plato & herodotus 12

DRAFT ONLY Bryan Carr

Science as Suggestion:

Cosmological & Mythic intertext as background in Herodotus and Plato 1

'You don't know what you're talking about!' cried Humpty Dumpty. 'How many days are there in a year?' 'Three hundred and sixty-five,' said Alice. 'And how many birthdays have you?' 'One.' 'And if you take one from three hundred and sixty-five, what remains?' 'Three hundred and sixty-four, of course.' Humpty Dumpty looked doubtful. 'I'd rather see that done on paper,' he said.Alice couldn't help smiling as she took out her memorandum-book, and worked the sum for him:

365 - 364 1 Humpty Dumpty took the book, and looked at it carefully. 'That seems to be done right—' he began. 'You're holding it upside down!' Alice interrupted. 'To be sure I was!' Humpty Dumpty said gaily, as she turned it round for him. 'I thought it looked a little queer. As I was saying, that seems to be done right -- though I haven't time to look it over thoroughly just now -- and that shows that there are three hundred and sixty-four days when you might get un-birthday presents -- ' 'Certainly,' said Alice. 'And only ONE for birthday presents, you know. There's glory for you!' 'I don't know what you mean by "glory,"' Alice said. Humpty Dumpty smiled contemptuously. 'Of course you don't -- till I tell you. I meant, "there's a nice knock-down argument for you!"' 'But "glory" doesn't mean "a nice knock-down argument,"' Alice objected. 'When I use a word,' Humpty Dumpty said in rather a scornful tone, 'it means just what I choose it to mean -- neither more nor less.' 'The question is,' said Alice, 'whether you CAN make words mean so many different things.' 'The question is,' said Humpty Dumpty, 'which is to be master - - that's all.' 2

1 What follows here are the preliminary and still unorganized findings of an ongoing investigation into the assumptions at work in texts of Herodotus and Plato, and their (sometimes distant) predecessors. I’ve undertaken this work because I think these archaic writers not merely interesting but important; but it may seem at first that I am involved with trivia. I hope to show that the ancients had a very different notion of what was trivial, and that we cannot read them well if we do not permit ourselves to attend to the details they thought worthwhile. But though I enjoy skulking in the dusty half-lit side-chapels of footnotes, I cannot pretend to real scholarship. My "method," if that's what it is, comes perilously close to free-association, and although I do distinguish between connections that can be backed up with evidence and those that cannot, I tend to assume that the ancients were more clever than I, or at least closer to their own motives, and that any idea that occurs to me would have occurred to them. I do maintain there is a difference between seeing something and making it up-- though I acknowledge that I have problematized the distinction. I try to use the bait best suited for the occasion, for plausibility is a shy creature. Accordingly, my snare is sometimes Jungian, sometimes structuralist, sometimes a causal argument with reference either to conscious intent and influence or to a broader tradition (what anthropologists call "diffusion.") But none of these do I use exclusively. I am indebted to Duane Christensen, Jonathan Crimmins, David Crookes, Pete Dello, John Holthouse, and Ernest McClain for specific suggestions which I have incorporated into this paper.

2 Lewis Carroll, Through the Looking-Glass, & what Alice found there. Ch. VI

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I take my cue from the most famous remark Socrates ever made: the unexamined life is not worth living. This evaluation, as Nietzsche saw, profoundly modifies earlier Greek thinking, though not exactly as Nietzsche believed. There is a real question in Greek thought about whether human life can be good, expressed starkly in the famous remark of Solon: Call no man happy until he is dead. Sophocles quotes this at the end of Oedipus Rex, that founding document of psychoanalysis. This Freudian inheritance should dissuade us from shrugging off Solon’s apparent pessimism as irrelevant to ourselves. Indeed, the extent that we assume Solon is wrong, or can be wrong, may be due to our having come (via Freud’s adaptation of ‘examination’) to regard Socrates’ adage as self-evident—and perhaps too easily applied.

The thesis this paper intends to illustrate, without however arguing for it explicitly, is that the world of the fifth and fourth centuries BC was the culmination of a period of a shift in the world-view of Indo-European peoples. This worldview is accessible to us mainly via late literary remains of mythology and religion, and any reconstructions of it are liable to be disputed, but my argument is that through the Bronze Age, human consciousness had a different mode, which can be characterized as one of participation. “Participation” is a term derived from Aristotle and Plato (whose words and are translated thus), pertaining to the manner in which the particular relates to the universal. It thus enters the scholastic vocabulary; Barfield is at pains however in Saving the Appearances to underscore that it is not, strictly, a technical term. Still later it figures in Malebranche, whence Lévy-Bruhl took it to describe what he considered the main principle of primitive mentality, a mode of thinking which did not include the principle of non-contradiction. Lévy-Bruhl began with a case from the anthropologist Karl Von den Steinen, according to whom the Borono, a Brazilian tribe, claimed to be a type of parrot called arraras. Since a human being simultaneously being non-human violates non-contradiction, Lévy-Bruhl invoked what he called the law of participation to describe this manner of thinking.3

Lévy-Bruhl’s formulation and account of “how natives think” has been subject to many criticisms, which I will not here consider. Whether the parallels (which I do not assume were strict equivalences) were between human tribes and their totem animals or between the seasons of the year, the revolution of the heavens, and the tuning spiral of fifths—examples that will occupy us below—I take for granted that such correspondences were matters of experience and not mere intellectual parlor games. The fundamental issue is not whether Lévy -Bruhl’s specific descriptions all hold up under scrutiny, but rather whether there can be held to be a shift in the manner and mode of human consciousness between the late Bronze Age and our own day, and what was the nature of this shift. That is, it is not a question of mere revision of beliefs, but a genuine reshaping of the kind of experience human beings had. In particular, I am suggesting that it was not lost upon the best minds of the ancients that, as the various inter-phenomenal parallels and equivalences considered—I shall present several examples—came under critique, this same critique was both symptom and cause of a shift in experience. This shift had occasioned a crisis in belief, manifest in the widespread arising of a form of deep pessimism whose possibility is always latent in the human condition. I argue that Herodotus depicts this fatalism and near-nihilism not just with historical vignettes but with knowing recourse to a number of cosmological tropes. I hold, too, that Plato just as knowingly appropriates these same preexisting motifs in order to argue against pessimism, to assert that there are conditions in which human life is good. That this way entails a recapturing (under a new and wiser mode) of the same participation that was fading, is part of my thesis, but will not be rigorously argued for here.

This paper will require (and doubtless test) patience, partly from the material (which is not 3 See, e.g., Lévy-Bruhl, How Natives Think; Barfield, Saving the Appearances; Jonathan Z. Smith, “I am a parrot (red)” in Map is Not Territory.

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difficult in itself, but is quite disparate) and partly from my own limitations. Our familiarity with Oedipus notwithstanding, from Sophocles to Freud is a long way; and indeed my net is cast very wide and has hauled in, willy-nilly, King Midas and King Arthur, ancient Greek tuning systems, an allegedly Neolithic calendar from Lascaux, Hebrew gematria and Norse myth, a horoscope for the beginning of the world, and the last supper of Jesus and his disciples. All of this is placed against a more or less continual dialectic between Plato’s dialogues and Herodotus’ Histories. I believe there is enough substantial thematic continuity to warrant the frequent refocusing I ask of the reader, shifting between different eras, different subjects, different disciplines. Eventually, I hope, the suspicion will take root that not all of this continuity is the creature of my own idée fixe. Read this, then, in the spirit in which one would explore Herodotus himself, as he turns from Persian engineering to Egyptian religion to the proclivities of fate, gods, and mortals.

It is Herodotus who has preserved Solon’s remark for us, in a conversation between Solon and Croesus, the tyrant of Lydia. If one reads carefully, one perceives that, far from haphazardly slapping his sources together, Herodotus knows what he is doing.4 Herodotus specifically underlines that his project is to trace the cause of the conflict between the Hellenes and the Persians, and after a brief mythic preamble, Croesus is the place he begins. He's like an old storyteller telling you to pull up a seat if you've a notion to hear the tale. "Well," he says, "it all started with Croesus, the tyrant of Lydia..."5

Who is most fortunate?

Croesus, at one time among the most wealthy and successful of ancient rulers, entered into a war with Cyrus of Persia after being satisfied by the Delphic Oracle that if he did so, he would "destroy a great empire," little suspecting that the empire would be his own. Herodotus, however,

4 In this assertion, both an axiom and a conclusion, I am guided by, among other things, a number of findings made by Ernest McClain, whose patient decoding of Plato and other ancients has revealed a very particular musical grammar, hinging on a careful correlation between the matter at hand (justice, the story of Atlantis, the myth of Er) and musical tuning, with special attention to the gap where any tuning system founders. My general approach as regards McClain’s work is usually to stipulate his findings, not argue for them (though I do try to establish a prima facie case for considering the approach). I am not able to make any original contributions to ancient musicology, and I cannot pretend to decode any of the ancients' texts on any deep level. What I am interested in, above all, is the question of why. In this, I've followed the lead of Leo Strauss, and of Giorgio de Santillana. McClain has taught me to be on the lookout for jests and tell-tale inconsistencies which point beyond the context of a work to a cosmology shaped by music, but also astronomy, metrics, and mathematics in general. Strauss (and Voegelin) taught me to be suspicious of the reduction of Plato to the chaser-after-ideas-in-the-sky to which he is stupidly reduced, and to read closely whenever something puzzles me. De Santillana taught me to be always aware of the mythic backdrop-- an intertext which not only Plato assumes. The question I always am asking is: given the resonances McClain or de Santillana and von Dechend point out, what does it mean? Why did the ancients write like this? McClain once mentioned that Gilbert Ryle told him, Plato would never have planted "all that musicology for you to find." And surely Ryle was right, if by this he meant that Plato was not playing hide-and-seek games with his readers. But since the numbers are there on the surface of the text-- the Tyrant and the "greater and lesser births" in the Republic are only the most obvious examples-- we are not entitled to dismiss them as games. By the same token, though, we ought not to disregard the fact that Plato is writing about justice, the city, understanding, realization. Music somehow fits into all of this, illustrates it, provides a partial grammar for it. My contention is that these authors made use of mathematics partly as a dependable code which could be relied upon to keep its meaning; but they used it to stimulate realizations that went beyond mathematics, partly by making use of short-cuts, double-entendres, and lapses meant to stimulate independent reflection. This paper will investigate more closely a few examples and suggestions.

5 It is important to note that Herodotus specifically calls Croesus a Tyrant and not just a ruler. It would take us quite far afield to undertake a close investigation of the attitude in Herodotus towards tyrants, for instance the house of Pisistratus, once allied to Solon and later opposed by him. However, his general antipathy is well-established and uncontroversial. It is not too much to say that between Herodotus and Plato the shift of 'tyrant' as a term without opprobrium to one loaded with moral disapprobation becomes complete; and Plato will use the term in a specific musico-mathematical way in the Republic.

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first shows us Croesus' court some time before the war has begun. Solon, onetime ruler of Athens, has stepped down from that position and is traveling around the Mediterranean world. After visiting the Pharaoh Amasis (Ahmose II), soon to be Croesus' ally against Persia, Solon comes to Lydia and stays with Croesus, who proudly displays his great wealth. The content of their interview is famous. Croesus begins in what is, for us, a very significant way. “My Athenian guest,” he says, “the report of your wisdom [sophies] and travels has reached us. We hear that because you have a love of wisdom [philosopheon], you have visited many lands because of your desire to see.” It is not always noted that this is possibly the first recorded mention of explicitly “philosophical” conduct. It is under this rubric of “philosophy” that the content of the exchange unfolds. Anxious to know how impressed Solon is, Croesus asks him who he would estimate to have been the most fortunate of all mortals he has either seen or has heard of. Solon does not hesitate:

Tellus the Athenian; his country was flourishing in his days, and he himself had sons both beautiful and good; he lived to see children born to each of them, and these children all grew up; further, after a life spent in what our people look upon as comfort, his end was surpassingly glorious. In a battle between the Athenians and their neighbors near Eleusis, he came to the assistance of his countrymen, routed the foe, and died upon the field most gallantly. The Athenians gave him a public funeral on the spot where he fell, and paid him the highest honors.6

Not to be deterred, Croesus, "expecting that at any rate, he would be given the second place," inquired again as to who, after Tellus, was most happy. Solon responds with the story of Cleobis and Bito, two Argive brothers whose "fortune was enough for their wants," and who "were besides endowed with so much bodily strength that they had both gained prizes at the Games;" but again, it is the manner of their death that Solon lingers over: their mother was to attend a festival for Hera, but the oxen did not come home from the field in time to draw the cart.

So the youths, fearful of being too late, put the yoke on their own necks, and themselves drew the cart in which their mother rode. Five and forty furlongs did they draw her, and stopped before the temple. This deed of theirs was witnessed by the whole assembly of worshipers, and then their life closed in the best possible way. Herein, too, God showed forth most evidently, how much better a thing for man death is than life. For the Argive men, who stood around the car, extolled the vast strength of the youths; and the Argive women extolled the mother who was blessed with such a pair of sons; and the mother herself, overjoyed at the deed and at the praises it had won, standing straight before the image, besought the goddess to bestow on Cleobis and Bito, the sons who had so mightily honored her, the highest blessing to which mortals can attain. Her prayer ended, they offered sacrifice and partook of the holy banquet, after which the two youths fell asleep in the temple. They never woke more, but so passed from the earth. The Argives, looking on them as among the best of men, caused statues of them to be made, which they gave to the shrine at Delphi..

How much better a thing for man death is than life. This verdict too is reiterated by Sophocles (Oedipus at Colonus), but his source is probably a more distant myth which Solon/Herodotus is quoting.

When Croesus angrily inquires whether his own good fortune and happiness are as nothing to Solon, the latter replies with a famous verdict which has the strength of a proverb. He has already remarked "how much better a thing for man death is than life;" now he backs up this dour

6 The episodes of Croesus’ story which concern us found in Herodotus’ Book 1, mainly in sections 30-45 and 85-93. I will not cite every individual passage specifically.

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assessment with an argument.

Seventy years I regard as the limit of the life of man. In these seventy years are contained, without reckoning intercalary months, twenty-five thousand and two hundred days. Add an intercalary month to every other year, that the seasons may come round at the right time, and there will be, besides the seventy years, thirty-five such months, making an addition of one thousand and fifty days. The whole number of the days contained in the seventy years will thus be twenty-six thousand two hundred and fifty, whereof not one but will produce events unlike the rest. Hence man is wholly accident….Call him, until he die, not happy but fortunate."

This argument depends upon a distinction between fortune and happiness, and Solon's point is that one cannot force a correspondence between these two concepts. Solon refers to what Croesus has hitherto enjoyed as eutychia, "good fortune" or more precisely "good chance," but this implies that there is another sort of chance which may yet befall Croesus. To this end he spells out a mathematical "proof," the math of which is accurate, but whose stated rationale is flawed. The flaw is not incidental, but decisive and telltale; it would not have passed unnoticed, nor was it meant to. We will examine this erring calendar further below; here let it suffice to say that Herodotus (or Solon) inserts an extra month in alternating years, ostensibly to match the seasons; but he vastly overcompensates. Herodotus then goes to say that Croesus, for having dared to call himself the happiest of men, soon learned the truth of Solon's distinction.

I have encountered two reactions when talking about this passage. One response is to note the inexactitude about the arithmetic and the calendar, to which I will devote considerable attention below, to claim that the Greeks seem not to have understood their own calendars (they varied, often from city to city), and point out that the documentary evidence is rife with reports of confusion about when the year began and ended, when the festivals should occur, and how long the year was. The other is to note the theme that human life is fraught with changing fortunes, that happiness is never secure, and that overstepping divinely-set bounds (whether with ambition, or self-satisfaction) inevitably invites disaster, a reaction which usually occurs in a cycle; and then to call this a staple or common theme in ancient literature. Both of these responses are non-explanations. It is true that calendars were many and in conflict anciently, but this is known from the documentary evidence, which means it was known anciently. In other words, the question of calendrical accuracy was an issue for the ancients, and an occasion for reflection; it behooves us then (if we want to understand them) to pay attention to what they actually say and not simply assume they are making mistakes, or that we already know what they mean. The commonality of the theme of hubris and divine limits did not prevent many from overstepping those very bounds; to call it "common" or a "stock motif," and leave it at that is to offer no account at all. The questions to be asked are rather, Why was it so common? Why was it expressed in terms of limit, overstepping, and cycles? Is Herodotus merely repeating a formula, or is he doing something with it?

In Herodotus, "the most Homeric of writers" as Longinus called him (On the Sublime, 13:3), we see the emergence of a way of thinking and being which is consciously adapting and maintaining old forms. Both the Iliad and the Odyssey preserve countless oral formulations, as we have known since Parry and Lord's pioneering work. Despite the Homeric corpus' status as written text—and this is not in doubt—Homer presents us with a written version of what oral poetry was like at its best: a body of poetic experience intended to appeal to hearing and memory with continually memorable phrases: "keen-witted Odysseus," "fleet-footed Achilles," "the wine-dark sea." This was a world before the invention of the word "cliché." Likewise, there are type-scenes (the inventory of warriors, the meeting on the beach), the shape of which is recognizable, into which the characters and the language of the poem can slip as into a ritual form. Herodotus set

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out to imitate Homer advisedly. He recognized and cultivated both his kinship with his predecessor and, as importantly, his differences from him. Herodotus' concern with humanity, his impartiality, his curiosity, and his eye for the moving detail are all honestly inherited from Homer. It is instructive that both the Iliad and the History begin with an inquiry into causes: "Which of the gods caused them to quarrel?", Homer asks of Achilles and Agamemnon; and Herodotus writes of the Greeks and Persians, he says, "to put on record what were the origins of their feud." But Herodotus' gods are remote and channeled through the media of the oracles in a way that Homer's are not. Herodotus could more easily have put his histories into hexameters than he could have honestly and convincingly written of Aphrodite being injured on the field before Troy--though it is not an accident that he did neither. Herodotus already belongs to the age of rationalizing about the divine, a point that is not lost upon him. But though he writes in prose instead of meter (not a negligible point) and knows that his distance from Homer is considerable, he conceives of himself as writing in the same tradition.

One of the ways in which the Solon-Croesus episode seems to partake of the more general tradition is its presentation of the "type scene" which could be called the king and the wise councilor. Homer gives us an archetype in Nestor's conversations with Agamemnon and the other heroes of the Iliad (though even in Homer, the seeds of the degeneration of the counselor-figure into Shakespeare’s Polonius may be glimpsed). Such conversations could indeed be expanded into whole dialogues, as occurs in Xenophon's Hiero, which imagines an exchange between Simonides the poet and the Tyrant Hiero of Syracuse, in much the same fashion as Plato's dialogues. The motif lasts all through the Middle Ages and Renaissance and beyond: although the dialogue form has disappeared, the gist is still discernible (albeit inverted) in Machiavelli's The Prince. Herodotus shows us many such exchanges, and their aftermath; and he leaves it to his readers to evaluate the wisdom (or lack thereof) of the counselor's words.

Not long after Solon had departed, Croesus did indeed experience the "nemesis" or vengeance of the gods, Herodotus reports. Croesus dreamed that his older son Atys was killed by an iron weapon. Anxious to forestall such a fate, he forbade Atys to join in any armed games or hunts, and made plans to have him marry to excuse the omission. However, when a particularly savage wild boar began to ravage the countryside, Atys persuaded Croesus to allow him to go on the expedition to kill it, arguing that a boar cannot wield weapons, and complaining that he was being made to seem emasculated before the people and especially his new wife. Croesus agreed, but sent along Adrastus to keep him safe. Adrastus was a refugee prince from a neighboring kingdom; he had formerly accidentally killed his own brother, and had come to Croesus, "about the same time" as the wedding of Atys, to be purified. While on the hunt, in a mis-throw, he mortally wounded Atys with a spear. When Atys' body was brought home, Adrastus begged Croesus to execute him. Upon Croesus' refusal, Adrastus killed himself at Atys' grave. This episode in Croesus' story will occupy us more fully below.

