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"YOU ARE THAT!"
The Upanishads Read Through Western Eyes1
© Robert Druecker, February, 2008
The original title of this lecture-"'You Are That! "'-was a quotation, from the
Chandogya Upanishad, of an exclamation made several times by a man named "Uddalaka" to
his son Svetaketu. The "That" refers to a realm or state of being, known as "Brahman." One
who experiences it is called a "knower of Brahman" (brahmavid). Uddfilaka was a knower of
Brahman, speaking to his son out of his direct experience.
The classical Upanishads are expressions of and invitations to this direct experiencing.
So, understanding them is a matter of understanding what that experiencing is like, not a matter
of believing or knowing some truths about the world. Thus, the lecture, in elucidating the
meaning of its title, will convey a sense of the experience of Brahman, which is what the
Upanishads as a whole are about.
But, of course, their ultimate aim is not simply to produce understanding in this sense, but
rather to eventuate in the actual experiencing of the Brahman-realm. Even Sankara, the most
highly esteemed expositor of the Upanishads, a man noted for his theoretical acumen, wrote: .
One should consider theoretical reflection as 100 times more efficacious than
oral instruction, and meditation as 100,000 , times more efficacious than
theoretical reflection. As for [the direct experiencing of the Brahman-realm],
it has consequences which defy all comparison. ·
The revised title of the lecture is: '"You Are That!': The Upanishads Read Through
Western Eyes." For I have followed Aristotle's recorrimendation to begin with the things .best
.
.
.
.
known to us; where 'us,' in this case, ~efers to the St John's community. Thus,Part One will
give a sense of what the Brahman-realm is like by elaborating on an analogous experience in
Homer and Aristotle. Part Two, much of which will be delivered on Tuesday afternoon in the
Conversation Room, will elucidate the experiencing of Brahman in a more direct way.
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Finally, many of the writings in the Upanishads are dialogues involving a knower of
Brahman. Yajfiavalkya is the central figure in the conversations in the oldest Upanishad. In
working on this lecture, I have asked him, as a knower of Brahman, for some help. So, during
the lecture Yajfiavalkya will be providing us with his sense of what it is in Homer or Aristotle
that is analogous to the Brahman-realm.
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Part One: vos1v and Jl.w:iul (Conjunction)
A.Homer
Homer frequently refers to human beings or gods waking up to, or realizing, the full
significance of a situation (voEtv) or to their ability to do so (v6oc; in some uses). 2
Paradigmatically the verb in the aorist expresses an individual's sudden flash of insight.
Resisting his parents' entreaties, Hektor has held his position, as he watches Achilleus coming
toward him. He is pondering what might happen should he retreat or should he offer to return
Helen; but then Achilleus closes upon him: "And trembling took hold of Hektor when the
realization suddenly struck him [what single combat against Achilleus really meant], and he
could no longer stand his ground there, but ... fled, frightened ... " (I, 22.136-37). 3 When the
progressive aspect is used, it conveys the process of pieces gradually fitting together to form a
wholly new picture, as when Theoklymenos tells the suitors that the ·realization is dawning upon
him that there is an evil on the way which they will not be able to avoid (0, 20.367-70).
Because of the intensity of the character's involvement in the situation, the experienced
shift in significance is often accompanied by strong emotion, as seen in the Hektor-example
earlier. When the insight concerns an individual object, instead of a situation, then the
realization is always accompanied by such emotion; it is as if the shift in the meaning of the
situation were compressed into a single thing or person. So, Menelaos, having caught sight of
Paris, leaps down from his chariot. Then "when [Paris] realized the full significance of
· Menelaus standing there among the champions, the heart was shaken within him'~ (I, 3 .29-31~
the full significance being that Menelaus is drawing near, full of an overwhelming desire to kill
Paris.
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'Realization of significance' has a variety of meanings that spread over a directional arc. 4
A character begins in a situation in which he has already seemingly recognized (ytyvrocnct::tv) the
surrounding things or people as definite individuals that are familiar. Then their real significance
is awakened to, a corresponding emotional impact is experienced, and a way of dealing with the
newly perceived situation comes to light and the will to do so arises. Thus, the present naturally
extends itself into the future. When the primary meaning is at either end of this arc, the other
parts of the arc are co-present. Thus, when the emphasis is on present clarity of mind, as when
Kirke tells Odysseus that no magic can work on his ability always to realize what is the real
meaning of the situation in which he finds himself, the insightful character of his future aims,
plans, and actions is also on her mind (0, 10.329). Or when the accent is on willing an action in
the future, it iilVolves a clear vision in the present (e.g., I, 144-49).
The realization of significance may or may not be prepared for by a thought process. But
when it is, it itself is distinct from the preceding reasoning, in the same way as 'seeing' one of
Euclid's proofs is different from figuring out how it is justified in terms of previous propositions.
Yajfiavalkya now observed to me that realizing Brahman, too, could be characterized as
including an emotional response, joy (ananda), and a way of acting, calm responsiveness to the
whole situation.
The realization may penetrate to great depth and extend {ar in space and time, like
Theoklymenonos's referred to earlier or like that involving Athena when she speaks to Achilleus
as he is drawing his sword to kill Aga.inemnon-the breadth and depth of which took a whole
Dean's Lecture to elucidate a couple of years ago.
The more intense the situation and the deeper and broader the realization, the more likely
it is that the characters are raised above their ordinary abilities, so that they are able to see almost
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all the implications and consequences of the situation with unusual clarity and to act with
extraordinary foresight. This experience of being raised above the ordinary is a divine
manifestation. 5
Homer most often mentions Athena and Apollo in such moments. For instance,
Odysseus's sudden realization of the true meaning of return-its being the right time to reveal
himself to Telemachos-is the presencing of Athena (0, 16.155ff). And Hektor's sudden
waking up to danger when he was about to oppose Achilleus is Apollo's manifesting himself (I,
20.375ff). These two examples point to the difference between the two gods. Athena remains
untroubled and serene in the midst of action while she is discerning at every juncture what the
instant requires, is planning the deed with precision, and is poised and ready to bring it about
energetically. Apollo, on the other hand, is associated with a cognitive attitude of stately
objectivity and a ranging gaze, distance and freedom, clarity and good form. He is the god of the
saving, or preserving, awareness (crcocppocruvri) expressed in the Delphic dictum, "Know
thyself," meaning, 'Realize what human beings really are, that is, how great a distance separates
them from the omnitemporal gods' (HG, 216-17, 215, 52, 57, 59, 78-79, 66). Yajiiavalkya
remarked that such traits as serenity in the midst of action, the freedom of a ranging gaze, and
saving, or preserving, awareness pertain to the Brahman-realm as well.
In a manifestation of Athena or Apollo, the god is revealed as the very essence of the
realization. That is, the realization's ultimate meaning is that it is a ray of the divine illumining
· human life. Homer realizes that the complete lucidity in which we sometimes act Is a connection
. with something superior to us, even though we think of it as a quality of our own minds. In
decisive moments what a warrior realizes is both himself and the deity together (HG, 7, 247, 174,
184-85) . .Yajiiavalkya commented that in the Upanishads, this non-separateness of the human
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and 'divine' is known as "non-duality" (advaita; BU, N.3,32): "Whoever meditates on a
divinity that is other (anyiim) [than himself], thinking, 'This [god] is one (anyah), I am another
(anyah),' does not know ['I am Brahman']." (BU, 1.4.10).
Homer's recognition of moments in which the divine and the human are non-dual is
sharply opposed to a view that would see Athena and Apollo as external 'causes' of the events he
is narrating (HG, 213). Yajiiavalkya said that, somewhat similarly, we are invited to awaken to
Brahman not as an external cause but rather as what is most profound in our experience.
When the god is present in moments of non-duality, the warrior's ego and personality
recede into the background (HG, 241f). That sort of impersonality, which also characterizes our
moments of experiencing the truth of a Euclidean proposition, is inherent in the Brahman-realm,
according to Yajiiavalkya.
The divine coming-to-presence has been said to occur at "the critical moment when
human powers suddenly converge, as if charged by electric contact, on some insight, some
resolution, some deed." Lightning comes forth from the clouds to strike buildings or trees which
have risen from the earth; so, too, the divine suddenly emerges from the background to shock an
individual only when the individual has gone forth from himself toward the background (HG, 6,
210, 195). Yajiiavalkya noted that the instant1of recognition of the Brahman realm is _also
compared to "a sudden flash oflightning" (BU, 11.3.6; cp. KeU, IV.4). Moreover, he thought
that the going-forth toward the background might be, in some way, analogous to a 'movingtowards' Brahman, going-forth involved either in practicing meditation or in coming to wonder,
'Who aml?'
While, in the examples given so far, the divine manifestation has come _in an awakening
to significance or in an elaborating of a plan, this should not lead us to think that deity is
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encountered in the inward turn. The appearance of the goddess is not, for instance, Achilleus' s
pondering whether to kill Agamemnon or to check his anger (I, 1.193 ), but rather the resolution
of his introspection in a flash of certitude (HG, 174, 48). Yajfiavalkya agreed that introspection
neither characterizes the Brahman-realm nor is a means thereto. However, there is, he said, a
different sort of inward turn which can facilitate its realization.
There are many instances in which a god is there, at a moment when none of the
characters is aware of it. But at times, when awakening to the full significance of his situation, a
warrior may realize that his very awakening is itself the manifestation of a god. An interesting
example occurs when Poseidon appears to the Aiantes in the likeness ofKalkas. At first neither
brother is aware of the presence of a god; but, after Poseidon departs like a hawk, Aias son of
Oi:leus realizes that some god, whom he does not recognize, has addressed them, while
Telemonian Aias notices only his own increased strength and energy (I, 13.43-80). On other
occasions the human being recognizes the god by name--sometimes only after the encounter, but
sometimes already at its inception (HG, 207-08).
A god may be especially 'close' to a particular individual in that the human being
regularly displays the qualities of the particular god, as Athena acknowledges Odysseus does (0,
13.330-32; HG, 192-95). There is even one person who seems to be fully awake to
divin~
presence-Homer himself, who
sees events through and through even when the participants see only the
surface. And often when the participants sense only that a divine hand is
touching them the poet is able to name the god concerned and knows the
·
secret of his purpose. (HG, 195-96)
According to Yajiiavalkya this variation, .among human beings, in the frequency with which, and
degree to which, they notice the divine presence in moments of waking up to meaning matches a
corresponding variation in noticing Brahman.
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So far in Homer we have emphasized cognition. This is appropriate in that cognition in a
broad sense is the way in which we come to realize Brahman. However, it gives a distorted
picture of the world as Homer depicts it. For there are many gods-Ares, Aphrodite, Poseidon,
Hera, and others-who manifest themselves in the world in addition to the two who are
especially associated with realizing significance. Moreover, the appearance of a deity often
involves an inner phenomenon other than awakening, as when Hektor's body is "packed full of
force arid fighting strength" (I, 17.211-12) or when Athena puts "courage into the heart" of
Nausikaa (0, 6.140). Yajfiavalkya said that these phenomena of enlivening, energizing, and
strengthening were included, along with realization, in what the Upanishads call the "Inner
Controller" (antaryamin; BU, III.7.1). 6 Also, that Homer realized that they, too, were divine
manifestations shows that he did not think of non-duality as limited to cognition.
Second, a deity often manifests itself by affecting a character from outside. Most
notably, Patroklos's aristeia was put to an end by Apollo, who "stood behind him, and struck his
back and his broad shoulders with a flat
~troke
of the hand so that his eyes spun" (I, 16.791-92).
Yajfiavalkya pointed out that events like this might be echoes of Brahman as "pouring forth," or
"emitting," all things (MuU, I.1. 7). He added that just as Homer recognizes the one Apollo both
in his striking of Patrdclus and in Hektor's realization referred to earlier, so the Upanishads
express the realization that the inner controlling and the outer emitting are one, in stating: "This
Self is ... Brahman" (BU, II.5.19).
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B. Aristotle and Averroes
Now for help in thinking through the experiences highlighted by Homer, we turn to
Aristotle. In moments ofrealization, we are in a state of what he called "being-at-work," what
I'll call 'activity.' Activity is "complete over any time whatever"; it is not a temporal
phenomenon. In distinction from it, a motion "is in time and directed at some end ... and is
complete when it brings about that at which it aims" (NE, 1174a15-21). For example, whereas
the activity of dancing is 'all there' at each moment, the motion of learning to dance is complete
only when you've actually become a dancer.
Homer's gods Athena and Apollo are manifested in activities of ours which would be
"choiceworthy in themselves" (NE, 1144al) even if they didn't make anything in addition. The
active state of our ability to awaken to significance is what is best and most powerful in us and is
"either divine itself or the most divine of the things in us." When it is directed toward the most
divine, timeless things, it is a pure beholding (NE, 1177a13-21).
One living in this state of activity would be living a life that "is divine as compared with
a human life." Hence, Aristotle said, "one ought to immortalize" (NE, 1177b25-34). That is,
one ought to be as much as possible in this best state of activity, that of the immortals, like
Athena, in Homer or that of the impersonal divine in Aristotle. Wlien we are in that state, we are
for a period of time in the same state as the divine itself is in, over the whole oftime. 7 Moreover,
"each person would even seem to be_this [best state of activity]" (NE, 1178al). "[A]nd so the
person who loves and gratifies this is most a lover of self' (NE, l 168b33).
Yajfiavalkya commented that the Brahman-realm, too, has the characteristics of not being
a temporal phenomenon, of being a sort of pure beholding, and of being our true self. Moreover,
it, too, is impersonal, not divided up into essentially different Athena-moments and Apollo-
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moments. Finally, knowers of Brahman, living the life of their true self, are leading a life that
transcends the human. Thus, most of us live in ignorance of our true self.
But whereas Aristotle agrees formally with the implication of Apollo's "Know thyself,"
that we are ignorant of our true self, yet Aristotle's recognition of the true self as divine seems to
contradict Apollo's insistence on the separation between the human and the divine. Yaj:fiavalkya
said that when a similar contradiction is voiced in his tradition, the response offered is that the
contradiction is only apparent. Someone who took the "You" in "You are That!" to refer to his
ordinary sense of self, would be engaging in self-inflation. Students are encouraged to ponder
'Who am I?' as a practice, in order to shift them from the ordinary to the true sense of self. So,
Yaj:fiavalkya said, he and Aristotle could both take "Know thyself' in a double sense: 'With
respect to your ordinary sense of self, think mortal thoughts, but recognize that the true you is
divine activity.'
In On the Soul Aristotle began to sketch what might be entailed in realizing the
Aristotelian analogue to "You are That!" namely, the immortalizing involvement in the best
activity. One of Aristotle's foremost interpreters, Averroes has worked out a detailed portrait in
color, which fills in Aristotle's black-and-white sketch in a way that has interesting parallels to
'the Upanishadic picture. To that portrait'we now turn.8
We shall now refer to this best state of activity by its customary name in philosophical
texts, "intellection." In Aristotelian fashion Averroes began his account of intellection with what
is clearer to us and ended it with what is clearer by nature. There are three main figures in his
initial portrait-the "material intellect," the "disposed intellect," and the "agent intellect."
Averroes followed Aristotle's comparison of intellection to the action of a craft, in which
some material, like clay, receives a form, say, that of a bowl (OS, 430al0-14). When I acquire a
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simple intelligible, such as, 'straight line,' it is received as form by the material intellect-which,
not being corporeal, is material only in the sense that it serves as material-for. My disposed
intellect, 9 now having the acquired intelligible as an active disposition ('€~t~), is in what Aristotle
calls a first state of maintaining itself(' sxciv) in (' f,\I) its completed condition (r€A.o~), with
respect to this intelligible. Henceforth, we shall misleadingly say that it is 'in first actuality.'
The accomplished dancer, when not actually dancing, is a dancer in first actuality. When she is
actually dancing, she said to be a dancer 'in second actuality.' So, too, when I am actively
contemplating the intelligible 'straight line,' perhaps in the course of a demonstration, my
intellect is in second actuality.
According to Aristotle, "the soul never engages in intellection without an appearance"
(43 la24), which Averroes takes to mean imaginative appearance. 10 Thus, when I am led up to
(' cnayroyft) a particularly suggestive instance, say a good image of a straight line, that image is
what specifies that the material intellect will receive the intelligible 'straight line.' Averroes said
that the material intellect, as so determined by my imagination, 11 is "conjoined" with it and that
my disposed intellect is precisely this conjunction of the material intellect with my imagination.
One of the unusual features of Averroes's interpretation is that according to him there is
only one material intellect. My disposed intellect and your disposed intellect are the results of its
conjunctions with the different images in our respective imaginations; we actualize it differently.
In this way the one material intellect is said to be incidentally many. 12 Moreover, since my
imagination is corporeal, therefore, the intelligibles of mundane things in me and, consequently,
my disposed intellect itself are generable and corruptible. 13 Yajiiavalkya observed that one
might also say that the one Brahman is incidentally many individual selves (jfvatman).
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Now, before the intelligible 'straight line' can be received by the material intellect, what
is irrelevant in the image in which it is 'embodied' must be taken away ('acpmpsro). This
abstraction brings it into the state of actual intelligibility. To elucidate this act of abstraction,
Averroes referred to another of Aristotle's comparisons: The passage from potential to actual
intelligibility is like a color's transition from potential visibility to actual visibility when the
lights in a room are turned on. The 'light' that illumines the darkness of the image, producing
the abstraction of the latent intelligible, is the agent intellect.
However, this picture of the agent intellect as shining from the outside onto a potential
intelligible embedded in an image is only the way it first appears to us. Averroes said that if we
consider its role in the intellectual insights we have when we draw conclusions from the
intelligibles that we have acquired-perhaps, that one and only one straight line may be drawn
between two points-we come to a deeper view. In reality the agent intellect is related to the
intelligibles of my disposed intellect as form to material. It is somewhat as though the agent
intellect were a light 'full' of Color itself. What really happens when it shines on an image is
that the image's conjunction with Color itself draws out of the latter a particular color, one which
)
had been potentially within Color itself. Then that particular color is received by the material
intellect. Even in my acts of intellecting simple intelligibles in the world, the agent intellect is
incidentally in partial conjunction with my imagination. 14 I am to a degree intellecting it, so that
it, then, is at work as the form of my disposed intellect. 15
For Averroes this understanding of the agent intellect meant that it is itself the source of
the intelligibility of the corporeal world. For since the image arose on the basis of sense
perception of things in the world, the potential intelligibles in my imagination are due to the
potential intelligibles in the things in the world. Consequently, he took the agent intellect to be
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Aristotle's unmoved mover from the Metaphysics (1072b18-30; 1075a5-11). Hence, there is
only one agent intellect; and it is its very activity of unchanging, eternal self-intellection.
Correlatively the potential intelligibles of things in the world are their actualities, their being-atwork maintaining themselves in their respective states of completeness. The agent intellect is
responsible for their potential intelligibility in the following sense. For each of them its state of
completeness is the closest state to the agent intellect's self-intellection that its materials are
capable of attaining. 16 Yajiiavalkya noted that the agent intellect as responsible for all
intelligible being is somewhat analogous to the one source of all existence in his tradition.
But how can the self-directed intellection of the agent intellect be responsible for our
intellection of the intelligibles in things outside of itself in the world, when it and the object of its
intellection are absolutely one? As reflexively turned toward itself, it is not aware of the
multiplicity of the potential intelligibles of mundane things as such. Yet it nevertheless does
comprehend them, somewhat in the way that the craft of pottery-making, in a sense,
comprehends the forms of all the bowls for which it could be responsible. But to be actively
responsible for the intellection of this intelligible on this occasion, the agent intellect must also
be 'turned outwards,' as it were, away from itself, in order to shine on the appearances of
mundane things, in hu'man beings' imaginations.
As outward-turned, prior to illuminating the appearance, it seems to be lacking any
intelligible. And yet any one of them can be brought into focus from itself by an image. Thus,
surprisingly, the agent-intellect-as-turned-outward is pure potentiality, pure material-for; it is the
material intellect.
Ill order to appear as such, that is, as empty of intelligibles of mundane things,
it must become "temporarily ignorant of itself." 17
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This self-forgetfulness is concretely realized by its conjunction with our imaginations.
By virtue of that conjunction, the agent intellect becomes 'ignorant' of being the self-intellecting
source of all intelligibility; it appears, instead, in each of us in a double form-first, as our
partially actualized receptivities for intelligibles (our disposed intellects) and, second, as light
eliciting those intelligibles by abstraction from our images. At this point Yajfiavalkya interjected
that the agent intellect's ignorance of itself seems to be in amazing agreement with the role of
ignorance in the Upanishads: A knower of Brahman "knows knowledge and ignorance, both of
them, together" (IU, 11). For Brahman, too, turns outward, so that ignorance, that is, awareness
of multiplicity, is one of its aspects. 18 But Brahman is both knowledge and ignorance; the two
are inseparable. 19
From the human point of view, as I learn more, the agent intellect becomes the form of
my disposed intellect to an ever greater degree. In this way my three principal differences from
it will decrease. First, in acquiring more intelligibles, my disposed intellect becomes less and
less a partial view of the agent intellect. Second, in advancing to intelligibles which are less and
less referred to the corporeal world, my disposed intellect becomes more pure.
20
Third, in
coming to ever more encompassing intelligibles, it approaches the agent intellect's unitary
VlSIOn.
Ultimately, while still "in this life,"21 I may arrive at the point where I have acquired all
the intelligibles. 22 Then I will have achieved a state of complete conjunction23 with the agent
intellect. My disposed intellect will have lost all traces of individuality, 24 which are what made
it my disposed intellect; it will have perished as such. All of me that is not intellect is "cut off'
from my intellect, which is identical with the agent intellect. 25 In this sense the state of complete
conjunction has been said to involve an "existential break" from the world.
26
Once again
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Yajfiavalk:ya was surprised to recognize in this existential break an analogue in the Aristotelian
tradition, at such a deep experiential level, to a prominent feature of the realization of Brahman.
In complete conjunction I experience myself permanently27 as shining forth intelligibility,
but this 'myself is not the self! used to think I was. For the conjunction removes what had been
preventing my recognition of the ag~nt intellect as being my form. 28 Averroes said that then the
agent intellect, united with us as our form, functions as our sole operative principle. 29
We
might wonder what life in this state of conjunction would be like. One suggestion is that I might
experience it as "a wakeful loss of rationality," a loss of consciousness of my humanity. 30 I
would not be engaged in thinking things out; I would not be conscious of myself as an
individual, as a member of the human species.
Alternatively, guided somewhat by his own experience, Yajfiavalkya proposed that
perhaps I might be aware of myself (what Aristotle in the Ethics poi.rited to as my true self)
engaged in self-intellection, while simultaneously being aware of experiencing my ordinary self
involved in its everyday activities against this backdrop. Yajfiavalkya mentioned two
possibilities, the second of which was not analogous to his own experience. First, in each
instance of intellection, I could perhaps experience the agent intellect as transitioning from
unitary self-intellection to the offering of an aspect of itself to my imagination. Second,
analogous to the end of the path outlined in the Yoga-Sutras (that is, kaivalya), 31 it could be that
engaged in self-intellection I ignore and desist from everyday activities, and so, ultimately,
wither away and die_. 32
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1
NEH-supported lectures given at St. John's College, Annopolis, on February 15 and 19, 2008 and
dedicated to the memory of Ralph Swentzell, who did so much to further the study of Eastern Classics at St. John's
College.
2
This and the following few paragraphs are based on K. von Fritz, "NOO:E and NOEIN in the Homeric
Poems," Classical Philology 38. (1943), 79-93.
3
The translations from Homer are based upon those listed in the bibliography.
4
This "directional arc" is analogous, at a higher level, to Merleau-Ponty's arc intentionnel on ~e level of
sensing (Merleau-Ponty, 158).
5
The following few paragraphs are based on W. Otto, The Homeric Gods: The Spiritual Significance of Greek
Religion (New York: Pantheon Books, 1954).
6
The Inner Controller is depicted mythologically as follows:
He entered in here right to the tips of the nails, as a razor slips into a razor-case ....
When he breathes he is called 'breath'; when he speaks, 'speech'; when he sees,
'eye'; when he hears, 'ear'; when he thinks, 'mind.' They are just the names of his
actions. Whoever meditates on any one of these does not know [the Self], for [the
Self] is not completely active in any one of them. One should meditate on them as
[being] simply the Self (BU, 1.4.7)
7
Aristotle, Metaphysics, 1075a7-l l: "So, the condition the human intellect .. . is in at some period of time
... is the condition the intellection that intellects itself is iii over the whole of time." Cf.: "For the gods, the
whole of life is blessed, and for human beings it is so to the extent that there is in it some likeness to such a
state of activity" (NE, l l 78b25-26).
8
I am indebted to my colleague, Michael Blaustein, for a: very fruitful recent conversation about Averroes.
This section is based upon the works of Altmann, Black, Blaustein, Hyman, Ivry, Leaman, and Zedler
listed in the bibliography. Leaman and Zedler have been particularly helpful for the early part, but I have
taken most of it from Black. In the later part I have relied heavily on Blaustein's working out of the details
of the relation between agent and material intellects and have made significant use of Altmann and lvry,
especially the latter's thoughts about conjunction while we are still alive. However, responsibility for any
.
errors that there may be in the interpretation of Averroes is mine alone.
9
OSl...11 Y ~('aql bi al-ma/aka), which means intellect in natural disposition, aptitude, faculty; intellectus
in habitu.
10
Also: "the intellective [part of the soul] intellects the [intelligible] looks in appearances" (43 lb2).
I accept Nussbaum's (1978) suggestion about the meaning of <pavwia. It is based on such
passages as the following 428al, 7, 14ff, & 29ff; b30fi), wherein the link between <pav•o"ia and <paivi::cr0at
seems compelling.
11
In fact, for Averroes the imagination or, more properly, the cogitative power-which, together with the
imagination and memory; prepares what is given in sensation, so that, when illumined by the agent
intellect, the intelligible look can appear through and in-form the material intellect-is a fourth intellect, the
passible intellect (LC, 449.174, cp. 409.640).
"The cogitative power has the following functions : it can make an absent object appear as though
present; it can compare and distinguish the re-presented_objects with each other; it can judge whether a
given re-presented object bears a relation to a directly presented sense intention" (Zedler, 1954, 441).
12
Zedler, 1951, 175.
13
Yet because the human species is eternal, the succession of human souls in which intellection ofintelligibles of
mundane things occurs ensures the continuity ofintellection in the material intellect and the omnitemporality of the
intelligible looks of mundane things as such. Through the repeated presentation of potential intelligibles in
imaginative appearances, this succession "provides a replica in time and in matter of the eternal" intellection of the
agent intellect (Zedler, 1951, 173). It is possible that the belief that souls migrate into different bodies in succession
is a reflection in the form of popular myth of the truth of the omnitemporal unity of the material intellect in the
multiplicity of disposed intellects (Altmann, 82).
14
The agentintellect in this incidental connection would be what Aristotle referred to as the intellect that enters
from outside the door": "It remains then that intellect alone enters additionally into [the seed of a human being]
from outside the door (0upa0ev) and that it alone is divine, for corporeal being-at-work has nothing in common with
its being-at-work" (De Gen. 736b27). Cf:
�17
But the intellect seems to come to be in [us] while being an independent thing, and not to be
destroyed... . [I]ntellecting or contemplating wastes away because something else in us is destroyed,
but it is itself unaffected (without attributes). But thinking things through and loving or hating are
affections (attributes) not of the intellect but of that which has intellect, insofar as it has it. For this
reason, when the latter is destroyed, the intellect neither remembers nor loves, for these acts did not
belong to it but to the composite being which has perished; the intellect is perhaps something more
divine and is unaffected (OS, 408bl8ff).
What Averroes actually says is that the incidental connection constitutes a "disposition" [ ..il~I
(Isti'dad), which means readiness, willingness, preparedness, inclination, tendency, disposition, propensity;
dispositio] of the agent intellect, but one located within human souls. It is a disposition to receive the
intelligible looks of mundane things. Thus, the material intellect is in reality the agent-intellect-as-havingsuch-a-disposition-in-human-beings.
15
"[T]he material intellect is perfected by the agent intellect and intellects if' (Blaustein, 285; italics
added).
16
Based on Aristotle, Metaphysics, 1072bl2: "[I]t is beautiful and in that way a source."
17
Blaustein, 214-15.
18
Aurobindo, 61-62 and 94.
19
Aurobindo, 58 and 72.
20
When my disposed intellect is actively engaged in intellecting an intylligible look, it is also intellecting
itself, since, as Aristotle points out, the intellect is one with what it intellects, in that the second actuality of
both is identical, as lumber's being built is one with the activity of building. In contemplating itself as
informed by the intelligible look, my intellect is also directed toward the image, which specified which
look was to be received, in the same way in which, when we look at a painting, we are directed toward the
scene which we see in it. However, since the mundane thing toward which the intellect is directed via the
image is not pure intelligibility, therefore, the disposed intellect's self-intellection is not pure selfintellection; its act ofintellection is not absolutely one with its object ofintellection (Blaustein, **). In this
way it differs from the self-intellection of the agent intellect. For the object of the agent intellect's
intellection does not point beyond itself.
21
lvry, 83.
22
What had been my intellect would now be either fully (Blaustein, 272, 283) or partly assimilated to the
agent intellect. That is, either 'I' would be engaged in intellection of everything intelligible or, having
abandoned all the contingent aspects of my intellection, I would be focusing solely on its formal aspects,
which are supplied by the agent intellect, so that I would be participating in an aspect of the formal
governing source of the whole (Leaman, 101-03).
23
Ji......wl (ittisal) = connectedness, unitedness, union; juncture, conjunction, link; connection; contact [from
J.,..._, (wasala) =to connect, join, unite, combine, link, attach]. Continuatio =a following of one thing after
another, an unbroken series, a connection, continuation, succession [from continuare =to join together in
uninterrupted succession, to make continuous]. Wasala may be a reformulation of Aristotle's 0\St~.
Altmann (83) states that the notion reflects Plotinus's cruvfut-rEtV [=(tr.) join together; II (intr.)
border on, lie next to; combine, be connected with]. Consider: "[W]e lift ourselves up by the part [of the
soul] which is not submerged in the body and by this conjoin at our own centres to something like the
Centre ofall things .... [W]e must suppose that [our souls conjoin] by other powers, in the way in which
that which is engaged in intellection naturally conjoins with that which is being thoroughly intellected and
that that which is engaged in intellection ... conjoins with what is akin to it with nothing to keep them
apart" (Plotinus, VI.9.8.19-30).
Altmann (83n) also mentions that Plotinus refers to his experience of union as a contact ('acpi]).
However, in Averroes "conjunction" is to be distinguished from "union": ..ib.wl (ittihad)= oneness,
singleness, unity; concord, unison, unanimity; combination; amalgamation, merger, fusion; union [from ..i:.._,
(wahada) =to be alone, unique; II to make into one, unite, unify; to connect, unite, bring together,
amalgamate, merge]. In Greek the corresponding word is 'tvmcru; = combination into one, union.
24
In its perfected state as engaged in intellection of the agent intellect, the disposed intellect is called the
"intellect that has arrived" (intellectus adeptus).
25
Blaustein, 272.
26
Altmann, 74, characterizing the position of Averroes' teacher.
27
Ivry, 83.
�18
28
Blaustein, 284. Cp. further: "[T]he material intellect's awareness of itself even when it is not thinking of
any intelligible form .... is itself kind of actuality, however empty. Averroes claims that this kind of selfawareness is in fact the obverse of the [agent] intellect's fully conscious awareness of itself; the material
intellect's awareness of its own potentiality is a dim awareness of its actuality as the [agent] intellect."
29
It is interesting to note that with respect to conjunction, the agent intellect exercises all four kinds of
responsibility that Aristotle describes in the Physics. It is responsible for my attainment of conjunction in
functioning as my end (tf:A.oi;). Moreover, it is responsible for the motion oflearning, by which I approach
conjunction; for my learning is really its producing intelligibles in me by revealing itself to me as the form
of my disposed intellect (Blaustein, 276-77). Since the agent intellect is what I am more and more coming
to intellect and, so, to be, it is also responsible for conjunction in the way a form is. Finally, it is also
responsible as material, since the material intellect is ultimately identical with it. The same could be said of
Brahman, with the key difference that its responsibility is not limited to the realm of intelligibility.
30
Blaustein, 272.
31
Patafijali, IV.34; see also Feuerstein's comment (p. 145). Kaivalya is "the aloneness" of seeing.
32
Finally, as far as Averroes' position with respect to individual immortality goes, there are two interesting
possibilities. He may have thought that the only immortality was the impersonal immortality of the state of
conjunction and that philosophers were orienting their lives accordingly. The belief in personal
immortality on the part of ordinary people would then be the closest approximation to the truth of which
they were capable. On the other hand, he may have held that while a few intellects may attain conjunction
of, all souls are immortal (Zedler, 1954, 451-52). There is a somewhat similar divergence in the
Upanishadic tradition between Sankara's position that the individual self is in a sense unreal and
Ramanuja's view that individual selves, while not independent, are real.
a
�19
Part Two: Cit (Pure Awareness)
To begin the final section, we return to Aristotle. In the Nichomachean Ethics, he states:
[O]ne who is seeing is aware ('mcr8cive-rat) that he is seeing, and one who is hearing
[is aware] that he is hearing, ... whenever we are perceiving [we are aware] that we
are perceiving and whenever we are engaged in intellection (vocoµev) [we are aware]
that we are engaged in intellection (l l 70a29-3 l). 1
To what aspect of experience is Aristotle pointing here? The prevalent view has been that he
means that, say, perceptual consciousness is accompanied by a reflection on, or a thought about,
that consciousness:2 'I know that I'm looking at you seated there before me.' However, this
seems to occur only intermittently. Hence, an alternative interpretation has been proposed3 that
perceptual consciousness is always selfaware, aware (of) itself,4 but not conscious of itself,
although, at any given time, we may notice selfawareness to a greater or lesser degree.
Yajfiavalkya emphasized to me that it is only through diligent practice that I could learn to
recognize the difference between reflective consciousness and selfawareness in my own
expenence.
To clarify the difference bet_ween selfawareness and reflective consciousness, we shall
draw upon some descriptions of experience by the philosopher J.-P. Sartre. 5 Consciousness is
necessarily always aware (of) itself, but precisely as being conscious of an object beyond itself.
"[T]his awareness (of) consciousness ... is not positional; that is, consciousness is not for itself
its own object. Its object is outside or'l.t by nature .... We shall call such a consciousness
'consciousness of the first degree' ... " (S, 23-14). In this lecture 'consciousness' will always
-mean positional consciousness, consciousness of ari object.
Let us take as an example of first-degree consciousness my perceptual consciousness-ofthe-microphone-on-the-lectern-say, in the mode of staring-at. 6 That perceptual consciousness
is not an object for itself, whereas the mike-on-the-lectern is an object for it. But in each such
�20
act of consciousness, there lives an attentive presence by virtue of which the consciousness is
aware (of) itself. When, as is usually the case, the attentive presence goes unnoticed, we
experience only a dim awareness (of) consciousness.
Yaj:fiavalkya interjected that in his tradition this awareness is called the "witness" (sakshz;
SU, Vl.12-14) and the selfaware quality of consciousness is called "self-luminousness"
(svajyotir). He added that this is what he was referring to when he said: "'You cannot see the
seer of seeing; you cannot hear the hearer of hearing; you cannot think of the thinker of thinking;
you cannot perceive the perceiver of perceiving'" (BU, IIl.4.2). And: "'It is the unseen seer, the
unheard hearer, the unthought thinker, the unperceived perceiver. Other than this there is no
seer, ... hearer, .. . perceiver"' (BU, 7.23). I responded that Sartre seemed to agree with him that
this awareness cannot be the object of consciousness: This sphere "is a sphere of absolute
existence, that is, of pure spontaneities, which are never objects ... " (S, 77).
As opposed to this selfaware, first-degree consciousness-of-objects, which makes up
most of our waking lives, there arises from time to time "a consciousness directed onto [the firstdegree] consciousness, [that is,] a consciousness which takes [the first-degree] consciousness as
its object." Sartre calls it a "second-degree" or "reflecting consciousness." Whereas in the
previous case there was no duality at all to synthesize, here "we are in the preserice of a synthesis
of two consciousnesses, of which one is consciousness ofthe other." When I think, 'Staring at
this mike on the lectern is wasting time,' this act of reflective consciousness involves a synthesis
of the thinking consciousness and the reflected-upon consciousness-of-the-microphone.
Moreover, just like a first degree consciousness, second-degree consciousness, here, my
thinking, is selfaware (S, 28-29).
-
When the thinking consciousness posits the previously unreflected-upon staring
consciousness as its object, it is not its own staring that it is positing. What the reflecting
�21
consciousness exclaims about the staring, concerns not itself, but the staring consciousness,
which is reflected upon. Hence, what reflecting consciousness is turns out to be selfaware
consciousness of another, prior, selfaware consciousness, which, in tum, is consciousness of an
object that is not a consciousness. It is truly re-fleeting, that is, bending backwards, to look at an
earlier moment of consciousness.
The fact that it is not its own staring that the thinking consciousness posits in reflecting
on the staring consciousness raises the question whether the I that seems to be thinking "is that of
the consciousness reflected upon" and not, in fact, an I supposed to be "common to the two
superimposed consciousnesses." Indeed, one suspects that the reason why every reflection
possesses a sense of self is that the reflective act itself gives birth to the sense of self in the
consciousness that is reflected upon (S, 28-29). 7 Sartre offers an example in order to test this
hypothesis:
... I was absorbed just now in my reading. I am going to seek to recall the
circumstances of my reading. . . . Thus I am going to revive ... also a certain thickness
. of un-reflected-upon consciousness, since the objects were able to be perceived only
by that consciousness and remain relative to it. That consciousness must not be
posited as the object of my reflection; on the contrary, I must direct my attention onto
the revived objects, but without losing sight of the un-reflected-upon consciousness,
while maintaining a sort of complicity with it and making an inventory of its content
in a non-positional way. The result is,,not in doubt. While I was reading, there was
consciousness of the book, of the heroes of the novel, but the I was not inhabiting that
consdousm;ss ... (S, 30; second set of italics added)
Here Sartre reawakens the original selfaware consciousness and dwells in the awareness.
That awareness is also a precondition for reflection. Should he reflect, 'I was absorbed in
my reading,' then, instead of dwelling in the awareness-component of the original consciousness,
he would, as it were, transform it into an act of consciousness, the object of which is the original
consciousness, (of) which the awareness was aware. An I is present to that second-order
consciousness. 8 So, we m~y call it 'self-consciousness.'
