1999, was transcribed and
polished by Adam Schulman and Curtis Wilson.
�8
THE ST. JOHN'S REVIEW
life, and something about certainty and belief. I am interested in all that. So I
shall give only a general landscape, a sort of orientation on that question, and
we can develop particular aspects during the discussion, I hope.
I give you my plan. First, Newton in the 18th century: triumph and
critique. Then I come to what I call the other Newton and the life of Nature.
Then, the mathematical, deductive frame. Then a sort of conclusion about
Nature and mechane-the Greek word. All of you know Greek-you are
supposed to.
The pivotal place, the most important place in the Principia where we
speak of the science of real nature is Prop. 7 of Book Ill. In Latin,
Gravitatem in corpora universa fieri, etc. Here everything is suspended; it is
the critical place, the most important place. That Prop. 7 is a sort of summit
in a certain path, in a certain road you follow. We go up to Prop. 7, and then
there is a sort of a descent. You can think of the ascendant and the
descendant paths in Plato's Republic. The highest point is reached with Prop.
7, which asserts that there is universal gravitation; there is some sort of
weight of gravity toward all the bodies. In Latin, it is in the accusative. The
previous propositions have as their purpose to reach that summit, passing
from motions to forces, and then unifying forces. So you have motions in
front of you-in the heavens, somewhere-and you study those motions,
and you draw the notion of force from those motions, and then progressively
you unify those forces. This force is the same as the second one, the second
one is the same as the third one, etc., and then at the end, you end up with
just one force. And you are allowed to call it weight. It is just weight, just
gravity, pesanteur, le poids. Things have a weight toward each other. In fact,
here in Prop. 7, things have weight toward each particle of matter. Each
particle of matter is a center of weight around itself. This is the crowning
point of Book III, Tbe System of the World. For that purpose you use the
previous theorems of Books I and II, but not much from Book II, which is
about fluids.
Now after Prop. 7 you have a descent, which is an a priori
argumentation. You know that there is universal gravitation, and from that
you draw consequences, and the consequences are placed in our world; they
are terrestrial and celestial consequences of universal gravitation. And then
Newton has a sort of program of deduction and research. It is not completely
done. In many cases he says: "We would like the observers to see if... ,"
''We would like the astronomers to decide whether... ," etc. So, once you
have accepted the idea of universal gravitation, you reorganize the world,
and you are able to pose interesting questions to the world. Do tides behave
this way or that way? Do the satellites of this planet behave in this way or
�DEGANDT
9
another way? Universal gravitation is a sort of guiding light to pose questions
to nature in an a priori mode. And then you have various aspects: orbits of
planets, shape of the Earth (called Ia figure de Ia terre in the 18th century),
then the tides with their ebb and flow, the Moon, the precession of the
equinoxes, the comets; and with the comets comes the end of Book III. This
is the program which is set in Book III. But this is also the list of themes that
were addressed by scientists in the 18th century. This is the agenda of
physics in the 18th century, almost in that order. It is strange.
The orbits of planets: the greatest scientist of that time was Christiaan
Huygens, and Christiaan Huygens admitted that for the orbits of planets the
system of Newton is marvelous. It gives extraordinary consequences, which
are exactly adapted to what we can see in the orbits of planets-much more
than in Descartes's system. The Cartesian system had no answer, even no
question concerning the geometrical aspects of the orbits. And here Huygens
said, it's a marvel: we can now say why the eccentricities of the orbits are
constant, we know why the planes of the orbits pass through the Sun, which
is so important dynamically speaking, but in Cartesian terms it has no
importance. There's no reason why the center of the vortex should be always
on the plane of the orbit. And the inclinations of the orbits always remain the
same; it's important in Newtonian terms, in Cartesian terms it has no
particular sense. Many details of the orbits of planets can be explained. You
can give an account of them through universal gravitation. So Huygens was
satisfied, except that he found the theory absurd. Well, of course. I insist
upon Huygens, because very often people say that Newton was not accepted
on the Continent before a late date. It's not true. A man called Huygens
wrote and published in 1690 vigorous praise of the system of Newton.
Next, let's come to the shape of the Earth. This gave rise to a quarrel
between some quasi-Cartesians and the Newtonians in the years 1735-36,
especially amongst Frenchmen, in particular the Cassinis, Clairaut, Bouguer,
Maupertuis, la Condamine. And the French decided to send two expeditions,
one to Lapland, toward the North Pole, and the other to Peru and to the
Equator, to determine the length of the meridian, and then to see whether
the Earth is flattened at the poles. I could tell you much more about that, it's
a really funny story, an extraordinary story, especially the story of the
expedition to the Equator: extreme problems of health, difficulty with the
Indians, with the Viceroys. One member of the expedition came back only
36 years later. That expedition was not lucky. The expedition to Lapland was
much more lucky and successful, and they proved that the Earth is really
flattened. But it was not a proof of Newton's system, because many
Cartesians admitted also that the Earth was flattened. Voltaire said: Now
�10
TilE ST. JOHN'S REVIEW
Newton has triumphed, etc. Here I should mention the mundane belleslettres, etc., the people who wrote about Newton without understanding.
That is the usual fate of science.
The tides: the tides provided the occasion of an important discussion in
1739-40. The question was posed by the Academie des Sciences de Paris: can
we explain the tides by universal gravitation? The answer of the Principia
was yes; but in how much detail? And so several people tried to develop the
details of the explanation of the tides via universal gravitation. But this was a
big task. Sometimes it is said that the success in carrying it out was complete;
that is not true. The subject is very complex, and it is especially complex
because you have a simple cause, but many, many intermediate phenomena:
resonance in basins, inertia of the water, etc., and it is very hard to see
whether the theory was really corroborated by those studies. The studies
were written by Euler, Maclaurin, and Daniel Bernoulli.
Concerning the Moon, there was a very interesting discussion and crisis
in 1747-48, because Euler, d'Alembert, and Clairaut became aware--or more
clearly aware-that a certain motion of the Moon, the motion of the Moon's
apse, cannot be explained by universal gravitation, for you derive only half
the observed motion of the apse. They had to redo the derivation. Euler
thought there could be some fluid complicating the process. D'Alembert was
skeptical, as usual; he said, probably there must be some magnetic influence,
or the Moon is hollow, with an irregular shape inside. And Clairaut said,
well, let's try to compute. He made calculations, and he showed in 1749 that
there is no need to change the law of gravitation, no need to introduce a
further mechanism; the calculation works perfectly well, once you have
admitted a certain way of doing the approximation. So the result was a
success, after a crisis for universal gravitation.
The precession: well, let's skip that and turn to comets. Halley's Comet
returned in early 1759. On the basis of Newton's theory, Clairaut predicted
the return of the comet to within approximately one month. This was a
popular success, a popular triumph for Newton's theory. Some people said,
"One month is marvelous." Others said, "Well, one month, that's much!" And
Clairaut had to compute the influence of the big planets in perturbing the
path of the comet.
So these are the triumphs of the Newtonian theory in the 18th century
which were synthesized, summarized in Laplace's M§canique celeste, which
was published around the tum of the century (around 1800). For instance,
Laplace wrote "La tbeorie de Ia pesanteur a devance les observations": the
theory of gravity has preceded observations. It was in advance.
�DEGANDT
11
This could be misleading. There were other questions that were not so
easily solved; in some cases the theory did not work. For instance, the
attempt to calculate the trade winds via gravitation didn't work; the study of
the resistance of fluids-it is a very, very difficult, complicated problem that
was not successfully solved in Book II of Newton's Principia. But, on the
whole, one can say that this [Laplace's Mecanique celeste] marks the triumph
of the system of Mr. Newton, especially in the French-speaking part of
Europe. In that day the English-speaking part was not as active as the Swiss,
the French, the people in Berlin (but in Berlin there were Swiss and French).
So I come to the limits and the critique of Newton's system. First, the
theory of Newton is absurd. It starts from a stupid assumption: that two
particles of matter can do something to each other at a distance, without
touching each other-a sort of magic or sympathy. "Attraction" was a wellknown word for things that were crazy. Daniel Bernoulli in his book about
tides starts by writing, "Get incomprehensible et incontestable principe queM.
Newton a si bien etabli . .." The phrase is marvelous: This incomprehensible
and indisputable principle that Mr. Newton has so well established. How can
you establish something incomprehensible?
And all the discussion should be placed inside a larger context, a
philosophical context and also a theological context, the context of a crisis of
causality. People at that time, the beginning of the 18th century, became ill at
ease with the notion of cause: what is a cause? And philosophers like
Malebranche or Berkeley, or even Maupertuis and d'Alembert, tried to
dismiss the traditional notion of cause. And the Newtonian system was a part
of the discussion. In the Newtonian system you cannot say you have reached
a cause, but nevertheless you go on, doing useful computations and
predictions, etc. For instance, Berkeley has a beautiful sentence in his
Treatise Concerning the Principles of Human Knowledge: "Those men who
frame general rules from the phenomena, and afterwards derive the
phenomena from those rules, seem to consider signs rather than causes." Not
causes but signs. Physics has to do with signs only. This is Berkeley.
Then around 1750, there was a sort of turn, a sort of new fashion.
People were expecting, awaiting a new science, for instance the new science
advocated by Diderot, the friend of my d'Alembert. And Diderot's idea, for
instance especially in his Pensees sur !'interpretation de Ia nature, in 1754, is
that "le temps des geometres est passe." Mathematics are void. Nothing
happens in mathematics; you only translate the first statement in various
ways, in mathematical discourse. Diderot knew that from his friend
d'Alembert, who said so: mathematics is just translation. It is time to go to
new objects, a new style of science, especially concerned with living beings,
�12
TIIE ST. JOHN'S REVIEW
because Nature is living and productive. This had to do with the secret,
subterranean influence of Leibniz-Leibniz who spoke very often of ipsa
natura, in a sort of pre-Romantic thought. And Nature is made of a chain of
beings. And people like Diderot were very interested and enthusiastic about
that chain of various beings from the stone to the man, even further-we
don't know. With the polyp, for instance, between two domains of nature:
the polyp is at the same time an animal and not an animal, we don't know
exactly. And all those new objects cannot be studied by the methods of
mathematical physics. So Newton for these people was an old-fashioned
scientist.
And the most systematic criticism came from the German Romantic
movement. There were also English Romantics concerned with this criticism,
for instance, if you read William Blake or Coleridge, they discussed Newton;
for them Newton is a representative of a particular sort of science. In Blake's
extraordinary world, Newton represents a certain figure. But I am more
interested by German Romantics, people like Goethe, Schelling, Hegel. For
them Newton was the symbol of dry, mathematical abstraction, of the
scientific understanding that desiccates Nature. Thus in Hegel or in Schelling,
in texts dating from around 1801 and 1802, for instance Hegel's De orbitis
planetarum, and the beautiful dialogue written by Schelling called Bruno:
there you swim in the ocean of infinite beauty, etc., you see everything from
a high vantage point. It's philosophy at its smoothest and its most dangerous,
perhaps. But it's fun; you should read Schelling's Bruno. And for these
authors, the composition and decomposition of force is a violence done to
Nature, because force is something unitary, autonomous, and active, and
force cannot be decomposed. There's no sense in trying to decompose a
force. In Nature there are degrees of freedom, in accordance with the Great
Chain of Being, and those degrees of freedom statt from the stone, which is
a complete prisoner of gravity, and then you go to the solar system; and
Hegel and Schelling say that the solar system has a certain higher level, and
has its own freedom. The planets are in a certain sense free, and more free
than a pure stone, which is the slave of gravity. And then, of course, a still
higher level is that of the animal. And then you come to the Spirit. And
finally, consciousness and knowledge are the highest points of Nature and
must be included in that large science of Nature.
That is, Newtonian science is abstract, it is partial, it explains only one
level of Nature, and it is non-reflexive: it does not explain itself, whereas
Romantic Naturpbilosophie explains itself. Genius is a part of Nature. My
imagination is a part of Nature. In a text of Navalis or Schelling, you explain
how the knowledge of man is a part of the operations of Nature.
�DE GANDT
13
The strange thing is that there is a big misunderstanding in all that,
because Newton would have agreed. Newton was on their side, in fact. But
we have discovered it only recently, in the last 40 years or so, I would say. I
will try briefly to show how Newton would have agreed with the Romantic
view of Nature. First, is Newtonian science abstract? Is mathematics abstract?
No. Newton maintains that his fluxions are in Nature; they do exist in Nature.
There are fluxions; you can see them. They are the real operation of Nature.
For instance, I remember a passage in Colin Maclaurin, who is sometimes a
faithful Newtonian. He says: the French Cartesians have invented fictions:
they have invented infinitesimals and vortices. But our Newtonian concepts
are rooted in Nature, very deeply; they are faithful to Nature. And Newtonian
science tried not to be partial, not to explain just one domain of facts. The
concept of centripetal force should be useful in other domains, should be
extended to, for instance, the cohesion of bodies, to electricity, to chemical
properties, even to nervous transmission in the brain. That is, Newtonian
science tends to be also reflexive, to explain how knowledge is possible-it's
the limit of that program. Even sensibility, immediate knowledge, would be
explained in Newtonian terms if the program of Newton had been
completely achieved.
We have the traces of that immense program in various manuscripts,
but also in some published texts, where Newton says we should go from
phenomena to forces, and then classify forces into certain large classes of
forces, and then we come to the causes of those forces, which are different:
forces are not causes. Thus we proceed from the motions to the forces, from
the forces to the classes of force, from the classes of force to the causes, and
ultimately to God Himself, who is the highest cause. And philosophy, natural
philosophy, should go up to God, should attain God. And then, in that vast
program, the Principia is just a small part of the statue, just the torso or the
leg, I don't know; but it's only the beginning of a part of a vast program.
And then, in the second edition of 1713, Newton added a strange text
to the Principia, a text called "Scholium Generale," which I think you read in
your classes. It contains an extraordinary avowal of the shipwreck, of the
failure: "Causam gravitatis nondum assignavi." I have written 500 pages of
difficult physics, and I end the book by saying: "I don't know the causes."
But physics is about the causes. In Descartes, in Aristotle, all physics is
always about causes. So you end your book of physics by saying: I have not
found the causes; then it's useless!
Here is a little comparison that is not, I think, completely false. When
Daladier came back from Munich in the autumn of 193&-Chamberlain went
to London, Daladier came to Paris, after the discussion with Hitler, and they
�14
THE ST. JOHN'S REVlEW
said, "We have peace for the world," etc. in 193&--and Daladier in the plane
saw how crowded the airport was, there were thousands, tens of thousands
of people waiting for him at the airport, and he said to his counselor, "I shall
be lynched." And the counselor: "No, no, no, they are just here to cheer
you." And then Daladier said "Ah, /es cons." It's untranslatable, it's not very
good French. It means something like, "How can they be so stupid? How can
they be so stupid to applaud when I bring back such a failure?" He knew
that Munich was really a failure. But apparently the other people did not
know it. I think that Newton must have at some time had that sort of feeling
in his mind: they cheer me, they applaud the Principia, but they don't know
how enormous the task was, and this was not what I wanted. I gave that, but
I wanted much more . ... "Ah, les cons."
In the Scholium Generate Newton added a small addition, very strange,
which gives you a hint, a trace, of that vast program which extends to the
whole domain of Nature, about a certain spirit. The last paragraph of the
Principia begins: Adjicere jam liceret nonnul/a de spiritu quodam
suhtilissimo. You are good in Greek but not in Latin, I've heard. "Let it be
allowed to add something [that hypocritical manner of Newton's]-about a
certain spirit, vety subtle . .. , etc." And that spirit has many active operations,
as you know. And that spirit could be, in some. sense, the most overt way in
which Newton gave an indication of his larger philosophy of nature.
Probably he had the hope of proving mathematically that nature is active,
living, operative. But the road was too long, and he covered only a very
small part.
So Newton was called by John Maynard Keynes "the last magician." Is
that program about the life of nature a sort of dead end? Because the
Principia was taken as a complete system; and in the 18th century there
were few people who cared about the spiritus quidam, etc., and all that
hidden part of the program of Newton. And all those vague statements about
God and spirit were almost without influence. Actually, it's not so simple;
you should look more closely at the definition of "natural philosophy" in
English authors. For instance, on the last page of Locke's Essay Concerning
Human Understanding, you have a definition of "physics," which includes
angels, spirits, and God. So physis for Locke includes spirits, even up to God.
And I have found authors that were influenced by Newton and were
influential in their turn, who should be studied more. I am thinking for
instance of a certain David Hartley. In his book, Observations on Man, his
Frame, his Duty, and his Expectations (1749), Hartley has a complete theory
about vibrations and that notion of spirit, pervading a sort of aether,
pervading all nature. It even penetrates our nerves and brain and explains
�DEGANDT
15
the functioning of our brain. He speaks of a sort of harmony that can
establish itself between things that are at a distance from one another. His
theory includes even psychology, morality, and theology. So Hartley has a
complete Newtonian philosophy of nature and spirit and God, based on that
Newtonian notion of spirit. And strangely enough, that man Hartley
influenced Jeremy Bentham as well as Joseph Priestley. And he is sometimes
associated with the birth of utilitarianism and the theory of the association of
ideas. But there is almost no study on Hartley except a French one, Elie
Halevy, La naissance du radicalisme philosopbique, Vol. 2. And I have found
a sort of Hartleyan or Newtonian quotation in an unexpected place: Laurence
Sterne, A Sentimental journey. In the chapter, "The Bourbonnais," we read:
Dear sensibility! source inexhausted of all that's precious in our
joys, or costly in our sorrows! ... 'thy divinity which stirs within me'not that in some sad and sickening moments, 'my soul shrinks back upon
herself' . .. but that I feel some generous joys and generous cares beyond
myself-all comes from thee, great SENSORIUM of the world! ["sensorium"
is the Newtonian word for the presence or place of God] which vibrates
[I'm not sure he isn't confusing "spirit" and "sensorium," but those
notions are so strange] if a hair of our heads but falls upon the ground, in
the remotest desert of thy creation . ...
That is action at a distance. If a hair of a creature falls in a desert, you
feel it, because there is that universal vibration of the aether. And that
explains sensibility. That explains also why we are sometimes pushed
outwards, and we can perceive what happens elsewhere-not in our body
only. And sensibility was an important slogan in the 18th century. It has
something to do with the Newtonian program.
I had here a digression about the logic of that Newtonian program, and
what could be called the Paracelsian mode of science. At that time there was
not only the mechanical picture, but also something else, another way of
doing philosophy, another way of looking at nature, at life, at knowledge,
which was influenced by Neoplatonism and by Hermetism and well
represented by the alchemists and the Paracelsians. But that can be a theme
for later discussion.
Maybe we could be cynical and say that all that hidden program of
Newton, all those speculations about spirits and sensorium, have not much
to do with real science, that they remain marginal. Hartley is mostly
forgotten. Maybe that's just right, and the fame of Newton rests not on
alchemy and theology, but on the mathematical theory of gravitation.
Our usual reading of the Principia is far removed from the unified and
vital conception of nature. Is it totally unfaithful to Newton to read the
�16
THE ST. JOHN'S REVIEW
Principia just as a piece of mathematical physics? I think Newton is also
responsible for that.
Newton accepted another tradition just by writing physics
mathematically. Newton accepted the tradition of mathematical physics,
which is an old thing. This is what I could call the Archimedean tradition.
You have read Archimedes' treatises on the equilibrium of planes and on
floating bodies. The natural charge is at the beginning, or maybe at the end.
That is, you put the real thing in the principles, and then you draw the chain,
you tum the crank. It's not so easy to tum the crank, but the real physical
charge is at the beginning. You pose a certain assumption, you postulate
lambanomena or aitemata at the beginning of the theory. So it's not a study
of the causes, but it's building a deductive apparatus.
And this is exactly what Galileo does. The name of Galileo appears
here in a very essential way, because Galilee is in some sense the father of
Newton, or Newton is the son of Galileo. They do the same job. And Galilee
accepts the restriction of not dealing with causes, whereas Newton is more
embarrassed ("I have not found causes"). Galileo says: We shall not study
causes; we shall just assume a certain definition of accelerated motion, and
then we turn the mathematical crank, we arrive at a certain consequence,
and we try to see if the consequence works in the real world. That's the way
we have to deal with Nature in our science. Of course, it is a deceiving
science, because we don't deal with causes. But that is not the job of this
sort of science.
I'm just paraphrasing an important passage from the Third Day of
Galilee's Discourses on Two New Sciences; I believe it is part of your
curriculum. So, Newton does the same. He has the physical charge in the
principles, and then comes the mathematical deduction. And at the end, you
can see whether it works, whether it is adjusted to the physical facts. And the
Galilean influence is much deeper also. I mean that the very notion of
gravitation is Galilean gravitation. What is gravity? We don't know the cause
of it, we don't know whether it is impulsive or attractive, whether it is a
question of pushing something, or being drawn, being pulled, being
attracted. We don't know that, we don't have to decide that. The only thing
that we know and that is important for the rest is that gravity implies a
certain law of acceleration around the particle having mass. Every particle
creates around itself a field of acceleration. This is the only thing we need to
know. And it's the basic thing at the beginning of the Principia. That is,
universal gravity is generalized Galilean weight, nothing more, nothing less.
Everywhere in the world, at each instant, there is action of Galilean weight.
�DEGANDT
17
And we just observe it by observing accelerated motion. We know nothing
more and we don't need to know anything more.
That deductive frame-you put the physical charge at the beginning,
and then you draw mathematically, deductively the consequences-that
frame is not so new. It is a Greek frame, it is a Greek_ pattern, a Greek
invention: deductive science. Deductive science applied to physical reality.
And I think many commentators on modern science have not been
sufficiently aware-myself, I have discovered it progressively-of the
immense importance of the four mixed sciences. What are the four mixed
sciences? Music, astronomy, optics, mechanics. This is the list you have in
Aristotle's Metaphysics 13.3 or Physics 2.2. And you have the same list in
Galileo's Discorsi. You know that place [Third Day, following Cor. I of Prop.
II of On Naturally Accelerated Motion] where Salviati has unrolled his text in
Latin, and then Simplicio says, Well, all this is very good, but I would like to
see the experiments. And Salviati doesn't say, Oh, Simplicia, you are a
university scholar, always fond of Aristotle. No! He says: you are perfectly
right! He says: Voi, da vera scienziato, which is slightly ironicaL You are a
real scientist, Simplicia. And why are you a real scientist, Simplicia? Because
you ask what is usually asked in those sciences which apply mathematical
demonstration to natural conclusions, as is the case [and here come the four
sciences] ne i perspettivi, negli astronomi, ne i mecanici, ne i musici [in the
writers on optics, astronomy, mechanics, and music].
So Galileo accepts the traditional frame of those mixed sciences. What
he does is nothing else than renewing and extending those ancient sciences.
For instance, when he wanted to demonstrate the isochronism of the
pendulum, in the letter to Guido Ubaldo of 16o2, he says: I want to prove it
senza trasgradire i termini meccanici-without trespassing beyond the
boundaries of mechanics. For him the isochronism of the pendulum should
be proved inside traditional mechanics.
So I have much to say about those four mixed sciences. And I think if
we really want to discuss the question, Do we have real knowledge of nature
in Newton's science? we should first deal with the question of the relation of
those four disciplines to nature. For instance, there is a very important fact,
which I discovered recently, one month ago, in the last issue of Early Science
and Medicine (February 1999). Ulrich Taschow from Halle discusses music in
Nicole Oresme. Maybe Oresme is a well~known name for you-a figure at
the end of the medieval period. And Oresme uses music as a very important
example for his latitudines formarum. And Tasch ow discusses the
importance of music, and he remarks (p. 44) that it is strange that all the
sciences apply to nature but only in a certain, special sense. Astronomy has
�18
THE ST. JOHN'S REVIEW
to do with the celestial spheres, which are not ordinary matter; they are
made of quintessentia, the fifth substance, which is not ordinary matter.
Optics has to do with species, which is not material. And music, which was
the theme of the article in Early Science and Medicine, has to do with ratios
between sounds, and these, too, are nothing material. Thus the three upper
sciences have to do with things which are in nature but are not exactly
material, which are quasi-material, of some sort of super-essential matter; it is
thus, you see, in the case of sound, of planetary orbits or heavenly spheres,
and of the rays of light, or the rays which come from your eye.
But mechanics is an exception because mechanics is a very terrestrial,
down-to-earth discipline. It has to do first with military engines, and with
levers, pulleys, cranks, fortifications: that is mechanics. Mechanics is really
down-to-earth, an everyday science. Astronomy, optics, and music are not
everyday sciences. They have not much to do with the real world. So
mechanics is an exception, and it would be very interesting but difficult to
try to follow the strange evolution of mechanics, and even of the
word, mechane, mechanika, mechanike. What is it exactly? Mechane is a trick.
You are a mechanician when you are clever, you are tricky, you know the
roundabout way, you don't deal directly with the thing. You are like Ulysses:
Ulysses is a master of mechanics. Whereas Achilles goes straight on, Ulysses
knows a trick: polumechanos Odysseus-maybe you remember that.