Croesus mourned Atys for two years. After this time, Herodotus says, Croesus tried to verify which of the Greek oracles was the most accurate, and to that end contrived an experiment. He dispatched messengers to the various oracles, with instructions to put a particular question on a particular day, 100 days after setting out. The question was, "What is Croesus doing today?" For his part, Croesus did something unlikely-- he cooked turtle and lamb together in a bronze pot. Only the oracle at Delphi correctly divined this, winning Croesus' patronage thereafter.

Notice this moment of Croesus testing the oracle-- "tempting God," in the very precise terminology of the Bible. The New Testament word "temptation," periasmos, simply means test-- it is related to empirical. No writer in the ancient world is more concerned than Herodotus with the oracles, and in particular their slipperiness. Only Plutarch, as far as I know, writes more about

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them, and critiques them more harshly. But Herodotus is writing far earlier, and shows us something important. Human consciousness, which has taken the gods for granted for a very long time, is shifting. It is possible to test the gods.

Hinge of myth and history

Julian Jaynes devotes an entire book to scrutinizing and explaining this shift, in The Origin of Consciousness in the Breakdown of the Bicameral Mind. I shall not argue in depth for accepting the mechanism Jaynes hypothesizes to account for this change, nor the interpretation he puts upon it; but that something happened about 3,000 years ago, around the end of the Bronze Age, is witnessed across the board in the ancient world. Not only did military catastrophe befall nearly every major city in the Mediterranean and Near East within a matter of decades (which leaves the question, why?); the literary record bears witness as well7. One can see God receding from the pages of the Hebrew Tanach; the familiar God who walks in the cool of the evening in Eden, wrestles with Jacob and assaults Moses with intent to kill, changes into a very different figure, a lawgiver, an arbiter of destiny, both majestically distant, and intimately present but unseen. By the time of Plutarch, the lament goes up that "Great Pan is dead," and the oracles, he tells us, have fallen silent. This evolution remains almost completely to be accounted for, despite Hegel and Marx, Aurobindo and Ken Wilber. The story here is only a small sub-plot. I cannot here delve into the various mappings that have been offered of this trajectory of human development. But I do contend that Herodotus and his tradition is aware of the development.

Eliade draws the distinction between myth and history as the difference between the cyclic repetition of archetypal patterns and the occurrence of new events understood as unique. On the one hand, the mythic world in which all events follow the template of the timeless story laid down once and for all by the gods: the Hopis who tell the story in order for the year to begin again, the planting and the journey that repeats always the same events; an echo of which one hears even in the narrative of Passover-- "Why is this night different from all other nights?"-- and the Paschal exultet-- "This is the night." (That liturgy has preserved these experiences is not accidental; modes of action are further below the radar of critique than are texts). On the other, the "profane" events which belong to the order of history, which, whether progressive or meaningless is still "one damn thing after another." It is too simplistic to argue, as was once the fashion, that "Greek" historical thought is "cyclic" and Biblical Hebrew thought "linear," but the distinction does point to something. The emphasis upon the historicality of the Christian narrative has always been claimed to set it apart from the religions of antiquity: the story of Jesus the messiah is supposed to have happened not in the far-away Nifelheim or the ancient bygone, but in a landscape whose contours are known, some days' or weeks' journey from the capitol city of the Roman Empire, under the reigns of Augustus and Tiberius and certain local officials. This is often seen either as an enormous category mistake (the ancient response) or a lie to be actively denied (the modern attempt to reduce Christianity to myth). Here I will not develop this argument, but confine myself to underling the significance of Eliade's point: the importance of the notion of historicality itself, which in great measure Herodotus himself created.

Herodotus stands on the threshold between these two worldviews, and in some fashion, he seems to know this. His History--the first book of its kind, as was clearly not lost upon him-- is not just a collection of digests of royal chroniclers' records. Herodotus is collecting an enormous amount of information about the whole world. It is hard to avoid the impression that, like the Celtic chronicler Nennius in the 9th century AD, he has "made a heap of all that [he] could find." The worldview of Herodotus' ancestors, which took the oracles for granted and assumed the gods

7 See, in addition to Jaynes, James Jugel, The God of Old; David Friedman, The Disappearance of God.

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were there, was passing away. This was partly from the impact of the critique made by thinkers like Xenophanes ("if cattle or horses or lions had hands and could draw, and could sculpture like men, then the horses would draw their gods like horses, and cattle like cattle; and each they would shape bodies of gods in the likeness, each kind, of their own"); but truly, Xenophanes and men like him were simply a symptom of a shift that was already underway. I suspect it was ill-understood at the time, (nor have we got much better at unriddling it), but to think that it was unnoticed is to insult our ancestors’ powers of observation. Probably then as now, some blamed the gods (today we tend to say "history" or "progress" or "the way things happen,"), and some blamed each other. My guess is that writing, more than any other factor, was at the root of the trend—a hypothesis which was already suggested byPlato. I believe a careful reading of the texts (and probably some other artifacts they made, if only they had survived) reveals that some thinkers were using writing--the very thing that was slowly eating away at the habits of memory, imagination, and oral language which underlay the experience of the mythic worldview--to salvage what could be kept from the ruins left by the critique. To do this, it was not enough to decry in overt language the waning of the gods. On their own terms, thinkers like Xenophanes could not be gainsaid, for to engage with critical logical intelligence to prove that the gods existed was impossible. In that sense, the gods did not exist. But it is possible to set up in language a mechanism that can push the careful observer out beyond logic. Plato in particular is very clear about the experiential dimension of his doctrine-- "it cannot be put into words," he insists in the Seventh Letter, but depends upon a sudden realization a "spark" which leaps from one heart to another. (If this is the doctrine of a arch-rationalist and hypostasizer of definitions, I'm a Pobble without toes).

The texts of Plato are full of trap-doors and jokes which are meant to fall open and allow you a moment when you see that more is going on than rational argument, and more than can be done with rational argument. But Plato is not the only one who does this. 8

Another and equally important point Eliade highlights is the interplay of mythical and cosmological cycles. At the New Year celebrations when the old order is passing and being regenerated, Eliade finds many indications that the historical residue of the year is discarded for the mythical essence. The calendar is thus the site of an intersection of astronomical and seasonal prediction and ritual observation. The new year-- which comes often at one of the spokes of the solar cycle, whether solstice, equinox or cross-quarter day-- is a time of ritual purgation of sins and of historical "particularity," as the mythical archetypes are reasserted against the mundane specifics of ordinary events. The time of this purgation often also coincided with the extra-calendrical time. Frazer surmised:

We infer with some probability that the sacred Twelve Days or Nights at midwinter derive their peculiar character in popular custom and superstition from the circumstance that they were originally an intercalary period inserted at the end of a lunar year of three hundred and fifty four days for the purpose of equating it to a solar year reckoned at three hundred and sixty-six days.9

Eliade has more recently reiterated this; but equally important as the calendrical aspect of the argument is the psychological or sociological; for the myths and rituals Eliade explicates all indicate a kind of purgation or purification associated with the New Year rites; in short, a katharsis. This brings us back to Plato, for the moment of realization Plato speaks of, the "spark" leaping between teacher and disciple, is very akin to the katharsis Aristotle names as the function

8 I follow Leo Strauss here, as an exegete reading "between the lines;" though I do not interpret such esotericism as Strauss does, nor believe with him that this art was ever lost. (Nietzsche, for instance, clearly writes esoterically.)9 Frazer, The Golden Bough, vol. IX, ch 8 sec 2; p 342

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of tragedy, but it is a moment, not merely of purgation, but of realization: there is a positive content to it, not just an evacuating. Herodotus' narrative shows Croesus attaining just such a realization, at the most extreme moment of his personal tragedy.

The answer about lamb and turtle was the first of four oracles Croesus received from Delphi. The second came in reply to his query as to whether he could expect success in war with the Persians: "If Croesus attack Persia, he shall destroy a great empire." The third oracle, in response to further inquiry, told him that "When a mule shall become king of the Medes, then run away, on the pebbly shore of Hermus—be not ashamed." This Croesus took to prophecy a laughably unlikely event-- as if the oracle had said Croesus should worry only "when Hell freezes over." Finally, an oracle is reported which came in response to his asking how to help his surviving, younger, son, who was born mute. The answer was, "Do not seek to hear this longed-for voice, even the voice of your son; for the day he speaks will be a day of sorrow."

Croesus' attack on the Persians was a disaster; the great empire he destroyed proved to be his own. Cyrus, the ruler of Persia, was of mixed parentage (like a mule sired by a donkey on a mare). When the final catastrophe was upon him, his city in flames and his palace overrun, Croesus, not caring whether he lived or died, did not bother to defend himself even when a Persian soldier was about to kill him. At that moment, his mute son cried out, "Do not kill Croesus!" and the soldier, who had not known his target was the enemy king, stopped, to take Croesus prisoner instead.

Croesus' story is all about the intermixing of good fortune and bad, woven together so tightly as to be impossible to separate. The exclamation of Croesus' son does indeed come on a day of tragedy for the king, but it also saves his life. A second exclamation--his own--does so again. Cyrus prepared a stake and a pyre for the execution of Croesus by burning. The flames had already been lit when Croesus was seen to be speaking--one word, uttered three times, as if to himself: "Solon. Solon. Solon." Cyrus had his interpreter ask Croesus why the king said this word. Croesus replied, eventually, that it was the name of a man he wished could converse with every king; and, upon being further pressed, told what Solon had advised him. Cyrus, realizing that Croesus had gained wisdom, was moved to pity him and tried to have the fire put out; but it was only when Croesus beseeched Apollo in prayer that the skies darkened and rain extinguished the pyre. Thereafter, Herodotus says, Croesus served Cyrus as his counselor-- thus beginning the cycle again.

Historians tend to think that Croesus was executed, and that the story of his being saved is a remnant of a mythological story. Which it may well be; for the point here is that Herodotus is weaving together aspects which the mythical worldview assumed with new elements conforming more to the critical stance he cultivates. He is careful to discriminate between what others report and what he has seen himself, and often voiced opinions about "what really happened" and what, on the other hand, are idle tales. On the other hand, he assumes a vast number of associations and images of thought from the past-- a vast linked cosmology that takes for granted not only the gods but the interconnectedness and mutual relevance of different aspects of the whole cosmos. The story of Croesus illustrates this quite clearly. Croesus' doom is "the nemesis of the gods" which comes upon him, a feature of a cycle of causes which seems to describe the Greek tragic worldview in general. This cycle has been distilled by critics; I do not know any single source which clearly outlines it in each particular, but the outline is clear from Theognis and Sophocles, and the fact that it is very similar to the outline of events found over and over in the Old Testament indicates that it is probably a feature of the ancient world generally. First comes koros, fullness, satiety. Then come hubris, pride, then ate, a term that means variously delusion, fury, appetite. Sometimes there is a sin, hamartia, a word two thousand years of critics have made a

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centerpiece of Aristotelian theory even though he mentions it only twice in the Poetics. Quick to follow is nemesis, the divine vengeance of the gods for overstepping the bounds assigned to humanity. And in response to this one finds ones proper humility. Implicitly, one might feel satisfied, a sense of koros again. This cycle is implicitly traced in Herodotus over and over; but it is named explicitly in Croesus' last advice to Cyrus. This occurs as Cyrus is pursuing the forces of the Queen Tomyris; Croesus advised him, against the counsel of the other advisors, to press on and continue the advance, into enemy territory. This proved to be Cyrus' death, though again the gods seem to have had their share of responsibility; they sent a dream to Cyrus warning him that his death was to come; but, says Herodotus, Cyrus misinterpreted it. However, it is one figure in Croesus' final speech to Cyrus that is of interest here: "if you feel yourself to be a man, and a ruler of men, lay this first to heart: that there is a wheel on which the affairs of men revolve, and that its movement forbids the same man to be always fortunate."

This is the Wheel of Fortune, which has gone on to Boethius, Dante, the Carmina Burana, Chaucer, Shakespeare, the Tarot Deck, and a television game show. It is the summation and recapitulation of the lessons which are implicit not only in the whole Croesus cycle, but repeatedly in the Histories as a whole. Cicero speaks of this wheel, and indeed the name of the Roman goddess Fortuna is thought to derive from Vortumna, "she who turns the year" (compare "vortex" and "autumn"). There are fragments from Sophocles and poetry from Pindar that indicate that the Greeks explicitly identified this cycle with chance, or with the Moirae or fates. Of course, the wheel of the year is the sun's turning through the twelve signs of the zodiac. The staying power of this image is very strong; even by the time of the first documented Tarot decks, in the early 1400's, it remains an established trope, appearing as one of the major trump cards. Later, after the image's position in the deck is settled (it is the 10th trump in most Tarot decks) the wheel comes to be flanked by the four cardinal signs of the zodiac-- Taurus, Leo, Scorpio and Aquarius--as does Trump 21, the World card; but this association is not a recent innovation, for the link between the wheels and these figures is traceable not to the speculations of Renaissance magi but to the vision in the first chapter of the book of the prophet Ezekiel, who saw the wheels within wheels, ranged between four beasts: Bull, Lion, Eagle and Man. These four signs are the signs of the solstices and equinoxes at the time of Ezekiel, and these cardinal points of the year (though, because of precession, not always these zodiacal signs) are also aligned with important points on the tone circle by both Ptolemy and Manilius.

The music of fate

I hope to demonstrate that behind Herodotus' story of Croesus and his use of the Wheel of Fortune is a grammar that includes both the astrological zodiac (which is not surprising, considering the link between astrology and fate) and the musical octave. We associate Pythagoras with tuning theory and geometry; but to the ancients he was more known as an expert on the destiny of the soul and the meaning of metempsychosis or reincarnation. "He taught," Porphyry tells us in his Life of Pythagoras, that "past events repeat themselves, in a cyclic process; nothing is new in an absolute sense." Eudemus (Aristotle's pupil) indicates that this is eternal recurrence in the Nietzschean sense: "If one believes the Pythagoreans, the same things will recur exactly, and I shall be holding my pointer, talking to you as you sit, and everything else will be exactly as it is now..." (Phys., fr 27) This cycle is also the Orphic Wheel, known from inscriptions on gold plates found in graves: the wheel of birth and death, the cycle of incarnations. "I have flown out of the sorrowful weary wheel," one such inscription reads. Empedocles describes the cosmic cycle and struggle of Love and Strife as "a turning wheel," and "Time itself is thought to be a wheel," Aristotle says in the Physics (223b).

The isomorphism between zodiac and the tone circle is well attested anciently, matching the

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twelve semitones with the twelve signs. The twelve semitones of the chromatic scale are not the only way the space of an octave can be divided, but it is a very widespread one, in part for the reason that one may make 12 fifths up or down from a given note before one comes to a note seven octaves above or below where one began. One generates an octave by doubling or halving a string length; one generates a perfect fifth (above or below) by taking 2/3 or 3/2 of a string length, and a perfect fourth by taking 3/4 or 4/3. The consonance between seven octaves and twelve fifths is not perfect, because the ratios defining each are not commensurate: taking the former seven times does not yield the same thing as taking the latter twelve times. The gap or discrepancy between these two (or any such two) fractions is called, in music theory, a "comma." A comma is any slight discrepancy that arises when we add intervals tuned in precise ratios: it is a situation in which two different sums give pitches which are almost the same. When the ear hears two pitches which differ by such a small amount, it strains to bring them into unison or into harmony, and is frustrated in either direction, unless the error is so small that it is not discernible. In Circle of Fifths tuning (often called "Spiral fifths" for the reason that the circle is not a perfect circle, but rather encounters the comma), the comma is found at the thirteenth note. One can also tune from the root and the octave at the same time, and in this case one will push the comma into the middle, to the tritone-- six semitones above the root, and six below the octave.

As noted, the twelve notes in the series of perfect fifths are often arranged in a circle, running (for instance) C-G-D-A-E-B-F#-C#-G#-D#-A#-F-C. (Obviously, as a circle, the series of notes can start anywhere). Because this circle falls into twelve parts, bounded by twelve tones, this "Circle of Fifths" is also easily seen as isomorphic with the 360-degree circle, and with the twelve months of the year. However, the slight gap between the two measurements-- the iterations of 2/3 and 1/2-- requires a degree of inexactitude in order for the circle to be a circle.

If one counts out where the seven octaves fall in the Circle of Fifths, one finds that with one exception, each octave contain two of the notes named in the circle of fifths:

1:1 1:2 1:4 1:8 1:16 1:32 1:64 1:128

D D D D D D D DD A E B F# C# G# D# A# F C G D1 2/3 4/9 8/27 16/81 32/243 64/729 128/2187 (...etc....)

All intervals except the tritone and the octave have inversions. The fourth inverts to the fifth, and vice-versa. The third inverts to the sixth, and the second to the seventh; major inverts to minor. Thus a minor sixth inverts to a major third, and a minor third to a major sixth. Because of this, the octave circle has a symmetry, fanning out from the root on either side down to the tritone10.

The position of the tritone as exactly between any two notes which are octaves of each other means that in the circle of fifths it is always directly opposite from the root tone. This makes the tritone the natural place for the discrepancy between fifths and octaves to be most difficult to correct. For this reason, it is often the case that, faced with a comma, we would prefer to have a single pitch which is somewhere between the two alternatives, even if this means sacrificing the exact tuning which gave us each series of intervals. Like a bump under an ill-fitting rug, the difficulty can only be moved around or broken up. Modern tuning chooses to split up and equally distribute the discrepancy; but if one chooses to preserve as many pure ratios as possible as

10 Of course it is not the note G# per se that is inharmonious. Notes are not harmonic or dissonant except in relation to other notes. It is the interval between D and G# which is considered dissonant, and this interval also obtains between C and F#, or between F and B; in short, between the root tone and the tone that lies midway between the root and its octave, or between any two notes that are exactly three wholetones away--hence the name tritone.

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closely as one can, the unavoidable discrepancy will tend to gravitate towards one particular place in the scale, the interval precisely between root and octave above, namely the tritone. In the case of spiral fifths tuning, to turn the spiral into a true circle, one could start at the lowest bound of the seven octaves and adjust in one direction, or at the highest and adjust in the other, but that will only push the discrepancy to the other end. If on the other hand, one tries starting at both ends and moving in both directions, this will bring most of the pitches into closer resonance with each other, but the difference will gravitate to the tone furthest from both ends: the tritone (in this case, G#/Ab).

There is one more thing to note about the tritone interval. Because spiral fifths tuning is generated by successive multiplication of 2/3 by 2/3, each tone in it has a precise fractional representation. If the root is 1, the fifth will be 2/3. Repeating this six times gives us the tritone (with six tones on either side, for a total of thirteen from root to its duplicate 7 octaves above). The fraction which represents the tritone is 64/729. The significance of this number, for us, lies in the denominator: the 729 parts, of which 64 are selected. These numbers will be important below, but for now the reader can leave them aside; I will reiterate them when they are relevant. However, the tritone has another possible expression which is not rational. Its location precisely "between" a tone and its octave above or below is not arithmetical, but harmonic. Since the octave ratio is 1:2, our root, D, is at string length 1, and the octave below will be at string length 2. But a string of length 1.5, being 3/4 the length of the longer string, does not sound the tritone; it sounds a Fourth: in this case, G. The fifth, A, will be at 1 1/3 = 1.333. Right in between will be the tritone, at 1.4142... the square root of 2.

Expressed thus, the tritone is not, and cannot be, rationally put in relation to the tone or its octave, nor indeed to any of the other 'perfect' intervals. This might seem, on some accounts, to explain its unsettling acoustical effect. But it is not always appreciated that this number, the famous scandal of the Pythagoreans, has a musical role. We will now see how its place in the tone-circle makes it analogous to the calendar and what light this casts on Solon and Herodotus.

