Counting and Re-counting Plato

First published The World & I, August 1986.

Plato is playful but he plays in many ways. In what may seem to us a most trivial way he plays with words. Wordplay and puns are as common in the dialogues as they are in the plays of Shakespeare, and they are often as labored. Scholars have tend­ed to ignore this, merely remarking that Greek tastes obviously differed, and, by implication, dif­fered from our more refined sensibilities. The Plato of the academics cannot be a punster, or if he is, then he should be excused and read as if he were not.

The objection to Plato’s playfulness, however, especially on the grounds of some imagined cultural difference, may obscure a deeper meaning contained within the wordplay and puns.

Anybody who has ever heard anything at all about Plato must have heard that “he believed hi ideas” or that “he had a doctrine of forms,” and those who inquired further would perhaps have been told that these “ideas” or “forms” represented reality or were reality, the real, what is real, or simply (in Plato’s usual terms) what is. These ideas or forms are, are real, and they must be contrasted with what is not fully real, with appearances which both are and are not.

It has often been remarked (though not universally accepted) that Plato is careful not to develop a technical vocabulary in the dialogues. If the ideas or forms are linguistically con­fusing to the modern reader without classical Greek, it may be observed that they are equally confusing to the reader with classical Greek. Plato varies his use of terms so that what often appears uniformly in English translation as “idea” may be one of several different Greek words Plato uses variously. This may be difficult at one level if the reader of the dia­logues cannot develop the habit of looking for the meaning behind a word that is a member of a group of words. At another level, it suggests to the thoughtful listener or reader the need to see through a metaphorical matrix that Plato provides to the meaning lying beyond.

One of the words Plato is fond of using is the word eidos, usually translated as “idea” or “form.” But Plato is playing with the words, with us, and with what is, because the word is derived from the Greek word eidon, which generally means “to see” and in the perfect tense means “to know.” It also has a technical meaning in medi­cine as “symptom.” Plato is paradoxi­cally saying that the eidos of some­thing, the form or idea of it, as the translators say, the “whatever it is that makes it what it is and not some­thing else,” is not an appearance, not something we see but an un-see-able symptom, an invisible appearance.

If Plato loads common words with paradox and places them with other words to form  matrices that somehow provide the limits of meaning, or which together in the matrix embrace the requisite meaning, he is no less playful with names of gods and men.

A compound example from the Phaedrus will make this clear. At the beginning of that dialogue, Phaedrus reports to Socrates that Lysias is in town “staying with Epicrates, in the house where Morychus used to live, close to the temple of Olympian Zeus.” Since there is no need for this to be the report of an actual historical event, Plato can choose names and places at will—or for reason. Now ‘Epicrates’ is the word for “superior” or “master,” and we can readily understand why he and his house are near the temple of Olympian Zeus, the father of gods and men. But what is indicated by letting it be known that it used to belong to Morychus? The reference that gives meaning to this is a statue of Dionysus Morychus in Sicily, which was outside his temple and thus separated from the prayers and the pleasing smell of the sacrifices inside. This gave rise to a proverbial saying: “Sillier than Morychus, who neglects inside affairs and sits outside.” All we need remember from the Phaedrus is the prayer to Pan at the end of the dialogue in which Socrates asks that he may be fair within and that outwardly he be compatible with what is inward. Presumably, Lysias (by staying where he does) shows that he thinks of himself as “superior” or “masterful” but that he is actually sillier than Morychus since he is concerned with power over externals instead of inwardly with his soul.

This play with names, however, has an added dimension in that it shows the paradoxical nature of humans. Here is Lysias, whose name means “freeing” or “loosing,” playing power games with Phaedrus and attempting to control and capture him by the use of words. It is as if we should be true to our names, and Lysias is not. He is not, therefore, allowed to speak in his own voice—because he is so dangerous and untrustworthy. Socrates, incidentally, can be trusted, and his name means “safe power.” The dialogue distinguish­es the Lysian rhetoric of domination from the Socratic rhetoric of freedom by laying bare the different concep­tions of love, the different purposes of persuasion. Lysias uses speech to gain an unnamed gratification from the be­loved and ultimately the control that would allow gratification on demand; Socrates uses speech to elevate the soul of the beloved so that it improves itself. If the contrast between name and char­acter is present implicitly in the Phaedrus, it is quite explicit in the Apology, for one of the accusers is called Meletus. This name means “care” or “con­cern” and Socrates deals with his accusation publicly only by showing that Meletus is the man who doesn’t care. He is a man who belies his own name, and we are reminded of the discussion in the Cratylus concerning whether names are natural.

The distance between the name and what is named is one region in which the soul moves as it learns. It is pre­sented with the discrepancy, the gap, and if the soul can cross it, then it will have understood. The recognition of the gap thus serves an educational func­tion, perhaps the most important edu­cational function, in that it provides the direction and definition of move­ment. Another educationally useful separation is that between word and deed, between name and action, be­tween what we say and what we do.

Things are not what they seem, not what they are named. But instead of seeing this as a cosmic conspiracy that should drive us to cynicism, Plato sees it as a great opportunity for coming to understand what is. There is no decep­tion in the universe. But there is decep­tion in us if we take it for granted that what is named is what is, that the appearances are the reality; we then deceive ourselves, mistaking image for form, or convention for nature.

Plato enjoys the uni­verse, delighting in the fact that the ap­pearances will lead us to know what is, to know the ideas, the forms, the kinds, the types, the shapes, the spe­cies, the notions, and the natures —whatever matrix or metaphor we think it appropriate to create and name. The images are our great help. The playfulness of Plato is now not just a happy (or, for some, an inele­gant) quirk of character. It is a reflec­tion of the universe itself. The universe itself is playful, and to approach it with a straight, unequivocal Aristoteli­an face is to restrict the possibility of understanding—as well as to lose the joy of learning in it. But if the cosmic is comic (to imitate Plato’s playful­ness), it is also tragic, or at least serious. Meletus may be the man who belies his own name, but the hemlock Socrates drank killed him. Or made him immortal.

