Polytropy

This essay is written as a distraction from current events, though I make some reference to them. I am prompted by questions of analogy provoked by

1. the similes of Homer and
2. a recent theater review in Harper’s that mentions the parables of Jesus.

Harper’s sticks to the traditional model of selling its magazine in print form. Thus the reader experiences not only this or that article, but the composition of articles that is each issue. I encourage everybody to subscribe. You will then indeed have on-line access to every article since the middle of the nineteenth century; this is what enables me to go back and quote (as I do below), by so-called cutting and pasting, Rivka Galchen, “New Drama,” March 2016, pages 80–1.

I might have skipped reading this review, since I have little interest in drama as such. I am a devotee of Somerset Maugham, but have never read any of his plays. I don’t think anybody else still reads the plays either, though they once were popular. I wonder if Collingwood is alluding to them when he writes dismissively in the Preface of The Principles of Art (Oxford, 1938),

Fashions which before the War seemed firmly entrenched, in spite of their obvious bankruptcy, and which even in 1924 were only moth-eaten, and hardly yet even beginning to be replaced by others, have begun to disappear, and new ones are growing up instead.

We have in this way a new drama, taking the place of the old “slice of life” entertainment, in which the author’s chief business was to represent everyday doings of ordinary people as the audience believed them to behave, and the actor’s chief function to take a cigarette from his case, tap it, and put it between his lips.

Some day I may investigate Collingwood’s reference. Maugham himself thought theater was going to be killed off by cinema (I think he says this in The Summing Up). If he was right, it is a slow death. I did felicitously read Galchen’s drama review, even though it began thus:

The Wooster Group, an experimental-theater company in New York, has been doing its ludic, fevered work for forty years now …

Any discussion of art that uses the word “ludic” is going to arouse my suspicion. I am not one of the initiates to whom the word means something other than “playful” does. Maybe Galchen did not want to use the latter word in an article about plays. Her next paragraph makes a grand claim about her subject:

When I saw their Hamlet, in 2007, I was, I confess, filled for the first twenty minutes or so with a longing for “ordinary” Shakespeare. But after the dulling effects of expectation and familiarity were killed off, the similarities between Ophelia and Gertrude began to make new sense; Shepherd’s quiet and somewhat distracted delivery of the “To be, or not to be” speech paradoxically made the words feel freshly meaningful; and by the end of the show, I felt as if, for the first time, I had glimpsed the play’s true spirit. It was the best Hamlet I have ever seen. The Wooster performers are clowns running a séance. What’s wondrous strange is that the ghosts reliably turn up.

Great. If I lived in New York on a budget that allowed it, I might go to see the Wooster Group. I confess to not getting a thrill out of reading Shakespeare; but I like to watch. My present interest in the review in Harper’s lies in what Galchen says toward the end:

In trying to follow the Wooster Group’s meanings over the years, I have come to think of them in relation to one of the stranger moments in the New Testament, when Jesus explains the parable of the sower to his disciples. This is the one about a farmer sowing seeds—some get eaten by birds, some land in rocky soil, but some find fertile ground and produce a good crop. When the disciples ask the meaning of the story, an irritated Jesus explains that the seeds are the Word of God, the varieties of soil are the varieties of people who hear the Word, etc. The story means just what it sounds like it means.

I too have found the Gospel scene strange. But to Galchen and the rest of us today, if Jesus’s story sounds like what it means, this is only because we have been trained to hear the meaning. We have learned to recognize parable, allegory, analogy.

Many people may not have learned. My father learned this when he went from being a lawyer to being a cook. He worked in kitchens where his colleagues could not understand when he was making an analogy. I am sorry that I cannot recall his full account; but in the example that he recounted to me, he had told his colleague that something was like being a caddy on a golf course, and his colleague’s response was, “Oh, were you a caddy?”