The line between octave and tritone runs from perfect self-resonance (the octave interval 1:2) to the strongest form of dissonance (1:√2)

The symmetry in the tone circle mirrors that of the assignment of planetary rulership over the zodiac signs, as laid out in the Thema Mundi or "horoscope of the world," which Ptolemy, Firmicus Maternus, and others use for this purpose. Maternus, writing in the 4th c. A.D., acknowledges that the chart is a pedagogical aid and not a real horoscope: "There was no birth chart of the universe; for it did not have any certain day of origin. There was no one there at the time when the universe was created by the plan of the divine Mind and foreseeing Will. … The divine wise men of old invented the birth chart of the universe so that it would be an example for astrologers to follow in the charts of men. (Firmicus Maternus, Mathesis, 3, 9, 10). Nonetheless, it is clearly based upon Babylonian precedent. Berossus records the opinion that a conjunction of all of the planets in Cancer was said to indicate the destruction of the world by flood, whereas a conjunction in Capricorn would indicate a conflagration. But Berossus is already writing at a time when the precession has pushed the solstices beyond Leo and Aquarius. The significant point is not the zodiac sign but the winter and summer solstices themselves. These once stood, respectively, between Aquarius and Capricorn and between Leo and Leo and Cancer. It is very significant that the signs framing the summer solstice were assigned rulership by the sun (Leo) and the moon (Cancer). From these, the planetary rulerships are arrayed symmetrically, one sign in the solar house and one in the lunar: Mercury rules Virgo and Gemini; Venus, Libra and Taurus; Mars, Scorpio and Airies; Jupiter, Sagitarius and Pisces; only Saturn, the "dark sun" as

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the alchemists called it, rules two neighboring signs, Capricorn and Aquarius.

There is thus an axis running from Winter to Summer solstice, which is framed by the arrangement of ruling planets in their respective zodiacal signs.11 This axis is also found in the tone-circle, running from root to tritone and framed by the intervals and their inversions. That this is more than a coincidence is seen not only from numerous associations of the planets and the Greek modes or the intervals (the music of the spheres being an extremely well worked-out trope until well after Kepler), but also from the specific alignments indicated by Ptolemy and Manilius. Both of these offer a set of correspondences which assigns each of the Greek modes to one of the seven ancient planets (Pliny attributes this association to Pythagoras). Because these modes correspond (roughly but precisely enough for our purposes) to the seven scales played on all the "white" keys of the scale--that is, the seven octaves which contain the circle of fifths--this is already significant enough. But Manilius' Astronomica (dated to sometime after the Battle of Teutoburg Forest in AD 9, to which it refers) also assigns the signs of the zodiac to the modes: two each to five of them, and Cancer and Capricorn alone to one each. For his part, Ptolemy, proposes a system which arrays the zodiac about a double octave. Ptolemy uses the Greek names for the notes, and his system puts Aries at the lowest tone as well as the highest, two octaves

11 I have not expanded upon it here, but Northrup Frye’s analogy between the genres Comedy, Romance, Tragedy and Satire (which mutates into Irony) and the four seasons also offers possibilities for further exploration of this worldview of correspondences.

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above. Directly across, at the middle octave, is Libra. The signs which are precisely between Aries and Libra are Capricorn and Cancer. Thus Ptolemy also associates the two tropical signs with the tone which is as far as possible from either end of the octave.

Again, it is not the particular signs that I believe to be significant here, but their indication of the cardinal points of the year. I take Ptolemy's link between the tritone and the solstices to be the fundamental point here, and will not expand upon his double-octave system, which however has been the object of important speculation. For my purposes, I want to concentrate upon the single octave scheme, which links the solstices with the octave and tritone. Note that it is not possible to tell from these different schemes which, between the tritone or the octave, would have been matched to the summer solstice and which to the winter solstice. (Both festivals seem to have been linked to a ritual combat between rulers; and the identification of Saturn with Kronos, the original usurper, seems to underscore this.) There is, however, a further set of clues to follow.

The mismatch of the sun and moon

We seem to have come some significant way from Herodotus, as you will have noticed, by such a detour as may have seemed congenial to the historian, enthusiast that he was for the tangential subplot. We started with Solon's conversation with Croesus. There Solon tells Croesus why he thinks human life is radically uncertain, why, in fact, death is better than life. (Again, please note that this ambiguous preferability of death is alluded to by Socrates over and over. The end of the Apology has Socrates saying that he is going to death, and his interlocutors to life, but which of them is going to the better end is obscure, except to "the god.") Again, Solon's arithmetical demonstration his rationale is as follows:

Seventy years I regard as the limit of the life of man. In these seventy years are contained, without reckoning intercalary months, twenty-five thousand and two hundred days. Add an intercalary month to every other year, that the seasons may come round at the right time, and there will be, besides the seventy years, thirty-five such months, making an addition of one thousand and fifty days. The whole number of the days contained in the seventy years will thus be twenty-six thousand two hundred and fifty, whereof not one but will produce events unlike the rest. Hence man is wholly accident….

If, rather than simply breezing past these numbers, we read carefully and follow the mathematics, we discover something surprising: things cannot actually work as Solon says. Although his addition is correct, comparing it with the actual year indicates that his rationale is completely implausible-- so implausible that it must have been apparent.

Solon's chrono-measurement refers to two sets of years: thirty-five with 12 months, alternating with another thirty-five with 13. According to his own reckoning, seventy years, without an intercalary month would have 25,200 days. This figure, divided by 70 years, gives:

25,200 days / 70 years = 360 days per year. Thus a twelve-month year has 30 days per month.

But Solon says that in order "that the seasons may come round at the right time," these years must alternate with years in which there is an extra month: a thirteen-month year, which Solon says should be every other year. If the extra month had the same number of days--30--, then such a thirteen-month year would have 390 days. Since the 12- and 13-month years would alternate, there would be thirty-five of each; and Solon says that these thirty-five extra months contribute a further 1,050 days to the total. Dividing this number by 35 confirms that the month is just as long as the other months:

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1,050 days / 35 months = 30 days per month

Calendars in use in Herodotus' world did make use of extra months. This device was needed to attempt to synchronize several unrelated cycles--lunar, solar, and calendar. The calendar year is a human construction and uses a whole number of days. Because the Babylonians used sexigesimal arithmetic, 360 days --60 x 60-- would have seemed the "ideal" year (giving one day for each degree in the circle),12 but the solar year, of course, is approximately 365.25 days long. Even rounding this off to 365 leaves a problematic 5-day "remainder," which had to be included in the calendar year by some device or other.13

The 28 phases of the moon, in theory, could yield a 13-month calendar of 364 total phases, but because a "phase" takes slightly longer than one rotation of the Earth, these 28 phases in fact correspond roughly to 29.5 days of the Moon's synodic cycle. Nonetheless, further to the north, a 28-day month was indeed stipulated, and seems eventually to have been conveniently divided into four 7-day weeks. It is sometimes suggested that a Druidic calendar, of 13 months with 28 days each, was used in the British Isles; these 13 months added to 364 days, leaving a single, extra-calendrical day. In his monumentally influential The White Goddess, Robert Graves associated this 13-month calendar with the Ogham alphabet, a list of native trees, and a set of constellations, arguing that the Druids' astrology, tree-lore and writing were all bound up in a single interwoven set of disciplines. Graves' scholarship has been seriously critiqued and there are today few academic references to it which treat it kindly. He is faulted for relying upon dubious sources or his own or others' misconstruals, and for making wild cross-cultural leaps. None of these accusations can be easily dismissed; in fact, Graves himself acknowledged that he disregarded the warnings of the respected scholar R.A.S. MacAlister, to the effect that Graves was taking too seriously the dreams of 18th-century Celtic reconstructions. (Graves has been roundly criticized for this, which is not quite fair, since he admits it in black and white and never pretends that scholarship has not the right to tell him he is "talking nonsense.") I will confess however, that despite or because of his poetic license, there is something of Graves' approach that appeals strongly: I do not mean so much his specific contentions, as the spirit in which he argues. He has doubtless laid himself open to all sorts of potential mistakes; but the way he thinks, I am sure, is closer to that of the ancients than is that of more careful and perhaps more correct experts. The mistake she makes are like those Pausanius or Euhemerus or Celsus would have made; and he does not pretend to understand them better than they understood themselves.

Be that as it may, the thirteen-month lunar year is not one of Graves' fancies; it entered even into English common law. One can find reference to it as late as Blackstone's Commentaries on the Laws of England, where he notes that there are "in common use two ways of calculating months, either as lunar, consisting of 28 days... thirteen of which make a year; or as calendar months of unequal lengths, according to the Julian division....whereof in a year there are only twelve." Blackstone even notes that it was the 28-day lunar month that was accepted by English law, because of its "convenience". This 13-month lunar calendar, each month with four weeks each,

12 The Euclidean circle lends itself very naturally to sexigesimal division because of the ease with which a hexagon may be inscribed within a circle. A compass set to the radius of a given circle may trace exactly six intersections of the circumference before coming back to its starting place. This makes base-60 a very attractive base for dividing the circle in theory; but we find that in practice, the year does not come in 360 days (nor, indeed, is the Earth's orbit a circle, despite how it might have seemed to the ancients. It is instructive however that Kepler, who first noted the ellipsoid shape of planetary orbits, felt himself able still to preserve the relationships between the planets, the Platonic solids, and the musical intervals).

13Thus, in Egyptian myth, Thoth successfully gains 5 days "outside the year" for Osiris to be born (as recounted for instance by Plutarch), defeating the decree of Ra.

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and a single extra day "outside the year," is certainly traceable to Druidic practice, though any too-confident speculation on exactly what the calendars of Northern Europe were is premature. Graves in any case links each month to a particular tree14 and the extra day to the mistletoe, the sole exception (according to Snorri's Prose Edda) among all the substances in the world, which had taken an oath not to harm Balder, after Balder had a troubling dream in which he foresaw his own death. The sacredness of mistletoe among the Druids is well known: Pliny, in particular, tells that the Druids cut mistletoe from a sacred oak, with a golden sickle, on the fifth day after the new moon following the winter solstice. Thus whether or not we accept Graves' equation of the mistletoe with the single extra-calendrical day, the association of mistletoe with the Winter solstice is not in itself controversial. This will be significant later.

In the Mediterranean world in Herodotus' time, however, the 28-day month seems not to have been used. The 29.5 day actual synodic cycle of the moon would have made a 13-month calendar too long. There was, consequently, a year of 12 months, with a total of 354 days (with months alternating between 29 and 30 days each), leaving 10 or 11 days to be added in; after three such 354-day years, there is a gap of slightly more than a full month between solar and calendar years. Indeed, the Babylonian calendar seems to have intercalated a month every three years to make up the difference, (and sometimes added an additional month at the discretion of the king (with due advisement)), precisely for the reason of "aligning the seasons," as Solon puts it. Solon, however, says that the month would be interposed every other year, a solution which, to my knowledge only the ancient Romans are believed to have used. However, the regular Roman year was 355 days long, not 360 as in Solon's arithmetic; and even in the case of the Romans, the decision was made by the pontifexes, not by the theory.

Returning to the specifics of Solon's arithmetic, summing up the length of both 12- and 13-month years, thirty-five of each, we get:

360 days x 35 = 12,600 days390 days x 35 = 13,650 days

and these two, added together, do indeed equal12,600 + 13,650 = 26,250 days,

just as Solon says.

Solon then goes on to note that of this large number of days, there are no two alike; a day of good fortune may easily be followed by one of disaster. The odds are very high that out of all these days, there will be one that brings bad luck or even catastrophe; and if such a day has not yet come, one has no grounds at all for believing that it will not come tomorrow. Thus Solon recommends suspension of judgment on a man's happiness until death.

But Solon's calendar is very strange. His alteration of 12 and 13-month years would make the average year be 375 days long. This would not make "seasons may come round at the right time" at all; on the contrary, they would make them diverge even faster than a 360-day year would. Solon's scheme vastly overcorrects. In fact, Solon has over-shot his 70 years (rounding them off

14 Graves’ tree-calendar is one of the features of his work most often criticized by Celticists. He derived it from the 19th-centrury scholar Edward Davies, an active figure, alongside poet and Freemason Edward Williams (a.k.a. Iolo Morganwg) and Williams’ bardic teacher Sion Bradford. Davies’ calendar may indeed be partly fanciful; but it is not without precedent; there is, for instance, a 17th-century altarpiece in Bad Teinach, Germany, which features, among many other Rosicrucian motifs, a round rose-garden with Christ in the center of twelve human figures (apostles?) accompanied by zodiacal symbols and twelve different (and to some eyes, discernible) species of tree.

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to 365 days each) by exactly 700 days; that is, by precisely twice as much as his first figure (70 years of 360 days each) fell short.

The proportions of his mis-counting are thus: 25,200:25,550:26,250

The first and last of these-- Herodotus' (or Solon's) own figures-- factor into primes that are 7 or less:25,200 = 24 x 32 x 52 x 726,250 = 2 x 3 x 54 x 7

But 25,550 --our own figure, which is 70 x 365-- introduces the (in comparison) very large and unwieldy prime15 73, because 365 = 5 x 7325,550 = 2 x 52 x 7 x 73

Though the ancient Greek calendar seems to have varied from city to city, the Athenian system is fairly well-understood. Like the Babylonians, they seem to have had a regular year of 354 days. Thus with every three years the accumulated difference is 33 days--over a month. This month is occasionally added as a thirteenth month, and the Athenians, like the Romans, seem not to have had a regular rule for such intercalation, leaving the decision to appointed officials, who observed the seasons. After Herodotus' time, Meton of Athens observed (from Babylonian records) that 19 solar years and 235 lunar months are different by a very small error, of only about two hours. In this cycle of 19 years, twelve have the regular 12-month cycle, and 7 have an additional 13th month. Well before Meton, however, the general 3-year cycle was known and established. The details of the scholarship are numerous, often intriguing and often obscure; but for our purposes, the main thing to be noted is that neither Herodotus nor (if he said what Herodotus puts in his mouth) Solon can have had, or imagined themselves to have, any workable system of year-measurement in mind. They meant something else.

The discrepancy is not immediately noted upon reading, of course, because the more provocative dimension of Solon and Croesus' debate--what is it that makes for happiness, how can it be known and how can it be sure?--occupy our attention, as it would have occupied the attention of Herodotus' listeners. The strange arithmetic, accurate but beside the point it claims to illustrate, is emphasized by way of its very pretending to exactitude, but would have required more leisure to consider. It operates as a kind of time-release provocation; only after the listener reflects upon the argument does he or she notices that it has been illustrated by an error. Even then, many will simply shrug. But if we ask what the inaccuracy means --"inquiring closely"-- we may yet get an answer.16

Solon's fundamental unit is a year of 360 days. His solar year may be divided into 12 months each; but it is the lunar year (and not the solar) which requires an additional month every other year. In other words, Solon is speaking as if the year is now solar, now lunar; he is combining two

15 73 would have been considered the 22nd prime when counting 1 as a prime, as the ancients sometimes seem to have. (This matches it with the final letter of the 22-letter Alef-Bet, Tav). This is not without interest, for the very simplest magic square made with prime numbers-- assuming one counts 1 as prime-- has the elements 1, 7, 13, 31, 37, 43, 61, 67, 73, with a magic constant of 111, (which is incidentally also the constant of the 6x6 magic square of the Sun, as given for instance by Agrippa). We shall mention this magic square again below.

16 Since Herodotus' original audience was a listening one, the point would have been even more easily missed. The debate about when Herodotus' works were collected into a book is an ongoing one; the argument I am making contends that either Herodotus or whoever shaped his final text intended this mathematical 'trap-door' to be noticed, and this probably presumes a reading, not merely a listening, audience.

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ways of measuring the year into a single amalgam.

This does not in itself, of course, indicate that Solon or Herodotus is thinking of the octave or the circle of fifths. The ratio of 12:13 does indeed call the context of music to mind: twelve semitones, and the thirteenth is the octave of the root. If we understand harmonic considerations to have exercised a determinative shaping upon Gospel narratives, it is easy to see these ratios recurring: the master, root tone, who leads twelve further followers, one of whom-- the thirteenth of the group-- betrays the master "with a kiss," i.e., by a very near miss, since by Pythagorean spiral fifths tuning, the thirteenth tone ought to be consonant with the root, but misses it by the comma.17 In comparison with the calendar one can see that the gap between the twelve-month solar calendar and the thirteen-month lunar division leaves a "comma," so to speak, a portion of the year that must fall outside, because the natural cycle will not align itself with pre-determined mathematics of convenience (a tidy 360-day year, for example), nor indeed will different cycles (for instance the sun and moon, or the measurements of octaves and fifths) fall into place neatly with each other.

Atys and Attis

The resistance of the cosmic cycles to the efforts of human ingenuity to reduce it to a perfectly predicable pattern, combined with its tendency-- which must surely have seemed perverse sometimes-- tantalizingly to approximate order-- must have seemed very like the ways of fate and destiny. Order did occur, and repetition did happen-- and yet, there was difference, and the same events did not always play out according to the mythical script of archetypes. The myths themselves knew this, it would seem, for the myths themselves encode the knowledge that something escapes their encoding. I do not know of any other way to put it. Plato is not writing science, though he uses the language of science to suggest. Millennia before Derrida had said that "philosophy always reappropriates for itself the discourse that delimits it," or before Godel followed Cantor's lead in finding how to rigorously discover ascertainable realms outside any given system of rigor, myth itself had seen both the limits of discourse and the discourse of limits.

Solon has described a wheel to Croesus which can be measured in two ways. This wheel is both the wheel of the year and the "wheel on which the affairs of men revolve," according to which no one is immune from experiencing ill fortune. Herodotus underscores this by showing how the "nemesis of the gods" befell Croesus immediately after Solon left, in the doom that befell his son Atys. This story needs a closer look now.

Croesus dreamed that his son Atys died from a wound from an iron weapon. Accordingly, he removed all occasion for Atys to be around iron weapons, and found him a wife, so that he might have excuse to remain home. At the same time, Herodotus tells us, Adrastus, son of Gordius of Phrygia, came to Croesus' court. Adrastus had accidentally killed his own brother and had fled his home city. Croesus received him and gave him ritual purification (katharsis). Sometime after the wedding, a wild boar came into the land ravaging the fields and terrorizing people. Croesus refused to allow Atys to join the party that was formed to hunt it, citing his dream as reason. But Atys argued with him: What iron weapon does a boar wield? And with what hands could it wield

17 Similar resonances can be seen in later materials, for example in Beowulf: there, when Beowulf takes twelve men to confront the dragon, the one who leads them there is "the thirteenth," the thief; moreover all but one abandon Beowulf at the crucial moment. Then, at the end after he has killed and been killed by the dragon, Beowulf is buried in a mound, and again "twelve men ride around it." McClain suggests that much dragon imagery from ancient mythology may derive from or relate to Pythagorean spiral tuning, and the trope of the dragon lying on a mound of treasure may well symbolize, in one connection, the circle of tones on such triangular tone-number matrices as McClain sketches.

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it if it had one? Croesus yielded to Atys, who complained that he was being shamed before his new wife; but he sent Adrastus to accompany Atys and keep him safe. The party did find the boar, and Adrastus hurled an iron spear-- missing the boar and killing Atys. Croesus refused to kill Adrastus, saying that the responsibility-- the aitia-- belonged to the gods; but Adrastus in remorse slew himself over the grave of Atys.

Adrastus' name means "inescapable" or "immovable;" Atys' is cognate with Ate, (figuratively "doom," literally "blindness") and resonant as well as with aitia, "cause" or "responsibility." This is the term Croesus uses when he says the responsibility for Atys' death lies with the gods, not Adrastus. It is also the word Socrates uses when on the last day of his life he recounts the beginning of his philosophical search: "I thought it noble to know the aitia of all things." But, as has often been noted by commentators, Atys' story is also the story of Attis, the shepherd favorite of the mother goddess Cybele. As is by now well known, from the Middle East to the North of Europe (and indeed beyond, as far as India and the Americas) there recur stories of a dying god, often consort or favorite of the goddess, who is killed. Sometimes, not always, he comes back to life. Frazer compared (not to say conflated) the stories of Osiris, Attis, Adonis, Tammuz, Balder, and Christ; and though the academic fashions have changed since his time, it has not been seriously questioned that some commonality obtains between them all; the question is what sort of commonality, how to account for it, and what it means. I do not depend upon (or even have) a theory of this, but I think I can point out some interesting facts which any such theory must account for; and I submit that the spirit of such theorizing is, on one level, more important than its verifiability.