�22
Sartre goes on to propose how, based upon this I
of self as
or reflection, I go on to construct a sense
aunity, first, of states, like, for example, my hatred of Peter, then, of actions, like my
playing a piano sonata or driving to DC, and, finally, of qualities, like my spitefulness. For
instance, let us suppose a first-order consciousness of disgust and anger, together with the
perception of Peter. If the self-consciousness reflected only on what was appearing in the firstorder consciousness, it would be thinking, 'I feel disgusted with Peter.' But instead, the angry
disgust at Peter appears as a profile, or perspectival view, of a disposition, 'hatred of Peter,'
similarly to the way in which a house will show itself to me in different profiles, depending upon
where I am standing. The hatred appears to be showing a 'side' of itself through the momentary
experience of angry disgust. For the self-consciousness the angry disgust appears to be
emanating from the hatred. On a later occasion, perhaps, the hatred will itself appear to
refledion as an actualization of a quality of spitefulness, which is in Me (S, 45-46, 51, 53). But
in neither case does the self-consciousness realize that the hatred or the spitefulness is arising in
the moment of reflection; rather it supposes that the state or the quality was already there in the
first-order consciousness. 9
This process resulting in a sense of self leads me to say things like "my consciousness,"
when in fact "[t]he I is not the owner of consciousness; it is the object of consciousness" (S, 77).
Yajfiavalkya noted that a process of construction of the sense of self (aham-kara) figures
prominently in the Upanishadic tradition, too. It leads to the arising of many fears and desires,
which, in turn, function as barriers to the realization of Brahman by keeping us 'glued' to
objects. I responded that here, too, there is a remarkable agreement with Sartre, who wrote:
"But perhaps the essential role [of the sense of self] is to mask to consciousness its own
spontaneity. . . . Hence, everything happens as if consciousness ... were hypnotizing itself over
that sense of self, which it constituted" (S, 81-82).
�23
Usually we do not notice the awareness-aspect of consciousness because we are so taken
up with what is appearing to consciousness. Yet on occasion awareness may stand out in our
experience. For instance, some people are engaged in a heated discussion at an outdoor cafe. A
nearby car suddenly backfires. Several of the participants may be so caught up in the
conversation that they don't even notice the loud sound. Others may be startled and shift their
attention to the street. But someone who was anchored in awareness would notice, but not be
jarred by, the sound.
Another example: On a good day the football quarterback Joe Montana, at the top of his
game, would experience a pass play as follows. 10 He was conscious of the linemen rushing at
him, of his receivers running downfield, and so on. But instead oflooking with hurried, anxious
glances, he experienced an awareness spread over the whole unfolding scene. All the players
seemed to be moving in slow motion, and everything appeared with great clarity and
distinctness. He was keenly aware of his own body, the motions of his limbs and an overall
sense of relaxation, as his arm drew back and the ball headed toward the receiver. 11 Taken by
itself this example may mislead us into thinking that awareness is dependent on the attainment of
a certain l~vel of skill, in this case, that of an MVP quarterback. But the previous example and
the following one make it clear that this is not the case.
A third illustration: Some automobile drivers-when they are not too distracted by their
thoughts--experience freeway traffic as follows: 'First, one driver cuts me off; then a slowpoke
is holding me up. My consciousness narrows to focus on the offending driver; and, irritated, I
react by honking or suddenly changing lanes.' Another driver may perceive the same cars on the
beltway as if they were moving in a force field. She is aware of that field as calling forth the
alterations in her driving required in order to maintain a smooth flow of traffic.
�24
A fourth instance: "Surgeons say that during a difficult operation they have the sensation
that the entire operating team is a single organism, moved by the same purpose; they describe it
as a "ballet" in which the individual is subordinated to the group performance ... ~· 12
The following story shows a transition out of awareness into consciousness:
Suppose a woman is engaged in sewing something. A friend enters the room and
'begins speaking to her. As long as she listens to her friend and sews in [awareness],
she has no trouble doing both. But if she gives her 'attention to her friend's words and
·a thought arises in her mind as she thinks about what to reply, her hands stop sewing;
if she turns her attention to her sewing and thinks about that, she fails to catch
everything her friend is saying, and the conversation does not proceed smoothly. In
either case . . . . she has transformed [awareness] into thought. As her thoughts fix on
one thing, they're blank to all others, depriving the mind of its freedom. 13
This example enables us to avoid the misconception that awareness is incompatible with words.
For it was a shift in the way in which she attended to speech, or to her sewing, that led to the
woman's loss of the ability to attend to both simultaneously.
A final case, as described by Merleau-Ponty (1945): Being most of the time in the
consciousness-mode, we live in a world that "only stirs up second-hand thoughts in us." Our
mind is taken up with "thoughts, already formulated and already expressed, which we can recall
silently to ourselves and by which we give ourselves the illusion of an interior life. But this
supposed silence is in reality full of words rattling around." However, occasionally we may
"rediscover primordial silence, J.nderneath the words' rattling around." Then we pass from the
mode of consciousness-of-objects to dwell in awareness. We experience "a certain emptiness,"
"a certain lack which seeks to fill itself," to be transformed into speech (213-14). Then there can
emerge "an authentic word, one which formulates something for the first time"-such as "that of
the child who is pronouncing her first word, of the lover who is discovering his feeling" (207..,
08), or of "the writer who is saying and thinking something for the first time" (214). In the mode
of awareness, we can live through a sort of original emergence.
�25
Words usually serve to keep our thoughts moving within already formulated articulations.
They could be said to function like "preciptitates" (Niederschlage) 14 of previous 'chemical
reactions,' whether our own or others'. However, when awareness becomes prominent, it acts as
a catalyst, which facilitates a fresh chemical reaction.
All the examples manifest an awake, keen involvement in experience together with an
absence of the sense of self and of self-focused emotions and motivations from the foreground.
And each of them foregrounds a different property of awareness in turn-'unstuckness' to
objects, 'spaciousness,' not merely in the spatial and the temporal senses, responsiveness to
dynamic qualities of the surrounding field, organic connectedness with who or what 15 is in the
field, moving out of awareness with the arising of a directing I, and a sense of emptiness out of
which newness arises spontaneously.
We might say that a good seminar could give evidence of some of these signs of
increased awareness. If over time the participants have developed seminar skills, as the surgical
team developed surgical skills, it could become experienced as a ballet. Along with the
development of those skills, some of the members may have cultivated their awareness to some
degree, paralleling the range of levels of awareness in the operating team. That cultivation may
e_nable them to experience "a certain emptiness," from which an "authentic word" may emerge
with greater frequency.
Such characteristics of awareness as those listed above have-led people in certain
pursuits, such as martial arts, to seek to cultivate it, so that it will become reliably foregrounded.
In developing a painterly vision, 16 for instance, one must learn to forget what things are, in order
to see how they are actually appearing to the eye, which means, how they are coming into being
before our eyes. As Merleau-Ponty says of Cezanne: "It is the mountain that he interrogates
�26
with his gaze. What exactly does he ask of it? To unveil the means, visible and not otherwise,
by which it is making itself a mountain before our eyes." 17
We might expand on this account in the following way. As a potential painter's
awareness becomes more prominent, she no longer sees things as already 'finished off,'
but~
instead, as having a potential for greater 'aliveness.' It is as if they were calling to her to join in
their emergence. Then she may heed the appeal and begin to paint. Now it is this particular .,
piece of fruit before her that she captures "coming into being before [her] eyes" in such a way
that it can do so later before our eyes. 18
Another example of the cultivation of awareness is found in psychoanalysis. Freud, in
his recommendations on the proper attitude to be adopted by the analyst, counsels a state of mind
characterized by, first, the absence of reasoning or
deliberate attempts to select, concentrate or understand; and [second] even, equal and
impartial attention to all that occurs within the field of awareness. . . . This technique,
says Freud, " .. . consists simply in not directing one's notice to anything in particular
and in maintaining the same 'evenly suspended attention' (as I have called it) in the
face of all that one hears ... " 19
That is, the analyst deliberately withdraws from consciousness-of-objects and dwells in the
awareness component of consciousness. This open attentional attitude is to be distinguished, on
the one 1hand, from a merely passive attention, in which the mind wanders freely from object to
object, and, on the other, from a focal attentional attitude, searching for a particular meaning. 20
Partly because evenly suspended attention was criticized as unattainable,21 Freud's prescriptions
to practice it did not become integrated into psychoanalytic training programs.
However, Wilfred Bion, probably the most thoughtful psychoanalyst of the latter part of
the twentieth century, forcefully advocated this practice in the following terms:
[T]he capacity to forget, the ability to eschew desire and understanding, must be
regarded as essential discipline for the psycho-analyst. Failure to practise this
discipline will lead to a steady deterioration in the powers of observation whose
maintenance is ~ssential. The vigilant submission to such discipline will by degrees
�27
strengthen the analyst's mental powers just in proportion as lapses in this discipline
will debilitate them.
*
*
*
*
*
*
*
*
*
*
To attain to the state of mind essential for the practice of psycho-analysis I
avoid any exercise of memory.. . . When I am tempted to remember the events of any
particular session I resist the temptation.... If I find that some half-memory is
beginning to obtrude I resist its recall.. ..
A similar procedure is followed with regard to desires: I avoid entertaining
desires and attempt to dismiss them from my mind. For example, ... it interferes with
analytic work to permit desires for the patient's cure, or well-being or future to enter
the mind. Such desires .. . lead to progressive deterioration of [the analyst's] intuition.
[There is an aspect of ultimate reality] that is _currently presenting the unknown and
unknowable [in the consulting room]. This is the 'dark spot' that must be illuminated
by 'blindness' [that is, ignorance]. Memory and desire are 'illuminations' that destroy
the value of the analyst's capacity for observation as a leakage of light into a camera
might destroy the value of the film being exposed. 22
The effect of not following this discipline is to interpret what the patient says in terms of
what the analyst wishes or already 'knows,' thus closing her off from what may be emerging for
the frrst time in the current hour. Bion's psychoanalytic state of mind is comparable to Socratic
ignorance. Both represent an opening of oneself, in a conversation, to notice possibilities
springing up that would otherwise remain unthought.
Another area in which a practice has been advocated for the enhancement of awareness is
philosophy. In the early twentieth century, Edmund Husserl proposed pursuing wisdom by
following a path that he called "phenomenology." By this he meant an account of the things
I
appearing to you precisely in the way in which they actually appear.
Philosophy students sometimes think that studying phenomenology entails mainly
reading books. However, learning to see the things appearing to you precisely in the way in
which they actually appear takes practice. Martin Heidegger, Husserl's best known student, had
great difficulty at the beginning of his study of phenomenology.
It concerned the simple question how thinking's manner of procedure which called
itself "phenomenology" was to be carried out.~ .. My perplexity decreased slowly ...
only after I met Husserl personally in his workshop .. .. Husserl's teaching took place
in a step-by-step training in phenomenological "seeing" which at the same time
demanded that one relinquish the untested use of philosophical knowledge.... I
�28
myself practiced phenomenological seeing, teaching and learning m Husserl's
proximity after 1919.23
The phenomenological seeing that one would practice is founded on an act called "the
phenomenological reduction." While it was instituted in the service of phenomenological
philosophy, Husserl was aware of the effect it could have by itself upon the person practicing it:
Perhaps it will even turn out that the total phenomenological attitude, and the
[reduction] belonging to it, essentially has, first of all, the vocation of effecting a
complete personal transformation, which would, in the first place, be comparable to a
religious conversion, but which beyond that contains within itself the significance of
being the greatest existential transformation to which humanity as humanity is
called.24
Yajiiavalkya noted that the designation "greatest existential transformation"-like the earlier
"existential break" associated with conjunction in Averroes-fits the experience of "waking up
to" (pratibodham) Brahman as well (KeU, II.4).
In characterizing the phenomenological reduction, I shall borrow the descriptions of the
later Husserl's closest collaborator, Eugen Fink, because they are vivid and strongly suggestive
of awakening to Brahman.
25
The phenomenological reduction is a two-part act (F, 41). Husserl
called the first component of that act a "disconnection" (Ausschaltung), or an "epoche," a
suspension ('s7toxft), of the "natural attitude," the attitude in which we take things for granted, or
as a matter of course (selbstverstdndlich).
Disconnection means that you deliberately abstain from all beliefs; you inhibit your
accepting of all the things you take as what 'counts' (Geltendes) for you (F, 3 9-40). You cease
living in acts of positional consciousness in Sartre's sense. As we observed Sartre doing, while
remaining disconn.ected you turn your attention from the objects of consciousness to the
consciousn~ss-of-objects.
You are not caught up with objects, but are attentively.'spread' over
the whole of consciousness~of-objects, without positing that as
an object. And you alter your
mode of attention from an active searching-for to a receptive letting-things-come. You are
�29
learning to do something involuntary, somewhat like preparing to receive "the visitation of
sleep," which comes in the way as the god Dionysus visits his followers, when they no longer are
distinct from the role they are playing. 26 You are not gradually acquiring things in the way the
disposed intellect acquires intelligibles.
The disconnection includes the "nullification" of the sense of yourself as an empirical
human being-it "un-humanizes" (entmenschlicht) you-in that it "lays bare the ... onlooker"
"already at work" in you, into which you now "fade away" (F, 40). In the terminology of this
lecture, you disidentify with your sense of self; and you pass into awareness rather than in
consciousness. Yajfiavalkya interjected that, involved in the realization of Brahman, there is a
similar correlation of the "de-construction of the sense of self' (nir-aham-kiira) with a fading
away into the onlooker, that is, the "witness," which was already at work.
You are now in a position to notice precisely what appears to you in just the way in
which it appears. As with Freud's evenly suspended attention, all the phenomena are treated
equally; none is assumed in advance to have priority over the others. As in the case of painterly
vision, you are not imposing your knowledge on your experiencing; you are operating 'prior' to
your identification of things or events. Your going backwards involves a sort of reversal of the
outward-turning action ofthe~agent intellect. For, viewed on one level, the agent intellect
elicited intelligibles from their latent state in the appearances, while the disconnection goes back
behind those intelligibles, which, due to language, are already at work in our ordinary experience
of the appearances. In its receptive attentiveness the disconnection has an 'empty' relationship
to experience, perhaps somewhat like the agent intellect in its 'empty' state as material intellect.
The second component of the phenomenological reduction is a leading-back, the reducing proper. 27 In it, "while explicitly inquiring backwards behind the acceptednesses ... with
respect to your belonging to the world," the onlooker blasts open (sprengen) with insights your
�30
"being held captive by your captivation" (Befangenheit) with the world. You experience this as
a "breakthrough" (Durchbruch; FK, 348). As a result you discover for the first time that
underlying all of your experiences has been a primordial conviction (Urdoxa in Husserl), an
unformulated, implicit acceptance of the world and of yourself as belonging to it (F, 40-41 ).
Here "world" refers, not to the collection of all things, but to what is originally given as a
universal background, i:h the way a horizon is given for vision. While particular beliefs of yours
may have occasionally broken down, that did not shake your implicit acceptance of the horizon.
You are now sharing in the onlooker's awareness of the world, which is the "universally
flowing and continuing [world-]apperception," the "underground" (Untergrund) out of which
every act of consciousness springs up.
In this sense phenomenology is said to make the
ultimate ground of the world available to an experience (FK, 349, 352, 340),28 one in which we
experience "how ... the world is coming about for us."29
Yajfiavalkya accepted that painterly vision, evenly suspended attention, and the
phenomenological reduction are at least partial Brahman-experiences, ones that go beyond the
spontaneously arising Brahman-moments on the football field or on the highway. However, he
pointed out two differences. First, they are cultivated in the service of other ends, painting,
healing patients, or pursuing wisdom, whereas realization of Brahman is the supreme end (BU,
IV.3.22), pursued for its own sake. Second, in the other contexts awareness is to be actualized
only on particular occasions, before the canvas, in the consulting room, or in the
phenomenological "workshop," whereas one remains continually in the Braliman-realm.
I responded that, according to Husserl, in going about the course of ordinary life, the
phenomenologist has the epoche as "an active-dispositional30 attitude to which we resolve
ourselves once and for all" and which "can be actualized again and again,"31 like the dancer's
repeated re-actualizing of the dancing that she has as a first actuality. I told him that this raised
�31
the question for me whether the knower of Brahman could be said to be Brahman in this
dispositional sense.
In the Upanishadic tradition you may engage in a meditative practice, in which you could
pass through several stages. At the beginning you deliberately concentrate and turn your
consciousness inward, whil~ endeavoring to dwell more and more in awareness. 32 You need to
keep reminding yourself to notice the awareness, which is always there. Initially you cannot
accomplish this while you are doing something else, because a thing or event always captures
your attention.
After a while you will be able to maintain this centering of yourself in awareness. While
· your mind gradually has become dominated by awareness, you still occasionally experience
moments of conscious reflection on the immediately preceding moment of awareness. 33 You are
now "allowing the mind to fluctuate." 34 The following analogy may convey some sense of what
that is like. "Suppose a neighbor were to ask you to look after her children .... When the
children come you could take one of three different courses of action." You could abandon
responsibility by telling them that they can do whatever they want as long as they don't bother
you. Or you could try to control them by telling them what to do and not to do. Or, finally, you
could~
allow the children to play. This "allowing" is not active, since you do not interfere. It
is not passive, since you are present with the children ... in a total way. It is like a cat
sitting at a mouse hole. It appears to be asleep, but let the mouse show but a whisker
and the cat will pounce. It is only by allowing that one truly understands what
allowing means.
'Allowing' brings awareness to the fore in a way that pushing away and controlling do not. 35
You are aware of movements from focused to unfocused consciousness, of shifts from perceptual
to thinking consciousness, of fluctuations from consciousness-of to empty awareness, and so
�32
forth, as well as of the reversals of all these. "Allowing is ... , so to say, what fluctuating
awareness is 'made of.'"
Eventually no reflection is experienced any more; this total wakefulness, completely
purifies one of the 'sleepiness' which is what the 'habit' of consciousness really is. 36 To be
aware you don't have to be conscious ofsomething; nor do you need to be someone, much less
someone special. 37
Positional consciousness-of-objects, which was first for us, here shows itself to be, in
fact, a derivative of non-positional awareness, which is what is first in itself. Initially
consciousness seemed to have the component of awareness; but now we may say that awareness
sometimes manifests itself partially in the form of consciousness-of-objects, while in itself it is
pure awareness (cit). Again, this is quite analogous to what Averroes said of the agent intellect.
In itself it is pure, having no reference to the world; but, through its outward turn, it conjoins
itself to our imaginations, resulting in the emergence from it of particular intelligibles.
Upon emerging from this absolute silence, you may be so forcefully struck by something
in the world that you consciously recognize that you are just pure awareness.3 8 You
momentarily become conscious of this objectless being "present with the children ... in a total
way" as yourself. You are now conscious of havib.g arrived in the Brahman-realm.39
Yajiiavalkya interjected that this recognition is what is expressed in the words: "I am Brahman!"
(BU, I.4.10). He added that this experiencing of pure awareness is what he was referring to
when he had said:
· "Though then he does not see [any thing], yet he does not see while seeing. There is
no cutting off of the seeing of the seer .... But there is no second (dvitfyam), no other
(anyad), separate from him, that he could see .... When there is some other (anyad),
then one can see ... the other." (BU, IV.3.23 & 31)
�33
I said to Yajfiavalkya that, according to this account, pure awareness seemed to be empty.
He responded that while it is empty of objects, it is full in the sense that it is an experiencing of
the moment-to-moment "going forth of things in different directions" (vyuccaranti), like "sparks
from a fire" (BU, 11.1.20). Alternatively it is an experiencing of the whole's springing forth
(sambhavati), which is like a spider's emitting (srjate) of a thread of its web or like plants'
springing up from the earth (MuU, 1.1.7). It is as if in pure awareness we had 'gone backwards'
to a point just 'before' things, self, and world emerge. I told him that what he'd said reminded
me of a passage in Sartre: "Thus, each instant of our conscious life reveals to us a creation ex
nihilo .. .. this inexhaustible creation of existence of which we are not the creators" (S, 79).
Yajfiavalkya continued by pointing out that what he had just said about pure awareness
being full is conveyed by the traditional name for the Brahman-realm, 'saccidananda.' The
three parts of the one word express the oneness of pure existence (sat), pure awareness (cit), and
pure joy (ananda).
Since there is no 'of,' as in 'consciousness-of,' awareness is pure sat rather
than being conscious of it. I said that Fink seemed to be giving voice to the same experience
when he referred to the unique identity of the onlooker and the universally flowing worldapperception (FK, 355). As "there is ... no other (anyad), separate from him, that he could see,"
so there are no objects to separate the onlooker from the flowing world-apperception.
Yajfiavalkya's report about the oneness of existence and awareness brought to my mind
something in the Thomistic branch of the Aristotelian tradition, which could make that oneness
partly understandable to me. I mentioned it to Yajfiavalkya: Thomas understood each of us to
·exist by virtue of a separate act of is-ing (esse), which is other than our essence, our humanity. A
human being is, not by virtue of being human, but by participation in, or reception of, is-ing
from, absolute Is-ing, just as a piece of wood that is afrre is so by participation in Fire (ST, Q.3,
A.4r). Absolute Is-ing is like the Sun, and a human being is like some part of the air. Each
�34
individual instantiation of the intelligible human essence remains illuminated, that is, continues
is-ing, only as long as absolute Is-ing is shining on it (ST, Q.8, A.Ir). That is why Thomas states
that what we ca// 'creation' is, in fact, an ongoing "flowing out, arising, springing out"
(emanatio) (ST, Q.44, A.Ir) from absolute Is-ing. This much ofThomas's view can help us to
understand how the Upanishadic experience of cit is an experience of sat.
Jacques Maritain applied Thomas' s understanding of the distinction between esse and
essence to interpret the experience of the knower of Brahman in the following way. 40 In
reflecting consciousness we experience our soul in its acts. What we experience in reflection is
not our intelligible essence but rather our self "prisoner of the mobility, of the multiplicity, of the
fugitive luxuriance of the phenomena and the operations which emerge in us from the night of
the unconscious-prisoner of the apparent self'(I45-46). But, as we have seen, the cultivation
of awareness, instead of consciousness or reflecting consciousness, enables those on the path to
realizing Brahman to pass from ordinary self-conscious experience "to an exceptional and
privileged experience, emptying into the abyss of subjectivity, ... to escape from the apparent
self, in order to reach the absolute Self'(I46). These practitioners "strip themselves of every
image, of every particular representation, and of every distinct operation to such a degree that ...
they reach not the essence df their soul but its existence, substantial1 esse itself'(I 48), "by an ...
annihilating connaturality"(I46), in the absolute silence of total wakefulness.
[F]rom the fact that existence is ... limited only by the essence that receives it ... one
can understand that this negative experience, in reaching the substantial esse of the
soul, reaches, at once, both this existence proper to the soul and existing in its
metaphysical profusion and the sources of existing, according as the existence of the
soul . . . is something that is emanating and is pervaded by an inflow from which it
holds everything.... It is the sources of being in his soul that the human being reaches
in this way." (153-54)
Thus, through practice, in experiencing pure awareness (cit), the knower of Brahman
has come to experience herself as the inflow of is-ing flowing out from abso.lute Is-ing
�35
(sat). One might say that the transition from experiencing myself as witness to
recognition of pure awareness is like going from having my finger on the pulsing of
the world to recognizing my finger as the pulsing of the world. Yajfiavalkya added
that Maritain's interpretation at least clearly distinguished the Sun of Averroes's
outward-turned self-intellection of intelligible essences from the Sun of outflowing
selfaware existence.
Now we are in a position to say that when Svetaketu realizes "You are That," he is
experiencing himself as the outflow of sat and recognizing as his true self pure awareness (of)
the moment-to-moment flying out of sparks, which are 'on the way' to becoming things-and
that this recognizing is that very going forth. Moreover, in this recognition Svetaketu is what is
recognized: "One who knows the supreme Brahman becomes that very Brahman" (MuU, IIl.2.9;
cp. BU, IV.4.13) and "becomes this All" (BU, I.4.10).
As earlier we wondered what the daily experience of the state of complete conjunction
would be like, so now the analogous question arises with respect to the Brahman-realm. In the
discussion of the phenomenological reduction, I had raised the possibility that we could acquire
pure awareness as a first actuality, in the sense of an active disposition. The knower of Brahman
would then alternate between pure awareness and consciousness-of, in the way that I can 'turn
on' my contemplation of the Pythagorean Theorem as I wish. This suggestion would parallel
Aristotle's experience that we are for intermittent periods of time in the same state as the divine
itself is in over the whole of time. The difference would be that instead of turning from one
mode of consciousness, say, perceiving or thinking, to a different one, intellecting, the knower of
Brahman would alternate at will between two different ways of total experiencing, between
consciousness and pure awareness. It would be somewhat analogous to looking at the.well. known duck-rabbit ambiguous figure and seeing it now as a duck, now as a rabbit.
�36
However, Yajfiavalkya said that living in the Brahman-realm is, instead, like a
hypothetical double seeing of both the duck and the rabbit at once, rather than like a seeing of
them in altemation. 41 The knower of Brahman is engaged with consciousness-of while
simultaneously remaining in the realm of pure awareness. The following analogy conveys
something of this:
The ordinary person only sees the reflection in the mirror but the realized person sees
the reflection as well as the mirror. "For instance you see a reflection in the mirror
and the mirror. You know the mirror to be the reality and the picture in it a mere
reflection. Is it necessary that to see the mirror we should cease to see the reflection
in it?" Similarly, the realized one continues to experience the world in his realized
state. Thus the realized person appreciates ''the distinctions" of sound, taste, form,
smell etc. "But he always perceives and experiences the one reality in all of them."42
Brahman-knowers' experiencing of the everyday world inthe mirror of purified awareness
enables their keen yet calm involvement in that world. In the analogy we could take 'seeing the
reflection' to stand for consciousness of the world, and 'seeing the mirror,' for pure awareness.
When I see the mirror along with the reflections, the latter are not being viewed 'from outside,'
as they are in the mode of consciousness, but rather as emerging out of awareness. One might
also apply the analogy to the self by saying that knowers of Brahman experience their ordinary
selves, too, as being virtual images cast by the mirror.
,
1
The mirror analogy may be applied to the modes of experiencing other than those
encountered specifically in meditative practice. Consciousness-of-objects-whether perceiving,
sensing, emoting, evaluating, thinking, and so on-and self-consciousness, too, are like a vision
of things in the virtual space of the mirror. There are two fundamentally different modes of
consciousness-of-objects, depending upon whether or not the object in question is an object in
the true sense. When it maintains itself throughout a succession of acts of consciousness of it, it
is an object in the etymological sense that it is something set or put (-jectum), before or over
against (ob-) the act of consciousness. This setting-over-against is what is meant by 'subject-
�37
object duality.' Such an object shall be referred to henceforth as an "Object." It has an identity,
to which we may return again and again.
The following example illustrates the different layers that may arise in perceptual
consciousness-of-Objects. It begins with the emergence of an hnplicit Object from the
background, continues with a prepredicative explicating of it, and goes on to various layers of
predicative development in the following way. While I am engaged in seminar, someone's
coffee cup may emerge from the margins of my consciousness and may attract my attention and
become an explicit object of consciousness. My attention may travel from its color to a figure on
the side, and then to its overall shape, and so on. 43 Then my interest may awaken sufficiently, so
that I think, 'The cup has a circular figure on the side.' This shift represents a transition from the
cup's just previously having become implicitly determined as having a circle on its side to its
being grasped in an active identification as determined by the circle on its side. 44 Then I may
think, 'The fact that the cup has that circular figure on its side is puzzling. I wonder what it
stands for.' My thought may subsequently be led to such Objects as 'the circular,' 'shape in
general,' and 'property.' 45
'Prior' to such perceptual consciousness of Objects and its developments, there is a
sensory consciousness of objects, which has beer\. vividly described by Erwin Straus. 46 We sense
objects in the same way in which we respond to the dynamic quality of a tone, which is "a state
of unrest, a tension, an urge, almost a will to move on, as if a force were acting on the tone and
pulling it in a certain direction."47 We are in a symbiotic relation (200) with the 'tones,' to which
we respond with incipient movements as we do to dance music (239). This pre-linguistic,
flowing realm is the ground from which Objects emerge (204). We live simultaneously in the
. Objective and the sensory and may experience the tension between them, as the latter resists
being fit into the former. Some people may be especially attracted to the loss of their stance
�38
over-against Objects, of their self-consciousness, and of the sharp distinctness within the
Objective realm (284, 275). Precisely because of its lack of subject-Object duality and selfconsciousness, sensory consciousness is occasionally mistaken for awareness by beginners.
However, it is just another mode of vision of the reflections in the virtual space produced by the
mrrror.
All of the above are distinctions that can be clearly seen in the vision of that virtual space.
In addition to seeing these, the knower of Brahman sees the virtual space and its reflections as
emanating from the mirror. This second sort of seeing is pure awareness. While awareness is
never totally absent from our experience, we notice it to varying degrees.
Usually the degree to which we notice it is very minimal as when we seem to be, in
Sartre's words, "hypnotized" by what we are conscious of. This is our 'default' mode of
experiencing. When we are reading, thinking, conversing in seminar, dancing, gazing at a
sunset, or "even stretching out a hand to open the door," we are absorbed in that moment's
action.
48
When we are self-conscious, we are also absorbed in the self-consciousness. In
absorption, awareness seems to have gotten lost; but it has only receded into the deep
background.
In some special moments, which have been called moments of "flow," 49 awarenes~
becomes prominent in an incidental way. We have not deliberately pursued it; it just happens.
The flow experience may be spontaneous, as in the earlier examples of the driver and the woman
sewing; or it may be skill-related, as in the examples of Joe Montana and the surgeon. One
might say that, in the case of the skill-related flow experience, through practice the body's usual
resistance to intended action is overcome. As a result consciousness as over against the body
disappears, allowing awareness to become prominent. We move out of flow when the over-
�39
againstness arises as the 'I' becomes active either in reaction-'Wow! This is so exciting!'--or
in action-' If I bear down, I can keep this going.'
As we saw in relation to painting, psychoanalysis, and phenomenology, prominence of
awareness may be deliberately cultivated in order to be able to engage in some pursuit. Here
awareness is practiced, so that the practitioner comes to experience the witness as a disposition.
Having it as a.first actuality, he or she can then activate it when engaging in the activity for the
sake of which it was developed.
Finally, in the double seeing of the knower of Brahman, pure mirror-awareness is
permanently prominent as a second actuality; and there is a 'loose,' 'unstuck,' clear
consciousness-of-objects as well. This is said to be the state of one "freed while alive"
(jfvanmukta; cp. BU, IV.4.7).
In virtue of the oneness of sat and cit, this double seeing is one with the out-flowing of
existence. Thus, the freedom manifests itself in that one's awareness is active, or creative, with
respect to the world, on the one hand, and one's action is responsive, or receptive, with respect to
it, on the other-a reversal of the usual receptivity of consciousness and activity of action. 50 In
the realm of action, this freedom is freedom to respond without a 'hitch' to the vectors in the
field of experience, wliich are analogous to the directional arc involved in realizing the full
significance of a situation mentioned in Part One. These field vectors include what Yajfiavalkya
takes Aristotle to be referring to when he speaks of feeling feelings or performing actions as
required (8c:i), in the required cases, with respect to the required people, in the required way, and
for the required reasons (NE, 1106b 17-2 7).
Another way of putting this is to say that the freedom of the knower of Brahman
manifests itself in the ability to be able to move freely through the world with grace and
effortlessness, which is called 'saving awareness,' crocppocruvri: 51
�40
For crocppocruVT) is precisely the virtue of general and unself-conscious self-possession,
of universal grace and effortless command neither specified by particular action,
which would transform it from crocppOcrUVTJ to some particular virtue, nor checked by
any opacity, which would translate it into a mode of self-control. What could work
better for its model than a pure [awareness ]?52
Knowers of Brahman have no inner barriers, which could get in the way -of their spontaneously
allowing what is called for by the current moment to emerge.
In conclusion, we note certainformal parallels between the role of Brahman in the
Upanishads and that of the agent intellect according to Averroes. First, each is the sourceBrahman, of all existence, and the agent intellect, of all being, that is, of all intelligibility.
Second, both are "self-luminous" and are responsible for 'seeing' in some sense. Third, the nondual relation between the individual self and Brahman is like that between the disposed intellect
and the agent intellect. Fourth, a 'self-forgetting' 'outward turn' 'occurs' in the case of each of
them. Fifth, both the experiencing of Brahman and the experience of intellection could be said to
involve a breaking-free from my ordinary captivation by the images on the walls of a cavelike
dwelling, an engagement in a practice, and, ultimately, an existential breakthrough to
"immortalizing." In that breakthrough, in both cases, I deconstruct my ordinary sense of self and
discover my true self as being both non-private (that is, not mine alone) and non-dual with
respect to the true self of others.
However, there are fundamental differences in other respects. Whereas in the one case
the captivation is by opinions and by the perceptual world and is broken through in becoming
free for intelligibles, involving a gradual movement of theoretical study, in the other case it is
captivation by the mundane way of experiencing objects, whether in sensory, perceptual, or
intellectual consciousness; and it is broken by a sudden shift from involvement in consciousness,
whether first-degree or reflective, to pure awareness, a shift which may be experienced on a path
of cultivation of awareness. Moreover, the nature of the one, impersonal, true self of us all, in
�41
which we share non-dually in our immortalizing, which for Averroes is the self-intellection of
the agent intellect, is pure awareness according to Yajfiavalkya. Finally, on the one hand, the
material intellect may realize conjunction with the agent intellect, which is the source of all
intelligibility in the world. On the other hand, in the Brahman-realm pure selfawareness realizes
that it is non-dual with the continual springing up of all existence, both sensory and intelligible,
of the world as a whole, including but not limited to the intelligible realm.
Yajfiavalkya thought that the following comment on Aristotle by Mr. Klein might
provide a fruitful direction to pursue in the question period: The receptive aspect of "vm:iv ... is
the state of wakefulness, a state of preparedness and alertness .... Nouc; ... when it is ... one with
the v01rr<i .... [o]nly then can be said to be wakefulness 'at work' ... " 53 Looking back to the
beginning, Yajfiavalkya wondered how Homer's realization of the full significance of a
situation, 54 Aristotle's reception of an intelligible, and Averroes's complete conjunction with the
agent intellect's self-intellection would compare, with respect to their degrees of wakefulness,
with dwelling in pure awareness.
I asked him how he would respond. He said: 'Perhaps the major difference between the
Upanishads and our three W estem thinkers might be that for the former the state of empty
"receptivity is supreme, that is, even more wakeful than "wakefulness at work."'
I rejoined: 'I'm not sure that I've really understood Averroes. But it might be that his
account of complete conjunction is a good partial depiction of Brahman. Insofar as Mr. Klein
was directing us to the experiential living-through of the moment in which the empty, receptive
intellect is one with the revelation of what is a profile of the full, unitary agent intellect, we do
seem to be pointed toward a face of Brahman, as it were, namely, the intellectual one.'
Yajfiavalkya had the last word: 'What you may be overlooking is that the empty,
receptive material intellect is an appearance of the outward turning of the full source of
�42
determinacy, the agent intellect, whereas, in the case of Brahman, the full and determinate is an
appearance of the outward turning of the empty.'
1
Compare: "Since [in all cases of seeing and hearing] we are aware ('mcr0av6µE:0a) that we are seeing and hearing,
it must either be by sight that we are aware [for example] that we are seeing or by some other [sense]" (OS, 425bl 112). "To each sense there belongs something special and something common. For example, what is special to sight
is to see, [what is special] to hearing is to hear, and similarly with the rest. But there is also a certain common power
that goes along with all of them, by which one is also aware that one is seeing and hearing (for it is not, after all, by
sight that one is seeing that one is seeing ... )." (On Sleeping and Waking, 455a12-5)
2
We may speak of self-consciousness in the sense of consciousness of myself only 'after' the construction of the
sense of self, which is discussed below.
3
By Kosman, who also made reference to Sartre's La Transcendence de !'Ego. I had been planning to use Sartre to
introduce the notion of selfawareness (seen. 4) as an alternative to anything in Aristotle. However, Kosman's
article, which I came across a couple of months ago, made it possible to cite Aristotle himself in order to introduce
this notion.
4
I write 'selfawareness' and 'awareness (of) itself' to suggest that the relationship between awareness and what it is
aware (of) is not the same as that between consciousness and the object of consciousness. I am following Sartre's
practice in L 'etre et le neant (pp. 18-20), where he writes 'conscience (de) soi' to refer to what I am calling
'selfawareness or 'awareness (of) itself'.
5
In La Transcendance de I 'Ego, from which the quotations are taken, Sartre uses only one word, 'conscience,'
which I have rendered as 'consciousness' when it is positional and as 'awareness' when it is non-positional.
Moreover, he does not here write 'conscience (de),' as he did later (see footnote 4).
Gurwitsch (1941) endorsed most of Sartre's position, to which Schiltz then objected. They debate this
issue further in Schiltz and Gurwitsch.
..
6
What is said will apply as well to consciousness that is imagining, remembering, judging, thinking, intellecting,
feeling, or evaluating.
7
See footnote 9.
8
The last two sentences represent my understanding of Gurwitsch (1985), 5, second paragraph).
9
Gurwitsch (1941) pointed out that this account of the arising of the sense of self is inconsistent with the fact that
reflection can accomplish no more than to render explicit the content of the reflected-upon consciousness (332-33).
He later (1985) offered a corrected account of the construction of the psychical empirical sense of self (15ff). It is
based on the recognition that both states and "qualities designate psychic constants, i.e., regularities of experience ...
rather than mental facts which themselves fall under direct experience" ( 15), as they do in Sartre.
10
I remember many years ago reading an article by him in The Washington Post, in which he described his
experience in somewhat these terms.
11
These characteristics are similar to those in the example of the violinist in Csikszentmihalyi: "A violinist must be
extremely aware of every movement of her fingers, as well as of the sound entering her ears, and of the total form of
the piece she is playing, both analytically, note by note, and holistically, in terms of its overall design" (64).
12
Csikszentmihalyi, 65.
13
Bankei, 58. I have substituted "awareness" first for "the Unborn" and then for "it," referring to her Buddha-mind.
14
This is Husserl's word (1964), passim.
