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                  <text>&lt;p&gt;The Greenfield Library Image Collection houses over 5,000 photographs, postcards, drawings, and other graphic materials.  The images in the collection document the history, academic, and community life of St. John’s College. &lt;/p&gt;
To learn more about the Greenfield Library's archives use policy or to obtain high-resolution images, please see the &lt;strong&gt;&lt;a title="Image Collection Use Policy" href="http://www.sjc.edu/academic-programs/libraries/greenfield-library/policies/#photographicarchivepolicy" target="_blank" rel="noreferrer noopener"&gt;Library’s Image Collection Use Policy&lt;/a&gt;&lt;/strong&gt;.&lt;br /&gt;&lt;br /&gt;Click on &lt;strong&gt;&lt;a title="Photographic Archives" href="http://digitalarchives.sjc.edu/items/browse?collection=7"&gt;Items in the Image Collection—Annapolis Collection&lt;/a&gt;&lt;/strong&gt; to view and sort all items in the collection.</text>
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                <text>Dr. James L. Whiteside's class of 1878, St. John's College, Annapolis, Maryland</text>
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                <text>Photograph of the St. John's College class of 1878, taken circa 1875 or 1876. An inscription on the back of the photograph's mount reads: &#13;
&#13;
"Dr. J. L. Whiteside's class of 1878, St. John's College, Annapolis, Md. Back row: Wright, Gontrum, Martin, ?, Sprigg, (Judge) Stump, Harter (Pres. Del. Univ., Dover), Reed, ?, 2nd row: Krebs, J. L. Whiteside (roommates), Weagley, Leason, Batson, Andrews, Billingslea, Dashiel (in Navy), 4 men sitting: Comegys, (Judge) Harlan (Baltimore), Washington, Gorter, (From 1921 Pa. Ave. N.W.)"&#13;
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                <text>Reading the Silences of the Text: Space, Word, and Japanese Linked Poetry</text>
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                <text>Audio recording of a lecture given by Esperanza Ramirez-Christensen on September 27, 2024 as part of the Dean's Lecture &amp; Concert Series. The Dean's Office has provided this description of the event: "Renga is a hundred-verse sequence composed during a session by a group of 3 to 10 or more poets in the Japanese medieval period (12th-16th c.); it is the precursor of the kasen, the shorter 36-verse version popular among Basho and his group in the early modern period. This lecture examines the socio-historical and cultural conditions that made such a unique genre possible, including the rules of progression from verse 1 to 100, and casts light on the way of reading the poem in its own time. We will pay attention to the influence of Buddhist philosophy in the understanding of poetry's function and practice in premodern Japan while reading 'Broken Beneath Snow,' a renga composed by a group of samurai and monks under the guidance of the renowned poet-monk Shinkei in the winter of 1468 in Tokyo. We will also look at examples of US college student renga from my Great Books classes as one of the genre's possible translations into a Western social poetry practice using the Internet."</text>
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                    <text>Studying Phlogiston in the 21st Century
We usually think of science as a progressive activity, where “progressive” means that
today’s science is not just different from yesterday’s science, but that it is better.
According to this view, old science is generally wrong, and the older it is the more wrong
it is. Why then at St. John’s do we learn science through so many “wrong” ideas? The
answer is that our science is not better or worse according to the age of the texts we read,
but it is better or worse according to how we learn to think. The conception that old
science is irrelevant is rooted in misunderstandings of the word “science.”
What is science? I think that there are three ascending levels of understanding science,
but it is only at the third level that we would be doing science. The first two levels
resemble science, and they are popularly understood to be science, but they are only its
superficial manifestations.

1. Science as a collection of facts
At the first of these levels of understanding, science is a collection of facts. For example:
The combustion of methane with oxygen is an oxidation-reduction reaction which
involves the breaking and forming of covalent bonds. The reaction occurs as CH4 +
2O2 → CO2 + 2H2O. The first of the reaction products, CO2, has a double bond
between the carbon and each oxygen, and these are each one σ bond and one π
bond. Two of the carbon’s p-orbital electrons are used for the two π bonds.... (etc.).

Many high school students memorize something like this in 10th grade chemistry, and
most students of college science face similar collections of facts in their studies. If science
means knowing these kinds of facts, it seems strange to read Joseph Priestley’s 1775 paper
“Experiments and Observations on Different Kinds of Air.” In that paper Priestley
describes combustion by means of “phlogiston.” Even more curiously, phlogiston may
not be a thing but a “principle” and may be related to the alchemical element of fire.
Phlogiston also seems to have negative weight. From a modern perspective, Priestley's
terminology is alien, his ideas are strange, and his facts are certainly wrong.
But what do we mean by facts? “Having the facts” passes for scientific understanding,
and having the latest fact is the trump card (“But there’s a new study which shows…”).
We belong to one category of people (perhaps called “rational”) if we believe the current
set of facts, but we belong to another set of people (perhaps “tin-foil hat”) if we reject
some of them. But what meaning can the word “fact” have if it only distinguishes
orthodox opinions from heretical opinions? In 1775 Priestley’s work gave the world new
facts, and the alchemical element of fire (old orthodoxy) was giving way to phlogiston
(new orthodoxy). Are ‘facts’ what we find in today’s headlines and textbooks? They may
1

�be called facts, but we know that most of them will later be called ‘false.’ Science-related
headlines are often interesting because they tell us that yesterday’s (or last year’s or lastdecade’s) headlines were wrong. Tomorrow, and next year, and one hundred years from
now, there will be new headlines and new facts.

2. Science as unifying concepts and theories
At the second level of understanding, science is a collection of unifying concepts and
guiding theories. For example:
Atoms are composed of a dense nucleus of protons and neutrons surrounded by a
diffuse region of negatively charged electrons. The number of protons in the
nucleus is the fundamental determinant of an atom’s chemical properties, while the
electrons occupy specific orbitals and are responsible for the nature of chemical
bonds (etc.).

Broadly speaking, anything that is called a science has its own unifying theories and
concepts. At this level we recognize that there isn’t such a thing as a mere fact. Facts aren’t
simple or isolated things, but are actually understandings that are only meaningful in a
complex expression of relations. Only when we understand those relations and unifying
concepts does the “fact” have meaning.
And yet, the theories to which our facts belong are not the heart of science, either. To
understand this, consider what happens when we take existing theories as the framework
within which we ‘do’ science. We would presume that those can account for what we see,
and we may conclude that there is little science left to be done. In 1900 Lord Kelvin said
“There is nothing new to be discovered in physics now. All that remains is more and
more precise measurement.” Tremendous revolutions in physics (quantum mechanics
and relativity) were looming in 1900, but as far as Kelvin could see, everything was
accounted for within the existing frameworks.
When we take existing theories as our guide, it’s like searching inside a box of our own
construction and we can’t recognize its walls as self-imposed limitations. How can we
understand the results of an experiment if we judge them according to what we think
they ought to be? How can we see beyond a theory if the theory is the lens through which
we look?

3. Science as a living inquiry
Science is not a collection of facts, but it also isn’t the theories or the lenses through
which we look. Science is a way of thinking, a way that is grounded in and contingent
upon observation. Observation is the touchstone which allows us to challenge our own
thinking. This is the third level for understanding science: as a living inquiry. To study
2

�science is not to study facts, nor is it to learn to think theoretically. Doing science means
learning to observe and coming to understand how observations are the basis for creating,
organizing, and possibly rejecting our own principles and theories.
As Priestley did in 1775, we can marvel at a single burning candle, at its light, its heat,
at the disappearance of its wax. We might even try burning a candle in a closed vessel
and watch what happens, and perhaps measure or weigh it as well. From our own work
we could experience the complex and seemingly disparate events of ‘combustion,’ and
perhaps wonder how they might be related. Without this direct experience, criticizing
Priestley on the basis of his errors, or his shortcomings, or his unwarranted assumptions,
is being scientifically lazy. We are merely taking the authority of later geniuses to criticize
the insights of an earlier one.
Science really is inquiry. When we can see it this way, we see it not as arbitrary ideas
but as an expanding enterprise that only makes progress by overcoming its own myopia,
often in seemingly radical ways. It is too easy to be trapped by our own preconceptions.
In 1971, Carl Sagan said “I think it is a kind of intellectual chauvinism to assume that all
the laws of physics have been discovered by the year of our meeting. Had we held this
meeting twenty or forty years ago, we would perhaps have erroneously drawn the same
conclusion.” Albert Einstein, Lewis Thomas, and others have said similar things, and no
one who believes otherwise is poised to discover.
If we perform combustion “experiments” 1 while reading a Chemistry textbook we
might feel that our work is correct only if its results agree with the book. An accident, a
curious occurrence, a “wrong” answer would be considered distractions from the goal.
Students in most chemistry labs are graded on the quality of their results because the aim
of the class is to determine whether they can do careful work within predetermined
bounds. This is an important skill, but science is more than having the skill of a technician.
Science is learning how to inquire, and nothing undermines an inquiry more than
supposing that the answer is already known. A belief that the question is fixed in advance
and that someone already knows the ‘right’ answer might keep us from seeing the
wonders that appear before our eyes. If they interfere with our ability to see and to inquire,
today’s theories and facts are no less a tyrant than yesterday’s.
At St. John’s we observe and experiment for ourselves with combustion while we read
Priestley and Lavoisier. The questions come to us as open, not with pre-fabricated
answers lurking behind them. We read Lavoisier along with Dalton, Gay-Lussac, and
others, but we do not read them because they proved Priestley wrong. We read them
because, like them, we too have wrestled with phlogiston, and we too have seen
1

The scare quotes are here because it’s not an experiment if the expected outcome is known in advance. It might be
a demonstration, an illustration, training, a recipe, or a test, but its aim is not discovery.

3

�combustion, and we too have tried to observe and weigh, and we too have tried to seek
better ways of understanding what we have seen.
One further reason to read older works is that they better reveal scientific thinking,
while papers from the early to mid-20th century onwards often contain only “results” and
a narrow statement of hypothesis. Older papers, right or wrong, are a far better way to
see and engage with the thinking that characterizes science. If we study only the facts, we
will only ever know today’s news. If we study the best thinking and strive to do similarly
ourselves, we will be better prepared to evaluate today’s news and perhaps even create
tomorrow’s.

Eric Poppele
Tutor and Director of Laboratories
December, 2016 (minor revisions in 2024)

4

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Ryan Shea taught at Providence College for eight years, including courses in philosophy of science, environmental philosophy, and nature writing. His research weaves together ancient philosophical biology (especially Aristotle), the scientific revolution, phenomenology, German idealism, and Goethean qualitative science. His main project is to learn what it might look like to read the “book of nature” in a participatory, contemplative, phenomenological, and poetic fashion. &#13;
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Ryan Shea offers this description of his lecture: Edmund Husserl inaugurated the modern discipline of phenomenology with the rallying cry, "back to the 'things themselves'." And yet, when reading the works of phenomenologists, one might reasonably worry that we have bracketed the natural world, that we have left out precisely the "things themselves." This talk pursues two distinct, yet intertwined, questions. We begin with Socrates's central question (ti esti), "What is phenomenology?" This leads to our central concern, "How might we practice a phenomenology of nature?" The work of the poet, scientist, painter, and dramatist Johann Wolfgang von Goethe will serve as a guiding light.&#13;
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                    <text>Thursday
September 12,
2024

The St. John’s Collegian
A Gadfly Publication

From the
polity
Rendelman Rundown:
Intramural Draft

Hello, Readers! This year I will be keeping you up to
date on all things intramurals. So, with summer over
and the season opening, I’m here with a recap of the
intramural draft. On Sunday, August 25th, the
captains gathered in the conversation room to decide
the fate of the current sophomore class. I won’t go into
specifics about the order of individual drafts, but I’ll
provide my impression of each team’s final draft class.
With the first overall pick of each round, last season’s
last-place team, the Hustlers, came in with a plan… sort
of. The team managed to retain some of their major
players with Amha Worku and Auggie Bellanca, and
pulled off two incredible picks: 6’7” Reagan Carr, a
basketball and Netball legend, and B-team phenom
Josh Calonje-Quintero. What the Hustlers truly need
is attendance, so only time will tell how their draft truly
pans out. If I had to assign a letter grade, I’d give the
Hustlers a B+.
Next, the Spartans: their four fearless leaders managed
to keep their standout Irish soccer star, Charlie
Mahon, and filled some graduate-shaped holes in their
volleyball team, picking up Hannah Winn, a former
Hustler. They also grabbed Ella Jackey, another great
soccer player, and had a pair of athletes returning from
a year in Fe. All in all, the Spartans did a good job,
earning them an A.
The Guardians picked next and used their draft to
supply a critical need: female athletes. After retaining
standout basketball player Henry Strand, the
Guardians made some key fixes, drafting Sofia
Argones— a speedy B-team beast— and a handful of
other stellar female athletes. The team’s two male
captains did a great job evaluating and meeting the
needs of the team. For self-awareness, they earn an A,
but in general I give them a B.
The Greenwaves had a strong draft, keeping a lot of
their previous freshmen. There were very few notable
moves, other than picking up Nate Burke from the
Hustlers and Jackson Snyder from the Guardians. The
Waves always have incredible energy, and I think that
would have remained the case regardless of the draft,
but I’d give the draft itself a B-. Continued on page 2

Vol. II Issue I

Printed Thursdays in Annapolis

LETTER FROM THE (NEW) EDITOR
The Collegian Wants You
If you read the final article of last year’s Collegian, you
may wonder why you’re holding this issue in your
hands: our previous editor, the illustrious El’ad
Nichols-Kaufman, announced last spring that the
Collegian would not continue, since he was taking
over editorship of the Gadfly and would not have time
for both. Nevertheless, here I am, writing a new front
page article, and here you are, reading it. This blessed
circumstance is due to the fact that I offered to take
over the Collegian instead, alongside my co-editor
Jacob Sharpe (‘27). Huzzah!
Editing a student publication is a significant time
commitment. Why would we volunteer to do this? We
each have our reasons. Jacob has written his own letter
for you on page 2—go read it. In this article, I’d like to
tell you why I want to keep the Collegian alive—and,
more importantly, why I need your help.
Last year, I didn’t think I’d have time to write for
school publications at all. The Gadfly didn’t get a peep
from me, and I was a stranger to the Collegian for the
whole first semester. I had too many other obligations
to focus on extracurricular writing. But then
something changed: I started having opinions—opinions on topics concerning the polity. And I
wanted to express them.
Suddenly, I found myself writing out of necessity. I
had things to say, and I wanted them to be heard and
considered by my peers. The Collegian provided the
perfect platform. I wrote about bike paths, whooping
cough, and Kirk Garner. Other students wrote about
commencement speakers, Mellon art displays, and
how many angels can fit on the head of a pin. I realized
that we need the Collegian. We need it not only to keep
up with school events, but to keep sane by— to share
our weekly thoughts and questions and to hear what
our friends are thinking about too. It fills an important
niche by being the most up-to-date student
publication. More notably, I believe it strengthens our
community by providing a structured forum for
respectful and well-thought-out discourse. I couldn’t
let it slip into journalistic oblivion. But I can’t keep it
alive without you.
So, why should you write for the Collegian? I’ve got a
few good reasons. First, the great thing about it is that
it is short and speedy. (Not to be confused with “harsh
and hasty.” We still expect high-quality journalism.)

This Week in Seminar

Freshmen:
Thursday, September 12: Homer: Odyssey, XVII–XXIV
Monday, September 16: Plato, Meno
Sophomores:
Thursday, September 12: Bible, Psalms (selections)
Monday, September 16: Bible, Amos; Jonah; Isaiah 40-55
Juniors:
Thursday, September 12: Milton: Paradise Lost, I–III
Monday, September 16: Milton, Paradise Lost, IV; V; VI Argument only; VII Argument, 1–39; VIII
Seniors:
Thursday, September 12: Hegel: Phenomenology of Spirit, Unhappy Consciousness (207-230);
Reason (231-232)
Monday, September 16: Hegel, Phenomenology of Spirit, Conscience and The Beautiful Soul (632658)

Friday Night Lecture:

Professor Graham Harman, “Footnotes to Aristotle”
Page 1

You don’t need to spend an afternoon crafting a threepage essay or conducting an in-depth interview— that
sort of writing has its place in the Gadfly. The
Collegian provides a different outlet: You can take a
few short words to speak your mind, report on a recent
event, or exhort your classmates to actually read the
seminar reading (as Jackson Green did last year). Your
thoughts and news will be published the same week
that you submit them.
The Collegian is yours: not just to read, but to write.
Anything you want to say to the polity is publishable
in the Collegian (barring slander, gossip, and
misinformation, obviously). We will publish opposing
opinion pieces in the same issue, if you send them. We
will publish your thoughts on college traditions, Friday
night lectures, and intramural politics. We will publish
anyone from tenured tutors to first-year students to
college maintenance staff. We will publish your reports
on waltzes, SCI meetings, and reading groups, your
complaints about the math manual, your questions
about administration, your satire and your social
commentaries— if you send them to us.
You must send them.
I took over the Collegian this year because the polity
needs it. At the same time, it needs you to keep it
thinking and breathing and holding us together. Will
you help us bring it to life this year?
Submit your articles to us (sjca.collegian@gmail.com)
on Mondays before midnight (see page 2 for details).
You’ll be in print by Thursday. We can’t wait to hear
what you have to say.
Love,
Helen Wagner

Nichols-Kaufman (left) with Wagner and Sharpe at
the college activities fair. Photo on film by Dora Vecoli.

Upcoming Events:

Saturday, September 14:
Art Exhibit Opening: “Theater of Turmoil,”
12:30pm, Mitchell Gallery
Folk Life Contra Dance, 7-10pm, Great Hall
Sunday, September 15:
Pangea’s Chuseok: Korean Thanksgiving,
6pm, Boathouse
Monday, September 16:
Gadfly and Collegian II submission deadline
Tuesday, September 17:
Waltz Lessons, 8:30pm, Great Hall (weekly)
Wednesday, September 18:
Wellness Wednesday, 11am-1pm, Quad
Professor Maxwell Stearns: Constitution
Day Lecture, 7:30pm, Great Hall

�Thursday September 12, 2024

St. John’s Collegian

Vol. II. Issue I

Letter from the (Other new) Editor
Help!

Hello, Polity!
You are reading this second page of the Collegian,
whether by happenstance through it being set down
upon its face, through a literary ardor that demands
you read this delightfully resurrected publication in
its full, or per Helen Wagner’s request that you read
my accompanying letter. Whatever your reason, I’m
glad you’re here. That we now have a Collegian to
read is a fortunate turn of events! Despite other
parties’ evil efforts to consolidate the college’s news
within the oppressive monthly confines of the
Gadfly, Helen and I have wrested the paper from the
maw of death and now the Collegian lives to die
another day. Huzzah!
But why did we choose to save campus journalism?
Why did we deem the opinions of Johnnies worth
saving? Furthermore, wherever will we find all the
time that the press demands of us? Helen has her
reasons for her endeavors on the front page (or on the
back page, if this issue is face-down). Go read it, if you
haven’t already. I, however, have my own little spiel
of reasons, which begins with the story of how the
Collegian was endeared to me.
I spent most of last year’s first semester reading as I’ve
never before, and Plato wore heavy on my soul.
Seeking the perusal of reading material but fatigued
with philosophy, I was led to the readily available and
frequently updated Collegian, which always had
something entertaining and clever to occupy my
mind. However, my relationship with the Collegian

remained as a reader, and I was not moved to write for
it until I was baited with an absurd attack article that
struck at the heart and soul of this campus (cigarette
smoking in non-designated areas). Of course, I was
forced to take up arms.
Writing a creative piece for the first time in who
knows how long was refreshing; in the sense that I
could spend an hour or two crafting a relatively short
article, and that there was a dedicated place for it to
go! It made me understand such a place’s necessity.
For people who have more extensive, and longerplanned articles, the Gadfly is a wonderful
institution. For others with less, but just as valuable
content to share, it is still requisite that this campus
have a Collegian. To be without one would silence
the many Johnnie voices that have a little to say here
and there.
This paper, as the only weekly one on campus, lends
itself particularly well to short snippets of opinion,
fact, and whatever lies in between. I’m fond of the
bursts of whimsy and wit we get from the polity, as
well as the more journalistic pieces that showcase the
diverse interests and activities of this campus. That I
can read a piece on desire paths on our campus, a

Aphorism of the Week

“Time is a game played beautifully by children.”
-Heraclitus

panegyric exulting the virtues of actually reading
Huckleberry Finn, or a spirited debate over cycling
infrastructure on a given Thursday—all studentcontributed and with unique impassioned voices, is
miraculous. The articles I’ve read in the past year have
confirmed that the Collegian is the home for anything
and everything you, the reader, have to contribute. It
builds community, gives a voice to all, and acts as an
outlet in the midst of a busy and stressful life. All these
joys of published glory are yours, if you choose to
share in them. And you should choose to share in
them! The only requirement is that you actually
contribute it to us. Email works, fax machine,
passenger pigeon (save their extinction).
So, please, find it within yourself to contribute
something unique and yours to our lovely paper.
Unless I steal your annual essay out of the Dean’s
Office, I won’t otherwise get this opportunity from
many of you. In this coming year, I look forward to
this Collegian being a blank slate for whatever you
have to give us. It can be the means of recording the
day-to-day happenings at this campus, a creative
outlet for ye who tire of thine manuscripts pertaining
only to the great books, et cetera.
If you want to write about the Metaphysics, though,
that’s okay too. Just make it pretty cool.
Submit your articles to sjca.collegian@gmail.com,
and you’ll see it in glorious Garamonded print on
Thursday. Welcome back!
Jacob Sharpe

St. John’s on Tv
During opening week, a South Korean film crew
from EBS (the Korean version of PBS) shot different
scenes around campus, including convocation. On
Saturday morning, a group of students assembled in
the Barr-Buchannan-Center to participate in mock
discussions: a seminar on the Meno led by Mr.
Haflidson and Ms. Langston and a math tutorial on
Galileo’s Two New Sciences. Among the participants
were Ms. Lee (’26) and Ms. Kim (’25). Ms. Lee
dreams of becoming a documentary director herself,
so she helped the crew with interviewing students and
faculty. “The concept of reading books and then
discussing them is very new to most of Korean
education,” she shared. Ms. Kim added: “Ten years
ago, there was another kind of documentary [about
St. John’s]. But at this time, we are focusing more on
how this education happens…: how we read books,
how we talk about [them] and why it is important.
And I think it is a really great opportunity not only
for South Korea but also for whatever country that
would watch.”
One of the members of the film crew, Mr. Hong,
explained: “The Korean government realized that
there is a social issue in South Korea, which is people
don't read. I think it's kind of a world worldwide
problem. People don't read these days... Especially in
South Korea, the country of Samsung, LG… So, the
Korean Government has decided to make a
documentary film to encourage people to read.”
There will be five episodes about the benefits of
reading, including the relationship between cognitive
ability and reading and reading in the AI era. While in
the US, they will also travel to New York to interview
BVG member and alumna Carla Echevarria (‘96) at
Google Gemini. Mr. Hong shared his impression that

the program at St. John’s is very “tough,” but is
“totally worth it.” Ms. Langston expressed her hope
for more collaboration between Korean institutions
and St. John’s. Much of this is driven by Dr. Yongwha
Lee (AGI01), professor at Incheon National
University and founder of the Great Books Center
there. Ms. Langston’s hopes for the documentary are
not limited to more visibility in Korea but extent to
the US as well. A technologically advanced country
embracing reading again is “an important story for
people here to hear as well,… I'm really hopeful that
this is going to be a fantastic way to let more people
see who we are and see the value of [this kind of
education].”
The documentary will air in the fourth quarter of
2024.
Helen Felbek

Intramural Article, cont’d

Finally, the reigning champs with the last pick of
each round, the Druids. The Druids did a great job:
they kept Ella Hedman, an incredibly talented
athlete across the board, and picked up a few B-teamers, nabbing Henry Redfield and Celina Lee who are
both key contributors. They had very little to be
upset about—a solid draft, another B+.
These grades are just based on my own impressions,
and soon the season will be in full swing. Only time
will tell regarding the impact of the draft.
Lainey Rendelman

Page 2

About the St.
John’s
Collegian
The St. John’s Collegian is the weekly newspaper of
St. John’s College Annapolis. We work to bring
quick and timely coverage of important events going
on, to help develop a more informed student body. If
you’re searching for more in-depth investigations and
reporting, as well as essays, art and culture, check out
the Gadfly, our affiliated publication, which is
published once every three weeks.
Want to submit an article? We always need more
writers, whether for opinion or reporting!
Submissions for news articles should be between 400600 words, while opinion should be kept short at 350
words. Just email sjca.collegian@gmail.com with
your article, and we will work to get it in print!
Longer form articles and more in-depth exploration
of ideas should go to the Gadfly, which accepts
submissions at gadfly.office@sjc.edu.
Contributors for this issue:
Helen Wagner, writer and editor
Jacob Sharpe, writer and editor
Helen Felbek, writer
Lainey Rendelman, writer
Liza Love, cartoonist
Dora Vecoli, photographer
Your new editors, Helen and
Jacob. Original cartoon by
Liza Love (‘27).