And then, does all that deal with nature? What is the link between
mechane and nature? I will not answer, but I'll just finish with a small
quotation from Sophocles' Antigone. You know the text. You remember
probably that the chorus says that Man is something extraordinary among
extraordinary things, a marvel of marvels or enigma of enigmas, polla ta
deina k'ouden anthr6pou deinoteron, etc. And you remember that Man does
violence to the Earth, and the word has some sexual connotation, apotruetai.
The poor Earth is fecundated at a certain price each year by the man with
the plow and the horses. And Man is a king of tricks. The word mechane
_occurs at various places in this chorus of Antigone. For instance, you have
the strange phrase, to miJcbanoen tecbnas, etc. And so Man is able to keep
away from Nature, to keep away from natural dangers. He has his shelter, his
weapons. The mecbane is a way to avoid the direct contact with Nature, in
some sense. Man has created another world, another realm, which is the
domain of mechane.
If we admit that in that text, the hymn to Man in Antigone, there is a
certain flavor of disrespect, almost blasphemy against Nature, then we should
not say, we should not believe that we have lost a certain contact with
Nature which was a privilege of the ancient world. The ancient world was no
�DEGANDT
19
more in contact with Nature than we are, in some sense. They admitted that
a certain mechane was there to protect them against Nature. That mechane
was also the genius of Man, because mechane goes up to the creation of
speech and laws, in the text of the chorus of Antigone.
In the beginning I spoke of nostalgia. Nostalgia is a noble and sweet
feeling. And Nature is in some sense our paradise lost. For every people,
every country, every century, Nature is always in some sense a paradise lost.
So, nostalgia is a sweet feeling. But the higher attitude seems to me to admit
almost to blasphemy or at least to attifact in our life, and to live with it.
Notes
1. Frans;ois de Gandt, Force and Geometry in Newton's Principia, trans. Curtis Wilson
(Princeton University Press, 1995).
2. Isaac Newton, Philosopbiae Natura/is Principia Mathematica, (first edition, 1687).
References are to the third Latin edition (1726) with variant readings edited by
Alexandre Koyre and I. Bernard Cohen, Harvard University Press, 1972. I will refer
to this work throughout as Principia. All English translations are by William H.
Donahue.
�Newton's New Theory
of Light and Colors
William H. Donahue
Isaac Newton is known for having invented many things: the Newtonian
telescope, universal gravitation, and the cat door among them. It is not
widely known, however, that he also invented the scientific journal article.
His invention appeared in the form of a letter, and was published in the
Philosophical Transactions of the Royal Society in 1672.' It was about light
and colors, and began with an account of his famous experiment with 'two
prisms, which he called "the E;xperimentum Crucis," by which he hoped to
show that sunlight consists of differently refrangible rays, each with its own
characteristic angle of refraction. This experiment, and Newton's description
of it, is my topic this morning, and so I shall begin by reading the pertinent
parts of Newton's article.
Newton begins:
Sir,
To perform my late promise to you, I shall without further
ceremony acquaint you, that in the beginning of the Year 1666 (at which
time I applyed my self to the grinding of Optick glasses of other figures
than Spherical,) I procured me a Triangular glass-Prisme, to try therewith
the celebrated Phaenomena of Colours. And in order thereto having
darkened my chamber, and made a small hole in my window-shut
[shutters], to let in a convenient quantity of the Suns light, I placed my
Prisme at his entrance, that it might be thereby refracted to the opposite
wall. It was at first a very pleasing divertisement [diversion], to view the
vivid and intense colours produced thereby; but after a while applying
my self to consider them more circumspectly, I became surprised to see
them in an oblong form; which, according to the received laws of
Refraction, I expected should have been circular.
William Donahue, a graduate of St. John's with a Ph.D. in the history of science from Cambridge
University, is the translator of Kepler's Astronomia Nova, and is now completing a translation of
Kepler's Astronomiae Pars Optica. With Dana Densmore he operates the Green Lion Press,
which publishes works of importance in the history of science. Mr. Donahue illustrated his talk
at appropriate moments with a video portr.1yal of the experiment prepared by Mr. Howard
Fisher and Mr. Adam Schulman. In the printed version of the talk, the illustrations will be three
diagrams drawn by Newton himself.
�21
DONAHUE
[2] They were terminated at the sides with streight [straight] lines,
but at the ends, the decay of light was so gradual, that it was difficult to
determine justly, what was their figure; yet they seemed semicircular.
[3] Comparing the length of this coloured Spectrum with its
breadth, I found it about five times greater; a disproportion so
extravagant, that it excited me to a more than ordinary curiosity of
examining, from whence it might proceed .... ( 47-48)
p
" "'
Fig. 1. XY is the Sun, F the hole in the window shutter,
ABC the prism, and PT the oblong image on the wall.
And having placed [the prism] at my window, as before, I observed, that
by turning it a little about its axis to and fro, so as to vary its obliquity to
the light, more than an angle of 4 or 5 degrees, the Colours were not
thereby sensibly translated from their place on the wall, and
consequently by that variation of Incidence, the quantity of Refraction
was not sensibly varied. [See Fig. 1.] By this Experiment therefore, as well
as by the former computation, it was evident, that the difference of the
Incidence of Rays, flowing from divers parts of the Sun, could not make
them after decussation [the point where nonparallel rays cross] diverge at
a sensibly greater angle, than that at which they before converged; which
being, at most, but about 31 or 32 minutes, there still remained some
other cause to be found out, from whence it could be 2 degr .49'. ( 49-50)
Note that there is a lowest position which the spectrum can attain, no
matter how the prism is rotated. When the spectrum is at its lowest position,
the prism is said to be in the position of minimum deviation.
This position has theoretical importance since one can show from the
sine law of refraction (which was known in Newton's day) that it is a
position of symmetry with respect to both incoming and outgoing beams;
and therefore that a light beam refracted by the prism should pass through
with its angular width unchanged. Newton refers to such a calculation in
Paragraph 6. During the experiment the prism was never rotated very far
from its position of minimum deviation, once that position was found . Thus
�22
THE ST. JOHN'S REVIEW
the spreading out of the beam in one direction cannot be explained by the
reference to the ordinary law of refraction alone.
We return to Newton's letter at paragraph 9:
[9] The gradual removal of these suspitions, at length led me to the
Experimentum Crucis, which was this: I took two boards, and placed one
of them close behind the Prisme at the window, so that the light might
pass through a small hole, made in it for the purpose, and fall on the
other board, which I placed at about 12 feet distance, having first made a
small hole in it also, for some of that Incident light to pass through. Then
I placed another Prisme behind this second board, so that the light,
trajected [passed] through both the boards, might pass through that also,
and be again refracted before it arrived at the wall. This done, I took the
first Prisme in my hand, and turned it to and fro slowly about its Axis, so
much as to make the several parts of the Image, cast on the second board,
successively pass through the hole in it, that I might observe to what
places on the wall the second Prisme would refract them. [See Fig. 2.]
Fig 2.
And I saw by the variation of those places, that the light, tending to
that end of the image, towards which the refraction of the first Prisme
was made, did in the second Prisme suffer a refraction considerably
greater then the light tending to the other end.
And so the true cause of the length of that image was detected to
be no other, then that Light consists of Rays differently refrangible, which,
without any respect to a difference in their incidence, were, according to
their degrees of refrangibility, transmitted towards divers parts of the
wall. ( 49-50)
The rest of my talk will consist largely of a careful reading of these
last two sentences, to try to understand what they mean and on what
�DONAHUE
23
grounds we might be able to judge of their truth. I say "we" because I hope
you will be participants in the reading. I'm not a Newton scholar, and am
approaching the text in the tradition of St. John's, as a thoughtful reader
rather than as an expert.
So let's jump in. I'll read Newton's conclusion again:
And l saw by the variation of those places, that the light, tending to that
end of the image, towards which the refraction of the first Prisme was
made, did in the second Prisme suffer a refraction considerably greater
then the light tertding to the other end. And so the true cause of the
length of that image was detected to be no other, then that Light consists
of Rays differently refrangible, which, without any respect to a difference
in their incidence, were, according to their degrees of refrangibility,
transmitted towards divers parts of the wall.
The first remarkable thing we notice is that Newton does not use the
word "color," even though it is the colors of the refracted spectrum
(Newton's word) that one notices, almost to the exclusion of anything else.
Indeed, he goes through considerable verbal contortions to avoid using the
c-word: "the light, tending to that end of the image, towards which the
refraction of the first Prisme was made, ... the light tending to the other end."
Instead, the question Newton sets out to answer is why the form of the
image is oblong:
It was at first a very pleasing divertisement, to view the vivid and intense
colours produced thereby; but after a while applying my self to consider
them more circumspectly, I became surprised to see them in an oblong
form; which, according to the received laws of Refraction, I expected
should have been circular.
The distinction here is between something about which he had few
expectations, though it was interesting and fun, and something else that was
not behaving as current theory predicted-a serious matter. In refractions,
the sine of the angles of the incident and refracted rays (let's accept this
term, for the moment) were believed to maintain a constant ratio
characteristic of the two media transmitting the ray. Had the ray behaved in
accordance with this rule, it would have had about the same shape after
refraction as before. This expectation had nothing to do with color: the
refracted ray could have exhibited various colors in various places without
being elongated, or it could have been elongated while remaining white.
And the elongation was considerable: Newton found the image to be about
five times as long as it was wide.
�24
TilE ST. JOHN'S REVIEW
Newton's conclusion is remarkable for more than just the lack of any
mention of color: nothing in the way of an explanatory mechanism is
proposed. In fact, the conclusion seems excessively modest, stating the
obvious-not the sort of brilliant theoretical leap we would expect of
Newton. Nevertheless, far from being obvious, it received considerable
criticism, some of it from respected scientists such as Huygens and Hooke.
So it appears that we are missing something, and need to look more carefully
at what Newton says.
And I saw ... that the light, tending to that end of the image, towards
which the refraction of the first Prisme was made, did in the second
Prisme suffer a refraction considerably greater then the light tending to
the other end.
He says "I saw." Well, this is stretching things a bit. He didn't "see"
these things in the way that one says "I saw the son of Diares here
yesterday." But it does tell us what Newton intends. He hopes to convince us
that his conclusion falls directly out of observation, without the intervention
of theories or hypotheses. Has he succeeded?
Let us continue reading.
"And I saw ... that the light, ... " Notice that he doesn't say "I saw the
light": indeed, light itself, whatever it may be is not simply visible, as one
learns in the optical part of the Junior Lab at St. John's. It becomes visible
when it falls on something. In our video of the experiment, we saw that the
first prism was illuminated by the Sun, and that the screen placed beyond it
was illuminated by something that came from the first prism. Our
understanding has to come into play here, in tracing the relationship
between the Sun, the prism, and what we see on the board. If, for example,
a cat were looking at this same scene, she would see the spectrum as an
independent thing, and probably try to catch it. But once we understand the
connection, I think it's fair to say that we "see" that something has happened
somewhere between the Sun and the screen. A few ancillary experiments,
such as those described by Newton, would serve to locate the change in the
prism itself.
So what is the nature of the event that occurs in the first prism? Is this,
too, something that we "see"? Newton is careful to avoid terms that would
suggest an explanation or hypothesis. He uses the language that was
commonly accepted in geometrical optics-ray optics-in describing the path
of a "ray" of light passing from one medium into another: it is said to be
refracted, and all this means is that its path is bent. So can we be satisfied
that this language is perfectly neutral?
�DONAHUE
25
The troublesome term here is not "refraction" but the term "ray" (I'm
lifting it from the next sentence, but it is obviously implicit here), which
carries a lot of baggage with it. Optics, like astronomy, had long existed in
two forms: the mathematical discipline and the physical/physiological theory,
Geometrical optics, as far as we know, originated with Euclid, and was a
mathematical treatment of how things appear. It involved what is called an
"extramission" theory of vision, in which the eye was thought to emit rays
that reach out to objects and, as it were, feel them, as a blind person senses
objects by feeling them with a stick. This type of optics explained why
distant things appear small, how binocular vision works, and so on. The rays
in this theory were visual rays, not light rays: it does not deal with light as
such, and in fact there doesn't seem to be any reason why a light source
would be needed in order to see.
Then there was the other side of optics, which concerned itself with
what light is and how the sense of vision works-the big picture. Aristotle's
account in De Anima and On Sense and Sensibles is an example. Aristotle
was familiar with ray explanations of reflection, and so set out to say why
vision could occur only in the presence of light. His opinion was that light
only served to act on a medium that is transparent in potency so as to make
it actually transparent. In other words, we don't see things in the dark
because the air is opaque. Nothing is travelling from the Sun to the prism:
the colors that we see are only there in the colored object-the screen, the
ceiling, the prism support, and so on.
Now, of course, there are problems with this account. Nevertheless, it
was widely taught and widely accepted, and could be made consistent with
the extramission theory, though Aristotle himself rejected the latter. And, as
you can appreciate, it's hard to know what to make of the prism and its
refraction on this view. If there is no such thing as a ray of light coming from
the Sun, but only rays between the eye and the thing seen, there can't be a
refraction of the ray. We are almost left without language to describe what
we have seen. And, of course, it would seem perverse to speak of what we
have seen without mentioning color, since what is seen is nothing but color.
Perhaps, if we were trying to see through Aristotle's eyes, we would say that
without the prism we see a white shape at a certain place on the screen, and
with the prism we see an elongated and multicolored shape higher up on the
screen. Possibly Newton could convince us Aristotelians that something is
forming a straight line on one side of the prism, and that on the other the
succession of images (imagining the screen to be placed at different
distances) spreads out. But I don't think we could be made to see light
passing from the Sun in a straight line and being refracted, because that isn't
what light, as we understand it, does.
�26
TilE ST. JOHN'S REVIEW
It's evidently hard to get a conversation going between Aristotle and
Newton: they're not speaking the same language. But that in itself says
something about the "experimental philosophy." Experiments are not just
perceptions; they aren't just experiences either. Experiments must be
expressed in language, and the language in which they are expressed is
never neutral. Language implies some level of shared understanding upon
which further discourse can be based.
In this example, the language Newton was speaking came chiefly from
the work of Kepler and Descartes. Kepler had reworked the tradition of ray
optics into a comprehensive physical theory that began with the nature of
light, gave an account of reflection and refraction (including an accurate
mathematical law of refraction), and described light's path from a luminous
source to an illuminated object and on to the retina of the observer's eye.
Kepler was a careful reader of Aristotle, and explicitly rejected Aristotle's
view that nothing actually flows from the Sun to the scenery.
Descartes acknowledged his debt to Kepler, but gave Kepler's
conclusions a Cartesian foundation and replaced Kepler's refraction rule with
Snel's. Although he believed that light is instantaneously transmitted through
a medium by impulse, he retained the ray optics as a useful mathematical
device.
Newton had read works of Descartes and other contemporary authors
of the mechanical tradition as an undergraduate. Interestingly, what little he
says about Aristotle's views seems to have come from a seventeenth-century
textbook writer: Newton may not have read Aristotle at all. His remarks in
early optical lectures display impatience and contempt for what he took to
be Aristotelian opinions. His intended audience had clearly outgrown such
puerilities.
So perhaps we should agree to speak his language, and to accept
tentatively whatever baggage it brings with it. And near the beginning of our
inquiry, before we became Aristotelians, we had agreed that something
happens in the first prism: the rays (whatever they are) are refracted through
a range of angles, even though the incident rays meet the prism at nearly the
same angle. What is the nature of this event?
To answer this question, Newton performs what he calls an
experimentum crucis. He got this term from Hooke, who used it in the
course of investigating colors in his Micrographia (1665).' Hooke brought in
the example of colors produced by thin films and plates to refute Descartes's
proposal that colors are somehow created by a spin imparted to particles in
refraction, there being no refraction in these instances. He remarks,
�DONAHUE
27
This experiment therefore will prove such a one as our thrice excellent
Verulam [i.e., Francis Bacon] calls Experimentum Crucis, serving as a
Guide or Land-mark, by which to direct our course in the search after the
tme cause of Colours. (54)
Now Bacon did not use this exact language, but in Aphorism 36 of
Book II of the Novum Organum he introduces instantiae crucis, or "crucial
instances." 3 The "crux," or "cross," in question was actually a road sign,
pointing out which road to take. Bacon writes,
They operate as follows. When in the investigation of nature the
understanding stands evenly balanced, unable to decide to which of two
... natures the cause of the nature in question should be ascribed ... ,
Crucial Instances show the union of one of those natures with the nature
in question to be constant and unbreakable, but that of the other
breakable and separable. The inquiry is then over, and the former nature
is accepted as the cause, the latter dismissed and denied. (210)
If we can assume that Newton was using this term in its full Baconian
sense, the crucial or signpost experiment was not intended as the sole means
of revelation of the truth expressed in the conclusion following it. Rather, it
was a way of deciding which of two competing alternatives to accept.
Although Newton does not give us another alternative in this letter, the other
fork in the road would have been that the prism materially altered the light,
spreading it out into an oblong shape. If this were the case, then we would
expect the light to be similarly affected if it were passed through a second
prism; that is, any small part of the light from the first prism, passed through
a second one, would also be spread out over an angle of nearly three
degrees. If, however, the different angles of refraction belong to the rays
themselves, each kind of ray having its own specific refraction, then the
second prism would not spread out the beam of light, but would bend each
kind of ray through the same angle through which it had been bent by the
first prism.
Although he did not make this alternative explicit in the 1672 paper, he
considered it in the Gpticks: '
Considering therefore, that if in the third Experiment the Image of the
Sun should be drawn out into an oblong Form, either by a Dilatation of
every Ray, or by any other casual inequality of the Refractions, the same
oblong Image would by a second Refraction made sideways be drawn
out as much in breadth by the like Dilatation of the Rays, ... I tried what
would be the Effects of such a second Refraction. For this end I ordered
all things as in the [single prism] Experiment, and then placed a second
Prism immediately after the first in a cross Position to it, that it might
again refract the beam of the Sun's Light which came to it through the
g~~~ n~:~~
f2k\
�28
THE ST. JOHN'S REVIEW
Q~~
s ..
D
R-
V ··N
H
Fig. 3.
And, in fact, this experiment was. also included in his optical lectures,
which were given before the present paper was written. So his omission of
the alternative was deliberate, and therefore we should be cautious about
drawing conclusions here.
I have described this situation much as I think Newton would have
characterized it (if he had chosen to make the alternatives explicit). Once it
is put this way, I think the result of the experiment is very clear and
compelling. But even if we concede that the two stated alternatives are the
only possibilities, some doubts remain. In particular, it is not self-evident that
the alteration option would necessarily require the light to spread out in
passing through the second prism. The light might well be altered in such a
way as to retain its new refraction angle in subsequent refractions.
And, in general, one can always find some way around a supposedly
crucial experiment, though often the detour is so obviously fictive as not to
merit serious consideration. In this instance, Hooke and Huygens remained
unconvinced; Newton believed their dissent to spring from excessive
fondness for their own hypotheses. But what really seems to have been at
issue was not a question of logical necessity but the much larger matter of
how to understand nature. The prevailing view was that science was done by
finding plausible explanations or hypotheses for the phenomena, basing
such explanations as much as possible on mechanical principles. According
to this view, Newton's experiment would be seen as designed to test two
competing hypotheses, with the idea that one of them would be logically
incompatible with the phenomena described.
I think Newton would object to this in two respects. First, he did not
believe he was evaluating hypotheses, and second, he did not consider the
evaluation to be a matter of strict deductive logic.
�DONAHUE
29
Newton's dislike of hypotheses is notorious. In a letter to Henry
Oldenburg, Secretary of the Royal Society,' regarding criticism of the present
paper, he wrote,
If I had not considered [these properties of light] as true, I would rather
have them rejected as vain and empty speculation, than acknowledged
even as an hypothesis. (264-65)
As for what he would propose as an alternative, his replies to Hooke
and others who expressed doubts about his conclusions give perhaps the
clearest testimony.
To the French Jesuit Ignace Pardies, he wrote,
For the best and safest method for philosophizing seems to be, first to
inquire diligently into the properties of things, and establishing those
properties by experiments and then to proceed more slowly to
hypothesis for the explanation of them. (285)
And to Oldenburg,
You know, the proper Method for inquiring after the properties of things
is, to deduce them from Experiments! And I told you that the Theory,
which I propounded, was evinced to me, not by inferring 'tis thus
because not otherwise, that is, not by deducing it only from a confutation
of contrary suppositions, but by deriving it from Experiments concluding
positively and directly. (285, n. 24)
Thus Newton's experimentum crucis seems not to be Bacon's or
Hooke's experimentum crucis. He had hoped that the experiment itself could
be described in sufficiently neutral terms, and could be clearly enough
organized, that the theory would simply fall out of it. In response to Hooke's
view, that Newton supposed light to be corporeal, Newton wrote,
I chose to ... speak of Light in general terms, considering it abstractly, as
something or other propagated every way in streight lines from luminous
bodies, without determining, what that Thing is.
When the experiment is expressed in such general terms, the correct
"reading" of the events would be natural, obvious, and direct. Other readings
would be possible, but, in Newton's view, would involve the assumption of
more than is evident in the phenomena. And this would constitute the
unwarranted introduction of hypotheses.
Many years later, in the "General Scholium" to the second edition of the
Principia, he stated the procedure more succinctly:
�30
TI!E ST. JOHN'S REVIEW
Hypotheses . . . have no place in experimental philosophy. In this
philosophy particular propositions are inferred from the phenomena, and
rendered general by induction.
Let's return to the sentences with which we began, keeping Newton's
intentions in mind while still reserving our judgment. First sentence:
And I saw by the variation of those places, that the light, tending to that
end of the image, towards which the refraction of the first Prisme was
made, did in the second Prisme suffer a refraction considerably greater
then the light tending to the other end.
In the language of the General Scholium, this is the "particular
proposition inferred from the phenomena." We know from his reply to
Hooke that when he says, "light," he only means to point at that "something
or other" that goes from the Sun through the prisms to the screen. The claim
is that no assumptions are made about its nature.
Second sentence:
And so the true cause of the length of that image was detected to be no
other, then that Light consists of Rays differently refrangible, which,
without any respect to a difference in their incidence, were, according to
their degrees of refrangibility, transmitted towards divers parts of the wall.
In the language of the General Scholium, this is the "particular
proposition" (first sentence) "rendered general by induction." All that has
been done here is to restate the proposition generally, without reference to
the apparatus involved (prisms and places on the wall). Yet it makes a
sweeping statement about the nature of light that represented a marked
departure from currently held views. Certainly, objections could be raised,
and were in fact raised. But Newton would claim that these involve making
further assumptions that are not supported by the phenomena. For example,
one could claim that to bundle all the rays together under the single name
"light" begs the question of whether it is all really unchanged in the course
of being refracted. Newton would reply that, though a change is conceivable,
there is no evidence supporting such a "hypothesis," and so it should not be
entertained. Should one devise another experiment that would demonstrate
such a change, Newton happily grants the "correctibility" of his conclusions.
As he said in the Principia, in the fourth of his "Rules of philosophizing,"
In experimental philosophy, propositions gathered from phenomena by
induction should be considered either exactly or very nearly true
notwithstanding any contrary hypotheses, until yet other phenornen:1.
make such propositions either more exact or liable to exceptions.
�DONAHUE
31
What, then, are we to make of this? Do we agree with Newton that his
procedure is the true one, or have we instead been rather persuasively sold a
bill of goods? Is Newton's method a way of avoiding hypotheses, or is it just
another set of rules about how to make them up? Do we now really know
something about the true nature of light itself, or is light still a slippery
demon, about which neutral statements can't be made?
Notes
1. Isaac Newton's Papers and Letters on Natural Philosophy. 2nd ed. ed. I. B. Cohen
(Harvard University Press, 1978)
2. Robert Hooke. Micrographia (New York: Dover, 1961).
3. Francis Bacon. Novum Organum. trans. and ed. Peter Urbach and John Gibson
(Chicago' Open Court, 1994).
4. Sir Isaac Newton. Opticks (New York: Dover, 1952).
5. Letters quoted by A.l. Sabra. Theories of Light from Descartes to Newton (London:
Oldbourne, 1967).
�How Did Newton Discover
Universal Gravity?
George Smith
As satisfying to our romantic conception of genius as the story of the apple
may be, Newton surely did not discover universal gravity in a flash of insight
while sitting in his mother's garden in 1667. For one thing, universal gravity
is much too complicated for that. His discovery involved a sequence of ten
increasingly problematic theses:
1. Orbiting bodies are retained in orbit, rather than moving forward
uniformly in a straight line, by forces directed toward central bodies.
2. These forces, and hence the resulting "centripetal" accelerations, vary
inversely with the square of the distance from the central body.
3. These forces act not only on the principal bodies orbiting the central
bodies, but on other bodies as well.
4. In the case of the Moon, the force in question is simply terrestrial
gravity.
5. In all celestial cases, the force in question is one in kind with terrestrial
gravity.
6. There is a force of this same kind on the central body directed toward
each body orbiting it, so that the two bodies-e.g. the Sun and
Jupiter-interact.
7. There are mutual forces of this kind between all celestial bodies----e.g.
between Jupiter and Saturn, as well as between each of these and the
Sun.
8. The forces in question vary in accord with the law of gravity-i.e., the
"motive" force on a body directed toward another body is proportional
to the product of the masses of the two bodies and inversely
proportional to the square of the distance between them.