In short, if the cosmos is to be understood as being structured of forms or ideas (which are always what they are) and of names, words, actions, and objects that are not always what they are (collectively known as “im­ages”), then this metaphysical ambigu­ity requires a similar ambiguity on the part of whoever wants to understand it (and especially, of course, on the part of whoever wants to understand him­self in it). If the universe is the inter­play between forms and images, be­tween “what is what it is” and “what is what it is not,” then the thoughtful student must participate in the inter­play.

This is the metaphysical origin of the so-called Socratic irony and of the equally well-known Platonic irony. The philosopher must be ironical because the cosmos he is trying to understand is ironical, or, more concisely, the psychological and the epistemological must reflect the ontological (which, incidentally, they do naturally since the soul is a part of the realm of being; thus a major part of the educational task is to recover one’s nature). For many of Socrates’ contemporaries (and, later, for Aristotle), irony is one of a number of “characters”—and one of the less pleasant ones at that. For them, to be ironical is to say one thing and to mean another (usually its oppos­ite). This is what we call sarcasm, and it was as offensive in Athens as it is now. But in Plato, at least, irony is to say one thing and to mean it and its opposite at one and the same time. The truth both is and is not in the words. The logical counterpart of this is that (contrary to Aristotle) every statement is both true and false. Words are a very special kind of image, different from actions, different from physical objects. All speech is metaphorical, with one thing standing for another, with one sign signifying something significant or some significant things, with some collection of signs signifying some segment of the universe.

Signs, too, are images in that they are not what they are. The dog may well be, as Socrates asserts, a philoso­phical animal, but the word ‘dog’ is not a dog, nor is the family pet the arche­type or form Dog. They are related as image to imaged through a process called “participation” although, as has been said, to have a name is not to have the named. But if some special place must be accorded speech, the language, an even more special place must be given to numerals and the numbers for which they stand, for these show more clearly than anything else the relation­ship between form and image. They are the paradigm of the cosmic structure, and hence of the soul’s structure.

Dialectical Dance

Plato’s writings are images. Perhaps no one has ever understood that better than Plato himself for he moves be­tween the image and what is imaged as surely and as gracefully as a dancer in a dialectical dance. This dialectical dance is itself an image of the dance of the birds sacred to Apollo, the cranes. As Theseus and his companions were returning to Athens, they performed the crane dance on the island of Apol­lo’s birth, Delos.

Danced with measured tread and to the accompaniment of harps, the dance of the cranes was an image of the maze on the dancing-floor which Daedalus built for Ariadne in Knossos. This maze, in turn, was supposedly an im­age of the Egyptian labyrinth, which, being Egyptian, was so old that no origin could be found; but it too was an image.

The dancing-floor image, with its fixed lines and geometrical patterns, suggests that what might be called the choreography of the dialectical dance is already composed, the movements al­ready established, but that the partic­ular style and interpretation are due to the individual dancer. The relationship might be considered an image of that between the soul, the common nature all humans possess, and the particular and partial ordering and disordering of the soul in this person or that. If this thought were pursued, it would lead to the conclusion that the Platonic dia­logues collectively constitute the ma­trix within which the human soul can be defined. They show the soul’s limits.

But if the choreography of the di­alectical dance is already composed, then it must be inherent in the nature of the logos itself, otherwise it would not be a suitable dance for any and all dialecticians. The dialectical dance is measured.

There is, then, a circle of image-to-imaged relationships—of logos to labyrinth to dancing floor to dance to dancer to logos-in-dancer to logos to labyrinth . . .  Thus, the relationship of image to imaged is, in a way, bi-­conditional or symmetrical, and we can move in either direction, as it were. It is well to remember that if the image needs that which is imaged, then that which is imaged equally needs the im­age. In terms of knowing, this might not need much argument to support it, but it is equally true in terms of being. And this would always be the case if, to recall Socrates in the Meno, all nature is akin.

The hearer of the dialogue called Polity (or Republic, as it is usually and somewhat misleadingly named) is in fact reminded, at the end of the discussion about politics in the city (St. 595-608), that all writing is image-making, that all poetry is imitative. It may be more of a warning than a reminder, a warning to Glaucon and others that words alone are not enough, not even the words of Socrates, and that to acquire a definition is not necessarily to acquire what is defined, that to articulate acquisitions is not to be.

The Polity, as we have it, is an image. To simplify the image-to-imaged relationship considerably, we have an English translation of Plato’s Greek text that claims to be the writ­ten account of Socrates’ spoken report of a conversation that took place “yes­terday” among a small group of young men about justice and in which, there­fore, justice was to be found. If justice (the idea or form of justice, that is) were not somehow in the conversation, then it would not be about justice. If Plato is both correct and successful, leaving out the middle terms would mean that the image we call the Polity participates in the form of justice.

The Polity, then, is an image. And it is also full of images. If these images could be placed, at least tentatively, in some kind of order or pattern, if from an original an im­age could be realized, or if, from an image, the original could be seen as that which is imaged, then the dialectical dance of the logos, of the soul, would have begun. The simplest way to attempt this is to regard the Polity as a com­plete universe, as a universe of dis­course, so that the internal images it contains must refer either to them­selves, or to other contained images, or to the dialogue as a whole.