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                    <text>niE COLLEGIAN
THE STUDENT WEEKLY OF ST.JOHN’S COLLEGE

ANNAPOLIS, MARYLAND

lA ORANA MARIA
PAUL GAUGUIN

76

13 DEC. 1971

�PAGE TWO
Tuesday, December 7

To the Editor:
I read the article by Mr Matters,
whom 1 unfortunately neither teach
nor know, with that rising, irri­
table interest which is produced by
aerious arguments seriously pro­
posed with which one finds onself
in almost total disagreement.
Mr Hattera must forgive ma in
at least one respect: in order to
do justice to his reasoning I
should have written my answer
during the Christmas vacation,
|&gt;ut by nest year the readers of
Tia
would have forgotten
what his issues werea As it is,
although what I have to say la
not sufficiently weII-composed,,
I feel myself entitled to refer
to his article and to answer his
arguments in the order in which
they appear.
I. Mr Hagfcara says, rightly, X
think, that those who come here,
students and tutors, accept a
theory of learning, but he is,
in ray experience, not right in
saying that they accept it “In
toto“ or do not question It, To
accept a way of life “in principle”,
that is, to live in consonance
with it and faithfully to it,
18 far from swallowing it “as
a whole” plthout asking questions
about it. The fact that the
program has Indeed changed little
since its institution is not
proof that It has not been thought
about but that it has. In prin­
ciple, commended Itself to the
participants. “To question”,
it seems to me, ought to mean
not to doubt, or to oppose, but
to wish to understand--In full
engagement. I do not think I
can ask questions concerning what
I do not accept as having worth,
IX, Mr Mattera chooses, again
rightly, 1 think, the absence
of the study of history as the
most telling negative characteris­
tic of the college. He claims,
- explicitly or implicitly, that

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ANNAPOLIS

26a6eG2

TUE-^ED’SATi 10-6

(I) history is a well-known and
available subject matter teachj
able in schools, (2) the study
a
of which forms a useful back­
ground to the study of texts,
and (3) which yields a well kno^/n
and obvious conclusion, namely
that man is mutable, (4) the
denial of which is Itself a
part of history, namely Greek
history,
I answer: Cl) the discipline
known as history is a near-lnfinita
oneI a large part of its study
consists in establishing what
it 18 that ia to be studied; a
competent judgnspait 1" this pre­
liminary matter alone can only
be acquired over a life-time; the
actual acquisition of historical
knowledge, once defined, is a
matter requiring enormous skill
J
in languages, archaeology, epl|
graphy, palaeography, etc,; it
|

�PACE THREE
In, in short* • subject natter
far aeli-cultivation and advanced
•t«dy,
(2) Such neager and derivative
"infometlon’' as can be conveyed
to beginning learners is far from
giving then a "background" for
reflection on taxts-»lt is eseentially a way of surreptitiously
inatilling the prejudice that
esrtaln works are written for
ulterior Motives, economic or
Aristocratic, or some other.
But supposing this "information"
to ba conveyed in the most
scrupulous way, it is still in
crucial cases vacuous--for Instance
tha "background" for the Homeric
epics is found to be largely
derived from Homer when traced
down. Furthermore, the interesting
vribcrs often have the property ’
of being stubbornly unconventional:
whatever their historical situation
say be—that precisely they are not.
(3) That history teaches that
san is mutable can not yet be
safely concluded—it may be that
history teaches that a small part
of mankind thought itself infi­
nitely transformable and was
proved—heaven for fend—catastro­
phically wrong.
(4) Jbuong the Greeks there
was not only Parmenides but also
lUraclltus, not only Plato but
Also Herodotus. Furthermore, the
vary fact that at this present
nooent it is possible to assent
to or dissent from the proposi­
tion that humsui nature is fixed
shows It to be not a "classical
understanding" but simply an
understanding. 1 do not think
that studies like sociology
and anthropology show otherwise—
every such text I have ever read^
AStAblished, clearly or by im­
plication, an anthropologizing
and sociologlzing animal, whose
nature it was to be the fixed
observer of the various and
changing natures of the human
aubjects of investigation.
Ill, Mr Mattera says that
"icisnee" , which he takes as

a given
pre-established object
with well-known characteristics,
is cumulative and that the program
denies this.
It is a curious
thing to say of a course of
learning sometimes accused of being
"history of science", 1 think
that Mr Mattera, who is, 1
understand, a sophomor^, has
forgotten that the advancement
from, or if you will, the defeat
of,the ancient physicists conies,
appropriately, largely in the
junior year, in which the founders
of modernity, whose point of
departure is almost invariably
a confutation of Aristotle, are
studied.
IV, Mt Mattera observes a "dis­
dain for contemporary Investi­
gations? « I think there is no
such dlpdaln (though perhaps
some avpr81on--the consequence
of acquaintance rather than
Ignoranpe) among the tutors,
but rather great perplexity in
the facp of an absolutely con­
founding proliferation of dis­
ciplines. I think we will
eventually find a way to make a
choice fnong them, perhaps with
the help of graduates of the
college.
V, He also observes a con­
demnation of the ways of other
collegeo. I think myself that we
should t^^ead tactfully on that
ground; nevertheless. If it is,
as Mr Mattera himself thinks,
possible to have good or bad
plans of education, and if one
thinks that the St John's
programs Is both very good
and—as he also thinks it is—
essentially opposed to that of
other schools, it is right and
proper that we should walk about
with a modest sense of exultation,
especially if we have experience
of the unhappiness of students in
other schools.
VI, Mr Mattera says that the
program is not In fact a "revival
of anything which has ever existed".
It is, of course, of no essential
consequence whether this is the
case or not, 1 am uncertain of
ray history here and do not believe

�PAGE POUR
anyone else's, nor do I much wish
to engage In the lengthy inves­
tigation by which I could assure
rayself of the truth of such a
statement, the verification of
a statement of historical
non-existence being the weariest
of all undertakings.
I do
know that the program Is a
realization of certain essential
features of liberal arts learning
as set out in ancient and medieval
treatises, for example the
Dldascalion of Hugo St Victor.
VII, Mr Matters objects to the
all-required nature of the pro­
gram, chiefly on the grounds,
as I understand him, that it
stifles freedom and kills the zest
for learning.
To take the latter first, I too,
find it to be, intermittently, the
case. This has to do partly with
the excessive magnitude and variety
of the tasks we require of ourselves,
but partly with something deeper and
less likely to be curable, namely
the essential perversity of the
attempt to Institutionalize
learning at all. Tet 1 offer
myself this negative consolation:

KITCHIN DRUGS
60 WEST STREET*ANNAPOLIS
268-22H

that there is no feasible alter­
native— that my nature, at once
Inert and distractable, needs
the whip of public obligation to
do what it most desires, that I
do not really want to forego the
conanunlty and purposefulness which
comes from having a thought-out
common plan of learning, and
finally, that the sad experience
of other schools shows that free­
dom of choice does not Induce
exhilaration.
Now, as far as freedom of
learning is concerned, Mr Matters
thinks that It is connected with
this very freedom of choice, but
I do not agree, for reasons the
first of which is very familiar—
that the freedom to plan one's
own education cannot be exercised
without a good deal of initial
knowledge, more than a student
ordinarily possesses at the mo­
ment of choice. But what is axire
important, the alternative to a
required program, namely a par­
tially or wholly elective plan,
which must of necessity be car­
ried on in large and department­
alized unlversltlas, in fact robs
the student of his freedom in one
vital respect—it presents him
with "fields” or "subjects” which
are pre-established and pre-delimited
so that the fundamental inquiry,
which concerns nothing if not the
nature and extent, the parts and
their relations, of the "learnable”^
Is obviated and the student is
obliged to begin under the hidden
constraints of burled decisions.
The perfectly open requirement to
read certain books, on the other
hand, is precisely Intended to
leave the student intellectually
free to formulate questions and
answers; in a word, the books are
pre-set so that the matter may not
be pre-determined. Since most
human beings need intellectual
nourishment in order to flourish
or to "realize themselves”, some
material for study must be pro­
vided; books of the highest
quality are that material which
is least conducive to witting or
unwitting censorship.

�PAGE FIVE

PAGE FIVE
Mr Matters furtfeertnore. quarrels wl th
the unified progras# as representing
a dubious teaching, that of “the unity of knowledge**# I would rather
say that the program only makes this
doctrine a center of concern, and
that the doctrine it does assume la
that of the unity of the k-nose£. He
furthermore asks why all the hocks
have to be read by all the students|
if each book is to stand by Itself,
how can the program list form a leg­
it irvte whole? I answer that almost
all the students should read the books
to preserve the communal character of
the conversation about them, and that
almost all the books should be read
because, while each book speaks best
for itself, any one of the others may
speak best against it or about it#
Iflll, Mr Matters notices a “general
distaste for contemporary affairs’*.
This evidently true observation is a
source of concern for many tutors,
which I, however, do not share, and
for this reason: it seems to ms that
the immediately second object of an
education in a republic is precisely
what it is ccninonly ©aid to be, the
making of citizens. But I prefer fal­
low citlsenft who have at some time
had so lively an absorption in the
good, or, at least, personal, things
of life, that they know what a good,
or, at least, human, life is. I do
not wish for fellow citizens who,
too early, conceived an avidity rather
than a distaste for contcjRporary so­
cial evils — I do not trust them to
know in what directions to look for
a solution. I think political activ­
ity should follow education, not ac­
company it, and I Cannot blame students
for lacking interest where they do not
yet mean to influence,
12. In ft last section Mr Matters
makes son« criticisms not of the pro­
gram but of the members of the col­
lege idiich amount to Imputing certain
vices to them. 1 do not quite know
what to say, but 1 am sorry that he
should feel so, Berhaps the arguable
point In this section is the question
of the “inequality of status of tutors
and students". Let me say in what 1

do not and do consider our equality
to consist . I think that the students
in my tutorials would not thank me If
I relinquished ray responsibility as
leader, mediator, adjudicator, pace­
maker, and chief learner and became
Indistinguishable form them in function.

Hence in respect to external role we
ought to be unequal. Furthermore,
since I have been engaged for fifteen
years tn the enterprise of which this
18 their third year, it would be ybry
peculiar if I were not, by cause of
seniority, superior to thm. Hence
in respect to accomplishment we are
apt to be unequal , Thus equality
within the school, that is, aside from
our obvious civil equality, seems to
me to consist solely in thist that we
are all, together, very small before
a very great matter, 1 can think of
no consideration more conducive to
good and essential equality,
1 feel obliged to end, as I began,
with an apology to Mr Mattera, It
is in the nature of this sort of a
reply that it has the air of "dispos­
ing of" the other's argument. I am
far from thinking that I have done
that—I have only sketched out a first
few counter-arguments, Hhafe is more,
in a real conversation my main effort
would be, on Che contrary, not to re­
fute him but to persuade hira to state
his arguments more fundamentally, more
radically, if you will; for whereas
their strength lies in their decent
seriousness, their real weakness seems
to me to be that they are framed on
a someid^at conventional level, I im­
agine that in the course of such a
conversation Mr Mattera, whatever his
views may finally be, would show him­
self to be in fact--and it must be
-obvious that I^can think of no batter
compliment—a very faithful member of
our college,

Eva Brann
Tutor

�PAGE SIX

WEDNESDAY
11,10 BEETHOVENJ Plaao Concerto
G
#4, .Jlchnabel
WOLF, Pra«astheac,i
Hans Hofcter, Gerald Moore
1,40 SCRIABIN, Poeffl of Ecstasy,
Stokowski
2,10 SCHUBERT, String Quartet
#14, Iniadeus Quartet

in
Area FW station#$
For continuous listening
tfCAO (102.7) &amp; WGWS (103.5).
fit your own risk
(UaJC (91.9) &amp; mt (97.9).
Kll listings are for IBCAO unless
otherwise noted. All ties# are
approximate. For further inforaation,

eisTiNCTive Qirrs

consult Forecast FBI.
African A Atian
Imports

Hand A Laath.r
Crafts

MONDAY
12.35 BRAHMS 8y». #4,
Toscanini, NBC
1,35 BARTOK, Piano concerto #3,
Katchan. Ansemtet
3
VERDI, Ai^a highs

J,V«lry
Ex.tid Clothing

TUESDAY
11.10 BEETHOVEN, Piano concerto
G
’^31 Artur Schnabel .
3
STRAVINSKY, Oedipus Rex
7.20 BEETHOVEN, Piano concerto
#3, Wilhelm Backhaus

268-4711
54’/2 WEST ST.
ANNAPOLIS

PHOTOGRAPHY CONTEST
Last week in the caajnss mailboxes was a notification of a photography
contest which is open to all mewbere of the St. John*8 Ccllsge community.
However, the Admiseione end Public Information Officse naglectsd to liet
the prizee to be awarded. They are herewith listedt

Firet priza (each category)
Second prize
Third prize
Honorable mention

S50
S25
SIO
Mo financial reward

Judging will be dene by three looel profeeeional photographers» Serion
Warren, Stu Whslsn, and Stanley Steerne. Mr. Ham end Wre. Felter will
serve on the judging committee as ex officio members.
Copise of the reguletione governing the first photogrephy contsst may ba
obtained from the Admieeions or Public Information Offices. A reminder
of deadlinest Phase I-Jenuary 30j Phase II-April 30. Photographs should
be labeled and eubmitted to the Public Information Office.
Wary Falter

�PAGE SEVEN

MOTiO
’

An Educated Audience: William Wellman b
"WingB** and the Truffaut/Hitchcock book®

This week’s column is a rather fonaleas one&gt; written because I happened
to be thinking about visual methods
of storytelling after seeing the silent
film “Wings" (being ghovjn at the Circle}.
The film is being shown without even
a musical score, creating an extraord­
inary involvement with the visual events.
Sound film directors are protected by
•the sound track, which distracts atten­
tion from their “cinematics", It may
ba that it was the closer attention
payed by audiences that produced achieve­
ments referred to by those who single
out the silent era as the roost creative
and imaginative in the history of Amer­
ican filas, "Wings" certainly makes
this claim seem plausible, even granting
the films of men like Hawks,. Ford, and
especially Hitchcock,
I have generally taken a spectator’s
attitude toward movies, but there was
a perlod--faralliar to every film lover—
when I half-serlously considered making
a film of ray own. At that time I read
a half-dozen books on film technique,
from camera operation and lighting meth­
ods, to editing and special effects.
I watched the films I saw then through
quite different eyes than I did before,
or have since. It convinced me that
a technical cinematic education can
add immeasurably to the enjoyment of
films. The issue hare is parallel to
one involved with music, which comes
up often during sophomore year at St
John's, Music is meant to be heard,
and may not even exist before it is
heard, A listener’s concern should be
with what he hears, and feels as he
hears, and not with what the composer
writes, the notes on the page. Even

so crudely stated this would make a
certain amount of sense, if it were
not the case that people hear nuire and
hear it better after studying musical
theory. There would. Indeed, be no
point in studying music at all other­
wise. As X said, my own experience
indicates that film and music are

alike in this respect, both being arts
with very detailed and exact technical
dimensions.
As 1 watched "Wings" I found rayself
being amazed at the visual skill of
its direction (by William Wellman, re­
membered also for "Public Enemy",
"Call of the Wild", "Beau Geste",
and "The Ox Bow Incident"). The style
was often quite startling and complica­
ted, very much at odds with the best
recent camera methods, like those in
"Sunday, Bloody Sunday", which almost
subordinate themselves to the narrative,
slowing the viewer to observe the char­
acters more as he might in actuality,
surrounded by the details and furniture
of their dally lives, I thought about
this primarily in terms of what the
introduction of sound, with its liter­
ary tendencies, had done to the pictor­
ial art of film construction.
Shortly afterwards I began reading
Francois Truffaut’s book of interviews
with Alfred Hitchcock, I was struck
at once by a comment of Hitchcock’s
about the silent film:
"The silent pictures were .the purest
form of cinema.... In many of the
filsia now being made there is very
little cinema. When we tell a story
on film we should resort to dialogue
only when it’s impossible to do other­
wise. 1 always try . first to tell a
story in a cinematic way, through a
succession of shots...."
Hitchcock's method, as it emerges in thei
interviews, demonstrates a unique vis­
ual preoccupation. He conceives his
projects always as a series, a rhythm
of scenes and images. Usually a sequence
of pencil sketches, drawings of frame
compositions, are the first form his
film projects will take. "Wfy mind is
strictly visual," he says. His pictor­
ial goal with respect to the audience
seems to be double: to make things
clear and to make them exciting, to
involve the audience and manipulate
them emotionally.

�PAGE EIGHT
"If you stand close to a train as
It is speeding through a station,
you feel it; it almost knocks you
down* But if you look at the same
train from a distance you don’t feel
anything. Tn the saa» way, if you’re
going to show two men fighting with
each other, you’re not going to get
very much by simply photographing
that fight. The photographic reality
is not realistic. The only way to
do it is to get into the fight and
make the public feel it,"
It is well known that often (as in
"Rope", "Lifeboat", and "Rear Window")
he takes on a project largely as a
technical challenge. He will Invent
Bcenes first as visual excitements and
then try to integrate them into the
plot—the whole cornfield episode in
"North by Northwest" is such an inven­
tion, But his concern is not with
tricks as such but with tricks that
work, that create a purely visual ex­
citement, In a scene conelaved not
Visually but as a moment in the rhyttss
ef the plot, ha will use his camera
to expose the essential. His concern
is net with the literary aspects of
storytelling and drama, his plots are
constructed visually. As Tpuffaut says,
in his introduction? "Whatever is saj^
Instead of being shown is lost upon
the viewer," He speaks of Hitchcock’s
"unique ability to film the thoughts
of his characters". What a character
feels about something is mlrrared by
the ways in which is Is photographed;
the audience sees it as the character
does. "Hitchcock is almost unique,"
he says, "in being able to film directly,
that is, without resorting to explana­
tory dlalcgue," Actors, naturally,
are not a large part of his concern.
It seems clear that Hitchcock has
preserved the pictorial achievements
of the silent film, and has thus succeeded
in making films that are exciting and
interesting to watch. In "Wings", viewed
in complete silence, the effect of
visual absorption is extraordinary.
The acting styles are somewhat exagger­
ated but even Clara Bow, who is most
guilty of this, roaraages to create a
believable character in spite of herself.
A striking example of visual exposition
is the changing manner in which Mary
(the character she plays) is presented.

as Jack (Buddy Rogers) gradually
realises that he is in love with her.
At first, parallel to his indifference,
she appears a rather horsey, tomboyish,
simpering type. She is costumed un­
becomingly and lit to emphasize the
Imperfections of her face. As the
film goes on, she begins to change,
subtly but distinctly, until at the
end we realize, just when Jack does,
that she is really quite a beautiful
girl. We have seen her through his
eyes, our view of her raatwing with
his.
In the quiet acenes, in the battles,
in the bombing of a small French
village, in every major sequence,
titles are scarce, presenting only
essential facts. There Is a chilling
sequence in which a large black
Geimai bomber called the Gotha is
loaded and wheeled out for takeoff.
Seen from above as it taxis on the
field it resembles a monstrous
insect, seen from beneath are the
white bombs clinging to its belly
like eggs.
A film as rich in striking images
as "Wings" can reacquaint a speotator with the importance of "cine­
matics". The filmgoer is so used
to seeing pictures without the
slightest visual Interest that he
almost forgets that they exist. It
has gone so far that even a cheap
blood-epic like "The Night of the
Living Dead" can be hailed as a
masterpiece because its director
can use a camera with a little
imagination. It soinetlraes seems
that on large-scale Hollywood efforts
the camera was just too heavy to
move, the film-makers too bored to
make the effort. The Industry
has gotten fat.
When a filragoer learns something
about motion picture technique, and
particularly if he thinks in terms
of making his own films, he bacomea
personally involved in the problems
of visual narration, can begin to
think in "cinematic" mays. There is
a greater sympathy for the nature of
a motion picture, a sense of co-oper­
ation, luith a director in the produc­
tion of his effects. Hitchcock claims
to resent the increasing knouiledgability
of his audience, because he thinks it
makes his job more difficult. To ma

�PAGE NINE
this seems entirely the wrong attitude
for a director to take. An educated
audience is more fully behind him then
any other, interested in the film in
much the same way that ha is, enjoying
his success and regretting his failures.
Learning about !lJagne?s harmonics hardly
makes "Parsifai** less thrilling to
hear, and no mors does understanding
the special effects and camera trick­
ery^,employed make the tower sequence
in Vertigo" less unneruing. In both
cases a new dimension is added, the
experience cesses to be a passive one.
In the future I may write about some
specific cinematic methods and ths
effects they can produce. For now
I urge you to sea "lilings", and to
watch it closely.
You might learn
something!
A film of Hitchcock’s will serve as
a good example,
I know this active
involvement works.
In "Rear li/indow*
James Stswart plays a photographer
layed up in his apartment with a broken
leg. For amusement he spies on his
neighbors across the court, observing
their lives and trying to figure them
out. He begins to suspect that one
of them has committed a murder, and
things proceed rapidly thereafter.
The astonishing thing about the film
is that, except for one crucial scene,
the camera shows us nothing escept the
inside of Stewart’s apartment and the
things visible from his window.
It
seems at once as if extraordinary skill
would be necessary to save such a film
from being dull. lUa want and expect
a certain variety in what we see.
But if we think about it we realize
that in actuality, being in such a
situation ourselves, boredom would
be the least likely possible sensation.
U/hat makes us expect to be bored is
our prior experience with run-ofthe-mill film-making. Hitchcock has
made "Rear lUindow" one of his most
absorbing and exciting films, be­
cause he places the audience in an
active, participating position. The
action is photographed from within
and not, as we have come to expect,
from without.
It is-a very simple
principle in theory, but very dif­
ficult in practice.
It is Hitchcock’s
visual emphasis that is at the bottom

of his success, and that same visual
approach must be present in every
powerful film.
At the Playhouse "One Day in the
Life of Ivan Denisovich" (G)
I will say very little about this
film, both because my space is lim­
ited and because it did not interest
me very much. The novel, by Alexander
Solzhenitsyn, has a large reputation,
and if it’s justified this adaption is
a very poor one.
The idea is fine, to explore the daily
lives of prisoners in a labor camp.
But this is not actually what the film
does. Thera is little intimacy, almost
nothing to command sympathy for the
charactersg A scene in which a group
of prisoners construct a wail in the
sub-zero winter was, for example, handled
in a fashion that gave no sense of a
group working together or even of the
overall process of construction. The
make up jobs are awful with black
charcoal lines visible in ovary close­
up on the healthy, well-fed faces of
the actors.
There were a couple of scenes which
could not, because of their context,
fail to be moving, but these were more
than balanced out by passages of complete]
artificial dialogue, sounding auspiciously
like badly translated word for word
liftings from a mediocre novel,(not
having read the book I cannot be certain
about that).
Anyone who can take a subject like
this and fail to make a depressing movio,
must be doing something wrong.
At the Capitol ’’Shaft” (R)
Held over; see last week's COLISGIAN
Guest Review
At the Flaza ’’Airport” (G)
’’Airport” as a motion picture never
gets off the ground. It belongs to
the ”Grand Hotel” genre of film, but
falls miserably to breathe any life
into the cliche»riddan formula, "^he
usual horde of stars and subplots are
there but to such an excess that ft
is not better direction but an aiif
traffic controller that is needed,
There are many questions that arise
while watching ’’Airport**, Is Helen
Kayes really the cutest little-oldlady ever to be seen in films? Why

�PAGE TEN

does George Kennedy, the tough-*talking
crew chief, smoke cigars while in bed
with his wife? Is Dean Martin deliv­
ering an accurate portrayal o£ Dean
Martin? Does Van Heflin, the mad
bomber, wish to blow up the plane
for hutnanltarlan reasons!
It would seen that the acting,
direction, and screenplay are what
make the difference between a film
like "Grand Hotel" (1932) and one
like "Airport" (1970).
Craig Freedman
Coning to town soon will be the
new Janes Bond film "Diamonds Are
Forever", with Sean Connery again.
It should be here when we get back
from vacation.

David Chute

WINNERI

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Sally kutsky
617 Arch St #3
Ann Arbor* Mloh, A8104
313-66S-M2S
Sean
St John's College
AeRspolls, )^ryls»d
DeeenheF 7» ISH

21404

Deer Sir*
I am a greduete nt St John's ('(8)
end eurrently e seeend yeer student
at the ORlvereity ef Miehlgen Lew
Seheol. The Deen of Admissions has
expressed en interest in St Jahn's end
its pregrem eed esked s* to dlseuss
it with him. He hex esked me te write
you end inform you thet he will eonaider seriouely eny epplieetiens he
reeeives frcw e St John's greduete*
Lew sehools ere currently swamped
with epplieitiens end I urge eny
seniors who are interested to epply
es soon es possible. Tou will heve
the slight edventege of being e euriesity, end the diff|eulty wigh eeeeptence in eny lew sehool is te be sing­
led out of the erowd. Of eeurse* the
Deen did not guarantee admissions* but
I think it might be worth e try*
Incidentally, 1 did net go te lew
sehool for two years after graduation
and am pleased with ny deeislon to go,
I eneourage St John's graduates wihh
no iwsediate plans for low sehool te
keep it in mind as a future possibility.
The problem of scsf dlseriminatien
has been end is being discussed a
great de*i ie the lew school admissions

offices. 1 wee told to inform you that
women and minorities will be eonsidered
equally (I'm not lOOX sonvineed about
equal), but I especially eneeursge
woiuin to eonsIder the lew as a follow-up
to a St John's education,
I will he delighted to correspond,
speak, »r arrange accomodations for
St John's students interested in the
University of Michigan Lew School,
Sincerely,
Sally Butnky

STARTS OECEWBER 15

Submitted by the Dean’s office

�PAGE ELEVEN
Until by chance we Meet again, my friend,
I love you true as If I’d never gone.
No passing time can our sweet bond unmend.
No friendship new obscure you in its dawn,

THE COLLEGIAN

I can no more forget your warming smile.
Or careless laugh, or wisely mirthful eyes.
Than I could give your least request denial —
The time my memory nocks, my love defies.
But In this an I constant more than you?
Have you In time your former self outgrown?
Will you, at meeting, emblem someone new.
And rend our love, being not the love I’d known?