My father did not mean to belittle this colleague; but my father’s new line of work had opened his eyes to what life was like for many people. He saw how management screwed over the worker, as for example with the split shift. I suppose he was like Barbara Ehrenreich in Nickel and Dimed: On (Not) Getting By in America (which had not come out yet).

Psychologists see fit to put analogies on intelligence tests. What is to a sock as a hand is to a glove? Perhaps indeed not everybody has a ready answer to such a question. But in that case, what does Homer expect his audience to make of such verses as are rendered by Chapman as follows?

Next (through the temples) the burst eyes his deadly javelin seeles
Of great-in-Troy Antenor’s sonne, renown’d Demoleon,
A mightie turner of a field. His overthrow set gone
Hippodamas, who leapt from horse and, as he fled before
Æacides, his turned backe he made fell Pelias gore,
And forth he puft his flying soule. And as a tortur’d Bull
(To Neptune brought for sacrifice) a troope of yongsters pull
Down to the earth, and dragge him round about the hallowed shore
To please the watry deitie, with forcing him to rore,
And forth his powres his utmost throte: so bellow’d this slaine friend
Of flying Ilion, with the breath that gave his being end.

This is from Book XX of the Iliad, Chapman’s lines 348–58 (which are different from Homer’s lines). Chapman’s language is itself difficult, more difficult than Shakespeare’s. You should know here that Æacides and Pelias are the same person: the grandson of Æacus and son of Peleus, namely Achilles. Also to seel is to close, when what is being closed is the eyes. I transcribe the archaic spelling preserved in the edition of Allardyce Nicoll, if only as a reminder that English spelling took some time to become standardized.

I have taken the example from Homer almost at random. Chapman usually points out Homer’s similes with a marginal note. The example that I have chosen illustrates the opening remark of William C. Scott, The Artistry of the Homeric Simile (Dartmouth College Press, 2009):

The similes in Homer are treasure troves. They describe scenes of Greek life that are not presented in their simplest form anywhere else: landscapes and seascapes; storms and calm weather; fighting among animals; aspects of civic life such as disputes, athletic contests, horse races, community entertainment, women carrying on their daily lives, and men running their farms and orchards.

The scene above of daily life in which youths torture a fellow creature, believing themselves pious to do so: we see this scene in Turkey today, when coup-makers are tortured by government supporters, who might themselves have been tortured, had the coup been successful.

In her Harper’s review, concerning the Gospel story of the sower, Rivka Galchen goes on to say, in her final paragraph:

Is it really a parable, then? Religious and academic commentators have offered many thoughts about this passage and about Jesus’ claim that he speaks in parables so that only the initiated will understand him—a troublesome idea to many Christians. And to many theatergoers. Shouldn’t meaning be simple and clear? For myself, I like the idea that Jesus’ straightforward parable and exegesis are both about seeing the surface of what is right there—the surface is the depth. Wooster Group shows are, in their way, exceptionally faithful to their sources …

Why should meaning be simple and clear? What would this even mean? Students today may learn a formula for the area of a circle:

The area of a circle is equal to pi times the square of the radius. Is this simple and clear? We may think so, because we have learned how to plug and chug. If the radius is 5, then the area is about 79, since pi is about 3.14. But what is pi exactly? There is a formula for it:

In words, pi is four times the alternating sum of the reciprocals of the odd numbers, taken in the usual order. My seventh-grade mathematics teacher could not tell me this, and I had to find the formula for myself. Why it is meaningful and correct is another question. One may define pi as the ratio of the circumference of a circle to its diameter; but what does this mean? Students today may think that finding ratios is another problem of plugging and chugging. Great. Here’s a circle, with a diameter drawn. How are you going to divide the circumference by the diameter? You might wrap a string around the circle, then measure the length of the string. But why should this unwrapping preserve a property called length? A standard puzzle proposes that a string has been wrapped around the earth along the equator, with no overlap. If you want to add a foot to the string, how high do you have to raise it above the earth, all around, so that there will still be no overlap? If this is a puzzle, it means our intuitions have no immediate answer.