15
It need not be living beings with respect to which we experience the connection: "The [mountain] climber,
focusing all her attention on the small irregularities of the rock wall that will have to support her weight safely,
speaks of the sense of kinship that develops between fingers and rock .. ." "This feeling is not just a fancy of the
imagination, but is based on a concrete experience of close interaction with some Other ... " (Csikszentmihalyi, 64).
16
A popular book on learning to draw, tells us of a subjective state that artists speak of, which is characterized by "a
sense of close 'connection' with the work, a sense of timelessness, difficulty in using words ... a lack of anxiety, a
sense of close attention to shapes and spaces and forms that remain nameless." It is important for the artist to
experience the shift from the ordinary state to this one. The student is encouraged to set up the proper "conditions
for this mental shift" and to become "able to recognize and foster this state in" himself (Edwards, 46). These
characteristics correspond quite well with the qualities of a consciousness in which awareness is in the foreground.
17
Merleau-Ponty (1961), 166, translation modified.
�43
18
The articulation in this paragraph emerged in a conversatibn with Nina Haigney, just a few minutes before I
delivered this lecture. It was an example of the sort of thing it attempts to articulate-a conversation, with
awareness to some degree in the foreground, allowing for the experience of"a certain emptiness," followed by the
·
emergence, in two people, of an, a least relatively, "authentic word."
19
Epstein, 194. The quotation from Freud is from "Recommendations to Physicians Practicing Psychoanalysis"
(1912).
20
Epstein, 195.
21
By Theodore Reik in 1948; see Epstein, 199-201.
22
Bion, 51-52, 55-56, 69.
23
M. Heidegger, On Time and Being, quoted in Ihde, 15; italics added and translation corrected at one point.
24
Husserl (1962), 140.27-33; to maintain consistency of terminology, I substituted "[reduction]" for epoche.
25
The same view is conveyed, in different language, by Husserl himself(l962), Sections 37-42.
26
Merleau-Ponty (1945), 191, where, however, the expression is not being used to characterize the
phenomenological reduction.
27
The distinction between disconnection and reducing proper parallels that in the Buddhist tradition between
mindfulness (sati) and seeing distinctly in detail (vi-pa§yana).
28
Cp.: "And so also must the gaze made free by the epoche be .. . an experiencing gaze" (Husserl (1962), 156.1315.
29
Husserl (1962), 147.29-32.
30
I take habituell to correspond to an adjectival form of 't~t<;.
31
Husserl (1962), 153.36-37 and 140.19-20.
32
Sekida, 62 and 93. This stage in the yogic tradition involves eight members, the last three of which are
concentration, meditation, and in-stance (samiidhi), which is opposed both to ex-stasy and to our ordinary counterstance vis-a-vis objects (Patafijali, II.29).
33
Sekida, 93; cp. Patafijali, I.42 and 44: coincidence wit hreflection (saviciirii samiipattih)
34
The quotations in this paragraph are taken from Low, 149-50; italics added.
35
When allowing the children to play, you are not caught up in their playing; so, you have a kind of distance from it.
Yet you are 'with' them, accompanying them. Thus, your distance is of a different kind than the distance that occurs
in Objectivation, where the Ob-ject is over against you (discussed below).
Moreover, while it might seem as though the Objective, perceptual world were free of captivation, when
compared to the dynamic, sensory realm (discussed below), in fact, the former is grounded in the primordial doxa of
the latter.
36
Sekida, 62 and 94. The role that this experience of pure awareness plays in the upanishadic tradition parallels that
of the "aloneness of seeing" (dr§eh kaivalyam; Patafijali, II.25) in the yogic tradition (Patafijali, III.50; IV.26 and
34).
37
Low, 40.
38
Sekida, 95.
39
This account ofrealization of Brahman is based on zen sources. However, as Shear points out, this experience of
awake, pure selfawareness lacks any empirical qualities or content. As a result differing references to it as the ·
Brahman-realm or Buddha-nature are not pointing to qualitative differences in the experience (1983, 57-59; 1990,
392).
40
The page numbers given in this paragraph all refer to Maritain, Quatre essais.
41
Carter, 54. Sekida, 91-97, also depicts the corresponding state in the zen tradition in this way.
Carter proposes the comparison with binocular vision. It is interesting that Bion, too, uses this analogy
(Grinberg, Sor, and Tabak di Bianchedi, 35-36).
42
Sharma, 43; first two sets of italics added. The quotation is from Ramana Maharshi as reported in D. Goodman,
ed., The Teachings ofSri Ramana Maharshi (NY: Arkana, 1985), pp. 42, 41.
43
Cp. the description in Husserl (1964), 124-25
44
Cp. the description in Husserl (1964), 206-08
45
Cp. the descriptions in Husserl (1964), tt#58-61, 80-82, 86-87 and in Husserl (1950), #10.
46
The page references in this paragraph are from Straus, Vom Sinn der Sinne.
47
Zuckerkandl, 19.
48
Sekida, 91. .
49
Csikszentmilalyi.
50
YUASA, 68.
�44
51
I believe that Kleist had the same phenomenon in view when he reported Herr C.'s words after two anecdotes,
one about a graceful dancer who lost his grace when self-consciousness arose and the other about a bear, who
effortlessly parried every thrust of Herr C. 's rapier with a graceful swipe of his paw:
' ... [I]n the same degree as, in the organic world, reflection becomes more obscure and
weaker, giace emerges there ever more radiant and supreme.-Yetjust as. :. the image
in a concave mirror, after withdrawing to infinity, suddenly comes right in front of us
again, so when consciousness has, as it were, passed through an infinite, grace will
again put in an appearance. Hence, it appears most purely in the human bodily
structure that has either no self-consciousness or an infinite self-consciousness ... '
(Kleist, 67)
That is, in our terms, grace emerges in the realm of animal, sensory consciousness, a realm which we can
experience, but not enter completely (Straus, 284). And it emerges again in the realm of pure self-awareness, in
which we are no longer caught up in first- or second-degree consciousness.
52
Kosman, 516; the ending in the original is "a pure, objectless knowledge."
53
Klein, 65.
54
Another question to pursue might be whether Homer's realization of full significance became narrower and more
limited in passing over into intellection.
ABREVIATIONS
BU
Brihadtiranyaka Upanishad
CU
Chtindogya Upanishad
F
Fink, E., Sixth Cartesian Meditation: The Idea of a Transcendental Theory ofMethod.
FK
"Die Phanomenologische Philosophie Edmund Husserls in der Gegenwartigen Kritik."
HG
Otto, W., The Homeric Gods: The Spiritual Significance of Greek Religion.
I
Homer, Iliad
IU
Isa Upanishad
KeU
Kena Upanishad
LC
Averroes, Long Commentary = Commentarium Magnum in Aristotelis De Anima.
MuU Mundaka Upanishad
NE
Aristotle, Nichomachean Ethics; translation altered in some places.
0
Homer, Odyssey
OS
Aristotle, On the Soul; translation altered in some places.
�45
S
Sartre, J.-P., La Transcendance de /'Ego: Esquisse d'une descriptionphenomenologique.
ST
St. Thomas Aquinas, Summa theologiae, Latin text, Volume II, containing Ia, QQ.2-11.
TU
Taittitrfya Upanishad
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(Albany: SUNY Press, 1987).
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(Milwaukee: Marquette University, 1968).
_ _,"Averroes and Immortality," New Scholasticism 28 (1954), 436-53.
_ _,"Averroes on the Possible Intellect," Proceedings of the American Catholic
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�
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You Are That!: The <em>Upanishads</em> Read Through Western Eyes
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Typescript of a lecture delivered by Robert Druecker, Annapolis tutor on February 15, 2008, as part of the Formal Lecture Series.
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Friday night lecture
Tutors
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PDF Text
Text
“Walking the First Steps of His Camino with John of the Cross –
An Exploration of the Dark Night of Sense”
Robert Druecker
INTRODUCTION
John outlines a road, or camino, which one could walk who is seeking to arrive at union with
God, insofar as it is possible in our present life. According to John what is possible in this life is a union of
my powers and faculties with God, but not a permanent one (AMC II.5.2). The camino is known as the
Dark Night of the Soul. It has two major aspects—the Dark Night of Sense and the Dark Night of Spirit.
This lecture deals with the first of these.
According to John a verse from one of the Psalms (46:10) is saying to us: “Learn to be empty of
all things, that is, both internally and externally, and you will see how (cómo) I am God” (AMC II.15.5).
External things are things the soul experiences through its senses, feelings, and imagination. As the soul
moves into this first dark night, it actively works at releasing its hold on all particular things. Then at
some point, it notices that, independently of its wishes and efforts, it is being led away from its efforts
to let go into an experiencing of its tight grip gradually turning into a relaxed open hand. The soul is then
entering the passive dark night of sense. It begins to experience God as flowing into it. Correlated with
this sensed inflowing is the soul’s awakening to ways in which God is manifesting his divinity in the
world.
The lecture will be in four sections, with a conclusion. For the most part I’ll be taking you along
with me as I begin walking the camino.
Section I: THE STRIPPING OF OUR ATTACHMENT TO THE SENSES
1
�In the active dark night of sense, we “strip” ourselves of our attachment to the senses. John uses
the following analogy, in order to clarify the meaning of this stripping:
AS night deprives the eyes’ sight of the light which allows visibles to be seen by it, SO
the dark night deprives the senses’ apetito of the savor, or liking, which allows things to attract it
(based on AMC I.3.1&4).
John’s word apetito here means something like our word “dependency,” as in a drug dependency, or
“addiction” – an immoderate desire for something. 1
According to the analogy, my soul still has things, but is empty of them, in the sense that it is not
preoccupied with them. As John puts it: “Although it is true that the soul cannot help hearing and seeing
and smelling and tasting and touching, this is of no greater import, nor …, is [the soul] hindered more
than if it saw it not, heard it not, etc.” (AMC I.3.4). When the light of my preferred flavors is turned off,
my personal preferences for and concerns with things are deactivated. I now use things simply for their
practical value and to satisfy my true needs.
By being detached from my preferences and likings, I don’t fill my soul with images or memories
of things, with hopes and wishes for them, with plans to get them, and so on. The reason, the inner
logic, for turning off the light is precisely in order that my soul not become already filled up. For then
there would be no “room,” no “space,” for my soul to become filled with G’s “light” in becoming
enlightened (AMC I.4.1).
The way it works is that if I’m not occupying myself with enjoying and pursuing particular things,
then I’ll be filled with “food” that will allow me to taste “all” things. (AMC I.5.4), in a newly experienced
state, called “loving awareness” (AMC I.5.7). For dependencies and enlightenment are contraries, as are
closing tightly and opening loosely. The dependency orients me toward what is finite, determinate,
particular, limited, thing-like, creat-ed, being (ens, that which is) (AMC I.4.2). This orientation makes it
John of the Cross: Selected Writings, ed. Kieran Kavanaugh, O.C.D. (New York: Paulist Press, 1987), p. 61, and San Juan de la Cruz, Obra
completa, I, ed. Luce López-Baralt and Eulogio Pacho (Madrid: Alianza Editorial, S.A., 1991), pp. 125-26.
1
2
�difficult for me to become transformed into what is in-finite, in-determinate, general, un-limited, nothing, creat-ing, act of be-ing, of “is-ing,” (esse = ser, the is of that which is)—as I must if I am to realize
union with God (AMC I.4.3).
So, dependencies lead me, ineluctably, to turn toward the creaturely and, simultaneously, to
turn away from the creative (AMC I.12.3). John says that when you turn toward some thing you stop
“casting yourself on the all.” Moreover, if you are to hold the all, you have to hold it without wanting
anything (AMC II.13.12). Thus, the deadening of my preferential likings allows me eventually to turn
toward “the all” and to do so without wanting to get something out of it.
Note that it is not the particular characteristics of the thing or of the liking that are relevant
here. Even likings for religious and devotional activities and objects can bind me to and fill my soul with
determinate, particular things, in the same way (AMC I.5.2).
The way John sees it, there is a deepening sequence of involvements—from savoring and liking
(gustar) to tasting and knowing (saber can mean both at once), from there to possessing (poseer), and,
finally, to being (ser) (AMC II.13.11)—so that the light of gusto comes to anchor me—my understanding,
my sense of self, and my will—in being like the creaturely (AMC I.4.2).
Section II: THEOLOGICAL REFLECTION ON TYPES OF UNION
In order to help us better understand the background for the contraries of closing and opening
or of emptying and filling, John shares a theological reflection on union with God. There are two major
sorts of union. One is the substantial union of God’s dwelling in each creature. This union is always
there. The other is a union-by-likeness of the soul with God, a union that arises through a transformation
of the soul. This second union is there only when there is a likeness of love, that is, when God’s and the
soul’s wills are “con-form in one,” when the soul is transformed into God through love (AMC II.5.3).
There are two varieties of the second union, first, a union with respect to my acts of will and,
second, a union with respect to my habitual disposition of will. Union-by-likeness-of-act and union-by3
�likeness-of-disposition are the two versions of the second type of union. Hence, in order to live one or
the other kind of the second union, I must strip myself of my creature-focused acts or dispositions of
understanding, liking, sensing, and willing (AMC II.5.4).
What continues throughout is an ongoing sense of the substantial union, one which does not,
however, become thematic for me, one which I do not consciously register. It, nevertheless, contributes
to motivating my entry onto the camino. Then as I go on walking, my recognition of the substantial
union grows.
John uses another light analogy in order to illustrate this theological reflection. A smudgy and
dirty window on which the sun is shining appears dark, as we look through it; the sun lights it up only
fairly dimly. A clean and pure window on which the sun is shining, on the other hand, appears bright,
completely illuminated by the sun. In this second case the ray of light will transform and en-lighten the
window, so that, according to John, the latter will “appear to be the same ray and will give the same
light as the ray,” even though its nature is other than that of the ray. John says that the window is light
“by participation.” The soul is the window; the light is the divine “light of God’s esse (ser),” God’s act of
be-ing, or “is-ing,” 2 which is always “shining” on the creature (AMC II.5.6).
Perhaps we might say that substantial union refers to God’s dwelling in, lighting up, or is-ing
forth, the creature in each instant. Then when my soul becomes cleansed, it is able to become aware of
this indwelling, of God’s continual creating of me; and, simultaneously, it can allow this creative activity
to show itself clearly in the world.
Section III: FOUR SHIFTS IN THE WAY OF LIVING A SPIRITUAL LIFE
John introduces the word modo, in order to refer to the way I am walking along the
camino, or, more broadly, the way one is living one’s spiritual life. My mode includes my ways of
In many languages other than English, the form of the word itself shows whether it is referring to a being, a thing which is, or to an act of being, of “is-ing”—for instance, ὂν : εἶναι :: ens : esse :: étant : être :: Seiendes : Sein. In these cases one can immediately see whether the referent
is the “is-ing one,” the “is-er,” on the one hand, or its “is-ing,” on the other.
2
4
�apprehending, feeling, liking, enjoying, sensing, acting, responding, etc., my “how,” as I am walking.
Many religious people think that the modo appropriate to the camino is just any kind of self-reformation
or withdrawal from the world. But what they are actually seeking subconsciously is, according to John,
to have a feeling of delightful communication with God and of consolations from God. They are, in fact,
pursuing themselves in God, rather than searching in God in himself (AMC II.7.5). But John tells us that
as I walk I will not only eventually leave behind my beginner’s ways but will also abandon every such
personal mode, or way, as I come to “possess all modes,” when I “pass beyond the limits of my nature.”
Only if I accomplish this, will I become able to “enter what has no mode,” namely, God (AMC II.4.5).
John focuses on at least four prominent ways in which I may be living the devotional life as a
beginner—I rely on my faculty of imagination; I center my practice on discursive meditation; I make an
effort to keep on working hard, in order to make progress along the spiritual path; and, finally, I relate
myself to God in a way that reflects my earlier relation to my parents and significant others. I, as
beginner, am expected, at some point on the camino, to notice the indications that I need to move on
and to leave behind these four ways of practicing my religious life. If I follow through and do so, I’ll
change from being a beginner to being a proficient, in John’s vocabulary. This shift will coincide with my
transitioning out of the active Dark Night of Sense into the passive Dark Night of Sense.
It is important to note that for John “the imaginative faculty and the fantasy” are each an
“internal bodily sense” (AMC II.12.1). They are the primary senses that are active in meditation. For in
John’s vocabulary, meditation is “a discursive act through the medium of images, forms and figures,
made up and imagined by” the imagination and fantasy. It is discursive in that it involves a mental
running about (dis-cursus), going from one religious image or devotional object to another (AMC II.13.4).
5
�In discursive meditation, for instance, I may imagine and meditate on “Christ crucified” or “God
seated on a throne.” In doing so I wish to become inspired by thoughts and feelings that may arise in
response to that object (AMC II.12.3). In The Spiritual Exercises of Ignatius of Loyola, 3 we read:
FIRST EXERCISE …. seeing the place. Here it is to be noted that, in a visible contemplation or meditation—as, for
instance, when one contemplates Christ our Lord, Who is visible—the composition will be to see with the sight of
the imagination the corporeal place where the thing is found which I want to contemplate…, as for instance, a
Temple or Mountain….
John’s directive, though, is that “the soul will have to empty itself of these images.” For it can
fantasize or imagine only what it has previously sensed through the external senses, namely, created
things. But created things “can have no proportion to God’s esse (ser)” (AMC II.12.4). That is, meditating
and imagining ultimately orient me toward and preserve my similarity to what is limited, particular,
determinate, and creat-ed—even though it is true that, at first, they had motivated me to step onto the
camino (AMC II.12.5).
I may be engaging in devotional work with my imagination when I am meditating discursively.
Or, alternatively, I may perform a daily ritual or recite particular prayers, such as saying the rosary. In
these ways, too, I am working at generating the proper emotions and motivations for leading me to turn
to God more often and to deepen my love for God. Although I see myself as working, in these ways, to
gain “spiritual sustenance,” John tells me that such nourishment “does not consist in working (trabajar)”
of any sort. At this stage I am not being “fed” through imagining, meditating, reciting prayers, or doing
spiritual reading. I must rather “allow the soul to be in quietude and repose” (AMC II.12.6).
Unbeknownst to me an opposition has arisen between what I think I’m doing and desire to be
doing, on the one hand, and what I am actually doing, on the other. For it turns out that even my initial
project of stripping away my preferences and likings (DN I.7.5)—or, in fact, any aspirations, or efforts
3
Trl. Fr. Elder Mullan, S.J. (NY: P.J. KENEDY & SONS, 1914), trl. modified; [45] - [47], italics added.
6
�(pretensiones), to please God or to have a more intense sense of God—is actually distracting and
drawing my soul away “from the peaceful stillness and sweet ease” (DN I.10.4).
A beginner who once or twice lets herself go and rests in such inner calm often reacts by forcing
herself to get back to work on the devotional project. In John’s view this betrays a misunderstanding of
her current location on the camino. Because she has not made the shift of modes, she thinks that in not
meditating she is being idle and lazy (AMC II.12.7). She may subconsciously have what has been called “a
gaining idea,” 4 an egoistic expectation of spiritual gain. She thinks she is here and God is there, and she
is making an effort to get there. Her sense that she was getting closer to gaining the sought-after
closeness to God used to give her emotional support (arrimo). But, now, when her devotional life has
lost its “juice” (DN I.7.5), she feels negligent or sinful (DN I.9.6; 10.4 & 2). She thinks, If I don’t feel I’m
working, that must mean I’m not doing anything at all (DN I.10.1).
However, in my enjoyment of the new state of “stillness and idleness, or ease (ocio) (DN I.10.1),
I may, instead, feel that there is no progress for me to make. I may gradually realize that if I let go of my
sense of myself as the doer, gave up caring (descuidado) about any inner or outer works, and stopped
“trying to do anything” (DN I.9.6), then I would be where I thought I was heading.
The shift in modes to which the beginners are being invited at this point is the major shift from
the active dark night of sense to the passive dark night of sense. In the latter, John says, “their faculties
are at rest and do not work (obrar) actively but rather passively, by receiving what God is working (obra)
in them” (AMC II.12.8). The difference is like that between continuing to labor at the work (obrando) of
4 S. Suzuki, in Zen Mind, Beginner’s Mind (NY: Weatherhill, Inc., 1973), p. 41: “We say our practice should be without gaining ideas, without
any expectations, even of enlightenment. This does not mean, however, just to sit without any purpose. This practice free from gaining ideas is
based on the Prajñā Pāramitā Sūtra. However, if you are not careful the sutra itself will give you a gaining idea. It says, "Form is emptiness and
emptiness is form." But if you attach to that statement, you are liable to be involved in dualistic ideas: here is you, form, and here is emptiness,
which you are trying to realize through your form. So ‘form is emptiness, and emptiness is form’ is still dualistic. But fortunately, our teaching
goes on to say, ‘Form is form and emptiness is emptiness.’ Here there is no dualism. When you find it difficult to stop your mind while you are
sitting and when you are still trying to stop your mind, this is the stage of "form is emptiness and emptiness is form." But while you are practicing
in this dualistic way, more and more you will have oneness with your goal.”
7
�walking the camino, on the one hand, and enjoying (gozar) that walking as a resting in the end-state, on
the other (AMC II.14.7).
John points to three “signs” that I am now being invited to accept and experience this major
shift. One is that, to quote a song by the Rolling Stones, from a while back,
I can't get no satisfaction
'Cause I try and I try and I try and I try.
Precisely because I continue in my mode of trying, I find that I no longer feel satisfied after engaging in
my activities of fantasy and imagination and of discursive meditation. A second sign I notice is that I
even feel disinclined to take them up again. The third sign is that I now actually like to remain alone in
inner peace (AMC II.13.2-.4). My familiar devotional life has become “arid.” I experience life-giving water
only when I am at rest, not at work, not meditating, not imagining.
John highlights typical reactions that beginners may have when their familiar devotional modes
become “tasteless” to them. Some may become irritable and peevish, like a spoiled child; others may
blame themselves for the loss of taste and feel angry at themselves; yet others may “kill themselves,”
figuratively, by performing physical penances (DN I.5.1 & .3; 6.1).
When I consider what I now prefer and compare it with what I used to like to do, I notice
something very interesting. Remaining in inner peace is something I cannot do, or, rather, something I
can do only by not doing (wéi wú wéi 為無為, Dao De Jing 63). I can enjoy it only if I don’t seek to enjoy
it. As John says: “It is like the air which escapes as soon as one wants to grasp it in one’s fist” (DN I.9.6).
If I want to do anything on my own, I will only end up blocking the refreshing idleness (DN I.10.5). If I
come to notice what John says is there in my experience, I may vaguely sense that instead of having to
work to attain my goal I am already there.
According to John all the changes in mode are the result of God’s taking my soul out of the state
of beginner and placing it in that of proficient, making me a “contemplative,” instead of a meditator (DN
I.1.1).
8
�John proposes an analogy that can serve to characterize all four modes, and especially the last
one, which we’ll look at now. The beginner’s sense of self-in-relation-to-God has been like that of an
infant in relation to its loving mother. She “warms her infant with the heat of her breasts, nurses it with
good milk and tender food, and carries and caresses it in her arms” (DN I.1.2).
Based on its experience the infant has formed a complex of feelings, attitudes, dispositions,
images, memories, behaviors, etc., in relation to its mother. We shall borrow a term from Carl Jung and
call such a complex an imago. Then we could say that the infant had formed—and was still forming—its
Mom-imago. In going beyond John’s analogy, we might introduce a parallel Dad-imago, a voice of
authority, forbidding and judging, punishing and rewarding. According to Jung, even much later in adult
life, when the parents are dead, the individual still experiences them as powerfully present in their
imagos, “as important as if they were still alive.” His or her “love, admiration, resistance, hatred, and
rebelliousness still cling” to those imagos, which often bear little resemblance to the way the parents
actually were, so transfigured are they “by affection or distorted by envy.” 5
My beginner’s religious experience of God has been characterized not only by feeling comforted
and nurtured, giving rise to an analogue of the Mom-imago, but also by feelings of prohibitions, of
rewards, of reprimands, and of forgiveness, generating an analogue of the Dad-imago. My complex
sense of who-God-is-in-relation-to-who-I-am will be referred to as my God-imago.
As is the case with Jung’s parental imagos, my God-imago is not limited to a visual image or to a
representation or concept of God, but includes the emotions I feel and the memories and attitudes I
have developed in relation to God. From the cradle on I have been unwittingly fashioning this Godimago from strong feelings, attitudes, and meanings, originally called forth in me by my everyday
exchanges with my parents, and other family members, neighborhood and school friends, and so on.
5
C. G. Jung, Jung Contra Freud: The 1912 Lectures on the Theory of Psychoanalysis, trl. R.F.C. Hull (Princeton University Press, 1961), p. 52.
9
�These real and fantasized interactions have made their contributions to my God-imago. I, as beginner,
have come to sense God as a living entity whose experienced “communications” to me I interpret as
they show up my thoughts and feelings and in the events of my life. 6
At the beginning of the camino, my initial love of God was needed in order for me to become
capable of taking the initial steps of working at stripping my dependencies of the liking for sensory and
temporal things (AMC II.7.2; 14.2). But the feeling of God’s presence led me to relate to God as to an
actual individual entity (ens), though an invisible, non-worldly one. This, in turn, led me to desire
consolations and rewards or to fear reprimands and punishments from the “God” that I’d projected. I
tried to “manage” my relation to God in a transactive way. But the God-imago to which I have oriented
myself cannot be similar to or proportionate to God (AMC II.4.3). For no creature bears a likeness to
God’s esse (ser), although there are “traces” of God in creatures (AMC II.8.3).
For this reason John’s analogy implies that a shift away from my God-imago is needed. He
depicts it as follows:
As the infant grows bigger, the mother gradually takes away the pleasure of her caress, and, hiding her gentle,
delicate love, puts bitter aloe juice on the sweet breast, and putting the infant down from her arms, makes it walk
on its own feet, so that, by losing the attributes of an infant, it may give itself to more important and substantial
things (DN I.1.2; cf. 1 Cor 13:11).
Just as the mother’s weaning induces the infant to alter its Mom-imago, so does God’s intervention of
“weaning” bring on the new experience of distaste and aridity. I hear this tastelessness as a “call” to set
aside my old God-imago, which accompanied my previous devotional practices. Now I leave behind i)
feelings of dejection when God seems no longer to be consoling me, ii) concerns to obey God by
This understanding of the formation of the child’s God-imago follows the view of Ana Maria Rizzuto, first presented in “Critique of the
Contemporary Literature in the Scientific Study of Religion” at the Annual Meeting of the Society for the Scientific Study of Religion (1970).
“God-imago” is used above instead of her term “image of God.” Rizzuto says she introduced her notion of the image of God, in order to
distinguish it from the philosophical-theological concept of God. In contrast to the image of God, “the concept of God comes to us through
whatever teachings, readings, liturgies, etc. have been presented to us.” “Although concept and image may converge in some respects, they
may also diverge significantly in others.” Rizzuto later expanded her account in the book The Birth of the Living God: A Psychoanalytic Study
(Chicago: University of Chicago Press, 1981).
6
10
�following spiritual maxims, or iii) feelings of closeness from meditating on my favorite religious images
(DN I.3.1).
In walking on its own feet, my soul reorients itself away from looking off to its God-imago, as
Comforting, Prohibiting, Rewarding Parent. Instead, it becomes sensitive and responsive to the way in
which it is now taking each step on the camino on which it is walking. What I used to feel as the
disobedience of prohibitions I now re-experience as a barrier to beginning to live a life beyond the
natural.
Ideally my soul soon comes to realize that its previous mode was motivated by “fondness for
itself and for all things” (DN I.Exposit.1). It senses that, at bottom, as John puts it, it wanted God to want
what it wanted. So, what it did not enjoy was not God’s will and what it liked was God’s will. It was
measuring God by itself (DN I.7.3). Now God is weaning it “from the breasts of all these enjoyments and
likings” (D I.7.5), and from its God-imago in toto.
Section IV: INTO WHAT DO THE FOUR CHANGES OF MODO SHIFT?
Having considered the four modes out of which I, as beginner, need to pass, in order to become
a proficient and to enter the passive dark night, we now look at the into-which. There is a single mode
into which God is leading my beginner’s soul. That one mode has been referred to above as the inner
peace of contemplative, loving awareness.
John writes that the state of contemplation is one of “attention,” of “awareness (noticia)” 7
which is, first of all, “general …, without particular intellectual insights (intelligencias) and without
When speaking about contemplation, John of the Cross doesn’t regularly use the ordinary words (conocimiento, conocer, saber) that are
translated as “knowledge” or “know.” Instead, he uses a word, noticia, which is the Spanish translation of the Latin notitia, derived from a verb
meaning become or be acquainted or familiar with, be aware of. He seems to have in mind the sense in which Augustine notitia in his
Confessions.
Augustine first used the verb in Book VII.x.16 in reference to an experience in which he entered into what is innermost (intima) in
him and “by some sort of eye of [his] soul … saw … unchangeable Light.” He then says: “One who has become aware of (novit) the truth has
become aware of this Light, and one who has become aware of this Light has become aware of eternity. Love has become aware of this Light.”
Eternity is not the sort of “thing” of which we can acquire knowledge, whether cognoscentia or scientia. But, as least briefly, he and his mother
7
11
�understanding (entender) what [the attention and general awareness is] about,” and, second, “amorous
and tender (amorosa)” (AMC II.13.4).
It is general not in the usual, conceptual sense, according to which a genus is more general than a
species. Or it is not that I’ve turned from imagining this or that individual devotional image on my wall to
recognizing a group of them as particular instances of a certain kind of religious object. 8 Rather when my
mind is not focused on objects, either sensory or conceptual, it is turned toward “the all,” in a state of
“clear and simple” awareness.
Contemplation might be experienced as “amorous and tender” in being like a look of warmth and
mutual understanding between two friends, in contrast to an objectifying gaze. It would be analogous to
an affectionate caress, as opposed to a medical palpation. 9 An artist recognized her periods of amorous
awareness, when,
by the way in which one looked at a thing, it was possible to bring about an intense feeling for and belief in its
living reality. … a complete transfiguration of the common sense, expedient view where … people and things
existed mainly in terms of their usefulness; it brought a change to a world of living essences … offering a source of
delight simply through the fact of being themselves. In short, it was a transfiguration comparable in a small way
to the transfiguration of falling in love. 10
My amorous and tender awareness, then, would be “a transformation of the world,” 11 in which I
experience people and things as more alive and more real, in the way a lover or an artist does.
became aware of, or “touched,” “the Wisdom by which all things were made,” which is “eternal” (IX.x.24). Thus, our experiencing eternity
much more like touching than grasping or grabbing, as in conceptual knowledge.
Later in Book X (xix.28 – xxiii.23) he uses both verb and noun in conjunction with his desire to come in contact with God and to
remain attached to Him. He realized that in order to pursue that desire he had “to pass beyond memory” (xvii.26), to awareness.
Here Augustine used notitia to refer to awareness of the following things:
1) of the blissful life, which he was seeking, in seeking God, and which all human beings want: “Where have they become aware of
(noverunt) it? … I don’t know how they became aware of it and so have it in I-know-not-what notitia.”
2) of numbers, which human beings have in a different kind of notitia, than that of the blissful life.
3) of eloquence, which even some who were never eloquent wished, from an inner notitia, to have, when they happened to
experience others being eloquent.
4) of joy, the notitia of which stuck so fast in his memory that he could be mindful of it, even when he was sad. All human beings
have had an experience of joy, and that’s what they call the blissful life. It is the notitia of that which they have in mind, when they want the
blissful life.
The above examples suggest that John of the Cross may be using noticia to refer to a preconceptual, undifferentiated sort of
familiarity, an awareness that is obscure in that sense.
8 Here John is not using “general” to refer to knowledge by concepts—as in “the concept of body includes heaviness”—as opposed to
particulars known by perception—for instance, “this book is heavy.”
9 The two examples in this sentence come from Erwin Straus, who offers a wonderful discussion of the contrast between detached and involved
awareness in Vom Sinn der Sinne (Berlin: Springer-Verlag, 1956), pp. 329-350.
10 M. Milner (Joanna Field), On Not Being Able to Paint (Madison, CN: International Universities Press, 1957), p. 21, italics added.
11 This is how J.-P. Sartre characterizes the way emotions alter our experiencing of the world. See his The Emotions: Outline of a Theory (NY: The
Philosophical Library, 1948), pp. 52-58.
12
�Moreover, in the state of contemplation, I do not experience an object of consciousness, do not
encounter anything as if it were standing opposite to me, the subject of consciousness. Contemplation is
“pure” in the sense that it is “pure of object-plus-subject.” My awareness is one with that of which there
is awareness, in a unity out of which both subject and object subsequently emerge. As a state of mind
without “yet a subject or an object,” it is prior to the correlation of subject with object: 12 “The moment
of seeing a color or hearing a sound … is prior not only to the thought that the color or sound is the
effect of an external object or that one is sensing it, but also [prior] to the judgment of what the color or
sound might be.” 13 In this sense contemplation would be an immediate experience. 14
At the very beginning of each moment of awareness,
there is a fleeting instant of pure awareness just before you conceptualize the thing, before you identify it…. It is
that flashing split second just as you focus your eyes on the thing, just as you focus your mind on the thing, just
before you objectify it, … and segregate it from the rest of existence…. just before you start thinking about it—
before your mind says, “Oh, it’s a dog.”
Instead of focusing on what I perceive, imagine, or think, in order to cognize it, label it, and think about
it, in contemplation I “experience a thing as an un-thing … experience a softly flowing [instant] of pure
experience that is interlocked with the rest of reality.” 15 Understood in this sense contemplation can be
seen to open me to what is in-finite, in-determinate, un-limited, un-thing, and, thereby, to prepare me
for selfaware union with the divine creating, God’s esse, or is-ing, as was stated in Section I.
CONCLUSION
My soul is “holding” its “direction-toward (advertencia) God together with [its] loving God.”
John analogizes this holding-together to my holding my eyes open, in order to allow the light “to be
communicated passively” to me, just as God “is being communicated passively to the soul.” This “divine
12 William James, Essays in Radical Empiricism and A Pluralistic Universe, “DOES 'CONSCIOUSNESS' EXIST?” (New York: E.P. Dutton & Co., 1971),
p.5. Also: “The relation itself is a part of pure experience; one of its 'terms' becomes the subject…, the other becomes the object.”
13
NISHIDA Kitaro, An Inquiry into the Good, tr. M. Abe and C. Ives, modified (New Haven: Yale University Press, 1990), pp. 3-4; italics added.
14 Such selfawareness is not to be confused with self-consciousness—the reflective I think which “must be able to accompany all my
presentations” (Kant, Critique of Pure Reason, B132)—in which pure contemplation first splits into subject and object. “Selfawareness” is an
attempt to translate into English Sartre’s “conscience (de) soi,” which he uses to refer to the pre-reflective I think. See his “L'Être et le Néant:
Essai d’ontologie phénoménologique (Paris : Éditions Gallimard, 1943), p. 20.
15 Bhante Henepola Gunaratana, Mindfulness in Plain English (Somerville, MA: Wisdom Publications, 2011), p. 132; italics added. One way to
sense what this instant of pure experience is like would be to compare “what you see with your peripheral vision as opposed to the hard focus
of normal or central vision” (p. 132).
13
�light” “is being poured” into my soul (se le infunde), in a way beyond the natural (AMC II.15.2-3).
Thereby my will “is changed into life of divine love” (LFL 2.34). Now my soul experiences what God
stated in the Psalm referred to in the introduction: “you will see how (cómo) I am God” (AMC II.15.5).
My soul sees how God is God in seeing the world in a fresh way, beyond the natural.
In order to convey how God is God, John (LFL 4.6) turns to the depiction of Wisdom in the Book
of Wisdom (7:24-27): “‘Wisdom is more mobile than all movable things’ … because she is the origination
and root of all movement; and … ‘remaining within herself stable and permanent, she makes all things
new (innova; καινίζει).’” He says that this means that “Wisdom is more active than all active things.” In
this movement, according to John, my soul is the moved. It has been “awakened from the dream of
natural vison to vision beyond the natural.” From its new perspective—from which it is seeing how God
is God, how Wisdom is Wisdom—it has the loving, general awareness (noticia) of that stable divine life
as originating and as making all things new, each instant. Each instant it experiences creatures’
movements as being in tune (armonía) with God’s moving (LFL 4.6), as emanating from “God’s being-atwork (ἐνεργείας)” (Wis 7:26).
Key to Abbreviations
AMC – Ascent of Mount Carmel
DN – Dark Night
LFL – Living Flame of Love
14
�
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Walking the First Steps of His Camino with John of the Cross: An Exploration of the Dark Night of Sense
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Typescript of a lecture delivered on November 11, 2022, by Annapolis tutor Robert Druecker as part of the Formal Lecture Series.
Druecker describes his lecture: "According to John a verse from one of the Psalms is saying to us: Learn to be empty of all things, both outward and inward, and you will see how I am God. Outward things are things the soul experiences through its senses, feelings, and imagination. As the soul moves into this first dark night, it actively works at releasing its hold on all particular things. Then at some point, it notices that, independently of its wishes and efforts, it is being led away from an active doing into a receptive undergoing. Its tight grip is gradually becoming a relaxed open hand. The soul is entering the passive dark night of sense. It begins to experience God as flowing into it. Correlated with this sensed inflowing is the soul’s awakening to ways in which God is manifesting his divinity in the world."
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Druecker, Robert
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St. John's College
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Annapolis, MD
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2022-11-11
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A signed permission form has been received stating: "I hereby grant St. John's College permission to: Make an audiovisual recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audiovisual recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online"
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text
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John of the Cross, Saint, 1542-1591. Noche oscura del alma. English
Mysticism
Purgative way to perfection
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English
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LEC_Druecker_Robert_2022-11-11
Friday night lecture
Tutors
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https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/a9152d8c3d33dffbb94407e3f8bb01dc.mp4
f2fa870f99f78ab33c0cdbea8682b6e4
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Looking in Freshman Lab III – Looking Into The Constitution of Bodies: How Does the Supposition of Particles Help Us to See?
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Video recording of a lecture delivered on April 13, 2022, by Annapolis tutor Robert Druecker as part of the Formal Lecture Series. The lecture is the third in a three-part series on Freshman Lab.
Note: The title frame at the beginning of the lecture reads Looking in Freshman Lab II, but the lecture is Looking in Freshman Lab III.