Until, by chance, we meet again , , , no more —
X think X fear the thing X hope most for.

David Chute
Peter Fairbanks
Francis Harkins
Tom Horvath
Bryce Jacobsen
Laura Jenkins
Arthur Kungle
Jack Lincoln
Tom Poiuell
Connie Rubino
Lane Russell
Steven Sadlis
Jeffrey Sinks, Editor
Paul Szabo
Jane Young

Tom Robinson

To The Carolers, Kt Al.
X would like to thank all
those who came caroling with
us Thursday night«^-eapecial ly
Maria Coughlin, who made the
original sign inviting’ every­
one, Christel Stevens, our
concert-mistress, and Kathy
Austin, who helped to map out
the route,
I would also like to thank
all the tutors whom we serenaded,
for their hospitality —especially
the Goldwlns and the Kieffers, who
received us very graciously.
Public expressions of Joy and
good-will are a sign of a healthy
community, I am proud of those
who came with us for their spirit
of friendship.
Merry Christmas,
Jim Tourtelott
PS Praise is also due to Doug
Anthony, and the Syndicate of
Bacchus, who provided the money
for candles, and Mrs Myatt, who
supplied the song sheets.

'’Just because you are seeing divine
light, experiencing waves of bliss,
or conversing with gods and goddesses
is no reason to not know your sip
code,”
—Baba Ram Dass
submitted by BalrJ Donabedlan

JMerrp (SOrisstmas
FROM

LAURA NCE LTD
48 MARYLAND AVENUE

Low-Comedy Seduction

Let us go then, you and X,
down to debasement.

—Roger Greene

�PAGE TWELVE

To Whom It Way Concern
Every so often a community-minded
individual attempts to focus concern
on a possible correction which merits
consideration by all members of the
St John’s community. This is rare} a
statesman here can hardly count on
any reward for his effort other than
a lury smile, an askance look, or a
terse statement implying agreembnt
or disagreement.
Thursday evening a large number of
the students on food service dressed
in compliance with a rule they felt
to be erroneous. The sentiment pre­
vailing was "It’s too much trouble to
argue", "This won’t last long", or
"I’m hungry". This is a sad display
of community spirit.
Why anyone who does not dine in the
dining hall desires to put dress re­
strictions on those who do, perplexes
ma.
Yet, more alarming is the "every
man for himself" student apathy which
indicates an unwillingness to do any­
thing for the sake of the community
as a whole. This self-centerednoss
is extremely discouraging for those
who might be motivated to share with
others here. Caring is the axiom
for change.
We all (the students) have at one
time or another thought of possible
innovations which might make St John’s
a better place to learn at, and a
more pleasant place to live. How
few have made use of the various
channels available in an attempt to
implement change!
I feel strongly
that this would not be so if there
weren't usually the tendency to
"rally to the defense" of the old,
but a sincere attempt to consider
alternatives. The students are often
by far the most guilty. Thursday
night was a demonstration of this.

Donna Demac

News of the World
IRIDAT, DECEMBER 3RD
Foreign Pakistan declared war
on India as heavy fighting broke
out on both the East and West
Pakistan borders. Reports fvots
the front said that Indian ground
forces penetrated Into Pakistani
territory, while Pakistani planes
bombed Indian airports.
Foreign Ministers Mahoud Ried
of Egypt, speaking in the General
Assembly, called on the UN to
force Israel out of
Arab territories,
Poraestlc White House Press
Secretary Ronald Zeigler an­
nounced that ths budget for the
fiscal year 1973 starting in
July would be about $250 billion
and would aim at full employment.
Unemployment in November rose
.2X to
SATURIiAY, DECEMBER 4TH
Foreign The UN Security Council
met to discuss the widening
Indian-Pakistani war. Meanwhile
the United States State Depart­
ment blamed India for the hosti­
lities,
A US govennent survey revealed
that since the United States
started to bomb Cambodia in 1970
2 million refugees were forced to
leave home as a direct result.
In a speech before the Spanish
parliament. General Franco announced
that there will be no reforms or
liberalization of his regime.
This ends a theory prevailing
for the last ten years that Franco
would start to pave the way for a
more liberal successor,
SUNDAY, DECEfiBER 5TH
Foreign Indian troops reported great
success in East Pakistan. They
claimed to have freedom of the
skies and to have surrounded the
Pakistani troops. In the UN Rus­
sia vetoed a security council
cease-fire order.

�PACE THIRTEEN
President Anwar Sadat of Egypt
agreed to hold talks with Israel
In New York,
Ponestlc A billion dollar
bequest to the Johnsc.i foundation
turned it from one of the nation's
smallest to the second biggest In
the country. Only the Ford founda&gt;
tion is bigger.
General A team of scientists at
the University of Southern Cali­
fornia discovered a virus causing
cancer in humans. This Is a tre­
mendous step forward in understanding
and curing the disease,
MONDAY, DECEMBER 6TH
Foreign President Nixon vowed
that the United States would remain
completely neutral In the IndianPakistani war, and the State De­
partment cut off all aid to India.
The United States will sell
Skyhawk jets to Israel, but the
acquisition of Phantom fighter­
bombers still remains Israel's
first priority.
Domestic The Senate voted 89 to
1 to confirm the nomination of
Lewis Powell to the Supreme
Court. Senator Harris of Oklahoma
cast the lone dissenting-vote,
TUESDAY, DECEMBER 7TH
Foreign India captured the town of
Jessore, giving them effective control
over half of East Pakistan. The UN
General Assembly voted 104-11 to call
for a cease-fire. This action, how­
ever, is not binding on member states.
Ten European members of NATO,
replying to US criticism, announced
that they would raise their joint de­
fense budget by $1 billion in 1972.
Domestic The House voted 210 to 186
to extend the anti-poverty program.
The measure included controversial
day care legislation.
WEDNESDAY, DECEMBER STH
Foreign India refused to accept a UW
cease-fire resolution as her forces
advanced further into Bast Pakistan.
Chile nationalized all food supplies
following a political and economic
crisis caused by food shortages.
Domestic President Nixon presented a
pension reform plan to Congress, The

measure called for tax exemptions on
savings and investments for retirement,
THURSDAY, DECEMBER 9TH
Foreign Indian troops surrounded
Dacca, the capital of East Pakistan.
A bcanbing raid on the city destroyed
an orphanage, killing 300 children.
Former Vice President Aly Sabry of
Egypt and former Minister of War
Mohammed Fawzy, both leading figures
in Gamel Nasser's government, were among those sentenced to hard labor
for a plot against President Anwar
Saoat, Sadat reduced Sabry's original
sentence from death to life ImprisCnment.
Ralph Bunche, former UN SecretaryGeneral, died.
Domestic President Nixon vetoed an
extension of the anti-poverty program
because of its child-care programs
which he denounced as weakening the
family and fiscally irresponsible.
The House passed a $26 billion tax
cut, including a plan to finance
election campaigns after 1976 by
income tax check-offs,
Steven Sedlis

TO WIN”
with

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Phones: 268-5401
268-1348
54 Maryland Avenue
ST. JOHN'S ALUMNUS

�PAGE FOURTEEN

THE SYNDICATE OF BACCHUS
THE DSV
and

ACTION ONE
invite tVe entire coimnunity to the
annual Christmas Party to be held in
FSK Lobby Tuesday, December 14th at
7:00 pm«
We will begin the festivities with
a buffet supper to which all are wslcome. Then the DSV will provide mixed
drinks, and you will provide the con­
versation and singing. Please bring
your husbands and wives, and help us
celebrate.

tides will benefit all.
The last meeting of the food com­
mittee on Wednesday, December Sth,
determined these items of informa­
tion,
Paul fJJeller is the new manager re­
placing Bob Ullrich, who has been
promoted to another position.
Neither ’’shrimp creole” nor ’’chick
en hawaiian” will ewer be served
again.
Replenishment of certain commod­
ities is in progress.
Another brand of white loaf bread
will replace "lUonder bread”.
Other delightful things.
Thee Smith

DELEGATE COUNCIL
FOOD SERVICE
To the student community, oncampus and offs

As expected, it is the duty of
the food committee not simply to
forward student complaints and sug­
gestions to Action One, but also to
direct similar remarks from Action
One to the student community.
It is
our hope that mutual concern be
achieved; that improvement of attitude
and action by one party be accompan­
ied with improvements by the other
party. Please lend your attention
to problems too easily regarded as
trivial,
A box has been placed in the lobby
of Randall, to be properly used as a
receptacle for gratuitously returned
dining hall articles (glasses, ash­
trays, plates, silverware, cups,
pitchers, etc,). The continual
return of infrequently borrowed ar-

DELEGATE COUNCIL ifllNUTES
7 December 1971 (Pearl Harbor Day)
1837 hours
(No delegate from Randall, Paca,
and half of Campbell)

Old Business
i'y"Miss Unger brought the revised
charter for the DIS division of CESC
The Council voted 10-0-0 to approve
the sub-charter.
Then the Council
voted 0-0-2 to allocate 150 to CESC
to pay bills,
2) Mr Main then asked for a con­
stituency report concerning academic
gowns. The following dorms came out
50-50 for the gowns: lUest Pinkney,
Campbell, Chase Stone, Humphreys.
Paca was simply in favor, so said Mr
Brown. East Pinkney was overwhelm­
ingly in favor and the off-campus
independents, showing their normal
iconoclastic streak, voted 25 for,
17 against.
Randall’s opinion was
not present. In view of this response
especially since no dorms seemed
against gowns, the Council voted
10-0-0 to ask President Ulaigle to

�purchase 350 goiuns for the student
body,
3) ffiiss Spear (F-C) luanted to knot#
the status of the Randall Lobby
renovation plans. No one seemed to
know tuhether the plan was still
extant.
New Business
4) miss Jenkins requested J5Q for
the expenses of Rob Wermin, the
Wime. The Council approved the al­
location 8-0-2,
5) (Tir Lincoln, in his other capa­
city, i.e, Headwaiter, said that the
number of missing glasses, plates,
cups, salt shakers, spoons, saucers,
khivBS, pepper shakers, forks, bowls,
pitchers, etc., from the Dining Hall
had reached proportions such that the
efficiency of the Dining Hall is
seriously Impaired, This is especially
true at the noon meal. He asked if
Delegates would please try to recover
these items and return them to the
Dinery,
6) Rlr Main statBd~that the Dress Reg- '
ulations at Evening Meal would be en­
forced beginning ll/sdnesday evening.
The Council agreed that it would be
extraordinarily appropriate of the
Council Members if they complied.

4M3 MARYlAh® AVE.

ANNAPOLIS • MARYLAND

PAGE PIPTEEN
7) Christel abdicated and left Doug
Anthony as Head SOB on campus. Any­
one wanting funding for small parties
should see Doug, He’s always up for
it.
8) At 1907 hrs the meeting adjourned.

Meeting lUith the Administrators
9 December 1971
1405 hours
(Discouraging attendance,)
1) Mr Main told the Dean that the
council had voted to ask President
Weigle to buy gowns. The ensuing dis­
cussion showed there are a great num­
ber of confusions and difficulties
involved (such as style of gown, decor­
ative nature vs formal nature) that it
would be wise if the, purchase step were
slowly taken. Mr Morrill (M-CS) said
that he thought the students of the
collage would rather see the rather
considerable amount of money involved
spent on something useful. The matter
is under consideration.
2) Mr Main said that the vandalism to
the Dean’s house and the college would
be taken care of by those responsible,
3) Mr Lincoln invited faculty members
and their families to eat as guests
of students at the eveiiing meal, par­
ticularly Monday, Wednesday, and
Thursday evenings.
This invitation
brought about a discussion of the dress
code enforcement. The resulting
clarification is that the Council urges
that the student body comply. The
headwaiter and his assistants have
the authority to refuse admission to
students failing to dress properly.
This authority comes from the Dean,
4) Mr Comber again brought up the case
of the missing lamp in the Baldwin Room.
The chair has been returned. Miss
Spear said her investigation is
continuing. 5) Mr Finch said that there are opening;
for volunteers at the Germantown
Primary School on Cedarpark Road. A
Miss Fisher will be here on January
13 at 3 PM(l500)to speak about this
program. Anyone interested should
see Mr Finch,
6) The meeting adjourned at 1503 hrs,
□.Lincoln
Sec.

�PAGE SIXTEEN

Fseturing

Soafood—Aged Beef—Raw Bar
Stsamad Clams Cocktails

Open 7 Days 11 A.W.—11 P.RI.
22 fflarkat Space
Annapolis, (Baryland
268-2576

On Saturday, January 8, 1972,
and Sunday, January 9»
the
R.A.M. Film Society will present
Jean -Luc Godard's "A Bout de
Souffls” ("Breathless"). Based
on an originaVstory by Francois
Truffaut, this brilliant film
was made in.1959 and stars Jean
Seberg, Jean-Paul Belmondo,
Lilians David, Daniel Boulanger,
Jean-Paul Melville, HenriJacques Huet, Claud Mansart,
Van Doude, andJean-Luc Godard,
The film takes place in Paris.
Paris where a young American
girl, Pat, who hawks HeraldTribunes on the streets, falls
in love with a Humphrey Bogart
parody named Michel who steals
cars, "borrows" money, and
kills-policemen. The two of
them (Seberg and Belmondo)
go nowhere with determination.
With no plot, nor real motive,
and only the slimmest pretexts
for action, this film moves
with such a frantic pace and
such, a high pitch of tension,
that the viewer is sure that
all this madness is going
somewhere.
."La Chinoise" and "Made in
U.S.A." have recently brought
Godard into the notice of the
American public, though they
do not have the solidity of
"A Bout de Souffle". Godard is

a rare and remarkable director-for he is unafraid to mix
Hollywood with Kant and Hegel,
Eisensteinian montage with
Rossellinian Realism, words
with images, professional
actors with historical
people, or the documentary
with the iconographic. More
than anybody else, Godard
has realised the fantastic
possibilities of Cinema as
a medium of communication
and expression. In his
hands the cinema has
become an almost equal
amalgam of the symbolic, the
iconic and the indexical.
His films have conceptual
meaning, pictorial beauty
and documentary truth.
Though Godard often defies
the conventional logic, he
does so with a deliberate
and precise purpose—under­
standing that logical
convention can be simulta­
neously unconventional and
real.
The short is to be
t
announced.

Peter Fairbanks

SPORTS
Basketball; Hustlers - 47,
Guardians - 50. After the
first quarter, there were some
raised eyebrows, the score
being 9-6, Hustlers leading.
People were wondering if, even
without Mr. Frame, the Guardians
could humble the highly touted
Hustlers ... those Hustlers
who came resplendent with a pair
of flashy freshmen, plus some old
standbys like Messrs. D'Addario,
Morrill and Mollin. But reality
asserted itself in the second
quarter. By halftime, it was21-8. In the second half
there was only a slight edge to
the Hustlers, mostly because of
some timely shooting by Mr,
LeVan, No telling what might
have happened if Mr. Frame had
been playing. Are you really

�interested, in knowing who scored
the most points? If so, read
the next sentence, Mr. Bell
scored the most pointe, eighteen
altogether.
Spartana-40, Druids-24.
After a slow start, the Druids
picked up steam and outscored
the Spartans in the second
quarter. They were only
trailing by two points at
halftime. But Mr. Maiatrellis,
et aX, (broke it open in the
third quarter, and the Spartans
coasted in to their first
victory, Mr, Maiatrellis
contributed sixteen points, as
did the Harris Brothers, The
Spartans, it will be recalled,
were quite inept last year in
basketball. But the September
Draft brought them Mr,
Maiatrellis and Mr, Harris,
who, all by themselves,
constitute a respectable team.
Then add Mr. Spirer, who was
refereeing last year. Now
add Mr. Harris the Younger,
and it begins to look like
a formidable group. Mr.
Gasner, a Johnny-comelately on our basketball
scene, completes their
starting five. Clearly,
they will be tough to
beat.
Badminton: Druid8-9O»
Spartan8-16, TLSTB.
Volleyball:Druids-55»
Guardian8-50. This was
an exciting game to watch,
replete with long rallies and
great "saves". The lead kept
fluctuating, as now one team,
and now the other, would
develop a hot hand. But the
steady Druids were hot when
it counted at the end, when
the Guardians went cold for
some reason. So, the Druids
are now 2-0, quickly taking
the lead in our volleyball
league. But who knows what
surprizes the new year will
bring?
Hu8tler8-55» Greenwaves-41«
The revamped Hustlers squared

PAGE SEVENTEEN

up accounts today. They now
have one win and one loss.
They definitely looked better
than they did a week ago.
But can they win the big ones?
These things will work them­
selves out in time. The
Creenwaves, who are still
experimenting with their lineup
have not hit on the right
combination yet, A little
change here . , , a little
there , , , and some other
team is going to be "shocked"
by them. Wait and see.
M.U.S.H, After prolonged
soul-searching, hand-wringing,
hair-pulling and foot-dragging,
we have finally come up with
winners for these annual
awards. They go, of course,
to the Most Un Sung Hero in
each sport. The competition
and interest in past years,
as in this one, has been keen.
The qualifications are simple:
substantial, positive contri­
butions to the team, coupled
with absolutely no mention
in any of these columns, and
no selection on any All-Star
team. In short, the Awardee
Is a Legitimate Un Sung Hero.
(Readers who are addicted to
acronyms may make of this
what they will.)
In soccer, our MUSH winner
is Mr, Asclk, who is well
known to all. The improvement
in his soccer skills over the
years has been considerable.
Honourable Mention goes to Mr,
Larsen of the Greenwaves and
Mr, Green of the Hustlers,
In football, we were
inundated with strong candi­
dates. We finally settled on
a pair of joint winners ...
Mr. Jarvis and Mr. Ellis,
Honourable Mention goes to
the Guardian entry of Mr,
Diggory and Mr. Elkins.
So, there you have them,
Dear Readers, heroes all.
These people, from now until
the Winter Solstice, are
hereby granted Genuine Hero

�PAGE EIGHTEEN

Status. They will be un­
abashedly praised, shamefully
deferred to, and obsequiously
fawned on. Lusty young
damsels will pursue them
relentlessly. They will do
brave things. They will be
above the Law. They will
be like Gods ... but only
until the Winter Solstice.
Fitness Test: Remember to
pass four of the tests by
Christmas Vacation.

Basketball
Hustlers
Spartans
Guardians
Druids
Greenwaves

W L
10
1'0
01
01
00

Pts.
3
3
1
1
0

This Week’s Schedule:
Tuesday, 4:15(Badminton)
HuBtlers-Guardians

Bryce Jacobsen

League Standings:

Volleyball
Druids
Hustlers
Spartans
Greenwaves
Guardians

W L
Pts.
206
11
4
10
3
02
2
01
1

Tills week’s
Chef’s Choice

Iflerry Christmas to everybody
from your fflother (Emma) !

TO OUR SUBSCRIBERS:
We are experimenting with different forms of mailing, and any
suggestions will be welcomed (however, we cannot afford envelopes)

THE COLLEGIAN
St John’s College
Annapolis, Maryland
21404

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                    <text>essay

Infinite Regress
ometime in the past few years, liberal arts college adminis­
trators across America decided that they had had enough.
They wondered: what is the goal of a liberal arts education?
Why study English instead of “Marketing/Advertising”? They
could maneuver around aesthetic concerns (that dropping out
of life in order to study Plato was... distasteful) but remained
unable to surmount the issue of practicality. Nobody wanted
to say that a liberal arts education would get you a certain kind
of job that paid a certain kind of salary. And then all of a sud­
den, everybody did.
You may have heard the phrase “critical thinking skills”
thrown around lately. Critical thinking skills . . . what are
those? Well, what seems to be certain is that C.T.S. are very
important for acquiring a job nowadays. Which kinds of jobs
these are seems less certain—and for what ends C.T.S. are
“necessary” even less so. The argument that follows from this
deduction is, of coiu-se, tenuous. (Mostly because is is not es­
pecially coherent.) It is also intolerably middle-brow: exactly
the kind of statement your parents might pronounce to rela­
tives during a family reunion at Olive Garden: “Johnny’s de­
veloping criricuZ thinking skills because they’re so necessary for
today’s job market!” Such is the critical equation: that college
is foremost about money.
Critical thinking is good. The world has changed for the bet­
ter because humans think critically. But at some point, maybe
in the past few years, this became insufficient—being a critical
thinker wasn’t just a necessary condition for being an educated
person. It became a prerequisite for employment, specifically
for a job carrying with it the kind of salary a college-educated
person might expect to earn. How did this happen? It does not
seem complicated. Over the years the job market has become
increasingly transparent. It is no longer as common as it once
ast year, gadfly coliunnist Michael Lacy made an astute was, perhaps up until the Nineties, when the Internet rose to
observation, which I’ve been mentally rehashing ever prominence, to gain employment by working for a friend or
since. “So much of what the gadfly was this year,” he said,
relative’s company. (This still happens, of course, but it is less
“was what ‘the gadfly’ was.”
acceptable.) And so a person could reasonably attend a liberal
This stuck "with me for a few reasons, but primarily because arts college, major in history, earn not even very good grades,
it revealed our self-involvement as a Staff, rather than a pub­ and then somehow—as if by magic—end up working the trad­
lication. As a member of the Polity, when I picked up an is­ ing desk for a Chicago securities firm. There was a man behind
sue, I wanted to see a reflection of the St. John’s community. the curtain, and that man’s name was Dad.
Instead, I saw distinct fingerprints of The Staff and what we,
The education of a person and that person’s employment
rather than the Polity, created the paper to be.
were once two wholly separate things. This was an eflfect of
That being said, the true object of this Letter is to inform fairly ridiculous income stratification. (Income disparity also
our old and new readers of the existence of what we are now accounted for the now-unfathomably low price of college in
calling G: A SUPPLEMENT. In theory’, this will be our literary the twentieth century, which has since been corrected for,
supplement to the more news-oriented gadfly. And while now that people who are not wealthy aspire to go to college.)
I take up this space to encourage you to submit yoxir poems, Years ago, you didn’t expect a job due to your degree; you ex­
translations, vignettes, comics, photographs, short stories, et pected one because of your social status. Nobody really need­
cetera. I also encourage you to help us shape our new endeav­ ed to worry about the practicality of a liberal arts degree when
or, as it truly belongs to you.
economic injustice guaranteed every college graduate a high—Elizabeth Spagnoletti payingjob.
Along with a fervent extolling of C.T.S. comes a swift con­
______________
The Gadfly
1 — For this issue. The “G” will be carrying what would nor­
demnation of utilitarian degrees: programs of study like ra­
mal appear in the gadfly.
diology or nursing or electrical engineering. (Or: massage

S

letter from the editor

Introducing “G”
L

�Aphasia, NY (Beyond the Zero)
Vandal propaganda on
The neighbor temple:
MEEK, smeared
Proud in David’s Star
Waging modest holy war
In this mumble drowned hamlet,
While the yoimg ones
Study stray voodoo.
Vast fatal papyrus, and
Deities that gather clouds in their wake.

»

A habitat under
Assault by disputed
Details of the
Wonder-drawn nightly
Fathoms, deep into the
Blue distant shores,
Vista speckled with
Foreign starlights.

A ceaseless argument of
Namely whom had been
Sewn lucid into the
Folds of that prayerscape, and the
Frequent invocations and
Conjurations of
Them imder strife.
Once happy hollows
Clove to their
Doomed horrors alleged, the
Judgment lain on those
Fallen fools, be it the
Core’s un-luminous furnace, or the
Vengeful wrath of the
Chthonic dominion below.
Upon those cleft of mortal thread.
Supplicants to the somber air.
Pleading, “whisper in my ear,”
But we don’t speak that Language
Since our towers fell.