Attis' story has not reached us in a definitive version. To some, it seems like a cluster of variants of Adonis', but because Herodotus refers to Atys, I will concentrate on Attis (and for other reasons on Balder). Although there is no need to decide which is the "original" between Adonis and Attis, the name of Attis is attached to more different narratives and may thus be the older. Like Adonis, Attis is shepherd, and is either a paramour or a devotee of the mother goddess Cybele; in some accounts he is born like Aphrodite from the severed genitals of an earlier deity. When he is driven mad on the eve of his own nuptials, he emasculates himself. Attis dies from his wound, but there is another version, preserved by Pausanias, according to which he is killed by a wild boar sent by Zeus in retaliation for the cult of Cybele beginning to eclipse Zeus' own. In one of the more surreal episodes of myth, Zeus answered Cybele's plea for her lover by causing his body to remain incorrupt and decreeing that his hair will continue to grow and his little finger will always move.18

It is supposed, on the authority of Clement, Maternus, Sallust and others, that Attis' rites were performed at the Vernal equinox. Since the Festival of Adonis was celebrated at midsummer (when the plants women are said to have ritually planted would sprouted and withered quickly, emblemizing Adonis' untimely death), they cannot have been in any simple sense identical by the time of the testimony we have. The same is even more true of Osiris or of Balder, who are farther removed from the climate and culture we are most immediately concerned with. Perhaps the celebrations of one or the other were moved for agricultural reasons, or political, or some other consideration. But in every case, the figure in question is celebrated as dying at one of the cardinal nodes of the solar year, aside from Osiris, whose festivals occur timed with the rising of Sirius and with the flooding and receding of the Nile. But aside from the calendrical connections, there are stronger thematic links.

It is Atys who, according to the oracle's last message to Croesus, Apollo wanted to have 18 The main sources on Attis--as should be clear from the above, they are not in harmony-- are Pausanias (7.17.9-10), Pessinus (7.17.10-12), Ovid (Fasti 4.223-242), and Catullus 63

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experience the downfall of the kingdom. Herodotus records that when Cyrus first made Croesus his advisor, Croesus asked permission to send one last question to the oracle from whom he had received so many answers:

Croesus, finding his request allowed, sent certain Lydians to Delphi, enjoining them to lay his fetters upon the threshold of the temple, and ask the god, "If he were not ashamed of having encouraged him, as the destined destroyer of the empire of Cyrus, to begin a war with Persia, of which such [chains] were the first-fruits?" As they said this they were to point to the fetters—and further they were to inquire, "If it was the wont of the Greek gods to be ungrateful?"

The Lydians went to Delphi and delivered their message, on which the Pythoness is said to have replied:

It is not possible even for a god to escape the decree of destiny. Croesus has been punished for the sin of his fifth ancestor, who, when he was one of the bodyguard of the Heraclides, joined in a woman's fraud, and, slaying his master, wrongfully seized the throne. Apollo was anxious that the fall of Sardis should not happen in the lifetime of Croesus, but be delayed to his son's days; he could not, however, persuade the Fates. All that they were willing to allow he took and gave to Croesus. Let Croesus know that Apollo delayed the taking of Sardis three full years, and that he is thus a prisoner three years later than was his destiny. Moreover it was Apollo who saved him from the burning pile. Nor has Croesus any right to complain with respect to the oracular answer which he received. For when the god told him that, if he attacked the Persians, he would destroy a mighty empire, he ought, if he had been wise, to have sent again and inquired which empire was meant, that of Cyrus or his own; but if he neither understood what was said, nor took the trouble to seek for enlightenment, he has only himself to blame for the result.19

Note again the question here of blame, aitia. Note also Croesus' sarcastic reference to the sacrifice of the harvest in his offering of the iron fetters as the "first fruits." The three year interval referred to by the oracle can be calculated: The established chronology dates the beginning of Croesus' campaign to 547 BC, and its end to 546. It is therefore approximately a year in duration, and not much more, for it includes only a single winter, during which Croesus decided to suspend hostilities, but Cyrus did not, pursuing him and routing his forces. Since we know too from Herodotus that before embarking upon the war, Croesus had spent two years in mourning for his son Atys, the three years bring us back to the very exchange with Solon.20

19 Compare Socrates' words in the Symposium about Diotima, who was able to postpone by ten years (but not prevent) the plague destined for the Athenias, by advising them as to what sacrifices to make; just as the Trojans were able to stave off their defeat by the Greeks for ten years. The story of Croesus’ ancestor, whose sins are the aitia of Croesus’ fate, is of course also the story of Gyges, who also significantly occurs in a Platonic context.20 Note that in this conversation, Solon has referred to an intercalary month being inserted every other year. This means that in a period of three years, there are (given his 30-day months) either two 360-day years and one of 390 days, or else (vise-versa), two of 390 days and one of 360. It is perhaps coincidental, but the sort of coincidence the ancients would have noted and used, that the sum of 360+390+360 = 1110, that is, 111 x 10; recall that of Agrippa's various planetary magic squares, the 6x6 square of the sun has the magic constant of 111. Moreover, as noted above, so has the prime-number magic square

43 1 67 15th 1st 20th61 37 13 19th 13th 7th 7 73 31 5th 22nd 12th

The number 73 here catches our attention because it is the single large prime factor of 365 (=5x73); all the numbers Solon explicitly uses factor into 2's, 3's, 5's and 7's. If one opts, against modern consensus, to call 1 a prime number (though the modern consensus, to be sure, has good mathematical rationale), and consider these 9 numbers members in

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Wisdom of Silenus

In short, Herodotus is pointing at the encounter between Solon and Croesus as the nexus of his theme. When he tells the nemesis which befell Croesus, he does so by historicizing a myth which tells of the killing of a hero by an unintentional executioner. Herodotus need not have had every resonance we note here explicitly in mind. But there is every reason to suppose that Herodotus' audience would have recognized the motif, and even the name Attis. Herodotus already belongs to an age when scholarship and mythography has taken over the living experience of the myth; when variants and exegeses and proposed etiologies are debated (compare the beginning of the Phaedrus). Herodotus would have known the background of Attis' story at least in some versions. According to accounts which make his madness occasioned by his imminent marriage, Attis is betrothed to the daughter of Midas, the famous king with the golden touch, indeed who had to beseech Dionysus to turn his daughter back to flesh from the golden statue he had unwittingly made her. Midas brings us to a new loop in our story. Croesus' great wealth, proverbial by Herodotus' own day (and the underlying theme in the conversation with Solon over who is olbos, blessed or happy), was connected to the gold in the Pactolus, where Midas washed in order to rid himself of the "gift" of the golden touch and which thereafter ran with gold. But the story of how Midas came to get this ability is also linked to our inquiry.

According to a tradition, preserved by Ovid, Cicero, Hyginus, and others, Midas was once host to a (possibly coerced) visit from Silenus, the leader of the satyrs and Dionysus' tutor. Silenus is etymologized variously as either "bubbling water," hence his connection with springs, or else "moon-man" (compare the moon-goddess Selene, and also Semele, Dionysus' mother). Herodotus mentions the capture of Silenus in 8:138 as transpiring in Midas' garden, situated near the spring of Inna, "the mule," where roses grew "with sixty blossoms each, of surpassing fragrance." The flowers' scent may have been intoxicating; in any case Silenus was certainly entrapped by wine, and some storytellers report that Midas himself mixed wine into the spring, lying in wait, knowing Silenus was to come by that way. The duration of Silenus' visit is given as either "for five days and nights," or in other sources as for ten days, and "on the eleventh day, Midas carried him back to Dionysus," whereupon the grateful god offered Midas a gift, and Midas requested that whatever he touch turn to gold.

Cicero tells us in the Tusculan Dispositions that Midas asked a question--what is the best thing of all for a human being?--before he released Silenus.21 Silenus tried not to give reply. He told, rather, fantastic stories, for instance of a huge continent beyond the Ocean stream-separate from Eurasia and Africa—with beautiful cities where lived enormous people, happy, and long-lived, under a remarkable set of laws. A gigantic host of them once embarked in ships to visit the Hyperboreans; but they returned, disappointed in what they found. Silenus also mentioned a terrible whirlpool, with a pair of streams nearby, trees growing on the banks of each with remarkable fruit. That of the first stream's trees caused terrible sadness, and whoever ate it would

the list of the first 22 primes, then they are in that list, respectively, as indicated in the second magic square above: 15th, 1st, 67th, 61st, 37th, 13th, 7th, 73rd, and 31st.Disregarding the ordinal status of these numbers (the nd's and th's), and summing them, one finds, surprisingly, that the top row and middle column sum to 36; all other rows and columns sum to 39 (and the diagonals to 38 and 40, which of course average to 39). I do not know of any reason why this should have been expected to happen. Neither do I insist upon its significance; but 36 and 39 of course are the 3rd multiple of 12 and 13, respectively. There are a good number of other resonances between the numbers 37, 73, and what we might call the "textual geometry" of Genesis 1:1, John 1:1, and the Aaronic breastplate, which I suppress here out of an effort to stay somewhat on topic. 21 This is an echo, perhaps, of a kindred story in the Hebrew tradition in which Jacob wrestles with someone—presumably God—and demands an answer and a blessing before releasing him.

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weep and pine away. But that which grew by the other stream rejuvenated even of the old--too much, in fact; for its eaters, after reversing through adulthood, adolescence, and childhood, became infants—and then disappeared.

The story of the Atlantic continent attributed to the drunken Silenus is of course known to us from Plato's Republic and Critias, where, however, it is said to have come down from none other than Solon. In his Life of Solon, Plutarch tells that Solon not only believed the story of Atlantis but had composed an epic poem on it. Aelian quotes Theopompus as his source for a report of a comedy by Thespis, or his pupil Pratinas, ridiculing Solon for telling utopian lies in his epic, and presenting him as Silenus, straying casually through Egypt and Asia. The motive for the ridicule may also be found in Plutarch, who relates that Solon objected to the ridiculous speeches Thespis had given his satyrs, asking whether he was not ashamed at telling "so many lies to so large an audience?" To Thespis' reply--"What does it matter? the whole play is a joke"-- Solon hit his staff on the ground, saying, "With such jokes in our theatre, they will soon be in our contracts and treaties!" In his work on the Greek myths, Graves observes that "Silenus and Solon are not dissimilar names and as Silenus was tutor to Dionysus, so was Solon tutor to Peisistratus who—perhaps on his advice—founded rites at Athens." Both names may moreover be related to Selene, the moon, or at least easily call it to mind.

Midas was entertained by Silenus’ stories, but he persisted in asking his question, and finally got his response, in which Silenus extracted his revenge for Midas' trickery and curiosity, for his answer-- the same opinion Sophocles will later cite-- had a sting in its tail: Best of all for mortals is not to be born; and next best, to die soon. Midas' conversation with Silenus was a well known story; and as we have seen, Silenus' melancholy advice was echoed often by the Greek tragedians. Aristotle's lost dialogue Eudemus, or On the Soul, which Plutarch cites, features the story of Midas and Silenus as well. This Aristotelian dialogue would seem to be a response to Plato's Phaedo, which also importantly turns upon the question of "what is best," and whether it is best for Socrates to die.

Silenus' reply is a gift of knowledge that has a reversal to it--a gift that is barbed, and prevents its own enjoyment, a qualification which pertains, too, to Midas' other gift, the so-called "golden touch." It was after he had repented of his greed, having beseeched Dionysus to remove the "gift," that Midas was told to wash in the river Pactolus, whence came the large deposits of gold in that river. This, as has been said, links Midas and Croesus, for Croesus derived his own great wealth from this river. But even more telling is the thematic connection, between Solon's and Silenus' philosophy. Herodotus leaves this connection implicit. He simply refers to Atys' marriage (without overtly referring to the tradition which makes Attis betrothed to Midas' daughter) and the presence of Adrastus, soon to be his accidental assassin, and makes Adrastus "son of Gordias, son of Midas" (in fact, some authorities think Gordias and Midas to have been the alternating names of the Phrygian monarchs). In short, Herodotus is drawing upon a tradition which unfolds the question of whether life is worth living, and does so in connection with Midas and with Attis. This question is bound up with the wheel of fortune, as Croesus' eventual words to Cyrus indicate, and this wheel in turn is the calendar, in which Attis is sacrificed yearly.

A detour to the north

If we trace the sacrificial victim northward, to the Teutonic and Norse milieu, we are confronted with a new set of variations. As with Attis, so with Balder, there is a plurality of versions and no way to identify the oldest strata. The Prose Edda relates how Balder dreamt of his own death, whereupon Frigg drew oaths from every creature--animal, vegetable, mineral-- not to harm Balder. Every item except one, of course, as must always happen in such stories; for she ignored

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the parasitic (and, as she thought, negligible) mistletoe. The gods took to entertaining themselves by throwing now-harmless but ordinarily deadly weapons at Balder. Loki, however, jealous and spiteful over the attention Balder received, learned of the omission of mistletoe, and sharpened a stick of it, which he put into the hand of Balder's brother, the blind god Hoder. Guiding Hoder's throw, Loki acheived the death of Balder. Then, when Frigg went through the world trying again to attain unanimity-- this time by asking every creature to grieve, so that Hel would let Balder return to Asgard-- Loki (in the guise of an old woman) refused. Balder had to remain in the world of the dead, until Ragnarok. In the Elder, Poetic, Edda, Hoder is killed by a new son born to Odin, Vali, who grows to manhood in a single day. The Poetic Edda says that both Hoder and Balder will emerge from Hel's realm after the final conflagration:

Unsown shall / the fields bring forth,all evil be amended;Baldr shall come; / Hödr and Baldr,the heavenly gods. 22

This story, retold in prose by Snorri in the 13th century, is understandably admired for its economy and its tragic logic. The position of Hoder, the blind assassin unwittingly used, in particular has puzzled many, as well as Loki's role. Much less well-known is the version Saxo Grammaticus tells in his Gesta Danorum, in which there is a real rivalry between Balder and Hoder. In Saxo's semi-euhemerized account, which Latinizes the names, "Hotherus" and "Balderus" are rivals for the hand of Nanna, the daughter of Geverus. This latter figure is the moon god, as is known from the medieval sagas of Wayland Smith and Dietrich of Bern, which record the combat between Gevarus and Ivalde. The latter comes to be imprissoned upon the moon for his impiety:

....sentAs exile to the Moon, where he stays yet,Drunk with the magic mead, yet not content,For with the Moon-god's rod of thorn is heFor ever beaten. On his aching backHe bears the load of faggots with which he,So it is said, did try to burn that GodWho is called Gevar, Ruler of the Moon.23

Hotherus is favored by Nanna, whose name may be (despite the distance in miles and years from Mesopotamia) related to Innana (I get to make such remarks, because I have no reputation to defend); but Balderus is determined to win her, despite the fact that she refuses him--quite politely, it must be said, since she implies that his station (he is a demigod, she a mortal) is too high for her. Gevar advises Hotherus how he may defeat Balderus, who is invulnerable to ordinary weapons. Gevar sends him on a long journey, seemingly modeled on mythical treks to the underworld, to the satyr Mimingus who keeps a magical arm-bracelet that endlessly increases wealth, and a magical sword. Camping next to Mimingus' cave, Hotherus is told to take care to pitch his tent in such a way that its shadow does not fall across the entrance, lest the shy Mimingus be frightened and stay within.

As he watched all night, his spirit was drooping, dazed with anxiety, when the satyr cast a shadow on his tent. Aiming a spear at him, he brought him down with the blow, stopped

22 The Elder Edda, Voluspa, 60

23 The Wayland-Dietrich Saga, tr. Katherine M Buck. Canto V

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him and bound him, while he could not escape. 24

There are a few odd things about this story. Dumezil notes that many commentators have given up trying to explain why the tent must be pitched in such a way as not to cast a shadow over the cave entrance, when the light seems to come from the cave and at night, since the strategy seems to be designed to give Hotherus warning by the appearance of Mimingus' shadow. It seems evident though that there is here a relic of some practice like that which still attaches to Imbolc, now called Candlemass or, more popularly, Groundhog Day. If one wonders what a satyr, satyrus Mimingus, is doing in a Danish heroic saga, one can always of course assume that Saxo is simply translating into Latin materials he does not fully understand and using whatever vocabulary he has at hand, thus not being too choosy about what terms he uses. But if we assume that Saxo is more intentional than that, perhaps more can perhaps be guessed. It may well be that Saxo chose the term because of all the terms available it best suited the clear import of the denizen he was treating. The satyrs and Silenoi are connected with Dionysus, the god of inspiration and intoxication, and in fact Silenus is captured by Midas after Midas has mixed wine in the spring of Inna, or the Asses' spring. It is not irrelevant to note that Mimingus' name seems likely to be derived from Mimr, the keeper of the spring of knowledge, from which Odin drank after giving one of his eyes for the right to taste it. (This spring, at the base of Yggdrassil the World Ash Tree (gnawed by Nidhogg the world serpent), recurs worldwide, most obviously in the four rivers which flow out of Eden, in the center of which are found a tree that gives knowledge and a serpentine denizen). There is even a version of the story of Odin's bargain in which he asks the guardian of the well for the secret of wisdom, and gives one eye for it. The answer he receives clearly reveals the same structure as the Midas story, the answer with a sting, the barbed answer that prevents its own use: the secret, Odin is told, is "look with both eyes!"

As to the sword which Hotherus retrieves, Saxo does not give its name. That Mistletoe was the name of a magical weapon, however, we know from several Teutonic myths.25 Misteltein, as it is called, is a sword from the hoard of the onetime king, now ghoul or draugr Thrain, in the saga of Hromund Gripsson. Hromund descends into the tomb of Thrain on a great chain, lowered by 59 other men, who await him above. As in Beowulf, the hero sees a hoard of treasure in which stands out a great sword, which he takes; but Thrain, still alive by witchcraft, challenges him to wrestling match, since he himself carries no weapon. After a tremendous battle in which Hromund's hip is dislocated (like Jacob), Hromund manages "by a foot trick" to trip Thrain and pin him. Thrain then oddly remarks:

"Now you want my advice having obtained my sword. I have lived long in my barrow

24 Saxo Grammaticus, Gesta Danorum Book III

25 The identification of Mistilteinn as the weapon meant by Saxo, and the further equivalence of the Balder myth with the druidic significance attached to mistletoe, has been called into question, most seriously by Jonathan Z Smith. (See his chapter "When the Bough Breaks" in Map is not Territory.) Smith's case is that Frazer, to whose work all these identifications get traced, depends upon too-loose analogy and misleading half-truths. His critique is not polite. Of the pivotal point in Frazer's argument, he remarks: "I can think of no other passage of less than one hundred words in the work of any other scholar which contains a comparable number of errors of fact and interpretation." As Graves would say, Smith has "a very broad back" for sheltering anyone who wishes to allege my own contentions here are equally ill-founded; it is with some relief that I note that a scholar of the stature and independence of Hilda Ellis Davidson was willing to followed Rydberg's lead in accepting Mistilteinn the mistletoe in Balder's story, and in finding the druidic parallels relevant. With all deference to Smith, to whom I am indebted for a number of lessons, and all caveats about Frazer duly made (for a good sense of my own reservations, see Wittgenstein's critique in his Remarks on Frazer's Golden Bough), I remain persuaded that the analogies, "loose" though they be, are not so loose as to have been meaningless, and that if the meaning of the corollaries Frazer glimpsed is not what he thought, there is still some meaning to be deduced (and not a mirage of Victorian condescension).