The formula for the area of a circle could not be written as the equation above, with rigorous meaning, for more than two thousand years. Euclid himself expressed the formula as an analogy: Circles are to one another as the squares on their diameters. Is this simple and clear? I think it is so, for those who have digested Euclid’s theory of analogy, otherwise known as proportion (the Greek is analogia). However, as I suggested in “Thales of Miletus,” the proof of the analogy of circles with the squares on their diameters is probably the most challenging of the Elements. It involves all of the difficulty of what we now know as calculus.

Scholars may write of the spirit of the Greeks. The spirit of Greek mathematics may lie in the analogy, which is also the spirit of Homer. But mathematics is difficult, whatever language it is framed in. How then did most of Homer’s listeners hear his similes? I have no answer; but could most of his listeners have been any more sophisticated than Jesus’s disciples, who could not just see what we think of as the plain meaning of the parables? Homer was the Bible of ancient Greece, telling readers and listeners of the gods and their relation to us. The similes make us feel; perhaps they also train us to think.

Scott’s book about the similes of Homer seems not to mention Jesus or his parables. Neither does an article now available on Jstor, Samuel E. Bassett, “The Function of the Homeric Simile,” Transactions and Proceedings of the American Philological Association, Vol. 52 (1921), pp. 132–147. Bassett does however make a useful general remark:

The “Homeric simile” must not be confused with the “simile in Homer.” The simple comparison is one of the most universal means of expressing thought. It marks the second step in the progress of ratiocination, being preceded by metaphor, of which it is the development, and being followed, at some distance, by the effort to think in abstract terms. To the child a lion is first of all

• a cat; then,
• like a cat, and, much later,
• an animal.

(Bullets mine.) One hot summer when I was in high school, I read a lot of books about arctic exploration. Perhaps in similar fashion, during summer visits to the beach now, I often read Homer’s Iliad. The hot sand and the blue water are somehow a ready canvas for Homer’s word-paintings of slicing, crushing, and impaling. It also poignant to think that the beach I am on is not far from where the Trojan War actually happened. Across the water I see Lesbos, an island that Homer sometimes mentions, as when, in Book IX (lines 132–8), Agamemnon hopes to induce Achilles to rejoin the war effort:

Seven Lesbian Ladies he shall have that were the most select
And in their needles rarely skild, whom (when he tooke the towne
Of famous Lesbos) I did chuse, who wonne the chiefe renowne
For beautie from their whole faire sexe, amongst whom I’le resigne
Faire Brisis, and I deeply sweare (for any fact of mine
That may discourage her receit) she is untoucht and rests
As he resign’d her …

The gift of the Lesbian Ladies will not be accepted until Book XIX, after Patroclus has died.

I had a hernia operation just six weeks ago, and I have not been supposed to carry what I usually do. What I usually carry to the Nesin Mathematics Village where I was, or the beach where I am now, is a stack of books, not expecting to read them all, but just in case I should want them. Travelling more lightly this time, I brought just the following (along with a couple of blank notebooks, partially filled in by me):

1. Simone Weil, The Iliad or The Poem of Force (Pendle Hill Pamphlet number 91, 1956: it is small, and we read it in the sophomore language tutorial at St John’s College, though I must not have been able to appreciate it then);
2. Henri Frankfort & al., Before Philosophy: The Intellectual Adventure of Ancient Man: An Essay on Speculative Thought in the Ancient Near East (Penguin, 1971: I bought it used, probably when I was a student, but I do not recall where);
3. Allardyce Nicoll, editor, Chapman’s Homer: The Iliad (Bollingen Series XLI, Princeton University Press, 1984: this is heavy, and I could have brought a lighter edition of Chapman’s Iliad, by Wordsworth Classics, but it had cheap paper and modernized spelling);
4. Mary Midgley, Heart and Mind (Routledge Classics, 2003: bought recently from Pandora Bookshop in Istanbul).