Druecker describes his lecture: "This is a lecture specifically for first-year students. It will tell a story of how the presupposition that particles exist is used and made precise by a succession of chemists, from Lavoisier through Mendeleev. Does it enable us to see anything new in the phenomena we encounter in the laboratory? How does its contribution to seeing compare with that of Archimedes’ and Pascal’s mathematical approaches to weights and fluids?"
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Druecker, Robert
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St. John's College
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Annapolis, MD
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2022-04-13
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A signed permission form has been received stating: "I hereby grant St. John's College permission to: Make an audiovisual recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audiovisual recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online"
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mp4
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Particles
Chemistry--Study and teaching
Chemistry--Experiments
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<a href="https://digitalarchives.sjc.edu/items/show/7629">Looking in Freshman Lab part I (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7350">Looking in Freshman Lab part I (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7628">Looking in Freshman Lab part II (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7627" title="Looking in Freshman Lab part II (video)">Looking in Freshman Lab part II (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7630">Looking in Freshman Lab part III (typescript)</a>
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LEC_Druecker_Robert_2022-04-13_ac
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Looking in Freshman Lab III – Looking into The Constitution of Bodies:
How does the supposition of particles help us to see? 1
LAVOISIER’S PROGRAM FOR GENERATING SEQUENCES OF EXPERIMENTS LEADING TO FACTS AND
IDEAS, BASED ON MEASURING WEIGHTS (1789)
In his “Preliminary Discourse” 2 Lavoisier lays out guidelines for how to arrive at knowledge in
the physical sciences in general and in chemistry in particular. Students should follow the same course
as “nature follows in the formation of a child’s ideas … [T]heir ideas ought to be only the consequence,
the immediate continuation (suite) of an experiment or observation” (0.6). According to Lavoisier the
child’s first ideas, engendered by its sensations of its needs, are of objects appropriate for satisfying
those needs. Insensibly over time, as a result of a sequence (suite) of such sensations and observations
of suitable objects, the child generates a succession “of ideas, all bound to one another.” As with the
child so in chemistry, if one were “an attentive observer,” one “could, up to a certain point, even find
again” in the sequence of sensations, observations, and analyses “the thread and the linking
(enchaînement) of those ideas, bound to one another, which constitute the totality of what we know” in
chemistry (0.5). 3
In accord with this account, we might say that Lavoisier will aim to show us a sequence of
sensations and observations of experiments and a corresponding sequence of ideas, which he generated
from them. In his case following “the course that nature follows” appears to consist: i) in linking “the
facts and the truths of chemistry in the order most appropriate for facilitating the insight (intelligence)
A Wednesday Afternoon Lecture, delivered at St. John’s College, Annapolis, on April 13th, 2022.
For all translations from the first chapters of Lavoisier, Antoine Lavoisier, Oxygen, Acids, and Water, H. Fisher, ed., C. Burke and M. Holtzman,
trls. (Santa Fe: Green Lion Press, 2019) was consulted and often followed word for word. The references in parentheses are to chapter and
paragraph number in that translation.
3
Dans notre première enfance nos idées viennent de nos befoins; la sensation de nos besoins fait naître l'idée des objets propres à les satisfaire,
& insenfiblement par une suite de senfations, d'observations & d'analyses, il se forme une génération sucçessive d'idées toutes liées les unes aux
autres, dont un observateur attentif peut même jusqu à un certain point y retrouver le fil & l'enchaînement, & qui constituent l'ensemble de ce
que nous savons.
1
2
1
�of beginners” and ii) in ensuring that the consequent ideas “derive immediately from the facts” and
“from experiments and observations.” This arrangement would be “the natural linking of experiences
and observations” “from the known to the unknown” (0.5, .6, .8, .10, .11).
As with the child our “sensations give birth to ideas” and ‘’ideas ought to be only what … follows
immediately an experiment or observation” (0.6). Then we are not led “to draw conclusions which by
no means derive immediately from the facts,” (0.8). By presenting the facts and ideas in this way,
Lavoisier will enable us, if we are attentive, to find for ourselves the thread binding those ideas to one
another. In coming to see this connection, we should be in a situation somewhat like that of Goethe’s
reader—mentioned in the first lecture on looking in Freshman Laboratory—who can follow similarity
through its transitions, by holding in her imagination a temporal sequence of appearances, until she can
derive them from one another.
Based upon our experience in the lab up to this point, the interpretation of “derive immediately
from the facts” is that our awareness of an experiment, whether we performed it or read Lavoisier’s
account of it, gives birth to an idea in us. The experiment suddenly “makes sense” to us. But it wouldn’t
have done so absent the foreknowledge we had acquired through experience. In this respect there is an
analogy with Euclid’s sequence of propositions. A given proposition at the place where it is enunciated
appears to derive immediately from the preceding propositions in the sense that given our familiarity
with the earlier ones, in some cases, insight into the truth of the later one may be born in us as we read
it. 4
Following Lavoisier’s course involves, first, describing all the equipment used in each experiment
and telling the step-by-step story of what was done and what occurred throughout. That story includes
both observations and notes of the qualities of the substances involved in the experiment and of the
The analogy could be extended to include Euclid’s postulates. Just as Euclid needs to request that we admit them, if we are to have the
sequence of insights generated by his propositions, so Lavoisier has to ask that we admit his “principle” “that, in every operation, there is an
equal quantity of matter before and after the operation” (see below), as a condition for the possibility of ideas being born in us immediately in
response to his experiments.
4
2
�weights of all of those substances. Other relevant quantities, such as temperature, pressure, and volume
of gases must also be recorded. 5 In addition, one experiment, even if repeated several times, would not
be sufficient:
Chemistry furnishes two means for determining the nature of the constituent parts of bodies: composition and
decomposition. When, for example, water and … alcohol… are combined, creating … eau-de-vie, we are entitled
to conclude therefrom that eau-de-vie is composed of alcohol and water. But the same conclusion can be reached
through decomposition, and we ought to be fully satisfied in chemistry only as far as we have been able to bring
together both kinds of proof (3.3).
Much of Lavoisier’s focus will be on concluding—from experiments in which he observes and
measures especially the weights of the substances before and after the experiment—to a fact that a
particular substance, having weight W, has been composed from two (or more) other substances, having
respective weights w1 and w2. For instance, after his first description of a pair of decompositionrecomposition experiments, Lavoisier writes that it “does not give us exact ideas about the proportion”
of the weights of the component substances (3.14). So, he goes on to perform a further experiment in
the same series, as a result of which one can determine that the one substance “diminishes by an
amount in weight exactly equal to that by which [the other] is increased” (3.25).
In the course of describing the next set of experiments, having noted that “since nothing with
weight passes through the glass,” Lavoisier writes, “we are entitled to conclude from them that the
weight of whatever substance has resulted from this combination … had to be the same as the sum of
the weights” of the substances that were there before the combination (5.7).
He only later 6 states the “principle” upon which he bases this claim: “Nothing is created, …; we may
posit in principle (poser en principe) that, in every” experiment, “there is an equal quantity of matter
before and after” the experiment, “and that there are only changes, modifications” of matter. 7 He is
In their papers at the end of Equilibrium and Measurement, Marotte and Gay-Lussac reported having done this.
Antoine Lavoisier, Oxygen, Acids, and Water, H. Fisher, ed., C. Burke and M. Holtzman, trls. (Santa Fe: Green Lion Press, 2019), p. 57, note to
5.7.
7 Traité Élémentaire de Chimie, T. 1er (Paris : Cuchet, Libraire, 1789), Ch. 13.
5
6
3
�positing this principle underneath his feet, as it were, like a foundation on which to stand, in order to be
able to investigate. A student 8 put it this way: “you have to find a foundation—which does not shift
around as much as what you are trying to see—on which to discover something new amid what is
shifting.” In this respect Lavoisier seems to be illustrating the following words of Socrates to Glaucon: “a
soul … is forced to seek on the basis of sup-positions (ἐξ ὑποθέσεων)” (Rep 510b). At a minimum
Lavoisier has recognized that such a sup-posit-ion is a necessary condition for being able to learn
anything from chemical experiments by keeping tally of the weights involved in them.
In spite of the support provided by the principle, however, just after having concluded to the
sameness of weights before and after the above experiment, Lavoisier goes on to write that “no matter
how conclusive this experiment may have been, it was not yet sufficiently rigorous,” due to the fact that
it was “not possible to verify the weight” of the resultant compound. “We can only conclude to it by
way of calculation, in supposing it equal to the weights of” the ingredient substances. “But however
evident this conclusion may be, in chemistry and physics it is never allowable to suppose something that
can be determined through direct experiments” (5.9). So, as long as all the weights involved in an
experiment are determinable by some experiment, he does not rely on what he can conclude by
standing on the principle he has posited. For physical scientists have “often supposed instead of
concluding,” and “these suppositions, from one age to the next, … acquire the weight of authority” (0.9).
We might say that when he concludes, Lavoisier encloses together all that he’s observed,
measured, and noted throughout an experiment, in order to come to a fact, which would be the
conclusion, or end, of the experiment. The act of concluding would then be a shift from taking
“composition” as meaning the process of putting (poser) two substances together (com) during an
experiment to viewing it as signifying the qualitative and quantitative make-up, or composition, of the
outcome of an experiment.
8
Katherine Bates in Freshman Lab class, 2020.
4
�For instance, from having made (ayant fait) a certain weight of white flakes out of a given
weight of oxygen and another of phosphorous, one is entitled to conclude to the fact (fait, factum) that
a certain weight of white flakes is made (est fait) of a given weight of oxygen and another of
phosphorous. A decomposition experiment of unmaking the white flakes would allow concluding to the
fact from an un-making. On this literal understanding of “fact,” it would not be correct to say it’s a fact
that a given substance is elementary, since no making or unmaking has shown that to be the case.
However, in view of the principle, such an enclosing-together is possible only if the “walls” of
the “enclosing room” let nothing come in or out, at least in the course of the experiment. That is, we
would have to suppose something which could not be determined through direct experiments, namely,
that “the great walls of the capacious world” are closed, in the sense that they cannot, “suddenly torn
asunder, have burst apart” 9 and have allowed material substances to pass through them in either
direction.
An example of particular ideas that derive immediately from a sequence of facts, each like the
one in the above example of white flakes, might be the idea that this kind of white flakes, which is found
to have various acidic properties (5.18), is a compound substance, or, to take another case, the idea that
water is a compound substance, composed of hydrogen and oxygen, approximately in the ratio of 1g :
5.2555g (8.12). In Lavoisier’s usage such ideas are “consequences” that we “draw” (0.8). An example of
a general idea would then be compound substance.
Perhaps, in the case of compound substance, it is as if we now not only were looking at these
white flakes and remembering them as the concluding frame of a “film strip” of the just performed
composition experiment, but also were seeing, as such a frame of a generalized film strip, any substance
for which such a sequence of experiments had revealed that instances of it were made of two or more
component substances.
9
Lucretius, De rerum naturae, VI.122-23: divolsa repente maxima dissiluisse capacis moenia mundi.
5
�We may take Lavoisier’s figures along with the accompanying text as a musical score in two
different ways. In one way they tell us how to “play” each experiment in our imaginations, picturing the
equipment, the ingredient substances, the sequence of steps and events, and the outcome. We may
write down his numbers for height of mercury, volume of a container, and weights of substances and
then do the calculations. Finally, based upon trust in his report and in his results, we may see that the
burning of phosphorus, which we had considered an alteration of one substance, can be analyzed as the
composition of one substance from two others.
Moreover, we may also see that having kept track of the change in volume and of the weights of
the substances we can conclude to the fact that, for example, 45 gr of phosphorus and 69.375 gr of
oxygen composed to make 114.375 gr of white flakes (5.7). Furthermore, based upon trust that Lavoisier
has done many repetitions of this experiment, we can draw the consequence that such white flakes are
composed of phosphorous and oxygen, roughly in the ratio 1 : 1.54 by weight. So, we now have the idea
of such white flakes as a substance composed of two other substances in this weight ratio.
In the other way of taking the musical score, we “play” Lavoisier’s score in our laboratory, with
equipment similar to his. Here we trust only what we observe, that is, see and measure. Thus—it is
hoped—we arrive at the same conclusion, consequence, and idea, but upon a different basis. In either
way through his “score” Lavoisier has given any human being access to the facts and ideas he has
generated. In that sense these latter are objective.
We also recognize that in addition to the resultant general insight that, in some cases, at least,
apparent alteration might be analyzable as the composition or decomposition of substances, Lavoisier
must have relied, in advance, upon three supplementary insights: 1) that this analysis could be most
productively carried out by keeping track of the weights of the substances involved, 2) that a condition
for the possibility of this keeping-track is the supposition of the principle that, in every operation, there
is an equal quantity of matter before and after the operation, and 3) that another condition for the
6
�possibility of this keeping-track is the supposition that the vessels used in the experiments are
impermeable to the passage of the substances involved.
One way to imagine the generation of these insights would be as follows. Suppose we had left a
piece of moistened steel wool in a jar with a top on it. When we return after several days, we notice not
only the rusting of the steel wool but also a sensation of air being sucked into the jar as we unscrew the
top. It would seem as if something had happened to the air, a reduction in amount, simultaneously with
the rusting. Perhaps we could repeat this experience on a larger scale, using a bell jar, inverted over
mercury, weighing some dry steel wool, before and after the period of several days, etc. If when we
calculated we found a significant reduction in the amount of air and a significant increase in the weight
of the steel wool, we might think that the rusting might be a combining of the steel wool with
something in the air. We could then go on to figure out how much of a reduction by weight the air
underwent and compare that with the weight gain of the steel wool (cp. CB 6). 10 We could note along
the way that our calculations would not be valid, unless we had made Lavoisier’s suppositions.
INTERLUDE: GAY-LUSSAC’S RECOLLECTION OF IDEALLY EXACT LIMIT-NUMBERS (1808)
Before returning to Lavoisier, we shall glance at a paper 11 by Gay-Lussac, which is read about a
week after Lavoisier is finished. Gay-Lussac generally proceeds in accord with the course recommended
by Lavoisier, of beginning with observations and experiments, concluding from them to facts, and
deriving ideas immediately from the latter. He did, however, introduce a new feature. The students
sometimes claim that Gay-Lussac introduced mathematics into Lavoisier-style chemistry. What are they
thinking of?
Gay-Lussac began by noting a contrast between the behavior of gases, on the one hand, and, on
the other, that of liquids and solids, which had been revealed by the experimental work of Edme
The Constitution of Bodies (Annapolis, MD: St. John’s College, Printed Spring 2021), p. 6. Future references to this manual will be noted “CB,”
followed by the page number.
11 “Memoire on the Combination of Gaseous Substances with Each Other” (1808), CB 37-42, translation modified in places.
10
7
�Mariotte. Mariotte showed that the same reduction in pressure, say, by 2/3, applied to volumes of any
two different gases, say, hydrogen and oxygen, would produce the same expansion of an increase by 2/3
in each of the two volumes, so that for an expansible container of a gas at any given fixed temperature
the product of the pressure-number and the volume-number remains the same, as its pressure and
volume vary. In contrast, as Gay-Lussac noted, “the same compression applied to all solid or liquid
substances would produce a diminution of volume differing in each case” (CB 37).
Thus, while the variations in volume of liquids and solids, with changes in pressure, “have
hitherto presented no regular law,” independent of the nature of the liquid or solid in question, the laws
of the variations in volume of gases are “equal and independent of the nature of each gas.” This
recognition probably led Gay-Lussac to the intuition that he could see something new by simultaneously
narrowing his gaze to experiments involving only ingredient gases and shifting his focus from Lavoisier’s
weight-experiments to volume-experiments. He writes that it is his intention to show thereby that gases
“combine amongst themselves in very simple ratios” (CB 37).
Gay-Lussac thinks that the cause of this key difference between liquids and solids, on the one
hand, and gases, on the other, is that the particles of the former are drawn close to each other by an
attractive force, which is not present in the case of gases (CB 37). Imagining the particular attractions
between particles makes for a complicated picture when we look at volumes of solids and liquids. In
addition, it is a picture which we cannot actually see because we don’t know anything about the smallscale details of the attractions which would allow us to predict any determinate experimental outcome.
So, in effect, Gay-Lussac “hears” attractions between particles as “noise.” That noise is silenced when he
listens only to gases and their volumes. Then, Gay-Lussac “listens” to the regularity Mariotte had found
to be independent of the natures of particular gases.
Gay-Lussac presents the facts from which his idea arose. He performed an experiment with a
colleague in which they found an “exact ratio of 100 of oxygen gas to 200 of hydrogen gas for the
8
�[volume] proportion of water.” This result led him to suspect “that the other gases might also combine
in simple ratios” by volume. In the next four experiments he performed, Gay-Lussac found that in two
of them the volume ratios of the combining substances were 100 : 100 and, in the other two, 100 : 200
(CB 38-39).
He goes on to offer “some fresh proofs, after which he states:
Thus it appears evident to me that gases always combine in the simplest proportions when they act on one
another; and we have seen in reality in all the preceding examples that the ratio of combination is 1 to 1, 1 to 2,
or 1 to 3 (CB 41).
He adds that when the result of the combination of two gases is a gas, its volume is also in a very simple
whole-number ratio with that of each of the components (CB 41; cp. Avogadro, CB 43).
Analogous to Archimedes in his first treatise, Gay-Lussac has found a way to see ideal-exact
limit-formations—in his case, to see, in chemical experiments, the unit and assemblages of units
(ἀριθμοί). When he looked at the ingredient and resultant gas volumes in his and others’ experiments,
“the thought occurred to him of another thing”—a unit or two units or three units—a thing not found in
his sensory experience, something as if he knew it “from before.” Socrates would have said that GayLussac “is recollecting that of which he grasped the thought” (Ph 72e-73cd). For instance, Gay-Lussac
saw the volumes of nitrogen gas and oxygen gas that combined to form nitric acid gas as “reaching
after” the One and the Two, respectively, but “in a condition of falling short” of them (Ph 74c-75b; italics
added). Edmund Husserl would have claimed that the unit volumes that Gay-Lussac saw were examples
of ideally exact limit-formations, like those encountered in Lecture II. 12
The last three of Gay-Lussac’s proofs are based upon the results of experiments performed by
Davy, in which the weights of the combining substances and of the resultant substances were given. In
order to “hear” the corresponding volumes, Gay-Lussac must reduce the weight ratios in each case to
volume ratios. He reverses Lavoisier’s procedure (see, for example, Lavoisier 3.25) for translating a
Husserl, op. cit., pp. 22-23; The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological
Philosophy, tr. D. Carr (Northwestern: 1970), pp. 25-26.
12
9
�measured diminution in volume into the corresponding diminution in weight. Gay-Lussac divides the
observed weights by the known densities of the gases in order to determine the volume ratios of the
experiments.
For instance, Gay-Lussac then heard, or, to shift metaphors, saw, the volumes of nitrogen gas
and oxygen gas that combined to form three nitrogen compounds as “reaching after” the One and the
Two, respectively, but “in a condition of falling short” of them (Ph 74c-75b; italics added)—like a chalk
mark reaching after the Straight. For the actual experimental results for these three compounds were
that the nitrogen volume was to the oxygen volume as - 2 : 0.99 and 1 : 1.089 and 1 : 2.047, respectively.
Gay-Lussac comments:
The first and the last of these [ratios] differ only slightly from [2 to 1], and [1 to 2]; it is only the second which
diverges somewhat from [1 to 1]. The difference, however, is not very great, and is such as we might expect in
experiments of this sort; and I have assured myself that it is actually nil (CB40). 13
This assurance suggests that hearing, or seeing, ideal-exact volume-units can allow us to correct
values arrived at by measuring weights. In an application of his new approach—without having to
perform any experiments, but simply by viewing a weight-experiment, through the lens of volume—
Gay-Lussac corrected the accepted density of carbonic acid gas.
Cruickshanks had experimentally determined its value to be 0.9569. When Gay-Lussac looked at
the volume results of an experiment by Berthollet, in which 200 carbonic oxide + 100 oxygen → 200
carbonic acid, he concluded that the relation of the densities is dcoxide = dcacid - ½doxy. Since the latter two
densities had been well established 14 by many experiments as 1.5196 and 1.1036, respectively, GayLussac saw that the density of carbonic oxide gas had to be .9678. The elimination of weight-noise—
“Reducing these proportions to volumes we find—
Nitrogen Oxygen
Nitrous oxide
100
49.5
Nitrous gas
100
108.9
Nitric acid
100
204.7
The first and the last of these proportions differ only slightly from 100 to 50, and 100 to 200; it is only the second which diverges
somewhat from 100 to 100.”
14 CB 41, n. 17.
13
10
�each experiment involving a particular kind of chemical reaction yields slightly different weight
relations—allowed Gay-Lussac to hear the ideal-exact sound of the volume, by which he could correct,
in the second decimal place, the previous value, which depended on weight-experiments.
In his experiments Lavoisier was measuring magnitudes, as dealt with by Euclid in Book V of The
Elements. Now Gay-Lussac is counting numbers, which Euclid treated in Book VII. Gay-Lussac has, thus,
opened the realm of chemistry to include the discrete as well as the continuous. This new seeing of units
and numbers of units in chemistry may be what the students glimpsed when they said that Gay-Lussac
had introduced mathematics into chemistry.
LAVOISIER AND THE ROLE OF IMAGINATION (1789)
We return to Lavoisier in order to consider the role of imagination in chemistry. In accord with
his aim to rely on what we observe and conclude when we perform experiments involving weighing,
Lavoisier wanted to avoid being led astray by the imagination. With respect to the things we want to
come to know, he presents “imagining them” as an alternative to his program of “observing them”
(0.41). Moreover, Lavoisier specifically warns us of the dangers of the imagination, “which constantly
tends to carry us beyond the true … [and] invite[s] us to draw consequences which by no means derive
immediately from the facts” (0.8). Especially “in the case of things that can be neither seen nor felt, it is
of the utmost importance to guard against the deviations of the imagination, which always tends to soar
beyond the true and which has considerable difficulty in confining itself within the narrow circle that the
facts draw around it” (1.10). Thus, what we imagine, in that it leads to consequences not immediately
derivable from the facts, stands squarely opposed to ideas, which do so derive by insight.
For instance, while Lavoisier spoke of particles, he did not go on to imagine what they might be
like in detail. “Lavoisier’s ‘particles’ are simply small portions of a substance, not necessarily either the
11
�smallest possible portions or even of uniform size.” 15 He drew no consequences from any suppositions
about the nature of the assumed particulate nature of matter.
Nevertheless, under certain conditions, he does draw tentative consequences, in an interesting
way, from imagining the behavior of particles, namely, their separation by warmth (1.1):
It is understandable that since they are … continually invited (sollicitées) by warmth (chaleur) to separate from one
another, the particles of bodies would have no connection among themselves and that there would be no solid
body if they were not held back by another force that would tend to bring them together and, as it were, to link
them to one another….
And so the particles of bodies can be considered as obeying two forces, one repulsive and one attractive,
between which they are in equilibrium (1.3 & .4; italics added).
This imagined picture—which involves considering-as—does not seem to acquire the status of a
consequence that Lavoisier would or could legitimately draw. On the one hand, he imagines “a real,
material substance, an exceedingly subtle fluid that insinuates itself throughout the particles of bodies
and separates them.” Yet the grounds for speaking of it are that the phenomena of bodies’ changing
state as they are warmed up or cooled down are “difficult to understand … without admitting that they
are the effects” of such an imagined substance. So, that substance would appear to be a supposition of
a different kind than his sup-position of the principle mentioned above as a foundation for the chemist
to stand on. He states: “Even supposing that the existence of this fluid were an hypothesis, we shall see
in what follows that it explains the phenomena of Nature quite felicitously” (1.7). “Explaining” must be
distinguished from concluding or drawing a consequence. The hypothesis of a subtle fluid would help us
to imagine a picture of what might be going on “beneath” or “inside” those things we can actually see
and measure in the lab.
“Since the sensation that we call warmth is the effect of the accumulation of” this imagined
substance, “whatever it may be,” Lavoisier names it, as being the cause of warmth (Lat. calor), “caloric.”
Yet in the same paragraph, he assures us that
15
Lavoisier, Op. cit., p. 13, note to 1.1.
12
�rigorously speaking we are not even obliged to suppose that caloric is real matter; it suffices … that it be a
repulsive cause of any sort that separates the particles of matter, and so we may view its effects in an abstract
and mathematical way (1.8).
Lavoisier seems to be inviting us to fantasize anything whatsoever as long as it helps us to imagine what
could be happening when bodies change state with changing temperature. Ultimately, whatever we
imagine will have to agree with any empirically established mathematical functions that express change
of matter as a function of temperature, as well as with the ideal gas law, which we have already
encountered in Ch. VI of Measurement and Equilibrium. 16
While the above account “determines the idea that we ought to attach to the word ‘caloric,’”
Lavoisier wishes to “give correct ideas of the manner in which caloric acts on bodies” (1.10). In the
course of doing that, he reports that caloric “plays in some way the role of solvent” in the case of every
gas, in that it “tends to separate” the particles of all bodies, opposing their attraction (1.28 & 1.30).
Since, in dealing with abstract things, we should not over-rely on the help of sensible
comparisons, Lavoisier offers several ways in which we may form a picture of these opposing
tendencies: “we picture (figure) to ourselves,” now a vessel filled with little lead balls into which a very
fine powder … has been poured,” now pieces of different kinds of wood, submerged in water (1.31-.34).
This use of the imagination to picture sensible comparisons clearly does not risk carrying us beyond
what is true.
These comparisons may call to mind that earlier in the lab Theophrastus, Aristotle, and Harvey
analogized the working of plant parts or animal organs to that of products of art. In those cases, though,
we could actually look at the part in question and see the similarity in it, somewhat as we can see a
particular expression in a face. However, the substance that Lavoisier is looking at in his imagination
bears no visible trace of anything expressive of lead balls or pieces of wood. We are imagining them
alongside or inside the phenomena we are looking at in the lab. Putting it that way is suggestive of the
16
Measurement and Equilibrium (Annapolis: St. John’s College, printed Fall 2020), pp. 128-30.
13
�transparencies that Archimedes and Pascal used to bring about an essential seeing in the lab. In the case
of Lavoisier, however, what we fantasize allows us to picture what could be happening below the level
of appearances that could account for them.
Lavoisier’s final discussion of caloric in Ch. I is based on the twin suppositions of the existence of
particles of matter and of particles of caloric. Having stated that caloric is both an elastic fluid and the
cause of the elasticity of bodies, Lavoisier poses the Socratic question, “what is elasticity”? It is the
property that “the particles of a body have of moving away from one another when they have been
forced to draw near,” a “tendency … that manifests itself even at very great distances.” That air can be
highly compressed presupposes that particles of air are already quite far from each other. But we know
from experiments that they tend to move even further away from each other. The only way to explain
that effect is by “supposing that the particles make an effort in every direction to separate” (1.44).
There may, in fact, be such a real repulsion between the particles of elastic fluids, since it would
be consistent with the phenomena, but Lavoisier thinks that such “a repulsive force … is difficult to
conceive” (1.45). Trying out another supposition leads him, finally, to the thought that
the separation of the particles of bodies by caloric is due to a combination of different attractive forces, and it is
the result of these forces that we seek to express … when we say that caloric communicates a repulsive force to
the particles of bodies. (1.46)
At the very least we may say that Lavoisier’s imagining of caloric did not lead him to cling to a
fixed supposition of what is going on “behind” or “inside” the things we can see with our eyes. He is
flexible in the ways in which he imagines the supposed action of caloric. He keeps his eye,
simultaneously, both on the phenomena and on the supposed separation of gas particles with increasing
warmth. He encourages us to play around with different suppositions, without mistaking any of them for
“the true” picture.
14
�DALTON’S SUPPOSITION OF ULTIMATE PARTICLES, OR ATOMS, AND MAKING USE OF THEM (1808)
(NOTE: The terminology used in the discussion of Dalton and his followers will be a translation
into a more modern terminology, established by Cannizzaro, 17 in which “atom” refers to a single
hitherto un-cutable, or in-divisible particle, which may or may not be attached to other particles by
attraction. And “molecule” refers to a separate particle, one not joined to other particles by attraction; it
may consist of one atom or of many.)
Dalton’s first great insight is that “we have hitherto made no use of” the pre-supposition that
each material thing is made up of a great number of atoms. There are two different uses that Dalton has
in mind, first, using experiments to make the particle picture more determinate and, second, using the
particle picture to propose and correct experiments.
First, chemists have not “inferred” from their experimental determination of the relative weights
of the ingredient and resultant substances to “the relative weights of the ultimate particles or atoms of
the [different kinds of] bodies” involved (CB 20-21). If they had done so, they could have seen i) how
many atoms of each kind of elementary substance were in molecules of various compounds, ii) the
relative weights of different elements in those compound molecules, and iii) the relative molecular
weights of the various compounds (CB 21).
The second use that chemists have not made of atoms is dependent on the first. For since the
chemists had no accurate, determinate atomic-molecular picture, they had no way of using particles “to
assist and to guide future investigations, and to correct their results” (CB 21). His claim is analogous to
saying that until he worked out the mathematics of the motions of heavenly bodies, Ptolemy could not
predict the date of a solar eclipse.
17 “The conception of [Avogadro and Ampère] contains nothing contradictory to known facts, provided that we distinguish, as they did,
molecules from atoms; provided that we do not confuse the criteria by which the number and the weight of the former are compared, with the
criteria which serve to deduce the weight of the latter; provided that, finally, we have not fixed in our minds the prejudice that whilst the
molecules of compound substances may consist of different numbers of atoms, the molecules of the various simple substances must all contain
either one atom, or at least an equal number of atoms” (CB 53).
15
�Dalton’s second great insight was that it was impossible to make any use of the presupposition of
atoms as long as chemists were thinking of molecules of, say, water, as being of diverse weights. Just as
Lavoisier could not make any real use of experiments, unless he sup-posed that there is an equal
quantity of matter before and after each experiment, so, too, experiments won’t be able to show
anything about the relative atomic makeup of substances’ molecules, unless we sup-pose 18 that
the ultimate particles of all homogeneous bodies are perfectly alike in weight, figure, &c. In other words, every
particle of water is like every other particle of water; every particle of hydrogen is like every other particle of
hydrogen, &c.... (CB 21).
We might say that Dalton has introduced into the world of presupposed, imaginary atoms the
supposition of ideally exact atoms. So, all ingredient and resultant substances will now be seen, at the
same time, in a double vision--both as weights, continuous magnitudes, in the lab and as atom-units of
different kinds, discrete multitudes, in the particle world. In this respect his seeing is like that of Euclid
and of Archimedes’ first treatise. The difference, though, lies in that things—in particular, things in the
material world—are thought of as “reaching for” and “falling short of” (Phdo 75ab) the exact limitformations of Euclid and Archimedes, whereas Dalton thinks of atoms as (tiny, invisible) things that
make up the actual material world. Thus, Dalton is not led to think of his homogeneous particles by what
he sees in the lab, in the way that Cebes might be led to think of Simmias by a picture of him or by a face
glimpsed in a crowd. Dalton isn’t viewing the substance in the lab as an image (εἰκών) of a number of
atom-units. He might, while looking at the particular substance, be supposing a huge number of
identical molecule-units. But the substance could not be said to image them. Moreover, at least so far,
the number of identical molecule-units would also be quite indeterminate.
18 Dalton’s word is “conclude.” The grounds for his conclusion are that “from what is known, we have no reason to apprehend a diversity in
these particulars” and that “it is scarcely possible to conceive how the aggregates of dissimilar particles should be so uniformly the same.” For
it is not conceivable to Dalton that, due to the great number of atoms in any body weighable in the lab, it could be impossible for chemists to
distinguish between the sameness of all atoms of each element and a distribution of the specific gravity of each element that is represented
graphically in the shape of a bell-curve.
16
�How well does Dalton execute his program and use his supposition of homogeneity? He shows
how chemists could go about determining the atomic makeup of molecules and relative atomic weights
of elementary substances and relative molecular weights of compound substances. First, in order to
guide chemists in deducing such “conclusions” from experimental “facts already well ascertained,” he
proposes “general rules” like the following:
1st. When only one combination of two bodies can be obtained, it must be presumed to be a binary one, unless
some cause appear to the contrary.
2d. When two combinations are observed, they must be presumed to be a binary and a ternary. (CB 22)
The first two pairs of conclusions that he goes on to mention are “1st. That water is a binary
compound of hydrogen and oxygen, and the relative weights of the two elementary atoms are as 1 : 7,
nearly” and “2d. That ammonia is a binary compound of hydrogen and [nitrogen], and the relative
weights of the two [elementary] atoms are as 1 : 5, nearly…” (CB 22). He accompanies his statement of
the conclusions with “arbitrary … signs chosen to represent” the atoms and their composites, as shown
in Figures 1a & b PLATE IV (CB 24-25).
PLATE IV. This plate contains the arbitrary marks or signs chosen to represent the
several chemical elements or ultimate particles.
1
2
3
4
5
6
7
8
9
10
21.
22.
23.
24.
25.
Fig.
Hydrog., its rel. weight 1
Azote, 5
Carbone or charcoal, 5
Oxygen, 7
Phosphorus, 9
Sulphur, 13
Magnesia, 20
Lime, 23
Soda, 28
Potash, 42
11
12
13
14
15
16
17
18
19
20
Fig.
Strontites,46
Barytes, 68
Iron, 38
Zinc, 56
Copper, 56
Lead, 95
Silver, 100
Platina, 100
Gold, 140
Mercury, 67
An atom of water or steam, composed of 1 of oxygen and 1 of
hydrogen, retained in physical contact by a strong affinity, and
supposed to be surrounded by a common atmosphere of heat, its
8
relative weight = ............................................ …………………
An atom of ammonia, composed of 1 of azote and 1 of hydrogen =
6
An atom of nitrous gas, composed of 1 of azote and 1 of oxygen =
12
An atom of olefiant gas, composed of 1 of carbone and 1 of hydrogen = 6
An atom of carbonic oxide composed of 1 of carbone and 1 of oxygen =
12
Figure 1a
17
�Figure 1b
Hence—given Lavoisier’s principle and the results of his and other chemists’ composition and
decomposition experiments, in which the weights of the bodies involved were ascertained—if we
presuppose atoms and suppose them to be homogeneous in Dalton’s sense and apply his heuristic
general rules, then both the relative weights of many atoms and the numbers of them in the molecules
of various compound bodies do follow as “conclusions.” In this way Dalton’s vision resembles that of
Ptolemy. 19
The manual directs our attention to a conclusion that follows directly from Dalton’s supposition,
without any need to apply his “general rules” to particular experiments. There was a debate, 15 years
This is true, provided Ptolemy’s mathematical apparatus be interpreted simultaneously as showing that for which the motions of the
heavenly bodies reach while falling short of it and that which enables the astronomer to say in advance where a given body will be in the sky on
a given date. But there is a difference between the two visions, unless Ptolemy be interpreted as considering his cycles and epicycles to be
invisible material bodies.
19
18
�after Lavoisier’s Treatise, between the chemists Berthollet and Proust as to whether or not substances
react and combine in definite and fixed weight ratios. For example, if 2 gm of substance A reacts with 16
gm of substance B, then 2½ gm of A will react with 20 gm of B, and so on, so that the ratio of the weight
of A to the weight of B is 1 : 8 in every case (CB 33). Lavoisier had pre-supposed that this was so, but
Berthollet claimed to have demonstrated experimentally that compositions of two substances occur “in
all ratios, up to [an] extreme value which … varies with the temperature.” Proust, though, claimed to
have found “fixed ratios” in his experiments (CB 104). 20
On the basis of Dalton’s supposition, Proust must be correct. For if every molecule of water is
made of the same number of homogeneous oxygen atoms and of the same number of homogeneous
hydrogen atoms, then in a given amount of water, say, one million molecules, the weight ratio of oxygen
to hydrogen must be the ratio –
(atomic weight of oxygen)(number of oxygen atoms per water molecule)(1,000,000) :
(atomic weight of hydrogen)(number of hydrogen atoms per water molecule)(1,000,000).
Whether or not Dalton’s “general rules” are “adopted as guides,” the ratios always have to be the same,
on the basis of his supposition. So, in imitation of Gay-Lussac’s correction of Cruikshank’s experimental
determination of the density of carbonic oxide gas (CB 41), Dalton could correct Berthollet’s empirical
claim. This might be like telling an astronomer, who reported having seen an eclipse of the moon
between 10:05 PM and 2:44 AM on a given night, that she must have fallen asleep for an hour and ten
minutes, because it had actually begun earlier, according to our mathematical calculations.
20 The manual adds a second necessary conclusion that follows directly from Dalton’s supposition of homogeneity, without reference to his
general rules, namely, the Law of Multiple Combining Proportions: “From Dalton’s doctrine of atoms it follows that whenever two elements
unite in more than one [ratio] there will be small whole number ratios among the [weights] of the first element that combine with a fixed
[weight] of the second—whole number ratios because the various [weights] of the first element that combine with a fixed [weight] of the
second must always represent whole numbers of atoms; and small because according to Dalton the most prevalent combinations may be
presumed to be those between the least numbers of atoms” (CB 30).
19
�AVOGADRO’S “ONLY ADMISSIBLE” HYPOTHESIS ABOUT SIMPLE GASES (1811)
Avogadro saw that in order to use particles, as Dalton wished to do, chemists needed to
eliminate Dalton’s guesswork, that is, his arbitrary, general rules, as heuristic “guides” (CB 22) to
determine the relative number of particles in compounds (CB 46). Avogadro’s key insight is that it is
necessary to provide “Dalton’s system … with a new means of precision through” connecting it with
Gay-Lussac’s discovery of small whole-number ratios of ideal-exact unit-volumes of gases (CB49). Then,
still looking through the Daltonian lens, Avogadro will be able to see the particles more clearly.
To review where we are at this point: we are supposing that all atoms of any given element are
identical, that all molecules of any given compound are identical, and that at STP all boxes of any given
gas contain the same number of molecules. The density of most gases have been determined by
experiment, as described above. Finally, as Gay-Lussac had shown, gases combine in very simple wholenumber ratios by volume. 21
Avogadro, with all of that in mind, realizes that “viewing” Daltonian particles “through” GayLussacian boxes gives him a way to bring the Daltonian picture into better focus. It makes particles, as it
were, into learnables (μαθήματα), about which one can learn, apart from doing experiments. He sees an
apparent necessity in the relationship between “the relative number of particles which combine and …
the number of composite particles which result,” on the one hand, and, on the other, “the ratios of the
quantities of substances in compounds.” 22 Avogadro believes that introducing a mathematics of
numbers of particles and boxes will enable him “to confirm or rectify” Dalton’s results (CB46).