Now, the Polity concludes with an image, a most vivid and detailed image, the story of Er, which recounts the journey of a “valiant man” who came to an end in battle. Traveling through but in some sense outside the universe, Er not only witnesses the final judgment upon souls after their various life spans but he also sees the fundamental struc­ture of the universe itself. He sees the rims of the spheres that contain the unnamed planets, and he sees and hears the eight Sirens on the rims whose sounds produce a complete scale. Around are seated the three Fates, daughters of Necessity. Their names are given—Lachesis, Clotho, and Atro-pos—and they sing respectively of the past, the present, and the future.

Not only are the Fates seated around but they are situated at equal intervals, and they provide the motive power for the circular rims of the planets by touching them. Clotho uses her right hand on the outside rim only (which certainly suggests the clock­wise motion of the Same to be found in the Timaeus), and Atropos uses her left hand for the inner rims (which sug­gests the Timaeus’s counter-clockwise mo­tion of the Other), although Clotho ceases from time to time. Lachesis, who is the only one who communicates with the souls, albeit through a spokes­man, puts “one hand to one and the other hand to the other, each in turn.” Upon drawing the diagram, as it were, it becomes apparent that the motive forces of the universe are at the three vertices of an equilateral triangle that circumscribes the outermost circle of the universe.

Since the whole universe is suspend­ed on a spindle from the lap of Necess­ity, the geometrical diagram images not a circle inscribed within an equi­lateral triangle but a sphere circum­scribed by a tetrahedron. If we were to go outside the dialogue, then the pic­ture resembles a woman using a drop spindle in spinning wool, with the spin­dle being turned by the fingers from time to time and the momentum of the spindle (looking like Er’s whorls from the top) carrying it round. It is possi­ble, however, to relate the geometrical solid image, the geometrical diagram, to the Polity itself, bearing in mind that the sphere enclosed by a tetrahed­ron was a well-known Pythagorean device or image.

Since the image is a geometrical one, a way is needed to image the Polity geometrically or, perhaps, arithmeti­cally, since it is usually possible to translate arithmetic into geometry. Various figures suggest themselves —the circles of Er’s universe, for ex­ample, or the Divided Line—but for a number of reasons, some of which will become apparent, more advantage can be gained if the Polity is first num­bered.

Measuring the Polity

The task of numbering the Polity may seem quite daunting, not least because a unit would be needed in terms of which to count the dialogue and no such unit is immediately appar­ent or available. And yet the question whether Plato had a unit of composi­tion has not been pursued although it is almost inevitable that he did. If he did, what was it?

The technological and social process­es of writing and “publishing” were such that Plato must at least have been aware of a physical unit of composition. Presumably, the dialogue was initially composed on wax tablets, which would lend themselves to correction, expan­sion, and amendment. We know that Philip of Opus was said to have tran­scribed the Laws “from the wax,” which lends credence to this view. In addition, the Polity is so intricate in its self-referring that for passages to be considered and revised side by side, as Adam, for example, in his authorita­tive edition of the text, requires, some system of indexing, storage, and re­trieval must have been employed. Cross-referencing a work of the Polity’s length would have required extensive organization, although we do not know how many tablets there were, how they were stored, or how they were re­trieved.

The simplest method would surely be, first, to have a standard-size tablet—of standard physical size, thus mak­ing storage easier, and, consequently, of standard-text size—and, second, to have them numbered. Thus, quite apart from any wish on Plato’s part to give an arithmetical structure to the Polity, his attention would inevitably have been drawn to the relation be­tween the substance of his text and the number of the tablet upon which it was written.

It would not be surprising if the numbers were, in fact, part of Plato’s original plan from the beginning, form­ing an important and integral part of the substance of the dialogue. Even if the numbers had not been within his original conception, Plato would have undoubtedly become aware of them simply in the course of using the tech­nological processes available to him.

Setting on one side the question of the size of the tablet, whether in terms of physical dimensions or in terms of amount of text, further light is thrown on the problem by the mode of what we would call “publishing.” That texts of various works circulat­ed is well-attested, and, for example, Socrates points out in the Apology the commonness and cheapness of Anaxagoras’ writings. But although texts circulated in copy form and were pre­sumably to be read, it must be remem­bered that “to be read” meant to be read aloud, there being. In general use, no such thing as what the modern world calls “silent reading.”

Thus the writer of any work must have been conscious of the time that it took to read, that is, to read his text aloud to a circle of friends, of students, of people with some common interest, or in some common place.

What we call “reading” is, in fact, “silent reading,” and this obscures the necessity for the “measured tread” of the crane dance. As we read to our­selves, we have greater control—per­haps greater latitude would be a better description—over the rate of reading, and we speed up or slow down accord­ing to a variety of factors, some of which are totally irrelevant to the subject-matter of the text and may even be hostile to it. But being read to changes the distribution of power in the situation—after all, the reader is reading and presumably chooses or is given a reading rate, and the hearer has to adapt accordingly. The experi­ence is much more like attending a musical concert than anything else, for there the conductor sets the temporal limits for the interpretation—estab­lishing the “measured tread”—and the hearer listens. This, in turn, means that the writer of texts, the compos­er, can and prob­ably must bear in mind the length of time that his work will take to per­form, to be read al­oud. There is the well-known story of Herodotus reading at far too great a length at the Olym­pian games and giving rise to the proverbial expression “in the shadow of Herodotus.”

Plato must have been aware of the length of time it would take to read aloud each of his works, and especially the Polity. In the absence of any tradi­tion or instructions, one way to get an idea of the length of time it takes to read the Polity out loud is simply to do it. This, of course, does not prove the amount of time required but it does establish what might be called an order of magnitude, the “measure” of the total tread. Even granted that we are not native speakers of classical Greek, and even granted that we do not know the customs for public speaking nearly well enough to be sure, and that we know even less about the habits and skills of listening, the fact remains that the time it takes to read the Polity aloud in Greek tends to approximate twelve hours. It can be done in slightly more or less time—and it is incidental­ly surprising how quickly we can adapt to various rates of speaking and lis­tening—and yet deviations from the twelve hours tend to produce a loss in clarity of argument, with a corresponding loss in the continuity of the dialogue. The dance stops.