9. The force of gravity is universal-i.e., the law of gravity holds between
any two particles of matter in the universe.
10. The force of gravity is one of the fundamental forces of nature-i.e., it
is not composed out of forces of other (known) kinds.
Now Newton, who by 1667 knew the principles of uniform circular
motion, may well have conjectured about some variant of the first few of
George E. Smith is both a philosopher of science in the Philosophy Department. of Tufts
University and a practicing engineer.
�SMITII
33
these theses in the late 1660s. Hooke and Wren were entertaining versions of
at least the first two in the late 1670s, after the account of uniform circular
motion Huygens published in 1673. We can even find a vague conjecture
along the lines of the third, fourth, and fifth in Streete' s Astronomia Carolina
of 1661, the work from which Newton learned his orbital astronomy. The last
five theses, however, reach increasingly far beyond prior thought. The last
two, we should not forget, were little short of mind-boggling at the time,
even for Newton himself.
A second reason for thinking that Newton did not discover universal
gravity in a flash of insight in 1667 is the little store he put in conjectured
hypotheses. His distrust of hypotheses did not appear for the first time in the
second, or even the first, edition of the Principia. We see it in his exchanges
over light and color in the early 1670s, where he complains that too many
disparate hypotheses can be made to fit the same facts. Indeed, given the
outspoken remarks he made about hypotheses after 1710, Newton would be
guilty of the rank hypocrisy with which Imre Lakatos charged him if he had
initially thought up universal gravity as a conjectured hypothesis, only to be
misled by bad data from Galilee in the "Moon test" of the late 1660s.' What I
am going to do in this essay is to free Newton of this charge of hypocrisy by
proposing a step-by-step sequence of reasoning by which he could have
arrived at these ten theses, one by one. We will never know for sure how
Newton arrived at universal gravity. All I can claim for the sequence I will
propose is that it is entirely compatible with the available manuscriptsespecially so when they are read in their own right, as they would have been
at the time, and not in the light of the subsequent Principia.
In fact, Newton's manuscripts and correspondence give us the best
reason for thinking that he had not discovered universal gravity before late
1684. Of particular note is his response at the time to the comet of 1680-81
(see Figure 1). Flamsteed had concluded from the bilateral symmetry of the
trajectories of the two comets observed in late 1680 and early 1681 that they
were one and the same comet that had approached the sun, only to be
repulsed by the latter's magnetism. When Newton heard of this, he became
very interested, informing Flamsteed of the alternative that the comet had
button-hooked around the sun, which Flamsteed proceeded to show was
also compatible with the observations. After intensely scrutinizing the data
and attempting to calculate trajectories, however, Newton concluded that this
is just not what comets do:
But whatever there be in these difficulties, this sways most with me that
to make the Comets of November and December but one is to make that
one paradoxical. Did it go in such a bent line other comets would do the
�34
THE ST. JOHN'S REVIEW
like and yet no such thing was ever observed in them but rather the
contrary. . . . Let but the Comet of 1664 be considered where the
observations were made by accurate men. This was seen long before its
Perihelion and long after and all the while moved (by the consent of the
best Astronomers) in a line almost straight. (Letter of 16 April 1681Y
This shows that, regardless of what Newton thought at the time about
the inverse-square governed trajectories of planets, he did not think the
centripetal force governing them extends to comets as well. His celestial
forces of 1681 were definitely not universal.
Newton's Alternative
Flamsteed's Idea
D
:
.
n
:
El
Flamsteed's Trajectories
Fig. 1. The Comet(s) of 1680/81.
Reprinted by permission from The Correspondence of Isaac Newton, Vol. 2 (Cambridge at
the University Press, 1960)
�35
SMI1H
Circular Motion and the Moon Test
The obvious question, then, is what are we to make of his so-called
"Moon test" of the late 1660s? This test is presented in a brief tract written in
Latin, as if for publication. The tract begins with an analysis of circular
motion, concluding that the tendency or endeavor of the object to recede
from the circle varies as v2/r, and hence as radius or diameter over period
squared (see Figure 2). A corollary of this is that if several bodies in uniform
circular motion about a central body satisfy Kepler's 3/2 power rule--that is,
the square of the periods of revolution vary as the cubes of the radii of the
orbits-then the endeavors of these bodies to recede are inversely
proportional to the squares of the radii of their orbits. The "Moon test" itself
compares the endeavor of the Moon to recede with the known value of the
acceleration of gravity at the surface of the Earth, using 60 Earth radii for the
radius of the Moon's orbit and Galileo's incorrect value for the Earth's radius
(taken from his Dialogue Concerning the Two Chief World Systems). Newton
concludes that "the force of gravity is 4000 and more times greater than the
endeavor of the Moon to recede from the center of the Earth," much greater
than the 3600 it should be if the inverse-square rule holds around the Earth
as well.
Fig. 2. The "Moon Test" of the late 1680s.
Newton considers the body revolving in the circle as being subject to an
"endeavor to recede" from the center C. This endeavor would accelerate it
through BD in the time it moves over the arc AD, were there not a
counteracting force. But by Galileo's Dialogue, the distances traversed in
accelerated motion are as the squares of the times, and by Euclid 111.36, AB1 =
DB·BE. From these propositions Newton deduces that the acceleration
produced by the "endeavor to recede" is given by:
lim[Bn]= lim[ 2AB' ] = v' oc v' oc.!...'
2
rz
t •BE
2r
r
p
where the limit is to be taken as t or AB goes to zero, and P is the period.
Figure reprinted with permission from john Herivel, The Background to NewtonS
Principia (Oxford at the Clarendon Press, 1965).
�36
1HE ST. JOHN'S REVIEW
How can I deny that what Newton is doing here is testing the
hypothesis that inverse-square terrestrial gravity is holding the Moon in its
orbit? My answer is simple.
Keep in mind that the most celebrated question in 17th century
astronomy was whether there was some way to choose between the
Copernican and Tychonic systems, where the latter (see Figure 3) has the
five planets going around the Sun and the Sun and Moon going around the
Earth. (By a simple relative motion argument, these two systems seem to be
observationally indistinguishable, for every object in each system will be in
the same position relative to all the others at all times.) Newton had read
Galilee's argument for the Copernican over the Tychonic system in the
Fourth Day that culminates the Dialogue and Descartes's argument for the
same in his Principia, and we can be confident that he found both wanting.
I
i
I
Fig. 3. Copernican vs. Tychonic World Systems
A Possible Line of Argument for the Copernican system: (I) The Earth conforms
perfectly with the 3/z power rule around the Sun. (2) The Sun does not
conform at all with the 3/z power rule around the Earth. Therefore, the Earth is
in orbit about the Sun, and not the Sun about the Earth. Lacuna: Why should
the 3/2 power rule hold around the Earth? Response: It does hold if the
endeavor of the Moon to recede is inverse-square! But is it?
Figure reprinted with permission from N.M. Swerdlow and 0. Neugebauer, Mathematical
Astronomy in Copernicus's De Revolutionibus, Part 2 (Springer-Verlag, 1984).
The 3/2 power rule, which Newton had learned from reading Streete, offers a
prospect of settling this issue, for the Earth fits in perfectly if it is going
around the Sun, while the Sun and Moon definitely do not conform with the
rule if they are going around the Earth. The trouble is, why should the 3/2
�SMIT1I
37
power rule hold around the Earth? I submit that with the "Moon test" of the
late 1660s Newton was trying to show that the 3/z power rule has to hold
around the Earth as well, by showing that the endeavor of the Moon to
recede is inverse-square. In other words, Newton was looking for a decisive
argument for Copemicanism. The fact that the other main calculation in the
tract shows that the endeavor of objects to recede from the surface of a
rotating Earth is small compared with the force of gravity, thereby answering
a prominent objection to Copernicanism, gives supporting evidence that
Newton was preoccupied in this tract with Copernicanism, not gravity.
I hope you noticed that all the talk in the "Moon test" tract was of the
endeavor to recede from the center, and not of centripetal forces. Newton
appears to have shifted to thinking in terms of centripetal forces only
following the correspondence with Hooke at the end of 1679. In his initial
letter of 24 November, Hooke asks
particularly if you will let me know your thoughts of that [hypothesis of
mine] of compounding the celestial motions of the planets of a direct
motion by the tangent and an attractive motion towards the central body.
(Correspondance 2:297)
In his subsequent letter of 6 January, after calling attention to his
supposition that the attraction is inverse-square, Hooke adds
not that I believe there really is such an attraction to the very center of
the Earth, but on the contrary I rather conceive that the more the body
approaches the center, the less will it be urged by the attraction .... But
in the celestial motions the Sun, Earth, or central body are the cause of
the attraction, and though they cannot be supposed mathematical points,
yet they may be conceived as physical and the attraction at a
considerable distance may be computed according to the former
proportion as from the very center. This curve truly calculated will show
the error of those many lame shifts made use of by astronomers to
approach the true motions of the planets with their tables. (2:309)
And finally, in the last letter of the exchange (dated 17 January
1679/80), Hooke says,
It now remains to know the properties of a curve line (not circular nor
concentrical) made by a central attractive power which makes the
veloCities of descent from the tangent line or equal straight motion at all
distances in the duplicate proportion to the distances reciprocally taken. I
doubt not that by your excellent method you will easily find out what
this curve must be, and its properties, and suggest a physical reason of
this proportion. (2,313)
The "excellent method" alluded to here is what we call the calculus.
�38
TilE ST. JOHN'S REVIEW
Newton himself coined the term "centripetal force," adapting it from
Huygens's "centrifugal force." Huygens used this term to designate the
tension in the string holding a ball in uniform circular motion, or equally the
static force exerted on the wall of a spinning surface restraining the ball. It
was a trivial step from that force to the balancing static force on the ball,
normal to the spinning surface.
A natural thought when trying to generalize uniform circular motion to
motion describing other curves is to treat it as involving an instantaneous
uniform circular component and a second component that displaces the
object from one such circle to another (see Figure 4). Huygens's theory of
evolutes, published in 1673, displayed the power of this approach. Newton
explored it further in the 1670s, developing a significant fragment of the
differential geometry of curves in terms of normal and tangential
components, but without getting anywhere on orbital motion. The difficulty
with this approach for that purpose is that it allows two seemingly
independent degrees-of-freedom, making the problem of determining a
specific motion underspecified. The shift to the idea that every departure
from inertial motion that an orbiting body makes always has to be directed
toward a single point in space in effect eliminates one degree-of-freedom.
?-·:::....:._:_:_:_:_:~- c
I
.. -
._._:-.:~.
G
Huygens's Centrifugal Force (a)
Huygens's Centrifugal Force (b)
Reprinted with permission from Joelle G. Yoder,
Unrolling Time (Cambridge University Press,
1988), p. 21, Fig. 3.2
Reprinted with permission from Oeuvres
Completes de Christiaan Huygens, T. 16
(LaHaye: M. Nijhoff, 1929) p. 308.
~p
iI
•
s
The Natural Generalization
Centripetal Force
Fig. 4. Centrifugal Force vs Centripetal Force
�SMITI!
39
Hooke almost certainly deserves credit for leading Newton into this shift.
One can think of the orbiting body as held in orbit not by a string, but by a
spring-for example, one obeying Hooke's law of elasticity. Newton himself
thought of the orbiting body, at least initially, as being pushed by impulses
toward the central point.
The Public Version of De Motu
We are now getting into the more documented part of the story. We
know that while he was visiting Newton in the summer of 1684, young
Halley told him of discussions in London about the trajectory described by
an orbiting body governed by an inverse-square force directed toward a
central body. Newton told Halley that the answer is an ellipse and that he
had proved this earlier. Unable to find the proof among his papers, he
promised Halley that he would forward it. The 1 0-sheet tract De Motu
Corporum in Gyrum was sent to Halley in November 1684. 3 It ·prompted
Halley to make a second visit to Cambridge, where he saw what was later
called a further "curious treatise," for Newton was continuing his efforts.
Halley had the initial tract entered into the Royal Society's Journal Book in
early December, in anticipation that more would be coming from Newton.
This registered version of the tract (see Document 1, Appendix) opens with
the coining of the term "centripetal force" followed by two other definitions
and four hypotheses. For my purposes here, the main thing to notice about
these is the absence of the second law of motion. In its place are two weaker
principles: the parallelogram rule for changes of motion resulting from two
forces compounded and the Galilean rule that in the very beginning of any
change of motion the displacement of the body from where it would have
been had it continued in uniform motion in a straight line is proportional to
the square of the elapsed time.
Newton derives 11 propositions from these hypotheses, the last two of
which reach beyond motion under centripetal forces to consider motion in
resisting media. The first proposition (see Document 2, Appendix) in effect
says that, if the only forces causing changes of motion of a body are always
directed toward a single point in space, then that body sweeps out equal
areas in equal times with respect to that point. In other words, centripetal
forces imply Kepler's area rule. This does not license an inference from the
area rule to centripetal forces. De Motu is throughout stipulating that the
forces are centripetal. What it does license is that, of the several ways in
which time can be represented geometrically in uniform circular motion-for
example, by angle or arc length-the preferred one for generalizing beyond
such motion to motion under varying centripetal forces is area. While the
�40
THE ST. JOHN'S REVIEW
point remains implicit, it also shows that the stipulation of centripetal forces
eliminates what I was calling a degree-of-freedom in the problem of
curvilinear motion. (The figures in Documents 2-4, Appendix, by the way,
are facsimiles of Newton's own hand-drawn figures.)
The second proposition gives results for uniform circular motion,
emphasizing in Corollary 5 the tie between the 3/2 power rule and the
inverse-square, stated now for centripetal forces. A scholium (or
commentary) immediately following announces that this corollary holds true
in the case of the heavenly bodies-that is, the major planets orbiting the
Sun and the minor ones orbiting Jupiter and Saturn.
The third proposition then provides the basis for generalizing beyond
uniform circular motion by establishing a rule for inferring how the
magnitude of the centripetal force must vary along a curvilinear path from
the geometric features of that path. It is a beautiful proposition, combining
the approach Newton took to inferring the magnitude of force in the uniform
circular case with the use of area to represent time in the general centripetal
case. It is the crucial theorem, opening the way to a general theory of motion
under centripetal forces.
After giving a couple of examples of application of this theorem,
Newton turns to the case of a body orbiting in an ellipse with the centripetal
forces directed toward a focus (see Document 3, Appendix). He concludes
first that the centripetal force acting on such a body has to be inverse-square
and second that the 3/2 power rule holds as well for any system of bodies
held in such orbits by inverse-square forces directed toward the same point.
In a scholium between these propositions Newton announces that
the major planets orbit, therefore, in ellipses having a focus at the center
of the Sun, and with their radii drawn to the Sun describe areas
proportional to the times, exactly as Kepler supposed.
Newton has been criticized for sloppy reasoning here on the grounds that he
has not really proven that the planetary orbits have to be perfect ellipses,
even under the assumption of centripetal forces. Still, he has answered an
important question under discussion at the time. From the near circularity of
the planetary orbits, Newton and several others had concluded that, at least
to a first approximation, an inverse-square force is governing these orbits.
The question was whether some secondary force superposed on the inversesquare force is then displacing the body from circular into elliptical or
otherwise oval orbits. Newton has shown that no such secondary force is
needed for the case Kepler laid out; the same inverse-square forces inferred
from the 3/2 power rule for circular orbits can yield Keplerian orbits as well.
The Keplerian circle is just a special case of the Keplerian ellipse.
�SMITH
41
Newton next takes advantage of the 3/2 power result to provide two
ways of determining the specific ellipses (see Document 4, Appendix). The
first, presented in a scholium, determines the ellipse from a sequence of
observations. One important feature of this method, evident in the figure, is
that it locates the other focus by taking the mean of several determinations.
The advantage ... [Newton says] is that to elicit a single conclusion a
large number of observations, no matter how many, may be employed
and speedily compared one with another.
An even more important feature is that it uses the 3/2 power rule to
determine the length of the major axis from the more accurately known
period-a controversial practice that theretofore had been adopted only by
Horrocks, and Streete following him.
The 3/z power rule plays an even more crucial role in the other
method, which determines the ellipse, given only a position and. velocity of
the body. The obvious further .ingredient needed for the solution is the
magnitude of the centripetal force acting on the body at this location. As the
figure suggests, Newton uses a second orbiting body to determine this force
(Document 4, Appendix). Specifically, his method, when reformulated
algebraically, amounts to using the semi-major axis and period of the
reference orbiting body to determine the value of th~ invariant quantity
[a3/P'] for the center of force about which the motion is taking place, and
then to obtain the force at the location a distance r from this center as
[a'/P']/r'. In other words, Newton has taken the step of using [a'/P'] as a
measure of the strength of the centripetal forces associated with any center
of inverse-square forces.
He adds that this method can be used to determine the trajectories and
then the periods of comets. So, at this point, late in 1684, he seems to have
abandoned his reservations of three years earlier about comets buttonhooking around the Sun. I have no idea what has changed his mind.
De Motu goes on to treat the problem of vertical fall under inversesquare forces and then motion under resistance, but these results have little
to do with the question of how he discovered universal gravity. What is
striking about De Motu when considered with this question in mind is how
few of the ingredients of universal gravity are to be found in it. There is no
sign of interactive gravity; the only things treated are what we now call "onebody" problems. All that he says about gravity is that his vertical fall solution
is "in accord with the hypothesis that gravity is reciprocally proportional to
the square of the distance from the Earth's center," adding that "gravity is one
species of centripetal force." More dramatically, mass is entirely absent. The
one place he categorically needs it is for resistance forces, where, after giving
�42
1HE ST. JOHN'S REVIEW
a method for measuring the ratio of the force to the force of gravity-more
precisely, the ratio of the deceleration from resistance to the acceleration of
gravity-for a single body, he says that the resistance force on any other
body can be obtained by compounding the ratios of the surface areas with
the density of the two mediums; he then adds that "the force of gravity is
ascertainable from its weight." He is in effect telling the reader to let the
deceleration from the resistance of the medium vary not inversely with mass,
but inversely with weight, from one body to another:
v .
reSISt OC
Pmedium Asurface V
WEIGHT
(where I am using his dot notation from five years later to denote the
decelerative effect of the resistance). Here force amounts to nothing more
than departure from uniform motion in a straight line. Further, in the earlier
centripetal force propositions, just as in the resistance propositions, his talk
of forces is somewhat superfluous, for he employs only what he
subsequently came to call the accelerative measure offorce. In other words,
everywhere Newton speaks of centripetal forces in this tract, he might just as
well have spoken of "centripetally directed departures from uniform motion
in a straight line." If you will let me speak anachronistically, the 11
propositions involve only what we now call "kinematics," putting them
totally within the tradition of Galileo and Huygens.
In sum, if we ask the question, how much of universal gravity had
Newton discovered as of November 1684, and we take the registered version
of De Motu at face value, then the answer is, not much at all-the first three
of the ten propositions I listed earlier and perhaps the fourth, but not any of
the others. Mind you, in saying this I do not mean to be denigrating De
Motu. Had Newton published just it and stopped, it would have been the
most important contribution to a~tronomy in the 70 years of the 17th century
following Kepler. Saying this, however, is just to call your attention in still
another way to how remarkably monumental the Principia truly was.
One last point about the registered version of De Motu. It gives rise to
some obvious questions that it neither addresses nor even acknowledges. Its
propositions refer the motion of an orbiting body to a single point in space,
the point toward which the centripetal forces governing the motion are
always directed. But the point to which the forces governing the satellites of
Jupiter are directed, the center of Jupiter, is not a single point in space, for
Jupiter is orbiting the Sun. Our planetary system, with its multiple centers of
orbiting motion, thus invites the question, to what point in space should all
�SMITI!
43
these motions be referred? Remember, this was what the issue between the
Copernican and Tychonic systems was all about.
Worse, since Jupiter and Saturn are centers of force, as well as the Sun,
what happens when a comet comes close to one of them? Do the centripetal
forces directed toward each of them affect it? For that matter, do the forces
directed toward each of these two planets affect the motion of the other?
Even further, do the centripetal forces directed toward, say, Jupiter extend all
the way to the Sun, and if they do, is the Sun put into motion, interacting
with Jupiter? If all the different centers of force in our planetary system are
contributing to the motions of every other body, then indeed to what single
immobile point in space should the motions be referred? Members of the
Royal Society reading the registered version of De Motu would have required
no prompting to raise these questions.
The Augmented Version of De Motu
De Motu was entered into the Journal Book in December 1684. The
manuscript of Book 1 of the Principia was delivered to London in April of
1686, with the manuscripts of Books 2 and 3 following in March and April, a
year later. To examine how Newton got from De Motu to universal gravity,
we will have to consider some documents that did not become fully public
until long after Newton died. The most important of these is an augmented
version of De Motu. This document is written in the hand of Humphrey
Newton with deletions and insertions by Isaac, the most famous of which is
the change from "hypothesis" to "law" on the first page. The precise date of
the document cannot be established. I am going to put it in later 1684, with
the suggestion that Newton, like so many of the rest of us, had a flood of
further thoughts as soon as the manuscript of the earlier version left his
hands. The eleven proved propositions of De Motu remain the same in this
augmented version, as do their proofs. The augmented version has three
important changes: (1) the opening section has been recast, with a new set
of hypotheses; (2) a paragraph now known as "the Copernican scholium"
has been added to the scholium in which the first method for determining
the ellipse is given; and (3) the very short scholium leading into the section
on resistance forces has been replaced by three paragraphs, which I will call
the "resistance scholium."
Let me start with it. It opens,
Thus far I have explained the motions of bodies in non-resisting
mediums, in order that I might determine the motions of the celestial
bodies in the aether. For I think that the resistance of pure aether is
either non-existent or extremely small. Quicksilver resists strongly, water
�44
THE ST. JOHN'S REVIEW
far less, and air still less. These mediums resist according to their density,
which is almost proportional to their weights, or rather (one could almost
say) to the quantity of their solid matter. Therefore the solid matter of air
may be made less, and the resistance of the medium will be diminished
nearly in the same proportion until it reaches the tenuousness of aetber ..
. . If air flowed freely between the particles of bodies and thus acted not
only on the external surface of the whole, but also on the surfaces of the
single parts, its resistance would be much greater. Aether flows between
very freely, and yet does not sensibly resist. All those sounder
astronomers think that comets descend below the orb of Saturn, who
know how to compute their distances from the parallax of the Earth's
orbit, more or less; these therefore are indifferently carried through all
parts of our heaven with an immense velocity, and yet they do not lose
their tails nor the vapour surrounding their heads, which the resistance of
the a ether would impede and tear away. Planets persevere in their
motion for thousands of years, so far are they from experiencing
resistance .... [emphasis added} (Math. Papers 6:79, Prelim. Man., 22-23)
What Newton seems to be invoking here is Descartes's conception of
density and weight, according to which gravity arises from the pressure
exerted by aethereal particles on bodies, with density corresponding to the
extent of the impediment which the larger "solid" particles put up against the
free flow of the aethereal matter through the body. In particular, Descartes
expressly denied that density reflects the total quantity of matter in a body,
for included in this matter are all the aethereal particles. I will come back to
this point in a moment.
In the second paragraph of the "resistance" scholium, Newton repeats
the assumption of the earlier version that terrestrial gravity is inverse-square,
and now mentions a re-performance of the "Moon test" of the late 1660s:
Motion in the heavens, therefore, is ruled by the laws demonstrated. But
if the resistance of our air is not taken into account, the motions of
projectiles in it are known from Problem 4 and the motions of bodies
falling perpendicularly from Problem 5, assuming indeed that gravity is
reciprocally proportional to the square of the distance from the center of
the Earth. For one kind of centripetal force is gravity, and from my
computations it appears that the centripetal force by which our Moon is
kept in its monthly motion about the Earth is to the force of gravity on the
sutface of the Earth reciprocally as the squares of the distances from the
center of the Earth, more or less. From the slower motion of pendulum
clocks on the summits of high mountains than in valleys it is clear also
that gravity diminishes with increase of distance from the center of the
Earth, but in what proportion has not yet been observed. [emphasis
added] (6: 79-80; 24)
�SM!lli
45
Newton's remark about the slowing of pendulum clocks on mountains
-undoubtedly alluding to observations Halley had made at St. Helena, of
which Newton first learned more from Hooke in the correspondence at the
end of 1679-is mistaken, the effect being undetectably small. But the key
point is the new and successful result for the "Moon test." If in fact Newton
used Picard's value for the circumference of the earth, the number he would
have ended up comparing with 3600 is 3611.8, reducing the greater than 20
percent difference between the two he had found in the late 1660s to 0.3
percent.
The third paragraph of the resistance scholium opens with the
sentence:
The motions of projectiles in our air, moreover, are to be referred to the
immense and indeed motionless space of the heavens, not to the moving
space which is revolved along with our Earth and our air, and is naively
regarded as immobile. (6;80; 24)
This takes me back to the new laws, nee hypotheses, at the beginning
of the augmented tract (see Document 5, Appendix).