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and gloated over my wealth, but no good came from that treasure, although you think it good. I never intended that you would use Mistiltein, my good sword, to harm me."Hromund then loosed the sword and rested it on his knee, and said: "Tell me now, how many men did you defeat in duels with Mistiltein." "Four hundred and twenty," said the drow, "and I never received a graze. I tested my skill with King Seming, who ruled in Sweden, and he saw that I would soon be the victor." "Long have you," said Hromund, " been harmful to men, and I will work it that you die first." He struck the head off the drow, and burned him up in the fire, then went out of the barrow. 26

The theme of the hoard which brings no real gain is also familiar from Beowulf. It is a moralistic commonplace, but it bears underscoring in this connection as it is such prominent motif in the Croesus story. A similar connection arises in the next episode, when Hromund loses Misteltien in a deep lake during a battle. During his recovery from his wounds, Hromund rests with the family of a fisherman, who one day brings in an enormous pike he has captured. Inside the fish's belly the sword is discovered.

This delivery-by-fish of a lost precious item is a motif too frequent to stand as a clue or connection in itself, but one may note its occurance in Herodotus: just before Solon visits Croesus, he has come from the court of the Pharaoh Amasis, who has broken his alliance with Polycrates the tyrant of Samos (Pythagoras' home), appalled at Polycrates' thus-far-uninterupted good fortune; no one, he warns, can be continually blessed; sooner or later disaster will strike, and the better the previous good luck, the worse the downfall will be. Yet even when, at Amasis' urging, Polycrates threw his valuable signet ring into the sea in order that he should suffer some loss, the ring was found in the belly of a fish27 which (because of its great size) a fisherman had brought to the court as tribute. This apparent good fortune Amasis read as a portent of disaster, and ended relations with Polycrates. For us, of course, the interesting thing about the anecdote is the epicycles it includes: the small circle of the ring travels in a circle away from and back to Polycrates, as part of a larger cycle which is Polycrates' own rise and (as Amasis has foreseen) fall, this last cycle being again the wheel of fortune. In the end, Polycrates dies in a manner Herodotus does not even want to mention-- its apparent ignomy makes some scholars suspect crucifixion-- and his corpse is exposed to the weather, or (as his daughter had dreamed) is "washed by Zeus and anointed by the sun," an omen which again he had misinterpreted as good.

Midas and Gyges

This misinterpretation of omens of course we have seen in Croesus case repeatedly, down to the fulfillment of the "unfortunate" omen of the mute child speaking-- an event which saves Croesus' life. The blessing which proves a misfortune and the misfortune which proves a blessing-- a kind of presentiment of the felix culpa of Christian liturgy, the necessary fault of Adam or indeed of Judas-- recurs over and over in these stories. Thus we have two stories of Balder and Hoder, one from one perspective and one from the other, as it were, which are reconciled only in the riddling prophecy that expects both to ride out side by side after the end of the world. 26 The Saga of Hromund Gripsson ch. 4. Tr. Gavin Chappell. Thrain is described as having been a powerful and very evil king, who has by magic long outlived the 70 years which are allotted as a human lifespan, according to Solon. The 420 men he killed, divided by the 60 men in Hromund's party, yields 70. I read the story thus: Thrain has gone round the octave circle seven times, and has found himself now at the impassable comma, where he lives in a perpetual half-life, undead.

27 This trope is repeated in a later story concerning Solomon, whose magic ring allowed him to command the demon Asmodeus, until its loss in the sea let the demon rebel and, for seven years, rule disguised as the king. Solomon regained his control when the ring was recovered from inside a fish.

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I have suggested that this blessing/curse is intimately imaged by the inherent impossibility of giving a rational tuning system which provided every interval in terms commensurate with each other. The octave, and the larger circle of fifths, was a sonic "image" of the cosmos, and as such its imperfection mirrored that of the universe itself-- or at least, of every attempt to depict the universe as a whole. In fact the ancient world and the modern alike are replete with instances of such "flaws," if we want to call them this: the Pythagorean comma finds its place with the incommensurability of the diagonal of the square (with which indeed it has a close mathematical relationship), the Ptolemaic epicycles, the extra-calendrical days, and the precession of Equinoxes. To this list could be added today the three-body problem, Godelian incompleteness, Chaitin's random numbers, quantum uncertainty, the entropic disappearing-act of information in communication theory, and the beautiful evasions of fractals. It is not possible to present even the ancient exempla of this inherent uncertainty in their quasi-systematic isomorphism. But the salient point is not that our maps are always misrepresentations and approximations, nor even that the distortion involved is in some wise inherent in the nature of things.

These were not merely epistemological difficulties for the ancients. Socrates puts very succinctly what is at stake: no one, he says, does evil knowingly; evil is ignorance28. This needs to be read with the famous story of yet another ring, the “ring of Gyges” told by Glaucon in the Republic Book II (with a reprise at Book X), since as is well known, Plato’s account is a different version of a story also told by Herodotus. In both versions, Gyges is a servant of the king of Lydia (Herodotus gives us the name Candaules). Plato calls him a shepherd (in fact, Glaucon says that the shepherd was “an ancestor of Gyges,” not until book X does Socrates refer to “the ring of Gyges”); Herodotus a bodyguard. In Herodotus, Gyges is prevailed upon by King Candaules to spy upon the queen as she disrobes for the night, because Candaules is certain that she is the most beautiful woman in the world. Gyges at first begs off, swearing that he already esteems the queen’s beauty above anyone’s, but Candaules, “since men’s ears are less credulous than their eyes” (I 8), is unsatisfied with Gyges’ assurances. He arranges for Gyges to be concealed in the royal bedchamber, but as he departs after getting his eyeful, she detects him. Summoning him the next day, the queen gives Gyges a choice: either die for the impiety you have committed, or avenge me by killing Candaules. Again Gyges begs to be excused from such a dilemma, but the queen will not relent; so Gyges kills Candaules in the same chamber where he had beheld the queen; he marries her, and becomes ruler of Lydia. In this he was confirmed by the Delphic oracle, to which the divided citizenry appealed. The pythoness added, however, that Gyges’ dynasty would only last to the fifth generation—that is, until Croesus.

In Glaucon’s story, Gyges (or his “ancestor”) discovers a tomb, in which he finds a ring that gives him the power of invisibility.

Becoming aware of this, he immediately arranged to become one of the messengers sent to the court. He went, seduced the queen, murdered the king with her help and seized the throne.29

This story is almost always read as if the shepherd used the ring to usurp the king, and indeed Glaucon’s later questions clearly stage the “what-if” thought-experiment that asks how one’s ethics is effected by the ability to evade detection. But in fact, the story does not say that the shepherd uses the ring at all. He becomes a messenger, seduces the queen, and with her help kills

28 Protagoras 345e.

29 Republic, 360b

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her husband and seizes power. It is not the human body that requires concealment, but the crime itself. Plato allows the magic ring to serve as a decoy, as if invisibility of the body was the real question, as a device to simplify the question, but the true ethical breakdown, far more complex and difficult to analyze, has occurred when the soul is able to wish to practice deception. The invisibility conferred by the ring is a red herring, a kind of token for the ignorance that Socrates says is the only real condition for doing wrong, because to see the invisibility as decisive is to remain in ignorance.

But what if there were a kind of ignorance built into the cosmic structure? The tragedian Sophocles indicates that it is the effort to avoid evil on insufficient knowledge that brings evil about. If, then, there were to be some inherent lapse of knowing or knowability in the cosmos, this would be tantamount to evil being unavoidable.

"It must needs be that offenses come. But woe to the one by whom they come. It would be better for him that a millstone were put around his neck and he were drowned in the depths of the sea" (Luke 17:2) 30

From one ancestor of Croesus we turn to the other, the source of his wealth. As has been mentioned, in order to be delivered from his own blessing-turned-curse, Midas washed his gold-making hands in the river Pactolus, imparting gold to this stream which became the foundation for Croesus’ legendary wealth. His daughter, who had been accidentally turned to gold, was also restored to him (later to be betrothed to Attis). Dionysus, after releasing Midas, bequeathed the king a reminder of his foolishness--a pair of asses' ears, which Midas took to covering by a tall cap. Only his barber knew; but the barber, unable to keep a secret, and unable to tell any human being for fear of his life, whispered the secret into the reeds or into a hole in the ground; and from then on the wind rustling in the reeds spread the whispered word.

There are, however, different traditions about how Midas received the ears of an ass. Midas was said to have been present at the musical contest in which Apollo, on the lyre or cithara, defeated his opponent, either Pan, or Marsyas. The judge of the contest was the mountain god Tmolus, or in some versions Midas himself. Tmolus decided for Apollo's lyre over Pan's pipes (in the story of Marsyas, the satyr is defeated when Apollo turns his lyre upside down but can still play, whereas the pipes can only be played in one direction). Midas, however, differed from the opinion of Tmolus, and Apollo, outraged, rewarded him with ears befitting his bad musical taste.31 As for Marsyas himself, the satyr was flayed for his presumption. Ovid has him crying out: "Why do

30 The context here is interesting: it concerns "offense" (skandalon) to "one of these little ones," but the phrasing is parallel to what is said regarding Judas: "The Son of Man must be betrayed; but woe to him by whom the Son of Man is betrayed. It would be better for that man if he had never been born." This narrowing of Silenus’ (and Ecclesiastes’) verdict from a judgment on the human race to a judgment on a few, even a single person (Judas) is, as far as I know, astonishingly unremarked by scholarship. It is one of the most pregant moments of intersection and inversion between Classical culture and the New Testament. Judas, too, has been represented as a piper, and sometimes the “bag” he is said to hold is interpreted as a bellows of a wind instrument.

31 The ears of the ass or mule, however, may also have been a feature of kingly accouterments in Anatolian culture, whose iconography might have seemed perplexing to Greeks. (It was also suggested anciently that Midas' long ears referred to his network of spies and informants). And of course there is the anti-Christian graffiti depicting Christ as a crucified ass or mule, a diatribe which resonates all the way to Nietzsche's Antichrist and his "asses' song" in Zarathustra. The link between these is the oracle which assured Croesus he would be safe until a mule ascended the throne of Persia, which he took to be laughably unlikely, coming as he did too early to profit from the example of Caligula's senatorial horse. Not only did the oracle respond to his later reproach that the mule in question was Cyrus himself, citing Cyrus' mixed parentage; Cyrus in the Hebrew scriptures is also called the Lord's anointed-- "Messiah." Another possibility is that the long ears refer to the shape of the lyre, which has two curved wooden lengths on either side of a space where the strings are stretched.

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you tear me from myself? I repent! A flute is not worth such a price!" This phrase of Ovid's may well quote earlier strata, for it has a resonance with Socrates' feeling of being estranged from himself; and one may note (with an eye to the closing pages of the Phaedo) that the syrinx is often made from seven hemlock stalks (this is mentioned, e.g., by Vergil (Second Eclogue), and remains a trope down through Keats, who in Endymion speaks of Pan on the "pipy hemlock.").

Pythius: a Croesian coda?

Herodotus makes allusion to Apollo's flaying of Marsyas at a very suggestive point in his narrative32:

When they had crossed the river Halys and entered Phrygia, they marched through that country to Celaenae, where rises the source of the river Maeander and of another river no smaller, which is called Cataractes; it rises right in the market-place of Celaenae and issues into the Maeander . The skin of Marsyas the Silenus also hangs there; the Phrygian story tells that it was flayed off him and hung up by Apollo. In this city Pythius son of Atys, a Lydian, sat awaiting them" (7:26-27) 33

Pythius offers to help fund the war with his fortune, but Xerxes, flattered and pleased by his support, not only refuses the offer, but gives Pythius a gift of seven thousand darics which is all that he lacks from four million.34

The next part of Herodotus’ chapter is devoted to Xerxes’ construction of the bridge over the Hellespont, the gap between the Asian and European continents. Herodotus allows a good deal of consideration to the specifics of the reinforcements and even specifies that the bridge from one side had 360 supports, and from the other 314. I leave aside consideration of these numbers, suggestive though they are, to come to the next passage, but I note that in ancient cartography, Europe and Africa are separated by a body of water that begins at the Hellespont and ends at the Strait of Gibraltar. (See, for instance, medieval “O-T” maps, so named for the T-shape of the water division of the round 3-part landmass).

32 The relevant passages are in Book 7, chs 31-40

33 Marsyas' is not the only myth associated with the area. "Celaenae-Apamea.... is the best-described site in Phrygia, and among the most remarkable,whether byreason of legend, history or natural position. Here were localized the myths of Lityerses and Marsyas, and here accoring to the Sibyl and probably to earlier tradition the ark of Noah first touched ground, and the coins of three emperors and a little ruined church on ther acropolis still commemorate this strange belief." ("Notes upon a visit to Celaenae-Apamea," D. G. Hogarth, The Journal of Hellenic Studies, Vol. 9, 1888 (1888), pp. 343-349).

34 If those researchers are correct who conclude that the daric is the 3000th part of a talent, then Pythius' wealth before Xerxes gift is equivalent to 9,993,000 darics of gold; Xerxes' gift thus brings the total to 10 million exactly: four million in gold and six million in silver (the metals of the sun and moon respectively). This 4:6 ratio is equivalent to the 2:3 ratio already implicit in Pythius' own claim to have 2,000 talents of silver (since a talent is worth 3,000 darics). Again there is a gap, and again the making-up of the gap, by a multiple of seven. Although this arithmetic must be tentative not only considering the uncertainty of ancient weights and measures but also the variables involved when silver is being compared to gold, the math is nonetheless suggestive.

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(Note “Gog et Magog” in this map’s north. The Biblical Gog (of Ezekiel 38-39 and Rev. 19-20) is frequently (following Franz Delitzsch) identified with Gyges.) If we read this map as a tone-circle, the water from theHellespont to Gibraltar would be a kind of geographic “comma;” and Xerxes’ proverbial hubris in attempting to bridge it (the initial destruction of his bridges by natural disaster caused him not only to execute his engineers and builders but, legendarily, to have the waters flogged with lashes), a musical fool’s errand as well as a military and political impiety. (This would also suggest a different approach to the story of Hero and Leander).

The narrative now returns to Pythius, who has been worried by an ominous eclipse. Pythius asks Xerxes to allow him to keep the oldest of his five sons at home, to comfort his old age. Xerxes, however, has been given an optimistic interpretation of the eclipse by his own astrologers, who claim that the sun is an omen for the Greeks and the moon for the Persians (then as now, it was difficult for political leaders bent on an ulterior purpose to get honest intelligence). He is enraged by Pythius' implication that his invasion will fail. In what reads like a hideous inversion of the covenant of the portions between Abram and God (Gensis 15:1-21), Xerxes has Pythius’ eldest son killed, and marches his army between the two halves of his body (38-9), on its way to its disastrous European campaign. (Given that the story in Genesis is also about Abram’s receiving God’s promise of progeny, the resonance seems more than happenstance.) Pythius' story recapitulates Croseus' tragic mistake: his request to Xerxes to allow him to keep his eldest son home, to protect him from the ominous intent of the oracular eclipse, only ensures the doom of his son. (A similar motif is seen in Herodotus' story of Oiobazus).

This horrible coda to the story of Croesus may thus be read as a musical parable (there are eight generations from Gyges to Pythius’ sons, inclusive; thus this is the “generation” (octave) where the Pythagorean comma is found. Counting all five of the sons plus the seven generations from Gyges to Pythius gives us the full circle of fifths. I do not insist on this, but note not only the contrast here between the halving of the body and the bridging of the two sides of the Hellespont, and the fact that the halves of the body are placed on either side of the road to the bridge (not both ends of the bridge but either side as the bridge is entered, a “splitting” of the sacrificial victim.

Herodotus never explicitly identifies Pythius as Croesus' grandson, nor asserts that his father Atys is the same Atys who died in Book I. But in that Book, Atys is killed after having been married,

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as is explicitly underlined by Herodotus, for he says that Croesus has arranged for the marriage, as an excuse to keep him from war and the iron weapons he dreamed would kill Atys; indeed Atys prevails upon his father toallow him on the hunt by claiming he is being shamed before his new bride in being held home. There is, thus, implicitly, time for the conception (and even the birth) of Pythius.

There is another reason to guess that Herodotus intends the identification. The eclipse to which he refers, which frightened Pythius by occurring as the Perisan army was about to depart Sardis at the end of winter, did not happen: there was no solar eclipse in 480, whether partial or total, visible from Sardis where Xerxes’ troops were encamped. (Sardis, Croesus’ capital city, is also located at the foot of Mount Tmolus, that is, the mountain named for the god who judged between Apollo and Marsyas). There are a few possibilities to partially resolve this historical/astronomical inconsistency. A source may have indicated an eclipse which occurred the previous spring, April 10, 481 BCE, at the beginning of the expedition, as Xerxes was set to depart from Susa. Alternatively, another date has also been suggested for Sardis: February 17, 478 BC. There is also a lunar eclipse which is known to have occurred in the spring of 480 BC. Thus, Herodotus or his sources have either fudged the chronology, or the setting, or both, or exchanged a solar eclipse for a lunar. In any of these cases, Herodotus has left us an inconsistency which we can either shrug off, "explain" as a mistake, or treat as a possible incitement to look deeper.35

It would seem that Herodotus has loaded his story with a misleading account of an eclipse (one which only a few would be likely to catch, moreover). Moreover, he has done so in conjunction with the final tragedy befalling Croesus' house-- a connection he again does not make explicit but leaves for readers (or very patient listeners) to perceive. He underlines a disagreement over the interpretation of sun and moon, in a context where it is even possible that he has described a lunar eclipse and called it a solar. All of this points us back to the initial question of Solon's discourse to Croesus, where again there is an arithmetical anomaly that turns upon the cycles of the sun and moon.

Math and marriage

Now recall the thema mundi, with its two halves, solar and lunar, which mirror the octave. Herodotus has continually shown the tyrant's attempt to overstep the bounds set to kingly-- and indeed to human-- agency, in terms of the tyrant's effort to second-guess the divine, to anticipate and even manipulate the favor of the gods, and how moreover this attempt repeatedly founders on the blindness which issues in the misunderstanding of the sings in question. This misunderstanding is figured by the confusion of the sun and moon, whose cycles do not coincide. You will recall that the trope of the "marriage of sun and moon" was an alchemical one for the conjunctio oppositorum. This union of opposites, of which Jung made so much, is a figure for a certain moment of realization in the mystical work, but its particular metaphor-- a marriage-- brings us to Plato. For Plato was also concerned with what could define and delimit tyranny; and indeed of the two most famous numerical puzzles in the Republic, one concerns a mating and children, and the other, the life led by the good king versus by the tyrant.

35 Pythius is also the subject in later sources of an obviously Midas-like episode: "The people once came to Pythius' wife with their bitter complaints. She pitied them, but could not relieve them. One day, it is said, in order to show her husband the vanity and folly of living only to amass silver and gold, and to convince him how little real power such treasures have to satisfy the wants of the human soul, she made him a great entertainment, in which there was a boundless profusion of wealth in the way of vessels and furniture of silver and gold, but scarcely any food. There was every thing to satisfy the eye with the sight of magnificence, but nothing to satisfy hunger. The noble guest sat starving in the midst of a scene of unexampled riches and splendor, because it was not possible to eat silver and gold." For the sources, see Plutarch Moralia 262D-63C; Pliny Naturalis Historia 33.10; Seneca De Ira 3.16; Polyaenus Strategemata 8.42. Most scholars seem to think these have conflated a figure called Pythes with Herodotus' character.