If we assume that Plato wrote the Polity with the intent of its taking twelve hours to be read—to be read aloud—then we have at our disposal another way of numbering the units of the dialogue simply by reference to the units of time.

Before embarking on such a venture it should be noted that the dialogue tells us, in St. 621b, that for the souls in Er’s story it was midnight. Since this is virtually at the end of the dia­logue, its starting point would have been noon. This is both dramatically plausible and organizationally conven­ient. Dramatically, it allows time for Socrates and Glaucon to rise (near dawn), to descend to the Piraeus, to see the processions, and to say their pray­ers to the initially nameless goddess, who later turns out to be Bendis, the Thracian goddess of the Moon. By the time Socrates and Glaucon are setting out for the city, Polemarchus and Adeimantus have seen and captured them and together they go off to Polemar­chus’ house, which can only be a few minutes’ walk away. Thus the dramat­ic conversation could easily be seen as starting at noon.

If the conversation being repeated took place “yesterday,” then its re­hearsal must take place “today” and the question arises as to when the recounting began. Organizationally, having noon as the starting point is undoubtedly convenient for it not only mirrors the dramatic events of the previous day but it also provides the time that could be most easily deter­mined. Noon was a well-established meeting time, and in the absence of clocks it could be determined fairly accurately even without the special gno­mon set up in the Athenian agora.

According to Proclus, an admittedly late authority, the feast of Bendis was held on 19 Thargelion, which would correspond to our June 5/6. If this is taken as the likely date, and if the lati­tude of the Piraeus is taken to be 38 degrees North, then the sun would have set at approximately 7:24 that evening. By a simple computation, it can be determined that at that time the following passage was being read (at the end of the 444th minute):

“Which of the gods in heaven can you point to as the lord responsible

for this, whose light makes our sight see in the finest way and the

seen things seen?”

“The very one you and the oth­ers would also point to,” [Glaucon]

said. “For it is plain your ques­tion refers to the sun.”

“Is sight, then, naturally related to this god in the following way?”


“Neither sight itself nor that in which it comes to be—what we

call the eye—is the sun.”

“Surely not.”

“But I suppose it is the most sun-like of the organs of the senses.”

“Yes, by far.”

“Doesn’t it get the power it has as a sort of overflow from the

sun’s treasury?”

“Most certainly.”

“And the sun isn’t sight either, is it, but as its cause is seen by sight


“That’s so,” he said.

“Well, then,” I said, “say that the sun is the offspring of the good I

mean—an offspring the good begot in a proportion with itself: as the

good is in the intelligible region with respect to intelligence and

what is intellected, so the sun is in the visible region with respect to

sight and what is seen.”

“How?” he said. “Explain it to me still further.”

“You know,” I said, “that eyes, when one no longer turns them to those things over whose colors the light of day extends but to those over which the gleams of night extend, are dimmed and appear nearly blind as though pure sight were not in them.”

“Quite so,” he said. (St. 508)

On the supposition of a twelve-hour reading time, beginning at noon, it appears that as the sun sets on the reader and hearers their attention is drawn to that of which it is an image.

The other notable time in the ephemerides for the day would, of course, be the end of twilight, the onset of ab­solute darkness—dark especially because the feast of the Moon goddess would take place at new moon. Twi­light ends on June 5/6 in the Piraeus at 9:14 at which time the reader was reciting the following passage:

“Then, democracy must, as it seems, be considered next—in what

way it comes into being and, once come into being, what it is like—

so that when we know the character of such a man in his turn,

we can bring him forward for judgment.” (St. 555b)

Is democracy best discussed after dark? Does its advent mark the extinc­tion of all light?

There is incidentally an isolated anecdote in Athenaeus to the effect that Plato invented a clock to tell the time at night. Perhaps it told polity time.

If these two passages, coinciding with sunset and the end of twilight, are taken as giving some plausibility to the general thesis of a twelve-hour reading span, it is possible to assign some numbers to the Polity. Since in twelve hours there are 720 minutes it is possible to divide the dialogue into that number of equal units. Experi­ence shows that such a unit is quite small, and for the present purpose it is sufficient to adopt the unit of time employed, at least on occasion, in the legal proceedings in Athens, namely, three minutes. Thus, the dialogue can be divided up into 240 units of three minutes each.

The Story of Er

It is now possible to address the  prob­lem of dividing up the text. Since the syllable is the unit of time in speech it is only necessary to count the total number of syllables in the Polity and to divide that number by 240 in order to determine the number of syll­ables in each three-minute unit of read­ing time. It is curious that this has not been done previously, curious simply because the process of syllable counting, known as stichometry, was well-established in the ancient world, both as a check for authenticity of the copied text and also as a measure for paying the scribe. It should, however, be noted that if, for whatever reason, the letters of the text were used—converting the time of syll­ables to the space of letters—no appre­ciable difference from the results of using syllables would emerge.

The use of the syllable as a stichometric unit may throw some light on the significance of the well-known anec­dote concerning the opening eight words of the Polity. It is recounted that among Plato’s possessions after he died there was found a table upon which were written the opening eight words of the dialogue in several different ways. At one level, this story must be an acknowledgment of the care Plato took over his writing and of the fact that the way the words were actually “published” was the right way. At another level, however, it simply affirms the eight words themselves—there being no hint or suggestion that the alternatives contained different words —and so there is reason to look for what is invariant in the eight words themselves. Obviously, one invariant, no matter what the preferred order of the words, is the number of syllables they contain, namely, eighteen. If the unit line of the Polity is taken to contain eighteen syllables, then it emerges that the dialogue contains 10,000 lines.