Newton has now changed the parallelogram and Galilean rules that
served as hypotheses in the registered D~ Motu into lemmas, replacing them
with a version of his second law of motion:
A change of state of motion or rest is proportional to the impressed force
and occurs along the straight line in which that force is impressed. (6:76;
13)
He gives no definition here of "motion," but from earlier unpublished
work and various work published by others on impact, we can infer that he
means the product of the bulk of the moving body and its velocity. (The
terminology, "laws of motion," at the time generally referred to laws
governing motion before and after impact of bodies, usually spheres; these
spheres were typically taken to be of the same material, so that bulk
amounted to their volume. The law Newton gives here, as stated, would not
have seemed new or unusual to anyone familiar with earlier papers on the
subject published by Wallis, Wren, and Huygens.)
Following this are two very different laws;
Law 3. The relative motions of bodies contained in a given space are
the same whether that space is at rest or whether it moves perpetually
and uniformly in a straight line without circular motion.
Law 4. The common center of gravity does not alter its state of motion
or rest through the mutual actions of bodies. (6,76; 13)
�46
THE ST. JOHN'S REVIEW
These two, which are never referred to in any of the demonstrations of
the proved propositions, are obviously responsive to the questions I posed a
little way back. The relativity principle is the same as Huygens had used in
his investigations of motion under impact. Newton himself had come upon
the center of gravity principle in his unpublished work on impact. It would
not have caused any consternation, for what it amounts to is a generalization
of the law of inertia to apply to a group of interacting bodies.
The only place where these two new laws make a difference is in the
added paragraph we may call "the Copernican scholium." The first part of
this reads:
Moreover, the whole space of the planetary heavens either rests (as is
commonly believed) or moves uniformly in a straight line, and hence the
common center of gravity of the planets (by Law 4) either rests or moves
along with it. In either case the motions of the planets among themselves
(by Law 3) are the same, and their common center of gravity rests with
respect to the whole space, and thus can be taken for the immobile
center of the whole planetary system. Hence in truth the Copernican
system is proved a priori. For if in any position of the planets their
common center of gravity is computed, this either falls in the body of the
Sun or will always be close to it. (6:78; 20)
The obvious question is, hasn't Newton now discovered universal gravity, for
how else can he be saying this? Let me answer by showing how else he can
be saying it.
Consider, for simplicity, the case of Jupiter moving uniformly in a
circular orbit, interacting with the Sun (see Figure 5). (The generalization to
the case of an ellipse can be found in Book I, Section 11 of the Principia.)
Now, as those at the time thought of it, the distance of two bodies from their
common- center of gravity formed a ratio, r1 to rH in the diagram, where the
former is the distance of Jupiter and the latter, the distance of Helios, that is,
the Sun, from their center of gravity. The center of gravity principle
expressed by Newton's Law 4 entails that this ratio must remain constant as
the two bodies move and interact with one another. (This is what Newton
had discovered in his early work on impact.)
The only way this ratio can remain constant and Jupiter be moving in a
circular orbit is for the Sun to be moving in a circular orbit as well, the center
of both orbits be their center of gravity, and Jupiter and the Sun always be
on directly opposite sides of this center (see Figure 6). Newton had already
shown that the force retaining Jupiter in such a circular orbit is proportional
to r/P/. Now, if this force is stemming from an inverse-square centripetal
force directed toward the Sun, then this last quantity must be proportional to
�47
SMITI!
;
;
/
,
.,. _.
....
----- ........... '
''
/
'\
I
\
I
\
I
Hellos
\
i 0 ~
r."'""'
I~~
r
..!!.._ =
I
I
\
constant
~
I
\
I
\
I
\
''
/
' ',
....... ____ .......... , ,
/
/
Fig. 5. Jupiter Interacting with the Sun.
the invariant quantity, [a3/P 2]H, characterizing the strength of the centripetal
forces directed toward the Sun, divided by the square of the distance
between Jupiter and the Sun, r,". Analogous reasoning holds for the Sun in its
circular orbit, so that rH/Pn 2 must be proportional to [a3 2 1 where the
/P ]/r l,
bracketed quantity with subscript J characterizes the centripetal forces
directed toward Jupiter.
For ease of exposition, I am now going to proceed algebraically where
Newton would likely have used Eudoxian reasoning. Dividing these two
proportions into one another, and taking into account that Law 4 requires the
periods of Jupiter and the Sun to be the same in this "two-body" problem,
we obtain the conclusion that the fixed ratio r./r1 must be equal to
, .......
....
----- .... ........ ....
/
/ /
''
\
/
\
I
, - - ...,
I
@:Hello;/
:
'
I
\
\\
'\
6)
I
/
I
'--""
\
loml
I
\
''
v.
11
rml
........ .......
_____ .... ... ... ,
~
[a'!P']"
2
~
r ;11
r,
[a /P'L
p~
r;ll
I
/
'
~)_
P'
J
I
\
~
\Jupiter
~rJ
'
\
v.
\
II
/
/
Fig. 6. Determination of ru
r,
PJ
3
2
[a'/P']J
[a 3/P']H
----
�48
1HE ST. JOHN'S REVIEW
[a3/P']/[a3/P'ln. Now both of the bracketed terms on the right were known in
astronomical units, that is, units in which the mean distance from the Earth to
the Sun is 1.0---the bracketed term in the numerator from the satellites of
Jupiter and the one in the denominator from Venus, Mars, or whichever
planet you prefer. So, Newton could now just calculate the ratio of rH to ~11
finding that it is around 1 in 1000, so small that their common center of
gravity has to lie more or less within the body of the Sun. In other words, he
could reach this conclusion not only without having the law of gravity, but
without even having yet expressly formed the concept of mass.
It is a short step from this two-body case to his so-called a priori proof
of the Copernican system (see Figure 7). Suppose, for the worst case, that
there are inverse-square centripetal forces directed toward each of the five
planets and the Earth. The greatest distance between the Sun and the
common center of gravity of all these bodies will occur when the Earth and
the planets all lie in a single straight line on the opposite side of this center
of gravity from the Sun. Saturn's satellite Titan could be used to determine
[a3/P 2] for it in astronomical units, from which Newton could conclude that its
effect on the Sun is only a fraction of that of Jupiter. Similarly, even though
he did not have an accurate value in as.tronomical units for the distance of
our Moon from the Earth, using the estimated value he had at the time to
obtain [a'/P'] for the Earth would have shown him that the effect of the Earth
on the Sun is much smaller than that of Jupiter. Even if, to be on the safe
side, one were to multiply the value of rH obtained from the Jupiter-Sun case
by 6 to obtain an upper bound on the distance of the center of gravity from
the center of the Sun, the result would be only around 3 Sun diameters, less
than 10 percent of the distance between the Sun's center and Mercury. Given
the much smaller values for Saturn and the Earth, Newton could conclude, as
he says, that the common center of gravity "either falls in the body of the
Sun or will always be close to it." Moreover, the reasoning just presented is
neutral between the Copernican and Tychonic systems insofar as the Sun and
Hello~
M
J
S
(){) Ct
Fig. 7. Generalizing to the "Proof."
The worst case: ru is at most 6 times the value obtained from the Jupiter-Sun case.
Thus Newton may fairly conclude that "... if in any position of the planets their
common center of gravity is computed, this either falls in the body of the Sun or will
always be close to it .... "
�SMITII
49
the other bodies can all line up in the manner shown in Figure 7 in either
system. So the reasoning is not question-begging; it does give a proof of
Copernicanism.
The glaring lacuna in this reasoning is that the effect on the Sun of any
centripetal forces directed toward Mercury, Venus, and Mars is no larger than
the effect of the centripetal forces directed toward Jupiter. There were no
known satellites of these three planets, and hence [a 3/P'] could not be
directly calculated for any one of these three. An upper bound for it,
however, could be determined. If you fully carry out the two-body problem
for Jupiter and the Sun that I outlined before, you find that the relationship
between the period and the mean distance between the two bodies is
slightly different when the two are interacting from what it is in the one-body
case. In other words, Kepler's 3/2 power rule requires a small correction
when the orbiting body is interacting with the central body. The correction
factor in the particular case of Jupiter interacting with the Sun is shown in
the following expression:
1
[a 3/P'lJ
1 +-::--::--::[a3/P')H
P'J = rJ"
'
Although the fraction [a3/P']/[a3/P']" is small in the case of Jupiter, it is not
negligible. Now, if any of Mercury, Venus, or Mars is interacting with the Sun
and the effect of this interaction on the Sun is greater than the effect on it of
an interaction with Jupiter, then a comparison of the numerical values for
this planet's period and mean distance with the numbers for the other
planets' periods and distances should show a small, but not negligible
discrepancy. The comparison shows no such discrepancy. Hence, it can be
concluded that if Mercury, Venus, and (or) Mars are interacting with the Sun,
then the effect of this interaction is less than that of Jupiter.
Did Newton already know this in December 1684? We have strong
evidence that he did. In late December, he initiates a brief correspondence
with Flamsteed, asking for various astronomical data, including the mean
distances and periods of the orbits of the satellites of Jupiter and Saturn. In
thanking Flamsteed for the data in his last letter in the sequence, dated 22
January 1685, Newton asks for
the long diameters of the orbits of Jupiter and Saturn assigned by yourself
and Mr. Halley in your new tables, that I may see how the sesquiplicate
proportion fills the heavens together with a small proportion which must
be allowed for. (Correspondence, z, 413)
�so
THE ST. JOHN'S REVIEW
The only small proportion which must be allowed for that shows up in
any of Newton's subsequent writings is the one I have just presented. The
reasoning I have attributed to Newton was therefore entirely within his
command.
So much for the first part of the "Copernican scholium." The remainder
of it is no less remarkable.
By reason of the deviation of the Sun from the center of gravity, the
centripetal force does not always tend to that immobile center, and hence
the planets neither move exactly in ellipses nor revolve twice in the same
orbit. There are as many orbits of a planet as it has revolutions, as in the
motion of the Moon, and the orbit of any one planet depends on the
combined motions of all the planets, not to mention the actions of all these
on each other. But to consider simultaneously all these causes of motion
and to defme these motions by exact laws admitting of easy calculation
exceeds, if I am not mistaken, the force of any human mind. Omit those
minutiae, and the simple orbit and mean among all the deviations will be
the ellipse of which I have already treated. If any one tries to determine
this ellipse by trigonometrical computation from three observations (as is
customary), he will have proceeded with less caution. For those
observations will share in the minute irregular motions here neglected and
so make the ellipse deviate a little from its just magnitude and position
(which ought to be the mean among all the deviations), and so will yield
as many ellipses differing from one another as there are trios of
observations to be employed. Therefore there are to be joined together
and compared with one another in a single operation a great number of
observations, which temper each other mutually and yield the mean ellipse
in both position and magnitude. (Math. Papers, 6:78, Prelim. Man., 20)
Suppose, then, we take the augmented version of De Motu at face
value, dating it just before the correspondence with Flamsteed, and ask, how
much of universal gravity had Newton discovered by the end of 1684? He
had completed a successful "Moon test" and so presumably had concluded
that the Moon is retained in orbit by terrestrial gravity. Insofar as he still
spoke of gravity as one kind of centripetal force, he may not yet have
equated celestial centripetal forces with terrestrial gravity. But he surely had
developed the idea that orbiting bodies can be interacting with the central
body; and his remark about the actions of all the planets on each other
indicates that he had extended this to interactions of the orbiting bodies with
each other. (Indeed, as we shall see in a moment, one of the topics in the
correspondence with Flamsteed was the action of Jupiter on Saturn.) The key
point, however, is that he has not gone beyond this in my list of claims
comprising universal gravity. Nothing in the augmented version of De Motu
�SMITII
51
gives evidence that he had discovered the law of gravity, or even had yet
singled out the concept of mass, given his remark about density being almost
proportional to the quantity of solid matter. The audience for whom Newton
wrote this tract would have found it perfectly intelligible without their having
any inkling of the law of gravity, or his concept of mass.
I should add that, however struck we may be by Newton's discouraging
remark about the actual orbits being beyond the force of the human mind,
his contemporaries would have been neither surprised nor dismayed by it.
Galileo and Descartes had argued that a science of resistance is impossible,
and hence, so too is a science of real motions of objects near the surface of
the Earth. Huygens had discovered that a cycloidal pendulum is perfectly
isochronous if the bob is a mere point, but then found himself unable to
define mathematically the isochronous curve when the bob is a real physical
body. The general view within the tradition of Galileo and Huygens-the
tradition in which, as I said before, De Motu falls-was to pursue a
mathematical science of the ideal case and then live with the fact that the
real world is not ideal. Some, like Kepler and Horrocks, had expressed
hopes for the perfectibility of orbital astronomy, but Descartes had suggested
to the contrary that planetary trajectories were sure to be subject to
intractable irregularities. Newton's expression of resignation was par for the
course at the time.
The Law of Gravity
Nevertheless, Newton himself had good reasons not to be so
comfortable conceding that the exact motions are beyond human reckoning.
The proved propositions of De Motu were opening the way to a bold
sequence of reasoning from Kepler's findings to a knockdown argument for
Copernicanism. The fact that our Moon, whatever its orbit may be, definitely
does not conform with Kepler's rules and hence poses a prima facie
counterexample undercutting this reasoning was bad enough. To concede
that the planetary trajectories are all incomprehensibly irregular is to invite
suspicions that the account of orbital motion in De Motu, while a pretty story,
is but one of any number of possible stories. Insofar as this was the very sort
of objection that Newton had raised against hypotheses in science generally,
he had good reason to look for some way of getting beyond just resigning
himself to the incomprehensibility of the motions.
When you think of the problem as one of finding the simultaneous,
coordinated adjustments that the six planets and the Sun have to make in
order to satisfy the global constraint imposed by the center of gravity
principle, the problem really does seem intractable (see Figure 8). But there
is another way of thinking of the problem: you can consider the motion of
�52
THE ST. JOHN'S REVIEW
\
.);i·'"'"
Fig. 8. From a Global Restraint to Individual Forces
"... In my last I made an allowance for the distance of Jupiter and Saturn one from
another diminishing their virtue in a duplicate proportion of the distance. But yet I
spake there but at random not knowing their virtues till I had your numbers for
Jupiter, by which I understand his virtue is less than I supposed. But I am still at a
loss for Saturn .... Now I am upon this subject I would gladly know the bottom of it
before I publish my papers .... " Newton to Flamsteed, 12 Jan 1685
any one planet under forces directed toward the other bodies. The degree to
which the planetary orbits approximate Kepler's rules shows that the other
forces have to be small in comparison to the centripetal force toward the
Sun. If these forces are small, however, the deviations from Keplerian motion
they produce must be small. Consequently, when considering the forces on
any one planet directed toward the others at any one moment, little error
will result from t.reating the other planets as in their Keplerian location at that
moment. Assuming all the forces are inverse-square with distance, this
approach will enable values of their magnitudes to be determined at least to
a high approximation. At a minimum, then, this approach should allow the
principal secondary force on each planet to be determined and the
circumstance in which it reaches a maximum, and from this, estimates of the
maximum deviation from the Keplerian ideal, and perhaps insights into the
pattern of the deviations, can be obtained for any one planet.
The clearest evidence that Newton was thinking this way at the end of
1684 comes from the correspondence with Flamsteed. One of Newton's
principal questions in initiating this correspondence was whether "you ever
observed Saturn to err considerably from Kepler's tables about the time of his
conjunction with Jupiter." Newton had clearly made a calculation of the
relative magnitudes of the Sun's and Jupiter's force on Saturn at their
conjunction and was looking for confirmation that the latter was large
�SMITI!
53
enough to have an observable effect. In response to Flamsteed's negative
response, Newton remarks,
In my last I made an allowance for the distance of Jupiter and Saturn one
from another diminishing their virtue in a duplicate proportion of the
distance. But yet I spake there but at random not knowing their virtues
till I had your numbers for Jupiter, by which I understand his virtue is
less than I supposed. But I am still at a loss for Saturn .... Now I am
upon this subject I would gladly know the bottom of it before I publish
my papers.
The remark about Saturn, which is in response to Flamsteed's having
been unable to observe the newly discovered satellites of Saturn, points to a
problem with this force approach. In contrast to the Earth and Jupiter,
Newton had no way of confirming that the centripetal force holding the one
fully established satellite of Saturn in orbit is inverse-square. Worse, the
absence of satellites around Mercuty, Venus, and Mars left him with no
effective way even to resolve the question of centripetal forces toward these
three, much less to assign values to their magnitudes. Is there some way
besides relying on [a'/P'] to get at their forces?
One way to attack this question is to revert to the two-body problem of
Jupiter and the Sun, asking what feature of each of these bodies their
respective [a~/P 1 l's are proportional to. The center of gravity principle
provides a second relationship that we have ignored so far: the product of
the weight and the distance of the two objects from their center of gravity
must balance one another. Applying this to the Jupiter-Sun case (see Figure
9) would then yield the conclusion that their [a3/P'l's are proportional to their
respective weights. The obvious problem with this, especially in the light of
···-- ....
',
/
/
,
r"
[a 3/P']"
/P']3
/P']
=_:__:_--"'-)
[a 3
[a 3/P']"
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[a 3
r,
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....
I
--
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'
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\
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'
r
I
. ··1
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'
�54
TilE ST. JOHN'S REVIEW
Newton's conclusion that gravity diminishes above the Earth's surface in an
inverse-square proportion, is that weight is a parochial quantity; thinking in
terms of what Jupiter and the Sun would weigh at the Earth's surface is not
going to accomplish much. This raises the question, what besides the
acceleration of gravity, which seems to be the same for all bodies, is weight
proportional to? The Cartesian answer, the quantity of solid marter in the
body, was not very promising, for how is one to determine how much solid
matter is in Saturn or Mars?
How Newton proceeded beyond the augmented version of De Motu
and the correspondence with Flamsteed is not so clear. The only document
we have before the first draft of Book 1 of the Principia is a fragment,
entitled "The Motion of Bodies in Regularly Yielding Mediums." It consists of
very worked-over drafts of some 18 definitions, 6 laws, and the two lemmas
from the augmented De Motu. This fragment, which opens with definitions of
absolute time, space, and motion, reflects very careful thought that Newton
must have been giving to concepts of motion and force, especially for
purposes of inferring forces from motions. Three of these definitions are
important for our purposes (see Document 6, Appendix). Quantity of motion
is now expressly defined as the product of velocity and the "quantity of the
body," which he says "is to be estimated from the bulk of corporeal matter
which is usually proportional to its gravity," indicating how a pendulum
experiment can serve this purpose. The term "corporeal matter" here
presumably contrasts with "aethereal matter." Next, the internal or innate
force of a body to preserve its state of motion or rest is said to be
"proportional to the quantity of the body." Newton appears to have thought
back through prior work by himself and others, most notably Huygens, on
motion under impact and conical pendulums in reaching these
pronouncements, and he is now equating the change of motion referred to
in the second law with the change in the product of velocity and the total
quantity of matter in the body. The definition of centripetal force is the usual
one, though notice that he is here still not identifying celestial force with
terrestrial gravity.
Finally (see Document 7, Appendix), the laws include a new one, "as
much as any body acts on another so much does it experience in reaction,"
the version of the third law of motion from his earlier work on impact. As
then, he does not expressly equate action with the product of quantity of
matter and change in velocity. When he restates this law in the first draft of
Book 1, he does expressly add, "By these actions the changes not in their
velocities but in their 'motions' (momenta) will come to be equal." In giving
�55
SMITil
Laws 3 and 4 of the augmented De Motu after this new law, he adds that
these three "mutually confirm each other."
On a separate page are two further definitions to be inserted into the
tract, forcing a renumbering of the original definitions. The first, Def.6, is for
density, which is defined as "the quantity or bulk of matter compared with
the quantity of space occupied." The second, Def.7, reads as follows:
By the heaviness of a body I understand the quantity or bulk of matter
moved apart from considerations of gravity as often as it is not a matter
of gravitating bodies. To be sure the heaviness of gravitating bodies is
proportional to their quantity of matter by which it can by analogy be
represented or designated. And the analogy can actually be inferred as
follows. The oscillations of two equal pendulums of the same weight are
counted and the bulk of the matter in each case will be inversely as the
number of oscillations made in the same time. But careful experiments
made on gold, silver, lead, glass, sand, common salt, water, lignite and
twill led always to the same number of oscillations. On account of this
analogy and Jacking a more convenient word I represent and designate
quantity of matter by heaviness, even in bodies in which there is no
question of gravity.
Newton shortly thereafter switched to the word "mass." The important
point here is that he has taken the trouble to carry out an experiment to
establish that weight is precisely proportional to quantity of matter, the
quantity entering into the second law and hence entering into the inference
from a change of motion to the magnitude of the force responsible for this
change.
Newton could have proceeded in either of two ways from this point to
the mathematical statement of the law of gravity. On the one hand, he could
have now concluded that the [a3/P'l's of Jupiter and the Sun are proportional
to their respective masses:
[a 3/P']1
W1
[a'/P']H
WH
Then the accelerative effect of the centripetal force on Jupiter toward the Sun
is proportional to the mass of the Sun and inversely proportional to the
square of the distance between the two:
MH
oc - - ,
r'
JH
�56
THE ST. JOHN'S REVIEW
and analogously the force on the Sun toward Jupiter is proportional to the
mass of Jupiter, etc. But then, in accord with the second law, the force on
each is proportional to the product of their masses and inversely
proportional to the square of the distance between them:
MH
Jrl
"" M-,F
M,
M __.:_, thatis
2
oc
Hf
Hcem
JH
JH
mM
'
foe--·
r
Alternatively, he could have first used the second law to conclude that
the force on each is proportional to its mass, the [a3/P'l of the other, and
inversely proportional to the square of the distance between them:
F
lcetl/
oc
M
[a 3/P']"
J
f2
JH
ocM
,p
Hce1ll
[a 3/P'] 1
H
•
f2
JH
He could have then invoked the third law to equate these two forces,
F
11cem
~F
lcen/
,
allowing him to conclude that their [a 3/P']'s are proportional to their
respective masses,
[a 3/P']1 ~ M1
[a'/P']"
M" '
again yielding, when generalized, the law of gravity,
mM
F"" - - ·
r'
The second of these two ways is the one he follows in the Principia,
while the first fits in with the attention he had given in early 1685 to the
question whether weight is exactly proportional to quantity of matter. Of
course, he may well have played these two ways off against one another,
using each to support the other.
Regardless, Newton would then have had the law for the inversesquare centripetal forces governing motions of the planets. By the same
reasoning as above, but now applied to the two-body problem of the Sun
and the Earth, he could conclude that the accelerative effect of the
centripetal force around the Earth is proportional to its mass, and hence the
centripetal force on the Moon must be proportional to the product of its and
the Earth's mass divided by the square of the distance between them. In
other words, the very same relationship that characterizes the centripetal
forces on the planets characterizes terrestrial gravity. But then no reason
remains for maintaining a verbal distinction between the centripetal forces on
�SMITII
57
the various celestial bodies and terrestrial gravity. That is, in all cases the
force in question is one in kind with terrestrial gravity, giving license to call
the governing relationship simply "the law of gravity." In saying this,
however, you need to understand that what we have so far is an account of
inverse-square celestial gravity, not inverse-square universal gravity. Many of
Newton's contemporaries who objected strenuously to universal gravity were
at least prepared, subject to empirical confirmation, to grant him his account
of inverse-square celestial gravity. Still remaining, then, in the discovery of
universal gravity is the step from the first eight theses to the last two.
Universal Gravity
Consider what the law of gravity is saying: if even so much as one tiny
particle of the Sun were removed from it, then the centripetal acceleration
Jupiter experiences toward it would be different, however slightly. This
suggests that the centripetal forces directed toward the Sun are somehow
composed out of forces directed toward the individual particles of matter
comprising it. Moreover, every particle of Jupiter must experience a
centripetal acceleration toward the Sun, and assuming they are interacting,
every particle of the Sun must experience a centripetal acceleration toward
Jupiter. It is a small step now to conjecture first that the mutual gravitational
force between Jupiter and the Sun is actually the resultant of mutual
gravitational forces between every pair of particles of matter comprising
these two bodies. But then, if other bodies experience centripetal forces
toward the Sun and Jupiter, the same conclusion extends to them, resulting
in the remarkable-and at the time exceedingly controversial--claim that the
law of graviry holds between every pair of particles of matter in the universe.
As was evident to everyone at the time, Newton included, this step involved
a much larger conjectural component than any of those preceding.
The last step-to the suggestion that the force of gravity is one of the
fundamental forces in nature (which occurs only in the Preface to the first
edition of the Principia, not in the text)--<:an be thought of as a corollary to
the universality of gravity. If indeed there are mutual gravitational forces
between every pair of particles of matter in the universe, then it is hard to
see how these forces can be resulting from the action of matter of some sort,
aethereal or otherwise, on these particles. The very universality of the force
of gravity is testament to its being more fundamental than other kinds of
force then known.
Such, then, is a step-by-step line of investigative reasoning that could
have led Newton from the first couple of theses about inverse-square
centripetal forces, which he had come to appreciate following the
�58
THE ST. JOHN'S REVIEW
correspondence with Hooke at the end of 1679, to the full complement of
theses comprising universal gravity, which he had command of a few months
into 1685.