One may take my title, “Thinking & Feeling,” as a translation of the title of Heart and Mind. I am without my copy now, since I lent it to somebody in Şirince who I hope will return it to me in Istanbul. (Note added later: she did.)

Meanwhile I have downloaded a copy of Heart and Mind from Library Genesis, and so I can quote (from pages 3–5) Midgley’s eminently sensible words (bold emphasis mine):

… Thought is not primarily the sort of thing which is tested in exams. It is the whole organized business of living—seen from the inside.

All this matters because many things on the current intellectual scene tend to make us disconnect feeling from thought, by narrowing our notions of both, and so to make human life as a whole unintelligible. We are inclined to use words like “heart” and “feeling” to describe just a few selected sentiments which are somewhat detached from the practical business of living—notably romantic, compassionate and tender sentiments—as if non-romantic actions did not involve any feeling. But this cannot be right. Mean or vindictive action flows from and implies mean and vindictive feeling, and does so just as much when it is considered as when it is impulsive. In general, too, ordinary prudent action flows from prudent feeling, though this is something to which we are so well accustomed that we take it for granted. It may seem like pure habit—until a sudden threat startles us into consciousness of the motive.

We are in fact so constituted that we cannot act at all if feeling really fails. When it does fail, as in cases of extreme apathy and depression, people stop acting; they can die in consequence. We do not live essentially by calculation, interrupted occasionally by an alien force called feeling. Our thought (including calculation) is the more or less coherent form into which our perceptions and feelings constantly organize themselves. And the compromise between various, conflicting, strong and constant feelings expresses itself in our heart or character.

Of course I am not denying that there can be discrepancies and conflicts between thought and feeling, or between feeling and action. There can. (They provide some of our most serious problems, which is why we have quite a good vocabulary for talking about them.) But they have to be exceptional …

Why, now, does all this matter? The unity of the human personality which I am stressing seems obvious. As I have said, however, it badly needs to be plugged today because of a whole web of theoretical habits which tend to obscure it and make it inexpressible. In this book, my main business will be with the strands of this web spun by British moral philosophy, which from the eighteenth century on has occupied itself with a dispute about whether morality is a matter of reason or feeling, ignoring the obvious fact that it is both …

“The unity of the human personality … seems obvious.” Unity is a theme of Collingwood, certainly of his Speculum Mentis, which aims for a recovery of the unity in life that was lost in the Renaissance. A reason for me to buy Midgley’s book was her quotation of Collingwood on the subject of creation in The Principles of Art. She says of him,

On his view, creators need not, indeed characteristically do not, know in advance what they are going to make. He sees the absence of a “preconceived end” as a mark of real art, a mark which distinguishes it from mere craft …

I suggest, therefore, that Collingwood’s attempt to show a modest sense of creation which implies no preconceived purpose while still asserting responsibility won’t work. It cannot therefore support his non-technical view of art. Nor—what is our present concern—can it support the idea of arbitrary and mindless creation in morals …

I think Midgley is oversimplifying here, and I wonder if it is because she has not considered creation in the way I looked at it (with Collingwood’s help) at the end of an article in 2014, “Freedom.” Before the act, I am not simply ignorant of what I am going to tell you on some occasion; but the way that I tell you (and myself) what I am going to tell you is just to tell you.

In a word, some of our expressions are incompressible. A lot of mathematics may be compressed into the circle area formula; but you cannot compress the Iliad. Homer might have been able to tell you that he was composing an epic about the anger of Achilles and the wrath of Zeus; but if you then wanted more detail, you would have to wait for the finished product.

In The Principles of Art, Collingwood begins his theory of imagination with the distinction between thinking and feeling:

1. Feeling is simple, while thought is “bipolar,” in the sense of being able to be done well or ill.
2. Feelings are private, while thoughts are public, in the sense of being able to be shared by many persons.
3. Because of these two distinctions, “thoughts can corroborate or contradict each other, but feelings cannot.”