—Carter Brown

therapy.) This is one of the few cogent parts of the argument
against specialization, against pre-professionalization. (One
may find a parallel in the medical commimity’s persistent con­
troversy vis-a-vis specialization versus general care.) A liberal
arts education prepares you in a way a degree in video game
design never will for the exigencies and pain and uncertainties
of everyday living: for the monster of modernity. It makes you
fully alive. Since market corrections along with the continued
eradication of inequality made impossible the prior terms of
a college education, it wasn’t surprising that a lot of young
people in the past decade or so felt like they had to choose be­
tween making money and a “life of the mind,’’ between being
comfortable and being free: between death and life.
So what to do with people for whom college is the means of
making more money? Tell them that a liberal arts education
doesn’t prepare you for a job but does develop C.T.S., which
will help you get a job, insofar as they develop you as a fully
functioning, highly capable hiunan being. There’s not a whole
lot wrong with this. But what is wrong is deadly. Why did we
cede that education is for profit-making? Degrees in engineer­
ing, or computer science, or cosmetology: they are not the
problem. The difficulty is that market capitalism has success­
fully encroached upon one of the last bits of sacred territory—
the liberal arts—hitherto protected as a means to abetter, more
democratic society. What do we have to show for it? Critical
thinking skills. It is terribly ironic that the institutions that
looked at the world and became determined to make it better
by educating people are now stuck defending themselves for
“practicality.” The revolution did not start in Accounting 101.
But this is where those college administrators, from Kenyon to
Swarthmore to Reed, have gone to console themselves.

titled this editorial with the intent of criticizing two things.
The first is that critical thinking skills, or the status associ­
ated with them, are an inherently regressive concept, especial-

I

ly within the object of my second criticism, which is the terms
set by market capitalism, terms with which we have agreed to
follow. After all, you can’t think too critically, lest everything
fall down. Lest you be required to reconsider the world.
I don’t know why C.T.S. were appropriated for the ends of
capitalism. And I don’t know why liberal arts college admin­
istrators were complicit in such theft. In the end, a liberal arts
education doesn’t give you much of anything at all except the
huge, great, life-giving ability to process, without breaking
down, the heady, outrageous stuff of living: the capacity to still
recognize life, and yourself, in the entropy. This is what you
came here for: not to get a job, but to be able to deal with hav­
ing to do so.
—J. Keenan Trotter

books

Summer Reading
recommend the following four books that I read this sum­
mer. They weren’t the only good ones I came across, but
these were the last of the bunch, read as the siunmer was
ending, and so imbued with that preemptive nostalgia which
marks the waning of a season.
1. Gypsy Rose Lee, The G String Murders, 1941. (The ety­
mology of the “G” is, perhaps happily, unknown). Gypsy Rose
Lee, the famous stripper intellectual (striptease is a subclass
of burlesque; vaudeville is its snobbishly genteel relative)
lived for a while at 7 Middagh Street in Brooklyn Heights.
Here W.H. Auden (with his lover Chester Kailman), Benjamin
Britten, Carson McCullers, Janet Flanner and a whole slew of
other celebrities, including Klaus Mann (Thomas’s son), dos­
sed down or dug in to form a roiling commune composed of

I

brilliant talents and irregular existences. (I got the reference
to G String Murders out of a book by Sherrill Tippins, Febru­
ary House, that tells this Brooklyn story; it was lent to me by
an Annapolis alumna, Cynthia Barry.) There Gypsy worked
on her first book with help from various members of the crew.
However, the thing is essentially her own, told in her own
name. It’s pretty racy, but a little too littered with characters
and strung together and, to me, a tad boring in the long run,
I didn’t read every page but looked to see who dunnit (my
hermeneutic method for reading mysteries). Yet you learn a
lot about the tough argot and the rough ways of a nearly by­
gone form of entertainment. (That “Little Flower,” Fiorello
LaGuardia, New York’s kookily wonderful mayor in the for­
ties—he used to read us kids the funnies on the radio during
newspaper strikes—shut down all the burlesque theaters in
the cause of family values.) Under the rubric Femmes Fatales
the book has been republished by Feminist Press, which takes
pride—imagine!—in the fact that women can write pulp fic­
tion. (Since the genre is often sexually exploitative, this surely
isn’t quite kosher as feminism.) The work seems to be good of
its kind, and it’s certainly fascinating as anthropology. Any­
how, it’s a phenomenon. She was a phenomenon who could do
something remarkable: raise vulgarity to wit. I think I’d have
liked her better in person than in her book, but then I got that
notion from her book.

Roadhead
Roadhead, the live-long monster of morning
sits in black platitudes waiting to sing
of all scrape scrapers and newborn winged Dongers
who with goggle mouths fly in the rain.
O roadhead, your mouth is a letter,
your arms are wrangle red nether.
So if I rise, and chuck you off
a cliff a biff, a whiff of the high air
think nothing, and fall down,
moonlight rich in your hair.

The Gammy Gaze I seldom shun
Especially when I’m on the run.
So enter wide enter.
Lay Down A Black Sneeze.
Come on sweet Lolly,
get on your knees.
You know Unckle and Aunt
they’re followers of the Floundoo Pipe
and Readiers of the Eagle:
It’s often that they fly along
on the wicked shore.

You know Rickie and Samantha
they’re better in the flesh,
if you can convince them to squirm
and spin the fucking bottle.
—Chris Johns

2. William Saroyan, The Human Comedy, 1943. A Santa Fe
alumnus, Laird Durley, gave me his copy, thinking quite right­
ly that it would speak to me, since the book was published not
long after I’d arrived in Brooklyn, America, from Nazi Ger­
many. Saroyan is as gently sweet as Gypsy is harshly raw. To
make it perfect, the two heroes, a four year old boy and his
teenage brother, are called Ulysses and Homer respectively.
It’s a lovely tear-jerker and remarkably right-minded. It ad­
umbrates the social changes of the sixties but as yet without
ideology—rather as feelings of the American heart. It even has
one redeeming vice: the opinion, twice enforced, that women
aren’t supposed to go to work. This is the American small
town and its folks—all yet in the age of innocence. And if a
cynic wants to argue that Americans never were that innocent,
it would be a truth of hindsight only. In the forties, they felt
that way to themselves and looked that way to escapees from
Europe. Spend two and a half hours in lost Eden!
3. F. Scott Fitzgerald, Tender is the Night, 1934. Fitzgerald’s
Great Gatsby has long been one of my favorite novels, partly
because I love that “elegant roughneck,” Jay Gatsby—I’ve had
him in seminar. But Tender is the Night seems to me even more
accomplished. It has a slow and sure tragic inevitability—from
hopeful, halcyon Riviera days to declining, dingy North Euro­
pean years—for a man who is willingly enslaved by loving duty
to his schizophrenic wife and insidiously seduced by his iner­
tial ambition to depend on her relatives’ money. The wife is
a masterpiece of madness: the inextricable strands of wicked
egotism and woeful pathology. But what is most to be savored
is the writing itself: the pungent observations wrapped in fig­
ures of speech that often seem tough to swallow, but when you
chew them over release their satisfying substance. This is a
great book, among the best American novels I’ve read, and it
needs more notice than a paragraph; if I ever get to do a pre­
ceptorial again. I’ll propose it.
4. Matthew B. Crawford, Shop Class as Soulcraft, 2009. I
don’t like motorcycles; if I was somebody’s mother I’d hate
them What’s more, some sixty years ago I rode behind a
young madman, up and down the steep streets of the side of
Athens that runs up the slopes of Lycabettus, and it put my
back out for months. I do watch American Chopper, for its
mixture of gross manners and exquisite knowhow. It’s the
knowhow that Shop Class, a book that goes straight to my soul,
is about. The writer owns a cycle repair shop, and though he
is modest, he must be first-rate. He makes a detail-informed
case for the soul satisfaction to be gotten from becoming an
expert (or serious amateur) at some hands-on craft and offers
a restrainedly appalled critique of the “separation of thinking
from doing” that governs a great deal of contemporary work.
It’s as much a passionate how-to-live and what-to-shun book
as a cool sociological analysis of our condition, whose central
issue he diagnoses as—I think that’s right—“individual agen­
cy.” Crawford studied political philosophy at Chicago, with
obvious benefit: like Socrates before him, he knows that, as
cleanliness is next to godliness, so craftsmanship is next to
philosophy. Compared to Shop Class as Soulcraft, its charm­
ingly talkative predecessor, the cult classic of the seventies,
Robert Pirsig’s Zen and the Art of Motorcycle Maintenance
(which makes irrelevant hay of Plato’s Phaedrus) seems about
ready for honorable retirement, except that it’s the more ju­
venile of the two books. Some chapters of Shop Class would

�make a splendid guerilla seminar.
Afterthou^t: Who’d have imagined that a Ph.D. in Political
Philosophy could net you a best-seller?
Whoever wants to talk about any of these four, or, for that
matter, any others, is welcome to give me a call. I’m in the
Campus Directory.
—Eva Brann
Tutor

personal history

Arthur Mallamo
forty-year-old memory occurred to me this summer while
I was attending a lecture about the effects of alcohol on
the brain, presented by a professor of neurology from Johns
Hopkins University. As I listened to the lecture and took
notes, my mind drifted to my friendship with the legendary
Arthur Mallamo.
Mr. Mallamo was my 7th grade gym teacher. He was also
a poet, a philosopher, and a comedian. He had a command­
ing presence and a pushed-in, twisted nose that led to much
speculation among us boys about how its unique shape was
acquired. Theories ranged from his being a professional wres­
tler to a Mafia hit-man. The truth was even more remarkable:
he was a WWII bomber and fighter pilot who’d been shot
down not once, but twice, and eluded capture both times. His
misshapen nose was a reminder of his ordeals.
If Mr, Mallamo liked you, his way of showing it was to tease
you in front of the class. One cold November day he had us
running around the track, our thin gym uniforms providing
almost no protection from the icy winds. As Mr. Mallamo ex­
horted us onward he bellowed, “Whoever comes in last has to
take Januszewski home for Thanksgiving dinner!” It was then
I knew we were getting along well.
He was also my health class teacher, which was where he
expounded on various life lessons. He’d speak earnestly to us
about living generously and about the value of dedicating your
life to service. “Gentlemen,” he’d say softly, “greed is a terrible
thing.”
One day a boy smuggled a very dead but otherwise intact
frog into the classroom. As soon as Mr. Mallamo’s back was
turned, the boy, in a display of boldness I will always remem­
ber, laxmched the frog into the air like a grenade. It landed
with an inert thud on the teacher’s desk. All eyes were on Mr.
Mallamo as he turned, carefully examined the frog, held it
aloft and said, “Gentlemen. This... is a frog. Am I going too fast
for you Januszewski?” We howled with laughter and loved
him for that.
Another day in health class, Mr. Mallamo explained how
alcohol rendered brains cells less and less functional. To il­
lustrate his point, he took the blackboard eraser in his huge
hand and dangled it at arm’s length. “Gentlemen... this is what
alcohol does to brain cells...” and he dropped the eraser onto
the desk surface, which sent a puff of chalk dust into the air. I
got the message: drink too much and your brain cells go poof.
This seemed plausible, but was it true?
This summer’s neurology lecture at Johns Hopkins jogged

A

Nuclear Physics is Interesting
im silence profond;
the wide deserted streets
hate the vanity of men.

I love without regret:
the majesty of human suffering,
the autumn,
a red hat to the west

Dedie aux Palmeri et Milligan
—Translated and arranged by Kelly Trop

my memory about Mr. Mallamo’s lessons. It turns out that yes,
alcohol, and drunkenness in particular, has a significant nega­
tive impact on an aspect of brain development called myelina­
tion.
Myelin is the material that forms a protective sheath around
nerve cells, or netnons, enabling them to communicate and be
social with each other. Proper myelination is vital for the ce­
rebral cortex, the part of your brain that helps you do well in
college. Healthy myelination is very good for the grey matter:
it enhances crisp thinking and efficient recall in our mental
processes. Like people, neurons work well when they are well
connected with each other.
One reason drinking is such an effective way to get high is
that alcohol easily penetrates the myelin sheath to mess with
cell function. The more intense the drinking, the more de­
structive the assault on the myelin sheath. If the myelination
process is impaired, intellectual activity is also impaired; neu­
rons become more rigid, less fluid, more easily irritated. Poor­
ly myelinated neurons work less efficiently, become poorer
communicators, and eventually die of loneliness.
In practical terms, impaired myelination makes it harder
to remember things, harder to concentrate, easier to be frus­
trated with new information. You could say a well-myelinated
brain is better able to enjoy exercising its intellect, and a less
well-myelinated brain will struggle more.
Healthy myelination is important at all ages, but, according
to the Johns Hopkins neurologist, the cerebral cortex in the
human brain desires a myelination “growth spurt” in the 1821 age range. The worst way to drink, from a brain growth
perspective, is to binge drink in college. That’s high-impact
toxicity.
Once again, I tip my hat to my old gym teacher and friend,
Arthur Mallamo. While he. didn’t have access to all the sci­
entific data, he was right to suggest that alcohol can diminish
brain power well after we’ve finished drinking. Since the life
of the mind is so highly valued at St. John’s College, it makes
sense to examine how our drinking pleasures influence our in­
tellectual pleasures. If there was a conflict between the two,
which pleasure would take priority?
If you’re mindful of how much you desire your intellectual
powers to flourish and would like to limit your drinking, then
the next time you’re at a party and someone offers you a drink,
feel free to say, “No thanks. I’m myelinating today.”
—Jerry Januszewski

analysis

likely come down to the Guardians and Druids -with Popov
throvting the disc, and handball looks to be wide open. Linus
Feder and Marin Skokandic give the Guardians solid experi­
ence on the soccer field, and on paper at least, the Guardians
look to be serious contenders to win the overall intramurals
he sophomore draft is over, and the fall intramurals sea­ championship.
son has finally begun. For the freshmen and anyone else
Green Waves In the Draft: After seeing Eric Shlifer light
who didn’t follow the draft (or for anyone who just likes readup
­ their B-team handball and basketball teams last year, the
ing about sports), here’s a recap of the first round of the draft Green Waves ensured that history would not repeat itself by
with some predictions of how each team is likely to fare in the taking him with the fourth pick in the draft. Shlifer will pro­
coming year.
vide some much-needed scoring in both of those sports as well
Druids In the Draft: Trading away their top two draft as adding his forehand to a fidsbee team with no clear-cut han­
picks in order to move up and get the first overall from the dlers.
—
Guardians, the Druids made David Campbell the number one
On the Field: The Green Waves look to be one of the most
overall selection in this year’s draft. Campbell, who played for balanced teams in the league after finishing second overall last
the Druids last year, should continue to anchor their basket­ year, despite failing to win any individual sports. They are the
ball and handball teams, giving them a proven scorer -with the clear favorites to win soccer this year with a deep roster fea­
ability to take over a game. He’ll also bolster an already strong turing John Dusenberry and Acacia Pappas and should con­
frisbee team, giving their talented throwers a big target in the tend in handball with strong play from Andrew Mize. The
end zone.
basketball team, anchored by the ageless Jerry Januszewski,
On the Field: The Druids soccer team has been decimated is solid as well. Frisbee continues to be a question mark for the
with the departure of Mikey Mowry, Taylor Reese, Corey Cas- Waves, but their depth should help them to a decent finish.
tellaw, and Eugene Samarin. After winning that title last year, With no glaring weaknesses, the Waves are definitely in the
the Druids will be hard-pressed to repeat last year’s success hunt for the championship.
and will rely heavily on Ezra Doucet. Basketball will also be
Hustlers In the Draft With the fifth pick in the draft, the
a challenge, especially without the alumni presence of other defending champions selected Dhidhat Vanichstian, a speedy
teams. On paper, frisbee looks to be their best sport, with a and remarkably complete athlete, who will be important in
large team and several good throwers, including Johnny Flem­ every sport. Dhidhat will provide extra offense in soccer and
ing. But after dropping the season opener to the Spartans, even continue to play A-team basketball and handball, contributing
that seems to be in doubt.
to a strong but potentially thin roster that needs new players
Spartans In the Draft: Ryan Eberlein, this year’s second in order to stay afloat.
overall pick, returns to the Spartans after taking a year off
On the Field: It is the beginning of a new era for the Hus­
from St. John’s. Eberlein should provide solid play in goal for tlers after the graduation of J.P. Snyder, who anchored the
a soccer team that struggled at that position last year and will team in nearly every sport After going imdefeated in basket­
make major contributions on the basketball court. Though his ball and handball last year (and losing only to the Green Waves
strong arm may be less important with Athenian reason ball in reason ball and soccer), the Hustlers may be in a rebuilding
reduced from an eight-game season to a tournament, it should phase. Luke Wakeen, Alton Lind, and Matt Gore are all very
help the Spartans end their two-year winless streak in hand­ good basketball players, but without Snyder, it will be difficult
ball.
for them to win by taking turns dominating the B -team half of
On the Field: Strong defensive play from Honore Hodgson games. Dhidhat and James Russell give them lots of goal-scor­
should keep the Spartans in every soccer game. If they can ing potential in soccer, but to really compete in any sport they
find a way to start scoring goals, they could be very dangerous. will rely on alumni Noel Brockett, Luke Russell, and Tobias
Their frisbee team still looks solid, but handball has not been Russell to round out their squad. If that trio continues to show
kind to the Spartans in several years. Look for them to focus up consistently, the Hustlers could repeat as overall champs,
on basketball, where Doug Anderson should thrive in a league but if not, they may just be stretched too thin to compete in
that lost most of its other big men with last year’s graduating anything.
class.
Guardians In the Draft: Knowing how intent the Druids
inal Thoughts As always, the freshman allocation adds
and Spartans were on bringing back Campbell and Eberlein,
a variable to intramm-als that is impossible to account for
the Guardians were able to trade down from the first to third
when looking at a team’s likely strengths. Any player could be
pick and still get the player they wanted: Tommy Bonn. Likely the one to put a team over the top, and teams needs new re­
the tallest student at St. John’s, Bonn’s basketball skills make cruits or they starve. Particularly in frisbee and soccer, which
the Guardians an early favorite to take home the title, though involve lots of players and lots of running, getting enough
his strong arm will also prove useful in both handball and fris­ people to have a bench is vital, so the teams that are able to
bee. The Guardians also snagged Daniel Popov with the first get players out have a distinct advantage. This year’s freshman
pick of the second round, last year’s frisbee MVP, and a poten­ class looks to be large and strong, which should make for an
tial soccer goalie.
exciting league. If you’re a freshman (or anyone else) thinking
On the Field: With the addition of Tommy Bonn to their all- about coming out for intramurals, give it a shot, and unleash
star roster of tutors and other alumni, the Guardians look to your inner Achilles.
have the strongest basketball team at the school. Frisbee will
—Gil Shank

The Draft

T

F

�Hard
Hard hard hard,
It’s so when the blowing winds backwash
and Orange Julias’s rule the night,
and lozenges gurgle up and down
in places where alleycats fuck other alleycats
to the sound of beautiful music.
I remember days when morning cartoons would play at night,
and in a symphony of smiles, flash flash flash,
I’d suck in, with pleasure, a lethal dose of the ordinary.

But never, in my most bogus dreams,
was I the living entre, spinning wide on a platter.
Like:
Gimme some money
Gimme some love
and if you like
do it with a leather glove.

Because in my bogus dreams,
I’m a slick alligator.
—Chris Johns

reading at large

The Seven Habits

Personally, I am quickly learning to differentiate between
a professional and an expert. A professional is someone who
does something for a living and then shares the tricks they
have learned to overcome whatever adversity that career of­
fers. Many such tips can be applied to life in general. An ex­
pert has a list of impressive degrees and paradoxically always
seems to have written at least one other book before the one
you are currently reading. Feel free to formulate your own
distinctions.
Personally, I was embarrassed to admit that I needed some­
one else’s tips to improve my own productivity, but I was more
embarrassed at being an aspiring writer who had written pre­
cisely nothing. If you share this problem, I recommend The
War of Art by Stephen Pressfield. I will not summarize the
book here, suflSce to say it is written by a man who has written
many cool things Qike Gates of Fire, a novel of Thermopylae)
and whose advice about overcoming resistance has helped me
immensely and will likely help anyone who struggles to fulfill
some creative endeavor. The trick, of course, is in being pro­
fessional. So, while I will most likely continue to be distrustful
of books that talk about “optimizing my synergy,” I will keep
an eye out for books that offer insightful and applicable exper­
tise. It’s less about self-help and more about just plain help­
ful. And no, I will never read Seven Habits for Highly Effective
Teens: I’m just too old.
—Kyle Amann

Johns &amp; Johnnies

Hanging Out

’ll never forget my mother’s push to get me to read The Sev­
en Habits of Highly Effective Teens by Sean Covey, a book
that easily belongs to the “self-help” category. Her motiva­ oh yes, it is time for the highly-anticipated return of Of Johns
tions for this were never clear to me; presumably, she heard and Johnnies.' You were anticipating it, right? Highly? A little?
somewhere that I would benefit from it. Without so much as Please?... Anyway, it’s the same deal as last year: you write me
skimming its content, I rejected the book and refused to even questions, I answer them as best I can. For those new to An­
napolis, topics I wrote on last year included role-play in the bed­
consider reading it.
My justification did not partake of anything identifiably room, what we talk about when we talk about sex, the meaning
rational, but relied instead on an inherent distrust of anyone of “queer,” and woman-friendly sex toy shops. This week’s ques­
who at that time claimed to know more than I did about my tion is on the less-adventurous side of things, but it touches on
life. I cynically upheld my distrust as refusing to be “taken in” a lot of issues that come up time and time again in the Polity, so
by someone trying to make money off of a burgeoning market withoutjurther ado;
composed of naive and desperate people.
ear Emma,
While it still seems to me that many self-help books fall
somewhere between pop-mysticism and parapsychology, I re­
I was wondering if you might be able to give me some ad­
cently changed my mind about condemning the entire catego­
ry. After all, once we sort through some complex philosophi­ vice concerning friendships and “hanging out’” here in gen­
cal ramifications, what is Aristotle’s Ethics if not prescribed eral. My specific question: is there any good/nice way to ef­
guidelines for positive human behavior? In today’s marketing­ fectively stop hanging out with someone that you really aren’t
centric society, it might well be called Mean Habits For An Eu- very interested in spending much time hanging out with (for
daimonian Man. (Memo to Mr. Sachs: Your proposed slogans whatever reason)?
—Mild-Mannered Misanthrope
are due for presentation to our focus groups by the tenth.)
The entire St. John’s experience is one that emphasizes self­
MMM, you seem like a no-nonsense sort of person, so here’s
betterment throu^ extensive reading, and although some
texts are more open about their practical applications than the short answer to your question: no.
But since you asked nicely. I’ll flesh it out for you. There
others, there are life-lessons to be found everywhere from
are
two ways to botch this immediately. One is to simply stop
Herodotus to Shakespeare. (But for the love of God, go easy
picking
up your phone, cease making eye contact, and reso­
on the Machiavelli.) So, it probably would not hurt to keep
lutely
ignore
their very existence. This is a fair amount of work
an open mind about modem authors who want to share their
to
execute,
and
it’s likely to leave the de-friended party con­
personal maxims for your sake.

I

fused and seething, at best Plus, it gets awkward, fast—have
class together? Mutual friends? Yeah, not so much. Even if you
hate this person’s guts, you’re not going to accomplish a whole
lot by treating them rudely.
The second way is to tell him or her off, explaining every
reason why that person is undesirable as a friend, and get in
a gigantic fight. Again, you now have an indignant, pissed-off
person, you’ve introduced a whole lot of unnecessary awk­
wardness into both your lives, you’ll probably feel guilty for
being petty, and... for what? Honestly, unless you think that
they are so screwed up that they absolutely need someone to
tell them this stuff—and you tliink that telling them will have
an impact on their Ufe other than thinking you to be heartless
and cruel—you’re better off keeping your trap shut.
There’s no good way to immediately cut short nascent
friendship, MMM. Don’t be afraid to say no to them if they
want to hang out; maybe you are going to spend some oneon-one time with another friend, maybe you’re going to study,
whatever. (It’s harder if you only hang out with one group
of friends and this person is in that group, but maybe this is
a good opportunity to branch out!) Avoid lying as much as
possible, and simply phase out spending time with them. Be
thoughtful. There’s no script for this sort of thing, but if you
do yoiur best to be considerate of others, you’ll be okay. In fact,
being considerate of others, especially if you don’t like said
others, will get you pretty far in life.
—Emma Gold

register

Freshman Bodies,
Freshman Souls
This reprinted article first appeared in the gadfly on Septem­
ber 2,1982. It was re-submitted by our current athletic director,
Leo Pickens. We’re sure Mr. Pickens is willing to stand in for the
first person voice used in this article and answer any questions
you might have about our great athletic program. —The Editors

he reasons, both physical and metaphysical, why every­
one ought to be apart of our sports program are many. I
list a few:
1. We have the best athletic program of any college in the
country.
2. Exercise is good for the body...unless you sprain an ankle
or something like that.
3. Most of us feel better, are more alert, and can get more
work done if our bodies are healthy and our souls are relaxed.
4. Friendly competition is one of the really fun things in life.
It is good for your soul.
5. Your circle of acquaintances will be greatly enlarged. This
is good for the soul, provided you can separate the wheat from
the chaff.
6. You will learn to accept, and bear with, thousands of splitsecond decisions from the officials, a few of which are wrong.
This is very good for the soul.
1. Do you like to strive for, and achieve, specific goals? If so,
consider our college blazers. They are much sought after, and

T

Courage
Tuck in your shirt,
or I’m going to make you.
Whether it’s a button down or a T,
I don’t care.
I want to see you tuck it in.

But you’re wearing sneakers?
Oh great. As if that matters.
Now go ahead and tuck it in.
But you’re not wearing a belt?
Yeah, well I have a black belt,
you son of a bitch. Tuck it in.