This insight immediately leads him to another: “It must then be admitted (Il faut donc admettre)
that very simple ratios [or relations] also exist between the volumes of gaseous substances and the
21 “The combinations of gases always form in very simple ratios (rapports) by volume, and that when the result of the combination is a gas, its
volume is also in a very simple ratio with that of [each of] its components” (CB 43).
22
“The ratios of the quantities of substances in compounds would appear to be able to depend only on the relative number of particles which
combine, and on the number of composite particles which result” (CB 43; italics added). Avogadro’s word “quantities” may cover both weights
and volumes. If quantities—weights or volumes—of two gases combine to form a third, the ratios of the first to the second to the resultant
“would seem to be able to depend only on the relative number of particles” in the first, the second, and the resultant volumes, respectively.
20
�numbers of simple or compound particles which form them” (CB 43; italics added). Getting milage out of
the simplicity of the relationship between lab experiments involving boxes of gases and pictures of the
numbers of atoms or molecules composing gases would be easiest if it turned out that, for all gases at
STP, the number of particles per box were identically the same. For then the weight ratio of two boxes,
or equivalently, the densities of two gases, would at once also show the relative weights of the two
gases in the compound molecule. In a way, the boxes would be acting like magnifying glasses, or lenses.
In order to see that, consider Figure 2. Suppose that it turned out that for every gas there were
DALTON’s supposed molecules
1 imagined molecule of oxygen
⃝
1 imagined molecule of hydrogen
AVOGADRO’s lens to ‘see’ weight
of Dalton molecules in Gay-Lussac
boxes
1 box of 100 imagined molecules of
oxygen
GAY-LUSSAC’s unit boxes of gases
weighed in the lab
1 box of 100 imagined molecules of
hydrogen
1 actual box of oxygen
1 actual box of oxygen
ﬦ
Weight of 1 oxygen molecule
-----------------------------------Weight of 1 hydrogen molecule
=
1/100 of weight of 100 oxygen
molecules
-----------------------------------=
1/100 of weight of 100 hydrogen
molecules
Weight of 1 box of oxygen
-----------------------------------Weight of 1 box of hydrogen
Figure 2
exactly 100 molecules of it in one Gay-Lussac box. Then the experimentally determined weight ratio of a
box of oxygen to a box of hydrogen (see left column) would have to be the same as the supposed weight
ratio of one oxygen molecule to one hydrogen molecule (see right column), because the lens shows that
the former ratio is the same as the ratio of the weight of 100 oxygen molecules to 100 hydrogen
molecules.
21
�But could Avogadro learn the relative numbers of particles per box of two different ingredient
gases that result in a compound gas? He claims that the hypothesis just stated in the previous
paragraph, “which presents itself first in this connection,” is not only the first to present itself and the
simplest but also “the hypothesis … which even appears to be the only admissible one” (CB 43).
How could he have learned that no other hypothesis could be admitted? Avogadro devotes
most of the rest of the first paragraph to hypotheses about the possible distances of gas particles from
each other. 23 But he summarizes these speculations by stating that “in our present ignorance of the
manner in which this attraction of the particles … is exerted, there is nothing to decide us a priori” for or
against any one of these hypotheses.
However, he concludes that “the hypothesis we have just proposed relies on that simplicity of
ratio between the volumes of gases in the combinations, which would appear to be unable to be
explained otherwise” (CB 44; italics added). In other words, the necessity of the simple relationship
between experimental boxes and numbers of particles—itself, the necessary result of bringing GayLussac and Dalton together—forces him to reject any hypothesis other than the simplest one. 24
Dalton’s first “object” had been to make “use of” the presupposition of particles, in order to
determine the relative weights of particles and the composition of composite particles (CB 20-21).
Avogadro can claim that relying on his new lens, or hypothesis, he was able to “see,” in all volume
experiments involving gases, the relative numbers of ingredient and resultant molecules involved, and
so, also, their molecular weights. In this way his first hypothesis makes the supposed, invisible realm
distinctly and determinately visible.
23 If you think of gas molecules as floating freely, unattracted by each other, then there is no reason to think that two boxes of different gases
would contain different numbers of particles.
24 In order to see that Avogadro’s hypothesis is the only way to arrive at this simplicity, one would have to work through all the known
experimental results involving gases, while trying out different numbers of molecules per box. For each trial the supposed molecular
composition of each gas would have to remain the same in all reactions. In doing this Avogadro seems to have seen that the simple relations
follow only from one hypothesis about the relation between number of molecules per box, namely, that a box of any gas contains the same
number of molecules.
22
�CANNIZZARO’S DETERMINATION OF A TABLE OF MOLECULAR AND ATOMIC WEIGHTS (1858)
Avogadro’s hypothesis lets us “see” the relative molecular weights of gases, “even before their
composition is known,” since the molecular weights have to be proportional to the experimentally
determined densities of the gases, as we’ve just seen. Cannizzaro’s first insight is that instead of focusing
on particular reactions and particular compounds “it is useful” (giova) to view all the elementary and
compound gases together and, in particular, “to refer” the molecular weights (or, densities) of all gases
to that of the lightest gas (CB 56), namely, hydrogen.
He sets up a ratio scale of relative molecular weights. Since it is a scale of relative, not actual,
weights, the weight-number to assign to the smallest molecule is completely arbitrary. With later
considerations in mind, he assigns to hydrogen the weight-number 2 on the scale, rather, than 1. All
other molecular weights will be determined by their ratios to that of hydrogen = 2. Then looking at unit
volumes through Avogadro’s lens, Cannizzaro can make a table of the molecular weights of all gases,
relative to this unit.
For instance, in order to determine the relative molecular weight of any gas, all he has to do is
look up the density—that is, the weight per box—at the same temperature and pressure, of hydrogen
and of the gas in question. Since
(molecular weight of gas x)/(molecular weight of hydrogen, viz., 2 = (density of gas x)/(density of hydrogen),
he has only to multiply the density of gas x by the density of hydrogen gas and then to multiply that by
2. And he has determined the molecular weight of the gas.
Cannizzaro list the molecular weights of some gases in the right-hand column of Figure 3 (CB
56).
23
�Names of Substances
Hydrogen
Oxygen, ordinary
Oxygen, electrised
Sulphur below 1000°
Sulphur* above 1000°
Chlorine
Bromine
Arsenic
Mercury
Water
Hydrochloric Acid
Acetic Acid
weights of the molecules referred to
the weight of a whole molecule of
Hydrogen taken as unity.
1
16
64
96
32
35.5
80
150
100
9
18.25
30
weights of the molecules referred to the
weight of half a molecule of Hydrogen
taken as unity.
2
32
128
192
64
71
160
300
200
18
36.50†
60
Figure 3
Cannizzaro’s second insight is that we must clearly distinguish between the criteria used just
now to arrive at the weights of all the gas molecules from those that yield the weights of the atoms and
the numbers of them in the molecules (CB 53). Avogadro—in the course of using his “lens” for looking
through equal boxes, at same temperature and pressure, in order to see molecular weights—had been
forced, in considering the composition of water, to recognize that a molecule of elementary oxygen
contains two oxygen atoms.
To see this let’s suppose, again, that there are 100 molecules of any gas in one box. In the
composition experiment, one box of oxygen combined with two boxes of hydrogen to form two boxes,
that is, 200 molecules, of water. If the oxygen molecule consisted of only one oxygen atom, there’d be
only 100 oxygen atoms available for forming 200 water molecules—not enough!
So, Avogadro “supposes” that the molecules “of any simple gas whatever,” like oxygen, are “not
formed of one single” atom, “but result from a certain number of these molecule joined together in a
single one” (CB 45). He also supposed that for instance, if oxygen and hydrogen molecules were,
respectively, O2 and H2, then one atom from each box of oxygen and of hydrogen would have to join to
compose one compound molecule; so, there would be 200 water molecules of the composition H2O,
since there are two boxes (200 molecules, or 400 atoms) of hydrogen and only one box (100 molecules,
or 200 atoms) of oxygen.
24
�But if oxygen and hydrogen molecules were, respectively, O4 and H2, then two atoms of oxygen
would have to join with one hydrogen atom from each box of hydrogen to compose one compound
water molecule. So, there would be 200 water molecules of H2O2. In either case the number of water
molecules “becomes … exactly what is necessary to satisfy the volume of the resulting gas” (CB 45), 25
that is, two boxes of water. Perhaps it is the principle of simplicity, reminiscent of Dalton, that decides
him in favor of H2O.
In order to determine molecular formulas in a more systematic and reliable way, Cannizzaro
considers in one view all of the elements that can be produced in gaseous form. In agreement with the
argument of Proust and the conclusion from Dalton’s supposition, he begins with fixed, determinate,
experimental ratios between the weights of the two component substances in a given compound.
Then the weight of the molecule is divided into parts proportional to the numbers expressing the [experimentally
determined] relative weights of the components, and so we have the [weights] of [the components] contained in
the molecule of the compound, referred to the same unit as that to which we refer the weights of all the molecules
[namely, hydrogen = 2] (CB 57).
This method allows him to construct the following table, shown in Figure 4 (CB 58):
Name of Substance
Hydrogen
Oxygen, ordinary
Oxygen, electrised
Sulphur below 1000°
Sulphur above 1000° (?)
Phosphorus
Chlorine
Bromine
Iodine
Nitrogen
Arsenic
Mercury
Hydrochloric Acid
Hydrobromic Acid
Hydriodic Acid
Water
Ammonia
Arseniuretted Hyd.
Phosphuretted Hyd.
[molecular
wt (H’s = 2)]
2
32
128
192
64
124
71
160
254
28
300
200
36.5
81
128
18
17
78
34
[weights of the molecule’s components]
2
32
128
192
64
124
71
160
254
28
300
200
35.5
80
127
16
14
75
31
Hydrogen
Oxygen
”
Sulphur
”
Phosphorus
Chlorine
Bromine
Iodine
Nitrogen
Arsenic
Mercury
Chlorine
Bromine
Iodine
Oxygen
Nitrogen
Arsenic
Phosphorus
1 Hydrogen
1 ”
1 ”
2 ”
3 ”
3 ”
3 ”
25 “When particles of another substance unite with the former to form a compound particle, the whole [compound] particle which should result
is divided into two or several parts (or separate particles) [each]composed of half, quarter, etc., the number of elementary particles going to
form the constituent particle of the first substance, combined with half, quarter, etc., of the number of constituent particles of the second
substance, which should combine with the whole particle (or, what comes to the same thing, [combined] with a number equal to this [last
number] of half-particles, quarter-particles, etc., of the second substance); so that the number of separate particles of the compound becomes
double, quadruple, etc., what it would have been if there had been no dividing, and exactly what is necessary to satisfy the volume of the
resulting gas” (CB 45).
25
�Calomel
Corrosive Sublimate
Arsenic Trichloride
Protochloride of Phosphorus
Perchloride of Iron
Protoxide of Nitrogen
Binoxide of Nitrogen
235.5
271
181.5
138.5
325
44
30
35.5
71
106.5
106.5
213
16
16
Figure 4
Chlorine
”
”
”
”
Oxygen
”
200 Mercury
200 ”
75 Arsenic
32 Phorphorus
112 Iron
28 Nitrogen
14 ”
In order to understand Cannizzaro’s procedure, let’s suppose that the relative weight ratio for
producing 100g of arseniuretted hydrogen has been found by experiment to be weight of arsenic : weight of hydrogen :: 96.15g : 3.85g.
Cannizzaro would divide the relative molecular weight, 78, of arseniuretted hydrogen into two numbers,
a, representing how much of the 78 is due to arsenic, and h, representing how much of the 78 is due to
hydrogen. So,
78 = a + h.
But also, since the 78 is to be divided in the same proportion as the 100, he knows that
96.15g : 3.85g :: a : h.
Solving these two simultaneously 26 tells him that the breakdown of the molecular weight of
arseniuretted hydrogen into the weights of its component elements has to be 75 parts from arsenic
atoms and 3 from hydrogen atoms.
At this very moment Cannizzaro says the following to his students (CB 59):
‘Compare … the various quantities of the same element contained in the molecule of the free substance and in
those of all its different compounds, and you will not be able to escape the following law: The various quantities
of the same element contained in different molecules are all integral multiples of one and the same quantity, which,
always being integral, ought rightly be called [the atomic weights relative to that of hydrogen as 1] (CB 59,
underlining added). 27
For instance, if we look for chlorine in the right column of Figure 4, we see that the number it
has been found to have is 35.5 or twice that, or triple that. So, 35.5 must be chorine’s relative atomic
weight; and its molecule must be diatomic; and, for instance, there must be three chlorine atoms in
26
27
If a + h = 78 and a/h = 96.15/3.85 = 25, then (78 – h)/h = 25. So, 78 – h = 25h, and 78 = 26h. Or h = 3 and a = 75.
His actual words are: “ought rightly be called atom.”
26
�protochloride of phosphorus (molecular weight = 138.5). A similar search for phosphorus tells us that its
relative atomic weight must be 32 and that there must be one phosphorus atom in a molecule of
protochloride of phosphorus. It is easy to see that we can now “express all chemical reactions by means
of the same numerical values [that is, these relative atomic weights] and integral coefficients” of them
(CB 60). That is, we can write reliable, accurate chemical formulas for such compounds. For the present
example of protochloride of phosphorus, the chemical formula must be PCl3. 28
MENDELEEV’S CONSTRUCTION OF THE PERIODIC TABLE (1870-71)
Mendeleev points to his fundamental insight right at the beginning of the excerpt in the manual.
In order to make the “inadequacy” of current atomic doctrine in chemistry “disappear,” he will “put at
the foundation of the study of the main [physico-chemical] properties of the elements their [relative]
atomic weights,” which Cannizzaro had worked out, less than 10 years before Mendeleev set to work.
Mendeleev’s bringing two previously separate realms into relationship may remind us of Avogadro’s
advancing to a new insight by bringing into relationship Gay-Lussac’s perception of small whole numbers
of boxes of gases and Dalton’s supposed ideal-exact atoms. Mendeleev indicates several steps by which
he came to his insight.
Chemists had long recognized certain “natural groups” of elements based on their physicochemical properties. For instance, lithium, sodium, potassium, rubidium, and cesium had been referred
to as alkali metals; they are good conductors of heat and electricity, are highly malleable and ductile,
have very low boiling and melting points and shiny surfaces, and are distinguished from other metals by
their lower densities and softness. Beryllium, magnesium, calcium, strontium, and barium were known
as alkaline earths; they are solid, hard, dense, and usually shiny, are less reactive than metals, are often
insoluble in water, and are found in the earth crust. Fluorine, chlorine, bromine, and iodine are non-
28
It is, of course, clear to Cannizzaro that the numbers may have to change as future empirical discoveries are made.
27
�metallic, have relatively low melting and boiling points and generate salts (ἅλς) when they react
chemically with metals; they had been grouped together as halogens. Other natural groupings were
“analogues to sulfur,” including oxygen, selenium, and tellurium; as well as analogues to nitrogen,
including phosphorous, arsenic, antimony, and bismuth (CB 81).
Initially the elements were put in groups due to their similarities with respect to these
properties. Then some chemists noticed among pairs or triples of elements of high atomic weight,
analogues to pairs or triples of elements of much lower atomic weights. This noticing of analogues “gave
the first impetus to compare the different properties of the elements with their atomic weights” (CB 81).
For example, the physico-chemical properties of cesium (w 29 = 133) and barium (w = 137) were
analogous to those of potassium (w = 39) and calcium (w = 40). With respect to such properties, they are
proportional, in the sense that
K : Cs (among alkali metals) :: Ca : Ba (among alkaline earths).
In other words, within the natural group of alkali metals, the ways in which K differs from Cs, in its
physico-chemical properties, is analogous to the ways in which Ca differs from Ba, in those properties,
within the group of alkaline earths.
Such analogies led to the insight that the way a given physico-chemical property alters, as we
consider, one after the other, the elements of increasing atomic weight within one natural group, may
often occur in parallel with corresponding changes in other natural groups. That insight, in turn, led to
“thinking of classifying all the elements according to their atomic weights,” as determined by
Cannizzaro, in order to see what might be revealed. Mendeleev reports that when we do this “we find
an astonishing simplicity of relationship” (CB 82).
29
The letter “w” will stand for relative atomic weight, according to Mendeleev’s figures.
28
�His illustration of that simplicity is the arrangement, shown in Figure 5, in two horizontal rows of
all the elements of relative atomic weight between 7 and 36, “in arithmetical order according to their
atomic weights.” He looks in two different ways at these rows.
Li=7
Be=9.4 B=11
C=12 N=14 O=16 F=19.
Na=23 Mg=24 Al=27.3 Si=28 P=31 S=32 Cl=35.5.
Figure 5
First, when he looks at a row by itself and attends, one by one, to the different physical and
chemical properties, he notices “that the character of the elements changes regularly and gradually
with increasing magnitude of the atomic weights” (CB 82; italics added). For instance, the
characteristics—whether qualitative or quantitative—of the elements in the row change from left
to right in the following ways:
i) from being basic to being acidic;
ii) from metals, through semi-metals, to non-metals;
iii) from being good conductors of heat and electricity to being insulators;
iv) from being lustrous and shiny to being dull;
v) from a boiling point of 1330°C rising in the middle and then falling to -188°C;
vi) again rising, from a melting point of -180°C, to a maximum and then falling to -187°C;
vii) density, too, rises to a high point and then falls, as shown in Figure 9;
viii) a graph of the relative atomic volumes [that is, the relative atomic weight (weight per atom)
divided by its density (weight per unit volume) = relative volume per atom] would be U-shaped
ix) and, finally, a graph of the volatility would also be U-shaped (CB 83-84). (See Figure 6 for viii and ix.)
Na
Mg
Al
Si
P
S
Cl
vii) Density:
0.97 1.75 2.67 2.49 1.84
2.06 1.33
viii) At Vol:
24
16
14
10
11
16
27
Figure 6
Second, when we compare the patterns of change, from left to right, along the top row with
29
�those along the bottom row, we find that “the character of the elements changes … in the same
way in both series, so that the corresponding members of them are analogues.” In this example,
the patterns of change are the same for all nine characteristics listed above. Thus, lithium and
sodium, the respective members of each series that are highest in basic character, metallic
character, luster, and conductivity are the leftmost ones, are also at the beginning of rising curves
of the graphs of melting and boiling points and density, and so on (CB 82).
Finally, Mendeleev stresses the importance of the forms of the compounds that are formed—in
order along each of the two rows—with oxygen and with hydrogen. The forms of these compounds
present regularities that are familiar to chemists from their experimental work. As we look from the
beginning of either row, “the corresponding elements in the two series have the same kind of
compounds” with oxygen: That is, two atoms of the given element combine with the following numbers
of oxygen atoms—1, 2, 3, … respectively, a uniformly increasing sequence of whole numbers, as the
atomic weight of the element increases. For instance:
The seven elements of the second series give the following higher oxides capable of forming salts:—
Na2O,
Mg2O2, Al2O3,
or MgO,
Si2O4,
P2O5,
or SiO2,
S2O6, Cl2O7,
or SO3.
Thus, the seven members of the above [second] series correspond in the same sequence to the seven generally
known forms of oxidation (CB 83).
Moreover, beginning with the righthand member in either row and moving left, a similar pairing
of compounds with hydrogen occurs—hydorfluoric acid (HF) and hydrochloric acid (HCl) are 1 : 1; water
(H2O) and hydrogen sulfide (H2S) are 2 : 1, and so on, up to 4 : 1..
Mendeleev states: “This regularity proves that the above comparison of elements presents
natural series in which it is impossible (нельзя) to assume any intermediate members” (CB 82-83;
italics added). The arranging of the elements in the order of increasing relative atomic weight has led
Mendeleev to see a new necessity, or rather impossibility, such as we might find in mathematics.
He goes on to present such pairings for all the elements. That he can do so “indicates a close
30
�dependence of the properties of the elements on their atomic weights.” As we have seen from his
example and as he goes on to show, all the individual relationships of the dependence of physicochemical properties on atomic weight are “periodic.” “First, the properties of elements change with
increasing atomic weight; then, they repeat themselves in a new series of elements, a new period,
with the same regularity as” in the series we just went through in detail (CB 84). Mendeleev is using
“period,” in the sense familiar to us from Ptolemy. Just as a heavenly body has different positions over
time and returns to its starting point, after completing one period, and then begins a repetition, a new
period, so a given physico-chemical property has different values as we consider, in turn, elements of
increasing atomic weight along one row, and returns to a value near its starting value, after completing
one period, and then begins a repetition, a new period, at the first element of the next row.
Once Mendeleev had thought to arrange all the elements in the order determined by their
atomic weights, these repetitive patterns suddenly became visible to him, as a picture of wave-like
motions. His experience might be analogous to suddenly seeing something appear in Figure 7.
Figure 7
31
�Mendeleev next goes on to show how he found the complete periodic dependence of the
physico-chemical properties on the relative atomic weights (CB 85ff). He lined the elements up in rows,
like the ones we’ve considered. Table II, in Figure 8, shows all the elements in eight columns—
Figure 8
the eight natural groups—and twelve rows. Rows 2, and 3 are the two complete series we’ve already
considered. However, the remaining elements revealed their periodicity only when Mendeleev lined
them up below one another in longer rows, in the following way:
Row 4 (group I-VII) + Group VIII + Row 5
above
Row 6 (group I-VII) + Group VIII + Row 7
above
Row 8 (group I-VII) + Group VIII + Row 9
above
Row 10 (group I-VII) + Group VIII + Row 11
Thus, one circuit begins with K and Ca’s properties and ends only with those of Se and Br; a new circuit
begins with Rb and Sr’s properties and ends with those of Te and I. And so on.
32
�Mendeleev concludes by returning to what Dalton saw as the second use that chemists had not
made of particles—using them “to assist and to guide future investigations, and to correct their results”
(CB 21). Perhaps Mendeleev thought that by his time it was not particles, but relative atomic weights
that still had not been made use of. He says that in order for a law, like his periodic law, to acquire
scientific importance its logical consequences have be useful, in the sense that they “explain the as yet
unexplained, give indications of hitherto unknown phenomena, and [allow] one to make predictions
that are accessible to experimental verification” (CB 89).
He does all that in the rest of his article. For instance, the element indium had been discovered
in 1867 and assigned the relative atomic weight of 75.6. Mendeleev saw that there was no open slot in
the periodic table for an element of relative atomic weight 75.6. But by comparing its compounds with
those of other elements, Mendeleev saw that indium would have to be placed in an open slot in in
Group III, row 7, with atomic weight about 113 (CB 91-92).
Moreover, Mendeleev investigated the empty slot in Group IV, row 5. He saw that there had to
exist an element of relative atomic weight “about 72” in that slot. Based on the known physico-chemical
properties of the elements in the slots around the empty one, he predicted the properties that the yetto-be-discovered element would have to possess. About 15 years later the element germanium (Ge), of
relative atomic weight about 72.5 and possessing those properties, was discovered (CB 93-95). Perhaps
chemists experienced this discovery as somewhat like reading a novel, coming away with a very precise
sense of the main character, and then meeting someone at a party who strikes us as perfectly fitting the
fictional portrait. It might seem as if we knew him “from before.” Would Socrates say that we are
“recollecting,” but in some to-be-determined different sense (Ph 72e-73cd)?
What do we make of Dalton’s seeing supposed particles—not actual chalk marks on the
blackboard or lines drawn on paper—as ideal-exact limit-entities, in the realm of μαθήματα, of objects
of study leading to insightful learning? Do they eventually lead to acts of insight into the actual material
33
�world, in the way that Archimedes’ learn-ables about weight or Ptolemy’s about motion do? How does
the way in which they allow us to see more in the world compare with the way Archimedes’
transparencies refine our vision?
Do Mendeleev’s successes in making use of the supposed particles and of their relative atomic
weights show that atoms and molecules are not merely supposed but also actually existing entities in
the material world?
34
�
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Looking in Freshman Lab III – Looking into The Constitution of Bodies:
How Does the Supposition of Particles Help Us to See?
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Typescript of a lecture delivered on April 13, 2022, by Annapolis tutor Robert Druecker as part of the Formal Lecture Series. The lecture is the third in a three-part series on Freshman Lab.
Druecker describes his lecture: "This is a lecture specifically for first-year students. It will tell a story of how the presupposition that particles exist is used and made precise by a succession of chemists, from Lavoisier through Mendeleev. Does it enable us to see anything new in the phenomena we encounter in the laboratory? How does its contribution to seeing compare with that of Archimedes’ and Pascal’s mathematical approaches to weights and fluids?”
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Druecker, Robert
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St. John's College
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Annapolis, MD
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2022-04-13
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A signed permission form has been received stating: "I hereby grant St. John's College permission to: Make an audiovisual recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audiovisual recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online"
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Chemistry--Study and teaching
Lavoisier, Antoine Laurent, 1743-1794
Chemistry--Experiments
Mendeleyev, Dmitry Ivanovich, 1834-1907
Cannizzaro, Stanislao, 1826-1910
Avogadro, Amedeo, 1776-1856
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<p><a href="https://digitalarchives.sjc.edu/items/show/7629">Looking in Freshman Lab part I (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7350">Looking in Freshman Lab part I (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7628">Looking in Freshman Lab part II (typescript)</a></p>
<p><a href="https://digitalarchives.sjc.edu/items/show/7627">Looking in Freshman Lab part II (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7682" title="Looking in Freshman Lab part III (video)">Looking in Freshman Lab part III (video)</a><br /><br /><br /><br /></p>
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Druecker_Robert_2022-04-13
Tutors
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https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/d04082d50b80ac869f37d0adc6760e0c.pdf
2f1fa11ad333f88b69b8d4bbe9c940bf
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Text
Looking in Freshman Lab – A Path to Experiencing the Blossoming of Things? A Two-part Lecture1
Robert Druecker
The spirit of this lecture—most especially of Part Two—is one of spreading seeds on rich soil.
Part One has three sections. Section One explains the visual thinking of Leonardo da Vinci and
the living movement that Chinese ink painters aimed to infuse into their paintings. Section Two could
be called “Theophrastus’s λόγος pours forth much.” Section Three shows how Goethe’s intuitive looking
discloses the formation and transformation of the leaf. Part Two walks along the path connecting the
approaches of Part One to the blossoming of things.
PART ONE
Section i: Visual Thinking and Living Movement
Before they actually go into the courtyard to look at and sketch magnolia trees, the students
read about a way of looking which they can immediately put into practice. The botanist and philosopher
Agnes Arber introduces them to an approach known as pure morphology. In it, rather than aiming to
analyze the shape or appearance of a plant in terms of function, she looks at form contemplatively, “not
only in itself, but in its nexus of relations.” Looking contemplatively requires engaging “in a “process of
mental visualization,” or “visual thinking,” making use of both “the bodily eye and … the mind's eye.”2
The morphologist must always begin her flights of thought by taking off from, and must always
end them by returning to, “the solid ground” of the visual appearances, thereby “chastening … the mind
through the discipline of the eye.” For there are “many subtleties, seizable by the eye,” that are
routinely eliminated in arriving at the mental concept (Arber, 1964).
Arber points out that this solid ground is not always easily accessible to the eye of the
morphologist. For one’s perception “depends upon preparedness of mind.” She herself had
1
�been familiar with the flowering plant Queen Anne's lace3 (see figure 1) for decades. Then one day she
Figure 1 – Queen Anne’s Lace
finally noticed that “the pattern of its growth is such that the main axis almost invariably terminates in a
reduced inflorescence.”4 Henceforth, whenever she observed the Queen Anne's lace, it “was found to
show this salient feature so strikingly as to leave” her “bewildered and humiliated at having been totally
blind to it year after year” (Arber, 1964).
The morphologist makes use of two media—words and drawings. With respect to the first, her
aim is to describe precisely. That is, she describes what the plant looks like, in a way that allows us to
form a distinct mental image of it. We can put the plant object into various mental categories we have
of known things and of familiar appearances. The better the fit in this placement, “the better described
the object becomes.”5 As a result we are able to read the description as a musical score and play, in our
imaginations, the melody of precisely this plant.
The morphologist’s second medium is visual expression. “‘The pen and the pencil are the two
principal means [she] can use for the depiction of beings’, and ‘of the two … the pencil’” is better able to
depict. Hence, “artistic power and morphological insight” are, in a certain way, correlated. For there is
much in all of a plant’s detailed visible characteristics “which cannot be expressed in words, but … can
2
�be portrayed by the artist.” Our visual thinking can then use these visible traits to interpret the
appearance.6 The preeminent botanist of the 19th century, Julius von Sachs, used to tell “the students in
his laboratory that ‘What one has not drawn, one has not seen’” (Arber, 1964).
Finally, according to Arber, “one of the factors which …. cramps the biologist's visual thinking” is
her tendency to see a thing from a human standpoint, instead of “as it is in and for itself.” Many of the
plant’s subtleties are on offer to the eye-and-mind if it “becomes one with what it sees, thus breaking
down the rigid subject-object antithesis.” Arber is here referring to a mental state in which she is not
conscious of herself as, so to speak, standing over against the plant. A Freshman Lab student said7 that
when we see what we see in our own way, we have a better sense of its individual tendency. Then it’s
as if we were touching it in our drawing. “Then it’s already inside me, in the way a character in a short
story I’m writing is inside me.” We might say that there is an individuality coming from two sources, the
individual thing and the individual looker.
This state of being-one-with is “prior” to the state of duality; it is a “self-identification with the
living thing.” Arber refers here to “Chinese and Japanese artists, who often identify themselves, as it
were, with a bird or a flower, thus revealing its individual character with an intuitive insight” (Arber,
1964). When these artists expressed that distinctiveness on paper, the drawing was said to exhibit
“living movement,”8 that is,
the transfusion into the work of the felt nature of the thing to be painted [or drawn] by the artist. At the moment
of painting, the artist must feel the very nature of the subject, which he transfers into the work, so that it can
affect all who see it with the same sensations he experienced when painting it. So, when painting a tree, feel the
strength of a tree shooting through the branches or, when painting a flower, the grace with which a flower expands
or bows its blossoms.9
In this quotation the repeated mention of feeling refers to a sensing that is both pre-conceptual and
prior to I-versus-object perception.10
Indeed, “the primary quality of all perception” is our feeling of dynamic properties, like “the
aggressive outward pointing of the triangle, the dissonant clash of the hues, the onrush of the
movement.” In applying the phrase living movement to drawings, we may seem to be speaking
3
�metaphorically. If so then the phrase “directed tension” may better capture what the viewer actually
experiences,11 namely, qualities like “compactness, striving, twisting, expanding, yielding,” in all sensory
modalities.12
The students’ looking can become sensitive to such dynamic effects visually received, but perhaps
not consciously registered in the moment. A lab student said that she could sense the energy of the
leaves of a tree, as if they were falling like drops from a fountain.13 They could sense those effects
“prior” to consciously registering the tree as object. When people become habituated to see what is
familiar, they become less spontaneously responsive to directed tensions.14
A good way to become (re-)sensitized to living movement is to practice gesture drawing in the
way outlined by Kimon Nicolaides in The Natural Way to Draw.15 He tells us that we are “to seek the
actual impulse of the gesture” in whatever we are drawing. We are not to confuse this impulse with
emotion. For instance, when we call a certain tree a “weeping willow,” we do not mean that it is sad,
because it “looks like a sad person.” Rather we are, first, responsive to “the shape, direction, and
flexibility of the branches,” which “convey passive hanging.” Subsequently we may notice a similarity
with “the … similar state of mind and body that we call sadness.”16 (See figures 2 and 3)
Figure 2 – Weeping Willow
4
�Figure 3 – White Pine (for contrast)
So, when the students are drawing the magnolias in the courtyard, they bear in mind-and-eye
Nicolaides’s advice that
a tree does not grow from the top down but from the bottom up. Start then at the bottom, and in a loose, easy,
tentative manner allow your pencil to move upward as you can feel that the tree moved up—upward and out
along the branches. Let your pencil follow the sense of movement through to the leaves. Do they spread like
bursts of flame from a skyrocket or do they fall down, dropping like water? As the tree reaches upward, it moves
out from its core into a three-dimensional form. (Nicolaides, p. 30; italics added)
We are to draw rapidly and continuously and to let our pencil swing around the paper, impelled only by
the felt sense of the living movement, without taking our pencil off the paper. “YOU SHOULD DRAW,
NOT WHAT THE THING LOOKS LIKE, NOT EVEN WHAT IT IS, BUT WHAT IT IS DOING. Feel how the figure
lifts or droops—pushes forward here—pulls back there—pushes out here—drops down easily there”
(Nicolaides, pp. 14-15).
While gesture is only one of many aspects of drawing that Nicolaides had his students practice,
if that aspect has not been felt and incorporated into the final drawing, the latter will lack aliveness.
Thus, in addition to conveying, in their drawings and descriptions, precisely how the magnolia appears
to their perception, the students express the active impulse which they felt “prior” to their objectperceptions.
Here are two examples of gesture drawings of a life model by his students (see figure 4).
5
�Figure 4 – Student Gesture Drawings
Section ii: Theophrastus’s λόγος pours forth much
Having begun, in the first class, by attending to looking—to our state of mind as looker and to
our way of looking, we now, with Theophrastus’s Inquiry Concerning Plants, turn to the looked-at.
Instead of looking contemplatively with an open gaze and with sensitivity to living movement, we are
invited to attend to certain determinate features of plants, to their differences with respect to a) parts,
to b) ways of responding to changes in their surroundings, to c) ways of coming-into-being, and to d)
ways of life (i.1).
Because we spend only five classes on plants, our reading centers on a) the parts of plants. The
fact that in order actually to see evidence relevant to the other three we’d need to be observing the
plants over a longer period of time raises a question for the students about how well they could come to
know a tree or a plant by looking closely and drawing over a short two-week period. One17 suggested
that our task is to tell the story of the tree, a story that would be composed of sub-stories of its various
parts, which were like characters in a novel. Yet in the lab we have only a short time to become
acquainted with it and with its characters.
Another student suggested that you can’t have a clear sense of how the tree trees, unless you
study the parts it uses to tree. A second said that looking very attentively at some one part might, in a
way, convey a sense of the whole. A third18 proposed that the key might lie in attaining a certain level of
6
�intimacy with the tree in her sessions of looking and drawing. It may have been helpful that the first
drawing exercise19 asked them to experience their drawing of the plant part as if it were a chance,
intimate, personal chat with a neighbor they hadn’t really known before. After it they’d have a deeper
sense for what that neighbor is like. One student20 said that she could later reawaken that moment of
close contact with the tree when she came to draw the whole.
Theophrastus points out that several factors make it difficult to determine precisely what is to
count as a part and what not. We notice that some portions of a plant, like flowers and leaves last only
to the end of the year, and, in addition, that new sprouts21 keep springing up. Thus, if these are included
as parts, the number of parts would be indeterminate. But we must include them since it is “when
[plants] are sprouting and blooming and bearing fruit that they not only seem but also are more
beautiful and more complete (τελότερος)” (i.2). They are complete in the sense that they are at their
peak, or end-state (τέλος).
It is striking that plants are at their high point when they are in motion, becoming more
themselves, growing twigs, leaves, blossoms, or fruit. For animals, as we shall see, differ fundamentally
from plants in that they are at their high point when they are keeping themselves—that is, their parts
and the capabilities of those parts to perform particular actions—at the very point at which they have
already arrived, that is, precisely when they are not still moving toward their end-state.
This difference should serve as a warning to us—in dealing with the difficulty of delimiting parts
and in viewing plants in general—not unthinkingly to rely on animal analogues. For instance, while it is
true that leaves are like certain animal parts, such as, horns, feathers, hair, in being cast off, on the other
hand, only plants, and not animals, are “capable of sprouting (βλαστητικόν) everywhere” (i.3-4). So,
too, the fact that during growth animals’ limbs emerge only in determinate places and that they have
limits of growth and maintain those limits means that we must be careful in speaking of the “limbs” of
trees.
7
�Theophrastus makes recommendations about what to focus on when we are looking at the
external parts of plants, that is, when we are doing morphology and inquiring about “μορφή as a
whole.” In spite of the fundamental difference, just mentioned, between plants and animals, he
recommends that in addition to noting which parts belong to all plants and which are proper only to one
or to several and which parts are similar to which other parts, he tells us to take note of which plant
parts have analogues among animals (i.4-5). The reasons for his last recommendation are: first, animals
are “more complete” than plants, in the sense that their activity is complete, and not on the way toward
becoming complete. The sprouting of plants, on the other hand, “seems to be a certain activity but an
incomplete one (ἀτελὴς)” (Aristotle, Physics 201b32)22; second, that we are more familiar with animals
(ii.3-5), partly because being animals ourselves we know them “from the inside.”
So, we can sometimes recognize a part of a plant more easily by seeing its similarity to a more
complete or more familiar part of an animal. We may even learn from looking for an animal analogue
and not finding one. For instance, a mouth and intestines belong to animals generally. But when we
seek for an analogue in the case of plants, we realize that there is none to be found. Then we
understand that, compared with animals, the plant is so “diverse and elaborate (ποικίλον)” that it “is
hard to speak about as a whole” (i.10-11).
Theophrastus next tells us what we are aiming at in noting differences among the parts of
plants. We look for them because “from them, in the case of each plant, the morphe as a whole
becomes altogether manifest.” In general there are three or four such differences: plants may have
some parts, such as leaves, but not others, like fruit; their parts may be dissimilar in color, in figure, in
proximity, in texture, and so on, or may be unequal in size; and they may be arranged in a different
order, as when the fruit is below rather than above the leaves (i.6-8).
Theophrastus then says that after enumerating the differences among the parts we are to focus
on each part by itself. We should begin by attending to those parts that are “greatest and common to
8
�most” plants, even though not all plants have all of them. The four parts to study first are roots,
stems—or, in the case of trees, trunks—branches, and twigs, that is, shoots coming from branches (i.911).
In addition to these four parts, there are other sorts of parts—first, parts of these four, such as
bark, wood, and core; second, impermanent parts, like flowers and leaves, mentioned above; and,
finally, things like sap, fiber, veins, and flesh which are “prior” to the others and which are common to
all the parts. Theophrastus says that these last are the initiator-rulers (ἀρχαί) of the other parts, which
come forth and appear to us as we draw. “Indeed, it is rather the case that [the plant’s] way of being
what it is (οὐσία) and [its] whole origination (of sprouts) (ϕύσις) is in these” latter parts (i.11-12; ii.1).