If the physical unit of composition were the focus of attention, then the tablet might be imagined to be of a width suitable to contain eighteen syll­ables. The height or length would then be of forty-two lines, and each tablet would contain eighteen times forty-two or 756 syllables. (These numbers, like all other numbers in this exposition, are well within a one-percentage accu­racy.) From what is known of Greek writing on papyrus, a section of text eighteen syllables wide is by no means impossible or even unlikely; after all, Homer’s lines are hexameters. But the length of forty-two lines is much less likely and it might turn out that there were 720 units after all, each with a height of fourteen lines. Other possibil­ities suggest themselves, most obvious­ly 1,000 units, each with ten lines of eighteen syllables.

However, for the present purpose of analyzing the Polity text, it has been found convenient to divide it into 240 equal units, and for ease of reference these have been called Bremer units. These Bremer units (or Br. units) must be sharply distinguished from the well-established and time-honored Stephanos numbers, since the latter are not of equal length, nor are they numbered consecutively, nor do they start from unity. Thus, whatever patterns the numbering of the dialogue would dis­close are frustrated by the incomplete, erratic, and arbitrary nature of the Stephanos pagination.

To give one simple example, it emerges from the use of Br. units that the objections of Glaucon and Adeimantus are contained in Br. 26 through 35. The symmetrically placed Br. units would obviously be Br. 206 through 215 and it need only be pointed out that in Br. 206 Socrates says:

“Shall we hire a herald, then, or shall I myself an­nounce that Ariston’s

son has decided that the best and most just man is happiest, and he is

that man who is kingliest and is king of himself; while the worst and

most unjust man is most wretched and he, in his turn, happens to be

the one who, being most tyrannic, is most tyrant of himself and of

the city?”

This passage begins the series of proofs in which the objections of Glaucon and Adeimantus are finally acknowledged to have been met. The end of the passage symmetrical with the beginning of the objections is marked at the beginning of Br. 216 by the following:

“Then in what way, Glaucon, and on the basis of what argument, will

we affirm that it is profitable to do injustice, or be licentious, or

do anything base, when as a result of these things one will be worse,

even though one acquires more money or more of some other pow­er?”

“In no way,” he said. (St. 591a)

Thus the objections themselves and the acknowledgment that they have been met are exactly symmetrical with each other in position and they are also equal in magnitude.

Once the Polity has been numbered in terms of Bremer units, or in any other suitable way, a wide range of symmetries and other patternings be­come apparent. However, to remain with the example of the objections of the two brothers, an examination of the objections reveals that they them­selves are subject to symmetry, being equally divided between Glaucon and Adeimantus. Glaucon’s objections occu­py Br. units 26 through 30, and are followed by those of Adeimantus in Br. units 31 through 35. This equality between the two broth­ers is carefully maintained and is also emphasized when Socrates, after hear­ing the two sets of objections, quotes the poem “Sons of Ariston, divine offs­pring of a famous man . . .” and continues by saying that something divine must have happened to them both. The feeling of equality is tem­pered somewhat by the facts that Glau­con is mentioned first and that it is Glaucon’s lover who has written the poem, but Socrates does not draw at­tention to any inequality although it is undoubtedly there.

After Socrates’ offer of help to meet the objections, it is Adeimantus who takes over the primacy by answering the questions of Socrates, but the peri­od is brief and after only 4 Br. units (Br. 36 through 39) Glaucon resumes the answering role and for exactly the same number of Br. units (Br. 40 through 43). In Br. 44 Adeimantus takes over the argument because he anticipates that the discussion of education will be use­ful, and he pursues education for be­tween sixteen and seventeen Br. units until in Br. 60 Glaucon resumes with the discussion of song and melody be­cause, as Socrates says, he is musical. (This remark of Socrates’ occurs exact­ly one quarter of the way through the dialogue.)

Glaucon continues with the discussion of “musical” education and then explores gymnastic, concluding with an agreement that the guardians must get the right education, “whatever that is.” This suggests that what has been described, even the purged forms of music and gymnastic, are not “right.” Socrates and Glaucon agree further that the guardians must have houses, but just as the length of their conver­sation equals the preceding conversa­tion of Socrates with Adeimantus, the latter interrupts. Had he been keeping count? Plato certainly had.

Adeimantus’ inter­ruption concludes with Br. 83 as So­crates says, at the beginning of Br. 84,

“So then, son of Ariston, your city would now be founded. In the

next place, get yourself an adequate light somewhere; and look

yourself—and call in your brother and the others—whether we

can somehow see where the justice might be and where the injustice.”

The “son of Ariston” is obviously Glau­con, although the previous answer had been given by Adeimantus. Thus, from the end of the conversation with Thrasymachus, the “prelude,” Plato has scrupulously observed an equality be­tween the two brothers in the following pattern:

Glaucon Br. 26-30

Adeimantus Br. 31-35
Alternation of primacy as the initiative passes from the brothers to Socrates.

Adeimantus Br. 36-39

Glaucon Br. 40-43

Adeimantus Br. 44-60

Glaucon Br. 61-76

Adeimantus Br. 77-83

The equality and alternation of the first six sections is apparent, and the only minor restriction to note is that in Br. 36 Socrates carries out the brief transition from the brothers’ objections to the construction of the city in words. It is not very significant, but it would reduce the span of Adeimantus by something less than one Br. unit. Also, the final third of Br. 60 belongs to Glaucon and not to Adeimantus. The general picture is quite clear, however, and the question arises whether the structure will continue.