In saying this, I do not want you to underestimate how many loose
ends there are in this extended line of reasoning. First of all, the nonKeplerian character of the lunar orbit still poses a potential counterexample
standing in the way of the increasingly wide generalizations Newton is
reaching with each new step. Also, the step from celestial to universal gravity
is assuming that the celestial forces can, as a mathematical fact, be composed
out of forces directed toward individual particles. Newton himself later said
that he was not confident that the law of gravity is anything more than just
approximate until he had proved that, in the case of spheres, the combined
action of all the individual particles is exactly the same as if all the mass
were concentrated at the center of the sphere-something that is not
generally true, but is so in the special case of inverse-square forces.
In addition to these are several empirical loose ends. Newton preferred
to have what he called, following Hooke, an experimentum crucis or crossroads experiment to select among alternative physical possibilities. The
trajectories of comets provided such a crossroads for the question of whether
the centripetal force directed toward the Sun acts on bodies other than the
planets; but he had yet to confirm this by successfully calculating actual
comet trajectories. The small correction to the ,;, power rule that he had
mentioned to Flamsteed provided a crossroads between Jupiter simply being
drawn toward the Sun and the two of them interacting with one another; and
similarly an appropriate perturbation in the motion of Saturn would
distinguish between pairwise interaction only, between the central and
orbiting bodies, on the one hand, and interaction among the planetary
bodies as well, on the other. On both of these Flamsteed had reported that
the data then available did not show the indicated effect. Finally, Newton
surely felt he needed an experimentum crucis separating universal gravity
from inverse-square celestial gravity. The one he came up with in the
Principia concerns the nonspherical shape of the Earth and the variation of
surface gravity with latitude. Even a century later, however, at the time
Laplace was writing his Celestial Mechanics, there were still residual
difficulties in the data on this question.
Newton had said to Flamsteed that he wanted to know the bottom of
the subject before he published his papers. In fact, however, he had not
really gotten to the bottom of it when he published the first edition of the
Principia in 1687, or even the third edition in 1726, the year before he died.
Empirical results that went a long way toward tying up the loose ends
�SMITH
59
continued to emerge throughout the 18th century, but as I just indicated
there were still residual difficulties in some areas at the beginning of the 19th
century. Even as late as 1875, when the American G. W. Hill was embarking
on his seminal researches in lunar theory, he remarked:
None of the values hitherto computed from theory agrees as closely as
this with the value derived from observation. The question then arises
whether the discrepancy should be attributed to the fault of not having
carried the approximation far enough, or is indicative of forces acting on
the moon which have not yet been considered.
And, of course, the theory of gravity in general relativity shows that we are
still in the process of gelling to the bottom of it. What Newton did was to see
with extraordinary clarity an evidential pathway along which remarkable
progress in getting toward the bottom of it might be possible.
Given Newton's deep distrust of conjecture, he was surely fully aware
of the loose ends when he published the Principia. Nevertheless, he
published it. This was more remarkable than you may realize. Here he was
in his mid-forties. He had carried out research in mathematics, optics, and
chemistry and alchemy for two decades, and had started several books, only
to abandon them unfinished or to limit the manuscripts to private circulation
among a few people. The only thing he had published was his "Light and
Colors" paper covering a tiny handful of the experiments in optics he had
conducted, plus his replies to correspondence elicited by this paper. With the
Principia, for the first time he finished and published a large-scale work.
Why the Principia, when nothing earlier? I submit that a large part of the
answer was the scope and majesty of the line of reasoning that I have laid
out in the present essay.
�60
TilE ST. JOHN'S REVIEW
Appendix
Documentl
De Motu Corporum in Gyrum
Definition 1. Centripetal force I call that by which a body is impelled or attracted
towards some point regarded as its center.
Definition 2. And the force of-that is, innate in-a body I call that by which it
endeavours to persist in its motion following a straight line.
Definition 3. While 'resistance' is that which is the property of a regularly impeding
medium.
Hypothesis 4. In the ensuing nine propositions the resistance is nil; thereafter it is
proportionally jointly to the speed of the body and to the density of the
medium.
Hypothesis 2. Every body by its innate force alone proceeds uniformly into infinity
following a straight line, unless it is impeded by something from
without.
Hypothesis 3. A body is carried in a given time by a combination of forces to the
place where it is borne by the separate forces acting successively in
equal times.
Hypothesis 4. The space which a body, urged by any centripetal force, describes at
the very beginning of its motions is in the doubled ratio of the time.
Document2
De Motu Corporum in Gyrum
Theorem 1. All orbiting bodies describe, by radii
drawn to their center, areas proportional to the times.
Theorem 2. Where the bodies orbit uniformly in
the circumferences of circles, the
centripetal forces are as the squares of
arcs simultaneously described, divided
by the radii of their circleS.
Corollary 5. If the squares of the periodic times are
as the cubes of the radii, the
centripetal forces are reciprocally as
the squares of the radii. And
conversely so.
Theorem 3. If a body P in orbiting around the
center S shall describe any curved line
APQ, and if the straight line PR
touches that curve in any point P and
to this tangent from any other point Q
of the curve there be drawn QR
Figures from DoGUments 3 and 4 reprinted by permission from Tbe Preliminary Manuscripts for
Isaac Newton's 1687Principia 1684-1685, (Cambridge University Press, 1989)
�61
SMITII
parallel to the distance SP, and if QT
be let fall perpendicular to this
distance SP: I assert that the
centripetal force is reciprocally as the
"solid" SP' x QT'/QR, provided that
the ultimate quantity of that solid
when the points P and Q come to
coincide is always taken.
Document3
De Motu Corpornm in Gyrnm
Problem 3. A body orbits in an ellipse: there is
required to find the law of
centripetal force tending to a focus
of the ellipse.
Scholium. The major planets orbit, therefore,
in ellipses having a focus at the
center of the Sun, and with their
radii drawn to the Sun describe
areas proportional to the times,
exactly as Kepler supposed.
Theorem 4. Supposing that the centripetal force
be reciprocally proportional to the
square of the distance from the
center, the squares of the periodic
times in ellipses are as the cubes of
their transverse axes.
Document4
De Motu Corpornm in Gyrnm
Scholium.
Hereby in the heavenly system from the
periodic times of the planets are
ascertained the proportions of the
transverse axes of their orbits. It will be
permissible to assume one axis: from that
the rest will be given. Once their axes are
given, however, the orbits will be
determined in this manner.
Problem 4. Supposing that the centripetal force be reciprocally proportional to the
square of the distance from its center, and with the quantity of the force
known, there is required the ellipse which a body shall describe when
Figures from Documents 4 and 5 reprinted by permission from Tbe Mathematical Papers of Isaac
Newton, 6. ed. D.T. Whiteside (Cambridge University Press, 1974)
�TilE ST. JOHN'S REVIEW
62
released from a given position with a given
speed following a given straight line.
Scholium. A bonus, indeed, of this problem, once it
is solved, is that we are now allowed to
define the orbits of comets, and thereby
their periods of revolution, and then to
ascertain from a comparison of their
orbital magnitude, eccentricities, aphelia,
inclinations to the ecliptic plane, and their
nodes whether the same comet returns
with some frequency to us.
[a'/P'ls
DocumentS
De Motu Spbaericornm Corpornm in Fluidis 4
Law 1.
Law 2.
Law 3.
Law 4.
Law 5.
Lemma
Lemma
A body always goes uniformly in a straight line by its innate force alone if
nothing impedes it.
A change of the state of motion or rest is proportional to the impressed
force and occurs along the straight line in which that force is impressed.
The relative motions of bodies contained in a given space are the same
whether that space is at rest or whether it moves perpetually and uniformly
in a straight line without circular motion.
The common center of gravity does not alter its state of motion or rest
through the mutual actions of bodies. This follows from Law 3.
The resistance of a medium is as the density of that medium and as the
spherical surface of the moving body and its velocity conjointly.
1. A body describes by the action of combined forces the diagonal of a
parallelogram in the same time as it would describe the sides by the action
of separate forces.
2. The space described by a body urged by a centripetal force at the
beginning of its motion is as the square of the time.
Document6
De Motu Corpornm in Mediis Regulariter Cedentibus'
Definition 11. The quantity of motion is that which arises from the velocity and
quantity of a body conjointly. Moreover, the quantity of a body is to be
estimated from the bulk of the corporeal matter which is usually
proportional to the gravity. The oscillations of two equal pendulums
with bodies of equal weight are counted, and the bulk of the matter in
both will be inversely as the number of oscillations made in the same
time.
Definition 12. The internal and innate force of a body is the power by which it
preserves in its state of rest or of moving uniformly in a straight line. It
is proportional to the quantity of the body, and is actually exercised
proportionally to the change of state, and in so far as it is exercised it
can be said to be the exercised force of the body, of which one kind is
the centrifugal force of rotating bodies.
�SMITI!
63
Definition 16. I call centripetal force that by which a body is impelled or drawn
towards a certain point regarded as its center. Of this kind is gravity
tending toward the center of the earth, magnetic force tending to the
center of the magnet, and the celestial force preventing the planets
from flying off in the tangents to their orbits.
Document7
De Motu Cotporum in Mediis Regulariter Cedentibus 6
Law 3. As much as any body acts on another so much does it experience in reaction.
Whatever presses or pulls another thing by this equally is pressed or pulled. If
a bladder full of air presses or carries another equal to itself both yield equally
inward. If a body impinging on another changes by its force the motion of the
other then its own motion (by reason of the equality of the mutual pressure)
will be changed by the same amourit by the force of the other. If a magnet
attracts iron it is itself equally attracted, and likewise in other cases. In fact this
law follows from Definitions 12 and 14 in so far as the force exerted by a
body to conserve its state is the same as the impressed force in the other body
to change the state of the first, and the change in the state of the first is
proportional to the first force and the second to the second force.
Law 4. The relative motion of bodies enclosed in a given space is the same whether
that space rests absolutely or moves perpetually and uniformly in a straight
line without circular motion. For example, the motions of objects in a ship are
the same whether the ship is at rest or moves uniformly in a straight line.
Law 5. The common center of gravity of bodies does not change its state of rest or
motion by reason of the mutual actions of the bodies. This law and the two
above mutually confirm each other.
Notes
1. Imre Lakatos, The Methodology of Scientific Research Programmes. Philosophical
Papers, Vol. 1 (Cambridge: Cambridge University Press, 1978) 201-222.
2. The Correspondence of Isaac Newton, 2 ed. H.W. Turnbull. (Cambridge: Cambridge
University Press, 1960)
3. The Mathematical Papers of Isaac Newton 6: 74-80 (abridged) and Preliminary
Manuscripts for Isaac Newton's Principia, 1684-85 (Cambridge: Cambridge
University Press, 1989) 12-27.
4. A. Rupert Hall and Marie Boas Hall, The Unpublished Scientific Papers of Isaac
Newton (Cambridge at the University Press, 1962) 267-68.
5. John Herivel, The Background to Newton's Principia (Oxford at the Clarendon
Press, 1965) 311.
6. Ibid. 312'13.
�·.~ REe-dbol~nhg. Newthonp's Exp~rime_nt fofr
1
sta 1s mg t e roportlona 1ty o
~ Mass and Weight
~
'
Curtis Wilson
Introduction
Newton was the first to draw an operationally verifiable distinction between
mass and weight. In the earliest manuscript in which he describes his
experimental confirmation of their proportionality (it is probably assignable
to the spring of 1685), he uses for mass the word pondus, which is Latin for
heaviness, but immediately says he means by it the bulk or quantity of
matter, independently of its weight. 1 Later he introduces the word inertia,
which is Latin for slothfulness, to characterize the quantity of matter. Kepler
had used this word in his Epitome astronomiae Copernicanae to describe the
tendency of a body to stay put; Newton instead means by it the resistance of
a body to changing its state of rest or uniform rectilinear motion. Just at the
time he was imagining and canying out the experiment that our title refers
to, Newton was in the process of formulating his second law of motion,
generally expressed now as F = Ma. For a given force F, the acceleration
produced is inversely as the mass M. This relation characterizes the action of
all motive forces, electrical, magnetic, gravitational, and so on.
But gravitational force, weight, is peculiar. A ball bearing and a boy's
marble of equal size and shape, weighed on a spring balance, have different
weights. But dropped from a height, they fall side by side, and reach the
ground simultaneously, or would do so in a vacuum. Here the weight is the
force in Newton's second law: W = Mg, where g is the acceleration of
gravity. For the accelerations of the two bodies to be the same, the weight
must be proportional to the mass.
Newton had noted that the same thing happens with the planets. By
Kepler's third planetary law, the accelerations of the planets toward the Sun
Curtis Wilson is Tutor Emeritus at St. John's College. In the planning and execution of the
experiment here described, the author was assisted by Howard Fisher and Adam Schulman of St.
John's College; the design and construction of the pendulums and other equipment was carried
out by Otto Friedrich and Alfred Toft of the laboratory shop; and Mark Daly, Superintendent of
Laboratories, assisted in both the planning and set-up of the experiment.
�WILSON
65
are inversely as the squares of their solar distances, independent of whatever
their masses may be. Thus a body placed at any given distance from the Sun
has an acceleration toward the Sun that is determined simply by its distance
from the Sun, and is independent of its mass.
This proportionality of weight to mass, fundamental in Newton's System
of the World, is also fundamental in Einstein's theory of General Relativity,
where it is referred to as the equivalence of gravitational and inertial mass.
The inertial mass is the M that appears in the above equation W - Mg, and
the gravitational mass is a factor to which W is proportional. Since 1890, tests
employing the torsion balance have repeatedly confirmed the equivalence,
with ever improving precision; the most recent confirmation (in 1971)
achieved a precision of one part in 9 x 10n.
The empirical confirmation of the proportionality of mass and weight
constitutes a pivotal step in Newton's argument for universal gravitation.
Newton describes the experiments he uses for this purpose at the beginning
of Proposition 6 of Book III of his Principia:
That the descent of all h.eavy bodies toward the Earth (allowing for the
unequal retardation arising from the very small resistance of the air) is
made in equal times, others for a long time have observed. The equality
of times can be observed most accurately by means of pendulums. I tried
the thing with gold, silver, lead, glass, sand, common salt, wood, water,
and wheat. I prepared two wooden boxes, round and equal. One I filled
with wood, and the same weight of gold I suspended (as exactly as I
could) in the center of oscillation of the other. The boxes, hanging by
equal threads of 11 feet, constituted pendulums altogether equal as to
weight, figure, and the resistance of the air. Placed side by side, they
went back and forth together, with equal oscillations, for a very long
time. Therefore (by Corollaries 1 and 6 of Proposition 24 of Book II) the
quantity of matter in the gold was to the quantity of matter in the wood
as the action of the motive virtue on all the gold to its action on all the
wood; that is, as the weight to the weight. And similarly in the other
cases. By these experiments, in bodies of the same weight, a difference
in mass of even less than the thousandth part of the whole could clearly
have been detected. [My translation]
Newton regarded these experiments as deeply significant. Earlier, for
instance, in a paper he sent to the Royal Society in December, 1675, he had
imagined gravity as due to an aether rushing into the Earth, and pressing
down each body it passed through, by impinging on the surfaces that the
internal parts of the body presented. Such a hypothesis was in accord with
the mechanical philosophy put forward by Descartes, Huygens, and others,
and for a time adopted by Newton himself. But by the spring of 1685,
�66
1BE ST. JOHN'S REVIEW
Newton had reached a new understanding. Gravity, for him, had become a
force acting on the very innards of matter so as to be proportional to a
body's inertia; it was an immechanical force, its cause unexplained. At the
same time, it had become quantitatively tractable-measurable-even in its
action on celestial bodies. The very masses of those bodies, millions of miles
away, had become measurable.
In the spring of 1998 the committee planning the conference on
Newton decided to seek an answer to the question: Can the experiment
described by Newton in the foregoing passage be carried out with the
precision he claims for it, using only such means as were available to him
(no stopwatches!)?
The Experimental Setup.
To replace Newton's round wooden boxes, we purchased plastic
containers, all of a size, such as are used for kitchen storage of flour and
sugar. For materials, in the trials reported here we chose three from Newton's
list of nine: sand, lead (Pb) in the form of lead shot, and glass in the form of
glass beads. (Originally we tried copper shot, but the shot was not uniform
in size, and the smaller pieces could sift down betwixt the others, so that the
center of gravity was not securely fixed.)
We wanted the bobs to have an inertia sufficient to keep them going
against the resistance of the air for a half hour or so. Filling one of the
containers with glass beads, we found we had some 7 kilograms. The next
problem was how to position equal weights of sand, lead shot, and glass
beads so that their centers of gravity would be similarly situated in their
respective containers. To our rescue came Alfred Toft, a retired engineer and
machinist, and Otto Friedrich, a retired carpenter, of the laboratory shop;
they have given many hours and much thought to our project. Their design
for the pendulum bobs is shown in Plates I and II. Each plastic container is
closed at top and bottom by two circular plywood plates. Within each
container are two additional circular plywood plates, placed symmetrically
from the ends, to position the material. The plates are held in position by
three carriage bolts supplied with nuts.
The pendulums were erected on the auditorium stage, where the
ceiling is about 5.9 meters from the floor. Each bob is supported by two
suspension wires, so as to prevent the bobs from rotating. As Plate II shows,
the suspension wires are not kinkless.
Now for a simple pendulum 5.8 meters long, a millimeter's difference
in vertical position of the center of gravity makes a difference in periO<;l that
is easily detectable, adding up in 25 minutes to about an eighth of a period,
�WILSON
67
or making a difference in the period of
each swing of one part in about 2500.
The lengths of the four suspension
wires were determined by stretching
them tightly between the same two
bolts, fixed in place; but we could not
be sure that they agreed to less than a
millimeter. Similarly, we could not
guarantee that the centers of gravity of
the three materials were similarly
situated in their containers to within
less than a millimeter. Newton left no
clue as to how he dealt with this
difficulty. To achieve the greatest
possible prectston, it appeared
important to avoid dependence on
length measurements.
Plate I. The lead (Pb) bob
The solution that we eventually
settled on was twofold. First, each
pendulum bob was made invertible,
with hooks at top and bottom, so that it
could be hung rightside up or upside
down. By averaging the period
determinations for a bob in these two
positions, we would obtain the period
for an ideal pendulum with center of
gravity in the center of figure exactly
midway between the endplates.
Secondly, we designated one bob,
hung on the downstage suspension, as
a standard clock; the periods of the
other two bobs, hung rightside up and
upside down on the upstage
suspension, could then be determined
Plate II. The lead and sand bobs
in comparison with the standard.
swinging together.
Because the clock bob was always
hung on one suspension, and the bobs
under test on the other, we could ignore the difference, whatever it is, in the
lengths of these two suspensions.
In making the bobs invertible, it was important to ensure that, when a
bob was upended, the contained material (glass beads, lead shot, or sand)
�68
THE ST. JOHN'S REVIEW
did not shift position. Messrs. Friedrich and Toft achieved this condition by
inserting a thin pad of styrofoam on top of the material, and compressing it
with the inner plywood plates. All three bobs were adjusted to the same
weight of 7150.5 gm, accurate to a tenth of a gram.
To set the pendulums (the standard and the one under test) in motion
simultaneously, we used a gate built by Messrs. Friedrich and Toft. The gate
was so placed that the swings would have an initial amplitude less than 10%.
Before a given run, we marked on the floor the shadows of the rest positions
of the two bobs, cast in each case by a light source directly above.
The Mathematics Involved
L
Figure 1.
Newton refers to
Corollaries 1 and 6 of
Proposition 24 of Book II
for the mathematics he requires in order to conclude,
from the equality of the
periods of two pendulums
of equal length with bobs of
equal weight, to the
proportionality of the
masses and weights of the
bobs. The essential argument is as follows.
Imagine two pendulums with suspensions of
nearly equal
length.
Consider these pendulums
when they have exactly the
same amplitude, and let this
amplitude be divided into
small equal segments (see
Fig.l). In each segment, the
driving force will be the
component of the weight W
acting along the bob's path;
if the distance of the bob
from the vertical line passing
through its rest position is x,
and the length of the
�69
WILSON
suspension is L, then this component is Wx/L. By Newton's second law, this
force will be proportional to the mass of the bob multiplied by its change of
speed in the segment considered divided by the time to traverse the
segment:
w~
L
oc
Mllv.
Llt
(1)
For corresponding segments in the paths of the two pendulums, x will
be exactly the same. The quantity t varies as the period T of each pendulum,
and the quantity /l,v varies inversely as T. We thus deduce from (1) that the
period squared varies as the length and the mass, and inversely as the
weight:
(2)
Suppose that our knowledge of the quantities T, L, M, W is uncertain or in
error by the quantities liT, oL, oM, and oW, which can be either positive or
negative. Now the uncertainty in a product or quotient, expressed as a
fraction of the whole, is the sum of the respective fractional uncertainties of
the individual factors. Thus the fractional uncertainty in T' is 2oT/f, and the
fractional uncertainty in L• MfW~• is the sum of SL/L, oM/M, and oW/W.
(These results can be obtained algebraically by substituting for each quantity
in (2) its supposed value augmented by the uncertainty, then ignoring
quantities that are the products of uncertainties.) Hence
(3)
Thus, the fraction 2ST/T is at most the sum of the terms on the
righthand side of (3). In our experiment, oW!W is 1 part in 71505, or about
.000014, and our procedure eliminates the more controllable causes of
variation of oL/L. Hence we can expect that
Z~T = 0~
+ .000014.
(4)
Thus if oM/M is .001, then ST/f will be (.001 + .000014)/2, or about
one part in 2000. Conversely, if pendulums whose weights are equal to
within .000014 of the whole weight agree in period to better than 1 part in
2000, we can infer that their masses are equal to within better than one part
in 1000.
�70
THE ST. JOHN'S REVIEW
Experimental Results
Mark Daly, Director of Laboratories, attached the suspension wires and
shadow-casting lights to the ceiling; he had also to let down the wires for
each experimental session, and take them up afterwards, since the stage was
used for other purposes between times. We held experimental sessions in
August and November, 1998, and in January and March, 1999. The idea of
making the bobs permanently invertible emerged only after the sessions in
March; it was carried out by Messrs. Toft and Friedrich during April and May.
Finally, on June 1, 1999, we determined the differences in period between
the redesigned bobs, as reported below.
In the first set of measurements the lead (Pb) bob was hung upright
from the downstage suspension, to serve as our clock. The task was then to
determine the difference between the periods of the downstage and upstage
pendulums, with the upstage pendulum carrying either the sand (Sa) or glass
(Gl) bob, hung in either upright or inverted position; this difference was to
be expressed as a fraction of the period of the Pb bob. Before beginning the
trials, we marked the rest position of each bob, indicated by one edge of the
shadow of the bob cast by the overhead light, on a sheet of paper taped to
the floor.
In each trial, the two bobs (the standard and the bob under test) were
released simultaneously from the gate, and the oscillations of the clock
pendulum were counted. When a measurable difference had built up
between the two pendulums, one observer barked out "Pip!" as the bob
under test crossed its rest position. (Originally, we had used "Now!" to mark
this moment; Fran(:ois De Gandt, hearing of it, observed that the French
"maintenant" would hardly serve. We then shifted to the more explosive
"Pip!" as our vocable marker.) The two other observers (one at floor level,
the other standing) determined where the standard bob was at this moment;
immediately· before and after this determination, the positions of maximum
amplitude of the standard bob were also determined. In all cases the upstage
pendulum was found to lag the downstage, standard pendulum.
Suppose (as in our first trial, with the sand bob in inverted position) the
lag in phase after 97 oscillations was x ~ 17.75 em of the standard bob's
swing, while the maximum amplitude of the swing just before this
measurement was 52.5 em, and just after, 49.0 em; we used the average of
these numbers as the amplitude (A) when x ~ 17.75 em. Then from the
fraction xJA we needed to deduce the fraction of the period T that it takes
the bob to move x units from its rest position (we will designate this fraction
as tiT).
�71
WILSON
The relation we need is deducible from equation (1). When the
amplitude of the pendulum's oscillation is small, as in our case (it was less
than So/o when this measurement was made), the solution is given by
X
·
--=s1n 21t•t ·
A
T
(5)
We shall not here undertake to derive (5) from (1), but merely remark that it
is an instance of the projection of uniform circular motion onto a diameter
of the circle. Imagine a circle of radius A, with a point moving uniformly
round it; imagine further that a perpendicular is dropped from this moving
point to a given diameter of the circle. At any moment t the projected point
will be x units from the midpoint of the diameter, in accordance with
equation (5). Thus, given measured values of x and A, equation (5) permits
us to solve for t/T.
The difference t has accumulated in the present case in a certain
number N of swings (97 in the particular measurement here used for
illustration). Then
(6)
where ~TIT is the fraction of the standard bob's period by which the test
bob's period exceeds the standard bob's period.
In the first determinations, the Sa bob was run twice in inverted
position and then twice in upright position against the Pb bob, and the
results of the two trials in each position were averaged, with the following
results ("i" stands for inverted, "u" for upright):
Expt. I
x(cm)
A( em)
N
l>T
1. Sa(i)
17.75
50.75
97
.000586T
2. Sa(i)
18.0
55.5
78
.000674T
.000630T
average
1. Sa(u)
5.5
54.5
81
.000199T
2. Sa(u)
6.5
50.75
94
.000217T
average
.000208T
The average of the two above averages is .000419T. This implies that
the period of the Sa bob, if its center of gravity were precisely at the
�1HE ST. JOHN'S REVIEW
72
midpoint of the cylindrical container, would be 1.000419 times the period of
our clock.