Perhaps they are the initial sources of “the impulse of the gesture” that Nicolaides asks us to seek.
In Theophrastus’s view we do well to begin our lab by observing the magnolia trees in the
courtyard. For the four parts with which we ought to begin our observation happen to “belong most of
all to trees, and the division into parts is more proper to them” than to any other plant. Moreover, the
variety of differences with respect to parts that we notice among trees will “indicate clearly” the
differences of the parts “of each of the other plants as well.” We’ll be able to discern differences in
color, in figure, in proximity, or in order of arrangement most easily in trees. So, it is a good approach to
refer the other plants to trees (i.11-12; ii.1; cf. i.6-8).
From another point of view, too, we do well by studying the magnolias first. For our
understanding becomes clearer if we divide according to the looks (εἴδη) of the plants. Most plants
exhibit one of the following four looks—tree, shrub, small shrub, or herb (iii.1). It is true that some
plants change their look from one to another of these, as well as that others “become quite different
and depart from their [mode of] origination (of sprouts).” Nevertheless, provided we don’t become
overly precise in marking the looks off from one another, we ought to divide with respect to the four
just mentioned. The reason is that something in their origination of sprouts is common to all four of
9
�them. So, it is reasonable to think that what’s responsible for their differences is also common to all of
them (iii.2, 5, 6).
Theophrastus makes the following more general observation: “The plant is a thing pouring forth
much (πολύχουν)” (i.10; cp. ii.3). According to our manual the progressive participle, πολύχουν,
emphasizes that a plant’s sprouting or blooming is “never finished, unlike the corresponding activity of
animals.” It seems that the “much” of a plant that is poured forth is or becomes its various parts.
Perhaps, Theophrastus’s idea is that if our looking were not oriented by the many helpful distinctions he
makes, we’d look at a plant and have only a global sense of the energy of water being shot up by a
fountain and then falling down.
With his guidance, though, and his foregrounding of differences of parts and of sprouting, or
budding, blooming and bearing fruit, what we see may be likened to a fountain having different-sized
and -shaped openings, putting forth water to different heights at different pressures. The water from
various openings may come forth in different colors. From some the water may gradually shoot higher
and higher; from others it may suddenly turn off. We’d miss much of this variety if we had not read
Theophrastus.
As we attempt to follow Theophrastus, how does our observation of the magnolias differ from
what it was like on the first day? Then, it seemed, we were invited, first, to begin by being open to
whatever came forth spontaneously from our sensory experiencing. Second, we were also initiated into
a state of mind prior to words, in which we aimed to sense and to express the plant’s doing; we avoided
slipping into the attitude of being a mere observer, over-against objects.
Theophrastus’s λόγος may have both benefits and drawbacks for us. On the one hand, it offers
us new perspectives. When we view plants from those standpoints, we find that new aspects disclose
themselves to our gaze. Instead of puzzling over some feature of the plant, we may now feel, “That’s it.
I’ve got it.” Or his λόγος may open our eyes to a part that is right in front of us, so that we don’t have to
10
�wait fifty years, as Arber did, before seeing it. Or, again, the disconnected pieces that we are looking at
may suddenly come together, like the pieces of a jigsaw puzzle. Moreover, additional layers of meaning
are added when we see the likeness of a tree-part to a more familiar and determinate animal-part.
Finally, our attending to similarities and differences between parts embeds them in a web of
relationships. In ways like these our tree comes to make more sense to us. This additional sense may,
in turn, lead us to say something new about it; and that may lead us to a fresh seeing, and so on.
On the other hand, the direction that Theophrastus’s λόγος gives to our gaze may come to
prescribe what we look for in a way that closes us off from other possibilities and more fresh
discoveries. We might “lock onto” the distinctions we’ve learned from Theophrastus in a way that our
“tracking” of them prevents us from noticing other “targets” on our radar screen. There is also a risk of
not noticing the impulses of living movement, which we had sensed on the first day. We might become
like someone who only notices and responds to the meaning of what a friend says, and is oblivious to
the speaker’s tone of voice, physiognomy, and gestural accompaniments. In such an event our drawings
and descriptions of parts and of their interrelationships would seem “dried up,” withered, lacking
aliveness.23
Both approaches, the impulse-approach and the logos-approach, go beyond ordinary
experiencing and awaken or enliven us to what is new. The aliveness of the first lies in our sensing the
impulse of the tree’s gesture, in our feeling “the strength of a tree, shooting through the branches.”
What is enlivening about the second is illustrated when the vague becomes sharp, as in “Ah, so that’s
it!” or when isolated fragments suddenly fit together into a whole. It’s like what occurs when we’ve
been observing a face and then “suddenly notice its similarity to another”; a new aspect of the face
lights up (Aufleuchten) for us in an instant.24 Experiencing either of these two kinds of aliveness feels
like a bud’s bursting into flower.
We die to either approach to aliveness when we become content to drift smoothly, carried
11
�along by familiar concepts—interrupted neither by a sudden sense of striving or twisting nor by an
unexpected connection between familiar things popping into mind. In the same way forming an opinion
(δοξάζειν)25 is enlivening; holding onto an opinion (δόξα) is not (cf. Theat. 189e-190a).
Moreover, both approaches to aliveness are characterized by their temporal priority to the
everyday, but in different senses. The priority exemplified by the impulse-approach is that of the split
second when a tree is just coming into focus but I have not yet “registered” it as a tree.26 One can train
oneself to stay in touch with that pre-conceptual awareness beyond the first fraction of a second. In the
logos-approach the priority is usually of very long duration. It has taken centuries for the language to
acquire the relevant individual meanings and the web of family relationships (συγγενοῦς) among them.
The experience of drawing them up now has the feel of “recollecting” (ἀναμνησθῆναι) a name you
“already knew before” but had long ago forgotten (Meno, 81cd).
Ideally we could experience the benefits of both approaches, while avoiding the downside of
either. As a student27 suggested, we could aim to alternate back and forth between them: Now we look
“through” the Theophrastian λόγος; now we sense the leaves spreading like bursts of flame or dripping
like water. Our encounter with the unique individuality of the plant incites us to endeavor to grasp and
articulate it on the level of logos. We seek to understand it through moving back and forth between
sensing the particular and comprehending it together with others and distinguishing it from others.
It might be possible, though, to be, somehow, experiencing in both ways together at the same
time and yet not quite in either of them.28 The Mustard Seed Garden Manual of Painting hints at this
possibility in a colorful formulation: We are inspired by the madness of a wild dog (kuang),29 and
simultaneously our mind is opened wide (大) to the oneness (一) of the Heaven (tiān).30
Finally, before leaving Theophrastus let us revisit a word, ϕύσις, that occurs right at the
beginning of his treatise (i.1), and which we have been translating as origination (of sprouts). The
transitive verb from which it is derived, “ϕύω,” means: I. bring or put forth (as, leaves or shoots);
12
�engender, or generate (as, offspring); (in reference to parts of oneself) grow (as, a beard); II. (in present,
seemingly intransitive) put forth shoots. The middle voice φύομαι means grow, wax, spring up or forth,
especially of the vegetable world.31 According to Theophrastus our task includes grasping the plant’s
mode of origination of sprouts, including buds and shoots—stems and their appendages, leaves,
flowers, fruits.
Aristotle’s account of ϕύσις in the Physics (192b12ff)32 will help us to refine our thinking about
it. Animals as well as plants have ϕύσις. Both—primordially (πρώτως)—have within themselves the
originator of and ruler over (ἀρχὴν) their moving (κινεῖσθαι) and their remaining-at-rest (ἠρεμεῖν). This
inner originator-ruler may be understood, Aristotle says, as a switch-over impulse (ὁρμὴν33 …
μεταβολῆς; perhaps, Umschalt-Impuls), an impulse that originates a “shifting of gears” from motion
(κινήσεως) to stand-still (στάσεως) or vice versa.
It is important to note that—as evidenced by the verb μεταβάλλω,34 from which μεταβολή
(switch-over) is derived—the switch-over at issue here has two features, which distinguish it from a
process or motion. First, it is a shift between alternative positions, as in turning the earth upside down
or turning about to face the rear. Second, it is quick and sudden, as if it took no time at all and as if it
were not gradually led up to by what preceded it. So, ϕύσις here is the source not of a process or
motion but of an instantaneous shift or change-over, as in flipping a light switch on or off.
This impulse may be what Nicolaides proposed that the draftsperson aim to sense and to
express through the body-mind’s intuitive sensing: “seek the actual impulse of the gesture,” whether of
the model’s pose or of the magnolia. If we looked more closely, it might even be possible to detect a
sequence of switch-overs in what had appeared to be a smooth growth process. In that case growing
would turn out to be a series of tiny growth-spurts, with pauses in between.35
In summary, the plant’s ϕύσις impels it to change over instantly from inactivity at a particular
place and time to putting forth (ϕύειν) leaves, shoots, flowers, or fruit, or, conversely, from sprouting,
13
�blossoming, fruiting to inactivity there and then. The plant’s individual acts of putting-forth, its ϕύειν,
then, are manifestations of the inner originator-ruler. It is the latter that is the plant’s ϕύσις.
Let’s now skip a few weeks ahead in the lab to the activities of unicellular animals, in order to
see how the switch-over impulse might show up in them, too. We study animals like amoebae with
some help from the theoretical biologist Jakob von Uexküll. We notice that when faced with tasks like
escaping a predator, feeding on a prey, or digesting what it has consumed, the amoebae’s protoplasm
has the power, in each situation, to form the structure the animal needs in order to perform the given
task and, afterwards, to un-form that structure again.
For instance, in eating and digesting, a compartment enclosed by a membrane, known as "a
vacuole … first becomes the mouth, then the stomach, then the intestine, and finally the anus.” “We see
the organs appear one after the other in a fixed temporal sequence; and each [organ], when its
performance is finished, disappears again.” Here the immediate “effect of the impulse” (Impulsfolge) of
the switch-over is to form the first organ the amoeba needs in order to exercise that organ’s function.36
The next switch-over is to exercise that function. Then it forms the second organ needed, and so on, in a
sequence of bursts of formation and un-formation or of action and cessation of action. Each forming or
using of an organ is, in one way, analogous to an act of sprouting by the magnolia.
We might say of either the plant or the amoeba that what it has at the ready is a complex power
with respect to its actions. This power enables it to display, in the appropriate ways as required from
moment to moment, the relevant features of the complex activity which comprises its way of being
what it is (οὐσία).
However, the plants’ part-making origination of sprouts and the amoebae’s organ-forming
origination of metaphorical sprouts also differ significantly. A plant’s switch-over to budding, blooming,
or fruiting is an initiation of a production. What it is producing is a part of itself, which will endure for at
14
�least long enough to become an object of study for Theophrastus. As producing itself, a plant’s switchovers are engaged in its continual process of coming-to-be.
In the case of the amoeba, the sequence of its “sproutings,” that is, its switch-overs to shaping,
to using, and to un-shaping organs, leaves it right where it began. That is, nothing like a sprout, twig, or
flower, or additional length persists; it comes to have no new part or augmented part. It is now what it
has been. It was already in a complete state, and its turnings-on and -off have served to maintain itself
in that same state of completeness. They are change-overs to or from actions, which hold, or keep, it in
its pre-existing state of completeness.
We might compare the plant, the amoeba, and the adult multi-cellular animal as follows. “The
urge towards self-maintenance … in the flowering plants … is expressed in repetitive branching.”37 The
branches that the plant puts forth become co-constitutive of it, by accretion. So, in one sense it remains
the same plant; in another sense it is always impelling itself to switch over to motion and to put forth
another sprout, thus becoming different. The impulse in the amoeba expresses itself in a temporary
“branching” and “unbranching,” so that it does not become altered or increased relative to what it was.
The adult multicellular animal’s maintaining itself leads it merely to move its “branches” around relative
to itself.
As we later read in the lab excerpt from Aristotle’s On the Soul (II.1), there are, in the case of
adult animals, two sorts of holding themselves (-έχεια) in their end-state of completeness (ἐντελ-). The
first one is an activity of keeping themselves in an active state of readiness, so that they are able to turn
on or off, at a moment’s notice, any one or several of their activities of the second sort. Moreover, each
of those latter activities—like sensing and chasing prey; sensing and fleeing from predators, etc.—makes
its contribution to maintaining the animal in its adult condition. In these examples they provide needed
nourishment and offer escape from death at the hands of predators.
So, the amoeba stays at its peak because it preserves its power to turn on and off, as needed, its
15
�working at its various jobs of self-maintenance, a working that includes a “just-in-time” production of
the tool needed to work at the respective job. As was just illustrated, the first and the second sorts of
staying-itself are each a being-at-work, or activity, or a set of several of them. This combining of action
and self-maintenance is nicely captured in Joe Sachs’s translation of “ἐντελέχεια” as being-at-workstaying-complete.38
What is true of amoebae also holds for adult multicellular animals, with the one major
difference that the organs of the latter are persisting parts of the adult animal. Generally there is not
even a momentary making or unmaking of an organ. The existing organs are simply switched over from
performing one action to performing another or from action to rest and back or into simultaneous
action—as in lying on the ground, then noticing and following with the eyes a potential prey moving
across the field, and then rising and running in pursuit. We might say that the animal had been “idling”39
and had then shifted into first “gear,” then into second, third, or fourth “gears.” The animal’s watching
and running are the analogues of the plant’s sprouting and flowering.
Section iii: Goethe’s Intuitive Looking and the Transformation of the Leaf
Our next author, Goethe, seeks to combine in a fresh way the impulse- and logos-approaches
that we discerned in the readings and practica of the first three laboratories. As suggested by the title
of his major work on plants, The Metamorphosis of Plants,40 he reconceptualizes Arber’s pure
morphology in two-steps.
First, as Goethe explains in introducing his aim,41 morphology is literally an account (λόγος) of a
structured shape, or form (μορφή; Gestalt), which, in assuming “that a connected thing is … fixed,”
abstracts “from what is mobile.” But when he gazes intuitively at the shapes of plants and their parts,
Goethe sees that “nothing in them is … at rest …—everything is fluctuating in continual motion.” What
he actually experiences as the referent of the expression “μορφή” is something “that is held steady only
16
�for an instant” in his experience. So, he replaces “Gestalt,” or “μορφή” with “formation” (Bildung),
which would be “μόρφωσις” in Greek. The word “formation” can refer to “both what has been brought
forth and what is being brought forth.” If he had stopped here, he would have written a work of
morphosis-ology, The Morphosis of Plants, illustrating the impulse-approach.
However, in Goethe’s intuitive vision “what has been formed is immediately again being
transformed,” that is, metamorphosized. What does this mean? In gazing intuitively at a tree or at
another plant, Goethe sees that while it “really does appear to us as an individual,” it actually “consists
of nothing but particular single things.” Furthermore, these single things: i) are similar (ähnlich) in
appearance, ii) are identical (gleich) in Idea (Idee), and iii) are alike (gleichen) to the whole plant or tree
(Aim 55-57; italics added).
Goethe’s intuitive gazing might be compared to viewing a ballet from three different viewpoints.
First, when I focus on several individual dancers, I notice that their movements, when not identical, are
similar to each other. Second, I am able to intuit in each of them the source (Idee) from which the
whole ballet first sprang up in the mind of the choreographer. Third, when I step back and take in the
flow of the whole dance, I can see how the movements of the individual dancers are like the larger
movement of the entire ballet. In viewing the ballet of the plant in this way, Goethe claims to be
recognizing “living formations as such,” that is, as alive and as moving on to their next formation. He is
also grasping the “outward, visible, tangible” dancers “in interrelation,” that is, as forming the ballet as a
whole. And he is shedding “light on these [dancers] as hints of the interior” (Aim, 55) Idea, whence the
ballet originated and which it expresses.
The name Goethe chose for that which stands for what is the same in Idea and tendency was
“leaf.” Here is a way to experience, right now, what he might have had in mind. Look at the sketch of
the two leaves below (figure 5) for a short period of time, with the question in mind, What are some
possible relationships between them?
17
�Figure 5 – Two Leaves
Now, after that pause, look at the next sketch (figure 6).
Figure 6 – Nine Leaves
18
�It shows leaves taken from the common buttercup, ordered from the bottom of stem, at the lowest left,
to top of the stem, displayed at the bottom right.42 Looking at the two leaves from the first figure, we
can intuit little kinship between them. When we look, in succession, at the nine formations in the
second figure, we see them as if "held steady for only an instant,” in their temporal sequence. The two
leaves from the first figure now make sense to us as successive moves in a dance of development.
Goethe has, in a way, developed into “moving pictures,” that is, into movies projected in the
imagination, Theophrastus’s image of “pouring forth much” and his accounts of differences and
similarities of parts. That is why Goethe says that “if we wish to look at nature in a way that is alive and
intuitive, we ourselves must remain as mobile and flexible as nature and follow the example she gives”
(Aim, 56). Through the mobile imagining of such a film, he is able to “make intuitive (anschaulich) to
us,” the “inner identity of the different plant parts,” “despite the greatest deviation of their outer form”
(## 60, 67). Thereby we may accompany, in our imaginations, “the outer form of the plant through all
its transformations,” while, at the same time, keeping a mental gaze on the inner identity—as we have
just experienced when we looked at the wheel of the nine schematic shapes of the buttercup leaf.
Viewed from a different perspective, Goethe’s emphasis on an underlying sameness throughout
the sequence of appearances might lead us to see that, in his moving pictures, the Same, while
remaining itself, is generating likenesses or images (εἰκόνες) of itself and of each other. Φύσις, as the
source of formation and transformation, could then be said itself to have “within itself the possibility of
acting as the source of repetition.” It would “have a primal character of ‘image-ability,’ a character
which makes possible all ‘difference’”—in the sequence of appearances as the plant is growing—as well
as making possible “all ‘recognition’”—of similarity, as in the above example of the nine leaves.43
Goethe’s view of the leaf as playing the key role was later revised.44 The shoot, or the unity of
the stem-and-leaf complex, came to be seen as the source of the plant’s dance. Later botanists thought
it obvious that “each branch shoot echoes the characters of the parent shoot.”45 The lab students, too,
19
�seemed to see the centrality of the shoot, two classes before they had even read Goethe. One46
proposed that each part of the tree began by coming forth as a shoot and then differentiating itself and
distinguishing itself as it grew. For another47 the shoot was like the tree or plant coming forth to say,
“Here I am,” making its identity known.
In the Metamorphosis Goethe shows that the flowering plant continually moves through the
following six-step cycle: expanding “from the seed to the fullest development of the stem leaf”;
contracting to the sepals of the calyx; expanding to the petals of the corolla; contracting to the style and
stamen; expanding to the fruit; and, finally, returning to seed by a contraction (#73). In effect the
sequence is bud - expansive shooting forth – bud – contractive shooting forth – bud - expansive shooting
forth – bud – contractive shooting forth, etc. The “motion” is not circular but rather like a graph of
waves moving around a circle, contracting and expanding alternately.
Let’s look at the second of the six transitions. When it occurs rapidly: “the stem, suddenly
lengthened and refined, shoots up from the node of the last fully developed [stem] leaf and collects
several leaves around the axis at its end.” Goethe suggests that, in examples like figures 7 and 8,48
Figure 7 - Cornflower with urn-shaped calyx beneath corolla
20
�Figure 8 - ‘Thai Delight’ Bougainvillea with leaflike bracts collected around the tubular flowers
since the stem leaves “still fully retain their shape, we can rely on the mere appearance.” For “we see
unaltered stem leaves moved closer together, in a kind of calyx right under the flower.” Goethe’s
intuitive looking discloses that the “the same organs which so far can be seen developed as stem
leaves,” now “often in a very altered shape,” are “collected around a common center,” as the leaves of a
calyx (## 31, 32, 34; italics added).
If the transition to the calyx should occur slowly, “as the stem leaves come together gradually,
alter, and gently steal over, as it were, into the calyx,” as in figure 9. Or the edges of the clustered
Figure 9 – Stem leaves and calyx of the sunflower
21
�and modified stem leaves may grow together, making them even less recognizable, as in figure 10.49
Figure 10 – Calyx of pot marigold
Goethe’s conclusion from such observations is that in forming the calyx, nature—instead of producing
several “leaves and nodes successively and at a distance from one another”—joins them “together
around a central point” (## 35, 36, 38).
Following this contraction of leaves in the formation of a calyx, the next transition is produced
by an expansion of the leaves, that is, the sepals, in the formation of the petals of a corolla. However,
the petals are so different in appearance from the sepals that we couldn’t recognize that they originated
from the sepals, “were we not able to eavesdrop on nature in several abnormal cases.” Here are three
of the examples of eavesdropping which Goethe mentions. In the first (figure 11) the color of some of
Figure 11 – Calyx and corolla of coreopsis displaying both green and more refined golden sepals
22
�the sepals is not green, as usual, but anticipates the gold of the petals. Sometimes (figure 12) even
Figure 12: Bee balm showing advancing coloration in stem leaves and a second flower emerging from within the first.
the stem leaves already show some of the purple of the petals. Finally, we can see “that stem leaves
transition into petals” in the abnormal case of a tulip (figure 13)50 where half of one petal is green
Figure 13 – Transition from stem leaf to petal in the tulip
and still attached to the stem, like a sepal, and the other half is colored like the other petals and raised
up as part of the corolla. It looks as though nature had skipped over the calyx in rushing ahead to the
corolla (## 40-44).
The six steps in the circular wave motion mentioned above are the steps in “progressive
metamorphosis,” which, “through transformation of one shape into another, climbs up, as it were, on a
23
�mental ladder, to that pinnacle of nature, propagation through two genders” (#6). The contraction in the sixth
step of the spiral staircase Goethe sees in his mind’s eye as “a mental junction (geistige Anastomosis)”
of pollen and ovule. He believes that this mental junction has, “at least for an instant, … brought the
concepts of growth and reproduction closer together” (#63). As he puts it more fully later:
as the plant … sprouts, … a propagation is taking place, but a propagation that differs from that of flower and
fruit, which takes place all at once, in that it is successive and appears as a sequence of individual
developments. This sprouting force that expresses itself gradually is in the most precise way akin to the force
that suddenly develops a large propagation (#113).
Hence, Goethe can call “sprouting a successive propagation, but flowering and fruiting a simultaneous
propagation” (#114). In the case of both sorts of propagation, there is “the development of innumerable
identical individuals,” whether from a bud or from a mother plant (Aim 57). So, we can view “flowers
that develop from the buds … as whole plants that are standing on the parental plant, just as the
[parental plant] is standing on the earth” (#95).
24
�PART II
Section i: GOETHE AND CHINESE PAINTING
Goethe’s constant endeavor to “make intuitive to us” the “inner identity of the different plant
parts,” in spite of their great outer diversity, helps us to “derive” all the transformations of “the outer
form of the plant” (# 84). It may be that in performing this derivation we become, as it were, identified
with the origination of the shooting-forth, so that in our imagination we pulsate rhythmically with it, in
its switch-overs from ON to OFF and back.
For Goethe making intuitive the inner identity and deriving the appearances requires a training in
a new way of looking and in a new way of using “the power of imagination and the understanding.” It
gradually will become easy for us to look at the appearances next to “each other in both a forward and a
backward direction.” We’ll be able to “say that a stamen is a contracted petal or, with equal
justification, that a petal is a stamen in a state of expansion; that a sepal is a contracted stem leaf … or
that a stem leaf is a sepal expanded” (#120)—as depicted here in Goethe’s drawing (figure 14).51
Figure 14 – Successive transformation of petal into stamen in white water lily
After the Metamorphosis we read some reflections by Goethe on his way of looking.52 Some
observers of nature, on the basis of isolated, single experiences, try to come up with an idea, hypothesis,
or theory (Experiment, 16). To them he says that while experiences may appear isolated, in reality they
interconnect both with each other and with the whole. In order to allow the interconnection to appear,
25
�we must multiply and diversify the initial experience, by arranging for a series of closely related
experiences. Then we can survey and see them all as revealing “a higher sort” of experience. What we
then see is, in reality “only a single experience” viewed from many different viewpoints or composed of
many facets (Experiment, 17-18). Instead of thinking of a box of slides as separate photos, he sees them
the “frames” of a film, and, hence, as presenting a single, temporally spread-out entity.
Goethe calls the object of this deeper view “the pure phenomenon.” When he looks at a
sequence of experiences in this way, what seemed to be wavering in the isolated experiences becomes
stable. What appeared merely accidental is eliminated, and what looked too complicated becomes
untangled (Experience, 24-25).
Goethe uses the word “idea” in two different ways. On the one hand, a scientist may think up
and formulate an idea in advance, and state it as an hypothesis to be confirmed by subsequent
experiments. On the other hand, Goethe himself holds his mind and his senses in a state of
“attunement” and “attentiveness as sharp as it is calm.” He is then able to see the pure phenomenon
displaying “itself in a continuous sequence of appearances.” He experiences it as a living idea. As
Goethe puts it—in language reminiscent of Nicolaides’s account of drawing a tree—he is experiencing
nature herself “as alive and active, striving from the whole to the parts” (Experience, 24; Fortunate, 54142).
It was in this way that Goethe experienced the idea of the metamorphosis of plants, blossoming
in himself (Significant, 39). Once he described the metamorphosis of plants to his friend, Schiller, and
made a schematic sketch of it. When Schiller responded, “That is not an experience. That is an idea,”
Goethe was taken aback and somewhat annoyed and said, “Then I may rejoice that I have ideas without
knowing it, and can even see them with my own eyes" (Fortunate, 540-41).”
This mental participating in nature’s productions is what he has been calling “intuitive looking”
(Power, 31). In it our “power of thinking is active in an objective way” (Significant, 37). Goethe
26
�understands objective thinking to mean that when he looks at a plant in his mental “film” what he is
looking at then “belongs to” him, so that he can produce it again in his mind (Polarity, 863). Such
belonging echoes what my student said, in the first class, about the tree being inside her, in the way a
character in a short story she’s writing is inside her. Goethe can generate the appearances “under
thousands of circumstances, their uniformity and mutability [being] looked at with an intuitive gaze …;
their determinateness … recognized and determined again by the human mind” (Experience, 25).
This objective thinking is the ultimate ground of Goethe’s ability to derive plant forms. It is “a
pregnant point from which much may be derived” (Significant, 40). Perhaps in looking at his mental film
of the appearances of a plant, Goethe participates in its unique switch-over impulse, in such a way that
he can generate those appearances and their modifications in his mind. The pregnant point of objective
thinking would be the point where the aliveness of the bud’s bursting-into-flower meets and is one with
the aliveness of our sensing the flower’s impulse (impulse-approach). Or, since objective thinking is not
limited to the study of plants, the pregnant point could also be where the lighting-up of one face’s
similarity to another meets and is one with our noticing the new aspect of the face (logos-approach).
What has Goethe shown us about how we can look in a different way? First, he emphasizes
that we need to be focused on two aspects of a plant—on its continual shifts over time and on the
interconnectedness of its parts. Second, by arranging our experiences of the plant in the proper
sequence, we can see the pure phenomenon revealing itself in and through them. Third, if we become
objectively one with the pure phenomenon, our mind will derive countless varieties of the plant’s
appearances.
In this way of looking, we hold ourselves back from imposing our preconceptions and from
projecting our hypotheses. We are participating mentally, in a way, in the plant’s origination of sprouts.
We are experiencing ϕύσις “as alive and active.” Goethe’s “pregnant point” is the source of
experiencing the immediate trans-formation of what has just been formed. Nicolaides’s advice, “to seek
27
�the actual impulse” of the tree, which appears to be static, changes the drawer’s looking into this
Goethean mode of “objective thinking.” In what is motionless to the ordinary gaze, Nicolaides has us
sense a lifting or drooping, a pushing or pulling, just as Goethe invites us to see an expansion or
contraction—what was called “living movement” at the beginning of Part One of the lecture.
“Living movement” is a translation of the second half of the First Canon of Chinese painting,
which, according to Sze’s The Tao of Painting, reads as follows: “Circulation of Ch’i makes living
movement.”53 In a later version it was changed slightly to: “Rhythmic reverberation of ch’i makes living
movement.”54 This canon of painting may be interpreted more broadly as a standard of what
constitutes alive drawing, or, more generally, alive looking, seeing, and thinking. Of the two parts of the
First Canon, the key is the first: “circulation of the Ch’i.” For the alive moving follows from it. “This
concept of the Ch’i in action governs all the principles and every work of art, down to each brushstroke.”
While the Ch’i is what brings forth and “permeates life and its movement,” it is not to be
identified with that life and movement; they emerge from it. In the same way, when the wind in
“stirring the leaves produces a rustle,” the rustling is of the foliage, not of the wind. Thus, living
movement is the rustling of the things, the stirring of the forms in the painting, and the motions of the
painter’s hand-and-arm (cp. Sze, 42, 54-55), all of which are brought forth and permeated by the
circulation or reverberation of the Ch’i (Sze, 52)
Chinese painters aimed to render the ch’i that resides in each form (Sze, 34). The forms of a
painting would be lifeless if they did not manifest something of that ch’i, which is moving and
transforming the depicted things. The painters recognized that “when one succeeds in conveying the
ch’i of each form, the result is an expression of the Ch’i that pervades the universe” (Sze, 35). In our
terms, to produce such a result, the painter must penetrate into the secret of the inner switch-over
impulse.
In Goethe’s formulation of such penetration, we transcend mere looking-at and pass over into
28
�intuitive looking, participating in nature’s productions. Intuitive looking allowed Goethe to see nature
herself “as alive and active,” as in the metamorphosis of plants. In the same way “Ch’i … has to be
grasped through intuition,” that is, by looking “in a certain way” (Sze, 52-53), so as to call forth the
receptivity and responsiveness of the heart-mind (hsin; Sze 35).
For Goethe the metamorphosis of plants was a succession of alternating expansions and
contractions. In Chinese painting what is important in nature’s perpetual motion is the constant
interaction of “the rising, floating, expanding, and active qualities of the Ch’i,” known as yáng, and “the
sinking, settling, shrinking, and passive qualities,” known as yīn. The painter sees “the cycle of growth,
bloom, and decay of a flower” as illustrating the operation of the yīn and yáng, so that the resulting
“painting of a flower at a given stage of development depicts either a yang or yin aspect of it” (Sze, 41,
54-55, 41). Goethe seems to have a more regular sense of the alternation of yang and yīn. Perhaps he
would prefer the second version of the First Canon, which speaks of rhythmic reverberation of ch’i.
Here is a passage—echoing Goethe’s account of his intuitive looking—that describes the
Chinese painter’s participation in one of nature’s formations:
In observing the way a bud opens into full flower, eventually to shed its petals, and the conditions under which
this process takes place, the painter is exploring an aspect of [ϕύσις]. He is able to understand [ϕύσις] when he
is thoroughly familiar with every stage of the process, can see it [namely, the bud opening, then shedding petals,
etc.] at each stage of the process and as a whole as analogous to other manifestations of the way of [ϕύσις]
around him, including himself, and can through his heart and mind55 become aware of the same pattern of
movement beyond his own limited horizon, on the scale … of the whole universe (Sze, 41).56
In this description one has only to replace “painter” with “observer of nature,” in order to have a good
account of Goethe’s “objective thinking.” In the painter’s way of observing, too, we are “accustoming
ourselves to hold the appearances against each other in both a forward and a backward direction.”
Moreover, just as the painter’s seeing the way of ϕύσις includes seeing it in himself and in the
whole universe, so, too, was Goethe himself transformed by his observation of nature: “[I and my]
brothers and sisters … think: ‘in every place/ We are in the Interior [of Nature].’”
29
�To myself a thousand times I say:
“All things she gives, gladly and lavishly;
Nature has neither kernel nor shell,
She is everything at once.
Examine chiefly only yourself,
Whether you are kernel or shell.” (Allerdings)
When we draw the impulse or when we look intuitively, how are we experiencing in a way
different from our everyday experiencing? When we participate in the formations of ϕύσις, as we draw,
look, see, or think, how are we experiencing?
Drawing-looking-describing is an action that aims to manifest outwardly what is appearing,
precisely in the way it is appearing to us. Taking our cue from Arber and Nicolaides, from Goethe and
the Chinese painters, we might compare ourselves to a musical instrument on which the plant is playing
its melody, when we are drawing, painting, or describing it. If we are in a state of calm attention and
flexible responsiveness to the plant’s “playing,” we are a well-tuned instrument. Our drawing or our
precise description is then the melody that the plant is playing.
Section ii: ΦϓΣΙΣ AND BEING
Drawings and descriptions aren’t the only kinds of melodies that may come forth from us in
response to the appearances of a plant. We might, instead, come up with a metaphor or write a poem.
The conclusion to this lecture borrows from the philosopher Paul Ricoeur’s reflections on the way of
experiencing that is proper to metaphorizing. His ideas, which are in part inspired by Aristotle, will
deepen our understanding of Goethe’s and of the Chinese painters’ way of experiencing.
In the discussion to follow, “intuitive looking” will be used to refer equally to Arber’s visual
thinking, Nicolaides’s gesture drawing, Goethe’s intuitive looking or objective thinking, and the looking
of the Chinese painters. The above characterization of intuitive looking as alive means that it presents
“all things ‘as in act.’” Intuitive looking allows “every latent capacity for action” in each thing to appear
as at work (ἐνέργειᾳ), “every dormant potentiality of existence [to] appear … as in bloom (éclose),” or,
30
�according to an alternative translation, as a new life emerging, like a chick, from the cracked shell of an
egg.57 In allowing human beings to experience things in this way, intuitive looking has an “ontological
function,” that is, a role to play in regard to the Being of beings. Intuitive looking allows the Being of
things to be manifested in such a way that it is made available for others to encounter, too.
The intuitive looker has an insight which is like a “glance … of genius.” Think of an instant in
which fresh aspects of things are, as it were, “in the process of being born” for you. In this instant you
would be experiencing things before conceptualizing them. That is, this insight would occur in “a preconceptual mode” (MV248-49/230-31, 253/236). The new aspects arising from, in, and to the intuitive
looking constitute an instance of genuine origination, or “sprouting.” As the Chinese painter shares in
nature’s production, so here, too, the one looking intuitively participates in the sprouting of novelty in
what is being looked at. Moreover, the resulting expression of the insight allows us to participate in the
“emergence” of those novel aspects, too.
This seeing of new aspects is a two-sided seeing. It is partly active thinking and partly receptive
sensing. In the case of Arber’s visual thinking and Goethe’s intuitive looking, the active part is a
thought—a fresh cognition, which arises spontaneously, due to the advance preparation of the
experience(s) by the observer. In the case of Nicolaides and the Chinese painters, the active part is the
body-mind’s moving the pencil or brush over the paper, as if their receptive looking called forth,
spontaneously, arm-hand motions that expressed what they were receiving. They are engaged in
“thinking in movement.”58 In either case the intuitive looking both “escapes any voluntary control”—
that is, either you see it or you don’t—and involves “doing something” (MV270/252).
When we are looking at things in the fraction of a second before taking them in their familiar
sense, we are, as it were, joining them in their coming-into-being (γένεσις) as they are sprouting
(φυομένων).59 The person looking sees things springing up, as if for the first time. Seeing them in this
way is what is meant by “seeing all things in act,” or “seeing them as natural bloomings, or hatchings
31
�(éclosions).” This mode of seeing and of subsequent showing of what is seen is alive, is “alive
experience” (MV391-92/364-65). In Goethe’s terms we are experiencing the things not as static shapes
but rather as formations.
To see in this way would be to see act—in the sense of being-active-staying-in-its-state-ofcompletion—and to see power—in a sense that would include the ability to produce different kinds of
motion or rest—as together, as simultaneous. An intuitive looker would then be seeing, first, “power as
act,” that is, would be seeing as a finished thing what is still only potentially that thing. A person gazing
intuitively would, second, be seeing “act as power,” or seeing “every achieved form as a promise of
novelty” (MV, 391-92/364).
Like the two paths we saw in Part One, that of the impulse-approach and that of the logosapproach, power and act are not mutually exclusive alternatives. Perhaps it is because one’s
heart-mind has penetrated to the inner switch-over impulse at the “pregnant point” that one sees
rest in a production of motion and motion in a resting. This could be one way of taking that to
which the Eleatic Stranger was referring when he said that it is “as if Rest and Motion were
embraced by” Being.60
One who is seeing in this way is reaching ϕύσις “in the primary sense.”61 “Comings-into-being
and sproutings (φύεσθαι)” are the rustling of the things in the wind of ϕύσις. They are not ϕύσις itself.
For, in Aristotle’s words, it is rather “the way of being what they are (οὐσία) of things that have an
originator of and ruler over motion within themselves precisely as themselves.” This originator-ruler
may be in them in either of two ways—as a power-to-do or as a holding-itself-in-its-end-state (Met.
1015a14-15, 18-19). In being able to experience the wind in the rustling of the trees, the intuitive
looker, upon seeing a thing as simply at work staying itself, can also see it as having capabilities to
become some new thing. Alternatively, when such a looker sees something in motion or as having the
potential to move, she can also see it as already having arrived at its goal. These ways of seeing are
32
�familiar from Goethe’s considering the appearances next to each other in both a forward and a
backward direction.
In order to assist in resuscitating this sense of ϕύσις, we “moderns” must look for places “where
appearing signifies ‘the coming-into-being of the things that are sprouting.’” One such place is where
we have begun the Lab, where intuitive gazing at plants shows us “the blooming, or hatching (éclosion),
of appearing” (MV392/365). We can then look at actions, makings, and motions metaphorically as
particular species of sproutings, bloomings, or hatchings. This may reawaken in us the boundlessness of
the original sense of ϕύσις, which is responsible for the “rustlings” of actions, makings, and motions.
Thus, it might be possible for St. John’s students to be in a position to connect what is being said
in the following passage to some of their own experiences in Freshman Lab. They’ll have something
toward which they can be looking off (ἀποβλέπειν) in trying to make sense of it.
Now what does the word ϕύσις say? It says that which is spontaneously blossoming on its own (das von sich aus
Aufgehende) (e.g., the blossoming (Aufgehen) of a rose), the unfolding that is opening itself up, the entering-intoappearance in such unfolding, and holding itself and persisting (Verbleiben) in appearance, in short, the rulingworking holding-sway (Walten) that is blossoming-abiding (-verweilende)….
Φύσις as blossoming can be experienced everywhere, e.g., …, in the growth of plants, in the emergence of
animal and human from the womb. But ϕύσις, the holding-sway that is blossoming, is not synonymous with these
processes, which we today still count as part of “nature.” … Φύσις is Being itself, by virtue of which beings first
become and remain observable.62
As we students of the early part of Freshman Lab listen to this passage written by the
philosopher Martin Heidegger, we are able to recognize its kinship with our experience so far in the lab.