At first glance, the pattern of equality is shattered in what follows. The following responsive contribution of Glaucon is very long and Adeimantus does not respond again until the end of Br. 130, a span of almost forty-seven Br. units, occupying two hours and twenty minutes. An exception to the absolute silence of Adeimantus should be noted, however, and it is found in Br. 100/101 when Polemarchus, by taking hold of Adeimantus’ cloak, initiates the digression. Adeimantus is named in Br. 100 and speaks only briefly in Br. 101 when he helps to capture Socrates for the second time. The transition occu­pies one Br. unit and Glaucon acts as respondent both before and after. Prior to the beginning of the digression Glau­con has spoken with Socrates for sev­enteen Br. units and subsequent to its beginning he speaks for thirty Br. units.

The last contribution of Adeimantus had been only seven Br. units, and this is clearly not balanced by seventeen Br. units (Br. 84-100), nor by thirty (Br. 101-130), nor by the whole forty-seven (Br. 84-130). And yet Plato seems to have taken considerable care to indi­cate both the equality of the two broth­ers and where that equality ceased.

The equality or balance can, of course, be restored, by marking off from the end of Adeimantus’ last conversation in Br. 83 an equal section of seven Br. units. This means that Br. 84 through 90 is that section of Glaucon’s conver­sation that balances with Adeimantus’ last talk. In other words, from Br. 26 through Br. 90, the two brothers bal­ance each other exactly and have equal shares in the three hours and fifteen minutes it takes to read those sixty-five Br. units. The tabulation would then be amended as follows:

Glaucon Br. 2&-3

Adeimantus Br. 31-35
Alternation of primacy

Adeimantus Br. 36-39

Glaucon Br. 40-43

Adeimantus Br. 44-60

Glaucon Br. 61-76

Adeimantus Br. 77-83

Glaucon Br. 84-90

If we make Glaucon’s contribution equal in this way and turn to Br. 91 to discover what topic is being discussed, we find Socrates saying,

“Now, it’s a slight question about the soul we have stumbled upon,

you surprising man. Does it have three forms or not?”

This identifies for us the superiority of Glaucon. The souls of the brothers are the same, up to a certain point, as it were, and then it is only Glaucon who is able to face, in the conversation, the nature of the soul. Glaucon’s soul is worthy of the question in principle, if not in fact, for Socrates immediately says,

“But know well, Glaucon, that in my opinion we will never get a

precise grasp of it on the basis of the procedures such as we are now

using in the argument. There is another longer and further road leading

to it. But perhaps we can do it in a way worthy of what has been said

and considered before.”

This most important remark is addressed specifically to Glaucon, not to Adeimantus and not to the others, and there seems to be the hint that although Glaucon expresses content with the present inferior method, he is about to embark on a longer journey, which, if it does not give a complete account of the soul, is nevertheless beyond his brother. The question of the soul’s nature in Br. 91 marks the divergence of the brothers, and beyond this point it appears they are not equal and balanced. To change the metaphor, at this point their paths separate, and while Glaucon pursues the upward path, Adeimantus can go no higher. This may possibly be too harsh a judgment on Adeimantus, but two things are clear. One is that even if he can go higher, in the Polity he does not do so, and the other is that after raising the question about the soul there remain one hun­dred and fifty Br. units, of which Adeimantus shares only forty with Socrates. These forty Br. units occupy only two hours of the remaining seven hours and thirty minutes.

The fact that Adeimantus does not go further on the upward path is evidenced in the content of the two passages after Br. 91 in which he acts as respondent. The first of these is made up of seventeen Br. units, exactly in the middle of the digression. The pattern of the digression is made up of twenty-nine Br. units of Socrates talking with Glaucon, followed by seventeen Br. units with Adeimantus, followed by another twenty-nine Br. units with Glaucon. An examination of the content does not reveal any new and higher levels of understanding. It is true that there are some magnificent passages—the image of the ship-owner, for example—but the whole section is essentially negative, even beginning with an objection. While it is right and even necessary to raise objections, Adeimantus seems to have a preference for them, and his character seems opposite and almost pessimistic. At the end of this middle section of the digression, Socrates points out to Adeimantus that the rulers, the philosophers, “must go the longer way round” (which implies that Adeimantus has not done it), and that unless he does so, he will “never come to the end of the greatest and most fitting study.” He then refus­es to discuss it any further with Adeimantus but does continue with Glaucon.

The other section in which Adeimantus talks with Socrates is of twenty-three Br. units, from Br. 180 through Br. 202 (corresponding approximately to St. 549 to St. 576), in which the degeneration of the best city and of the best man are gone through. This confirms Adeimantus as the expert in the worse, and the section ends with a summing up of the worst man, and, since he is the worst, Adeimantus can go no further. Glaucon relieves him, taking up the argument, and begins the comparison between the best and the worst which leads, as mentioned above, to the judgment beginning in Br. 206 about the original objections of the brothers. But here Adeimantus seems to have vanished, and when Socrates dramatically asks if he should hire a herald to announce “that Ariston’s son has decided that the best and most just man is happiest . . .,” it appears that Ariston has only one son.

And yet, we know that Ariston had not one, not two, but three sons, and the question arises whether Pla­to shows himself in the Polity. It ap­pears that he does.

From a consideration of the Br. units, confirmed more exactly by a direct syllable count, it turns out that Glaucon speaks with Socrates for twice the amount of time that Adeimantus speaks with Socrates. In all, Glaucon speaks with Socrates for 108,000 syll­ables, and Adeimantus speaks with him for 54,000, for a grand total of 162,000 syllables or very slightly more than nine-tenths of the whole dialogue. Even a casual reader of the dialogue would have some strong impression of the primacy of Glaucon, but it is useful to have that primacy quantified. It is not only useful but also striking.