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Here is where the numbers of the circle of fifths, above, pertain. I am now following McClain fairly closely (I hope). In Book VIII of the Republic (546a-d), Plato explains at some length how he relates "better and worse begettings" to his master sum, 12,960,000 = 604. This figure, which Cicero labeled "Plato's obscure number," governs the next passage, in which Plato says of the various numbers at work in his cosmos and city that "The root 3-4 mated with 5 produces two harmonies: one of them is equal an equal number of times, taken one hundred times over; the other is of equal length one way but is oblong: on one side, of one hundred rational diameters of five, lacking one for each; or, if of irrational diameters, lacking two for each; on the other side, of one hundred cubes of three." The curious oblong here has one side which is "one hundred cubes of three," that is, 2700. James Adam first suggested that the other side could be calculated at 4,800. He reckoned by reading "rational diameter" as the rational diagonal of a 5x5 square. Since 52=25, the Pythagorean theorem gives the area of the square of the diagonal to be 50. The rational estimate here would be 49, and thus the rational estimate of this length is the square root of 49, that is, 7. If on the other hand we eschew taking rational approximations, the irrational length is the square root of 50. The numbers 49 "lacking one," and 50 "lacking two," are each 48. Multiplying this as Socrates says we must "one hundred times," we get one side of our oblong as 4,800 units, and the other as 2,700. This gives a ratio of 48:27, or 16:9. These are of course two perfect squares, which makes the oblong define the right angles of a Pythagorean triple 3:4:5.

In any tuning system whatsoever, the octave is generated by the factor 2; all other tones must be created by other denominators. This unpacks to a small degree what Plato means in starting out from "3/4 mated with 5," for these prime factors account for all intervals, aside from the octave, in any tuning system known before Plato. But Plato's emphasis on the option of taking a rational estimate or honing in with irrational exactitude in his ratio 49:50 will be capitalized on later in the Laws, when a similar city built in discourse will augment the 18 guardians of the city with a further 19, for 37 in all. McClain understands these "new arrivals" as having been occasioned by a new prime factor, 7. In the Laws Plato refers over and over to "37 guardians" of the city, 18 from "the parent city," and 19 "new arrivals." This can be seen to correspond precisely to the way the musical proportions are generated in the Republic and the Laws. In the former dialogue, using the octave ratio as 360:720, one can generate precisely 18 tones from the ratios of 3 and 5 (recall that the factor of 2 generates only octaves). Since 720 is the highest number here (no tone being measurable outside the octave), one finds that there are eighteen numbers we can generate within this limit. They may be charted thus:

This triangular matrix is a figure of a type well-known from mathematics in antiquity (for instance from Nichomachus). The horizontal axis is a series of numbers increasing by multiplication by a given factor (in this case, 3); the axis sloping upwards towards the left is multiplied by another factor (in this case, 5). Note that the right-most number on the bottom row is 243, which if it were to be multiplied by 3 would put it at 729 (indicated in parentheses). This is again the tritone, and it is just beyond the limit established by the octave.

All the figures lower than 360 may be doubled, or quadrupled, without affecting their tone (because multiplying by 2 has no effect on a number's tonal value-- they remain octaves of each other). In this way all eighteen of these numbers can be fit into the 360:720 octave:

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This triangular matrix exhausts what can be done with the factors 2, 3, 4, and 5. That is, the numbers above are the only numbers between 360 and 720 that can be factored evenly into some combination of 2, 3, 4, or 5. However, adding the factor 7 into the matrix generates a whole family of further tones; in fact, precisely nineteen more, for a total of 37 "guardians" of the new city Plato outlines in the Laws. This yields significant reason to consider that McClain has discovered a genuine structuring principle in Plato's work.

It is known that Plato's friend Archytas did design a tuning system in which 7 played just such a role. In the system McClain finds encoded in the Laws, where the octave is denoted by Plato's number 5040 (=7!) and its half, 2520, the tritone lies within a very narrowly defined area reducible to the ratio of 49:50. It may well be that Archytas was the first thinker to systematically apply the prime factor of 7 to tuning theory. But evidence suggests that Herodotus, or his sources, already were thinking in terms of this number. The name of Solon, one of the "Seven Sages" of Greek antiquity (paralleling the similar group of the seven Rsis in Vedic India), was certainly attached to this thinking36. For if this 49:50 ratio is expanded to the simplest octave that can include it, we have 35:49::50:70

The ratio is thus framed by the octave 35:70. But it will be recalled that this is the very same ratio as we found in Solon's mis-statement of his arithmetic: 70 years in all; 35 with an extra, 13th, month. Interestingly, the ratio 49:50 is also a calendrical "comma", from, however, a non-Greek context: it is the calculation of the Biblical "Jubilee year," which occurs after 49 ordinary years; it is the occasion when debts are forgiven; it is also a common metaphor for the advent of the Kingdom of God in the Messianic age. This suggests that whatever tradition Plato and Herodotus drew upon was ancient and widespread.

So much, then, for Plato's number regarding marriages in the Republic. I cannot demonstrate conclusively that Plato and Herodotus share a common concern here, though it is tempting to wonder about Atys' wedding. As regards the tyrant, however, Herodotus' concerns are unambiguous. Though he nowhere gives us any general account of what he means by tyranny, he does depict for us many instances of the results of tyrannical hubris. Plato, on the other hand, states outright what he believes of the tyrant, namely that the tyrant is miserable, even if he does not know it. Debates over the merits of the tyrant's life are a feature of the sort of story Herodotus

36 A poem, ascribed to Solon, on "The Ten Ages of Man", has been preserved for us:“A child in his infancy grows his first set of teeth and loses them within seven years. For so long he counts as only a child. When God has brought to accomplishment the next seven-year period, one shows upon his body the signs of maturing youth. In the third period he is still getting his growth, while on his chin the beard comes, to show he is turning from youth to a man. The fourth seven years are the time when every man reaches his highest point of physical strength where men look for prowess achieved. In the fifth period the time is ripe for a young man to think of marriage and children, a family to be raised. The mind of a man comes to full maturity in the sixth period, but he cannot now do as much, nor does he wish that he could. In the seventh period of seven years and in the eighth also for fourteen years in all, his speech is best in his life. He can still do much in his ninth period, but there is a weakening seen in his ability both to think and to speak. But if he completes ten ages of seven years each, full measure, death, when it comes, can no longer be said to come too soon.”Philo, who quotes and comments upon this poem extensively in On Creation, 101-107, cites in this context many sevens from nature and history, giving a special place to the harmonics generated by the number.

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presents-- the meeting of the tyrant and the wise man—and as I have mentioned, the motif was expanded into a full dialogue in the Socratic style in Xenophon's Heiron. But Plato (against whom Xenophon may be responding) gives us a very precise estimate of the tyrant's unhappiness.

A prodigious calculation

Plato lays out five types of ruler (he differentiates nine elsewhere): (legitimate) King, Timocrat, Oligarch, Democrat, and Tyrant. He then compares their respective satisfactions, finding those of the King to be genuine, the Oligarch's midway between true and phantastic, and the tyrant's to be all the more so.

"Then I suppose the tyrant will be most distant from a pleasure that is true and is properly his own, while the king is least distant." "Necessarily." "And therefore," I said, "the tyrant will live most unpleasantly and the king most pleasantly." "Quite necessarily." "Do you know," I said, "how much more unpleasant the tyrant's life is than the king's?" "I will, if you tell me," he said. "There are, as it seems, three pleasures -one genuine, and two bastard. The tyrant, going out beyond the bastard one, once he has fled law and argument, dwells with a bodyguard of certain slave pleasures; and the extent of his inferiority isn't at all easy to tell, except perhaps as follows." "How?" he said. "The tyrant, of course, stood third from the oligarchic man; the man of the people between them." "Yes." "then wouldn't he dwell with a phantom of pleasure that with respect to truth is third from that other, if what went before is true?" "That is so." "And the oligarchic man is in his turn third from the kingly man, if we count the aristocratic and kingly man as the same." "Yes, he is the third." "Therefore," I said, "a tyrant is removed from true pleasure by a number that is three time three." "It looks like it." "Therefore," I said, "the phantom of tyrannic pleasure would, on the basis of the number of its length, be a plane?" "Entirely so." "But then it becomes clear how great the distance of separation is on the basis of the square and the cube." "It is clear," he said, "to a man skilled in calculation." The if one turn's it around and says how far the king is removed from the tyrant in truth of pleasure, he will find at the end of the multiplication that he lives 729 times more pleasantly, while the tyrant lives more disagreeably by the same distance." "You've poured forth," he said, "a prodigious calculation of the difference between the two men-the just and the unjust-in pleasure and pain." "and yet the number is true," I said, "and appropriate to lives too, of days and nights and months and years are appropriate to them." "But, of course, they are appropriate," he said. (Republic, 587b-588a, tr. Allan Bloom).

The association of rulers, just and unjust, with the wheel is ancient. Proverbs 20:26 reads: "A wise king is a scatterer of bad ones, and causes to return upon them a wheel." Here the referent of "bad ones" may simply be bad persons, or it may refer specifically to bad kings. The "wheel" in question has given some commentators pause, and some have wished to replace opan here with onam, "their sin." For this, however, there is no corroboration in LXX, Targum, or any other text. The wheel here may be a symbol of kingly power, or an implement of punishment and torture (as in the story of Ixion or St. Catherine) or both. But the salient detail seems to me to be not the noun "wheel," but the verb "return," which confirms that what is being described is a result of previous actions, a harvest being reaped, as indeed is sometimes deduced by association with Isaiah 28:27-28:

For dill is not threshed with a threshing sledge, Nor is the cartwheel [opan agalah] driven over cummin; But dill is beaten out with a rod, and cummin with a stick. Does one crush grain for bread forever? No, for the wheel of his cart [gilgal eglato] and his horses will damage it, He does not thresh it longer.

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The word gilgal in later use is given to the cycles of rebirth in those streams of Kabbalah which discuss reincarnation, like the Orphic wheel of rebirth. One may also note the figure of threshing and grinding grain, which raises the figure of the millstone, the wheel in Jesus' warning about "whoever offends one of these little ones" (Matthew 18:6). This is notable because the precise wording from Jesus is: "It would be better for him if a millstone were hung about his neck and he were drowned in the depths of the sea." The only other place where Jesus speaks of such a fate being better for an offender is his description of "the one by whom the Son of Man is handed over," i.e., presumably Judas Iscariot, in words which clearly evoke the verdict of Silenus: "It would be better for him if he had never been born." (Matt 26:24). This is significant because in both cases, Jesus also underscores the inevitability of the action: “It must be that offences come,” he says, “but woe to the man by whom the offence [] comes” (Matt. 18:7; compare Luke 17:1); and “The son of Man goeth as it is written of him; but woe to that man by whom the Son of man is betrayed” (Matt. 26:24; compare Mark 14:21). I cannot prove it, but I strongly suspect the millstone in question to be the great mill of the heavens, Amlodhi's mill whose stone coming off its axle was interpreted by von Dechend and de Santillana as the shifting of the celestial cycle from one pole-star to another.37

In Socrates' "prodigious calculation," the distance of the tyrant to the king-- 729-- is the same as the denominator for the tritone, the tone furthest away in either direction from the root and the octave. The placing of king and tyrant on opposite nodes of the octave circle would seem to have a legacy as late as the medieval era, when the parables of the fall of tyrants retained their appeal. The image of the Wheel of Fortune, whose popularity during the Middle Ages seems attributable largely to Boethius, typically features four compass points at which four human figures appeared. These were often labeled, clockwise from the left regnabo (I shall reign), regno (I reign), regnavi (I have reigned), and sum sine regno (I have no kingdom). This would all seem to be an unfolding and literalizing of Socrates' point, for according to him, the tyrant is already the most unfortunate of men, the most "out of tune" with himself. Socrates' life is replete with this assertion, scandalous to Thrasymachus, maddening to Callicles: it is far more unfortunate to commit than to suffer injustice. That Socrates took this conclusion with utmost seriousness is clearly maintained all through the Phaedo, in which Socrates prefers to suffer the death penalty on the grounds that this is the best thing for him to do under the circumstances.

Recalling the triangular matrix above with Plato's 18 "original guardians," it is of some interest that the number in the lower left corner, 512, still stands in a tritone relationship with 729 (lying, as before, just beyond the lower right corner of the included matrix). The octave ratio within which this relationship obtains is an octave of 432:864. This octave is easily obtained, by taking the series of powers of 3:

1 3 9 27 81 243 729

Taking the middle number-- 27 --one doubles it repeatedly (54, 108, 216, 432, 864), until one exceeds 729. This number, 864, and its half, 432, will define the octave. One then doubles the other numbers until they all fall between those limits:

512 768 576 432 648 486 729 864.

Note that this is simply the bottom row of the above matrix, except that 384 has been doubled.

37 For a discussion of the use and meaning of opan, "wheel," in the passage from Proverbs, see Daniel Snell, "The Wheel in Proverbs XX 26," Vetus Testamentum 39:4 (pp530-508).

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Rearranging these, one has a Greek Phrygian mode (according to the best guesses of scholars). From lowest to highest note:

864 768 729 648 576 512 486 432 D E F G A B C D

As McClain notes, the bounding values 432 and 864 recur repeatedly in Vedic cosmological theory. This mode and the Dorian are the only two Plato deigns to allow in his Republic. The Phrygian mode is associated largely (though not exclusively) with the aulos;38 the Dorian with the cithara. These two modes would have been the two between which Midas (or Tmolus, whose status as "mountain god" takes on a different connotation when one looks at the triangular shapes of the numerical matrices) had to choose in the contest between Pan or Marsyas and Apollo. The Phrygian mode, ironically, remains completely unchanged under reciprocation (the ratios' denominators and numerators may be switched without affecting the notes), meaning that this Silenic mode is the one that can actually survive being turned upside-down, whereas the Dorian mode requires an adjustment (albeit the minimal adjustment), under reciprocation. But we observe that Marsyas' punishment of flaying in essence turns him inside-out; wherupon the god, belatedly repentant, turned the satyr into the eponymous river, at the font of which Pythius encountered Xerxes (Herodotus calls it the Cataractes).39 ,40

In this exercise, one has chosen seven numbers, because one needs seven tones in any Greek mode (though one sometimes uses nine; see the Appendix below); and one chooses the middle number because this allows one to tune up and down at the same time, precisely as above when we discussed tuning via spiral fifths from the top and the bottom octave. Choosing the central number to double into the root and octave keeps the comma in the rest of the scale small; but of course it does not make the tritone go away; it only moves the tritone relation away from the octave. Note that this is the only tritone in the scale here because there are five of the twelve semitones missing. Observe too that the interval between D at 864 and F at 729 is a minor third. It is possible to expand this 432:864 octave into a full twelve-station tone circle. Doing so, one will find that any two notes defining a minor third interval will always be at a right angle. This means that putting 432/864 at 12 o'clock will entail putting 729 at either 3 o'clock or 9 o'clock. This number thus can mean more than one thing, but we find it persistently recurring in either perpendicular or opposed positions with the root/octave. This is also what we noted when we looked to Ptolemy's double octave and its mapping onto the zodiac: in that case the, the tritone 38 See Ancient Greek Music, Martin Lichfield West, p180

39 This river flows into the Maeander, of which Pausanius reports the claim that it plunged underground where it seemed to meet the sea at Miletus, to rise again in the Peloponese as the river Asopus. (Herodotus also says that the river Lycus passes underground for a while before re-emerging to flow into the Maeander). The speed of the river Marsyas (Herodotus' name Cataractus seems to be warranted), says the English commentator George Sandys in his 1632 edition of Ovid, is "abated by the other," the lazy labyrinthine Maeander, the river whose "mazy motion" finds its way even into Coleridge's Alph, which likewise plunges underground. Likewise, the Marsyas whose identity is maintained even after its having joined the Maeander: says Sandys, "whatsoeuer was offered to Maeander would not mingle with the streames of Marsyas; and what to Marsyas, was cast vp by Maeander." I submit that the satyr's transformation by being thus inverted is essentially equivalent to the reciprocation of the Greek Phrygian mode. This "underground stream" persists as late as Michelangelo, who knew very well that Marsyas had to do with identity, projecting his own identity and face upon the flayed skin of Saint Bartholomew in the Sistine's Last Judgment.

40 It is striking that Apollo acquires his characteristic instrument, the lyre, from Hermes, in repayment for the prank Hermes played of stealing Apollo's cattle-- an occasion upon which Apollo recruits the help of Silenus and the satyrs to search. As we have seen, Silenus seems by his name to be a moon-associated figure; it is interesting then that the aulos, the other instrument in this musical rivalry, is cast away by its inventor Athena when she observed how playing it puffed up her cheeks (like the waxing and waning moon), only to be picked up by the hapless Marsyas.

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was at right angles to the root/octave, because there were twenty-four notes (twenty-five counting the highest octave) instead of twelve; but in that case, too, it was aligned with the signs of the solstices. And here it is of interest that the number 864 is the sum, in isopsephia, of the Greek name Pythagoras. 41

Around and around

As regards isopsephia it is often noted that the number 729 is the sum for , the name given Peter by Christ-- the "rock" upon which He would build his church. This epithet for Peter, the first of the apostles, is given him immediately before the moment when Jesus rebukes him, emphatically and in extremely laden terms, when Peter protests that Jesus must never be "handed over and crucified:" "Get behind me, Satan. You are a stumblingblock to me; you are setting your mind not on heavenly things but on earthly ones." "Stumblingblock" here is, as elsewhere, , and indicates the trigger of a trap, as well as a rough-hewn cornerstone. It is also, as mentioned above, the word for the offences that “must come,” though “woe to the man by whom the offence comes.” 1 Peter 2:6-8 draws attention to the thematic continuity between these when he notes the possibility of being "scandalized" by or “stumbling upon” "the stone the builders rejected [which] has become the chief cornerstone."42 This ambivalence was not invented by the New Testament writers; it can be found in mythical strata whose essence predates the advent of Christianity by centuries, even if some of the documentary evidence we possess is late. We are already aware from the two different versions of Balder's story (Saxo's and Snorri's), that the position of the tritone and its "victim" is ambiguous. Christ himself is presented as a king, but a king who is executed, within the space of an octave (eight days) from his triumphal entry –an entrance he makes, n.b., on the back of an ass. In the Round Table literature, Arthur's table is

constructed, not without great significance, upon the advice of Merlin. By its name the Round Table is meant to signify the round world and the round canopy of the planets and the elements in the firmament, where are to be seen the stars and many other things. Wherefore one may say that in the Round Table the world is accurately symbolised.43

The Round Table contains one seat left empty originally in commemoration of Judas, but which becomes the Seige Perilous, reserved for the knight who will achieve the Holy Grail. This ambiguously privileged seat, the exception to the rule of the Round Table's egalitarianism, is "thirteen seats away from the king" in either direction.44

What I mean to underline here is that 729 may indicate either the tritone (from the root/octave) or the minor third, and thus be, on the tone circle, either at the antipodes from the root or at right angles to it. And this ambiguity coincides with the ambiguity of the atoning or sacrificed figure and the scapegoat/executioner figure as well. Is Hoder, the blind and manipulated god, to blame?

41 It is also the Hebrew gematria for "sun and moon," ShMSh v'YRCh, (without any definite article), as it appears in the MT's Psalm 148:3 and in Joel 2:10.

42 Note the feast of Ss Peter and Paul is June 29, the 180th day of the year-- midpoint of a 360-day year.

43 Queste of the Holy Grail, ch 6

44 The “extra chair” as a trope still occurs at every Passover meal when an extra place is laid at the table for the prophet Elijah. The youngest child is also sent to the door at a particular time to see whether Elijah will come in. (Similarly, in many synagogue Sabbath celebrations the congregation turns at a certain moment to greet the Shekinah who may be coming in through the door.) The “Empty Chair” has also become the name of a standard technique in Gestalt therapy, in which patients projects their symptoms onto the chair and address them, then switch places and take the role of the symptom to speak back. This is of course only a coincidence, but it demonstrates the way in which the trope of the empty seat can take on multiple resonances and associations, both positive and negative.

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Is Balder, as in Saxo's version? Is Judas, the piper? Is Peter, the “rock,” who denies his master? Or is it the "infernal machine," to use Cocteau's phrase, which dictates that the Son of Man "must be betrayed... but woe to him by whom the Son of Man is betrayed."?