We might add that blossoming brings to our minds the sudden putting-forth of shoots and the switchover impulse that is the originator-ruler of moving and of standing still. We also recognize in it the
plant’s staying itself in a way, while at the same time becoming other.
Looking ahead to the next section of the lab, on animals, we might wonder whether we’ll
encounter some new feature, which foreshadows what we’ll soon meet in seminar—the idea that there
is something—or rather not some thing—the Good itself, which might even transcend Being as
blossoming.
33
�1
A two-part lecture delivered on September 11-12, 2020.
Agnes Arber, The Mind and the Eye (Cambridge: Cambridge University Press, 1964), pp. 115-21, 124-26. (Translations of quotations
sometimes added or modified; italics occasionally added.)
3 The Queen Anne's lace flower resembles lace and often has a solitary purple dot in the center. Each flower cluster is made up of numerous
tiny white flowers.
4 a cluster of flowers arranged on the shoot of seed plants.
5 Jacob Klein, “On Precision,” lecture St. John’s College.
6 Agnes Arber, The Natural Philosophy of Plant Form (Cambridge: Cambridge University Press, 1950), pp. 210-11; quotation from P. Turpin,
1820.
7 Ms. Younji Youn, on August 31, 2020.
8 Sei do (sheng 生 + dòng 動).
9 Henry Bowie, On the Laws of Japanese Painting (NY: Dover, 1911), pp. 77-78; italics added.
10 “Feeling” here is to be taken in the same sense as “Empfinden,” which Erwin Straus characterized beautifully and distinguishes from I-versusobject perception (Wahrnehmung), in Vom Sinn der Sinne: Ein Beitrag zur Grundlegung der Psychologie (Berlin: Springer, 1936).
11 Experiencing directed tensions corresponds to Whitehead’s perceiving sensa in the mode of causal efficacy, which is prior to perceiving
objects in presentations (Vorstellungen), clothed with sense data, in space. See A. N. Whitehead, Process and Reality, revised edition (NY: The
Free Press, 1979), pp. 58 et passim.
12 Rudolf Arnheim, Art and Visual Perception (Berkeley: U of CA Press), 412-13, 416, 437, 444-45, 449. The phrase “directed tension” was
proposed by Wassily Kandinsky in Punkt und Linie zur Fläche.
13 Ms. Kelly Kane, on August 31, 2020.
14
“The dynamics is an integral part of what an observer sees as long as his natural sensory responsiveness has not been repressed by an
education geared to the static” (ib.).
15 Boston: Houghton Mifflin Company, 1941, pp. 14-18 and 30.
16 Arnheim, op. cit., p. 454.
17
Mr. Frederic Duch Clerici, on September 3, 2020.
18 The three students are Mr. Roman Paul Wlodkowski, Mr. Henry David Hills, and Ms. Younji Youn, respectively, on September 3, 2020.
19
Suggested to me by my friend, the artist, Betsy Kopmar.
20
Ms. Songeun Jang, on September 3, 2020.
21 Note on terminology: Sprout will mean (v.) to begin to give off shoots or buds; (n.) young plant growth, such as a bud or shoot. Shoots will
mean the new fresh plant growth of both stems and their appendages, the leaves and lateral buds, flowering stems and flower buds. Bud will
mean an undeveloped or embryonic shoot, normally occurring either in the axil of a leaf (= axillary bud) or at the tip of a stem (= terminal bud).
22 What is responsible for this seeming incompleteness of activity is the fact that the potential of which the sprouting is an activity is itself
incomplete (201b33).
23 As the DC-based painter Paul Reuther has said, when paintings give evidence of mastery of shape, line, value, and composition and yet lack
life it is often due to their not having a gestural foundation, as taught by Nicolaides (private communication).
24 Ludwig Wittgenstein, Philosophical Investigations (NY: The Macmillan Company, 1953), tr. G. E. M. Anscombe, modified, Part II, section xi, pp.
193-94.
25 Included in forming an opinion are all of the lively transformations of thought that follow in its wake.
26
Henepola Gunaratana, Mindfulness in Plain English (Boston: Wisdom Publications, 1991), pp. 149-50.
27 Mr. Adam Miller Powers, on September 7, 2020.
28 In Japanese this state of self-world interrelationship is known as jishu zammai (自主 三味). It is, perhaps, somehow both self-less absorption
(三味) and agency (主) by the self (自); and yet it is neither the one nor the other. It will be explored in a later lecture.
29 狂, the left side of which originally represented a wild dog.
30 天, where the upper horizontal line originally represented the Heaven, below which stands a human being, with arms stretched out wide.
31 Henry George Liddell; Robert Scott [1940], A Greek-English Lexicon; Machine readable text (Trustees of Tufts University, Oxford).
32 ταῦτα γὰρ εἶναι καὶ τὰ τοιαῦτα φύσει φαμέν. πάντα δὲ τὰ ῥηθέντα φαίνεται διαφέροντα πρὸς τὰ μὴ φύσει συνεστῶτα. τὰ μὲν γὰρ φύσει
ὄντα πάντα φαίνεται ἔχοντα ἐν ἑαυτοῖς ἀρχὴν κινήσεως καὶ στάσεως—τὰ μὲν κατὰ τόπον, τὰ δὲ κατ᾿ αὔξησιν καὶ φθίσιν, τὰ δὲ κατ᾿
ἀλλοίωσιν—κλίνη δὲ καὶ ἱμάτιον καὶ εἴ τι τοιοῦτον ἄλλο γένος ἐστίν, ᾗ μὲν τετύχηκε τῆς κατηγορίας ἑκάστης καὶ καθ᾿ ὅσον ἐστὶν ἀπὸ τέχνης,
οὐδεμίαν ὁρμὴν ἔχει μεταβολῆς ἔμφυτον, ᾗ δὲ συμβέβηκεν αὐτοῖς εἶναι λιθίνοις ἢ γηΐνοις ἢ μικτοῖς, ἐκ τούτων ἔχει καὶ κατὰ τοσοῦτον, ὡς
οὔσης τῆς φύσεως ἀρχῆς τινος καὶ αἰτίας τοῦ κινεῖσθαι καὶ ἠρεμεῖν ἐν ᾧ ὑπάρχει πρώτως …. Ὁμοίως δὲ καὶ τῶν ἄλλων ἕκαστον τῶν
ποιουμένων· οὐδὲν γὰρ αὐτῶν ἔχει τὴν ἀρχὴν ἐν ἑαυτῷ τῆς ποιήσεως, ἀλλὰ τὰ μὲν ἐν ἄλλοις καὶ ἔξωθεν, οἷον οἰκία καὶ τῶν ἄλλων τῶν
χειροκμήτων ἕκαστον, τὰ δ' ἐν αὑτοῖς μὲν ἀλλ' οὐ καθ' αὑτά, ὅσα κατὰ συμβεβηκὸς αἴτια γένοιτ' ἂν αὑτοῖς.
33 A rapid motion forwards, onrush, onset, assault; II impulse to do a thing, effort; III setting oneself in motion, start on a march, etc. in Liddell
and Scott, op. cit.
34 The verb μεταβάλλω means: I throw into a different position, turn quickly or suddenly, turn, i.e. plough, the earth; II turn about (Liddell and
Scott, op. cit.).
35 This possibility will be explored in Senior Laboratory.
36 J. von Uexküll, Theoretische Biologie (Frankfurt am Main: Suhrkamp, 1973), p.148.
37 The quotation from Agnes Arber, The Natural Philosophy of Plant Form (Cambridge University Press, 1950), p. 78, continues: “The plant in
endeavouring ‘to persevere in its own being’, repeats that being time after time, each daughter shoot or root becoming, in its turn a parent
shoot or root.” We see here the being-at-work-staying-itself of the potential, precisely as potential, which is the definition of motion (Aristotle,
Physics, Book III ). She also mentions there an interesting proposal by Baruch de Spinoza, who after having identified “‘the effort (conatus) by
which each thing endeavours (conatur) to persevere in its own being (esse)’” with life, stated that that conatus “‘is nothing but the actual
essence of the thing itself’ (Ethices, pars III, Prop. vii).”
2
34
�38
Aristotle, Metaphysics, Book 9, Chapter 3, 1047a30-31, trl. Joe Sachs (Santa Fe: Green Lion, 1999): “And the phrase being-at-work … is
designed to converge in meaning with being-at-work-staying-complete.”
39 The comparison of the soul as the first staying-complete to the idling of a car is due to Seth Benardete, in a course on the De Anima at the
New School for Social Research. Included in idling are the activities going on within the body that allow animals to maintain their structures and
to be ready and able to respond to changes in their environments. The fact that these are known as metabolic activities may be taken as a sign
that they are initiated and ruled over (ἀρχή) by onsets (ὁρμαί) of a switch-on or a switch-off (μεταβολῆς). The latter two expressions are, of
course, suggestive for those familiar with genetic regulatory mechanisms.
40 Johann Wolfgang von Goethe, The Metamorphosis of Plants, introduction and photography by Gordon L. Miller (Cambridge, Massachusetts:
The MIT Press, 2009), translation modified; hereafter cited by paragraph number preceded by “#.”
41 “The Aim Introduced” (1807) in J. W. von Goethe, Werke, Bd. XIII, pp. 55-59; J. W. von Goethe, Scientific Studies (NY: Suhrkamp, 1983), ed.
and trl., Douglas Miller (translation modified), pp. 55-56, italics added; hereafter referred to as “Aim.
42 The two figures are from R. Brady, “The Idea in Nature” in Goethe’s Way of Science: A Phenomenology of Nature, eds. D Seamon & A. Zajonc
(Albany: SUNY Press, 1998), pp. 94 and 107.]
43 The language in this paragraph is taken from Jacob Klein’s Greek Mathematical Thought and the Origin of Algebra, trl. Eva Brann (The M.I.T
Press, 1968), p. 82 (cited below as GMT). In context that which has “within itself the possibility of acting as the source of repetition” and has “a
primal character of ‘image-ability,’ … which makes possible … all ‘recognition’” is being itself. This possibility and primal character is “the effect
of … the ‘indeterminate dyad.’” Thus, when, following Goethe, we look at the formation and trans-formation and see that each leaf shape in
the sequence of shapes “is originally ‘alienated’ from itself, is not only ‘itself’ but also ‘another’ than ‘itself,’” we are witnessing an instance of
the indeterminate dyad at work (GMT 82; cp. 95-96). Goethe’s way of looking at plants might, in this way, plant a first seed in the students’
minds of what it could mean to say that being is ϕύσις.
44
Goethe himself implied that the word “leaf” was only a temporary makeshift. He wrote that “we would obviously need a general term by
which we could designate this organ that metamorphosed into such different shapes, and with which we could compare all the appearances of
its shape” (# 120). And, in any case, it should be clear that this difference in the ultimate unit does not alter the accuracy of Goethe’s mobile,
flexible tracking of the fluctuation in the plant’s putting-forth, in its gestural impulse of formation and trans-formation. A plant’s inner truth
would be its unique “gesture” of self-formation.
45 In The Natural Philosophy of Plant Form (Cambridge University Press, 1950), pp. 70-71, Agnes Arber reports the following: In 1875 the
botanist Julius von Sachs wrote: “‘The expressions Stem and Leaf denote only certain relationships of the parts of a whole—the Shoot.’”
Arber’s own view is that “we need … a synthetic standpoint combining the advantages of .… the conception of the shoot as the ultimate unit,
and the opposed conception of the leaf and stem as each being ultimate units.”
46
Mr. Frederic Duch Clerici, on September 3, 2020.
47 Mr. Adam Miller Powers, on September 3, 2020.
48 Figures 7 and 8 are Images 10 and 11, respectively, on pp. 26-27 of Goethe, The Metamorphosis of Plants, op. cit.
49 Figures 9 and 10 are Images 12 and 13, respectively, in ibid., pp. 28-29.
50
Figures 11-13 are Images 14, 16, and 17, respectively, in ibid., pp. 32 and 34-35.
51 Figure 14 is Figure 6 in ibid., p. 44.
52 These short works will be cited by title; the page references are to J. W. von Goethe, Werke, Bd. XIII; the translation was based in significant
part on that of Douglas Miller, found in J. W. von Goethe, Scientific Studies, op. cit.
53
氣運生動 (qì yùn shēng dòng), formulated by Xie He around 500 C.E. The following graphs and translations and the considerations in the text
about the first canon are mostly based on Mai-Mai Sze’s The Tao of Painting, Volume 1 (Princeton University Press, 1956), pp. 33ff: 氣 qì: vapor,
breath; air, manner, influence; Breath of Heaven, Spirit, Vital Force, vivifying principle. 運 yùn: turn, revolve; a circuit. 韻 yùn: beautiful sound,
rhythm, reverberation. Hence, 氣韻 qì yùn = (of literature, art) distinct style, flavor, spirit, character. 生 shēng (pictograph of a plant sprouting):
to be born; to give birth; to produce; life; to grow. 動dòng: (trans.) to move, stir, arouse, touch; to set into action; to displace—by some sort of
power, force, strength (力 li). Hence, shēng dòng = vivid, lively; living movement, alive power of moving (trans.).
54 : 氣韻生動 (qì yùn shēng dòng), which means ‘Ch’i reverberation (turning/bending back) [or uttering sounds (radical 180) that are round like
a cauldron (phonetic)] [is or makes] living movement, or alive power of moving’ (Sze, 49). However, while “circulation,” as “in the vast circuit of
the heavens and the cycles of the seasons” may suggest rhythmic motion, the movement of the Ch’i is not subject to “the limitations of a
measured beat…. Rhythm is only one aspect of the total action of the Ch’i.”
55 心 hsin.
56
In this passage “[ϕύσις]” replaces “the Tao” (道 = the head, or leader, seeing everywhere, is taking an initial step along the way).
57 Paul Ricoeur. La Métaphor vive (Paris: Éditions du Seuil, 1975), p. 61; The Rule of Metaphor, trls. R. Czerny et al. (Ny: Routledge, 1977), p.48;
translation modified; hereafter cited in the text as “MV61/48.” The above quotations by Ricoeur are from Aristotle, Poetics, 1448a24 and
1411b25, respectively. As Ricoeur notes, the “as” in this and subsequent passages derives ultimately from Wittgenstein, Philosophical
Investigations, Part II, section xi.
58 Maxine Sheets-Johnston, The Primacy of Movement (John Benjamins, 2011), Chapter 12 “Thinking in movement.” In particular she shows
how dance improvisation is a “paradigm of thinking in movement” (p. 420).
59 I have altered Ricoeur’s translation of Aristotle, Met. 1014b17-18. Here is the whole relevant passage: “In a sense ϕύσις means [a] the
coming-into-being of the things that are sprouting (φυομένων), as if one were to pronounce the upsilon in ϕύσις long; but in a sense it means
[b] the thing present within forth from which the thing shooting forth, is first shooting forth (φύεται). Again, it is [c] the [source] whence the
first motion in each of the beings that are by ϕύσις is present within it precisely as itself…. [e] The primary and authoritative meaning of ϕύσις
is the way of being what they are of things that have in themselves, precisely as themselves, a ruling source of motion … and [a] the comingsinto-being and [b] shooting forth (φύεσθαι) are called ϕύσις by virtue of being motions from this [ϕύσις in the primary sense]. And [e] [ϕύσις
in] this [primary sense] is [c] the ruling source of motion of beings that are by ϕύσις, in being present within [them] in some way, whether in
the way of power-for or in the way of holding-itself-in-its-end-state-of completion” (Met. 1014b15-20; 1015a14-15, 18-19).
60 Cp. Soph 247de: Str: “I say, then, that whatever possesses any sort of power—whether for making anything at all, of whatever nature, other
than it is or for being affected even the least bit by the meagerest thing, even if only once—… is in its very being (ὄντως ἐῖναι). For I set down
35
�as a boundary marking off the beings that it is nothing else but power”; and 250b: Str: “Then do you posit in the soul being as some third thing
beyond [Motion and Rest] as if Rest and Motion were embraced by it? And is it through taking them together and looking away toward the
community of their way of being that you say that both of them are?” The translations generally follow that by E. Brann, P. Kalkavage, and E.
Salem (Newburyport: Focus Philosophical Library, 1996).
61 Aristotle, Metaphysics, Δ, 1015a18-19, based on the Sachs translation, with changes, here and in the following quotations.
62 Martin Heidegger, Einfūhrung in die Metaphysik (Tūbingen: Max Niemeyer Verlag, 1953), p. 11; Introduction to Metaphysics (New Haven: Yale
University, 2000), trls. G. Fried and R. Polt, p. 15; translation modified.
36
�
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Looking in Freshman Lab I: A Path to Experiencing the Blossoming of Things? A Two-Part Lecture
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Typescript of two lectures delivered by Robert Druecker, Annapolis tutor on September 11 and 12, 2020 as part of the Formal Lecture Series. The lectures are the first in a three-part series on Freshman Lab.
Mr. Druecker describes the lectures: "Part One gives a sense both of what students at the beginning of Freshman Laboratory read about looking at plants and of how they look at trees and other plants. Part Two considers one 'Big Picture' that they might paint, if they follow the guiding thread of the impulse-to-sprout, encountered in those first few classes."
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Druecker, Robert
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St. John's College
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Annapolis, MD
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2020-09-11
2020-09-12
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A signed permission form has been received stating: "I hereby grant St. John's College permission to: make an audiovisual recording of my lecture, and retain copies for circulation and archival preservation at the St. John's College Greenfield Library; make typescript copies of my lecture available for archival preservation at the St. John's College Greenfield Library."
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Goethe, Johann Wolfgang von, 1749-1832. Versuch die Metamorphose der Pflanzen zu erklären
Arber, Agnes, 1879-1960
Nicolaïdes, Kimon, 1892-1938
Ink painting, Chinese
Buds
Flowers
Morphology
Magnolias
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<p><a href="https://digitalarchives.sjc.edu/items/show/7627" title="Part II"></a><a href="https://digitalarchives.sjc.edu/items/show/7350">Looking in Freshman Lab part I (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7627" title="Part II">Looking in Freshman Lab part II (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7628">Looking in Freshman Lab part II (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7630">Looking in Freshman Lab part III (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7682" title="Looking in Freshman Lab part III (video)">Looking in Freshman Lab part III (video)</a></p>
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Druecker_Robert_2020-09-11
Friday night lecture
Tutors
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https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/bb98f2039c549c670a0b8e326fd60716.pdf
b0c7ba37f5552797089bba7dd5ac02ea
PDF Text
Text
Looking in Freshman Lab II How measuring, weighing, and counterbalancing
can inspire us to see things in new ways
This is the second in a series of lectures 1 for freshman on ways of looking encountered in the
first year of laboratory. In the second segment of the class, the students are invited to consider various
ways of mathematizing the world. 2 They may come to see certain phenomena as μαθήματα, that is, as
objects of study that can be used to learn through insight. While these phenomena are also investigated
empirically, the lecture will explore whether they can be viewed in ways that lead to insight. 3
The lecture will be limited to the ways in which the characteristics of length and heaviness and
different sorts of equilibrium can lead the students to new ways of looking and seeing with the mind’s
eye.
PART ONE
The first exercise performed in the second segment of the lab is measuring the quantity length.
We measure the length of a table by laying out, end to end, a strip of cardboard—our standard unit
length—as many times as it will fit on the table, say, seven. Then, unless we are very lucky, so that it
happens to fit exactly seven times, we claim that the table is between seven and eight units long.
In order to measure the table more exactly, we make a new unit by dividing our first unit in half.
Then we may say, for example, that the table is between 15 and 16 new units long. Continuing the
process of bisecting, at some point—due to the thickness of the pencil mark or to the limitations of our
vision—we find ourselves, perhaps, after four bisections, unable to perform a further one. At that point
we might determine that the table was longer than 123 and shorter than 124 of the last standard unit.
We’d go on to say that the ratio of two lengths, that of the table to that of the last standard unit, is
somewhat greater than the ratio of the numbers 4 123 to 1 and is somewhat less than the ratio of the
1
�numbers 124 to 1. We claim we have measured the length of our table on “a ratio scale,” in that we
have determined “the ratio between a measured magnitude and the standard magnitude as … equal or
nearly equal [to the] ratio between two numbers” (E&M, p. 5). 5
We are asked (E&M, p. 5) think about whether any of the “practical limitations to achieving …
exactitude … in the exercise … might be overcome.” Let’s take this question as an invitation to imagine,
in a way proposed by the philosopher Edmund Husserl, 6 a series of practical refinements to our standard
and the corresponding improvements in our ability to measure length exactly.
We begin with our last cardboard standard, sharpen the pencil we used to make it, and make an
improved standard. Next if we think we can do better, we may sharpen the pencil more. Or we may
come across a different tool for making even finer marks that can be made closer together. And so on.
We imagine that as “technology progresses” we are able to distinguish separate lines that are ever
closer together. Perhaps a machine is invented that can draw lines .1 mm apart. We might be able to
view them under a microscope and see that the edge of the table falls between two of them. As we
imagine “the ideal of perfection …pushed further and further,” we never get to the point of thinking that
no further improvement could ever be conceived.
We can imagine repeated experiences of moving, in the "again and again” (im Immer wieder),
toward a more perfect standard. 7 If we think of this perfecting process as carried to its ideal limit, we
may think of an ideally exact limit-standard of length. That standard would be “like [an] invariant and
never attainable pole…, which” we’d approach, but never reach, as ever more perfect standards were
produced. 8
Our imagining of this progress and our thinking of this standard appear to have led us to what
Socrates, in conversation with Simmias, called recollecting. He spoke of recollection as a potential
accompaniment to our recognition of a thing we are sensing—an accompaniment that would take place
whenever someone “not only recognized (γνῷ) that thing but also thought (ἐννοήσῃ) of another thing,
2
�the knowledge of which isn’t the same” as the recognition of that thing. When we recognize a set of
marks on the cardboard, we think – short, parallel, straight-line segments, equidistant from each other.
As Socrates might have said: from these (apparently) equal distances and this (apparently) straight edge,
we think of the Equidistant Itself and the Straight Itself. From our perception of the equidistant marks
along the edge of the cardboard standard, we think that they “both are reaching after the [Equidistant
and the Straight] … and are in a condition of falling short of [them].” Socrates would say that “that of
which [we] grasped the thought (ἔννοιαν) was recollected.” It was not found in our sensing of the marks
on the cardboard. Rather it felt as if we knew it from “sometime before” (πρότερόν ποτε; as in a priori).
This kind of experience is what we call “learning through insight” (Phdo 72e-75b), as opposed to merely
making empirical observations, interpreting them, and learning through experience.
Recollection is a two-in-one experience—like visually recognizing something in a crowded room
as a face—or as a lyre—and, at the same time, thinking of it as Simmias’s face—or thinking of the boy
who is always playing that lyre. When, for the first time, someone recollected an ideal limit to the
perfecting process described above, it might have been experienced as a thought that suddenly fell into
her or his mind (in German: ein Einfall). The experience of recollecting may have shared certain features
with Wittgenstein’s description of the experience of suddenly “noticing an aspect”: “I’m considering a
face, suddenly I notice its likeness to another. I see that it has not altered; and yet I see it differently.” 9
As Socrates pointed out, however, an additional feature characterizes the recollection-experience. For a
key part of the way I see the “face” “differently” in recollecting is that I see it as wanting to be of the
same sort as the ideal-exact limit-standard—like Socrates’ pair of equal sticks, wanting to be of the same
sort as the Equal itself—but as falling short of it.
We are also asked (E&M, p. 5) to consider a second question: whether, given any table, we could
always subdivide the standard enough times, so that the length of that table would “turn out to be an
exact multiple of the subdivided standard.” Whereas the first question led us to recollection, involving a
3
�a two-in-one experience—recognizing a piece of cardboard with pencil marks on it and simultaneously,
together with that, thinking of an ideally sharp standard for length—this second question leads us to a
single seeing, or, perhaps better, a fantasizing. For it raises the possibility that the things in the world of
our experience might themselves actually be—rather than reach after being—ideally exact. If that were
the case, it would then be theoretically possible to express the length of every particular rectangular
table exactly as a ratio of whole numbers. We might then be thought to have accomplished a rationalization of the world.
At the end of Ch. I, we turn from length to the characteristic of heaviness, or weight. The first
two questions posed are: how would it be possible to determine that two weights are “virtually
indistinguishable” and how could we arrange different instances of heavy bodies “in a linear series,”
from lightest to heaviest. If we were able to do both, then we‘d claim that we could measure heaviness
on an ordinal scale (M&E, p. 4).
In order to experience what it means concretely to measure heaviness on an ordinal scale, we
use a device called a “substitution balance.” Here is a picture of one:
A
Weight
Counterweight
Figure 1
This instrument consists of a straight wooden beam that rests on a knife-edge called the fulcrum; from each end of
the beam a plastic pan is suspended…. the arms of the beam are not equal…. The beam is free to swing within the
limits established by the two bumpers (M&E 8).
4
�We place an object A in the weight pan on the right and enough clay in the counterweight pan on the
left, so that the beam comes to rest somewhere in between the two bumpers. Then we mark the
pointer’s position.
In order to determine experimentally that two bodies, A and B, are equally heavy, [we] carefully
remove A from the “weight” pan, “without disturbing the counterweight, and substitute B in its place….
If B causes the pointer to rest exactly where A did, then A and B are equal in their … weight; and if not,
not” (M&E 9).
Students find this balance and this experimental definition of equality of weight to be “counterintuitive.” It is especially puzzling to them to read: “No inferences whatever may be drawn, by means of
the balance, as to the comparison of the ‘weight’ and the ‘counterweight.’” Why can’t we say that the
sinking of the counterweight would show that it is heavier than the weight?
In response, after having tentatively considered A and B to be equally heavy, whenever B causes
the pointer to rest exactly where A did, the students formulated the following insight: It makes sense
because “whether A or B is in the weight pan seems to make no difference to anything at all, since
everything is the same either way. B leaves the pointer in the same position as A did.” As one student
said: Weighing using the substitution procedure “challenged my presuppositions” about what equality
of weight really means.
It was as though working with the method of substitution played an analogous role, for the
students, to the one Socrates plays for the slave boy in the Meno. The students, too, at the beginning,
without knowing, “suppose [they] know” how to determine equal weights; then they become aware
that they “don’t know” and are “perplexed” by the procedure proposed; and at the end they arrive at
“true opinions” about it (Meno 82e, 84ab, 85c).
After that each lab team is given an identical metal cylinder, called a baros, to use as unit
standard weight for making two pieces of clay, each equal in heaviness to one baros. By repeated
5
�halving they go on to construct a ratio scale for measuring weight and use it to assign weight-numbers
to various bodies, in a way very similar to their assignment of length-numbers to the edge of the table.
A student asked: “What’s the point of spending even more time with such primitive equipment,
like the substitution balance?” A possible response arises out of the fact that in performing the barosexercise many of the weighing teams ended up not using the method of substitution. Instead, they
reverted to their initial “knowledge” that the two weights at opposite ends of a horizontal beam are
equal. Perhaps, then, the student’s earlier realization of having had his presuppositions challenged may
have been like the slave boy’s true opinions, which had merely been “stirred up in him, like a dream”
(Meno 85c). It may be that his realization didn’t “stay put” but rather ran away (97d-98a), or, through
the lens of a different metaphor, flew up to mix in with and fly around with his previous opinions (cp.
Theat 197cff) about what weighing is.
Socrates says to Meno that in order for true opinions to “stay put” they must be tied up “with a
giving-an-account of what is responsible” (αἰτίας λογισμῷ)—a tying-up process that they’ve also agreed
to call “recollection” (Meno 97d-98a). Perhaps it’s a recollection-process that makes use of recollected
things, like a Square, in this case. Socrates had said earlier that in order for one to go beyond having true
opinions “stirred up … like a dream” and to come “himself to draw up [knowledge] again out of himself
(ἀναλαβὼν αὐτὸς ἐξ αὑτοῦ),” one needs to be asked “these same questions many times in different
ways” (Meno 85cd). Perhaps by thinking out afresh, each time, our responses to those questions about
the relations among the parts of a recollected Square, we become able to recollect them, too, and to
articulate them, eventually, with assurance.
After the baros-exercise, in discussion the students realized the mistake they’d made. Did their
questioning and the rethinking of the exercise lead them, at this point, genuinely to draw up again out
of themselves and to formulate an account of what is truly responsible for showing equality of weights?
Or not? They may have only been remembering that they were supposed to follow the recipe for the
6
�substitution procedure and had merely forgotten to do so. This latter suggestion is reinforced by the fact
that in an exercise three weeks later that again required a weighing using the substitution balance, no
one in the class actually used the counterweight.
PART TWO
Chapter II, dealing with equilibrium, revisits the balance from a different point of view. A
suitable balance allows us to go beyond measuring the heaviness of a single body to determining a
certain relationship among two bodies and two distances.
The students perform simple practical exercises in the lab and study a treatise on equilibrium by
Archimedes. How are we to think about the exercises in relation to the treatise? Does the latter provide
hypotheses, which the students test with the aim of learning, through their experience of the former,
what does happen? Or could Archimedes, be, as it were, the Euclid of weights-in-equilibrium? If so he’d
be offering us a way to learn through insight into what must happen when bodies are counterbalanced
on a true Balance.
At the beginning of the new chapter, we perform five simple exercises, in order to gain a sense
of how heavy bodies behave when suspended from a point. Then, in our imagination, we take a second
look at those experiments, in order to seek out the essence of the bodies’ behavior.
We, first, make a number of pinholes around the edge of a piece of cardboard as shown in
Figure 2, and suspend it from each in turn. After the cardboard comes to rest, we draw a vertical line
through each pinhole.
7
�A
B
C
D
A'
Figure 2
The lines drawn come very close to passing through a single point, which we call the cardboard’s center
of weight (M&E, p. 13). The name is apt in the sense that the cardboard shape “behaves as if all of its
weight were concentrated at or near” this point.
Second, we confirm this claim by, sticking “the head of a pin through this center” and then
balancing “the cardboard, in a horizontal position, on this pinhead.”
Third, when we “insert the pin through the center of weight and hold the pin horizontal,” the
cardboard remains at rest in any orientation in its vertical plane. This rest position is neutral, in the
sense that the cardboard has no preferred orientation; it does not rotate out of any position in which it
is placed. In comparison, the rest positions observed in our first set of experiments, where the center of
weight rotated until it came to rest vertically below the point of suspension, are stable. For even a small
displacement leads to oscillation and, ultimately, to a return to the initial position.
Fourth, if we were very careful, we could bring the cardboard to rest—at least for a short time—
with its center of weight vertically above a pinhole through which the horizontal pin was inserted. It
would then be in an unstable rest position. For if our hand trembled ever so slightly, the cardboard
would swing around in its vertical plane and come to rest in a stable rest position.
8
�Finally, what is even more puzzling, when the center of weight is not even on the piece of
cardboard, as in the case of the odd shape depicted in Figure 3, the lines drawn intersect at a point that
is not located on the cardboard.
Generalizing from these empirical observations, we claim that all heavy
bodies have a center of weight in the above sense and have the three kinds of
A
A'
rest position, which depend upon the relation of their points of suspension to
their center of weight.
Figure 3
Could we say that, beyond such a generalization, these few exercises have led us, whenever we
recognize a heavy body, to think, in addition, of a point that behaves as that body’s center of weight?
Would our experiences support the claim that the center of weight did not come from our empirical
observations of bodies in the lab? Rather it occurred to us in our observation of them in the lab. If so
our simple exercises with the pieces of cardboard would, perhaps, have allowed us to recollect the
center of weight, so that it felt as if we knew it from “sometime before” (Phdo 72e-73d).
In thinking of the center of weight, we seem to be looking “through” the body with a sort of Xray vision. Only the body’s center of weight and the point of suspension, its “bones,” show up as white
on the X-ray. The other parts of the body, its “soft tissues”, appear black. If the two bones were given,
then we could see in the mind’s eye—without our having to do further experiments 10—that the actual
amount of the weight and its disposition throughout the body would be irrelevant to the way the body
behaves when suspended. X-ray vision, thus, would allow us to separate something essential in the
situation of a suspended body from what is merely accidental.
We turn now to Archimedes’ treatise “The Centers of Weight of Planes” (M&E, pp. 14ff). Figure
4 is the second figure in the treatise. It depicts two magnitudes, A̲ and B̲ , 11 of equal weight and
9
�A
D
C
B
Figure 4
having centers of weight, 12 A and B, respectively. The previous figures, of the substitution balance and of
the cardboard cutouts, were schematic depictions of physical objects. How are we to interpret
Archimedes’ figures? In what new ways do they invite us to look at material things?
He clearly shares two ways of looking with Euclid. First, his vision is abs-tractive in Aristotle’s
sense. He, too, sees the “things that result from drawing [trahere] [something] away [abs-]” (τὰ ἐξ
ἀφαιρέσεως), namely, things that our mental removal of other sensible characteristics—like “hardness
and its opposite, and also hotness and coldness, and other pairs of contrary perceptible attributes,”
“leaves behind.” 13
If we look for bodies that have typical shapes, like oval, roundish, or oblong, our looking ignores,
or has “stripped off” all characteristics—including heaviness—except shape. If, instead, we were
preparing to look at bodies with Archimedes’ vision, we’d perform almost the same stripping-off.
However, in addition to shape we’d leave behind weight—a characteristic that does not, like shape,
manifest itself fully to the eye.
Second, Archimedes shares with Euclid—and with our previous consideration of the limitstandard of length—a vision of ideally exact limit-formations. For instance, in the Archimedean Figure 5
below, as we do with Euclid’s figures, we take it as imaging an ideally exact straight line, on which there
are three ideally exact points, 14 as indicated. But, in addition, we shall take the respective sizes of the
two rectangles as indicating an exact relationship between the weight of A̲ and that of B̲ .
10
�A
C
B
Figure 5
In particular, if we take the straight line AB in Figure 5 as representing a beam and C as
representing the tip of a fulcrum, then we’ll say that the figure images an ideally exact limit-balance. The
treatise will show us what must happen when we weigh heavy bodies on such an ideally exact limitbalance.
Furthermore, while Archimedes’ rectangular figures are, like Euclid’s, intended to be imagesand-likenesses (εἰκόνες) of exact shapes, in this lecture we shall focus on them only as indices of relative
amounts of heaviness. That is, we shall neglect the shapes of the two rectangles A and B as shapes and
attend only to their sizes, which will be taken to indicate the relative weights of the two represented
bodies.
We shall interpret not only Archimedes’ figures of weights but also bodies in the laboratory as
indices of relative amounts of weight. Many of the relevant features of indices are borrowed, with some
modification, from C. S. Peirce’s treatment of the index. 15 The connection of likeness between the
recognized object and the thought of the Thing itself, in the experience of recollection, is replaced, in
the case of an index, by a direct, factual, non-arbitrary space-time connection between the index and
the indicated thing. Here are some examples—many of which are experienced by animals—of indices
and what each points to: rock – hardness; frost – coldness; dark clouds - impending rain; (for a fish in the
sea) direction of greater light - warmer water; limping gait – physically impaired animal; scowling human
facial expression - displeasure or concern; particular way of pronouncing a word - particular geographic
place or social group. 16
11
�As can be seen from those examples, the “naturalness” of the connection between pointer and
pointed-to may involve innate knowing in some cases, in others, learning through experience 17 (neither
through teaching nor through insight)—including the experience of “artificial” correlations, such as,
between a beep from the oven and the cookies’ readiness to be taken out or between a red traffic light
and the urgency of stopping the car. Rather than “seeing” what is being pointed to, we may feel an urge
to, “hear” an invitation to, or tend to make an inference to it—for instance, at the sights of smoke or
footprints, at the sounds of thunder or of the doorbell ringing, or at the tastes of flavors. Thus, the
correlation need not be perfect, in order for a thing to act as an index.
Our earlier experiences both with weighing on the substitution balance and with suspending
pieces of cardboard from pins through holes, as well as our everyday experiences of lifting bodies and
our childhood play on seesaws, all contributed to our having learned through experience, or
associatively, the connections between, on the one hand, Archimedes’ rectangles or the bodies we work
with in the laboratory and, on the other hand, the weights that they indicate. Contrary to mathematical
symbols, these rectangles and those bodies indicate the relative amounts of heaviness in an inherent
way; bigger means heavier, in some rough sense. But it is a way that is in between being an image-andlikeness—it does not resemble its signified object, in this case, heaviness—and being arbitrarily assigned
to signify heaviness. Whereas recollection was a two-in-one experience, indication is an experience of
duality, but of a “naturally” connected duality.
There is a meaningful connection between magnitude of size and magnitude of weight, but the
relationship between the size of the rectangle and the magnitude of the weight has to be stipulated if
there is to be an exact account. If we sup-pose that inherent connection, then Archimedes may lead us
to recollect Equilibrium Itself. So, for instance, the ratio of the sizes of the rectangles A and B in Figure 5
is taken to indicate the exact ratio of the weight of body A̲ to that of body B̲ . 18 Our X-ray vision then
12
�shows us that the weight of any body at all could be indicated by the same rectangle A, provided its
center of weight were at A and its weight were equal to that of A̲ .
For the first time in the measurement segment, we are using things that we have recollected in
order to arrive at further insights into relationships within what has been recollected. This is a third way
in which Archimedes is following the Euclid’s way of seeing; he shows how a sequence of conclusions
can be generated from the ideal-exact limit-formations. For as the arithmeticians do based on “the odd
and the even” and as the geometers do based on “the geometrical shapes, the three kinds of angles,”
etc., Archimedes “is forced to seek on the basis of sup-positions (ἐξ ὑποθέσεων), proceeding not to a
beginning but to an end.” The conclusions about the equilibrium of weights are “in agreement with that
from which [he] set [his] inquiry in motion” (Rep. 510bd; Sachs trl., modified). In that way Archimedes
engages us in learning through insight.
The first part of Archimedes’ title is “On the Equilibrium of Planes.” In some of the postulates
and propositions, 19 we read: to be in equilibrium, or, equivalently, to sink, or incline, equally, and ii) to
sink, or incline, toward 20—which latter seems to be a specification of not to be in equilibrium.