To adapt Collingwood’s example to my present locale: the thought that the sea is a certain temperature on the Celsius scale today may be shared by all of us on the beach; but how each of us feels about it depends on her own situation. Collingwood allows that one person’s feeling about the sea temperature today—too warm, too cold, just right—may be like another’s. How can we know this? Normally we can talk about our feelings, thus converting them to thoughts. We can thus get hold of one another’s thoughts and compare them: we can form a ratio of our thoughts, so to speak.

In addition to the books listed above, I brought with me on this trip a print-out of Chapter I, “The Ionians,” of Part I, “Greek Cosmology,” of Collingwood’s Idea of Nature (Oxford, 1945). I was researching Thales as the originator of mathematical deduction. In fact Pappus is the better source for Thales as a mathematician, though Pappus lived centuries after Thales.

Collingwood formulates the motivating question of the Ionian school as,

“What is the original, unchanging substance which underlies all the changes of the natural world with which we are acquainted?”

He observes that this question requires some presuppositions (printed in italic in the book):

1. That there are “natural” things.
2. That “natural” things constitute a single “world of nature.”
3. That what is common to all “natural” things is their being made of a single “substance” or material.

This is echoed and refined by H. and H. A. Frankfort (apparently husband and wife) in the Conclusion of Before Philosophy:

Yet the doctrines of the early Greek philosophers are not couched in the language of detached and systematic reflection. Their sayings sound rather like inspired oracles. And no wonder, for these men proceeded, with preposterous boldness, on an entirely unproved assumption. They held that the universe is an intelligible whole. In other words, they presumed that a single order underlies the chaos of our perceptions and, furthermore, that we are able to comprehend that order.

The speculative courage of the Ionians is often overlooked. Their teachings were, in fact, predestined to be misunderstood by modern—or rather, nineteenth-century—scholars …

To return to the drama review in Harper’s, I would say the teachings of Jesus of Nazareth were destined to be misunderstood. The case in point is all of the world’s doctrinaire Christians. As for the unproved assumptions of the Ionians, of course such assumptions were made: any thought requires them, as Collingwood shows in An Essay on Metaphysics. We normally do not make our assumptions explicit; indeed, we are normally not aware of them. Modern mathematicians such as Bertrand Russell criticize Euclid for not making all of his assumptions explicit. They should laud Euclid’s great advance in making any assumptions explicit at all.

I wondered if the spirit of Greek mathematics was a reflection of the similes of Homer. Before Philosophy does not address mathematics as such, though in effect it describes Greek thought as mathematical:

In the first place, early Greek philosophy (in Cornford’s words) “ignored with astonishing boldness the prescriptive sanctities of religious representation”. Its second characteristic is a passionate consistency. Once a theory is adopted, it is followed up to its ultimate conclusion irrespective of conflicts with observed facts or probabilities. Both of these characteristics indicate an implicit recognition of the autonomy of thought; they also emphasize the intermediate position of early Greek philosophy. The absence of personification, of gods, sets it apart from mythopoeic thought. Its disregard for the data of experience in its pursuit of consistency distinguishes it from later thought.

I certainly want my students to learn and embrace the autonomy of mathematics. It would also be good for them to recognize mathematics as an interconnected unity. To name one example that I tried to develop in a course in the spring of the present year: while set theory starts out as a study of discrete objects, it comes to resemble the study of that continuous object first studied by the Greeks: the geometrical line.

I end with that simile, as wondrous in its way as any found in Homer. I am referring to the well-ordered set of ordinal numbers,

• one of which, zero, is least,
• each of which has a successor,
• some of which, the limits, are neither zero nor successors.

Each ordinal can be understood as the set of all less ordinals. The least limit is the set of all finite ordinals. As in calculus, it is of interest to know which functions are continuous. Addition and multiplication of ordinals are continuous in their right-hand arguments, but not left-.