Herodotus presents Croesus, in his discussion with Solon, as unaware of what is truly the best thing for man. As we have seen, Socrates claims that this best thing is to ask after the nature of virtue; that without this examination, life is not worth living. What bestows this worth is not decision about the nature of virtue, but inquiry. Solon's own conclusion is, at face value, more dour: the gods have shown that death is better for human beings than life, and it is only after the close of life that anyone may say of one that one was happy-- happiness cannot be knowingly enjoyed, and can only be averred in the past tense. Socrates both wants to be in harmony with himself, but in his confusion he is often, he says, "convicted" or "refuted" by his alter-ego. We know that Socrates referred to the sun in the Republic as the figure of the Good. But there was another calculation of the year which also required to be acknowledged, and which refused to come into synchronization with the year of the sun. The gap between these requires being adjusted for, not out of any theoretical exactitude but simply because the brute reality of our experience demands it. And yet there are not two years; there is only a single year, and multiple phenomena within it by which to take our bearings.

Compare the following passage from the Laws with the Themas Mundi:

All the rest of the country must be guarded in the following manner: we have marked out the whole country as nearly as possible into twelve equal portions: to each portion one tribe shall be assigned by lot, and it shall provide five men to act as land-stewards and phrourarchs ("watch-captains"); it shall be the duty of each of the Five to select twelve young men from his own tribe of an age neither under 25 nor over 30. To these groups of twelve the twelve portions of the country shall be assigned, one to each in rotation for a month at a time, so that all of them may gain experience and knowledge of all parts of the country. The period of office and of service for guards and officers shall be two years. From the portion in which they are stationed first by the lot they shall pass on month by month to the next district, under the leadership of the phrourarchs, rightways around the circle, towards the dawn. When the first year is completed, in order that as many as possible of the guards may not only become familiar with the country in one season of the year, but may also learn about what occurs in each several district at different seasons, their leaders shall lead them back again in the reverse direction, constantly changing their district, until they have completed their second year of service. [Laws, 760b-e]

This passage describes the circumnavigation of the city in a year, and then the retracing of the steps in the opposite direction, in a pattern that makes an exact analogue to the symmetry that we saw previously in the horoscope. Assuming that one began one's first year at Midsummer, in the sign of Gemini, one would then proceed around until one came to Cancer; then in the second year, one turn, boustrophedon, would move from Cancer around until one returned back to Gemini. The months will be matched: 1 to 12 and vice-versa, 2 to 11, 3 to 10, and so on until 6 to 7 and 7 to 6. We might well think of this reversal as an inversion of the previous year's journey: it turns it backwards and in a sense inside-out.

The 365-day year cannot be represented as a single square number, but it can be shown in a single square, for a 14x14 square (here I have shown one of o’s) and a 13x13 square (here made of x’s) can be superimposed, the unit corners of the latter occupying the unit centers of the former:

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This figure shows 365 nodes: (142)+(132) = 196+169 = 365.

The square can be further subdivided into a 3x3 grid of nine. There are five squares thus, in the corners and center:

with 41 elements each (25+16); and four squares thus, in the middle of the top, bottom and sides:

with 40 elements each (20+20).

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This representation of the year has in fact been deduced from the cave paintings of Lascaux by Franz Gnaedinger, an independent scholar, who pointed out that the first eight squares of such a year would come to 365-40 = 325, the same total as eleven lunar months measured in alternating totals of 30 and 29 days ((6x30)+(5x29)= 180+145 = 325). This allowed Gnaediger to reconstruct a hypothetical lunisolar calendar, based on earlier work by Marie E.P. Koenig and others45. Note that the fractions in both cases stand for approximations to the semitone: the division of the year into 12 parts as 12 semitones is obvious; the ratio of 8:9 not only references the octave, but is itself one well-attested ratio for the semitone. (It is also perhaps worth noting that this figure, rotated 45 degrees, would exactly resemble a tremendous “matrix” such as McClain reproduces, albeit a larger one than he has shown, and without any “shoulders.”)

These two figures, of 41 and 40 elements each, are essentially inversions of each other; they differ by only 1, but their arrangement is fundamentally different. The one is a superimposition of two squares (5x5 and 4x4), the other of two oblongs (5x4 and 4x5). The same is of course true of the larger figure: The Square of 365 is really two squares (14x14 and 13x13), and it can be inverted into a figure which superimposes two oblongs (14x13 and 13x14). This latter figure will again differ in its total elements by 1. Now if one travels back through the year in Plato's scenario in the Laws, the opposite circumnavigation of the city can be seen as an inversion of the first journey. If one takes these 364 days and adds them to the previous 365, one attains, again, 364+365=729; to which must be added a single day to make two years. Thus the number again appears at the end of the year, just as it seemed to do in connection with the Balder and Mistletoe myth; and even more striking, we have found it in a two-year cycle, just as Herodotus has described in Solon's words; a two-year cycle which Plato says is in place "in order that as many as possible of the guards may not only become familiar with the country in one season of the year, but may also learn about what occurs in each several district at different seasons," just as Solon said his two-year cycle was in place to let the seasons come around at the right time.

Socrates as / versus Silenus

In the dialogue the Hippias Major, Socrates and Hippias converse about the nature of the Beautiful. In order to keep Hippias willing to engage with him, Socrates has spoken part of the time in his own person, and part of the time as "a relative of mine," who he later says is "the son of Sophroniscus" (that is, Socrates himself), whose "impertinent questions" he reports to Hippias, and in whose person he continually violates decorum, bringing up exceptions to each ostensible definition Hippias offers.46

When Hippias finally takes the first step towards a real definition--rather than an example-- of the beautiful, he says he will name what no one ever will find undesirable. He then says that

for every man and everywhere it is most beautiful to be rich and healthy, and honored by

45 See Gnaedinger’s website, http://www.seshat.ch The calendar is at http://www.seshat.ch/home/lascaux.htm

46 Hippias' first suggestion-- that beauty is a beautiful maiden-- Socrates quickly disposes of. Next, Hippias suggests that the beautiful is simply gold, for whatever is beautiful can be quantified in its terms; but Socrates, speaking in his adopted persona, forces Hippias to abandon this suggestion again. In a comic exchange, "Socrates" and Socrates get Hippias to concede that a figwood ladle is more beautiful than a golden one, at least in the case when the flavoring and dishing of a pot of pea soup is concerned. Hippias is scandalized by reference to such mundane and trivial objects--with, moreover, clear connotational reference to low comedy (the word "pot," for instance, has some scatological resonance, and "figwood " may be a reference to the "shameful" acts in the Dionysian mysteries (they scandalized Clement of Alexandria as well) which concerned a figwood phallus --it was used by the god on himself on the grave of Prosymnus, just as Adrastus killed himself on Atys' grave).

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http://www.seshat.ch/home/lascaux.htm

http://www.seshat.ch/


the Greeks, to reach old age, and, after providing a beautiful funeral for his deceased parents, to be beautifully and splendidly buried by his own offspring.

What Hippias says, it will be noted, is remarkably close to the account that Solon gives to Croesus about Tellus the Athenian, who "had sons both beautiful and good; he lived to see children born to each of them, and these children all grew up;" he lived "in what our people look upon as comfort, his end was surpassingly glorious. In a battle ...he routed the foe, and died upon the field most gallantly. The Athenians gave him a public funeral on the spot where he fell, and paid him the highest honors." All the ingredients are here: long life, offspring, wealth, death and burial. Naturally, Socrates finds this definition, too, wanting. His rejoinder, again delivered in the voice of his alter-ego, disputes Hippias by comparing such a life as Hippias calls beautiful to that of Achilles or any number of heroes--who by common consent lived beautiful lives-- who were buried before their parents. As we have seen, Herodotus does have Solon mention explicitly just such a case, that of Cleobis and Bito, in response to Croesus' inquiry of who he would rank second in happiness. It is in that story that Solon declares "how much better a thing for man death is than life;" and it is telling that Socrates seems to refer to this evaluation near the very end of the dialogue. Again, Socrates imagines himself being addressed by his crass and disreputable persona, "that man who is continually refuting me; for he is a very near relative of mine and lives in the same house," he says, clearly speaking of himself. This alter-ego, a kind of anti-daimonion, accuses Socrates of incoherence, confronting him for his inability to answer such questions ("what is beautiful?") without self-contradiction. "And when you are in such a condition," "Socrates" asks Socrates, "do you think it is better for you to be alive than dead?"

As is well known, Alcibiades in the Symposium draws out a comparison between Socrates and Silenus. A number of reversals are at play in Alcibiades' speech, as commentators have long pointed out. Alcibiades speaks of having been "seduced" by Socrates but not physically-- in fact, he acknowledges that Socrates has rebuffed Alcibiades' own sexual advances. Alcibiades, known as a lover of beauty and ostentation, is a Midas-like figure, attempting to ply the wise Silenus with something intoxicating--his own beauty. But unlike Silenus, whose love for wine allowed him to fall into Midas' hands, Socrates remains uncaptured, though he does impart wisdom-- a wisdom which contrasts with the barbed wisdom of Silenus. Not only is Socrates the only character who remains sober and awake throughout the entirety of the Symposium (Alcibiades is already drunk when he storms in), but his philosophy is at cross-purposes with the clouding which drunkenness occasions.

For we know how precisely how much Socrates conceded to Silenic or Solonic pessimism. The kind of life he deemed worthwhile Socrates declares in the Apology (38a), in what is doubtless the most famous single phrase in all of the history of philosophy: but he does this directly upon the heels of proposing a counter-value to what Silenus told Midas. "Again I say that to talk every day about virtue and the other things about which you hear me talking and examining myself and others is the greatest good to man," he says, "and the unexamined life is not worth living." It is examination,— not the results of the examination, but examination itself— which can salvage the worthwhileness of life.

It is hard to doubt that Plato intends Socrates’ words (and that Socrates, if he indeed spoke them, also intended them) as a purposeful counter-proposal to Silenic melancholy. Indeed, the Symposium's contrast between Silenus and Socrates goes on at great length. In the Symposium, comparing Socrates' snub-nosed physiognomy with that of the mythical satyr, Alcibiades concedes that Socrates may appear unattractive, but his beauty is not apparent. Athenian piety featured small statues of Slienus which were hollow. On the outside they looked like the satyr-- an ugly old man-- but upon opening them, the viewer was confronted by cunningly-made scenes

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in gold or fine wood, and these containers were often also used for storing precious things--often, significantly, drugs. If you open the figure, "split it open in two," Alcibiades says, "it shows itself filled with with tiny images of the gods." It is not just that Socrates' appearance is deceptive. It is his being revealable as two that makes his beauty apparent.

Alcibiades goes on to compare Socrates also with Marsyas, whose music was so famous for being bewitching. "Are you not a flute-player, Socrates? That you are, and a far more wonderful performer that Marsyas. He indeed with instruments used to charm the souls of men by the power of his breath. But you produce the same effect with your voice only, and do not require the flute; that is the difference between you and him." This teasing description, with its innuendo and subtext, recapitulates both the relationship between the famously handsome Alcibiades and the ugly Socrates, and that between the beautiful god Apollo and the satyr. Then as now, "flute-playing" had connotations of fellatio, and Alcibiades in noting that Socrates "does not require the flute," is referring to his own inability to tempt Socrates; but in describing the effect of Socrates' voice, Alcibiades is also comparing Socrates to the singing god, rather than to Marsyas, as he has also reversed his own relation to Socrates (he says he wound up unsuccessfully pursuing him sexually rather than being pursued). This inversion is at work in the myth itself: in some versions, Apollo won the contest with Marsyas not simply by playing his cithara turned upside-down, but by accompanying his music with singing, which Marsyas was equally unable to do.

Alcibiades' description of the Sileni being "split open in two" cannot but remind us of Marsyas, crying out in Ovid of "myself torn from myself" (we do not know if Ovid was quoting something), as well as the Aristophanic myth told earlier in the Symposium, in which eros is accounted for by the story of twin beings who were split by Zeus. Moreover, Socrates in the Symposium also speaks in a different voice, just as he does in the Hippias Major; this time a female voice-- that of Diotima, the priestess and oracle, who, he says, taught him what he knows about love. In all of the dialogues, Socrates claims to know only two things: ignorance, and love. His ignorance is often assumed to be an "ironic" pose, adopted for the sake of prompting the conversation along, but in fact there is no reason to assume that Socrates is not perfectly sincere when he claims, as he does in the Apology, to "know that I don't know." This makes it all the more astonishing when Socrates claims expertise in the matter of love, as he does in the Phaedrus [257a] and Symposium [177d–e, 193e.] While it is true that Socrates expresses great conviction on a number of matters, he makes claims to know only in these two regards: ignorance, and love.

Socrates' perplexity is paradoxical: he knows that he does not know. This recursive ignorance is precisely the paradox of incommensurability: it is a particular quantity, specific but not specifiable. You can see how long the diagonal of the square is: but you cannot name it in the terms you have; or, if you name it, you must abandon the names you formerly had for the sides of the square. The only way one can name both is by approximation. And, one might add, since Socrates has expressly identified evil with ignorance, this is perhaps the only way to avoid the consequence that evil is inevitable.

Whether Plato intended the figure or not, the tone-circle is a striking emblem of the Socrates' double knowledge. At 6 o'clock the tritone in its incommensurable perplexity sits, refusing to align two closely approximate notes, the unsettling discord of being untuned with oneself. This is ignorance. But at 12 o'clock there is a moment of perfect harmony, an octave sounding in proportion of 2:1. Love. Socrates' teacher in love, Diotima, was not able to prevent the plague from besetting Athens; she could only postpone it. Love will not protect us from perplexity, and Aphrodite could not save Adonis. Indeed, the overtones of the octave give rise to the very other notes which occasion tonal incommensurability. To love is a great madness, Socrates says in the Phaedrus, but madness can be a gift and not a curse, the greatest of all gifts, if it comes from the

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gods. This ambiguous gift is the occasion of lament and panic in the greatest love-lyrics of the ancient Greek world-- the fragments of Sappho alone could furnish examples enough for a book-- and Plato's work may be coherently read largely as an effort to account for and salvage what is potentially transformative and divinizing in the experience of love, as well as cataloguing its sometimes disastrous misfiring (as for example in Alcibiades). Love, of course, is only one of many possible "acts of god" that may befall a person. Martha Nussbaum has shown how strong is the case for reading Plato--and indeed, Greek thought in general-- as wrestling with the question of what Bernard Williams called "moral luck:" the feeling of blame or praise given to people for things partly or wholly beyond their control, an issue that is powerfully at work, for instance, in the Oedipus cycle, and is seen as well in Croesus' words to Adrastus. "Man is wholly accident," Solon tells Croesus. The question that animates Plato is whether, or to what extent, one can agree with this assessment and still salvage the meaningfulness of human deliberation.47 How, and to what extent, can one provide safeguards from accidents of fate? The Wheel of Fortune levels many distinctions. Does it level all of them, or is there, as the Orphics and Pythagoreans believed (and the Buddhist dharma as well) a way off of the wheel? The answers to these questions are never given beforehand. In our own day there is a strong tendency to emphasize moral luck in certain circumstances. "I don't know what I would have done in her shoes," we say, thankful that we are not, like Antigone, faced with an apparent ethical dilemma such as Hegel thought he saw in the play (though it must be said, Antigone herself seems to see no such dilemma). The question is not an academic parlor game of casuistry. On the same grounds we are able to recuse ourselves from questions about torture, childrearing, interrogation of prisoners, and any number of other questions. Some degree of this recusal may be called for. But Plato feared that by itself it would lead to nihilism. To rest content with it, or to refuse to engage it, was to refuse to ask the questions which alone could reveal the meaning of human life.48 For Plato, love may be that meaning, but it evades formulation-- the experience of love always points beyond itself to the Beautiful and the Good. Yet in it alone can we be said to know anything but our own ignorance.

An anti-systematic system

One of the impediments to a reading of the ancients that discovers (or claims to discover) something new in them is the impression, often deserved, that what is being offered is a reason-- indeed the reason-- for reading them. One does not need to look far into Zechariah Sitchin49, for instance, to get the idea that he has scoured Sumerian and Babylonian myth (among other sources) with one idea only-- to find evidence of ancient cosmonauts; it is not so much that he disregards any evidence that might contradict him, as that he shows no interest in the ancients per se; everything is interpreted through the lens of his one idee fixe. Nothing could be further from my own rationale. I read Plato because of what he says on justice, politics, love, and above all for what he exemplifies of the spirit of dialogic inquiry. I read the myths as testaments of the human spirit in the face of vast aporias, and the Gospels as claims to tell of a decisive divine intervention into the order of things, both human and cosmic. In short, I seek to read them on their own terms. It is for this reason that I claim the understanding of the resonances between such different realms as music, mnemonics, ethics, and destiny and is significant.

It is all too easy to say of the notion of the wheel of fortune that it is a cliché (it was already a

47 For more on the question of the role of chance in mythic cosmology and its relation to the thematics of inversion, see The God Inside-Out: Shiva's Game of Dice.

48 Relativism cannot by itself coherently disperse the claims made by human judgment regarding excellence. There must be a Round Table, but there must also be a Seige Perilous.

49 See, e.g., Sitchin’s books in The Earth Chronicles (a single volume—any of them—will be more than enough).

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cliché by Tacitus' time, as we glean from his slighting words for Cicero's use of it in On Oratory). It is all too easy to shrug off the rise and fall of kings due to hubris as simply a constant of the ancient mind. Why was it such a pattern? Because the great cycles of nature were still palpably those upon which human survival relied and depended. Eliade noted (at the end of The Myth of the Eternal Return) that the resurgence of cyclic accounts of history, in thinkers like Spengler and Toynbee, was a matter fraught with significance, not because they might be right or wrong but because the model to which they appealed was itself being recycled. The fact that such motifs were "commonplace" in the ancient world did not prevent Ozymandius from erecting his colossi or Xerxes from flogging the sea; nor would they now, should it become possible to think again in their terms, prove sufficient to safeguard the biosphere from the indifference of consumers, or the wretched of the earth from the imperial pretensions of strong nations.

Arrogance will always find a way to misread the signs. But it is not beside the point to call for their rediscovery. It is not only that the writings of the ancients can only be understood in the language they used. Indeed, the writings of the ancients are already themselves copies and salvages from the great shipwreck of the catastrophic collapse of Bronze Age civilization. It was only in the days of Pisistratus (Solon's onetime pupil and protégé), that, according to Cicero and others, the texts of Homer were collected and established (a tradition that has given rise to sometimes acrimonious critical debate). The impact of writing and whatever other technical innovations whose habitual use was wearing away the "bicameral mind" (or however we describe the consciousness which preceded the rational critique) had been at its eroding work for many years. Herodotus and Plato are writing not at the beginning but towards the end of a great shift, and are aware of it. They are aware, that is, that something new has entered the mind and heart of humanity-- the awareness of history. This was incipient even with Homer. Twice, Homer says--in the persons of Alcinoos and Helen-- that the ruin of the generation of heroes has been brought about by the gods so that the future will have songs. (Sappho [fragment 30] says the same thing). This is not simply a matter of glory; it is the transmutation of suffering. But in Herodotus, who writes expressly to save things from the ruin of time, the epic transformation has changed into a different story.