In a similar set of measurements using the Gl bob, we found:
Expt. II
x(cm)
A(em)
N
t.T
1. Gl(u)
14.0
55.25
79
.000516T
2. Gl(u)
18.0
54.25
84
.000641T
.000579T
average
1. Gl(i)
14.5
55.25
79
.000535T
2. Gl(i)
14.5
53.25
84
.000523T
.000529T
average
The average of the two averages in Experiment II is .000554T. Thus
if the Gl bob had its center of gravity midway within the cylinder, it would
swing with a period equal to 1.000554 times the standard period.
This result differs from the period we found for the (centered) sand
bob (namely l.000419T) by 0.000135, or about 14 parts per 100,000.
In the remaining experiments, we made the sand bob our standard,
identifying its period as T', and used it to compare the glass and lead (Pb)
bobs. For the glass bob we found:
Expt. III
x(cm)
A(em)
N
t.T
1. Gl(i)
18.5
55.25
82
.000663T'
2. Gl(i)
18.5
57.35
75
.000697T'
.000680T'
average
1. Gl(u)
17.0
54.5
80
.000631T'
2. Gl(u)
24
55
81
.000888T'
3. Gl(u)
21.5
55.5
80
.000791T'
4. Gl(u)
21.5
56.25
80
.000780T'
average
.000773T'
The average of the two averages in Expt. III is .000727T'. Thus if the
glass bob had its center of gravity midway within the cylinder, it would
�WILSON
73
swing with a period equal to 1.000727 times the period of the sand bob here
used as standard.
In the final experiment the period of the lead (Pb) bob was compared
with the sand bob as standard:
Expt. IV
x(cm)
A(cm)
N
t.T
1. Pb(u)
20.5
55.25
83
.000729T'
2. Pb(u)
21.0
56.0
81
.000755T'
.000742T'
average
1. Pb(i)
12.0
55.5
83
.000418T'
2. Pb(i)
10.0
56.25
79
.000360T'
average
.000389T'
The average of the two averages is .000566T'. Thus if the Pb bob had
its center of gravity midway within the cylinder, it would swing with a period
equal to 1.000565 times the standard period T'.
This result differs from that for the (centered) glass bob in Expt. III
(namely 1.000727T') by .000162, or by about 16 parts per 100,000.
Thus the periods of the ideal (centered) glass and sand bobs as
determined in Experiments I and II, and the periods of the ideal (centered)
glass and lead (Pb) bobs in Experiments III and IV, agree to within about 1
part in 6000. We can therefore conclude that the masses in these three bobs
agree to within about 1 part in 3000.
How do these results compare with the precision of our individual
trials? The greatest spread of values occurred in the four trials with the
upright glass bob in Experiment Ill. There we found the phase differences
per standard period to be .000631, .000888, .000791, .000780. The standard
deviation of these values is .000092, which suggests a limit of precision of 10
parts in 100,000. The overall performance of this apparatus (including timing
by our "pip" method) seems to be fairly consistent with this specific instance.
Notes
1. john Herivel, 7be Background to Newton's Principia (Oxford: Clarendon Press,
1965) 316-317.
2. Hans C. Ohanian, Gravitation and Spacetime(New York: W.W. Norton, 1976) 19.
�The First Six Propositions in Newton's
Argument for Universal Gravitation
William Harper
I'm going to take you through Propositions 1-6 of Book Ill of the Principia,
so I'm going to miss the high point of the whole argument, but I'll leave you
all set to get it from Dana Densmore in the essay following mine.
What I will do will illustrate the feature of Newton's methodology that I
claim makes it so interestingly superior to mere hypothetico-deductive
inference. According to hypothetico-deductive method you make up a
hypothesis and then try to find out whether or not the predictions that follow
from this hypothesis fit the data you can realize in experiment. What backs
up a hypothetico-deductive inference is the fit between the predictions that
follow from the assumed hypothesis and the empirical data. I will be
emphasizing the background assumptions supporting Newton's famous
inferences from phenomena, inferences that open the argument for universal
gravitation. For each of the central inferences-the inference from the arealaw or area-rule behavior for an orbit to the centripetal direction of the force
deflecting a body into that orbit; the inference from the harmonic law for a
system of orbits to the inverse-square relation among those forces; and the
inference from the stability of a single orbit, that is, from the absence of
apsidal precession in that orbit, to the inverse-square variation of the force
maintaining a body in that orbit-! will be stressing the important way in
which it is backed up by systematic dependencies that go beyond the
requirements of hypothetico-deductive inference.
In all three of these classic inferences from phenomena, the theorems
that Newton cites from Book I to back up the inference are always in a
group of theorems. If you look at the whole group of theorems, you'll see
that in every one of these cases, it's not just that a theorem would give you,
say, from the assumption of inverse-square variation the harmonic law for
the system of orbits, or from the assumption of the harmonic law the inversesquare variation. It will turn out that we are getting systematic dependencies
that go beyond just making these equivalent to each other. Thus, if the rule
William Harper is Professor of Philosophy at University of Western Ontario, London, Ontario.
�HARPER
75
relating periods to distances gives less than the 3/2 power, then the force
falls off less rapidly than in the inverse-square relation, and if the rule gives a
power higher than 3/2, then the force falls off more rapidly than in the
inverse-square relation. So you have systematic dependencies that are
making the phenomenal parameters measure corresponding values of the
theoretical parameters that are inferred. This, I will claim, illustrates a kind of
empirical success that informs Newton's applications of his rules of
reasoning-a success stronger than mere prediction. To realize this kind of
success, a theory has not only to predict the phenomena, but also to have
the parameters be accurately measured by those phenomena. And we'll see
in the classic application of the first two rules of reasoning-in the Moon-test
(the first part of a unification of the celestial domain with the terrestrial
domain)-we'll see that the appeal to these rules of reasoning is supported
by a striking example of this kind of empirical success. And then, when we
get to Proposition 6, I will go through the series of phenomena, all of which
are measuring proportionaliry of weight to mass. The first of these was
illustrated for you in the pendulum experiment just presented. And I will
argue that these are all phenomena giving agreeing measurements, bounding
toward zero a single universal parameter which I shall call 11. The
methodology that is used in this argument in the Principia is in fact the
methodology that informs an important part of the testing programs for
General Relativiry. Indeed, I will mention some later experiments that bound
this !1 toward zero far more precisely than the data available to Newton.
We're going to start with Jupiter's moons, then we'll go to the primary
planets, then to the Moon and the Moon-test, then to Proposition 5, and that
most wonderful Rule of Reasoning, the fourth rule of reasoning. And we'll
end with Proposition 6 and the third Rule of Reasoning. That is the order in
which the rules get applied in the Principia, and the order in which I'll be
presenting them.
To begin: here's the first proposition in the argument for universal
gravitation.
Proposition 1
The forces by which the circumjovial planets [or satellites of Jupiter] are
continually drawn away from rectilinear motions and are maintained in
their respective orbits are directed to the center of Jupiter and are
inversely as the squares of the distances of their places from that center.
The first part of the proposition is evident from Phen. 1 and from Prop. 2
or Prop. 3 of Book I, and the second part from Phen. 1 and from Corol. 6
to Prop. 4 of Book I.
The same is to be understood for the planets that are Saturn's
companions (or satellites) by Phen. 2.
�76
lHE ST. JOHN'S REVIEW
Ilke the proposition, the cited phenomenon (Pheno. 1) consists of two
parts. According to the first part, "The circumjovial planets, by radii drawn to
Jupiter's center, describe areas proportional to the times." Notice that the first
part of the proposition, the centripetal direction, follows from the first part of
the phenomenon, the area rule. The second part, "And their periodic times,
the fixed stars being at rest, are as the 3/2 power of their distances from that
center," is Kepler's harmonic law. This is the phenomenon from which
Newton is inferring the inverse-square part of the proposition. If you look at
Phen. 2, it's the same combination of the area law and the harmonic law for
Saturn's satellites.
Now we want to look at the argument, and so let's start with the first
part: the area law as a criterion for centripetal force. The proposition that is
referred to explicitly in Prop. 1 of Book III is Prop. 2 of Book I:
EveJY body that moves in some curved line described in a plane, and that
by a radius drawn to a point, either unmoving, or moving uniformly
forward with a rectilinear motion, describes areas around that point
proportional to the times, is urged by a centripetal force tending toward
that point.
If the body is moving in a plane, and by a radius drawn to a point is
sweeping out areas at a constant rate, then the force deflecting that body into
that orbit is directed right at the center.
Proposition 1 of Book I, the very first proposition of the Principia,
reads:
The areas by which bodies made to move in orbits described by radii
drawn to an unmoving center of force lie in unmoving planes and are
proportional to the times.
For an unmoving center, if the force is directed right at the center, then the
body will move in a plane, and will satisfy the area law with respect to radii
from that center. Now notice, Newtoh is talking about unmoved centers here.
His definitions and the scholium on space and time are designed to allow for
absolute rest. But look at Carol. 6 of Proposition 1:
All the same things hold by Coral. 5 of the Laws of Motion when the
planes in which the bodies are moving, together with those centers of
force which are situated in those planes, are not at rest but move
uniformly straight forward.
So Proposition 1 would work for any inertial center. And Carol. 5 of the
Laws of Motion tells us that the motions of bodies in a given space are the
same among themselves, whether the space is at rest, or moves forward in a
straight line with any uniform velocity. This is Galilean relativity.
�HARPER
77
But, the thing I want to focus on here is Corol. 1 to Prop. 2 of Book I:
In nonresisting spaces or mediums, if the areas are not proportional to
the times, the forces do not tend toward the point where the radii meet,
but deviate forward from it in the direction in which the motion takes
place if the description of areas is accelerated ...
So if the rate at which areas are being swept out is increasing, the
center of force is off center in the direction of motion.
But if the description of areas is retarded, the forces deviate backward, in
a direction contrary to that in which the motion takes place.
If the rate at which areas are being swept out is decreasing, then the force
that is deflecting the body is offcenter backwards.
We can sum up our main result as follows. Prop. 1 says that a centripetal force gives you a constant areal rate; Prop. 2 says that a constant
areal rate gives you a centripetal force. And Corol. 1 to Prop. 2 asserts that if
the areal rate is increasing, the force is directed off center in the direction of
motion, and if the areal rate is decreasing, it is directed off center against the
motion. So these results follow from the proposition: The areal rate is
constant if and only if the force is towards the center. If the areal rate is
increasing, the force is off center in the direction of the velocity, and if it is
decreasing, the force is off center backwards. Newton has much more than
just the equivalence between constancy of areal description and the
centripetal direction of the force; he has systematic dependencies, which
make a constant areal rate measure the centripetal direction of the force
maintaining a satellite in its orbit.
These propositions are proved on the assumption that the center can
be treated as inertial. But the application is to Jupiter and Jupiter's moons.
This system is subject to a tremendous centripetal acceleration, as the whole
system revolves around the Sun. So Newton in Prop. 3 extends the results of
Props. 1 and 2 with their corollaries to systems that are not in inertial motion:
Every body, that by a radius drawn to the center of a second body
moving in any way whatever, describes about that center areas that are
proportional to the times, is urged by a force compounded of the
centripetal force tending toward that second body, and of the whole
accelerative force by which that second body is moved.
The proof is based on Corol. 6 of the Laws of Motion, which is a much
bigger generalization than that of Corol. 5, which just extends results to
Galilee invariance.
If bodies are moving in any way with respect to one another, and are
urged by equal accelerative forces along parallel lines, they will all
�78
TI!E ST. JOHN'S REVIEW
continue to move with respect to one another as they would if they were
not acted on by those forces.
So, to the extent that the actions of the Sun on Jupiter and Jupiter's moons
can approximate equal and parallel accelerations, they can be ignored.
Newton gives a way of getting evidence that such things can be ignored. If,
he states in Corol. 2 of Prop. 3, the areas are very nearly proportional to the
times, the remaining forces will tend toward body T very nearly, and
conversely if, he adds in Corol. 3 of the same proposition, the forces tend
very nearly toward T the areas will be very nearly proportional to the times.
(In Prop. 3 the letter T stands for Terra, the Earth, and L for Luna, Earth's
Moon; but of course the proposition and its corollaries apply just as well to
Jupiter and its moons.) So the fact that the motions of Jupiter's moons very
closely approximate area-law motion carries the information that the
accelerative forces on Jupiter and on Jupiter's moons are very nearly equal
and parallel.
Now in stating the first part of the evidence for Phen. 1, Newton says
that the orbits of these planets [satellites] do not differ perceptibly from
circles concentric about Jupiter, and their motions in those circles are found
to be uniform. These are observational results. The fact that this holds shows
that you are not going to go very wrong in treating the Jupiter-system as
though it were inertial. We'll see how close the approximation to circular
orbits is in a moment.
Before we do, I want to talk about the second part, the harmonic law
as a phenomenon carrying information about the inverse-square relation
among the forces maintaining the satellites in their system of orbits. Here is
Corol. 6 of Prop. 4 of Book I:
If the periodic times are as the 3/2 power of the radii, and therefore the
velocities are inversely as the square roots of the radii, the centripetal
forces will be inversely as the squares of the radii, and conversely.
Therefore the harmonic law proportion is equivalent to the inversesquare relation of the accelerations in the various orbits.
But I want to pay even more attention to Corol. 7 of Prop. 4:
And universally, if the periodic time is as any power Rn of the radius R,
and therefore the velocity inversely as the power Rn·l of the radius, the
centripetal force will be inversely as the power Rln- 1 of the radius; and
conversely.
Having the periods vary as R" is equivalent to having the force vary as
R'"'". Corol. 6 immediately follows from this by plugging in 3/2 for n. We are
thus able to infer from the phenomenon-the harmonic law for Jupiter's
�79
HARPER
satellites-that Jupiter's force on the satellites is inverse-square. Now we also
have the systematic dependencies that tell us what happens in alternatives to
the phenomena. The index n could be higher than 3/2, in which case 1 - 2n
would be less than -2, so that the force would fall off more rapidly than in
the inverse-square proportion, while if n were less than 3/2 the forces would
fall off more slowly than in the inverse-square proportion. And so we have
alternative values of this phenomenal magnitude carrying information about
alternative power laws. These systematic dependencies make the harmonic
rule phenomenon (n ~ 3/2) for a system of orbits measure the inverse square
(-2) power rule for the centripetal forces maintaining bodies in those orbits.
These relations may be summarized as in Chart I (where "iff" stands for "if
and only if').
Chart 1:
Harmonic law for a system of orbits measures inverse-square law
Prop.4, Book I, Corals. 7 & 6 are proved for concentric circular orbits,
but can be extended to ellipses; t= period; R = radius of orbit;
Corol. 6 follows from Corol. 7 when n
Harmonic law
3/2.
Accelerative measure
phenomenon
t
<X
RVZ
iff
t
Corol.6
Corol.7
~
oc
R"
iff
of centripetal forces
fac oc Rl
fac
oc Rl·2n
Additional systematic dependencies follow from Corol.7.
Alternative phenomenon
n > 3/2
n < 3/2
iff
iff
Alternative power laws
(1-2n) < -2
(1-2n) > -2
We need to say something about the data available to Newton. First let
me give you, from the most recent Explanatory Supplement to the
Astronomical Almanac, the present-day values for the orbital eccentricities of
the four satellites of Jupiter; in each case these are the distance of Jupiter's
center from the center of the orbit, divided by the orbit's radius. The four
numbers are:
1. Io
0.004
2. Europa 0.009
3. Ganymede
4. Callisto
0.002
0.007
As you see, they are very small; thus the orbits are really close to
concentric circles.
�80
THE ST. JOHN'S REVIEW
Next I give you Newton's values for the periods of the satellites
(expressed in decimal form), compared with the periods given by the
Explanatory Supplement, with the differences.
Satellite
Newton's values
E.S.N.A. values
Differences
Io
1.769143518
1.769137786
+0.000005733
Europa
3.551180555
3.551181041
-0.000000485
Ganymede
7.154583333
7.15455296
+0.000030373
Callisto
16.688993055
16.6890184
-0.000025344
The biggest difference here is less than three seconds in a revolution.
Evidently these periods could be established rather precisely by the
techniques available in Newton's time.
Newton gives a table with determinations of the radii of the orbits of
the four satellites; the table below is the one he gives in the second and third
editions of the Principia, with observational results due to Borelli, Townly,
and Cassini. The numbers are in semi-diameters of Jupiter, with the largest
semi-diameter used as unit (Jupiter is visibly flattened). To the table I have
appended the corresponding present-day values from the Explanatory
Supplement, with the differences from Newton's numbers.
1
2
3
4
Borelli
5l/3
8%
14
241
/3
seffii-
Townly by micrometer
5.52
8.78
13.47
24.72
diameters
Cassini by telescope
5
8
13
23
of Jupiter
Cassini by eclipses
5113
9
14~!..
253/m
From the periodic times
5.667
9.017
14.384
25.299
From Explan. Suppl.
5.903
9.386
14.967
26.34
-.236
-.369
-.583
-1.041
Mean distances
From the observations of:
Differences in last two rows
In addition to the data in the table, Newton cites observations by
Pound, carried out in 1719 and 1720, using a 123-foot focal-length telescope,
the lens for which had been presented by Christiaan Huygens's brother
�81
HARPER
I
i"
'
l
'
..
Fig. 1.
Reprinted with permission from King, H.C. 1be History of the Telescope, (New York: Dover, 1979)
Constantin to the Royal Society a number of years before. Newton paid to
have erected a huge maypole in Wanstead Park; the lens was attached at the
top of the maypole, and the micrometer was fixed separately near the
ground. The lens was apparently controlled by wires (see Figure 1). Pound's
data are much more precise than the data given in the above table, as the
comparison shows. Of the earlier data, Cassini's data from eclipses are the
most precise.
Mean distances in
semidiameters
1
2
3
4
From Pound's data
5.965
9.494
15.141
26.63
From Explan. Suppl.
5.903
9.386
14.967
26.34
.062
.108
.174
.29
Differences
�82
THE ST. JOHN'S REVIEW
Now I want to look at the fit of the harmonic law to the data. Newton
compares them by just computing distances from the periods, using the
harmonic law. For that he uses a certain constant for the R3/P 2 value; it's the
one that he takes from Cassini's or Townly's estimate for Io, the first satellite.
Suppose, instead, we compute the standard deviation of the values of R3/P'
for the four satellites; this is given by
(J
-~~')
,
where L(x') is the sum of the squares of the deviations of the four values of
R3/P 2 from their mean value, and N is the number of items, 4 in our case. The
standard deviation for the average of the Borelli-Townly-Cassini values is
.079, that for the Pound data is .0003.
Another way to show how the harmonic law fits the data is to plot the
logarithm of the period against the logarithm of the distance measured in
semi-diameters of Jupiter. To have the periods be given by some power-law
of the distance is to have there be a straight line that fits the data when one
log is plotted against the other. To have the law be the three-halves power is
to have the slope of that line be 1.5 (see Figure 2). The first line, to the left,
has slope 1.5. Solid squares stand for Borelli's values, triangles for Townly's
values, diamonds for Cassini's values obtained with eclipses, stars for
Cassini's values obtained with the telescope, hollow squares for Pound's
values. You can see that even the earlier, cruder data in Newton's table fit
the harmonic law very well. In the case of Pound's values, the line with
slope 1.5 is just a line connecting his data-points; and you cannot see that it
is not straight. Also, note how close it is to the three-halves power law.
3.0
2.5
Slope 1.5
2.0
•
,,
Borelli
•
f
~
Townley
Cassin! E
Cassin! T
LO
-e-
Pound
~
0.5
'5
3.0
35
3.0
Fig. 2.
3.5
Log (Distance) (r I Rj}
�83
HARPER
So the empirical support for the harmonic law in the case of Jupiter's
moons was very strong in Newton's day. And the investigation that Newton
got Pound to do improved the precision considerably.
Prop. 2 parallels Prop. 1, but concerns the primary planets.
Proposition 2
The forces by which the primary planets are continually drawn away
from rectilinear motions and are maintained in their respective orbits are
directed to the Sun and are inversely as the squares of their distances
from its center.
The first part of the proposition is evident from Phen. 5 and from Prop. 2
of Book I, and the latter part from Phen. 4 and from Prop. 4 of the same
book. But this second part of the proposition is proved with the greatest
exactness from the fact that the aphelia are at rest. For the slightest
departure from the ratio of the square would (by Book I, Prop. 45, Coral.
1) necessarily result in a noticeable motion of the apsides in a single
revolution and an immense such motion in many revolutions.
Phen. 5 reads as follows:
The primary planets, by radii drawn to the Earth, describe areas in no
way proportional to the times but, by radii drawn to the Sun, traverse
areas proportional to the times.
There is a famous diagram that illustrates this wonderfully; it is from
Kepler's Astronomia Nova (see Figure 3). 1bis gives an Earth-centered view
of the motion of Mars starting in 1580 and ending in 1596. With respect to
the Earth, Mars's motion is sometimes progressive, sometimes ceases
altogether (is stationary), sometimes retrograding: it is not close to the area
law. But with respect to the Sun, the area law is very closely approximated.
Newton provides a separate phenomenon stating that the orbits of the
primary planets-here he does not include the Earth-encircle the Sun.
Phen. 3
The orbits of the five primary
and Saturn-encircle the Sun.
planets~Mercury,
Venus, Mars, Jupiter,
This phenomenon does not beg the question berween the Tychonic
and Copernican systems; it is compatible with either.
Here is Phen. 4:
The periodic times of the five primary planets and of either the Sun
around the Earth or the Earth around the Sun~the fixed stars being at
rest~are as the 3/2 power of their mean distances from the Sun.
�84
TilE ST. JOHN'S REVIEW
Let me go directly to the graph, plotting log [periods] against log
[distances] (see Figure 4). Here I am using as unit for the periods the period
that Newton cites for the Eatth, and as distance-unit the distance from the
Eatth to the Sun. In the graph the Earth appears exactly at the origin. You
again see a very nice straight line; we've got data from Kepler and data from
Boulliau.
But we do have a problem with the application of the harmonic law to
the planets: the proof that the inverse-square law follows from the harmonic
law is carried out for concentric circular orbits. For Jupiter's moons, the best
data at the time did not show any departure from uniform motion on
concentric circles. But for the planets there were appreciable eccentricities,
already known. Many commentators have suggested that there is a real
difficulty here: how do you apply a theorem that holds for circular orbits to
the non-circular orbits of the planets?
Fig. 3. This is the accurate depiction of the motions of the star Mars, which it
traversed from the year 1580 until 1596, on the assumption that the earth
stands still, as Ptolemy and Brahe would have it.
Reprinted with permission from Johannes Kepler, New Astronomy (Cambridge University Press,
9 )
�HARPER
85
4
i
"'
'8
3
--Stope 1.5
-~
!0.
a
D Kepler
2
0
~
t Boulliau
-1
2
3
Log (Distance) (AU)
-1
-2
Fig. 4.
The result for circular orbits, however, goes over directly into a result
for elliptical orbits. Figure 5 is derived from a diagram in Newton's De Motu
of November 1684; it shows an elliptical orbit, and a circular orbit with the
same center of force, and a radius equal to the semimajor axis of the ellipse.
Fig. 5.
�86
THE ST. JOHN'S REVIEW
At the point P the force maintaining the body in the circular orbit is identical
with the force maintaining the body in the elliptical orbit. The period in any
elliptical orbit having that same focus as center of force and having the same
semimajor axis will be equal to the period of the body moving in the circle.'
So the periods in the ellipse and the circle are the same.
Prop. 11 of Book I shows that the power law for the force that is
directed towards a focus of an elliptical orbit and maintains a body in that
orbit must be inverse-square. This result, however, is compatible with a
system of elliptical orbits about a common focus, where, even though for
each orbit, the force is inverse-square over the distances tested by this orbit,
yet the centripetal forces for the different orbits are not related to one
another inversely as the squares of the distances. Suppose that the periods
for those several elliptical orbits are as some power n of the semimajor axes.
This is equivalent to having the periods in the corresponding concentric
circular orbits as the power n of their radii (see Figure 6). Then we can apply
Coral. 7 of Prop. 4 Book 1: the centripetal forces maintaining bodies in those
corresponding concentric circular orbits will be as the 1-2n power of their
radii. But this, again, is equivalent to having the values of the forces at the
Fig. 6. A circle and corresponding ellipses of eccentricities .2, .4, .6, and .8,
respectively. Given the same inverse-square acceleration field, the periods of all these
elliptical orbits will be the same as the period of the circular orbit having its radius
equal to the common semi-major axes of the ellipses.
�HARPER
87
semi-major axis distances be as the 1-2n power of those semimajor axes.
Thus Carol. 7 of Prop. 4 carries over directly from circles to ellipses, however
eccentric they are.