Take a cue from me, and whether
you want to or not,
take the shirt, unbutton your pants,
shove your shirt down your pants
and zip up again, so that the
shirt, is. Tucked, in.
—Chris Johns
the pathway is clearly laid out Striving for goals is good for
your soul.
8. It is probably true that the more pure fun occurs in the
athletic program than in any other area of the college. Fun is
good for your soul.
9. If you get involved in team sports and become a “good
team player,” you have realized that there are things in the
imiverse that are more important than your own ego. This is a
great good for your soul.
10. The benefits of exercise and friendly competition,
learned while one is yoimg, should be maintained for the rest
of your life. ..i.e, they should become habitual. For virtue, as the
Philosopher said, is a habit.
11. You will get to know numerous alumni, tutors, and staff
members who participate in the program. This is good for
your soul, or ought to be...provided that they are the proper
sort of role models.
12. Our showers are the best at the college; always plenty of
hot water.
13. Are you bothered by, or worried by, tobacco fumes in the
air? Come to the gym. The whole building is a nicotine-free
zone.
14. If you perform some sort of heroic deed on the athletic
field, your name will be mentioned in our weekly column. He­
roes are always acclaimed. But do not be carried away by this.
Remember that “the paths of glory lead but to the grave.”
15. A high percentage of our best students are active partici­
pants in our program.
16. Those who play, stay.
17. The gym is not particularly well-equipped, as gyms go.
But it has washers and dryers, and a Coke machine...and I will
explain to you, if you ask me, how you can get yourself in tip-

�top physical shape, without any equipment at all.
18. You can sit in an old-time barber’s chair in my office. You
can pump yourself up and down, and adjust the slope high or
low. Where else can you do that?
19. All work and no play makes Jack a dull boy.
20. It is better to li^t a candle than to curse the darkness.
So there you have it...twenty good reasons why you should
participate in our athletic program. If you are not convinced
by all of this, come and talk to me...I can probably think of
some more good reasons. Or better yet, talk with the upperclassmen. They will tell you all sorts of strange, interesting,
and wondrous things.
—Bryce Jacobsen, Class of 1942 and
FORMER Athletic Director

etiquette

Speaking of Tutors
To All Our Students,
Many of you seem to be in some uncertainty about how to
handle greeting Tutors on campus.
The primary rule-of-thumb is this: you, the Student, are so­
cially obliged to greet a Tutor first, unless it’s reasonably clear
that he or she is otherwise engaged. Failure to initiate such a
greeting, at least when it runs no evident risk of intrusion, is

rude or insulting. You may be forgiven for such a lapse, but
you should still be ashamed of it. Sometimes Tutors may greet
you first, but this makes no difference; although they’re free to
initiate, they’re not the ones obliged to do so.
Note that the polite default is not a rigid rule, binding in
every single case without regard to circumstance. There is,
of course, some tact involved in judging when your expected
greeting might be thought intrusive, an attentiveness and dis­
crimination that’s worth cultivating.
I would counsel you all not to let the challenge or inconve­
nience of having to make such a judgment lead you into im­
politely ignoring your Tutors or foolishly pretending that you
haven’t seen them. Status-conscious social primates that we
all are, the latter tactic is remarkably transparent at almost any
angle or distance. I would also observe that a slight intrusion,
if there be one, will almost always be felt far less keenly by a
Tutor than the appearance of a snub.
—Carl Page
Tutor
MASTHEAD Elizabeth Spagnoletti &amp; J. Keenan Trotter, Edi­
tors; Marin Skokandic, Business Manager; Megan Faulkner,
Copy Editor; Chris Johns, Michael Lacy, Annika Schweibert,
Assistant Editors.
SUBMIT: GADFLY@SJCA.EDU
The photo above was taken by Rachel Ulrich.

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                    <text>1
Convocation Address
St. John’s College, Santa Fe
August 29, 2024
J. Walter Sterling, President
Good morning, again, on this beautiful day here, on our Santa Fe Campus of St. John’s College,
here over 7000 feet above sea level, in the foothills of Monte Sol and the Sangre de Cristo
mountains.
A beautiful day, and a significant day, ending one chapter, and opening a new one, for all of our
new students — beginning this evening for you freshmen, with the terrible beauty of the Iliad
and an opening question. Thus begins a new rhythm of life, as the bell rings, each Monday and
Thursday evening, and you enter seminar.
So, welcome to you freshmen, Class of 2028, and first semester graduate students. Welcome
family and friends joining us, the faculty of the college, all of our staff, and our returning
students. Welcome to low-residency graduate students and family members and others joining us
online. A special welcome to Katarina Wong, president of the St. John’s College Alumni
Association and member of our Board of Visitors and Governors.
My remarks will seem aimed at our freshmen. For our new graduate students, including lowresidency students, please know you are just as integral to our community of learning, and the
heart of all this is intended for you, too. What you are undertaking exemplifies, in its own
extraordinary way, the convictions and aspirations of our college.
I will explore two themes: First, to reflect with you a bit on what it means to join this
“community dedicated to liberal education.” — Our most foundational document, modestly
titled, “The Statement of the Program,” has long opened with the assertion that, “St. John’s
College is a community dedicated to liberal education.” — Second, I will propose four sources
of sustaining strength, for the journey you’ve begun.
“A community dedicated to liberal education.” Who is this community? Let’s begin with you 90
freshmen. You come from all over geographically, and from all varieties of backgrounds. From
25 states, and from 6 countries abroad — Albania, Canada, China, Egypt, India, Nepal. From
public, private, and homeschool educations. Some grew up right here in Santa Fe, some daring
few have entered the United States for the very first time to join us here. Within the U.S., some
have traveled very far: 3,500 miles from Palmer Alaska, 2,300 miles from Pownal, Maine.
You discovered St. John’s along various paths: from a deep love of books, or the advice of a
favorite teacher, from a Johnnie family member, or moved by the visit to campus or the Summer
Academy, some thrilled by the people they met here, or the conversations they joined, some
drawn to this bold vision of what a college education can be, some arriving after attending other
colleges or being out of school in the world of work for a season.
The community you join is small in a way — 400 undergraduates, 100, graduate students — but
it contains more varied backgrounds than many larger communities, and, because of the shared

�2
course of study, and the constant conversation together which you have already begun, you will
experience more diversity and empathize with and learn from this wide range of backgrounds,
beliefs, and perspectives more than is likely in the relative anonymity and dispersion of more
conventional colleges. We are also a campus community, including our staff and faculty who are
united by uncommon dedication to the program and to your and their own learning. Our constant
practice of shared inquiry requires, and fosters, mutual civility and respect, inclining naturally
toward empathy and friendship. Such civility and respect are modeled daily in the classroom by
our tutors. We do not seek facile agreement or hard-edged debate. We seek to reason together
and, as our Statement says, to learn from our differences and discover our shared humanity.
Radiating out from our campus, you now join the community of all Johnnie alumni, whose
education was shaped by the same program and community, if varying in details, over the years
and decades. And you now live in this remarkable city of Santa Fe, New Mexico, a city in which
this college has found a home for 60 years.
To what are we dedicated? “Liberal education.” You know already you have chosen a college
that aims to offer as complete an undergraduate education as possible in the most important
respects, “a complete and generous education,” to borrow a phrase from Milton — that is, to go
as deep as possible into the fundamental questions, to the roots and foundations of things, and to
be as broad as possible in respect to the range of human faculties and fundamental domains of
knowledge and life. You will be required to, or given the opportunity to, translate Plato and
Sophocles from the original Greek, in which you will acquire basic competence, and you will be
asked to work through Einstein’s 1905 paper on special relativity, equation by equation. You will
sing and analyze music. You will draw flowers and conifers and dissect biological specimens and
observe light’s wave-particle duality. You will study the works of Adam Smith and of Karl Marx.
You will study Euclid’s Elements and the genesis of and techniques of calculus. You will begin
tonight with seminar conversations on Homer and then as seniors explore the works of George
Eliot, Virginia Woolf, James Joyce, William Faulkner, Toni Morrison... and so much more!
You may be challenged by those who see in the phrase “liberal education” neglect of the
practicalities of life. But this is a mirage. Every college and university, all of what we call higher
education today cannot avoid balancing three aims, simply put: the pursuit of truth or knowledge
as an end in itself, preparation for citizenship or political life, and preparation for career or the
practicalities and necessities of our work-life. Liberal education properly pursued advances all
three aims, in a well-balanced way. The truth is that what distinguishes St. John’s is not that our
aims and values are unusual; it is that we are able to pursue certain widely shared values in a
more uncompromising way than most educational institutions. Most educators and academics,
when asked, would love to have smaller classes (like yours), discussion-driven classes (like
yours), and highly self-motivated and curious students (like you). They too believe all or most
students would benefit from much more time with great works of literature and philosophy, read
patiently and thoughtfully, and with deeper logical and mathematical study, and from many other
areas that are too often neglected. But they and their institutions, for many and varied reasons,
are not incentivized and not able to offer these things quite so well as we can. Most other
institutions have added aims and added constraints. They must strike a different balance or have
a necessarily narrowed focus.

�3
You may also be challenged to explain the relevance of studying so closely classics of the past. I
recall many years ago hearing our revered former dean Eva Brann answer a parent’s challenge to
that effect in this pithy way, as I recall it: “Our world is technology and democracy. Those are
Greek words, and to understand our world today you must ultimately understand its roots in
Greek thought.” — Properly interpreted, you could almost deduce our whole program from that
premise. We are not studying the past as past; we are studying the living roots or natural history
of our present world.
Liberal education, pursued in this broad and deep way, is not only relevant today, it is needed
seemingly now more than ever. It strengthens you, where current society is weak or faltering. It
cultivates the habits of mind and character that are needed now to face the dystopian trends of
our technological society and the polarization and loss of civility in our political life and
discourse. The remedy to these depends on and passes through a renewal of education, one that
points strongly toward the heart of what we quietly pursue at St. John’s. I am convinced that
there are more people today who see the need for that renewal than there were 10 or 20 or 30
years ago.
I offer those as some opening reflections on our community dedicated to liberal education.
Now, “Noble things are difficult.” So goes a Greek maxim you will translate. You arrive here, I
hope, eager and energized for the work ahead, curious, with senses sharpened. But you also
know it will be challenging. You came here not for something easy but for something substantial,
and therefore challenging. You will struggle at times.
Let me point to what I see as four sources of strength and sustenance that seem to me well-suited
to lift you up, to lift each of us up. My hope is that making them explicit can make them more
available.
The first, perhaps easiest for us to see on the surface, is not to lose sight of the seriousness or
grandeur of the work itself, its height or excellence, its depth or gravity. The works we
characterize as “great books,” and the kinds of questions you will pursue, are truly impressive,
often enigmatic, often dazzling and elevating. Do not let their difficulty eclipse that vision. When
the work of the day falters or becomes a grind, remind yourself that you really are doing that
hard work and persevering, in order to illuminate the most fundamental matters, to cultivate the
kind of soul that can dwell near and benefit from great wisdom and beauty and the works that
express them.
Second, you have, we have, one another: There is much in life that isolates us, and typically it is
when things seem darkest or most difficult that we feel most isolated. Here, you are closer to
many others who can offer empathy, understanding, and support, than most students out there
are. The small size of this community, your daily study and life together, the common
curriculum, the familiarity which your tutors have with what you are doing and with the
members of their classes, the staff who know well the character of this campus, the program, and
all the resources available for getting through times of difficulty, your friends, and your
classmates and room and hallmates. There are truly always more folks you can reach out to and
connect with, nearby, prepared to help — and likewise, you are there for them. Sometimes it’s

�4
hard to see that — here and in life — but I really believe it can be very true here, for each of you
— and you should be ready to reach out, open up, and rely on those around you.
Third, let yourself experience this place: the city of Santa Fe and our natural setting. For some of
you, this is familiar — home or like home — for many of you it may be unlike anywhere you
have lived. The geography, climate, culture, and history here are truly extraordinary, and you
would do well to cultivate actively an interest in and attachment to the place you are in. That is
true wherever we are, but there is so much here that invites and rewards the effort of active
attention and exploration.
The world-renowned author, and longtime friend and supporter of our college, Scott Momaday
— who passed away this January and whose Native peoples were of this land and its history —
was one of the great thinkers and writers of place and land. I have thought about him often since
his death. As he wrote, each of us, “ought to concentrate his mind upon the remembered earth, I
believe. He ought to give himself up to a particular landscape in his experience, to look at it from
as many angles as he can, to wonder about it, to dwell upon it. He ought to imagine that he
touches it with his hands at every season and listens to the sounds that are made upon it. He
ought to imagine the creatures there and all the faintest motions of the wind. He ought to
recollect the glare of noon and all the colors of the dawn and dusk."
This place, which seems austere to some, rewards our care and attention. The evening sky at
sunset, the brightest stars most any of you will ever live among, the smell of the land after the
rain. Likewise, the art, music, and history open to us, just in a two-mile radius. If you can really
make this place part of what it means to be a Johnnie at this college, that alone will carry you
forward like a wave.
Finally, joy: Cultivate a spirit of joy. This does not mean carrying things lightly. What you do
here is serious, but not at all grim. Avoid the temptation often pressed on us by the loud voices in
the world, to dwell on what is melancholy in things, especially when facing hard work and
challenges. Find joy in what you do here, in playful fun, in the deep wonder of insight, in
exercising resilience in the face of adversity. Delight in the range of what you are undertaking
and in the many flashes of beauty in these works. Find joy in perplexity, knowing it’s a
precondition for learning. Find joy in cultivating your attention (against the great counterforces
of this age of distraction). Enjoy physical exertion and moving your body in this wonderful
setting. Delight in the landscape. Enjoy the company of your friends and companions.
Success at St. John’s involves a blend of humility and audacity, as does a worthwhile and
adventurous life. The program naturally elicits both, in different ways. If you can remain attuned
to sources like these that can strengthen you, that can invigorate you and pull you up and over,
through, or around the obstacles of the moment, each of you will, I am confident, flourish here.
I declare the college in session. CONVOCATUM EST.

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                    <text>Music:

The Representative Liberal Art

Dean's Lecture, Friday, September 2, 1988
Wendy Allanbrook - Eva Brann

I.

fn General (Eva Brann)
There is an old tradition concerning this, the first lecture of

the new year of learning.

It is supposed to be dedicated particularly

to the freshmen among us.

The others, upper-class students and

tutors, are not supposed to mind if they hear things not entirely
fresh to them.

This is an occasion for talking straight and being

explicit about what this community, which the freshmen r..ave newly
entered, is like.
Consider that phrase, "what St. John's is like."

It is part of

our pride and of our anxiety that this college is not like any other.
And yet we intend it to be like something, namely as much as possible
like the idea for teaching and learning it embodies,

the Program.

This program consists almost as much of what we staunchly don't do as
of what we do do.

So this lecture will be about the Program, about

what is in it and what is not.

But we have chosen to talk about the

program by means of an example.

It is what you will soon learn in

your Greek tutorial to call a paradigm:
how many things work.

one pattern which indicates

This paradigm is music.

However, we want not only to tell but to demonstrate how things
are intended to happen here.

We hope that as this lecture proceeds it

will show, practically, three things:
First, that although the program is a firm course of learning, it
is also full of live questions and problems which the faculty argues
1

�about.

One such current concern is precisely the standing of music

and its shadow effect, the absence of the visuai arts.

Obviously the

program that is will keep you very busy, but it is very likely to
rouse in you an occasional interest in the program that isn't and
might be.

Let me inject a preachment here:

Prepare to live a

schizophrenic life ("Schizophrenic'' is a Greek word meaning splitminded).

On the one hand trust the program to be a thoughtful and

experience-laden guide to the studies of your next four years.
other hand, hold everybody and everything responsible.

On the

Ask your

tutors now and then--not so often as to become pests who wreck the
daily process of learning--why you are doing what you are doing.
them respond.

Make

And reserve the highest respect for those tutors who

admit they have no pat answer and begin to think in front of and
together with you.

As the year goes on you will discover that there

is a presence that haunts this campus.

It is that of a man called

Socrates who said that to carry on in life without asking questions
about it is simply insupportable.

He will be, as it were, egging you

on.
The second thing we want to show you is that it is possible to
think together.

We've all heard a lot of talk about "thinking for

oneself," as if anyone could possibly think for us.

The miracle is

that we can think for ourselves together; it is that strange
possibility which makes this school a community of learning.--By the
way, I should say right now that such cooperation, too, will become
questionable.

You will read a text later on this year which will

claim that although the friendship of like interests is a wonderful
thing, to be totally happy is to be totally wrapped up in thought,

2

�absolutely self-sufficient.

But the soul of this school is

conversation, which is audible, cooperative thipking.
study is not only allowed.--It is encouraged.

And common

In the question period

we can talk--if you like--about the role of competition in this
scheme.
The third, dependent, effect we want to demonstrate is the really
important one.

It is that we can approach a subject on very different

levels and with very different preparation.
I will be talking about music in the widest sense.

Mrs.

Allanbrook will specify and make concrete some of my broad
indications.

Moreover, I am a, by now confirmed, amateur of music,

while she has a lot of musical learning.

My deficit will not, I hope,

keep me from making some sense nor will her expertise keep her from
reaching some fundamental questions.
I am now getting closer to the topic, music, and it is precisely
the matter of amateurism which brings me to it.
college of amateurs.

You have come to a

All your tutors will have some expertise, but

usually not in the classes in which they are guiding you.

In those

they will indeed be merely amateurs, which is just French for lovers-lovers of learning, of course.

I will tell you what my expertise was,

because it will be to the point later on.

I was an archaeologist,

which is to say, a kind of grass-roots art-historian.

I got to sort

out sherds of Greek pottery and to reconstruct the pictures on them,
often revealing dramatic and sometimes deliciously scandalous goingson.

Then I had to put a date to them, which takes close looking.
But in music I am an amateur, and thereby hangs a tale important

to the program.

This program stands under the aegis of an activity

called philosophy.

In a few weeks you will have learned enough Greek
3

�to know that the word philosophy means "the love of wisdom."

Now, the

reason it is possible to put a whole school under this aegis is that
to engage well in philosophy it is truly sufficient to love the
enterprise, just as the first and last entrance requirement for this
college is an ardent willingness to be here.

There

~.

sadly, some

people who care very much about philosophical questions and are just
not good at talking about them.

But they are very rare.

Philosophy

requires disposition more than talent.
It is otherwise with music.

It is possible to love music with

all one's soul, to live with it and by it and yet to have an
uneducated ear, an ear that hears the effects without discerning the
elements.

Music has this enormous and mysterious power:

Whereas one

must be literate to love, say, a great novel, it is possible to be
entirely enraptured by music and entirely illiterate iri it.

It is

because music can touch the soul by means of effects which are deeply
rational and may yet remain stubbornly unapprehended that music is the
hardest part of the Program to teach.

Why, then, should it be a part

of the Program at all?
A good way to begin is with the name.

Music is that which

belongs to the Muses, nine ancient divinities.--If you transfer to
Santa Fe sometime later on you will easily learn their names because
the dorms are called after them.

These goddesses are in charge of all

kinds of human cultivation, epic, lyric, tragic, comic poetry, miming,
dancing, even history.
astronomy.

The grandest of these is Urania, the muse of

This fact will figure later on.

daughters of Memory.

All the Muses are the

This fact yields a double inference:

arts come to human beings by divine inspiration.

4

First, the

And indeed, your

�first and second seminar books begin, or very nearly begin, with the
words:

"Sing, Goddess.

. . " and "Tell me, O Muse . . . "

arts come to us through tradition or through memory.

Note that a

third possibility, the one most familiar to us is missing:
arts are our own creation.

Second, the

that the

That possibility was not added until the

Renaissance, the start of modern times.
In the beginning, then, music embraced all the arts.
that

will

preoccupy

you in the middle

of

human cultivation is seen to have two aspects.
soul and gymnastics for the body.
the place where you go naked.

the

year,

In a book
Plato's Republic

There is music for the

"Gymnasium" is a Greek word meaning

So music is for the shapeliness of the

soul, and gymnastics is for the candor of the body.

However, it turns

out in that book, there are even greater things than psychic and
physical cultivation.

These higher studies are those which later come

to be called the liberal arts.

They are higher because they do not

just cultivate and shape you but because they put you into a relation
with the way things are, or, as you will soon learn to say, with
Being.

One cultivates the arts for pleasure and self-development, but

the liberal arts one pursues for the sake of truth.

Incidentally,

these arts are traditionally called "liberal'' for three reasons.
First because they are taught to the free children of politically free
parents, second because they liberate these youths from their dogmatic
opinion, and third because they are done freely, without money-making
in mind.

If you look at our college seal you will find there a little

ditty on this theme.
They are called arts because they are elementary approaches to
the elementary subject matters.

Today there is much talk about skills

vs. subject matter, process vs. product.
5

In the liberal arts there is

�no such distinction:

Studying the subject and learning the skill are

almost completely one.
Traditionally these arts, of which there are seven, have been
divided into two sets.

The lower, and basic, set of three is called

the trivium or "three-way."
speech:

These trivial arts are the arts of

grammar, logic, rhetoric.

of "trivial" in this school is:

Therefore the proper understanding

of absolutely fundamental importance.

The second set, the quadrivium, or "four-way," contains the arts
of reason in nature.

The Republic, the work I mentioned above, sets

out what these are and how they are to be studied.

The four arts--

they happen to be sciences, but sciences liberally learned happen in
turn to be arts--are these:

arithmetic, geometry, astronomy and a

fourth I will mention in a moment.
I need not tell you that you have come to a liberal arts college,
indeed one of the few in the world where the liberal arts tradition is
taken quite literally.

Let me show you how much we mean it, how much

your day will be dominated by these arts:
Morning:

Here is the schedule:

Trivium, done in the Language Tutorial.

Lower

Quadrivium in the Mathematics tutorial.
Late morning and early afternoon:

Upper Quadrivium, done largely

in the Laboratory.
Late afternoon:

Cultivation of the body, done largely in the

Gymnasium.
Evening: -Let me backtrack here.

The Republic not only describes the quadrivium

but tells how to study it, namely liberally, philosophically, not for
practical purposes nor even as performances, but for the sake of

6

�reflection and insight.
there is philosophy.
Evening:

Beyond the liberal arts and all through them

So let me continue:

Conversation about books that reflect on the nature

of things, done in the Seminar.
Night:

Continued conversation.

On Fridays, a Lecture.

Possibly some sleep.

And once a week you will come together to sing in Chorus.
Now is the moment to come back to the topmost liberal art, in
Plato's

book,

the

one I had omitted just now.

It

is

called harmony.

The word itself means a fitting-together, a system, and in the
narrower sense those fitted tonal structures out of which music is
made.

For these are a paradigmatic system.

So we have come to music

as the coping stone of the liberal arts.
Why should this Greek author have put music, of all the arts, at
the top, with and above the study of the heavens?
reasons.

I can think of four

The first is complementary to the reason why the Greeks

assigned a muse, the aforementioned Urania, to astronomy.

It is that

they thought that the stationary heavens, being organized on the model
of a musical scale, were not only a rational but a beautiful system,
as they said, a "cosmos," meaning an ornament.

The second is that

they thought that each moving planet (the Greek word planet means
''wanderer") in its orbit sounds forth a lovely note as it revolves and
that all together these make a ravishing harmony.

The third has to do

with the fact I mentioned earlier on; that the conscious apprehension
of music involves the study of number, as the production of musical
instruments involves the study of geometry.

Leibniz, a philosopher

you will study as Juniors, says, that music is the soul's counting.
One might say that it is also the ear's measuring.

7

Indeed as you will

�d~s~over,

there are certain ever-fascinating problems in mathematics

to which we pay great attention, and which are spectacularly well
exemplified in music.
music.

The whole quadrivium appears to be assembled in

In fact, in a moment I shall claim that it coopts the trivium

too.
The fourth reason is closely bound to the third:

Music is not

only a kind of mathematics, but also a wonderfully peculiar kind.
might call it "qualitative mathematics."

Here is what I mean:

One

In

number theory one does not, on the whole, want to say that some number
relations are more agreeable than others.
some, very definite, number relations
They are called consonances.

In music it turns out that

~more

agreeable than others.

Others make you shudder.

For example,

the tone that sits exactly between the two C's of our major scale, F#
sounds so dreadful when sounded together with C that it is said to
belong to the devil.

Behind it there lies a simple but scandalous

mathematical fact, the fact of so-called irrationality.
I mean by qualitative mathematics.
mathematics.

That is what

You could even call it miracle

And that is also why we think that something is

necessary for studying music that we expect for no other tutorial:
some common prior experience.

It is . for this reason that you will be

going to Chorus in the year before the music tutorial--to have the
specific common experience of this rational magic.
But now I have committed a sin against logic.

I have explained

why music is the topmost liberal art without saying how this activity,
so specially named after the goddesses of the cultivating arts, comes
to be a liberal art at all.
and ask rather:

Let me attack this question in new terms

Why is music traditionally a liberal art when the

equally ingenious visual arts are not?
8

I can think of three answers--

�and a fourth, which is more a wonderful problem than an answer.
First there is simply more hard music theory than there is art
theory.

There is, for instance, a physics of music as there has never

been a physics of aesthetic color.

There is, to be sure, a science of

structured space which is analogous to the number theory of wellfi tted notes, namely perspective.

But perspective came late into the

visual arts and left soon.--It is not as

n~cessary

to painting as

structured numbers are to music (though in fact we used to have in the
Program a lovely sequence on perspective as a preliminary to the study
of optics).

I do not really know why there is more teachable theory

of music than there are principles of visual arts.

It must be

something like the same reason why there are many respectable Sunday
painters and very few bearable Sunday composers.

Moreover, space has

vastly more possibilities of being filled than does time, so that the
spatial arts are correspondingly less easily developed from basic
elements.