Allen Upward:

The rise of history was once attributed to the invention of writing. We have now learned that the art of writing had flourished for many thousands of years before. What transformed historical literature was the invention of prose.50

Milan Kundera, writing of Cervantes, puts it thus:

Poor Alonso Quijada meant to elevate himself into the legendary figure of a knight-errant. Instead, for all of literary history, Cervantes succeeded in doing just the opposite: he cast a legendary figure down: into the world of prose. "Prose:" the word signifies not only a nonversified language; it also signifies the concrete, the everyday, corporeal nature of life.... Don Quixote tells Sancho that Homer and Virgil were describing characters not "as they were, but rather as they must be, to stand as examples of virtue to future generations." Now Don Quixote is himself far from an example to follow. Characters in novels do not need to be admired for their virtues; they need to be understood, and that is a completely different matter. Epic heroes conquer, or, if they are themselves conquered, they retain their grandeur to the last breath. Don Quixote is conquered. And with no grandeur whatever. For it is clear immediately: human life as such is defeat. All we can

50 The Divine Mystery, p151

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do in the face of that ineluctable defeat called life is to try to understand it. 51

Certainly the invention of prose did bring to a fruition something that had always been inherently possible in the technology of writing itself. Herodotus writes no longer in the age which can take the gods for granted, but he wants to keep them available. By his era, there was a sense in which the position on the Wheel of Fortune where the human self-image rode was already tipping beyond the apex, into the realm of reganvi, "I have reigned." The break-up of the archaic worldview took many centuries and had many stages. My contention here--haphazardly illustrated, as I am all too painfully aware-- is that certain figures, Solon, Herodotus, and Plato among them, understood intuitively the shift that was underway, and undertook to salvage in as many ways as they could what was worth, and capable of, being salvaged from the way of experiencing the world that was all but vanishing from the habits of humankind. Taking all due responsibility for the defects of my presentation here, I believe that to some extent this mode of experience was asystematic and resists orderly depiction. Of their own research into the archaic worldview, De Santillana and Von Dechend observed:

There is no system [of archaic knowledge] that can be presented in modern analytical terms. There is no key, and there are no principles from which a presentation can be deduced. The structure comes from a time when there was no such thing as a system in our sense, and it would be unfair to search for one. There could hardly have been one among people who committed all their ideas to memory. 52

Earlier in the book, De Santillana further characterized in positive terms what one would find instead of system. "They thought rather in terms of what we might call a fugue, in which all the notes cannot be constrained into a single melodic scale, in which one is plunged directly into the midst of things." It would be hard to find a better description of Herodotus, late arrival though he is (and knew himself to be); nor of Plato, despite the 20th century's toiling to render him a "metaphysician."

The point is not that the tone circle, the calendar, the wheel of fortune, the zodiac, were all one, as if the ancients conceived of them as correspondent point-for-point. But the figure of the circle attracted all of these phenomena, and others, for the obvious reason that they are all cyclic. Seeking a correlation beyond a certain limit of precision would be foolish. Even within a single field-- the calendar, or geometry,or music-- it was clear that there was no perfect correspondence between phenomenon and model. An irrational resistance to measure arose in each field separately. But this did not mean that the order perceived in the phenomena in question was unreal. Rather, the gaps in this order all were conceived as analogous. Placing all the models on a circle, with the respective gaps or "commas" all at 6 o'clock, would not thereby cause all the disparities to align. But it became possible to see the disanalogies as "meta-commas," as it were, of the same species as the irrationality of the square root of 2, or the extra-calendrical "remainder."In this way, the differences between scale and calendar and zodiac could confirm rather than confute the correlation. It was thus not a question of discovering objective correspondences that might be refuted by counter-examples or confronted with disturbing unanswerable questions. It was rather a matter of seeing what could be done with the phenomena. The places where the correlations did not "work" were not counter-evidence to a scientific hypothesis, any more than the fact that marble cannot be molded like clay is a refutation of the

51 The Curtain, as Essay in Seven Parts p10

52 Hamlet's Mill p 56. Edmund Leach, who had apparently skipped this chapter, nonetheless scoffed in his review for the New York Times, "[The] authors' insistence that between about 4000 B.C. and 100 A.D. a single archaic system prevailed throughout most of the civilized and proto-civilized world is pure fantasy."

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intent of a sculptor. One finds what can be done, and what cannot, with marble, and with clay; with words; with paint; with hollow reeds and taut strings. The "resistance of materials" is akin to what equivalences do and do not obtain between the different phenomena.

We will look in vain if we seek in the Ancients for a single system in which there were no contradictions; if we try to find a grand, over-arching correlation between octave and sky, ethics and physics, the details of the cosmos and the ends of destiny. This is not because there were no correlations, but because there were too many. The very fact of the impossibility of system became for them the occasion for meta-system. Only when the question of what were "objective" correlations became pressing, did this meta-system, this anti-systematic system, begin to break down. And when the meta-system broke down, an enormous salvage effort was brought underway.

There is an irreducible element in the cosmos that will not be factored out by any human ingenuity; not even by human stories of divine ingenuity. This brute irrationality afflicts every ideal scheme, every would-be smoothly-functioning plan, every design for painless or easy achievement of any end. For there is always some other, competing end; to act is always to generate a reaction. No choice is innocent, since it excludes. This is the aitia of all things, the cause or responsibility. This search is precisely what Socrates says in the Phaedo he desired to know, and which has always motivated his search.

Conclusion

Let us list our themes—themes I am painfully aware of not having organized, though I must plead that the disarray is to some degree not of my making but is inherent in the tangle which the tradition is and probably always was. The cycle of the Wheel of Fortune, the Zodiac, the Tone Circle, are all analogous to one another. Each features a comma or irreducible flaw. The location of this flaw is at one of the cardinal points of the solar year, marked by the four “living creatures” Ezekial saw, and which remain connected with the Wheel of Fortune as late as the tarot (as, indeed, does the icon of Midas53). Typically though not always, the Winter Solstice is the site of the extra portion of the year, and by analogy, with either the Pythagorean comma or with the tritone or both, as well as with the nadir of the wheel of fortune. Here we find a strong suggestive link with the mistletoe, the weapon which killed Balder, wielded (in Snorri's version) by blind and unwitting Hoder. Likewise in Herodotus' account of Croesus learning the bitter truth about the wheel of fortune, his son Atys [who is clearly derived from Attis] is killed by the unwitting Adrastus. Atys is named as the father of Pythius whose story repeats the tragedy of Croesus, and who is linked explicitly to Marsyas. Marsyas' fate comes from a musical myth implicating Midas, source of Croesus' wealth, and the famous interviewer of Silenus, who tells him that the best thing for human beings is not to be born. Socrates, continually compared with Silenus and with Marsyas, makes the thematic of his whole life the question of whether it is good to be born, and Plato who tells his story repeats endlessly parable after parable in which the musical and calendrical subtext is clear. The resonance with Silenus and his satyrs extends even into the north

53 Here is as good a place as any to mention the afterlife of the figure of Midas and his asinine experience. Besides Apulieus, whose Golden Ass is rife with clues about the content of the Mysteries, many other writers made use of the figure of the ass and the lyre. Before Socrates, Aesop had already given us a myth concerning the ass, whose hooves were useless for playing the lyre he found. And yet later generations would see the production of the story of “The Donkey Prince” or “Donkey Musician,” a beast (enchanted, like Apulieus’ hero) who undertakes to learn the lyre and becomes very proficient (he stands behind multiple later fairy and folktales including of course “The Bremen Town Musicians.”) Finally there is the Medieval yarn of Fauvel, the dun-colored donkey. Not only does Fauvel become a great ruler in the world, but he is lifted to his high position precisely by the medieval allegorical figure Dame Fortune, who (in a move that would have delighted Plato) he eventually, and unsuccessfully, sets out to marry.

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in the permutation of the Balder-Hoder myth where the satyr Mimingus guards the deadly weapon (identifiable as “mistletoe,” the archetypal exception). The resonances between these mythical figures and the Biblical Messiah I leave mostly unexplored, but the analogies are clear, and certain close structural parallels in language where Christ refers to certain extreme cases of the lost sinner54—often assumed to be Judas but never in fact directly named in context—saying it “would be better” for such to either not be born, or to be drowned by the weight of a millstone, despite the necessity and inevitability of their sin, make it hard to believe there is no connection at all.

This is a good deal of material, and if I have left it somewhat jumbled, I almost feel I cannot be blamed, though doubtless I could have sorted and arranged better. What does this heap show? What is it purported to show?

I have argued very little for any specific interpretation. My suggestions for instance about any particular isomorphism between the world map, the year, the scale, the heavens; between a text of Plato and one of Herodotus and one of Snorri—these may each and all be challenged. If I have offered too few “predictions,” this paper may be harder to falsify, but only, some might say, by taking a great many pages to say all too little. This may be a fault, but my aim has been not to show my own ingenuity at proposing solutions to puzzles or indeed at inventing puzzles, but rather to provide reason for thinking that the texts of the ancients—myth, history, cosmology, philosophy—reflect a coherent, unified worldview, but not a system, at least not in the modern sense. To be sure, per hypothesis, by the time Herodotus and Plato wrote, this worldview was in decay. Our evidence does not allow for a “reconstruction” of this asystematic system, but the numerous analogies we can adduce (of varying plausibility, but plentiful enough), show what it was like: a host of analogies and parallels, of connections, of participation.

It cannot be repeated often enough: nothing written here "explains" the stories of mythology, history, scripture, or philosophy (and certainly does not show that a given story has no root in actual events). Plato did not "hide all that musicology" in his dialogues, and Herodotus did not sneak in unworkable calendars in order to prove something about the calendar. They took for granted that the calendar, or the musical scale, were pertinent to questions about the design of the best city or the crossroads of Fate and ambition. These categories flowed into one another for them. To be sure, the very nature of the shift of consciousness I am describing was that this relevance was becoming critiqued. It would not be long before Pliny-- or indeed Aristotle-- could smile at Pythagoras' cosmology. Plato knew that the correspondences between music, geometry, modes of governance, and so on were not "really there". But there was something worth keeping in the way of talking about them that was passing which he wanted to keep-- a sense of the mythical, of participation, the experience of being involved with and connected to what one perceives. The calculable is the realm which critiques; but there is in experience what resists calculation, and this, Plato saw (though I do not think he invented the comparison), was analagous to the inherent necessity of approximation in temperament, or the inexact match of the calendar's cycles.

54 This theme needs to be read alongside that of the single lost sheep of a hundred, for whose recovery the shepherd rejoices, more than for the 99 who were not lost—a theme found in the same chapter of Matthew (Matt. 18; compare Luke 15); moreover, the Synoptic warnings concerning “offence”, e.g. Matt. 18:8 “Wherefore if thy hand or thy foot offend [] thee, cut them off, and cast [them] from thee: it is better for thee to enter into life halt or maimed, rather than having two hands or two feet to be cast into everlasting fire,” are a curious counterpoint to what one might call the “wisdom of Caiaphas,” who in the fourth Gospel (on the heels of the raising of Lazarus), advises: “consider that it is expedient for us, that one man should die for the people, and that the whole nation perish not.” The writer adds, “this spake he not of himself: but being high priest that year, he prophesied that Jesus should die for that nation; And not for that nation only, but that also he should gather together in one the children of God that were scattered abroad.” (John 11:49-52; see too John 18:14).

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This contrast and interplay between the calculable and the incalculable persists in chronological and liturgical time to this day. At the beginning of the Christian Year on the first Sunday of Advent, the Gospel is read:

Of that day and hour knoweth no man, no, not the angels of heaven, but my Father only. But as the days of Noah were, so shall also the coming of the Son of man be. For as in the days that were before the flood they were eating and drinking, marrying and giving in marriage, until the day that Noah entered into the ark, and knew not until the flood came, and took them all away; so shall also the coming of the Son of man be. Then shall two be in the field; the one shall be taken, and the other left. Two women shall be grinding at the mill; the one shall be taken, and the other left. Watch therefore: for ye know not what hour your Lord doth come. But know this, that if the master of the house had known in what watch the thief would come, he would have watched, and would not have suffered his house to be broken up. Therefore be ye also ready: for in such an hour as ye think not the Son of man cometh. 55

It is not a coincidence that these words are read (in one version or another as they are variously presented in the different Gospels) at a very precisely calculated time once every 365 days.56 The liturgical year, an exactly-calibrated system of interlocking ritual, text and music, begins with a resounding warning of the impossibility of exactitude--and not just exactitude, but of anticipation. The lectionary's recitation of the passage is a systematic reminder of the inevitable foundering of all system. Meditating upon this often, one might see how the system points beyond itself in the very moment of its breaking-down. It is not for us to make the seasons come round at the right time. The seasons will come round in any case. We must have words for when this is; but it is well for us if we remember that the words will not call the seasons to come. The question is, who is—and who is believed to be— master; or perhaps, whether mastery is the right word at all for what is in question.

Un petit d'un petit s'attend, n'avale Homme petit d'homme petit -- Ah! degrés de folles!Un dol de qui ne sort cesse, ental deux qui ne se mèneQu'importe tome petit Tout Gai de Reguennes

Appendix

In the Laws, Plato gives 5040 (=7!) as the ideal number of citizens for a state. Herodotus/Solon's number 1050 (the total number of intercalated days he includes in his 70 "years") has a curious relation w/ this sum if we also reckon w/ the "great year" as 26,000. This number would seem to be extraneous to our calculations, and a consideration of it superimposes a different set of ratios; but the interplay of these two sets proves interesting.

Recall that Solon's totals are

55 Matt. 24:36-44. Compare Luke 17:26-37

56 The whole liturgical year is a vast semi-stable system, intended to provoke awareness of its own limits. It is possible to read this passage as reiterating both the halving of the octave (one taken, and one left) and to the tonal and calendrical significance of the Flood story, which is rife with "overtones" of its own as an allegory of tuning both the year and the scale See Hamlet's Mill and The Myth of Invariance. I hope it is obvious why I do not regard these multiple significances as a drawback: no matter what the story "originally meant" (and I take it for granted that probably it also referred to actual memories of some kind of catastrophic inundation), it drew to itself not simply multiple associations, but multiple meanings, which came to be cultivated intentionally.

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25,200 (the days in his un-adjusted 70 years of 360 days each)25,550 (which Solon does not mention but which wd be 70 years of 365 days each)26,250 (Solon's adjusted figure of 70 years, 35 of which have an extra 30 days for 390 days each)

25,200*---------------------*(25,550)*-------------------**-------------------*26,250

26,250 - 25,200 = 1050

26,250 - 25,550 = 700 (of course)

26,250 - 26,000 = 25026,000 - 25,500 = 450

5040/1050 = 1.8 or 9/5700/450 = 1.5555... or 1 + 5/9700/250 = 2.8 or 1 + 9/5

note the reciprocals, and note the recurrence of the figure “1 + …” In base ten, of course, this can also mean “10 + …” or “100 + …”, and so on. Thus it is interesting to note that the name Solon in Greek is and adds in isopsephia to 5140 (=5040+100); while the “Great Year” we are using here, 26,000, is of course 10,000 short of the natural Sumerian sexagesimal counter 36,000.

Note too, that the ratio 35:70 is not just the octave which defines the tritone at 35:49::50:70. It is also the 'half-week' which figures in Daniel and Revelation-- "time, times and half a time;" 3.5 x 360 = 1260 days, the time the woman stays in the wilderness and that the two witnesses lie dead. This assumes a symbolic year of 360 days, of course. But the proportion is again found when the 'Great Year' is put in ratio with the 1050 extra days Solon allows; for

1050/250 = 4.2and 3.5 years = 42 months (1 month = 30 days)

Note: 1.8 + 4.2 = 6 2.8 + 4.2 = 7

We are now in dangerous territory, for we are considering numbers from more than one context and there is no a priori reason to assume they were meant to be related. It is only the consideration of Plato's 5040 that gives us occasion to find 5040/1050 = 1.8It is only the consideration of the Great Year that gives us occasion to consider 1050/250 = 4.2

These are, respectively, the ratio of the total number of Solon's intercalated days to Plato's 5040, andthe ratio of Solon's intercalated days to the difference between the Great Year and Solon's total allotted mortal lifespan (26,250 - 26,000)--the smallest unit within these 1050 days (5/21 of them).

The figure 2.8, on the other hand, does not arise w/ respect to Plato's 5040, but only from the Great Year and Solon's totals. (It is the ratio the 700 days, by which Solon overshoots, to the 250 difference of 26,250-26,000).

The Greeks would not have calculated with these decimal figures, of course, but with either ratios

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or whole numbers. Thus the figure 2.5 could not be expressed, but 25 could, and 25 is the smallest figure that could be expressed as a 2 and 5. Twenty-five will not go evenly into 70; but it will go evenly into 700; and it does so 28 times. And here is our lunar 28, a number which recurs in the total number of logoi in Herodotus' histories. These are allocated among the 9 books, in a ring-composition (or “menorah”) pattern: there are three logoi or discourses to each book except to the central, fifth book, which has four logoi:3 3 3 3 4 3 3 3 3If it were found that some structural or thematic pattern ran in fives through each of the 28 logoi, we would have strong corroborating evidence for Solon's 70 and 700 as an intentional pointer towards something in Herodotus.57 (I don’t insist upon it, but we might also see in this equation 700=25x28, a sleight-of-math reference to the diesis 125:128).

These numbers have a resonance with McClain’s musical matrix numbers as well. 26,250, as mentioned, comes to 375 days per year (the average of 360 and 390). It is perhaps coincidental that 375 is the gematria for the Hebrew name Solomon (SLMH=300+30+40+5), but one may be forgiven for wondering if it is entirely coincidental, given the clear derivation of the story of Solomon’s ring and Asmodeus from wither Herodotus’ story of Polycrates, or else some earlier predecessor of both. The wise Solomon is the mirror-image of the foolish Midas, and the attribution of the dour book of Ecclesiastes to Solomon bears comparison to the tradition that Midas, following his philosophical deflation in his encounter with Silenus, retreated from public and political life (as did Solon, of course— it is during his ten-year travels that he encounters both Amasis and Croesus). The nadir of Ecclesiastes’ worldview, it seems to me, lies in a verdict precisely isomorphic with Silenus’: “Wherefore I praised the dead which are already dead more than the living which are yet alive. Yea, better is he than both they, which hath not yet been, who hath not seen the evil work that is done under the sun.” (Ecclesistes 4:2,3). Best for man is not to be born; next-best, to die soon.

As McClain points out, 375, being the second member of the fifth row of the matrix of multiples of 3 and 5, can function as the central tone in a set of nine tones: Bb F C G D A E B F#. If it should transpire that there is some reason for correlating these tones with the nine books of Herodotus, this would be a strong piece of evidence.

The 28 discourses thus arranged show two sets of four 3’s around a single 4. In one way this emphasizes 4-ness; in another, the combination of 3 and 4, that is, either 3+4=7 or 3x4=12. (I note all the 3’s sum to 24, and recall the “24 elders and the four living creatures” that Revelation inherits from Ezekiel). Multiplication makes this as 3 x 3 x 3 x 3 x 4 x 3 x 3 x 3 x 3or(34) x 4 x (34) = 81 x 4 x 81 = (812) x 4 = 6561 x 4 = 26,244

The difference here between this and Solon’s total assigned life-span of 26,250 days is a mere 6; the first perfect number, and of course the number of the circle. I am aware that no conclusion can be drawn from such “near-hits,” though I am sorely tempted to speculate upon it. But there is a lesson to be drawn even from this powerful inclination, and the lesson is more than a bathetic reminder that the human mind imposes order on randomness wherever it can. The ancients too knew that human beings have the capacity for wishful thinking, projection and self-deception. But they knew too that this strong inclination to find meaning meant that meaning was something that could be found; and yet, too, that human minds had a role in causing it to be there. Finally,

57 The arrangement of Herodotus’ work into nine books is thought to be the work of 3rd-century Alexandrian librarians, but the rationale sketched here offers the possibility of an earlier date. See Silvana Cagnazzi, 'Tavola dei 28 logoi di Erodoto,' in Hermes 103 (1975), pp 385-423; or http://www.livius.org/he-hg/herodotus/logoi.html

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http://www.livius.org/he-hg/herodotus/logoi.html


they knew that the most pregnant occasions for this meaning were not in the iron inevitability of logic but in the interstices where logic could provide a framework for poetry. The perfect coincidence of the octave or the ideal sum where arithmetic simply dictates an outcome is a kind of beauty but also a kind of monotony. It is in the gap of the comma, despite its accompanying discords, that the power of the mind find room to grapple, maneuver, and to leap across.

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plato & herodotus 12

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