It is striking because the exactitude suggests deliberate intent, although it is hard to say why Glaucon should be portrayed as deserving exactly twice as much of Socrates’ time as Adeimantus. It is, perhaps, curious that after an elaborate and systematic attempt to keep the two brothers equal (that is, until Br. 91), the final outcome shows the double value of Glaucon. What is more curious is that the breakdown of the equality should come just at that point in the conversation when one of the cardinal doctrines of Plato—the tripartite nature of the soul—is about to be stated and argued. There is not only the question of its being Plato’s own original view, but there is also the difficulty of attributing such an origin­al view to someone else, even if that someone else is a favorite brother. Rather than giving Glaucon the re­sponsibility for the three-part soul (and much else besides), it would make much more sense to assume the respon­sibility oneself, and Plato’s problem would then be to devise a way of doing that without becoming a named partic­ipant in the dialogue (which would cause all sorts of other complications).

Together with this question of intel­lectual responsibility there is also a simple arithmetical question. If we take the section of the Polity from Br. 91 where the soul’s nature is first mentioned to the point at which Adeimantus offers Glaucon as a model for the timocratic man (Br. 179), it turns out that the section contains eighty-nine Br. units. Of these, seventeen Br. units belong to Adeimantus and the remaining seventy-two Br. units con­tain the discussions of the tripartite nature of the soul, the idea of the good, the divided line, the image of the cave, the mathematical studies and dialectic —all the philosophical contributions that have been regarded as Plato at his most characteristic. Conversely, al­though there are some excellent things said in the other parts of the dialogue, there is nothing the real Adeimantus and the real Glaucon might not have said. It should also be observed that the seventy-one Br. units neatly bisect the contribution of Glaucon, so that he does not have double of Adeimantus’ talk with Socrates, but rather the three brothers each have an equal share of that precious relationship. On the whole, this is a much more gracious and satisfying outcome.

Once having seen the possibility of there being, as it were, two Glaucons, a real Glaucon and a Plato-Glaucon, it is not hard to find a hint or two in the words (as opposed to the numbers) of the text to mark the transition. In Br. 91, the following exchange takes place between Socrates and Glaucon:

“Then it is in this way, my friend, that we will claim that the single man—with these same forms in his soul—thanks to the same affec­tions as

those in the city, rightly lays claim to the same names.”

“Quite necessarily,” he said.

“Now it is a slight question about the soul we have stumbled upon,

you surprising man,” I said. “Does it have these three forms in it or not?”

“In my opinion, it is hardly a slight question,” he said. “Perhaps, Socrates, the saying that fine things are hard is true.” (St. 435)

There are three forms of the soul and three sons of Ariston, there is the question of same names, and suddenly Glaucon becomes “you surprising man” when in the previous speech he had been “my friend.” What was so sur­prising? That he had become Plato-Glaucon?

The transitional passage at the con­clusion of Plato-Glaucon’s section is also suggestive—if we know what we are looking for:

“Then,” I said, “this is the way this polity would come into being and what it would be like—given the fact that we are only outlining a polity’s figure in speech and not working out its details precisely, since even the outline is sufficient for seeing the justest man and the unjustest one, and it is an unpracti­cally long job to go through all polities and all dispositions and leave nothing out.”

“Right,” he [Glaucon] said.

“Who, then, is the man correspond­ing to this polity? How did he come into being and what sort of man is he?”

“I suppose,” said Adeimantus, “that as far as love of victory goes, he’d be somewhere near to Glau­con here.”

“Perhaps in that,” I said, “but inthese other respects his nature does not, in my opinion, correspond to his.” (St. 548)

Of course, it does not correspond to Glaucon’s nature for Glaucon isn’t Glau­con. This would also make some sense of the fact that, unlike the other discus­sions of the kinds of man, in this case of the timocratic man his charac­ter is discussed before his genesis. He does not need to have a genesis for he is already before the group, but he does need to be reestablished as the original Glaucon who went down to the Pi­raeus with Socrates and not the Plato-Glaucon of the preceding eighty-nine Br. units. It seems likely that it was well understood by Plato’s contempo­raries which sections of the Polity were Plato’s own, especially his own.

Although this discussion may have some merit in itself, its purpose here has been to illustrate what can be explored if a way is found to quantify the Polity. Without the numbering of the dialogue it is hard, if not impossi­ble, to grasp the symmetries and other patterns that are built into it. For example, it has not been mentioned thus far, but the discussion of the soul in Br. 91 is arithmetically symmetrical with Br. 150, which, it emerges, con­tains the beginning of the Divided Line. The symmetry is satisfying, but it still remains to elucidate its meaning. That cannot be done until the symmetry is recognized, and the value of Bremer units (or any similar numbering) is precisely that it makes such patterns clear for the first time.

It is now possible to return to the original supposition of this exposition, namely, that the story Er relates is an image of the dialogue itself. That the planets are numbered but are not given their well-established names suggests that for the purposes of the Polity they are to be seen not only as themselves but also as standing for others.

In fact, it is obvious that the order of the unnamed planets represents the order in which those who make a constructive contribution to the dialogue speak. Thus, to use the Latin names familiar to us, Saturn is played by Cephalus; Jupiter, Saturn’s son, by Polemarchus, Cephalus’ son; Thrasymachus takes over from the god of war, Mars; Mercury is imaged by Glaucon, while Adeimantus plays Venus. The allocation of the Sun to Socrates seems particularly appropriate. The Moon must then represent Plato, getting its light from the Socratic sun, and the sphere of fixed stars (the field of planetary movements) is the Athenian democracy, which provides the background for the events in the Piraeus and for Plato’s writing of the Polity.