This is one of those great questions which I leave dangling

before you.
Secondly, music has always been known to have a potent influence
on bearing and character.

You will read several books this year, the

Republic among them, which will claim that music--and the dancing that
goes with it--is crucial in the shaping of citizens.

The ancients do

not think, as we tend to do, that music primarily expresses our souls,
but rather that it impresses them, stamps them with character.
Imagine an unlikely event which will drive the point home:

Suppose

all children in our democracy were to learn to dance the minuet in
kindergarten, to move every day for a year to a slow and stately music
in modestly connected couples.

Wouldn't America be a different

9

�country?

I cannot think of any visual work that would have such an

effect--if only because one can close one's eyes but not one's ears.
There is also another reason why the visual arts do not impress
themselves as directly on the soul as does music which I leave to
last.

I do, however, except architecture.

•

Architecture was,

incidentally, the one visual art which was at certain times a
candidate for being counted among the _liberal arts.
Third, music has just the reverse relation to words than have the
visual arts.

We rightly wince just a little at those people who can't

look at a painting in a museum until they have run to look at its
title.

But we think that is is a part of musical discernment to

listen as carefully to the words of a Passion or an Opera as to the
music.

Pictures displace words, but words and music are meant to go

together.

Now thinking takes place in words.

Consequently the

meaning of music must be somehow closer to our thought than the
meaning of a painting.

How music and words have meaning separately

and together is a confounding and enchanting question which you will
hear more about tonight.
Following my own advice to you earlier on, let me stop here to
tell you forthrightly what I think about the presence of music and the
absence of the visual arts from the . program.

I think that the Greeks,

who produced works of visual art, especially of sculpture and
architecture, which once very palpably pierced my soul, had deep
reasons for including music among the liberal arts while excluding
these visual glories.

And we in turn have good reason to stay with

the liberal arts and, in preserving our integrity, to exclude
something very wonderful--exclude it from the Program, I mean, of
course, not from the campus.

On the campus we should have, and do
10

�have, a lot of opportunities to do and see such art.

But even in the

Program itself there is sporadic room, for example, in Seminars,
Lectures, Study Groups and Preceptorials on the visual arts.
Particularly those Preceptorials, the small semi-elective study groups
which you will join in your last two years,• are a good place for
tutors to offer such studies.
the following title:

"Greek Temples, Gothic Cathedrals and Mid-

Western Grain Elevators."
of their own.
preaching:

I myself would like one day to offer

These last have a certain utilitarian glory

Here, incidentally, is the moment for yet another

Come to the question period!

For there you will hear with

what passion and reason the contrary argument can be made.

And there

you yourselves can join in this perennial conversation.
Finally, then, there is that fourth distinction between music and
the visual arts which I have left to the last because it is the
trickiest, most fascinating yet.
representative.

The visual arts are by and large

They re-present , or imitate, a visible object.

They

convey a likeness, a similarity, an imitation, in such a way that one
can find some sort of rough geometric relation--it is of the kind
called projective--between, say, a portrait and its sitter or a
landscape painting and its natural scene.

It is the representative

nature of the visual arts that accounts for · the effect I just
mentioned, that these arts go to the soul less directly than does
music:

They require an intermediate recognition. I must tell you that

the hottest and most crucial issue in modern esthetic theory is the
"representationality" of all the arts in general and the imitative
nature of painting in particular.

There are people who claim that a

cat in one painting and a cathedral in another are more like each

11

�other than a painted cat is like a live cat or a painted cathedral is
like a stone cathedral.

They think that imitation (or as you will

soon learn to say, mimesis) is no factor in what makes a painting a
painting.

I mention this to show how fascinatingly extreme the

arguments about representative art have become.

Music, however,

appears to have no such diverting problem; on the face of it, music
hardly appears to be representational in the projectivai way of
paintings.

Take your favorite symphonic movement and ask yourself and

your new roommate what it represents.
surmise.

It's an invitation to wild

And yet music seems to show so much and mean so much.

Here

lies a captivating problem, and so begins the specific demonstration .
Is music really in no way representational?

We will see how we can

think about particular pieces of music in the light of this large
questions.

I have talked about music as a liberal art, and now we

will be drawn into its actual and specific pursuit.

12

�II. In Particular (Wendy Allanbrook)
If I were again a student, seated in the audience tonight, the
question I would be askingis "Why should one want to say that music
is representational?

Isn't it precisely its non-representational

quality that gives music its glory?"

This was surely my opinion when

I was in college; I remember clearly the day I discovered a

learn~d

treatise that corroborated it, and spent hours in the stacks of the
college library fiercely underlining pregnant passages. I have since
lost my original copy of the treatise, a work by an eminent nineteenth-century music critic, Eduard Hanslick, entitled The Beautiful
in Music, but I have no difficulty guessing the formulations that
pleased me so: for instance, "The ideas which a composer expresses
are mainly and primarily of a purely musical nature." [23] or "[Music's] nature is specifically musical .... [Its] beauty is not contingent upon nor in need of any subject introduced from without but ... it
consists wholly of sounds artistically combined." [47]

It is no

longer clear why this notion of musical autonomy was so important to
me then, against what heresy I was defending the sweet art.

When,

later on in my education, I came up against those who would argue the
other way, I fought bitterly, and then fell.

Often one becomes most

passionately interested in pursuing the notions of which one once
thought the opposite; I appear before you tonight with the enthusiasm
of the converted.
I shouldn't play quite so dumb, of course; there is an obvious
enemy in question.

For example, music that attempts a one-to-one

correspondence with natural phenomena we often find ludicrous, and
often indeed it is meant to be gently comic; there is something
13

�delightfully fey about those sixteenth-century madrigals that imitate
cuckoos, and it is even more fun when, as was intended, you are
singing them yourself.

Another connection that gives musical repre-

sentation a bad name is the one Hanslick seems principally to have
been inveighing against:

the noti~n of "self-expression," which

leads to the vice of musical biography:

in this passage Beethoven

rails against his deafness, here Mozart mourns his father's passing.
These claims are unsupportable, if only because so often our biographical expectations are

frustrated.

Mozart wrote some of his

most sunny and popular music in the period just after the death of
his father.

Do we accuse him of lack of feeling on this account

(some have), or dismiss the connection altogether?
There seems to be a common agreement that music exists in another world than the fine arts and those that have to do with speech.
One of your tutors, Mr. White, recently gave a lecture in which he
discussed ways in which the fine arts and the poetic arts can be said
to imitate.

His point of departure was a well-known comparison, by

the eighteenth-century German critic, G. E. Lessing, between a Greek
statue and a passage in Vergil's Aeneid.

Both depict the violent

death of the Trojan priest Laokoon in the coils of a sea serpent, the
one work in stone and the other in metrical speech.

The statue,

because it must choose only one moment in time for its representation, avoids the harrowing death cry of the priest and depicts a
more restrained moment, prior to that of the greatest agony, in order
not to become merely ugly or grotesque. The poetry, because it moves
through time, can describe the terrible bellow of the priest, the
desperate distortion of his features, because one by one it can leave

14

�them all behind.

Music, too, is a temporal art, but can you imagine

any way of making it the third in this comparison?
no commonality at all.
man?

There seems to be

Where do you make out the monster, where the

How can we even specify what moment the composer has chosen?

Unless the music is explained by a companion text--and this is really
a special case--I see no way of talking about the three with the same
analytic language.

Unlike poems and paintings, the subject of a

musical composition cannot be translated into a meaningful
proposition.
But what do we gain by severing all the connections the art
bears to the human sphere?

In fact, it was only in the nineteenth

century that those who think about music decided to cast her thus
adrift.

And that came about largely as a development of that novel

notion Miss Brann mentioned, that the arts are our own creation.

If

they are, it is not a giant step to the conviction that they are
created anew by every artist, that every work is a personal statement
of a private seeing--or hearing--that the audience is privileged to
share. Music becomes pure feeling--the art of self-expression, the
inner mysteriously made outer, and although this has its attractions,
it is not an aesthetic that is supportable for long.

No wonder

Hanslick was in revolt; one begins to have some fellow-feeling for
him.
As a result of this legacy, modern philosophers make an extraordinarily vexed question of expression in music.

That they use the

word "expression'' is in itself indicative, for I suspect that were
they to free themselves from the notion of feelings as the sole
proper subject matter for music, they might not be so squeamish in
their discussions.

As one critic recently remarked, we go through

15

�such tortured arguments, and all we get is the freedom to attach the
predicate ''sad" to the slow movement of a Beeth6ven Symphony.

But

other formulations had guided thinking about music for the previous
millenia, formulations that more successfully made the connection
between human beings and the art of shaping sound in time.

Miss

Brann mentioned the ancients' belief that music can impress our
souls, give them shape.

Aristotle, in remarks in the Politics about

the importance of music to the education of a citizen, makes specific
claims for the depictive qualities of music in its relation to the
human soul:
Rhythms and melodies especially contain
to

the true natures of anger and

likenesses

gentleness,

and

further of courage and temperance, and of all their
opposites,
this

and

of the other moral qualities

is clear from its effects,

for when we

(and
hear

these things we are changed in our soul.)
Aristotle's claim is that music makes "likenesses" of human passions
and qualities, to which we naturally respond.

Elsewhere, in the

Poetics, he calls the poetic and musical arts all "modes of imitation"

(mimesis in the Greek)--modes of imitation of human beings in

act.

Imitation is another degraded word today, for it implies origi-

nals out there, of which the artist simply takes a copy, and it is
more modern to consider the artist both the origin and the original.
But if the original is the ways of human beings in the world, is the
whole of God's cosmos, and there are infinitely many ways of taking
that copy (I'll call these variations "style"), then the task of
imitation seems not degraded, but endless, various, and noble.

16

�The crucial question then becomes, how do we make these musical
copies?

The answer lies in the qualitative mathematics of which Miss

Brann spoke earlier.

How does the soul count, the

There are two principal ways, I would maintain:

~

measure?

the way that number

•

shapes time--we call that rhythm--and the way that number informs
pitch--it's harder to come up with a generic name for that.

I hope

not to be too provocatively simple when I say that in this counting
only two numbers count, namely 2 and 3 (some Renaissance theorists
counted to 6, and we could do that too, but for our purposes this
evening it isn't necessary).

I'll tell you briefly what those

numbers mean, and then move to exemplify them.

About rhythm I'll be

most brief, for you probably know that the available rhythms reduce
to counts of 2 and 3, or some combination thereof.

Think of 2, or

duple, as a march or simple alternation of left foot and right.
3, or triple, insert a hop on every left.

With

There are more elegant

ways of adorning a walk to get a triple; the minuet Miss Brann
mentioned goes to the count of 3.

But more of this later.

The 2's and 3's of pitch are rather more concealed, to the
extent that we commonly call by the name "5" what really ought to be
called "3."

Yet the phenomena are sufficiently important and dazz-

ling to have been credited to a discoverer, Pythagoras, and surrounded with their due mead of apochryphal stories about the circumstances of the discovery.

The note we designate as 5 in the string of

organized pitches we call a "scale" actually stands third in the
order of generation. Take a string, and divide it in two equal parts.
Pluck either half, and the resulting pitch will reduplicate the
original, but higher--that interval we call the octave, which orders

17

�tonal space by its regular recurrence over the entire series of
pitches. It puts the cap on our eight-note scale, which will sound
all too familiar to anyone who has ever had a piano lesson:

[Ex. 1] .

Next in this soul's counting divide the string in thirds, and you
have the fifth, so called from its position as number 5 in the
ascending scale.

It provides an intermediate resting-place in the
/

octave's span, dividing it almost, but not quite - (and this is crucial) in half.

You'll recognize it from the sound of this perennial

five-finger exercise:
reverse:

[Ex. 2].

By the way, the process works in

if I want to divide a taut string into perfect halves, all

I have to do is find the octave--our ear is indeed the measurer.
While the octave is other, it is still somehow the same as our primal
pitch, so the fifth is the first independent other; the octave is the
encloser, the fifth the first enclosed.

We will honor the order of

experience by calling this pitch 5, and the interval it forms with
our starting-place the fifth.

Never forget, however, that it stands

proudly third in order of generation, and that its generating number
is 3.

You will go more deeply into these miracles of embodied number

in the music tutorial sophomore year, counting at least as far as 6,
but for now this is all the theory you need to know.
I shall try to put these various 2's and 3's to the work of
imitation.
ways.

And I shall claim that they do this work in two important

It's hard to find proper names for them; we've learned to be

wary of the time-honored distinction between form and content in
almost all its applications, and in a temporal art like music I think
there is almost no defense for it.

I find myself, however, stuck

with modern names like "reference" and "process," or perhaps "reference" and "syntax" (I can't decide).

18

These duos take more explana-

�tion, but they don't halt and

freeze the persistent motion of the

tones the way "form and content" do.

If we wanted to be trendy, I

could point out that we are on the cutting edge of modernity here,
for our categories could be formalized into the modern pursuits of
semiotics, or the study of signs, and narratology, which is nothing
more than the study of beginnings, middles, and ends.

Actually, that

is - not such a bad description of what I want to talk about.

I shall

present you with three musical examples to illustrate these modes of
imitation.

In them the 2's and 3's of rhythm will intersect with the

2's and 3's of pitch to make dazzling imitative configurations.
Given the embarassment of riches in music history, I can only be
suggestive, not inclusive; I shall also be decidedly anti-chronological.
I shall begin where those who know my preoccupations could well
have predicted--with the music of Mozart. It was the music of Mozart
that I most wanted, early on, to defend as pure, and precisely the
same music I later found to be most delightfully contaminated with
reflections of human activities.

Furthermore, this particular work

of Mozart's, the piano sonata .in F major, K. 332, a favorite example
of mine, is precisely the kind of music the purists would argue is
the most autonomous music your money can buy--instrumental music.
Here there intrudes no voice uttering sounds that are signs of other
presences, and thus forcing a translation to mundane
can such music point beyond itself?
porary with Mozart gives

me~ning.

How

A French writer roughly contem-

us a hint of how this might be:

Michel Gui

de Chabanon, actually an advocate of music's integrity, perhaps
despite himself articulated one crucial way in which music can represent:
Imitation in music is not truly sensed unless its

19

�object

is music.

imitate

In songs one can

warlike fanfares,

melodies,

etc.

It

hunting

successfully
airs,

rustic

is only a question of giving

one song the character of another.

Art,

in that

case, does not suffer violence.
I'll translate this to our own purposes.

Once music has a history,

it can hardly fail to make reference to this past, - to provide its own
vocabulary of expression.

Miss Brann mentioned the educative value

of minuets, and that is apposite here.

Much of the art music you

know, the music played in symphony halls and on good-music stations,
pieces itself together from the more mundane music we use to accompany daily activities.

The tempting world of human motion is out there

to imitate, and some of our greatest composers have taken advantage
of it.

Love songs, lullabies, dances and marches, hymns, when are

lifted from their usual environment and placed in the frame of a
symphony or sonata, cannot help but point us back

to the particular

occasion that produced that humble popular gesture.
One of the most prominent identifying characteristics of these
gestures is rhythm.

The music of the minuet, a noble dance, is there

to assist the dancer in maintaining a noble posture--restraint,
control, refinement.
dignity.

Practicing it, we may over time learn grace and

Hearing it, we cannot help but think of these mobile vir-

tues; our body strains to move with them.

This smooth even count of

three is character-building and character-evoking--truly "qualitative
mathematics."

To help you count that three, let me play a minuet

part way into the first movement of the Mozart sonata.

It comes at a

crucial point in the piece, when a base has to be touched, a sense of
arrival created--not home plate, but, to use a further spatial meta20

�phor, diagonally opposite.
motion.

Sense the dignity and tranquility of the

When you hear what precedes it, you will feel it all the

more by contrast:

[Ex. 3].

This movement has a profusion of gestures; it might be described
by the question "How many qualities has 3?"

For it shows us 3 in

many lights, often reminding me of one of those magic sugar eggs with
the hole at one end, into which you look to marvel at the perfection
of the detail observed in its miniature world.

First we hear a

singer, her breast swelling as she reaches for her high note.
ber, this is all conveyed to us on the piano:

[Ex. 4]

Remem-

She should

continue, but instead her utterance is answered by two voices, not so
clearly vocal anymore, one following the other at a brief interval
and singing the same melody--imitative counterpoint is its proper
name, and to Mozart's audience it had a rather old-fashioned ring-pompous and over-serious:

[Ex. 5].

Another length, a simple unit of

minuet, moves to the close, so that our first "sentence'' has three
parts or clauses, of equal time but not necessarily equal weight.
The next sentence is devoted to the rhythms of a hybrid minuet--a
minuet crossed with hunting horns.

We recognize the horns because

the characteristic pitches of their calls in the field are imitated:
[Ex. 6] .

After a satisfying and discrete paragraph of this hunting

minuet, the movement "turns on a dime" to a dark, passionate music
often called "Storm and Stress," after the Romantic temper that
affected it.

Whole pieces were written in this style, but here it

becomes just one affect among many.

In its restlessness, however, it

serves the subversive function of undermining home base, and moving
us to that new place we must reach if we are to have any sense of

21

�having moved at all.

And--as you have guessed--at the end of this

so-called travelling music, we arrive at the well-shaped minuet you
heard before:

[Ex. 7].

The new arrival place marks the end of the

beginning and the beginning of the middle, and quite naturally this
new place is identified with 5 (3).

The drama of the

r~st

of the

piece will be the return to 1 via some cunningly shaped paths.

The

image of some sort of narrative does not seem to me to be far wrong,
much more apt than the formalist analysis.

Our delight in this

imitation is the delight in the reflections of

the many-wayed won-

ders of a close and ordered world, disposed to form the crucial nodes
of a well-wrought narration.

What is peculiarly musical about it is

that there is no real story in the sense we expect one, no proposition, no picture of Laocoon.

Yet in this passage-through-time we

sense an order, intuit a deep intent, and are deeply satisfied.
This Mozart example is an example of imitation in the most direct
and evocative fashion; I could show you many others.
like to offer an example of a different sort:

But now I would

first off, vocal music

(music with a text), sacred, not secular, and grand and special
rather than playful and habitual.

It is a piece those of you who

have completed the music tutorial will know well, the culminating
aria of Bach's St. Matthew Passion, "Mache dich, mein Herze, rein."
It occurs after the Crucifixion, immediately following the moment
when Joseph of Arimathea claims Jesus' body from Pontius Pilate.
This scene follows the procedure of others in the Passion:

a passage

from the Gospel of Matthew narrating the scriptural event is set in
the simplest speech song, and then commented on by an observer outside the time of the narrative, in verses by an eighteenth-century

22

�poet.

The commentary itself usually has two parts--a discursive

passage in a free declamatory style, sometimes called arioso, and a
more summary, epigrammatic statement, set in the full panoply of . an
aria, a closed musical form.

This particular scene takes place in

the evening, and the arioso text ponders the theological meaning of
eventide:
In the cool of the evening, Adam's fall was manifest.
In the evening the Saviour casts him down.
In

the evening the dove returned,

and brought

the

olive

branch in its beak.

o beautiful time!

O Eventide!

The covenant of peace is now made with God,

for Jesus

has

completed his cross.
His body comes to rest.
Oh!

dear soul, ask, go, and let the dead Jesus be given
to you.

O salutory, o precious keepsake!
In this poetry the peace of the evening and the covenant of peace
become one:

Adam and Noah are fulfilled in Jesus, who has paid the

most memorable price for the sins of all.

Eventide becomes a sym-

bol--and I think I use that difficult word correctly--for the peace
of God that passes all understanding.

Symbols are the theological

way--the cross is paradigmatic--and the text of the Passion is suffused with them.

So is the music, sometimes in an abstract and

impalpable way, such as the reach up to B flat on the word "blood"
(German Blut) in the scene of the Last Supper. Others, like the aria
that follows this arioso, move us directly--musically--at the same
time that they undergo this translation to a deeper Christian mean23

�ing.

At the end of the arioso the singer (a male, a bass) addresses

his own soul, telling it to go receive the dead Jesus, and then, in
the most tender and moving aria in the Passion, enjoins his heart to
prepare itself for the corning of Christ.
Make yourself pure, my heart.
I want to bury Jesus himself.
The poetry of a second section, the music of which we will not
examine, amplifies the symbolism:
For

he

is henceforth to have his rest in

me

forever

and

ever.
World, get out, let Jesus in!
Bach suits actions to words. That's a conventional phrase

most

analysts like to fudge with, and given the text the composer has to
set here, that must seem to you exactly what I am doing.
not particularly fertile in musical ideas.

The text is

How do you draw a musical

picture of a heart purifying itself? of a believer burying Jesus in
himself (as the second part of the text suggests)?

The task seems

preposterous, perhaps even blasphemous. I'll suggest an absurdly
simple answer.

You write a cradle song, a lullaby.

Cradle songs

from time immemorial have used rhythmic 3's in groups of 2; that is,
each 3 is a rock of the cradle, with the extra odd beat catching the
pause of the cradle at the extreme of its swing, poised for return.
These 3's are then grouped in 2's:

the cradle rocks back and forth.

Let's hear the instrumental introduction to the aria, to concentrate
on the effect of the rhythm.

Notice that the bass sets up the rhythm

briefly before the melodic voices enter;

th~

about it that the singer merely shares:

[Ex.

24

motion has an eternality
8] .

�Perhaps I should explain further why I find this device so
wonderfully appropriate.

On the surface it would seem to satisfy

neither purification nor burial, the dual requirements of the text.
But remember that the arioso text made death into sleep, an image
that is important throughout the Passion.

The believer--our last

example was Joseph of Arimathea--holds the blessedly resting Jesus in
his arms; this- male figure universalizes the pieta, the figure of the
weeping mother holding Jesus in her arms after the descent from the
cross.

Mary holds a full-grown son who is beyond the solace of

rocking, but the symbolic believer is allowed a maternal lullaby.

It

is thus, the aria argues, that believers should receive the Christ.
In fact, the aria is an injunction to the believer to accept in full
serenity the final agony of Christ as the bringer of peace to the
world.

Thus to bury Him is to rock Him to sleep with a mother's

lullaby.
There is some final musical detail I cannot omit describing
before you actually hear the singer's voice.

I have tried to show

how Bach, in setting this seemingly unsuggestive piece of text,
manages to explode it into deeper meaning using a musical gesture
that becomes symbolic, moving the believer both physically and cognitively to a deeper Christianity.

Strikingly, Bach sacrifices the

text to the hypnosis of the eternal.

Syntax, prosody, all those

things that suggest human meanings in human time, are suspended, and
even that element that makes musical syntax, the 5 (our 3), disappears to some extent.

Musically the 1, the center of gravity, is

instead held up on top, and a scale descends against it with each
rock of the cradle:

[Ex. 9].

The singer's line is wholly unvocal; it

imitates a characteristic Baroque instrumental line where one instru25

�ment plays the parts of two, first high, then low.
further apart so you can hear the two:

[Ex. 10].

I'll split them
A further

distortion of our natural expectations is the actual setting of the
text, rhythmically and melodically.

"I want to bury Jesus myself"--

"Ich will Jesum selbst begraben"--"Ich will Je-- sum selbst begra-ben."

Je- and gra- are stressed unnaturally by the move to a melodic

peak on an offbeat:

this extraordinarily awkward vocal line does

violence to both melody and text in the service of the hypnotic
cradle song.

Singer, song, and syntax are dissolved in the cosmic

lullaby that is the rocking of Jesus to the sleep of sin.

All human

history focusses on the descent from the cross; that moment of time
must stand for eternity.

When syntax must reassert itself, at the

end of this musical section, we are wholly prepared for the vocal
awkwardness on the final "begraben"--"bury"--the deep leap down from
the 2 to the 1, the octave to the prime, precisely the kind of
musical tone-painting we have grown to scorn this evening.

Bach has

habituated us in the course of this aria to music become meaning; we
accept a musical barbarism as a convincing theological symbol:
[Ex. 11] .
There is other music I should have talked about, were there
time, for example, the repertoire of many-voiced sacred Renaissance
vocal compositions.

There dance is absent, and composers eschew any

obvious translation of textual images into musical ones.

Yet the

theorists of this music are most emphatic about its imitative quality.

The object of imitation is nothing less than "wondrous Nature,"

as their prime spokesman, Gioseffo Zarlino, a sixteenth-century composer and writer, states.

"Every composer ought to follow the beau26

�tiful order of nature, and he will be considered excellent in proportion to the resemblance of his procedures to those of nature."

Zar-

lino's "wondrous Nature" is a world informed by number, by our 2's
and 3's.

One of his cardinal principles is unity in variety, fol-

lowing nature, which, he says "does not produce identical individuals
in a species, but always somehow varied."

"Numbers and proportion

invite us to variety, for in them we do not find two similar proportions following one another."

Here he is speaking about the harmonic

proportion, a important number relation named after its embodiment in
music.

We have already heard the simplest form of that relation, in

lowest whole numbers--the dovetailing of the 2 and the 3, or the
octave and the fifth.

[PLAY] ·

Harmodzein, the Greek word for the

dovetailing of joints in carpentry (it also can mean to "set in
order," or "govern," and also to "betroth") describes the way the
octave and fifth lie harmoniously together, a concordance of dissimilar elements, giving their name to a number relation you will meet
elsewhere in the program. To

Zar~ino

this relation comes closest of

all musical relations to the sound of perfection, and so it must end
every composition; for, in his words, "Perfection is characteristic
of the end and not of the beginning of a thing."