The second proof of the second part of Prop. 2 of Book III appeals to
the precession theorem, Prop. 45 of Book I. What is orbital precession? If the
planet returns to aphelion after precisely 360° of motion, there is no orbital
precession. But if it returns to aphelion after moving through (360 + pY, that
would be to have p 0 of forward precession in an orbit. Carol. 1 of Prop. 45
of Book I tells us that if the centripetal force is as any power of the radius,
that power can be found from the motion of the apsides, and conversely. If
the whole angular motion with which the body returns to aphelion is to the
angular motion of one revolution, or 360°, as m to n, the force will be as the
power [(n'/m') - 3] of the radius. Now if you have a stable orbit with no
precession, p - 0 and n!m - 1, and that gives exactly the (-2) power. If you
have forward precession, p > 0 and n/m < 1, so that the exponent in the
power law is less than -2, and the centripetal force is falling off faster than an
inverse-square force. If you have backward precession, p < 0 and n!m > 1,
so that the exponent in the power law is greater than -2, and the centripetal
force is falling off more slowly than an inverse-square force. These relations
are summarized in Chart II.
Chart II
Corol. I, Prop. 45 of Book 1: Zero orbital precession measures inverse-square law for
distances explored by orbit. Precission p is expressed in degrees per revolution, x is
equal to 36° - 3. The sketch show positive precession, that is having the same
36O+p
direction as the orbital motion
~
Precession is p degrees
p > 0
p
0
p < 0
iff
iff
iff
iff
Power law is f~, oc Rx
X < -2
-2
X
X > -2
i
Newton proves this result for orbits with negligible eccentricity, but it can be
extended to orbits of arbitrary eccentricity. 2
So again we have systematic dependencies: absence of precession
carries the information that the force toward the central body is inversesquare. As Newton puts it in The System of the World, his earlier version of
Book III of the Principia,
�88
THE ST. JOHN'S REVIEW
But now, after innumerable revolutions, hardly any such motions have
been perceived in the orbits of the circumsolar planets. Some
astronomers affirm there is no such motion [e.g. Streete]; others reckon it
no greater than what may easily arise from causes hereafter to be
assigned, which is of no moment in the present question.
If you can account for all of the precession by perturbation (Newton
did not know how to do that), then for any planet for which this can be
done, the zero leftover precession measures inverse-square variation of the
centripetal force. The only planet for which such an outcome has failed has
been Mercury. In 1859 Le Verrier found that some 38 arcseconds per century
of the precession of Mercury's apse could not be accounted for on the basis
of Newton's inverse-square law, and in 1882 Simon Newcomb revised this
estimate upward to 43 arcseconds per century. The unaccounted for 43" per
century of precession would measure a -2.00000016 for the exponent of the
force.
We now turn to the Moon. Prop.3 of Book III reads:
The force by which the Moon is maintained in its orbit is directed toward
the Earth and is inversely as the square of the distances of its places from
the center of the Earth.
On average there is about 3°3' of precession per revolution. Thus, the
inference in Prop. 3 is made somewhat problematic by the known orbital
precession. Newton says that it can be neglected since it is caused by the
action of the Sun. We know that he never actually succeeded in showing that
the whole 3°3' of forward precession resulted from solar perturbation; it was
first demonstrated by Clairaut in a work published in 1752.
Newton uses the Moon-test (Prop. 4) not just to identify the force that
maintains the Moon in its orbit with terrestrial gravity, but as additional
evidence for the inverse-square proposition (Prop. 3). In the Moon-test he is
comparing two phenomena. The first of these is the length of a seconds
pendulum at the surface of the Earth as determined by Huygens in Paris.
From this value, Huygens showed that you could derive a value for the
distance fallen by a body in one second. Huygens's determination of this
distance was so stable over repetitions that his measured value for the onesecond-fall at Paris of 15.096 Paris feet could be trusted to about ±.01 Paris
feet. (The Paris foot, we note, is somewhat bigger than our English foot.)
The second phenomenon is the value of the Moon's centripetal
acceleration, calculated for the distance R of the Moon from the Earth's
center. Here Newton introduces a correction for the action of the Sun on the
Moon; the centripetal component of this action is on average subtractive
from the acceleration due to the Earth's action. Newton takes the subtractive
�HARPER
89
component to be 1/178.725 of the Earth's centripetal attraction, just enough
to cause the precession of 3°3' per revolution, in accordance with Carol. 2 of
Prop.45. In fact, as Newton knew, the centripetal component of the Sun's
action is only half as great as this.
If we take Newton's several estimates for the Moon's distance, and
introduce the correction, then, assuming the inverse-square law, we get an
incredible agreement with Huygens's value for the one-second distance of
fall at the Earth's surface. I want to claim that the outcome does not depend
on Newton's correction. If we do not apply that correction, and use all six of
Newton's cited lunar distances (59, 60, 60, 60 •;,, 60 '/,, 60 1 together with
h),
his cited circumference of the Earth (123,249,600 Paris feet) and lunar period
(39,343 seconds), we find
15.041 ± .429 Paris feet
as the measured value of the one-second fall at the surface of the Earth
corresponding to the centripetal acceleration in th<j lunar orbit. The
Huygens's value is well within these error bounds.
Thus the crude data for distances, yielding values for the Moon's
acceleration toward the Earth, back up Huygens's measurement of the
acceleration of gravity. They do this not by improving the precision of
Huygens's measurement, but by showing that big deviations from Huygens's
result are more improbable than they would be on Huygens's data alone.
The agreement in these measurements is an example of a kind of empirical
success that comes from having agreeing measurements of the same
parameter from two separate phenomena. The data from the two
phenomena reinforce each other, and increase what we might call the
resilience of the measurement, its resistance to large deviations.
Newton now appeals to his first two rules of philosophizing to infer
that the force maintaining the Moon in its orbit is terrestrial gravity.
According to Rule 1,
No more causes of natural things should be admitted than are both true
and sufficient to explain their phenomena.
And according to Rule 2,
Therefore, the causes assigned to natural effects of the same kind must
be, so far as possible, the same.
Newton's conclusion is then:
And therefore the force by which the Moon is kept in its orbit, in
descending from the Moon's orbit to the surface of the Earth, comes out
equal to the force of gravity here on Earth, and so (by Rule 1 and Rule 2)
is that very force which we generally call gravity.
�90
TilE ST. JOHN'S REVIEW
I want to claim that this application of these rules is not an appeal to a
general commitment to simplicity. The application is a very particular kind of
simplicity: two phenomena count as agreeing measurements of the same
parameter. And that result exhibits a kind of empirical success: the theory is
succeeding empirically by having its parameters be accurately measured by
the phenomena it purports to explain.
I now turn to Prop. 5:
The circumjovial planets [or moons of Jupiter] gravitate toward Jupiter,
the circumsaturnian planets [or satellites of Saturn] gravitate toward
Saturn, and the circumsolar [or primary] planets gravitate toward the Sun,
and by the force of their gravity they are always drawn back from
rectilinear motions and kept in curvilinear orbits.
Thus, according to Newton, the inverse-square centripetal forces directed to
Jupiter, Saturn, and the Sun are, all of them, gravitation. He goes on to
extend this result to the planets that do not have satellites,
for, doubtless, Venus, Mercury, and the rest, are bodies of the same sort
with Jupiter and Saturn.
The following scholium is offered in support of this generalization:
Scholium. Hitherto we have called "centripetal" that force by which
celestial bodies are kept in their orbits. It is now established that this
force is gravity, and therefore we shall call it gravity from now on. For
the cause of the centripetal force by which the Moon is kept in its orbit
ought to be extended to all planets, by Rules 1, 2, and 4.
Here is Rule 4:
In experimental philosophy, propositions gathered from phenomena by
induction should be considered either exactly or very nearly true
notwithstanding any contrary hypotheses, until yet other phenomena
make such propositions either more exact or liable to exceptions.
This rule should be followed so that arguments based on induction may
not be nullified by hypotheses.
To understand this rule we need to know what is the difference between a
legitimate rival and a mere hypothesis that can be dismissed and should
carry no weight. I want to suggest that a mere hypothesis is an alternative
proposal that does not realize the ideal of empirical success sufficiently to
count as a serious rival, where the ideal of empirical success is accurate
measurement of the parameters of the theory by the phenomena that the
theory explains.
�HARPER
91
Finally, I want to illustrate this ideal of empirical success at work in the
case of Prop. 6, which reads:
All bodies gravitate toward each of the planets, and at any given distance
from the center of any planet the weight of any body whatever toward
that planet is proportional to the quantity of matter which the body
contains.
Let Q - f/m be the ratio of the gravitational force on a body to its
inertial mass, so that the acceleration will be equal to Q. The question is
whether, at a given distance from the center of a planet, Q is the same for all
bodies.
The first thing we have here is the pendulum experiment, to
demonstrate the proportionality of mass to weight in terrestrial bodies. For
pairs of samples of nine different materials, used as the equal-weighted bobs
of equal-length pendulums, Newton claims to find the periods equal to a
precision of .001. The equality of the periods counts as a phenomenon
measuring the equality of the ratio of weight to mass for laboratory-sized
bodies near the surface of the Earth to a precision of .001.
Next we have the Moon-test, which argues that-the Moon's acceleration
toward the Earth is such that, if the Moon were brought down to the surface
of the Earth, it would (by the inverse-square law) have the same acceleration
as other terrestrial bodies. Consider Huygens's pendulum measurement as
giving a value Q 0 , and take differences /!, from that. The six estimates of the
Moon's distances used in the third edition yield a bound on /!,of .03.
If we turn to the harmonic law for Jupiter's moons, and use the inversesquare law to adjust their accelerations to the distance of one of the moons
from Jupiter's center, from the data in the table we get about the same
bound on /!,(namely .03). If we use Pound's data, the bound is enormously
· more precise.
From the harmonic law for the primary planets, adjusting all the
accelerations to the Earth-Sun distance, we find a bound on /!,of .004.
Newton then cites bounds on the polarizations of the orbits of Jupiter's
moons. If the Sun's gravitational force on a moon of Jupiter has to that
moon's mass a ratio different from the corresponding ratio for Jupiter, then
the orbit of that moon will be polarized either away from or toward the Sun.
Newton claims to limit A in this case by a calculation which he does not
describe for us; no one has found the actual details of his calculation. The
numbers here are due to Kenneth Nordved~ who showed that the correct
results go in the opposite direction from Newton's results, and are
considerably less sensitive than Newton claimed.' Applying Nordvedt's
calculation to the tolerances for distance estimates exhibited by the data in
�92
1HE ST. JOHN'S REVIEW
Newton's table we get a bound on 11 of .034; applying tolerances estimated
from comparing Pound's data with distances from the Explanatory Supplement
we get a bound of .004. We could do the same with Saturn's moons.
Our moon is a great example to use for this. Laplace, it turns out,
carried out a calculation in 1825 to limit 11 to a few parts in 10·'; his
calculation has recently 0997) been defended by Damour, a present-day
celestial mechanician. And today we can determine the Moon's distance by
lunar laser-ranging; by this method Dickey et al. have shown that 11 is less
than (2±5)x1Q-". Thus the results obtained from celestial objects are now in
the same ball park as, or even slightly better than the Moscow experiment,
which is the best result achieved by using torsion balances on laboratorysized objects. So you can see that the calculations on astronomical bodies
and the experiments on terrestrial bodies are going in lockstep, pinning
down what we call the weak equivalence principle.
Chart III (see next page) summarizes the chief results obtained for 11
from Newton onward. As before let Q - f/m. For any given center c toward
which any given bodies 1 and 2 gravitate, let 11(c,1,2) - Q1 - Q2, where the
fs involved in the g·s are inverse-square adjusted to the same distance from
c. Following Newton's third rule of philosophizing, we can interpret the
phenomena listed in Chart III as agreeing measurements bounding toward
zero a single universal parameter A representing differences between ratios
of passive gravitational to inertial mass that would be exhibited by any
bodies at any similar space-time locations.
All these phenomena count as agreeing measurements bounding
toward zero a single general parameter representing differences between
bodies of the ratios of their inertial masses to their weights (inverse-squareadjusted if necessary) toward planets.
In Coral. 2 to Prop. 6 Newton generates his last rule of reasoning, a
rule that is directed precisely at this kind of investigation and this kind of
empirical success. Coral. 2 reads:
All bodies universally that are on or near the Earth are heavy (or
gravitate) toward the Earth, and the weights of all bodies that are equally
distant from the center of the Earth are as the quantities of matter in
them. This is a quality of all bodies on which experiments can be
performed and therefore by Rule 3 is to be affirmed of all bodies
universally.
So all bodies, however far from the Earth, are gravitating toward it with
weight proportional to their masses. And here is Rule 3:
Those qualities of bodies that cannot be intended and remitted [that is,
qualities that cannot be increased and diminished] and that belong to all
�HARPER
93
bodies on which experiments can be made should be taken as qualities
of all bodies universally.
Rule 3 is explicitly applied to the terrestrial case, but it also applies more
generally to the constraints on A. Thus an ideal of empirical success of a
certain kind-agreeing accurate measurements of parameter values from
phenomena-is the centerpiece of the methodology that Newton's work
started. And it still guides science today-guides gravitation-theory
experiments that are testing General Relativity.
Chart III: Constraints on A
1. Pendulum
experiments
Newton 0685)
Bessel 0827)'
Eotvos 0922)'
Moscow 0972)'
I!.<
lQ·!l.
I!.<
.03
Newton"'"'
I!.<
Pound
A<
.03
.0007
I!.<
.004
I!.<
.034
.004
2. Moon test
3. Harmonic Law
1
Qupiter s moons)
4. Harmonic Law
(primaty planets)
5. Bounds on
Polarization
of satellite orbits
I!.< .001
A< 2 X }Q·S
I!.< 2 X 10-9
Jupiter's moons
Newton*"
Pound
A<
Our moon
Laplace 0825)"
Lunar laser ranging 0994)"'"'"'
0.54 X 10·'
/!.< (25) X 10"
A<
~wm, C.M., Theory and Experiment in Gravitational Physics (Cambridge: Cambridge University
Press, 2d revised edition, 1993), 27
•• Isaac Newton, Pbi/osopbie Natura/is Principia Matbematica, Phenomenon I, Book Ill.
...Damour, T. And Vokrouhlicky, D., "Equivalence principle and the Moon," Pbys. Rev. D, vol.S3,
no.8, 1996, 4198-4199
.... Dickey et al., "Lunar Laser Ranging: A Continuing Legacy of the Apollo Program," Science,
vol.265, 1994, 485.
Notes
1.]. Bruce Brackenridge, Tbe Key to Newton's Dynamics (Berkeley: University of
California Press, 1995) 119-23
2. Valluri, Wilson, Harper, journal for the History of Astronomy, 27 0997), 13-27.
3. Kenneth Nordvedt, "Testing Relativity with Laser Ranging to the Moon," Physical
Review 170 0968), 1186.
�94
THE ST. JOHN'S REVIEW
Cause and Hypothesis:
Newton's Speculation About the Cause
of Universal Gravitation
Dana Densmore
Introduction
Isaac Newton (1642-1727) demonstrates in Principia' that gravity operates
on and between all bodies, terrestrial and celestial. The gravitational force is
found to be directly proportional to the quantity of matter in what we might
call the "attracting" body and directly proportional to the quantity of matter
in what we might call the "attracted" body, as well as inversely as the square
of the distance between the bodies. Furthermore, when one body "attracts"
another, the geometrical center of force is found to be at the center of mass
of the "attracting" body (assuming spherical bodies). Finally, Newton shows
that every particle of one body "attracts" every particle of every other body.
These are the elements of universal gravitation.
These characteristics of the phenomenon, and the fact that Newton is
no more able than we to avoid speaking of "attraction," suggest that the
power of gravitation lies in the bodies themselves, that it is an innate.quality
of matter. Thus, when two bodies "attract each other," that is, are impelled
each toward the other, as Newton shows they are, it seems to be a mutual
action of particle upon particle.
Newton says he would would like to keep any assumptions of cause
out of Principia. But he must repeatedly apologize for using the language of
gravity-as-an-innate-property-of-matter, and repeatedly warn the reader that
he means no such assumption. And, indeed, one can hardly imagine how we
could speak about the behavior of bodies and their motions and the forces
acting on them without using the language of some mechanism.
Dana Densmore, a graduate of St. John's College, is a scholar and author of Newton's Principia,
Tbe Central AJ8ument. She is Chief Editor at Green LiOO Press.
�DENSMORE
95
But does he manage to keep the question open when it comes to the
actual demonstrations? As he develops his crucial propositions showing the
properties of universal gravitation in Book III, can we continue to keep the
open mind he advocates, or must we at some point abandon that bit of
principled naivete and settle on one particular hypothesis?
I'm going to invite you to think through with me whether Newton does
leave all these options open in his demonstrations by looking at the
culminating, or at least penultimate, proposition in the sequence that derives
what we now call universal gravitation. But first let's look more closely at
what range of mechanisms he seems to be allowing for, and also at what his
own speculations might have been.
Hypotheses on the Cause of Gravity
Tbe Range of Mechanisms Newton Mentions. What are the hypothetical
mechanisms Newton claims to keep open?
In the General Scholium which ends Principia (added in the Second
Edition, in 1713), Newton states that he does not "contrive hypotheses" about
the cause of gravity. By "contriving hypotheses" Newton means making up
something without a basis in the observed phenomena.
The reason for these properties of gravity, however, I have not yet been
able to deduce from the phenomena, and I do not contrive hypotheses.
(764)
We may infer from this that Newton found nothing in the phenomena
which suggested to him the mechanism of the operation of gravity; we can
infer that, could he have found such evidence, he would have put it forward
and built upon it.
In the Scholium following Book I Proposition 69, he spells out what
one may understand when he says "attraction":
By these propositions we are led by the hand to an analogy between
centripetal forces and the central bodies towards which those forces are
apt to be directed. For it is in conformity with reason that the forces
which are directed towards the bodies depend upon the nature and
magnitude of the same bodies, as it is in magnetic bodies. And whenever
instances of this sort occur, the attractions of the bodies are to be
estimated by assigning the appropriate forces to their individual particles
and gathering together the sums of the forces. (298)
This is a critical place: he has just demonstrated the proposition which
introduces the effect that the mass of the central body has on the quantity of
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THE ST. JOHN'S REVIEW
centripetal force. But lest we get the wrong idea about the word "attraction,"
which, in addition to his use just above in this Scholium, he has used
repeatedly in the proposition, he immediately continues:
The word "attraction" I here use generally for any attempt whatever of
bodies to approach one another, whether that attempt arise from the
action of the bodies (whether mutually seeking one another or of setting
each other in motion by emitted spirits), or whether it arises from the
action of the aether, or of air, or of any medium whatsoever (corporeal
or incorporeal) in any way pushing bodies floating in it towards each
other. (298)
We are being told, and not for the first time, to keep our minds open to
encompass all of these possibilities whenever Newton speaks about
attraction, or, as he is often careful enough to put it, when a body is
impelled toward another body or toward a center of force or forces. In the
commentary after Definition VIII, for example, he says:
I use the words "attraction," "impulse," or [words denoting] any tendency
whatever towards a center, indifferently and promiscuously for each
other, in considering these forces, not physically, but only
mathematically. Therefore the reader should beware of thinking that
through words of this kind I am anywhere defining a form or manner of
action, or a cause or a physical account, or that I am truly and physically
attributing forces to the centers (which are mathematical points), if
perchance I should say either that the centers attract, or that the forces
belong to the centers. ( 46)
He says that he is speaking of the centers and forces mathematically,
and the mechanisms behind them may be whatever they happen to be. The
forces may belong to the centers, or they niay belong to some other agency;
he does not define the form or manner of the action.
Here Newton gives us a range of mechanisms. The tendency of bodies
to approach each other may come from the actions of the bodies themselves.
This could be some innate property of matter that operates directly on other
matter as they mutually seek each other. We might call this category where
the tendency to approach comes from the action of the bodies themselves
the "occult power of matter," since some hidden virtue of the bodies is
operating. In this case the bodies are operating on each other at a distance.
It could also be, according to Newton in this Scholium, matter
operating on other matter indirectly, for example setting each other in
motion by emitted spirits. Here, a power of matter is operating indirectly
through physical, quasi-physical, or incorporeal agents.
Or perhaps the action does not originate in the matter but outside it. It
might be pushes from behind. One could imagine gremlins there pushing or,
�DENSMORE
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with Newton, pushes from particles of the medium in which both bodies
move. This medium also, Newton says, could be either corporeal or
incorporeaL
Newton's Own Speculations About the Cause of Gravity Before and Around
the Time of the First Publication of Principia. Let's look into Newton's
indications of his own ideas about the cause of gravity. This could be our
best evidence about what he was thinking when he wrote both the
disclaimers about cause which we find in Principia, and the proofs which do
or don't make assumptions about cause.
We find two interesting things. First, Newton repeatedly put forward
hypotheses that fell squarely into the mechanism of impulsion by direct
contact, including one offered not long before the publication of Principia
And second, he claimed to be adamantly opposed to any supposition of
physical action at a distance.
Newton's writings before Principia show his attempts to explain gravity
by the collision of material particles.
His student notebook from the 1660s shows a thoroughgoing
mechanistic philosophy following Descartes and Boyle. Every action can be
understood as motions of matter, of a matter which fills space. A material
aether provided the explanation for all apparent actions at a distance. His
explanation of gravity from around 1664 consisted of a descending wind of
aether particles flowing into the earth and pushing heavy bodies down
with it.
The matter causing gravity must pass through all the pores of a body ...
For it must descend very fa~t and swift as appears by the falling of bodies
and the great pressure toward the Earth . . . The stream descending will
grow thicker as it comes nearer the earth .... 2
In 1675 Newton sketched out another aether theory of gravitation, in
"Hypothesis on Light," a document transmitted to Henry Oldenburg for the
Royal Society of London. The mechanical action of the aether is basically the
same: a wind of the aether particles drives the heavy bodies down.
For if such an aetheriall Spirit may be condensed in fermenting or
burning bodies, the vast body of the Earth, wch may be every where to
the very center in perpetuall working, may continually condense so much
of this Spirit as to cause it .from above to descend with great celerity for a
supply. In wch descent it may beare downe with it the bodyes it
pervades with force proportionall to the superficies of all their parts it
acts upon .... 3
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TilE ST. JOHN'S REVIEW
In a letter to Robert Boyle three years later, Newton speculates on the
cause of gravity. The mechanism has changed, but it is still entirely material
and mechanical: now, instead of the pressure of a downward flow of aether
particles, he pictures a pressure arising from a density gradient and a
transition from finer to grosser particles.
And, first, I suppose that there is diffused through all space an aethereal
substance, capable of contraction and dilation, strongly elastic; and, in a
word, much like air in all respects, but far more subtle ... When two
bodies, moving toward one another, come nearer together, I suppose the
aether between them to grow rarer than before ....
I shall set down one conjecture more ... it is about the cause of gravity.
For this end I will suppose aether to consist of parts differing from one
another in subtility by indefinite degrees: that in the pores of bodies,
there is less of the grosser aether in proportion to the finer, than in open
spaces; and consequently, that in the great body of the earth there is
much less of the grosser aether, in proportion to the finer, than in the
regions of the air and that ... from the top of the air to the surface of the
earth, and again from the surface of the earth to the centre thereof, the
aether is insensibly finer and finer. Imagine, now, any body suspended in
the air, or lying on the earth; and the aether being, by the hypothesis,
grosser in the pores which are in the upper parts of the body, than in
those which are in the lower parts; and that grosser aether, being less apt
to be lodged in those pores, than the finer aether below; it will
endeavour to get out, and give way to the finer aether below, which
cannot be, without the bodies descending to make room above for it to
go out into. 4
This speculation was written eight years before the publication of Principia.
We may draw this conclusion from these proposed theories. Before
writing Principia, at least at some time before, Newton himself looked to a
mechanical explanation as being the natural and plausible and scientific one.
The material impact mechanism is thus one that must be taken seriously
among the options, one that he would want to leave open. However, he
seems to mean Principia to be more general, allowing for these hypotheses
and others as welL
Our second piece of evidence for Newton's views comes from letters
written to Richard Bentley five years after publication of Principia In these
letters Newton expressed horror that, when the first edition of the book was
published in 1687, some attributed to him the hypothesis that gravity is an
innate property of matter acting at a distance. We saw that he had difficulty
avoiding that language in Principia and often fell into it, albeit usually
followed sometime soon by a disclaimer.
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You sometimes speak of gravity as essential & inherent to matter: pray,
do not ascribe that notion to me; for ye cause of gravity is what I do not
pretend to know, & therefore would take more time to consider of it. 5
'Tis inconceivable, that inanimate brute matter, should (without ye
mediation of something else web is not material) operate upon & affect
other matter without mutual contact; as it must be if gravitation in the
sense of Epicurus be essential & inherent in it. And this is one reason
why I desired you would not ascribe innate gravity to me. That gravity
should be innate inherent & essential to matter so yet one body may act
upon another at a distance through a vacuum wthout the mediation of
any thing else by and through web their action and force may be
conveyed from one to another is to me so great an absurdity that I
believe no man who has in philosophical matters a competent faculty of
thinking can ever fall into it. Gravity must be caused by an agent acting
constantly according to certain laws, but whether this agent be material
or immaterial I have left to ye consideration of my readers. 6
Newton here asserts that there must be some agent acting directly on
the attracted body; he seems willing to leave open the possibility of that
agent being incorporeal; but he says that the action at a distance of a
gravitational power innate in the attracting body strikes him as absurd.