The original image in this discussion was a geometrical diagram of a sphere inscribed in a tetrahedron, a regular pyramid. The apex of the tetrahedron is the location of Necessity, from whose lap the spindle of the sphere (or spheres) is suspended. The three daughters of Necessity define the circumscribing equilateral triangle, which is a section of the tetrahedron, and, moreover, they provide the motive power for the rotation of the spheres about their axis, the spindle. Since the rims which are revealed as the section through the spheres represent the planetary orbits in some way (and the Sirens their heavenly music), the geo­metrical diagram is, at one level, an image or model of the universe, of the cosmos.

It has been suggested above that, at another level, the geometrical diagram is an image or model of the Polity itself. If this suggestion is pursued and anoth­er level of interpretation is attempted, then it seems highly likely that the daughters of Necessity are replaced by the sons of Ariston who share equally in the dialogue and are, therefore, lo­cated at the vertices of an equilateral triangle. Since Necessity is the mother of Lachesis, Clotho, and Atropos, her place in the diagram must be taken by Ariston, the father of Plato, Glaucon and Adeimantus. The identification of the three daughters with the three sons is not at all impossible, but what is more imme­diately significant is the replacement of Necessity by Ariston. In the philoso­phical content of the Polity the role of Necessity is not emphasized and, in­deed, preeminence is given not to Aris­ton (“best”) but to his verbal relative Agathon (“good”). It is the Good that is the cause of all being and of all know­ing and it is therefore appropriate that the Good take its place at the apex of the tetrahedron.

To make this substitution is to rep­resent the cosmos in a new way, and it would be tempting to interpret the spindle as the Divided Line and to ascertain whether the geometrical dia­gram fits the dialogue as quantified. However, in terms of the dialogue it­self, the three sons of Ariston are suspended from their father, but in another way they are suspended from their intellectual father, Socrates. While it is true that the Sun is presented in the Polity as the offspring of the Good in the visible world, it is equally true that Socrates is the offspring of the Good in the human world. Most fundamentally, as the Good is the source of all being and knowing, so Socrates is the source of the being and knowing of the Polity itself, for without him it would never have existed and without his recounting of the conversa­tion it would not now be known.

Insofar as the conversation took place “yesterday,” it is under the au­thority of Lachesis the measurer, who sings of the past. As it is recounted “today,” the conversation falls under the authority of Clotho the spinster or spinner of the thread of Me, who sings of what is, of the present; it is well to remember the widespread use of spin­ning as a metaphor for story-telling —witness our word “yarn.” Finally, the dialogue is subject to Atropos, who rules over what will be, over the future, and although she cannot be turned or avoided, nevertheless her terrible pow­er, is mitigated by the message from Lachesis, which falls exactly at the arithmetic center of Er’s story:

“Virtue is without a master: as he honors or dishonors her, each

will have more or less of her. The responsibility is the chooser’s;

god is not responsible.”

While the shears of Atropos will snip Clotho’s thread of life, as measured by the rod of Lachesis, the kind of life that is led depends on whether we learn from the dialogue and whether we are persuaded by Er’s tale and always keep to the upper path.

Although in one sense Socrates takes the place of Necessity, in anoth­er sense he is sub­ject to a kind of ne­cessity in that, apparently, he must tell his tale, he must recount the story. Although his story-telling may change what is, in a certain sense it may have “results,” those “results” are not the outcome of Socrates as cause, and he does not tell his story with a purpose beyond the story itself. He tells it because he must and in that sense he operates like and under Necessity. He cannot take from hearers their responsibility to choose and he cannot control what they make of the story they hear. Indeed, he can­not even control whether they hear it or not. Cephalus leaves before the tale is told and there is no indication that Polemarchus, for example, hears it to the end although apparently, from what we know, he does not leave. The reader or hearer of the dialogue does not know whether Pole­marchus heard it or not. But possibly neither does Socrates. Although this may well be so, the three sons of Ariston do perform the same function as the Fates, namely, as movers. In different ways, the sons of Ariston, admittedly suspended from Socrates, make the circles of the dialectical dis­course revolve—and Adeimantus, of course, in the opposite direction, the Other.

Returning to the replacement of the mother and her three daughters by the father (Ariston/Agathon/Socrates) and his three sons, it become immediately obvious that the female is supplanted by the male. We are reminded that the Polity takes place on the feast of the Moon goddess and during the course of the discussion the power of the Sun and Apollo is given priority. How this is to be understood is far from clear. It would be easy to apply the principles of Robert Graves (in The White Goddess and elsewhere) and to see in this the intellectual account and myth of the supposed social transference of power, as the matrilinear is replaced by the patrilinear. But this view does justice neither to Graves nor to Plato. The fact is that in the Polity itself the equality of men and women is strongly asserted —same nature, same education, same function—and it appears that a whole new relationship between the sexes is adumbrated, a relationship that is not immediately and obviously acceptable either to the Sun or to the Moon, to Apollo, or to Bendis. It should be re­membered, moreover, that, according to the received myth, when Theseus introduced the crane dance at Knossos, it was the first time that men and women danced together.

It would be illuminating to know the choreography of that dance, to know the measure of its tread. It would be equally helpful to know the song or scale that Er’s Sirens sang, to know the ratios of the string lengths necessitat­ed by the planetary distances of the cosmos. But if Er’s story is an image not only of the cosmos but also of the Polity itself, then those ratios should be built into the dialogue. That those ra­tios are built into the dialogue, together with the measure of the dance’s tread, will only be apparent to those who are willing, with Socrates, to count and to recount “today” the conversation that took place “yesterday” down in the Piraeus. •