[EXAMPLE 8]

A latet

music that calls itself harmony (the examples we have been listening
to this evening) will add another element to this dovetailing to fill
it in, to make it less perfect and hence more sensuous (one eccentric
modern theorist calls the fifth the "pre-sexual'' interval); this more
homogeneous entity we call a "chord."

But still the guiding relation

remains the same--the harmonic proportion, the miraculous blending of
the 2 and the 3.

27

�I have somewhat perversely tonight been giving you a music
history in reverse, and it would be remiss of me not to add a postlude that takes it back to origins, so to speak.

We have been

dealing all evening with compounds--more than one line at a time--and
now we will turn to simples.

But only in the sense that we are no

longer combining two pitches at a time; any implication that this
one-line music is simple in the se-nse of "primitive" is wholly alien
to my intention.

I have heard it said of the repertoire of Gregorian

chant that it is abstract, ethereal, above the world and its relations, out of time in its simple temporality.

I don't believe that

any example of this most human of arts can be like that, nor do I
think that we endow it with any greater dignity or spirituality in so
asserting.

The goal is to let a sacred text speak out as simply and

eloquently as possible, and again the 2's and 3's do the work.

The

text of the Latin hymn I have chosen, in unrhymed Latin verses, is
from the Easter Mass, and it is a meditation on the miracle of the
Resurrection.
Let

It reads, in part:
Christians

off er their thankful praises

to

the Paschal Victim.
The Lamb hath ransomed the sheep:

the sinless Christ

reconcileth sinners to the Father ....
Tell us, Mary; what did you see in your wayfaring?
I

saw

the tomb of the living

Christ,

and

the

from

the

glory of Him rising ....
We

know

that Christ has truly

risen

dead; have mercy on us, Victor King.

Amen.

At the center of this text is an act of human witness, at the conclu-

28

�sion one of human celebration.

At no time does the chant call atten-

tion to a particular phrase--it never makes "word pictures"--but the
whole is animated with human pulses and human breaths.

The rhythm of

the poetry is primarily trochaic--a stress on the first,

third,

syllable, etc--and the musical rhythm by and large follows this
grouping into 2's:

"Victi~

paschali laudes irnrnolent

Christi~ni."

The 2's and 3's of pitch- order the ebb and flow of the melody.

The

octave is the limit of rest, the fifth (our 3, remember) the limit of
tension. These seemingly narrow melodic limits set the theater for a
narration without a story, for a dramatic mimesis of the condition of
the human soul.

When we hear the third phrase begin on the 5 and

rise up to the octave above, our chests swell, our pulses race, at
this brave effort against the center of gravity, the 1.

On the

return we compose ourselves, fold our hands, reflect, always in
sympathy with the passion objectified in the music.

We haven't here

the histrionic swelling breast of the operatic soprano, but the
effect is only dissimilar in its restraint.

Above all chant is

singing: is breath and how long one can hold it, the tightening of
the vocal chords in order to attain a higher pitch:

[Ex. 12] .

posed this music is, and ordered, but inhuman it is not.

Corn-

For it is

never without passion, if passion can be defined as the suffering or
tolerating of the physical and emotional effects that devolve from
the exertion of our human equipment.
Hanslick, in his efforts to make mock of musical imitation,
turns one memorable phrase that might seem in its sarcasm to put an
end to the question altogether.

"The animal to which music is most

indebted," he says, "is not the nightingale but the sheep."

29

The song

�of the sheep is, of course, that of the gut, the taut string, and we
are being reminded to turn our attention away from frivolous thoughts
of connections between music and nature to the sober practicalities
of the making of pure musical sound.

But, as I've tried to say

tonight, I think his example contains in it the very image that is

•

his undoing, for it is the physics of the taut string that makes
Aristotla say the
There
musical
makes

following~

seems

to be

tunings
some

also in the Politics:
in

us

a sort of

(harmoniai) and

kinship

rhythms,

philosophers say that the

soul

to

which
is

a

tuning, others, that it possesses tuning.
I submit that this music is an imitation of "wondrous Nature," our
nature, as it uses musical number in the act of prayerful praise.
further submit that very little music is not like this in some way,
if we but look and listen.

30

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12

Victimae paschali laudes Sequence for
the Solemn Mass of Easter Day
..

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II

�Victimae paschali

1.

Victimae paschali

laudes .

laudes immolent Christiani.
~angs

1. Ta the Paschal Victim let Christians offer

cf praise.

2.

Agnus
redemit oves:
pe•=•=atares.

2.

The Lamb
has
redeemed
the
sheep.
reconciled sinners to the Father.

3.

Mars
et vita duelo conflixere miranda:
regnat vi \ILts.

3.

Death and life have en~aged in miraculous combat.
of life is slain, &lt;ye"t") liv.ing he reigns.

4.

nob is Mari a.,.
quid vidisti in via?
Die
vi vent.is, et gloriam vi di resLU-genti s:

4.

Tell LlS,
Mary, what YOLl saw on the way?
I saw the sepul 1.:hre
of the living Christ and the glory of his rising.

Christus innocens Patri

5. Angelicas testes, sudarium; et vestes.
mea:
praecedet sues in Galilae~m.
5.

Tt1e angel

is risen.

6.

i·=

reconciliavit

Sinless

has

Christ

dux vitae

mortuus,

The leader

Christi

Sepulc:rum

Surrexit Christus spes

'"'i tni::s:;;e ·: ~~ th(;: ·= hr-cud and v·e·'5tur•::. Christ ;ny
He will gc before his own into Galilee.

C1'-edend1_tm est mag .l. s

·:;cJl i

Mari ae ve1·-ac i

qua1u

.J1_1dae·~n..1m

l · ;;:Jp~

ti_tt-b.::&lt;.e

fallac:i.•

6.

Mary
alone is more ta be
deceitful crowd cf Jews.

7.

S·=im1_:s Cl1ri ·: ;tum ·: ;urr···::?;&lt;i ·:; ·:;i:-? a 111c1~t1_1i ·:; V•::?r•::?:
F:i?&gt;: , mi st:ir· ere.

-r
I

~·~e
know
that Chr i ·;t has tr1_1l y r-i ·:;en f ram
conqueror and king, have mercy en us.

o

believed

th;?

than

vi ct;~r -

the

Je:ad.

1..\Ji pi::J •::f Bur-,dund\'
Celeve~~h

c~ntur y)

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                    <text>Leibniz’s New Geometry
Brendon Lasell
July 26, 2007
In February of 1682, Gottfried Wilhelm Leibniz published a paper giving the
ratio between a circle and a circumscribed square. In fact, he claimed that (see
diagram) when the circumscribed square BC is 1, then the circle is equal to
1 1 1 1 1
− + − + etc.
1 3 5 7 9
The announcement appeared in the second issue of a new journal, the Acta
Eruditorum, the Acts of the Learned. The journal was intended to give learned
men a way to announce their new discoveries, and it was the first such journal
in Germany. Leibiniz’s paper does indeed present something new: nothing like
the equality he gives had never been seen before.
Leibniz’s paper thus serves to introduce readers to new mathematical knowledge. At the same time, the paper introduces its readers to its author. But the
paper is only an introduction. A reader struck by the novelty of its claims would
not be satisfied with what he can learn there about the new mathematics and
its new author. The paper neither gives a argument for its main assertion, nor
does it explain how the author came to it. Instead, he only gives an enunciation
of a theorem, seen from several points of view. Intrigued by the mathematics,
we may want to know something about the author who is boldly making such
claims; but here too we are frustrated. The author only gives his initials, G.
G. L., and if we investigate, we only find out that he is a relatively unknown
court historian for a Duke in northern Germany. He is a new man among the
learned just as his assertions are new in mathematical learning. In February
of 1682 we cannot let what we think about Leibniz guide our thinking about
Leibniz’s mathematics. Readers of Leibniz’s paper are thus left with no choice
but to begin by looking at the enunciation of his new theorem from the points
of view he gives us, neither looking ahead to a demonstration or analysis, nor
looking back to an established body of work by the same author.
Leibniz presents his new theorem above all from the point of view of tradition. His essays begins as follows:
Geometers have always tried to investigate the proportions of curvilinear figures to rectilinear figures, but even now, after applying
algebra, they still have not succeeded — at least with the methods they have published: for these problems cannot be reduced to
1

�algebraic equations, but they are beautifully useful, especially for
reducing mechanics to pure geometry.
Leibniz is doing what geometers have always done. He is trying to find the
proportion of a curvilinear figure, the circle, to a rectilinear figure, a square.
But geometers have not always succeeded at these tasks, even now in 1682, after
they have learned from Descartes to apply algebra to solve geometric problems.
Leibniz, however, succeeds at his task. Leibniz goes on to say more about
the problems that geometers have solved, about their aims in solving these
problems, and how his new solution satisfies these aims. Thus, when he gives us
the proportion between a circle and a square, he asks us to look first of all not
at circles or squares, or even at curvilinear and rectilinear figures in general, but
rather at what geometers have always tried to do. His own work belongs not so
much directly to geometry as to the history of geometry. It is a step forward in
the progress of geometry.
Now if we look at Leibniz’s new theorem as a solution to one of many problems that have been solved in the history of geometry, then it is natural to
ask what light this new solution sheds on the process by which one comes to
solve such problems in general. In an earlier letter where Leibniz presents the
same theorem on the proportion between a circle and a square, he writes that
“nothing is as important as seeing the origins of discoveries — they are worth
more than the discoveries themselves in my opinion.” In a much later essay, he
writes that seeing the origin of discoveries is important in that it helps “the art
of discovering.” From the point of view of the art of discovery, geometry is not
about circles or lines so much as about the general art of coming to new truths.
When we look at Leibniz’s claim that the ratio of a circle to a circumscribed
square is
1 1 1 1 1
− + − + etc.,
1 3 5 7 9
we should then think first about the general art of finding proportions between
curvilinear and rectilinear figures, and about the light this theorem sheds on that
art. This is the point of view from which we will look at Leibniz’s mathematical
work tonight. Starting from this new theorem about the ratio of a circle to
circumscribed square, we will look at how Leibniz presents the art of discovery
that is behind this theorem. We will begin by looking more closely at how
Leibniz presents the tradition that his discovery about the circle belongs to, a
tradition whose most prominent member is Archimedes, and how he breaks with
that tradition. Next we shall broaden our scope to look at some of Leibniz’s
later papers, where he presents more discoveries and lays out the method behind
them. Here it becomes clear that Leibniz defines his new contribution to the art
of discovery above all in opposition to Descartes. In particular, he introduces
new objects into geometry that Descartes could not deal with, and a new way
of representing these objects. Finally, we will return to the problem we started
with and sketch how Leibniz’s new understanding of geometry leads him to
discover the proportion between a circle and its circumscribed square.

2

�1
1.1

The tradition of the curved and the straight
Archimedes

Let us return to the opening sentence of Leibniz’s paper. There he writes
that the problems of finding the proportions between curvilinear and recitlinear figures are “beautifully useful, especially for reducing mechanics to terms of
pure geometry.” He continues, “Those who have looked more deeply into such
things know this; few have done so, but they are among the most outstanding mathematicians.” The only example Leibniz gives of a “most outstanding
mathematician” is Archimedes. Leibniz gives an example of a problem solved
by Archimedes. Archimedes found the proportions between a cone, a sphere,
and a cylinder constructed on the same circle. Here is a diagram. As Leibniz
points out, Archimedes showed that given a circle AB, a sphere with the same
diameter DC, touching the circle AB at the center C of AB, a cone ADB whose
base is AB and whose vertex is D, and a cylinder ABF E whose base is AB
and whose top EF touches the sphere DC at C, then the cone ADB is to the
sphere DC as 1 is to 2, and the sphere DC is to the cylinder ABF E as 2 is to
3.
Archimedes’ problem is an example of the kind of beautifully useful problem
that Leibniz himself intends to solve. Why are these problems beautifully useful
for Leibniz? It is easier to begin to see its beauty than its use. The beauty of
the problem is first of all visible in the diagram itself. It is a simple diagram:
only a few straight and curved lines traced on a sheet of paper. It is balanced
perfectly between left and right. Again, as we go up and down the diagram there
are repeated elements: the curved lines that are the circumferences of the circle
at the top and bottom of the cylinder, along with the equator of the sphere.
The straight vertical sides of the cylinder also add to our impression of vertical
symmetry. Yet the vertical symmetry is not perfect. It is sharply broken by
the straight diagonal sides of the cone, culminating in a point. The surface
simplicity of the diagram is broken in other ways as well. Our imagination
leads us beyond the simple plane surface of the drawing to a solid depth, and
the sphere, cylinder, and cone then come to life and separate from each other.
When we thus start to see the complexity behind the simplicity in the diagram,
we begin to perceive its beauty. It is not merely simple, but rather gradually
alludes to the complexity it is drawn out of. Our attention is drawn to the
diagram because of its striking emptiness and stays with the diagram because
its finitude offers little to distract us and its symmetry gives our attention a
way to move without leaving the diagram, circling over its surface; yet as our
attention is held fascinated by this surface it gradually opens up, leading us to
into depths that were not at first seen.
The theorem is, of course, more than simply a diagram. Archimedes proves
that the cone is to the sphere is to the cylinder as 1 is to 2 is to 3. When
we consider the statement of this theorem our attention is drawn away from
the diagram to the simple numerical ratios of 1 to 2 to 3. The simplicity here
is of a different kind. These numbers are not visible, and do not call on the

3

�imagination. While the cone, sphere, and cylinder are among the simplest things
in geometry, 1, 2, and 3 are the simplest things in arithmetic. In contrast to the
cone, sphere, and cylinder, these numbers are strikingly empty, and when we
turn our attention to them there is little to hold it in place. The only movement
we are led to follow is a movement onward: we go from 1 to 2 to 3 to 4, and
continue to infinity. There is no natural circling of our attention back to where
it began at 1. The simplicity of 1, 2, and 3 togther is thus not a beautiful
simplicity.
When Archimedes then identifies the simple geometric relations between
the cone, sphere, and the cylinder together with the simple arithmetic relations
between 1, 2, and 3, we are astonished. We would not expect these two very
different kinds of relations to be identical. There is nothing about a sphere and a
cylinder as they present themselves to our imagination that would suggest that
they are to each other as the number 2 is to the number 3. But Archimedes
can prove this. Step by step, in a long argument, he takes us to a point where
we must admit the identity. This surprising identity, and its demonstration, are
beautiful. They are beautiful not only because of the beauty of the diagram, but
because as we follow the proof we move our attention back and forth between
arithmetic and geometric simplicity, and unexpected depth gradually emerges.
As the geometric diagram has a kind of beauty of its own, independent of any
connection with arithmetic, what happens is primarily a beautification of arithmetic. By being linked to an elegant geometric configuration, the numbers 1, 2,
and 3, which by themselves appear rather empty and uninteresting, acquire an
unexpected depth. We can now see the relation between 2 and 3 in the relation
between a sphere and a cylinder, and 2 and 3 thus become worth dwelling on
and wondering at in a way they were not before.
Following Leibniz’s lead, we have been looking how Archimedes discovery of
the ratios between a cone, sphere, and cylinder is beautiful. Now to see this
beauty well we would have to look not only at the enunciation of Archimedes’
theorem, but at its demonstration. Leibniz does not do this, and we do not have
time to do it tonight. But I hope we have seen enough to glimpse something
of the way Archimedes’ theorem spreads something of geometric beauty over
arithmetic.
Now Leibniz does not merely say that problems of finding proportions between curvilinear and recitlinear figures is beautiful, but that these problems
are beautifully useful. But it is hard to see what is useful about Archimedes’
theorem. Once we know what the ratios between a cone, a sphere, and a cylinder are, there is nothing obvious we can go and do with this knowledge. Leibniz
suggests that such problems are useful for “reducing mechanics to terms of pure
geometry,” that is, for reducing the study of machines to terms of pure geometry.
But this theorem hardly appears to lend itself to designing machines.
We might turn to Archimedes other works in hope of finding some clue to
the usefulness of the theorem Leibniz gives and others like it. But here again,
we would be disappointed. It is true that some of the techniques Archimedes
uses to find the ratio between a sphere and a cylinder do appear elsewhere in his
mathematical works, and perhaps he even uses this ratio as a step in another
4

�argument. But there is, I believe, little in his mathematical works to indicate
that he finds these kinds of problems useful.
But Leibniz may not only be thinking of the extant writing of Archimedes.
We know something of Archimedes not only through his writings, but also
through the writings of historians. Here we are told that Archimedes was in
fact a wonderful engineer. His mechanical ability plays a central role in one of
the most striking episodes of the story of the rise of the Roman Empire. Archimedes built machines that were able to drive a powerful Roman army from
his native city of Syracuse. The best telling of the story is in Plutarch’s life of
Marcellus. It is worth spending a few minutes here to try to bring Plutarch’s
telling of the story to life before us, so that we may see better how Leibniz’s
invocation of Archimedes’ name may shed light on the tradition he is taking up
in squaring the circle.
Archimedes appears in Plutarch’s life of the Roman general Marcellus. Marcellus was involved in three great wars, stretching from his youth to his old age.
The bulk of Plutarch’s life is concerned with the last of these three wars, a war
between Rome and Carthage. These two great cities fought each other to decide
who would be the dominant power in the known world. Rome, of course, eventually won, destroying Carthage completely about sixty years after Marcellus’
death. But during Marcellus’ lifetime the question was very much in doubt.
Carthaginian armies were moving through Italy, threatening the city of Rome
itself, and battles were also fought in Spain, Africa, and Greece. Not long after
this war with Carthage had broken out, Marcellus was in charge of a Roman
army in Sicily trying to defend Roman interests. Rome had come to rule Sicily
in a war during Marcellus’ youth, but the new war with Carthage had emboldened some Sicilian cities to try to break free of Rome. Syracuse, the largest
and wealthiest city in Sicily, was one of these cities. Just before Marcellus had
arrived, a Syracusan general, Hippocrates, had “gratified the Carthaginians and
acquired tyranny for himself by killing many Romans.” When the Roman army
came to Syracuse Hippocrates, by spreading lies about Roman cruelty among
the Syracusans, encouraged them to refuse to listen to Marcellus’ ambassadors.
Marcellus than attacked by both land and sea. Marcellus was confident of his
success,
relying on the size and splendour of his preparation and on his own
reputation. But to Archimedes and the machines of Archimedes all
this was of no account. This man did not set out to make these as
if they were worth being serious about; most of them were born as
byproducts of geometry at play, after Hiero the king had become
ambitious and had persuaded Archimedes to turn something of his
art from mental things to bodily things, and by mixing its reason
somehow or other through sense perception with use, to make this
reason more manifest to the many.
When the Roman army and fleet attack, Archimedes’ machines shot arrows,
cast heavy rocks at them, inflicting heavy damage. When the Roman ships
came up to the wall, the Syracusans used machines devised by Archimedes to
5

�grab hold of the ships with iron claws, lift them out of the water, and drop them
again. The Romans quickly retreated in fear, giving up a direct assault, and
settling into a siege that would last almost three years. Through Archimedes’ ingenuity alone the Syracusans had driven off Marcellus and the Roman army and
fleet. Marcellus compares Archimedes to Briareus, a mythical hundred handed
monster. According to Plutarch,“in reality, all the other Syracusans were a body
for the preparations of Archimedes, while the soul moving and turning everything was one.” In driving off the Romans and preserving Syracusan freedom
Archimedes has momentarily become a perfect tyrant over Syracuse. According
to Plutarch’s description, it seems that Archimedes is not simply the ruling soul
in Syracuse, but the only soul. Marcellus is right to find this situation both
mythical and monstrous.
Thus the geometry of Archimedes is wonderfully useful. It generates as a
byproduct an amazing array of machines that are capable of repelling a mighty
army. Even so, according to Plutarch, Archimedes held the art of making machines, mechanics, an art by which he had acquired a godlike reputation, in
contempt:
Archimedes possessed so great a spirit and depth of soul and such a
great wealth of theorems that he chose to leave behind no writings
about the things by which he had acquired the name and reputation
of having the understanding of a god rather than of a man; instead,
considering the business of mechanics and, in general, any art that
grasps at what is useful, to be ignoble and base, he directed his
love of honor to those things which have beauty and superfluity
unmixed with necessity, things incomparable with everything else,
and which furnish demonstration with a rivalry against matter, the
latter bringing size and beauty, the former precision and enormous
power; for it is not possible in geometry to grasp more difficult and
weightier hypotheses in simpler and purer terms.
Now remember that Leibniz, when speaking of the kind of problems Archimedes solved, calls them beatifully useful. They are both beautiful and useful.
Earlier I tried to point to some of the ways Archimedes finding of the ratio between a sphere and a cylinder may be beautiful. We later turned to Plutarch’s
life of Marcellus trying to find how Archimedes’ art might be useful. There we
indeed see that Archimedes’ succeeds in turning pure geometry to mechanics,
making his wonderful machines. But Leibniz not only attributes both beauty
and use to Archimedes’ art, but says that the uses themselves are beautiful. In
contrast, in Plutarch’s account, the mechanical uses of Archimedes’ geometry
are contemptible in comparison with the pure beauty of geometry indifferent
to use, to which alone he devoted his writings. Here then we begin to see a
way in which Leibniz has broken from the tradition he sets before us. Leibniz
suggests there is a harmony between beauty and use, while Archimedes (at least
Plutarch’s Archimedes) turns away from use towards a pure beauty belonging
to matter in a rivalry with demonstration.

6

�Before we finish with Archimedes, I should give the rest of Plutarch’s story.
After being repelled by Archimedes’ machines, the Romans retreated, but they
did not give up. They settled into a long siege, and after a few years found a
way to take the city by strategem, without a frontal assault. When Marcellus
had Syracuse in his power, he set his soldiers loose to plunder it. As the Roman
army ran through the streets taking everything they could get their hands on,
Archimedes was looking over a diagram, examining something by himself, and
failed to notice that the city had been taken. A Roman soldier came up to
Archimedes and ordered him to come with him. Archimedes did not want to
go before he had finished his problem and established its demonstration. The
Roman soldier became angry, drew his sword, and killed him.

1.2

Leibniz’s innovation

Let us return now to Leibniz’s paper on the ratio of a circle to its circumscribed
square. There, as we saw earlier, Archimedes appears as part of the geometric
tradition of finding proportions between curved and straight things. After mentioning Archimedes and his theorem, Leibniz goes on to give a series of more
modern proportions, found by nameless mathematicians, for other figures, and
then turns to the unsolved problem of finding the ratio between a circle and
a square. According to Leibniz, no one has yet been able to “bring the circle
under laws such laws.” Others have found approximations, including first of all
Archimedes, who showed that the ratio of a circle to a circumscribed square is
greater than 21 to 28 and less than 22 to 28. But approximations are not what
Leibniz is looking for; he is looking for an accurate expression.
Now according to Leibniz, “many have not fully understood what they are
looking for” when trying to find the quadrature of the circle, that is, the ratio
between a circle and a circumscribed square. To clarify the what would count as
a solution to the problem, Leibniz gives a classification of kinds of quadrature.
A quadrature can either be done by calculation or by construction, and in either
case it may be either accurate or not. There are therefore four different kinds
of quadratures: accurate calculations, approximate calculations, accurate constructions, and nearly accurate constructions. No one has yet given an accurate
calculation or construction for the quadrature of the circle, while Archimedes
gave an approximate calculation, and others have given nearly accurate constructions. Leibniz claims his own quadrature is an accurate calculation.
The simplest kind of accurate calculation would show that the ratio between
the circle and the square is the same as the ratio between two whole numbers,
just as Archimedes shows that the ratio between a sphere and a cylinder is the
same as the ratio of 2 to 3. Leibniz calculation is not that simple. As we saw
earlier, he shows that if the area of the square is 1, then the area of the circle
will be
1 1 1 1 1
− + − + etc.
1 3 5 7 9
Leibniz goes on to explain that this means that
in relation to the correct value for the area of the circle,
7

�1
1
1
1
1
1
1

will be
−
−
−

1
3
1
3
1
3

+
+

1
5
1
5

−

1
7

greater,

yet with an error less than

......

less,

..........................

......

greater,

..........................

......

less,

..........................

etc.

1
3
1
5
1
7
1
9

etc.