One result of this statement of his view for our understanding of
Principia is to warn us away from jumping to the conclusion that innateforce-action-at-a-distance was his secret opinion, a covert hypothesis, and
that his protestations about keeping the question open were mere rhetorical
smokescreen, falsely pretending an open-mindedness he did not in fact bring
to the work.
But perhaps he did want to leave that option open as well. His many
disclaimers in Principia about meaning by attraction whatever impels bodies
together suggest that he intends a completely general demonstration.
Now we're ready to look at Newton's development of universal
gravitation and see whether he really was able to carry it all the way through
without resorting to any hypotheses about cause, explicit or implicit.
Development of the Principle of Universal Gravitation
The first part of this job was done by William Harper (see the preceding
essay). He wasn't looking particularly at this matter of the mechanisms, but
in fact, through those propositions, through Proposition 6 of Book III, there
was no step that eliminated any of the mechanisms or assumed any. I am
satisfied with that, and probably for each of you to be satisfied with that you
would want to yourself work through those propositions with this questions
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TilE ST. JOHN'S REVIEW
in mind. I am going to start with Proposition 7, which is where things get
interesting in terms of looking at whether he assumed any mechanisms.
Proposition III.? asserts:
That gravity is given in bodies universally, and is proportional to the
quantity of matter in each.
We will look carefully at the steps of this proof.
III. 7 calls upon Proposition 69 of Book I.
Let's see what 1.69 requires and proves. The proposition postulates a
system of many bodies in which every body "pulls" every other body, but for
the purposes of the proof he is looking at two bodies in particular. So he
says that A attracts all the other bodies and B attracts all the other bodies. He
says "pulls." And the proposition speaks of an "accelerative attraction" of all
bodies toward each body. We are also given that the accelerations produced
by that pulling are inversely as the squares of the distances from the pulling
body. These are all things that we are given. They are hypothetical in the
sense that all the propositions in Books I and II are hypothetical. They are
not grounded in the phenomena of our world. They are part of the
mathematical toolbox that can be used to be applied when we have
phenomena and experimental observations from our world. So we can't
complain about any of these assumptions. They are explicitly assumptions.
What 1.69 proves is that, given these stated conditions, the absolute
forces of the pulling bodies will be to one another as are the bodies
themselves. That is, the forces will vary as the quantity of matter in the
attracting bodies.
III.6 had shown that the motive forces, or weight, varied as the quantity
of matter in the attracted bodies. 1.69 is setting up another dimension for us
by bringing in the quantity of matter in the attracting body.
We have already noted the Scholium following I.69, which goes on at
length in asserting that when Newton says "attraction" he doesn't mean to
suggest a particular mechanism. We want to continue reminding ourselves of
that:
The word "attraction" I here use generally for any attempt whatever of
bodies to approach one another, whether that attempt arise from the
action of the bodies (whether mutually seeking one another or of setting
each other in motion by emitted spirits), or whether it arises from the
action of the aether, or of air, or of any medium whatsoever (corporeal
or incorporeal) in any way pushing bodies floating in it towards each
other. (298)
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Therefore, despite the strong suggestion in the wording of the
proposition that the condition being set up here is one of attraction, one at
least of pulling, if not of full-fledged "occult power of matter," Newton is
claiming to be using this word only for the observed effect of tendency
towards the center of force or forces. (He starts out in Book I talking about
"forces"; in Proposition 1 he was referring to a "center of forces." As he goes
along he drops that plural and starts talking about "center of force," but I
think it's worth keeping in mind that, at least originally, he meant to make it
general enough that it was not necessarily a single force.)
The disclaimer about the mechanisms is not contradicted by the
condition also made explicit in !.69 that the "attractions" appear in some
sense mutual. It is simply given as one condition that A pulls B with an
accelerative force inversely proportional to the square of the distance to B,
and as another condition that B pulls A with an accelerative force inversely
proportional to the square of the distance to A. (The Scholium that
immediately follows makes it clear that "A pulls B" means only that B tends
toward A.)
No mechanism for this pulling is presented, and no claim suggested
that there is a mutuality inherent in the mechanism. We will return to this
difficult question of mutuality very soon, and consider what it is, or rather,
what different things mutuality means to us in different contexts.
For now, we continue carefully stepping through Newton's argument.
Having mentioned 1.69, we must hasten to remind ourselves that 1.69 is a
hypothetical proposition. Before we can use it we must prove that its
conditions hold in our world.
That is the first piece of work in III.7. We must prove that all bodies
attract all other bodies inversely as the square of the distance between them.
Step 1:
That all the planets are mutually heavy towards each other, we have now
already proved ....
The first condition for I.69 is that each body attracts all other bodies.
III.6 established that all planets gravitate towards each other: that is, if we are
to use "attraction" for "any attempt whatever of bodies to approach one
another," III.6 established that each body is attracted to all other bodies. If
each body is attracted to all, the bodies to which it is attracted must be
"attracting," whatever that might mean. Thus all bodies must be "attracting."
If all bodies are attracting, then A attracts B and B attracts A. We have
fulfilled the first condition of I.69.
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TilE ST. JOHN'S REVIEW
Step 2:
... as well as that gravity in any one of them, considered separately, is
inversely as the square of the distance of places from the center of the
planet.
The second condition for invoking !.69 is that these attractions be all
taking place according to an inverse square force law. We got that from
Book III Proposition 1 for Jupiter and Saturn with their respective moons,
from III.2 for the circumsolar planets, and from Ill. 3 for the moon to the
earth.
So putting these things together, we have established that the
accelerative force of gravity towards each one of the planets varies inversely
as the square of the distances from the centers of the "attracting" planets.
Thus we have the required force law for Jupiter in relation to its
moons, Saturn in relation to its moons, the primacy planets in relation to the
sun, and the earth in relation to its moon. By the third Rule of
Philosophizing,
The qualities of bodies ... upon which experiments can be carried out,
are to be taken as qualities of bodies universally.
This reasoning applies equally to the universality of heaviness in bodies
and to the universality of the inverse square force law. Thus we have met the
two conditions of 1.69.
We've gone from what we can observe about Jupiter and Saturn and
the circumsolar planets and what we deduced about the moon (with a little
more difficulty, because there's only one body there), and we're now saying
that it is true of all bodies, or any potential planet that we might have.
Step 3:
And the consequence of this (by Book I Prop. 69 and its corollaries) is
that gravity in all is proportional to the matter in the same bodies.
The first Corollary of !.69 extends the proposition to any number of
bodies. Applying the proposition, we can conclude that gravity tending
towards any planet is proportional to the matter contained by the body at the
center of force.
We still haven't assumed a mechanism, although we must now wonder
how, under the various hypotheses, the size of the central body might affect
the amount by which the "attracted" body is impelled. By some mechanisms,
you might imagine that it wouldn't make a difference. It seems that we might
be learning something about what mechanisms are possible by the fact that
the attracting power is proportional to the quantity of matter there.
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Step 4:
Further, since all the parts of any planet you please A are heavy towards
any planet you please B ....
This is established in III.6. We use this in Step 7.
Step 5:
... and the gravity of any part is to the gravity of the whole as the matter
of the part is to the matter of the whole ....
This is also established in III.6 and is used in Step 8.
Step 6:
... and to every action there is an equal reaction (by the Third Law of
Motion).·...
Assuming that the gravitation of A towards B and B towards A are
mutual actions in the sense of Law 3, "the mutual actions of two bodies upon
each other are always equal and directed to contrary parts" by that law.
This is a crucial step and we will return to it. Here in this step he has
only made a statement of the law, and he has stated it accurately.
Step 7:
... [therefore] the planet B will in turn gravitate towards all the parts of
the planet A ....
Now he's drawn some conclusion from Step 6. Hidden between Step 6
and Step 7, there's something lying in that bracketed [therefore]. We'll have
to return to it, but let's take it provisionally for now.
Step 4 told us that all parts of any planet A will gravitate towards any
other planet B. By Law 3 and Step 6 we conclude that any planet B will
gravitate towards all the parts of planet A.
Step 8:
. and its gravity towards any particular part will be to its gravity
towards the whole as the matter of the part to the matter of the whole.
By Step 5, the gravity of a part of planet A towards any other planet B
is to the gravity of the whole of A towards B as the matter of the part of A is
to the matter of the whole of A.
By Law 3, the gravity of the whole of B toward each of the parts of A is
equal and opposite to the gravity of each part of A towards the whole of B.
Therefore the gravity of B towards any part of A will be to B's gravity
towards the whole of A as the matter of A's part to the matter of A's whole.
That is what was to have been proved.
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1HE ST. JOHN'S REVIEW
We have used Law 3 to go from the quantity of matter in the attracted
body to the quantity of matter in the attracting body. But we did leave an
assumption hidden between Steps 6 and 7 of III. 7 to be looked into more
closely. That assumption was that the gravitation of A towards B and B
towards A are mutual actions in the sense of Law 3. To evaluate the
legitimacy of that assumption, we must look carefully at the Third Law.
Mutuality and Attraction
The Third Law says "That to an action there is always a contrary and equal
reaction; or, that the mutual actions of two bodies upon each other are
always equal and directed to contrary parts."
What does this mean? The law speaks about actions which are mutuali
it is these which are equal and directed to contrary parts. So we must look at
what we mean by mutuality.
Furthermore, we need to understand what attraction is, generally and in
the particular case that concerns us here, so as to assess whether this law
may be applied to gravitational attractions.
Mutuality. Let's start with mutuality.
In Book III Newton proves that every body is attracting every other
body (or, more generally expressed, every body is impelled toward every
other body; or, as he also puts it, there is a power of gravity towards every
body). Newton uses the word "mutual" for this situation: "all planets are
mutually heavy towards each other." A is attracted towards B, and B is
attracted towards A. There is a simultaneity, a symmetry, and a kind of
reciprocity.
Let us think what we mean by "mutual." It's important to get clear for
ourselves how we understand this word, in order to be alert to the way we
are interpreting it when we read the wording of proposition III. 7 and of the
third law of motion. Being clear about our common sense understanding of
the word is the first step to clarifying what may be a technical meaning for
Principia.
A series of thought experiments may help here.
I say, "I like you." You say, "The feeling is mutual." You mean, "I hear
that you like me, and it is also the case that I like you, and I recognize that
this means there is a symmetry. We like each other."
When things are mutual, they are reciprocal, but reciprocity can come
after the fact, and it can refer to only one side of the transaction. You do me
a favor, and I then feel an obligation (or a grateful desire) to do you a favor.
When I see an opportunity, I reciprocate and return the favor. The exchange
is then completed and we are mutual benefactors. But there may have been
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105
a cause and effect relationship. Perhaps I reciprocated because you did me
the favor.
This was not necessarily the case in our first mutual relation, in which I
said I liked you and you pronounced the feeling mutual. Let's assume that
this was not the case in which my liking you stimulates your gratitude or
sense of obligation to reciprocate. I liked you independently of anything you
felt. You similarly liked me not because I liked you, but because something
in your soul moved towards me. The mutual liking was simultaneous and the
one feeling was not caused by the other feeling. The relation is mutual,
reciprocal, simultaneous, symmetrical. But it is not mutual cause-and-effect.
Now let's say that I am attracted by the strawberries in the refrigerator.
As a consequence of this attraction, I move towards the refrigerator. My
moving towards the refrigerator is caused by the strawberries, but not by
anything the strawberries did. They may not even be in the refrigerator;
someone else might have gotten there first. My moving is caused by the
strawberries in the sense that something in my soul yearned towards them
and made me move in what I supposed to be their direction. This case is
clearly not mutual. The strawberries feel no inclination to move towards me;
in fact, should they be imagined to have any inclination, it would probably
be against being eaten.
But now suppose my husband and I see each other across the placita.
We each feel attracted to the other. We move towards each other as a
consequence of the attraction each feels inwardly. Nothing the other does
causes this movement; it is caused by our own inner inclinations. If one
paused, the other might still move under the influence of the attraction
which sprang up in his or her soul. But suppose neither pauses; we meet in
the middle. In common language, this is a mutual attraction and the coming
together is a mutual action.
Now suppose two billiard balls on a table are tapped by two agents
with sticks such that the balls approach each other in the middle of the table
and meet. Ball A has been impelled towards ball B, and ball B towards ball
A. The cause of the approach of one was different from the cause of the
approach of the other, and the motion of one did not cause the motion of
the other. But they approach each other in a simultaneous, symmetrical way.
In common language, we would say that they mutually approached.
Attraction. Now let's look more closely at what we mean by the word
"attraction."
We have seen that in Principia Newton stretches the term to cover any
tendency whatever of one body to move towards another. This of course is a
technical meaning which requires our constant attention to keep stretched.
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THE ST. JOHN'S REVIEW
Once we slacken the tension on the term, it snaps back to cover a much
smaller area. Let's look at its coverage in its relaxed state, that is, how we
mean the term in comrilon language.
Attraction is most comfortably understood in relation to besouled
entities. Its original sense is that of a movement of the soul towards
something the soul sees as good. We may be attracted to another soul, or to
a material thing, or to an idea. Any of those things can move us, that is,
cause a motion in our soul, and that motion in the soul may result in some
other motion, as when I move to the refrigerator because of the attraction I
feel for the strawberries.
It is rather by analogy that we speak of attraction among inanimate
things (such as "inanimate brute matter"). We see that the sttawberries seem
to attract with no mechanical mediation. By analogy, when we see no
mediating cause, we use the term attraction. So when the horse pulls a stone
using a rope, we don't call that attraction, we call it pulling. But if the horse
just stood there, and the stone approached, we might say the horse had
attracted the stone. Of course, we don't see that, but we do see iron filings
moving toward a loadstone with no visible means of pulling, and we call that
attraction.
Aristotle did not consider stones besouled, but by analogy with the
workings of souls, he said that stones had within themselves a tendency to
seek the center of the earth. They are not animate, and yet in a certain sense
they have a goal, and are heavy until they reach that goal. [They are active in
the sense of energein and not prattein; see Physics 255a28-30.l
Similarly, we can speak of attraction in the narrower sense as a possible
cause of gravity in Principia. In this narrower sense, it is a tendency of the
bodies, whether possessing souls or not (and I believe Newton did not think
of them as possessing souls, but that may be something for further
consideration), to seek to move towards other bodies, without being pushed
or pulled by a material mechanical mediating agent. This is the mechanism I
earlier called "occult power of matter."
Third Law of Motion. So let's now look at the 1bird Law of Motion and see
what it might mean in connection with attractions.
Law3
That to an action there is always a contrary and equal reaction; or, that
the mutual actions of two bodies upon each other are always equal and
directed to contrary parts.
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Commentary:
Whatever pushes or pulls something else is pushed or pulled by it to the
same degree. If one pushes a stone with a finger, his finger is also
pushed by the stone. If a horse pulls a stone tied to a rope, the horse will
also be equally pulled (so to speak) to the stone; for the rope, being
stretched in both directions, will by the same attempt to slacken itself
urge the horse towards the stone, and the stone towards the horse, and
will impede the progress of the one to the same degree that it promotes
the progress of the other. If some body, striking upon another body,
should change the latter's motion in any way by its own force, the same
body (because of the equality of the mutual pushing) will also in turn
undergo the same change in its own motion, in the contrary direction, by
the force of the other. These actions produce equal changes, not of
velocities, but of motions-that is, in bodies that are unhindered in any
other way. For changes in velocities made thus in opposite directions, are
inversely proportional to the bodies, because the motions are equally
changed. This law applies to attractions as well, as will be proven in the
next Scholium. (55-56)
This last sentence is the one we need to be concerned about. It was
added in the second edition.
The Third Law has two parts. The first is that every action has an equal
and opposite reaction. The second is that in all mutual actions of two bodies,
the two actions will be equal and directed to contrary parts.
One might think that the second is merely a restatement of the first, but
it will help to recognize them as independent. The first part applies to every
action. The second speaks about particular pairs of actions.
First, every physical action has an equal and opposite reaction. If I
walk, I push backwards against the earth, and as much motion as I gain
forward the earth gains backwards. "Motion," or Newton's "action" (motus)
is defined in Definition 2. "The quantity of motion is the measure of the
same, arising from the velocity and the quantity of matter conjointly."
Therefore my small mass gets a noticeable velocity forward, while the great
mass of the earth gets an imperceptible velocity backwards. These opposite
directions are the "contrary parts."
Or suppose we are walking not on the earth but on a small boat whose
bow we have just rowed up to the dock. As we walk to the bow of the boat,
the boat moves back away from the dock. In the water with a friend and a
rope, we see that when we pull on the rope, our friend starts moving
towards us, but we also start moving towards the friend. Not only are these
examples consistent with our experience, but in addition we can understand
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THE ST. JOHN'S REVIEW
them mechanically. The Third Law seems true, at least for actions which
involve mutual contact.
And we notice right away that in the Law's statement and in the bulk of
its commentary, all the descriptions and examples do involve mutual contact.
It is only the last sentence that suggests anything other than pushes and
pulls. We will come back to consideration of that tacked-on last sentence,
and the question of attractions as Third Law mutual actions, in a moment.
The second part of the Third Law says that the mutual actions of two
bodies upon each other are always equal and directed to contrary parts. Here
we are given two actions which are said to be mutual. In light of the first
part of the Law, we know what sort of actions Newton is talking about when
he says mutual: they are the actions which are each other's reactions. When I
walk, the mutual actions are my being propelled forward and the earth (or
the boat) being propelled backwards. When I pull you with the rope the two
actions are our actions in moving towards each other.
Nowhere does the Third Law state or suggest that any two actions we
might select in the world are each other's equal and opposite reactions.
Indeed, such an idea is absurd. Even where there is some formal symmetry,
we have explored cases where there is clearly no cause and effect action and
reaction.
Let's go back to our billiard table with the two wielders of cue sticks
hitting two balls towards each other. Although, when we see the two balls
approach each other, we would say in common speech that they are
mutually approaching, we cannot say that the balls' two actions in so
approaching are "mutual" in the sense of the second part of the Law. They
are approaching each other, they are even directed to contrary parts; but,
impelled by independent taps of the different sticks, they are unlikely to be
approaching with equal quantities of motion. Even if the quantities of motion
are equal, it is by accident, or because the tappers have agreed to tap
equally, not because the approaches are each other's reactions.
We see that the word "mutual" in Law 3 is a very specialized sense of
the term, defined by the law itself as those pairs of actions which result from
each other and are equal and opposite. Many pairs of actions which are
"mutual" in the common language sense are not mutual in the Law 3 sense.
Not only are the two approaching billiard balls not displaying mutual
actions in this sense, neither are my husband and I when we walk towards
each other across the placita, attracted by each other and each desiring a
meeting. Every action, by the first part of the Law, has an equal and opposite
reaction, and so do these. The actions of the billiard balls have produced
their equal and opposite reactions in the cue sticks and arms of the human
agents. My walking towards my husband has had its equal and opposite
�DENSMORE
109
reaction in a motion of the earth, as does his movement towards me. But our
approaches, however simultaneous and symmetrical, are not mutual in the
sense of the second half of Law 3.
Gravitation Attractions as Third Law Actions. Well, do we assent to the
proposition that gravitational attractions are 1bird Law actions and reactions?
Or, perhaps more to the point, what could Newton be picturing as a
mechanism for these "attractions" that would make them fall under the Third
Law along with the pushes and pulls resulting from material contact?
Our first thought might be that including gravitational attraction under
the Third Law suggests that Newton is thinking that gravitational impulsion is
indeed mechanical, that he is picturing the mechanism as somehow,
somewhere, a result of something pushing or pulling.
Well, perhaps it is. Perhaps the planets are being pushed from behind
towards the sun. And perhaps the sun is being pushed towards the planets.
But is this mutual in the sense of Law 3? Not a bit: it's our two billiard balls
again.
Since to every action there is an equal and opposite reaction, the
gremlin pushing the sun will rebound back with a change in its quantity of
motion equal to that by which the sun's motion changes. The gremlin
pushing the planet will also move back with a change in its motion equal to
that change of motion with which the planet moves towards the sun. But
there is no reason to expect that the motion of the planet towards the sun
will be equal to the motion of the sun towards the planet, any more than to
expect the two billiard balls to have the same quantity of motion after being
tapped.
Even if a causal chain were postulated that went directly from the
action behind the sun to the action behind the planet, it would still not make
the resulting approaches Third Law mutual actions. In fact, no interaction we
might trace among successive aether particles connecting the sun to the back
of the planet is going to make those final actions mutual.
It does seem that the pushes of gremlins, or the impact or differential
pressure of aether particles (such as the two hypotheses mentioned above
which he had put forward earlier, before writing Principia), it does seem
that any of those mechanisms are simply inconsistent with the inclusion of
an appeal to the Third Law in the propositions on gravity.
Conclusion
Let's now tum back to the steps of Book III Proposition 7.
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THE ST. JOHN'S REVIEW
The first step of Ill.? showed that all planets are mutually heavy in the
common language sense. The sixth step of III. 7 asserts that to every action
there is an equal reaction by the Third Law. These assertions are both
unexceptionable.
Step 7 says "[therefore] the planet B will in tum gravitate towards all
parts of planet A".
This conclusion seems to be expressed a bit carelessly, conflating the
two parts of the statement of the Third Law. It is not because every action
has an equal reaction that Step 7 follows, since each could have its reaction
elsewhere, as in recoil of its pusher-gremlin or in aether particles bouncing
back. Rather, Step 7 follows (if it does) because the mutual actions are each
other's reactions.
This has not actually been proved, but we see from its invocation that
Newton believes it to be true of the mutual actions of gravitational tendency.
The proposition depends in another way on the applicability of the
Third Law to gravitational attractions: it invokes Book I Prop. 69, which
includes an application of the Third Law in its own proof.
Furthermore, Newton asserted the applicability of the Third Law to
gravitational attractions in IlLS cor 1 as the justification for the gravitation of
the sun towards the planets. This is not part of the main line of the
argument, but adds to the evidence that he believed the Third Law to apply
to gravitational attractions.
This is yet further supported by his arguments in the Scholium after the
Laws of Motion, combined with the final sentence of his Law 3 commentary.
Newton believed that whatever caused gravity was a mutual action
between the two bodies in the sense of Law 3. His use of this assumption in
Step 7 of Ill. 7 is not a fluke or a slip.
And yet aether pressure, as well as, it seems, any other strictly
mechanical explanation, depends on third party actions such that the two
movements cannot be each other's mutual Law 3 reactions.
In fact, what about our "proofs" that gravitational attraction obeys the
Third Law from the Scholium after the Laws? They depend on the First Law
of Motion and Corollary 4 of the Laws (that the center of gravity of a
collection of bodies will remain at rest or move uniformly), and that corollary
explicitly states that "external actions and impediments are excluded." Only
then will the system remain at rest, that is, only then will the forces look
equal and opposite. (That is what those thought experiments in the Scholium
deal with, that a system will remain at rest and therefore, he concludes, the
forces must be equal and opposite.) This requires that, in talking about "the
actions of the bodies among themselves," only the two bodies may be
�DENSMORE
111
considered. No gremlins, no bungees, no Cartesian vortices, no Newtonian
aether pressure.
We seem compelled to conclude that, by the time of Principia, Newton
had completely rejected the possibility that there was a material aether
impelling the bodies together.
Furthermore, he could not, or at least did not, derive his principles of
universal gravitation allowing that, or any other mechanical intermediation,
as a possibility. He may have declined to offer an hypothesis about cause of
gravity, but he could not, or at least did not, leave the full range of options
open.
So I leave you with the question to ponder: What might Newton have
speculated could make a Third Law interaction between two bodies (or
particles) once mechanical intermediation and action at a distance have both
been ruled out?
Notes
1. Isaac Newton, Phi/osophice Natura/is Principia Mathematica, (first edition,
1687). References are to the third Latin edition (1726) with variant readings
edited by Alexandre Koyne and I. Bernard Cohen, (Harvard University
Press, 1972). I will refer to this work throughout as Principia. All English
translations are by William H. Donahue.
2. University Library, Cambridge, MS 3996, ff 97, 121. Published in Certain
Philosophical Questions: Newton's Trinity Notebook, ].E. McGuire and
Martin Tamny, (Cambridge University Press, 1983). Transcription of
Newton's notes entitled "Of gravity and levity," 362-365 and 426-427.
3. Newton to Oldenburg, 7 Dec 1675, Correspondence of Isaac Newton, Vol I,
365, (Cambridge University Press, 1960). Hereafter this will be cited as
Correspondence.
4. Letter to Boyle, 28 February 1678/9, Correspondence, Volume II, 288-295.
5. Newton to Bentley, 17 January 1692/3. Correspondence, Volume Ill.
6. Newton to Bentley, 17 January 1692/3. Correspondence, Volume III.
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THE ST. JOHN'S REVIEW
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Kraus, Pamela
Brann, Eva T. H.
Carey, James
Ruhm von Oppen, Beate
Sachs, Joe
Van Doren, John
Williamson, Robert B.
Zuckerman, Elliott
McShane, Anne
Wilson Curtis
Fisher, Howard
Sachs, Joe
Flaumenhaft, Harvey
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