Archimedes does not follow Euclid’s procedure by stating precisely what it is for weights to be “in
equilibrium” or, for that matter, for a point to be “held fixed” or to be “the center of weight.” 21 Perhaps
for the first two of these expressions, he relies on the reader’s everyday experiences with things like
seesaws; for the third he may be counting on the reader’s having played around with suspending objects
from strings, just as we did in the earlier exercises. Or one might adopt a view introduced in the last
century 22 and claim that Archimedes defines these phrases implicitly. Then the statements in which he
uses them would aim to specify, without ambiguity, how they are to be interpreted in terms of other,
familiar terms.
He also often 23 mentions equal or unequal weights at certain or equal or unequal distances,
before making explicit, in Prop. 4, that each weight is taken to be “at” its center of weight and that each
13
�distance is from a body’s center of weight to what the manual calls “a pivot”—what was referred to
earlier as the “point of suspension” of the cardboard or the “fulcrum” of the substitution balance.
Whereas length and weight are characteristics of individual bodies, being-in-equilibrium
specifies a relationship among five entities. For the setting-out of the above figure, involving bodies A̲
and B̲ , they would be—the two weights, A and B, their respective centers of weight A and B, and the
pivot point C, 24 on the rigid, straight, weightless beam ACB.
The first postulate of the treatise states “that equal weights at equal distances are in
equilibrium, and that equal weights at unequal distances are not in equilibrium but incline toward the
weight which is at the greater distance.” The insight expressed here is of a kind familiar from Euclid.
Recalling what the students had said in relation to the substitution balance, we see that if we exchanged
the two equal weights with each other, it could make no difference to anything at all. Everything would
be the same either way.
In addition to the X-ray vision involved in seeing centers of weight, Archimedes introduces a few
other ways of looking. Prop. 4 mentions “the magnitude composed from both magnitudes.” 25 When we
first glance at Figure 6 below, we see two separate bodies, A̲ and B̲ , of weights A and B, respectively,
and their respective centers of weight, A and B.
A
D
C
B
Figure 6
Then, in a second, compositional looking, we see “the magnitude composed from both magnitudes,”
that is, we imagine A̲ and B̲ as composing two parts of a single body, say, A̲ /B̲ , in which they are joined
by a rigid, straight, weightless beam, AB.
In this way we are thinking of A̲ and B̲ as forming a shape reminiscent of the odd cardboard
14
�shape from the beginning of Ch. II, shown again in Figure 7. We then imagine
A
A'
molding that cardboard (illustrated on the left side of Figure 8)—simultaneously
shrinking and straightening its central portion into a straight line and shaping the
two end portions into congruent rectangles—all the while still viewing it as one
object, so that we end up with the shape on the right side of Figure 8.
Figure 7
Figure 8
Another way of looking is the reverse of the above, namely, decompositional looking. Just as we
can compose, so we can decompose. We can view a single body as two separate ones.
Archimedes sometimes accompanies compositional or decompositional viewing with a third
mode of looking. In the proof of Prop. 4, he shifts from viewing a point as the center of weight of a
composite body A̲ /B̲ to seeing that same point as a pivot about which the two bodies A̲ and B̲ , into
which A̲ /B̲ is considered to be decomposed, are in equilibrium. 26
In these ways Archimedes is inviting us to shift back and forth, at will, between ways of looking.
First, like seeing Figure 9 now as a duck and now as a rabbit, we can consider a figure as depicting either
15
�Figure 9
two separate bodies A̲ and B̲ or one composite body A̲ /B̲ . Second, like seeing Figure 10 now as an old
Figure 10
woman and now as a young one, we can consider a particular point as either a center of weight or a
pivot point for equilibrium. Whereas, for a viewer who actually does see them, the shifts back and forth
between seeing the duck or the rabbit or between seeing the young or the old woman—each of which is
a genuine seeing—are involuntary, for us the shifts Archimedes prescribes are voluntary; and each of
them might be more a viewing-as or even only a thinking-of. 27
In Prop. 6, in a virtuoso display of all of his ways of looking, Archimedes shows us that what the
students had unthinkingly assumed in working with the substitution balance, namely, the so-called “Law
of the Lever”—that “bodies will be in equilibrium at distances from the pivot which are reciprocally
proportional to the weights of those bodies” (M&E 20)—must be true of an ideally exact limit-balance.
Figure 11 shows two bodies A̲ and B̲ that are given as having commensurable weights, A and B,
16
�Figure 11
and as having their centers of weight on a straight-line beam at points E and D, respectively. Their
weights are also given as having the following relationship to their respective distances from a point C,
located on ED between E and D – C�D� : E�C� :: A : B. What is to be shown is that A̲ and B̲ are in equilibrium
about point C.
The givens permit us to carry out the proof by assigning particular numbers to the distances and
weights. In Figure 12 C�D� is shown as 5 units long and E�C� as 3 units, where each unit is labeled N� .
Figure 12
Moreover, in the construction E�C� has been extended to the left by 5 N� and C�D� to the right by 3 N� , as
pictured. In Figure 13 A̲ is shown divided into 10 equal unit weights Z̲, and B̲ into 6, respectively.
Figure 13
17
�Then in Figure 14 the centers of weight of the 10 Z̲ are shown as having been placed at the
���� and those of the 6 Z̲ at the midpoints of the remaining N� on
midpoints of the 10 N� on the left end of LK
����.
the right end of LK
Figure 14
Now Archimedes simply has us look at these 16 Z̲, successively, in different ways and in relation
to the given weights A̲ and B̲ :
As we look at the 16 equal weights Z̲, each at the midpoint of an equal length N� , we see
����, five pairs of Z̲s situated symmetrically about point E, respectively;
i)
on the left end of LK
����, three pairs of Z̲s situated symmetrically about point D, respectively;
ii)
on the right end of LK
����
iii)
on the whole of LK, eight pairs of Z̲s situated symmetrically about point C, respectively.
Hence, we see, by the first postulate, that each pair must be in equilibrium about the point about which it is
symmetrically situated.
By shifting from duck to rabbit, we consider each of these pairs of Z̲s (ducks) as a composite weight
(rabbits). By simultaneously shifting from old woman to young woman, we see that for each composite of two
weights, the point of equilibrium (old woman) of the pairs in question—E for i), D for ii), and C for iii)—is its center
of weight (young woman).
By again shifting from duck to rabbit, we consider each of the three sets of pairs of composite weights
(ducks)— i) the five pairs on the left (from L to H), ii) the three pairs on the right (from H to K), and iii) the eight
pairs on the whole (from L to K)—as itself a composite weight (rabbits). So—by an analogue to Euclid’s first
common notion: Composites of weights having the same center of weight also have that center of weight—we see
that E is the center of weight of i) the composite of the 10 Z̲s, D of ii) the composite of the 6 Z̲s, and C of iii) the
composite of the 16 Z̲s.
By X-ray vision we then see that
i)
the composite of the 10 Z̲s is the same as A̲ as originally given, since both have the same center
of weight E and same total weight.
ii)
the composite of the 6 Z̲s is the same as B̲ as given, since both have the same center of weight D
and same total weight.
So [by a common notion: Composites of pairs of weights (the first pair is the composite of the 10 Z̲s and the
composite of the 6 Z̲s; the second pair is A̲ and B̲ ) having the same respective centers of weight (E for the first
member of each pair and D for the second) and pairwise equal in weight are equal and have the same center of
weight.], we see that the center of weight of the composite weight A̲ /B̲ is also C, the center of weight of the
composite of the 16 Z̲s, that is, of the composite of the 10 Z̲s and of the 6 Z̲s
18
�Finally, by shifting back from rabbit to duck, we consider the composite weight A̲ /B̲ (rabbit) as two
separate weights A̲ and B̲ (duck). And simultaneously, by shifting back from young woman to old woman, we
consider C, the center of weight (young woman) of the composite weight A̲ /B̲ , as a pivot point for equilibrium (old
woman). So, we see that: “therefore if A̲ be situated at E and B̲ be situated at D, they will be in equilibrium about
the point C.” QED
Given two bodies on a beam that counterbalance each other in the lab, we consider them, first,
as counterbalancing on an Archimedean true Balance. That is, as we perceive the lab situation, there
occurs to us, in recollection, the thought of two ideal-exact centers of weight and an ideal-exact pivot
point on the true Balance. On the basis of our sup-position based on the experienced “natural”
connection to ideal-exact weights and of his suppositions about the μαθήματα, Archimedes’ Prop. 6 may
have enabled us to learn through insight (μαθεῖν), precisely which relationships among those five
entities associated with the two given weights are necessary, in order for them to be seen as a complex
image-and-likeness (εἰκών) of what Socrates could call Equilibrium Itself—that at which our actual
counterbalancing in the lab can be thought of as aiming, while still falling short. If so then we now
expect that the closer our laboratory equipment comes to imaging an ideally exact limit-balance, the
more exactly our experiments will manifest the Law of the Lever.
PART THREE
At the beginning of Chapter III of the manual, we again take up the Archimedean approach to
looking at situations of counterbalancing. But now, first of all, Archimedes has stretched the meaning of
being-in-equilibrium to refer to two portions of a body of water pressing down upon certain “parts” of
the water below them, instead of referring to two solid bodies on a beam about a pivot. His treatise On
Floating Bodies shows us how to consider this pressing-down as analogous to weights’ tending to push
downward on a beam and, thereby, to incline it to sink.
Second, he offers us a way of looking different from the X-ray vison and the compositional or
decompositional looking familiar from the earlier treatise. We shall use this way of looking, in order to
19
�see, or imagine, certain things into given laboratory situations, almost as if we were looking at the latter
through a PowerPoint transparency, placed over the actual things in the lab. For instance, as we look at
a piece of wood floating in a bucket of water, we’ll be able to use our imagination and see that a portion
of it must be below the surface of the water and why it must be so. It might be as if the “giving-anaccount of what is responsible” (αἰτίας λογισμῷ), which Socrates and Meno agreed to call “recollection”
(Meno 97d-98a), were transformed into an imagining of what is responsible.
In the previous treatise Archimedes had us look at his figures with a voluntary considering-as,
analogous to the involuntary seeing of a figure as a duck or as a rabbit. As a result of that treatise, we
were able to consider both drawings of his figures and certain beam and pivot arrangements in the lab
as imaging the true Balance. However, the multiple shifts in looking required to see the truth of Prop. 6
are so elaborate that we are not in a position to execute them while we look at a given beam and pivot
arrangement in the lab. That is, we can only “apply” Prop. 6, as when we refer to the Law of the Lever;
we cannot “see” it immediately in the given beam and pivot arrangement.
In his second treatise Archimedes offers a recipe for looking that shifts what we can
immediately see as true of a given object in a pail of water in the laboratory—without relying on the
mediation of the statement of a proposition, which we remember having proven.
This new way of looking is introduced in Prop. 2, where Archimedes shows that “the surface of
any liquid 28 which remains motionless,” such as the water in a bucket, “will have the form of a sphere
which has the same center as the earth.” In this and the next few propositions, the treatise depicts the
given liquid as a portion of a sphere, which is to represent an earth-size ball of liquid. If the given liquid
were water in a bucket, we’d be imagining a ball of water the size of the earth and a tiny portion of it,
which coincided with the water in our bucket.
20
�Archimedes justifies this way of imagining by showing that if we supposed that the surface of
the water in the bucket did not coincide with the surface of a sphere, then we’d be led to contradict
ourselves. Figures 15 and 16 are two versions of a schematic picture of what we’d see under this
Figure 15
Figure 16
supposition.
21
�If the surface ABLCD 29 of the water (colored blue) in the bucket, did not coincide with the
surface of a sphere centered at the center K of the earth, then we could describe some other sphere, an
outline of which is partially pictured in pink, as ZBECH, centered at the center K of the earth, passing
through point B on the surface ABLCD of the water in the bucket. As shown, the sphere ZBECH would
also pass through two other points, one (Z) above the water in the bucket and one (E) in the water. In
this way the supposed spherical surface would be above the surface of the water in the bucket from Z to
B and below the surface of the water from B to E.
In order to allow us to see the contradiction that would be lurking here, Archimedes has us look
at two things, which we have imagined into the figures above: first, the two thin pyramids of water ABK
and BLK; second, an imagined smaller sphere—part of which is shown as XOP–whose center is also K,
and which cuts through the water in the bucket and intersects the pyramids in XOP. Then he allows the
small spherical slice KXOP to play a role analogous to that of the beam-and-pivot in his previous treatise.
He has asked for (postulated) only one thing of us in this treatise—that we assume that a liquid,
like water, is such that
if its parts lie evenly and are continuous, that part which is pressed the less is thrust out by that which is pressed
the more; and each of its parts is pressed by the liquid which is vertically above it, if the liquid is not enclosed in
anything and is not pressed by anything else (M&E, p. 25).
In the above two figures, the pyramidal slice of water represented by ABK, which is inside the
corresponding portion of the sphere (ZBK), is smaller than the slice BLK, which encompasses the
corresponding portion of the sphere (BLK), congruent to ZBK. Hence, we can see that the part above OP
is being pressed more by the water above it than is the part above XO by the water above it. Therefore,
when applied to this situation, the postulate requires that the part XO be thrust out by the part OP,
which means that the water has to be in motion—a contradiction of the given motionlessness of the
water. Therefore, the supposition that the surface of the water in the bucket did not coincide with the
surface of a sphere is necessarily false. QED
22
�Archimedes goes on to show how imagining an object and a bucket as placed within and near
the surface of an earth-size ball of water could lead to other discoveries. In the next proposition he
supplies the fourth ingredient in his recipe for looking, namely, a shape imagined as being mentally
outlined within one of the two pyramids in the liquid and as equal and similar to the shape of (the
immersed part of) a given object.
Say, we look at a heavy piece of wood—which happens to be exactly as heavy as the same
volume of water—being slowly lowered into the bucket, until it remains at rest exactly where it happens
to be when released. Suppose that this remaining-at-rest happened before the wood had been
completely immersed in the water, as depicted in Figure 17, and that at the instant when the lowering
stopped all motion ceased in the bucket.
Now imagine looking at this piece of wood through a transparency of an earth-sized globe of
water, positioned so as to intersect with a plane through the center of the earth in the blue hemi-sphere
KALBCMRYND and having “the form of a sphere which has the same center as the earth” (Prop. 2,
enunciation). In what follows what is pictured is always the intersection with that same plane
Figure 17
23
�through the center of the earth. The brown figures BEZC and BHTC represent, respectively, the parts of
the wood above and below the surface of the water.
Then imagine over the transparency of the globe of water another transparency with two
adjacent pyramids, “equal and similar to” and “continuous with” each other and each “having for its
base a parallelogram [lying] on the surface of the liquid, and its vertex the center of the earth” (Prop. 3,
proof). The left pyramid, KXLBCMO, is shown containing the submerged part, BCTH, of the wood.
In the right pyramid, KOMRYNP, we imagine a third transparency, showing “a magnitude [RYSG]
… cut [out] from the liquid, equal and similar to the [submerged] part of the” wood, outlined in pink and
in the same relative position, in relation to the right pyramid, as is the submerged part of the wood, in
relation to the left pyramid.
Finally, we imagine, over the other three transparencies, a fourth one (outlined in green in
Figure 17) containing the surface, XOP, of a portion of a smaller sphere cutting through the bucket,
below both the wood and the cutout, and also centered at the center K of the earth.
Having superimposed such a detailed set of transparencies, we look at the one having the two
pyramids. It is clear that each would contain two pairs of portions of things pressing-down equally—
namely, the submerged wood HBCT and, seen through the third transparency, the congruent cut-out
SRYG, respectively; and the remaining pyramidal portions XLBHTCMO and OMRSGYNP pressing
equally—on the left and right “parts,” XO and OP, respectively, of the surface of the smaller sphere,
shown on the fourth transparency. But it is also clear that the portion of the wood protruding above the
water, BEZC, would be pressing on XO without being paired with anything additional pressing on OP. So,
we see that OP would be “that part which is pressed the less.” Thus, by the postulate OP would be
thrust out by XO, so that there would be motion in the water—a contradiction of the supposition that
the water remain motionless. Therefore, the piece of wood could not have come to rest before it was
completely immersed in the water. QED
24
�Here Archimedes has employed all the ingredients in his recipe for looking, namely, the four
transparencies through which we look at the actual object in the bucket. They show, respectively:
a) a spherical earth-sized globe of water, centered at the center of the earth, a small portion of the
surface of which coincides with the surface of the water in the bucket,
b) two equal and similar, adjacent pyramids of water, cut from the globe, continuous with each
other, and having vertices at the center of the earth, in the left of which is the immersed (part of) the
object,
c) in the right pyramid, a cutout of water equal and similar and similarly placed to the immersed
part of the object, and
d) a spherical surface, with center also at the center of the earth, and which cuts through the water
in the bucket, near its bottom.
In contrast to the components of the figures in the first treatise—beam, pivot, and weights—these
ingredients are mental additions to the things actually visible in the laboratory and to what a
representation of them would show. The objects on the transparencies are neither images-andlikenesses nor indices of the bodies in the lab.
As we are looking we add them mentally to any given object-in-bucket situation in the lab that
we wish to understand, such as those to which the next few propositions in the treatise might refer—for
instance, a piece of wood taped to a piece of metal that stays wherever it is released in the water, some
wood floating partly above the surface of the water, or a metal block that comes to rest at the bottom
of the bucket.
Imagining the first transparency containing the globe of water and imagining the other
transparencies laid over it will allow us to see clearly, in various situations in the lab, whether or not,
with the specified givens, the left or right “part” would be being pressed more. For all we need do is look
at matching pairs of congruent shapes in the left and right pyramids and look for anything else that
might be pressing down on either of the two arcs that does not have a match on the other side. This is
the second step in cooking with the recipe. We think about what we see through the transparencies, in
the bucket of water. We can see in the mind’s eye whether or not there is equal pressing right and left.
In the final step we may consult the postulate and see with insight whether or not, based on it, either
“part” must be “thrust out.”
25
�When we first looked at the wood and bucket of water, we did not have anything like an earthsized globe of water or pyramids in mind. In the first step Archimedes’ recipe leads us to look at the
bucket while imagining the transparencies overlaid onto the actual bucket. So, in using this treatise, in
addition to recognizing the wood and bucket of water, we are thinking and imagining all that is in the
four transparencies.
We might say that one who is following Archimedes’ recipe “sees a thing according to an
interpretation,” 30 or, rather, several interpretations, as instructed by Archimedes. Each transparency
might be like a textbook illustration, which would always be accompanied by an interpretation. We can
imagine each transparency as superimposed over the sight of the bucket. That will enable us to think of
the transparency’s figure as being “in” the bucket. We may then view that figure as ingredient in the
bucket. Perhaps, also, we might see it in this way.
In the second step we think about what we have thought and imagined onto the wood and
bucket of water. By viewing the latter through the transparency, we can see in the mind’s eye whether
or not there is equal pressing right and left, and if not, we likewise see, in the third step, that the
postulate requires there to be motion and that the supposition of motionlessness has been
contradicted.
Is it the case that familiarity with Archimedes’ recipe for looking is a recipe for essential seeing,
that is, for seeing what is essential in certain situations? Does it enable an imagining-and-thinking that,
in turn, allows something essential to be seen and a truth to be recollected?
As noted near the beginning of the lecture, the experience of recollection is a two-in-one
experience, like that of visually recognizing something as a face and simultaneously having a thought of
it as Simmias’s face. It is seeing a straight line on the blackboard as an image-and-likeness (εἰκών) of the
Straight Itself. When we follow Archimedes’ recipe, our experience seems rather to be a dual one of
recognizing the water, the bucket, the objects, and, separately, of imagining-and-thinking. However, it is
26
�a dual one in which the correlation is due entirely to Archimedes’ instructions; we have had no
experiences of pyramids of water, cut from the globe, or of cutouts of water from which we could have
learned, associatively, to connect them to an object in a bucket of water. As opposed to the “naturally,”
or inherently, connected duality of index and indicated, this duality is externally superimposed. 31 We
“lay” the figures from the transparencies over the figure of the bucket of water on paper or over our
sight of it in the lab. 32
A Friday Night Lecture, delivered at St. John’s College, Annapolis, on February 25th and 26th, 2022; revised, April 17, 2022.
This kind of mathematization is independent of the “new mathematics” of Viète’s algebra and Descartes’s analytic geometry. So, no
equations are involved.
3
All page references to the manual are to a revised version, entitled MEASUREMENT AND EQUILIBRIUM: Archimedes’ and Pascal’s Ways of
Looking at Weight, Water, and Air, edited especially for a Graduate Institute Preceptorial offered in Santa Fe in the summer of 2021.
I would like to thank all of the members of my Freshman Laboratory classes in the last several years and, especially, the participants
in the Graduate Institute Preceptorial in Santa Fe in the summer of 2021: Isabel Ballan, Bill Blais, Patricia Burk-Travis, Nicolae Federspiel-Otelea,
Hugh Himwich, and Susan Olmsted,.
4 In calling 1 a number, we are diverging from the strict sense of “number” as an assemblage of units.
5
The way our table stands (σχέσις; Euclid, Elements, Bk. V, Df. 3) relative to the length of our new smallest unit is nearly the same as the way
the number 123 units or 124 units stands relative to one unit.
6 This approach was proposed by the phenomenological philosopher Edmund Husserl in “Die Frage nach dem Ursprung der Geometrie als
intentionalhistorisches Problem.” See The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to
Phenomenological Philosophy, tr. D. Carr (Northwestern: 1970), trl. modified/Die Krisis der europäischen Wissenschaften und die
transzendentale Phänomenologie (Haag: Martinus Nijhoff, 1962), pp. 353-78/365-86. The quotations in the following two paragraphs are from
this work.
7
“From the praxis of perfecting, of freely pressing toward the horizons of conceivable perfecting in the ‘again and again’ [im ‘Immer wieder’],
limit-shapes become sketched out, toward which, as invariant and never attainable poles, the particular series of perfectings is progressing”
(Husserl, ib., 26/23).
8 Our imagining of this progress and our thinking of this standard leads us to view the standard in the way we may have looked at a chalk line on
the blackboard in the Freshman Mathematics Tutorial. We’d have seen it as imaging a line that matches Euclid’s definition of straight line—
perfectly sharp, without thickness or waviness or fuzziness. All the shapes referred to by Euclid were ideally sharp in this sense. Whenever we
look at a drawing of one of them, what we are invited to think of is characterized by ideal sharpness. (We could perhaps arrive at an “ideal
visual acuity” in the same way.)
9 The example is borrowed from Ludwig Wittgenstein, Philosophical Investigations (NY: Macmillan, 1953), tr. G. E. M. Anscombe, p. 193.
10 Nevertheless, the manual later (M&E, p. 19) proposes an exercise in which, simultaneously, the cardboard is replaced with a meter stick and
an axis through a hole drilled at the 50 cm. mark substitutes for a pin through a potential center of weight of the cardboard. By adding or
removing small amounts of clay as needed, the students are able to bring the meter stick into the three different kinds of rest position. In what
way, if any, does this exercise deepen our insight into the center of weight or of the possible rest positions?
11
Here and throughout the treatment of Archimedes, the manual’s symbols are changed.
12 “Center of weight” is mentioned in some of the postulates (4, 5, 7) and in several propositions (e.g., 4 and 5) and proofs (e.g., of 6 and 7).
13 The translations of Aristotle generally follow those of Joe Sachs, in Aristotle’ Metaphysics (Green Lion Press, 1999), K.3, 1061a29-b4. See also
Sachs’s note on p. xlix.
14 The points A and B represent, of course, the two centers of weight, at which the two bodies A̲ and B̲ are thought of as suspended.
15 Cf. C. S. Peirce, Collected Papers of Charles Sanders Peirce (8 Vols.). (1931–58). Ed. Charles Hartshorne, Paul Weiss & Arthur W Burks.
(Cambridge, MA: Harvard University Press), 4.447: “The kind of representamen termed an index. … is a real thing or fact which is a sign of its
object by virtue of being connected with it as a matter of fact and by also forcibly intruding upon the mind, quite regardless of its being
interpreted as a sign. It may simply serve to identify its object and assure us of its existence and presence. But very often the nature of the
factual connexion of the index with its object is such as to excite in consciousness an image of some features of the object, and in that way
affords evidence from which positive assurance as to truth of fact may be drawn. A photograph, for example, not only excites an image, has an
appearance, but, owing to its optical connexion with the object, is evidence that that appearance corresponds to a reality. … An icon has such
being as belongs to past experience. It exists only as an image in the mind. An index has the being of present experience.”
16 Most of these examples, as well as some in the next paragraph, are taken from
https://legacy.cs.indiana.edu/~port/teach/103/sign.symbol.short.html.
1
2
27
�17 A special case of learning through experience is getting the hang of seeing photos as photos, and not as mere patterns on paper. This kind of
learning through experience is relevant to the image-and-likeness, rather than to the index.
18 Using three different symbols involving the letter “A,” we may say: “Body A̲ , having center of weight at point A, and of weight indicated by
rectangle A…” The same rectangle is taken both to represent a body and to indicate the amount of that body’s weight.
19 See Postulates 1-3 and 6 and Propositions 1-4.
20
The manual points out (14, n. 1) that the Greek word for being-in-equilibrium (ἰσορροπεῖν) could also be translated inclining-downwardequally. The manual has already sometimes used “downward tendency” as equivalent to “weight” (M&E, p.9). Perhaps we are to imagine that
two bodies, each tending or striving to move downward, are joined by a weightless beam-and-pivot arrangement and are each endeavoring, in
a struggle against one another, to incline the beam downward on its side of the pivot, and, in the case of equilibrium, are doing so with equal
effectiveness. When one of the two wins the contest, the beam will come to sink, or incline, toward (ῥέπειν ἐπί) the side on which the winner is
located.
21 For instance, Prop. 3 claims that “two weights [A̲ and B̲ in the above figure] will be in equilibrium” with each other. Prop. 4 takes A to “be the
center of weight of magnitude A̲ ” and proposes that D be “held fixed.”
22 Padoa, A., “Essai d’une théorie algébrique des nombres entiers,” Bibliothèque du Congrès international de philosophie (1900) 3.
23 For example, Posts. 1, 2, and 6; Props. 1, 2, and 3.
24 If, inspired by Archimedes, we look at two weights in the lab, with the question of their being in equilibrium in mind, we can consider them as
if they were situated at the ends of an ideal-exact straight-line, imaged by a seesaw on a playground, and ask: About which pivot point on the
seesaw will neither side sink down. This Archimedean looking could be called seesaw vision. We, as it were, see an ideal-exact seesaw into the
given actual situation—imagining the weights’ centers of weight at its opposite ends and indicating their amounts by the sizes of the respective
rectangles.
25 Or: “of both taken together.” See T.L. Heath, The Works of Archimedes (NY: Dover Publications, Inc., 1912), p.191; underlining added.
26
If D is “the center of weight of a magnitude [A̲ /B̲] composed” of two magnitudes [A̲ and B̲ ], then the composite magnitude “will be in
equilibrium “if D is held fixed”—the manual’s footnote adds: “that is, as a pivot.”
When we first arrived at the notion of a center of weight as a point on the piece of cardboard, at the beginning of Ch. II, we stuck a
pin horizontally through it and showed that it was then also in a neutral rest position after any rotation about that point. That is, from a point’s
being the center of weight of a body, it followed that the body would be in (neutral) equilibrium about that point. Archimedes appears to be in
agreement with this suggestion that being a center of weight is the more fundamental notion and that being in equilibrium about a point
follows from it. Thus, it makes sense for the manual to have introduced the former before the latter. It is easy to see the truth of the converse
of Archimedes’ assumption, namely, that if equal weights are in equilibrium about a point, then that point is the center of weight of the weight
composed of the two equal weights.
27
In one paragraph Wittgenstein asks the reader to consider, as an example of “the danger of wanting to make fine distinctions,” the aspects of
a triangle”—such as, seeing it “as a triangular hole, as a solid, as a geometrical drawing; as standing on its base, as hanging from its apex; as a
mountain, as a wedge, as an arrow or pointer.” In the next paragraph he gives the response of an interlocutor: “‘You can in doing so think now
of this, now of that, can view (ansehen) it now as this, now as that, and then you will see it now in this way, now in that way.’” Wittgenstein
immediately points out that it would be an error for the interlocutor to think that there is some way to make the this or that more determinate,
by spelling out further what you are thinking of or that as which you are viewing it or the way in which you are seeing it: “— In which way? There
is as a matter of fact no further determination.” See Wittgenstein, op. cit., translation modified and underlining added, p. 200.
28 “The Greek word is derived from the adjective ὑγρός, which means ‘moist’ or ‘wet’” (M&E, p 25n).
29 In what follows we often speak of three-dimensional shapes, like spheres or pyramids. But, for convenience, all of the labels are of the
shapes’ intersections with a plane passing through the sheet of paper, or the computer screen, as the case may be.
30 This example is borrowed from Wittgenstein, op. cit., p. 200, but used in a different sense.
31 In that respect it is like Peirce’s “symbol.” See Peirce, op. cit., quoted above.
32 The above analysis of Archimedes’ second treatise would also apply to Pascal’s Treatise on the Equilibrium of Liquids. Pascal uses one
transparency. The figure on it is one or another version of VI, VII, or VIII in Figure 18 below.
Figure 18
The box may be imagined to be filled with a weightless liquid (M & E 41: “without counting the weight of the water”). The large weights on the
right are each of 100 pounds, resting on a piston, over the right-hand aperture; the small one in VII is 1 pound. The ratios of the right aperture
to left aperture are 1 : 100. The heights of the liquids are all the same. The weight of the liquid in the large tube in VIII is 100 pounds; that of the
liquid in the narrow tubes in VI and VIII is 1 pound. This Pascal box-and-tubes transparency may be laid over situations like those in IX, X, XI, and
XII in Figure 19—representing vessels partially submerged in a river, and containing mercury or copper or cork, in part—in order to see what
28
�Figure 19
must happen. In laying it over, we must mold the narrow tubes of the vessel and of the Pascal-transparency, so that they are exactly
superimposed; and, similarly, for the vessel’s wide opening and the Pascal-transparency’s wide tube, and so on, as suggested by Figure 20.
Figure 20
=
Figure 21 may suggest a way of relating the Pascal transparency to those of Archimedes.
Figure 21
29
�
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Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and for a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>. <br /><br />Click on <strong><a title="Formal Lecture Series" href="http://digitalarchives.sjc.edu/items/browse?collection=5">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://anchor.fm/greenfieldlibrary" title="Anchor.fm">Anchor.fm</a>, <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a>, <a href="https://podcasts.google.com/feed/aHR0cHM6Ly9hbmNob3IuZm0vcy84Yzk5MzdhYy9wb2RjYXN0L3Jzcw" title="Google Podcasts">Google Podcasts</a>, or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe.
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St. John's College Formal Lecture Series—Annapolis
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29 pages
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Looking in Freshman Lab II – How Measuring, Weighing, and Counterbalancing Can Inspire Us to See Things in New Ways
Description
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Typescript of two lectures delivered on February 25 and 26, 2022, by Annapolis tutor Robert Druecker as part of the Formal Lecture Series. The lectures are the second in a three-part series on Freshman Lab.
Druecker describes his lectures: "This will be the second in a series of lectures for freshman on ways of looking they encounter in Freshman Laboratory. In the second segment of the class, the students are invited, in various ways, to consider the mathematization of nature. They may come to see certain phenomena as μαθήματα, that is, as objects of study leading to acts of insight. While they also investigate these phenomena empirically, our question in the lecture will be whether they can be viewed in ways that lead to insight. The phenomena considered at the beginning— the characteristics of length and heaviness and various sorts of equilibrium—may introduce the students to some new ways of looking. The lecture will highlight those ways. Questions: Are they new in your experience? Are they helpful in learning from your studies in the lab?”
Creator
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Druecker, Robert
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St. John's College
Coverage
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Annapolis, MD
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2022-02-25
2022-02-26
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A signed permission form has been received stating: "I hereby grant St. John's College permission to: Make an audiovisual recording of my lecture, and retain copies for circulation and archival preservation in the St. John's College Greenfield Library. Make an audiovisual recording of my lecture available online. Make a typescript copy of my lecture available for circulation and archival preservation in the St. John's College Greenfield Library. Make a copy of my typescript available online"
Type
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text
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pdf
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Physical measurements
Physics--Study and teaching
Equilibrium
Physics--Experiments
Archimedes. De corporibus fluitantibus
Leonardo, da Vinci, 1452-1519. Trattato della pittura
Relation
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<p><a href="https://digitalarchives.sjc.edu/items/show/7629">Looking in Freshman Lab part I (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7350">Looking in Freshman Lab part I (video)</a></p>
<p><a href="https://digitalarchives.sjc.edu/items/show/7627">Looking in Freshman Lab part II (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7630">Looking in Freshman Lab part III (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7682" title="Looking in Freshman Lab part III (video)">Looking in Freshman Lab part III (video)</a></p>
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English
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Druecker_Robert_2022-02-25-26
Friday night lecture
Tutors
-
https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/959daaa42167cbcea0e0f4e7b04b461e.mp4
dc5cfe9ca062a9f18c99be75b1648b07
Dublin Core
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An account of the resource
Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and for a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>. <br /><br />Click on <strong><a title="Formal Lecture Series" href="http://digitalarchives.sjc.edu/items/browse?collection=5">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://anchor.fm/greenfieldlibrary" title="Anchor.fm">Anchor.fm</a>, <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a>, <a href="https://podcasts.google.com/feed/aHR0cHM6Ly9hbmNob3IuZm0vcy84Yzk5MzdhYy9wb2RjYXN0L3Jzcw" title="Google Podcasts">Google Podcasts</a>, or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe.
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St. John's College Formal Lecture Series—Annapolis
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formallectureseriesannapolis
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00:53:07
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Looking in Freshman Lab II – Measurement and Equilibrium: How Measuring, Weighing, and Counterbalancing Can Inspire Us to Look at Things Differently
Description
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Video recording of a lecture delivered on February 25, 2022, by Annapolis tutor Robert Druecker as part of the Formal Lecture Series. The lecture is the second in a three-part series on Freshman Lab.
Druecker describes his lecture: "This will be the second in a series of lectures for freshman on ways of looking they encounter in Freshman Laboratory. In the second segment of the class, the students are invited, in various ways, to consider the mathematization of nature. They may come to see certain phenomena as μαθήματα, that is, as objects of study leading to acts of insight. While they also investigate these phenomena empirically, our question in the lecture will be whether they can be viewed in ways that lead to insight. The phenomena considered at the beginning— the characteristics of length and heaviness and various sorts of equilibrium—may introduce the students to some new ways of looking. The lecture will highlight those ways. Questions: Are they new in your experience? Are they helpful in learning from your studies in the lab?”
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Druecker, Robert
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St. John's College
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Annapolis, MD
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2022-02-25
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moving image
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Physical measurements
Physics--Study and teaching
Equilibrium
Physics--Experiments
Archimedes. De corporibus fluitantibus
Leonardo, da Vinci, 1452-1519. Trattato della pittura
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<a href="https://digitalarchives.sjc.edu/items/show/7629">Looking in Freshman Lab part I (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7350">Looking in Freshman Lab part I (video)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7628">Looking in Freshman Lab part II (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7630">Looking in Freshman Lab part III (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7682" title="Looking in Freshman Lab part III (video)">Looking in Freshman Lab part III (video)</a>
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Druecker_Robert_2022-02-25-26access
Friday night lecture
Tutors
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https://s3.us-east-1.amazonaws.com/sjcdigitalarchives/original/05055287b50332b71a17bbcf1ead1f0c.mp4
9a5f334ad8c436bea1960e9794b8f7b3
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Items in this collection are part of a series of lectures given every year at St. John's College. During the Fall and Spring semesters, lectures are given on Friday nights. Items include audio and video recordings and typescripts.<br /><br />For more information, and for a schedule of upcoming lectures, please visit the <strong><a href="http://www.sjc.edu/programs-and-events/annapolis/formal-lecture-series/" target="_blank" rel="noreferrer noopener">St. John's College website</a></strong>. <br /><br />Click on <strong><a title="Formal Lecture Series" href="http://digitalarchives.sjc.edu/items/browse?collection=5">Items in the St. John's College Formal Lecture Series—Annapolis Collection</a></strong> to view and sort all items in the collection.<br /><br />A growing number of lecture recordings are also available on the St. John's College (Annapolis) Lectures podcast. Visit <a href="https://anchor.fm/greenfieldlibrary" title="Anchor.fm">Anchor.fm</a>, <a href="https://podcasts.apple.com/us/podcast/st-johns-college-annapolis-lectures/id1695157772">Apple Podcasts</a>, <a href="https://podcasts.google.com/feed/aHR0cHM6Ly9hbmNob3IuZm0vcy84Yzk5MzdhYy9wb2RjYXN0L3Jzcw" title="Google Podcasts">Google Podcasts</a>, or <a href="https://open.spotify.com/show/6GDsIRqC8SWZ28AY72BsYM?si=f2ecfa9e247a456f" title="Spotify">Spotify</a> to listen and subscribe.
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St. John's College Formal Lecture Series—Annapolis
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formallectureseriesannapolis
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01:38:48
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Looking in Freshman Lab I: A Path to Experiencing the Blossoming of Things?
Description
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Video recording of two lectures delivered by Robert Druecker, Annapolis tutor on September 11 and 12, 2020 as part of the Formal Lecture Series. The lectures are the first in a three-part series on Freshman Lab.
Mr. Druecker describes the lectures: "Part One gives a sense both of what students at the beginning of Freshman Laboratory read about looking at plants and of how they look at trees and other plants. Part Two considers one 'Big Picture' that they might paint, if they follow the guiding thread of the impulse-to-sprout, encountered in those first few classes."
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Druecker, Robert
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St. John's College
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Annapolis, MD
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2020-09-11
2020-09-12
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moving image
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Goethe, Johann Wolfgang von, 1749-1832. Versuch die Metamorphose der Pflanzen zu erklären
Arber, Agnes, 1879-1960
Nicolaïdes, Kimon, 1892-1938
Ink painting, Chinese
Buds
Flowers
Morphology
Magnolias
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English
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Druecker_Robert_2020-09-11
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<a href="https://digitalarchives.sjc.edu/items/show/7629">Looking in Freshman Lab part I</a> (typescript)<br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7627" title="Part II">Looking in Freshman Lab part II</a> (video)<br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7628">Looking in Freshman Lab part II</a> (typescript)<br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7630">Looking in Freshman Lab part III (typescript)</a><br /><br /><a href="https://digitalarchives.sjc.edu/items/show/7682" title="Looking in Freshman Lab part III (video)">Looking in Freshman Lab part III (video)</a>
Friday night lecture
Tutors
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