Therefore the whole series contains all the approximations or values
greater than or less than the correct one: for if it is continued far
enough the error will be less than a given fraction, and thus also
less than any given quantity. The whole series therefore expresses
the exact value. And although we cannot express the sum of this
series by one number, and the series may be produced indefinitely,
nevertheless, because this series keeps to a single law of progression,
we sufficiently perceive the whole with our minds.
Here Leibniz has done something very bold. In looking at the table he gives,
one might think he is only giving us more approximations. He gives us a series of
expressions that each give an approximate value for the area of the circle. Each
expression comes closer and closer than the last to being accurate, but none of
them ever is accurate. And each expression is more complex than the last, so
that we have to use long and complicated expressions to get a very accurate
value for the area of the circle. If, for example, we wanted to find the area of
1
the circle with an error less than 100
, we would have to take the sum
1
1 1 1 1
− + − + ... − .
1 3 5 7
99
If we added and subtracted all 50 terms in this sum, we would get something
equal to the correct value, plus or minus .01; we would therefore have a pretty
accurate approximation of the correct value, up to two decimal places. If we
wanted an approximation up to three decimal places, we could use a sum with
500 terms. Leibniz, however, sees more here than some rather laborious new
ways to calculate an approximate value of the area of the circle. He sees a
completely accurate calculation that gives the exact value of the area of the
circle.
This is the bold new leap Leibniz makes. To make it, he must see the series
as giving a single value, rather than infinitely many values. This value cannot
be contained in any individual sum of a finite number of terms; rather, it is
contained in the “law of progression” that guides the whole series. This law
tells us how to move from one sum to the next; it tells us, for example, how to
move from the second sum,
1 1
− ,
1 3
to the third,
1 1 1
− + ,
1 3 5

8

�and then how to move from this sum to the fourth,
1 1 1 1
− + − .
1 3 5 7
The law of progession is the same at every step; no matter how far we go in
the series, the way to move from one sum in the series to the next is the same.
If anyone gives us a sum that occurs in the series, we can easily find the next
sum by following the law. For Leibniz, we can therefore sufficiently perceive the
whole series of sums, and it is thus just as good as a single number. Because
the series gives us arbitrarily close approximations to the area of the circle, its
value must be identical to the value of the area of the circle. Leibniz has thus
given us a different kind of solution than we might have expected. When we
first posed the problem, we were looking for a number that gives the area of
the circle. But Leibniz tells us we did not understand the what we were really
looking for: we were in fact looking for a law. Leibniz thus replaces numbers
with laws. The primary mathematical object is a law.
Now any law, in mathematics or otherwise, is universally obligatory. Everyone should obey the law. To obey the law, everyone must first understand
what the law is. A law should therefore be something that is publicly declared
and can be grasped by everyone . Accordingly, Leibniz introduces the law of
progression of his series as a means by which we perceive the whole series. The
law of progression is manifest to everyone. It becomes manifest here because
Leibniz has presented it here in a table that makes us grasp it at a glance. By
laying out the series of sums in a table, with neatly aligned rows and columns,
we see just how we should move from one sum to the next, and how each new
sum relates to the circle. The law of progression is captured in the visible relation between one row and the next. We thus grasp as well as we need to what
is contained in the two “etc.”s at the bottom of the table, which contain the
infinitely many unwritten sums and errors.
Expressing the series of approximations in terms of words alone would not
have been as effective as Leibniz’s table in making clear what the law behind
the series is. In fact, any complicated mathematical truth is hard to grasp when
expressed in words alone. We see this all the time in reading ancient mathematics. Even in the relatively simple propositions in Euclid, it is sometimes hard
to understand what a proposition is about by reading the enunciation alone.
Only after we see it set out in terms of a diagram does it become clear. The
difficulty in understanding the bare enunciations becomes even greater in the
more complicated works of Apollonius and Archimedes. Yet in all these authors there is a stubborn insistence on formulating everything in plain Greek,
no matter how odd or unreadable the resulting sentences become. They do
not resort to symbolic shorthands to try to make it easier for us to grasp the
patterns behind what they are saying. In the resulting tension between the diagrams and the text in Greek mathematics we perhaps see the rivalry between
matter and demonstration that Plutarch speaks of. The diagram is a kind of
matter, lending beauty and size to the proposition, while the text is where the
demonstration is found, providing power and precision. Each keeps jealously
9

�to its own domain, the diagram not trying to become a symbolic text, and the
text not trying to become a picture. Leibniz collpses this tension. Text and
diagram coalesce in a table expressing an underlying law. The strife of ancient
mathematics disappears behind a new harmony.
When Plutarch first introduces Archimedes, he writes that his machines are
the result of King Hiero persuading him
to turn something of his art from mental things to bodily things, and
by mixing its reason somehow or other through sense perception with
use, to make this reason more manifest to the many.
When making his machines, Archimedes himself thus blurs the line between
reason and sense perception in trying to make his geometry useful. He blurs
this line in the interest of making his geometry manifest to the many, an interest
that Leibniz shares. But as we saw earlier, Archimedes appears to hold the
usefulness of his geometry in contempt. It is nothing compared to the beauty
of the geometry on its own. For Leibniz, I believe, the beauty of geometry
is not separable from its usefulness because he sees finding laws as its object.
The theorems of a Leibnizian geometer reveal laws, and these laws are by their
nature manifest to the many. These laws are naturally useful because they let
us easily grasp powerful universal truths. It is only a bad geometer who fails to
make himself perfectly clear, and only an idle pretence to suppose that there is
some independent realm of pure theorems high above the understanding of the
many.

2

Leibniz against Descartes

In considering how Leibniz’s paper in February of 1682 is new, we have so far
concentrated on how Leibniz’s solution moves beyond the work of Archimedes,
the first geometer he names as belonging to the tradition of finding proportions
between curvilinear and rectilinear figures. But this tradition has many later
members, and Leibniz refers to their work as well. To be truly new, Leibniz’s
solution has to go beyond not only Archimedes, but all previous modern mathematicians as well. Now in many places in his mathematical writings Leibniz
gives the names of his important predecessors and describes their work, and
it would be impossible here to give a complete picture of his understanding of
the tradition leading up to him. But there is one mathematician with whom
he contrasts himself more than any other: René Descartes. Descartes not only
made important contributions to geometry that Leibniz depends upon, but also
made some harmful errors that Leibniz tries to correct. In many of his published mathematical writings there are passages that point to these errors of
Descartes. In this part of the lecture we will try to sketch how Leibniz saw
himself as correcting the errors of Descartes.

10

�2.1

Descartes’ error

Leibniz criticizes Descartes in a paper titled “On Finding the Dimensions of
Figures” published in May of 1684, two years after his paper on the area of the
circle. This paper sets forth a general method Leibniz uses to find the areas of
figures. After briefly describing the method and some of the things it can do,
he writes:
I have many things of this kind by which Geometry is advanced
immeasurably far beyond the boundaries set down by Viète and
Descartes. For the ancients did not wish to use lines of higher degrees, and [they called] the solutions that were found by using them
Mechanical. Descartes blames them for this and receives into Geometry all curves whose nature may be expressed by some Algebraic
equation, that is, by an equation of a definite degree. He is right
to do this; but there are infinitely many other curves that nevertheless can still be accurately described, and Descartes erred no less
than the ancients when he excluded them from Geometry and called
them Mechanical, evidently because he was unable to reduce them
to equations and treat them by his rules.
This is a criticism that Leibniz returns to again and a again in his mathematical
papers. According to Leibniz, Descartes expanded the proper objects of geometry, including in it lines that the ancients rejected as mechanical. But Descartes
himself does not go far enough. He introduces a new criterion for judging if
a line is geometric, and his criterion is too narrow: he ends up rejecting some
lines that are just as geometric as the ones he accepts. Leibniz tries to correct
this error and include all lines that belong to geometry. As Mr. Burke puts it,
there is an analogy: as Descartes is to the ancients, Leibniz is to Descartes.
To understand better Leibniz’s criticism of Descartes, we will turn briefly
to the text where Descartes makes the statements Leibniz is criticizing, the
Geometry, which was published in 1637, about forty-five years before Leibniz’s
first mathematical papers. There Descartes gives a way to simplify “all the
problems of geometry,” by freely introducing “arithmetic terms into geometry,
in order to make [himself] more intelligible.” He uses, for example, the term
“multiplication” to describe finding a fourth proportional: if the line AB is a
unit, and we have to “multiply” BD by BC, then Descartes simply constructs
a fourth proportional BE for AB, BD, and BC, so that AB : BD :: BC : BE.
BE is called the “product” of BD and BC. Descartes’ new arithmetic language
enables him first to reduce all statements about geometry to statements about
straight lines, but he quickly notes that “often one does not need to trace these
lines on paper, and it suffices to designate them each by a single letter.” By
designating geometric lines by letters and interpreting geometric relations in
terms of arithmetic, he can use algebra to express geometric statements. For
those of you who have not read the Geometry, I would say that the result is
something like what you see in high school algebra, where geometric curves are
expressed by equations using systems of coordinates.
11

�Descartes claims that his new method was unknown to the ancients, who
seem to have been held back by their scruples about using arithmetic terms in
geometry because they did not see with sufficient clarity the relation between
these two subjects. To prove that his method is capable of going beyond the
ancients, Descartes solves a problem that the ancients could not solve, the socalled locus problem of Pappus. We do not have time to go into much detail
here, but in very general terms, this problem involves finding curves that satisfy
certain conditions. We are given some properties of an unknown curve, and we
have to find the curve that has these properties. The form of the problem is thus
the same as that of countless other ancient geometric problems: for example,
the problem of finding a square equal to a given polygon, or the problem of
finding a mean proportional between two given lines. What is unusual about
Pappus’ problem is that we do not know in advance what kind of curve line we
are looking for. When we try to solve the problem, we may therefore want to
understand what kind of curves line there are; that is, we may want to classify
curved lines in general. But ancient geometry never deals with curved lines in
general. It only gives us a handful of examples, such as the circle and the conic
sections. Pappus gives us a case where these well known curves are solutions
to his problem, but he does not have a way to describe the curved lines that
solve his problem in more general cases. According to Descartes, even in the
simple case where the solution is a conic section “he does not at all try to
determine or describe this curved line, any more than he tries to explain the
curves” that satisfy the problem in more complicated cases. Descartes claims
he can do all this, determining and describing the solution in the simple case
where Pappus only asserts what the solution is, and explaining the solution in
more complicated cases.
Now the key to Descartes’ general solution of the problem is a new understanding of what it means to find a curve. The ancients did not understand the
nature of curved lines, and therefore excluded lines that properly belonged to
geometry. Among the lines they excluded are precisely those that solve Pappus’
problem. By broadening what counts as a solution to the problem, Descartes
is able to solve it. His solution is thus a model for the type of solution which
Leibniz gives for the quadrature of the circle, where he broadens the definition
of number to find an accurate value of the area of the circle. According to
Descartes
one should no more exclude the complex curves than the simpler
curves, provided that one may imagine them to be described by
a continuous movement, or by many successive movements each of
which is entirely regulated by those which precede it.
Descartes is thus able to include within geometry lines described in our imagination by all sorts of complicated machines, lines that the ancients would have
rejected as mechanical. A little later Descartes gives a somewhat different formulation of which curves may be called geometric, identifying them with
those curves whose points necessarily have a some relation to all the
12

�points of a straight line, a relation which may be expressed by some
equation.
In what follows, Descartes makes it clear that he is thinking of an algebraic
equation, that is, an equation formed by adding, subtracting, multiplying and
dividing known and unknown quantities; for example, y = x2 or x3 −2xy+1 = y 2
are both equations of geometric curves for Descartes. The equation of a curve
determines what kind of kind of curve it is, and Descartes gives his solution to
Pappus’ problem by using equations.
It is this latter formulation of what counts as a geometric curve that Leibniz objects to. Leibniz sees no reason to limit ourselves to algebraic equations,
since equations can express relations other than those that come from adding,
subtracting, multiplying, and dividing known and unknown quantities. In addition to algebraic equations, Leibniz introduces new equations which he calls
transcendent. These new equations are expressed in a new symbolism, which he
calls a calculus. The curves corresponding to these equations are transcendent
curves. They are the curves that Descartes mistakenly casts out of geometry.
While Descartes was right to include all algebraic curves, and not just the few
simple ones the ancients used, the circle and the conic sections, he was wrong to
exclude transcendent curves. Just as by introducing algebraic curves Descartes
can solve a problem the ancients could not, so also by introducing transcendent
curves Leibniz can solve problems Descartes could not.

2.2

Leibniz’s new curves

Leibniz at first only mentions the new calculus used for describing the new
transcendent curves, without giving examples. It is only a few months later, in
a paper titled “A New Method for Maxima and Minima, as well as for Tangents,”
that he shows us the new calculus. By a “calculus” Leibniz seems to mean a
symbolic system, that is, a collection of symbols and rules for manipulating
them. Ordinary algebra is thus a kind of calculus for Leibniz. His new calculus
is based on the old algebraic calculus, but it includes one new symbol, the
letter d. Leibniz first introduces d using the diagram on your handout. We are
given a straight line AX, called the axis, a curved line passing through V , a
perpendicular V X from the curved line to the axis, called an ordinate and a
tangent V B to the curved line. Leibniz takes an arbitrary straight line and calls
it dx, and then defines dv to be the line such that
dv : dx :: V X : BX.
He calls dv the “difference of the vs.” Leibniz goes on to give the rules for
manipulating this new symbol. For example, he writes that if y = xv, then
dy = x dv + v dx.
He does not demonstrate these rules when he first introduces them in the “New
Method.” Instead, he gives some examples. As the full title of the paper suggests, the examples are concerned with finding maximum and minimum values
of quantities, and with finding tangents to curves.
13

�Leibniz’s presentation of the new calculus is at first perplexing. He throws
us into the middle of it without explaining why a new calculus is needed, what
it is supposed to represent, or why it works the way it does. Instead, he gives
us at least three ways to think about the new symbol d:
1. in terms of the proportion dv : dx :: V X : BX;
2. as something that represents “differences,” so that dv is the “difference of
the vs;”
3. as a letter that is manipulated according to certain rules when combined
with algebraic expressions.
Of these three ways of thinking of d, I believe the second, in terms of differences,
is the most fundamental. It can explain both the proportion Leibniz starts with,
and the rules the new symbol must obey. Moreover, thinking of the new calculus
in terms of differences most directly helps us understand why the new calculus
helps us solve new geometric problems that Descartes’ algebraic calculus cannot.
A few years earlier, in a letter to a friend, Leibniz writes of what he calls
the “method of differences.” This method is based on the same method introduced in the “New Method”, but in the earlier letter Leibniz uses “differential
figures.” According to Leibniz, a differential figure is one whose ”series of ordinates coincides with the series of differences from another series.” 1 The notion
of a series of differences contains, I believe, the fundamental insight behind the
new calculus. Consider again the figure in your handout. We could have taken
any point V on the curved line and drawn an ordinate V X to get new values
for both V X and AX, that is, for both v and x. There are therefore infinitely
many possible ordinates for the curve through V . So far we have done nothing
that the ancients did not do, as those of you who have read Apollonius know.
But what Leibniz does that the ancients do not is consider these ordinates as
a series; that is, he supposes that there is an ordered progression of ordinates,
where every ordinate has an ordinate that immediately follows it. For Leibniz,
after the ordinate V X there is a next ordinate V1 X1 . And immediately after
V1 X1 there is another ordinate, and so on. These ordinates form an infinite
series. It is in terms of this series that we can most easily see what Leibniz
means by d: dv is the difference V1 X1 − V X between consecutive ordinates.
Now Leibniz’s supposition is obviously absurd. There can be no next ordinate, because continuous magnitudes are infinitely divisible. Between any two
points V and V1 there is always another point from which we can draw an
ordinate, and therefore V1 X1 can never be the next ordinate. Leibniz is well
aware of the absurdity, but it does not stop him. He is willing to embrace a
way of thinking about geometry that he knows is false, in order to develop his
new method. And this absurdity, this geometrical falsehood, is not something
accidental to Leibniz’s new method. Leibniz indicates the centrality of thinking
of differences of ordinates by the notation itself: dv is a shorthand for “the difference of the ordinates. As he develops his new calculus and its applications,
1 Letter

to Tschirnhaus, p. 40

14

�both in the “New Method” and elsewhere, we see him again and again return
to thinking in terms of series of ordinates and their differences. This thought
is the engine that drives him to new discoveries, and we should try to follow
Leibniz in embracing this way of thinking. We should resist the temptation to
treat it straightaway as an error that needs to be corrected.
But how can we embrace what looks like an elementary mistake? The idea
of accepting false hypotheses in order to get at truth is not unknown in geometry. Every time we do a reductio proof we begin by setting down a false
hypothesis. We then go through the proof, using this false hypothesis to derive
in an orderly way other false statements until we come to something that is
manifestly absurd. We then throw away the false hypothesis and embrace the
contrary, true hypothesis once and for all. In Leibniz’s method, we also use the
false hypothesis to derive in an orderly way other statements and finally end
up with a true statement. But in Leibniz’s method, we do not throw away the
false hypothesis when we are done. Leibniz’s method is not a reductio method,
but in both methods we use false hypotheses in a carefully regulated way to
come to true conclusions. The use of these hypotheses is bound by rules: they
are not like Euclid’s definitions and common notions, or like the conclusions of
demonstrated theorems, which we can freely introduce in whatever context we
want. Rather, there are certain limited contexts in which reductio hypotheses
or Leibniz’s hypothesis about the series of ordinates can be used. In both cases
there are as it were laws to guide the way we incorporate false hypotheses in
our arguments. Leibniz new geometry thus depends on new laws for the logic
of geometry.
To see more clearly what the laws are that guide Leibniz’s hypothesis about
the series of ordinates, let us turn to a paper published a few months after the
“New Method.” There Leibniz gives what he calls the “general principle” from
which his method may may be deduced:
that a curvilinear figure should be considered as equivalent to a polygon with infinitely many sides; it follows that whatever can be demonstrated about such a Polygon — whether in such a way that we pay
no attention to the number of sides, or in such a way that it is more
and more verified the greater number of sides we take, so that the
error finally becomes less than any given number — can be declared
to be true about the curve.2
To return to our diagram, if we draw a straight line between V and V1 , the
points where consecutive ordinates meet the curve, and we do the same for
every ordinate in the series, then we will get a polygon meeting the curve at
the points V , V1 , etc. According to Leibniz, this polygon is equivalent to the
curve through V . Now this polygon is not simply a single, fixed, polygon; it
is a variable polygon that can have more and more sides. We can always take
a greater number of sides. And when we prove something that is true about
this variable polygon that becomes more and more true the more sides we take,
2 p.

62

15

�until it finally fails to be true by less than any given number, then we can say
that it is true about the curve. This is the basic law that guides Leibniz’s use
of the hypothesis that the curve is equivalent to a polygon.
Here is a simple example. Suppose we are given a circle. According to
Leibniz, we can assume this circle is a polygon with infinitely many sides. We
can use this assumption to prove that the area of the circle is half the product
of its perimeter and its radius. For if we take one of the triangles ACB making
up the polygon, and drop a perpendicular DC from AB to the center C, then
the area of the triangle is equal to half the product of AB and DC. If we sum
up all the triangles in the polygon, we will see that the total area of the polygon
is half the product of its perimeter and DC. This is true no matter how many
sides the polygon has. Moreover, the more sides the polygon has, the closer DC
comes to being equal to the radius AC. Therefore it becomes “more and more
true” that the area of the polygon is equal to half the product of its perimeter
and the radius of the circle. According to Leibniz’s principle, then, it follows
that the area of the circle is half the product of its perimeter and its radius.
There is a striking similarity between Leibniz’s treatment of a curve as equivalent to an infinitely sided polygon and his earlier treatment of an infinite series
of numbers as equivalent to a number. Recall that as we take more and more
terms in the infinite series
1 1 1 1
− + − + etc.,
1 3 5 7
it comes closer and closer to the area of the circle. One could say that the
equality between this series and the area of the circle becomes “more and more
verified the greater number of terms we take, so that the error finally becomes
less than any given number.” Leibniz argues that this series therefore expresses
a single value that is equal to the area of the circle. Likewise, the infinite series
of polygons that can be inscribed in a circle come closer and closer to the circle,
and statements we make about these polygons that are “more and more verified
the greater number of sides we take, so that the error finally becomes less than
any given number” are in fact true about the circle. Leibniz therefore concludes
that the circle is equivalent to a polygon with infinitely many sides. In the former
case, Leibniz argued that we perceive the whole infinite series as one number
because it keep to a single “law of progression.” The same argument would seem
to apply in the case of the infinite polygon: we sufficiently perceive the whole
infinite series of polygons as one figure because there is a law of progression that
takes us from one polygon to the next. This law of progression is equivalent to
the circle for Leibniz. Just as he earlier treated a law of progression as equivalent
to a number, so here he treats a law of progression as equivalent to a geometric
figure.
We turned to Leibniz’s general principle to clarify the assumptions behind his
introduction of the new calculus. The symbol d is supposed to mean differences
of, when we make the assumption that there is an infinite series of ordinates.
This assumption is obviously false. Yet it can be used to guide us to new truths
when we use it legally. The laws that guide the use of the assumption depend on
16

�a general principle that curvilinear areas are equivalent to infinite polygons. An
infinite polygon is in fact an infinite series of polygons, but it can be treated as a
single polygon because this series obeys a single law. This law in effect becomes
a mathematical object. There thus appear to be two kinds of new laws: the laws
that guide the arguments using the new hypotheses, and the laws that become
new geometric objects. But these laws are deeply entangled, and may in the end
amount to only one law. The progression from one polygon to the next in the
infinite series of polygons may be thought of as a series of steps in an argument.
Or the special kind of argument that uses the new assumption may be absorbed
within the object under consideration, so that Leibniz’s assumption is no longer
false in the new geometry: if by speaking of the “series of ordinates” Leibniz
simply means the law of progression for all finite series of ordinates, then there
is no need to restrict the assumption to special arguments. It would be as true
as any of Euclid’s postulates.
Leibniz, fortunately, does dwell on these deep and difficult questions. Instead
he simply introduces his new notation, tells us what the rules are, and moves on
to solving problems. Consider again the diagram from the “New Method.” If we
apply Leibniz’s general principle to the curve there, we can assume that there
is a series of ordinates, so that V X and V1 X1 are consecutive ordinates, but
only in the context of a certain kind of argument. We may treat the ordinates
as if they form a finite series in order to prove statements about them that “are
verified more and more” the more ordinates we take.
Here is an example of the kind of argument we can make. Let V X and V1 X1
be consecutive ordinates of the curve through V . Then as we take more and
more finely grained series of ordinates, the points V and V1 become closer and
closer together, and the line through V and V1 becomes closer and closer to a
tangent V B to the original curve. Therefore, according to Leibniz’s principle,
the line through V and V1 is tangent to the curve.
Leibniz gives his “general principle” in classical geometric terms, without
any new symbols, and we have given our examples geometrically. But he is
in fact following Descartes in trying to express the nature of curved lines with
symbols. His new symbol d is precisely what is required to express as a curve
symbolically as an infinite polygon. If we drop a perpendicular V T from V to
V1 X1 , then V1 T will equal dv and V T will equal dx. If we are given dv and dx,
we are given the infinitely small triangle V V1 T , and therefore the side V V1 of
the polygon. Leibniz calls this triangle the characteristic triangle; it expresses
the nature of the curve as an infinite polygon. To find dv and dx is to find the
curve as an infinite polygon. As we saw earlier, Leibniz gives rules for finding
dv in terms of dx, given the relationship between v and x. In other words, he
gives rules for finding the curve as an infinite polygon, given the relationship
between its ordinates and abscissas.
Leibniz’s new calculus is a powerful new tool for solving geometric problems. Anything that can be expressed in terms of an infinite polygon can be
expressed in terms of it. Since, as we saw earlier, both tangents and areas can
be expressed in terms of an infinite polygon, they can also be expressed in terms
of the calculus. Leibniz’s calculus can be used to square the circle, and Leibniz
17

�and those who came after him used his calculus to solve many new problems
involving tangents and areas. The new calculus helps us solve these problems
because it gives us a way of much more concisely expressing just the relevant
relations for these kind of problems. More importantly, it gives us a way to
express curves that we never would have been able to express before. Just as
algebra let us write down equations for curves that we would never have had
simple geometric expressions for, so Leibniz’s new calculus lets us write down
equation for curves that would never have had simple algebraic expressions.
These are the transcendent curves that he faults Descartes for excluding. They
are the curves that can only be thought of as infinite polygons.

3

Conclusion

Leibniz’s geometry is new because he has a new understanding of law in geometry. In contrast to Archimedes and the other ancients, Leibniz sees geometry
as aiming at what is useful, and accordingly tries to find the most clear and
concise way to express its underlying laws. With Descartes Leibniz shares the
view that geometry aims at the useful and that one should try to introduce new
symbols to make the underlying reasons as clear as possible. But in contrast
with Descartes, Leibniz explicitly makes laws an object of geometry, and therefore is able to see a broader range of laws that might be clearly expressed by new
symbols. Because Descartes was too attached to the symbols of algebra, he set
up too narrow boundaries for what counts as a geometric curve. Descartes has
no way to express the laws that curves give to the infinite polygons inscribed in
them, and therefore rejects the transcendent curves that can only be expressed
by these laws.
In paper published in 1686, Leibniz offers some harsh criticism of Descartes
and his followers. After giving a brief demonstration of an error Descartes made,
Leibniz writes the following.
Since nothing is simpler than our proof it is surprising that it did
not occur to Descartes or the Cartesians, who are most learned men.
But too much trust in genius led them astray: the former trusted
his own genius, the latter another’s. For Descartes, having the usual
vice of great men, finally became a little too confident. And I fear
that not a few Cartesians are gradually beginning to imitate the
many Peripatetics whom they mock; that is, I fear that they may
be getting accustomed to consult the books of their teacher rather
than right reason and the nature of things.
Descartes’ text has become a dead authority to his followers. It is this dead
authority that Leibniz frees himself from with his new geometry. Descartes’
geometry, like his physics, is prone to become rigid and lifeless, losing its connection to the original discoveries it made. The algebraic tools of Descartes’
geometry can come to seem too important on their own, and their function as

18

�expressing something is lost. Leibniz brings life back to geometry by once again
letting its laws express themselves.

19

�</text>
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