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    The McMaster Department of Philosophy has now put together the following notice commemorating Barry: Barry Allen: A Philosophical Life Barry…

The Ultimate “Esoteric” Reading of Plato

Brian Leiter

I imagine even the Straussians will be astonished by this:

In an extraordinary discovery, a British academic claims to have uncovered a series of secret messages hidden in some of the most influential and celebrating writings of the Ancient World.

The codes suggest that Plato was a secret follower of the philosopher Pythagoras and shared his belief that the secrets to the universe lie in numbers and maths….

[T]he latest study comes from a respected Classical scholar at Manchester University, and has been accepted for publication by a leading academic journal….

According to Dr Jay Kennedy one of Plato's most important beliefs was hidden in his writing….

'In antiquity, many of his followers said the books contained hidden layers of meaning and secret codes, but this was rejected by modern scholars.

'It is a long and exciting story, but basically I cracked the code. I have shown rigorously that the books do contain codes and symbols and that unravelling them reveals the hidden philosophy of Plato….'

The key to unravelling the Plato Code lies in a Greek musical scale of 12 notes popular among followers of the earlier philosopher Pythagoras.

Dr Kennedy discovered that key phrases, words and themes crop up in regular intervals throughout Plato's writings and that they match the spacing of these 12 notes in the musical scale.

His most famous work,  the Republic, for instance, is made up of 12,000 Homeric lines of text. Dr Kennedy found that every 1,000 lines, Plato returns to the theme of music.

In another dialogue, the Symposium, words describing harmony and unity crop up at the same regularly spaced intervals.

In the Greek musical scale some of the notes are harmonic, or pleasing to the ear. Others are dissonant or grating, and need to be followed by another note to relieve the musical tension they create.

At the location of harmonic notes in his writings, Plato wrote lines associated with love or laughter. But the dissonant notes were marked with screeching sounds or war or death.

Dr Kennedy, whose findings are published in the classics journal Apeiron, believes the pattern of symbols would have been obvious to the ancient followers of Pythagoras.

'As we read his books, our emotions follow the ups and downs of a musical scale. Plato plays his readers like musical instruments,' he said.

A century earlier, Pythagoras had declared that the planets and stars made an inaudible music, or 'harmony of the spheres' and that the secrets of the universe lay in maths.

The presence and nature of the hidden codes suggest that Plato may have signed up to the same belief – and that 2,000 years before the birth of modern science, he was leaving a message in his writing that maths and logical patterns ruled the universe, not the gods.

Dr Kennedy argues that Plato did not use the code for pleasure, but for his own safety. Plato's own teacher had been executed for heresy….

Dr Kennedy added. 'This is the beginning of something big. It will take a generation to work out the implications. All 2,000 pages contain undetected symbols.'

(Thanks to Jack Beaudoin for the pointer.)

Any comments from scholars on this 'discovery'?

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37 responses to “The Ultimate “Esoteric” Reading of Plato”

  1. TimC

    There are links to Dr. Kennedy's Apeiron paper and some other drafts here:

    http://personalpages.manchester.ac.uk/staff/jay.kennedy/#Links_to_Papers_and_Files.

    Reply
  2. marcus

    Kennedy's elaborate reading is rather esoteric and provocative.

    He wants to make two claims. First, he wants to say that the hidden structure in the dialogues is evidence for Plato's Pythagoreanism. Second, he thinks that analyzing the text in this way will show Plato's positive program brewing beneath apparently aporetic texts. The first is a historical point. The second promises philosophical pay-off.

    Now, I am not in the position to state whether the methods Kennedy uses to establish the formal/mathematical/pythagorean under current in Plato's text is correct. But, let's assume that it works. Then, it seems to be evidence for Plato's pythagoreanism. Yet, I don't see how the evidence offered in his essay actually reveals anything about Plato's positive philosophical doctrines. Kennedy, in his essay, does not give us any indication of what the positive program might be. He admits this much. I guess we have to wait for the philosophical pay-off.

    It has long been the dream of scholars to find Plato's hidden doctrine, the doctrine that was so influential on the Platonist tradition. Kennedy's paper might give us evidence that this doctrine was pythagorean, but this has always been the assumed position if we take the Platonist tradition to be reliable evidence. I just don't see how this approach will but any meat on the content of this doctrine.

    Next, the approach is rather elaborate. I worry that such esoteric adventures are unreliable grounds for drawing any substantive conclusions about Plato's positive, hidden philosophy.

    Reply
  3. Mike Otsuka

    What I find most astonishing is that this highbrow esoterica was reported in the Daily Mail, alongside their more usual fare of items such as "Tat's just tatoo much, Kylie! Miss Minogue tries out and edgier persona. Wizened face, daggy hair and podgy tum age her dramatically."

    Reply
  4. A Facebook User

    Hmmm. Is Kennedy correct that modern scholars tend to downplay the extent of Pythagorean influence on Plato? If so, that would surprise me, as my impression (mostly coming from modern scholars I've talked to and modern commentators I've read, but I admit it was surely not a particularly random sample) was quite different.

    I suppose this supports the uniformitarians, as apparently Kennedy finds these mathematical structures in the "early" dialogues as well, suggesting that Plato's interest in mathematics wasn't something that he developed later in his writing career, but again, the uniformitarian reading is hardly marginal, so again not something to shake the foundations of Plato scholarship.

    Perhaps Kennedy will find that the code reveals some shocking new doctrines, but so far it sounds like all he's discovered is that Plato wrote a novel form of mathematically influenced poetry. Though that in itself could have very interesting implications; it suggests that passages where he talks about poetry should be scrutinized more closely to see what connection they have to his own style.

    Reply
  5. Mohan Matthen

    This is an extraordinary hypothesis — and if it got by the notoriously sceptical editor of Apeiron, it must be well-argued. Of course, Pythogoras's influence on Plato was well known — Kennedy writes: "Plato’s philosophy has been associated with or even identified with Pythagoreanism by Aristotle". But K's thesis goes much further than this.

    He says that the dialogues are organized around D*n/12 sized chunks (where D is the size of the whole), and claims that this architecture has doctrinal significance that derives from the twelve-note Pythagorean scale. For example: "The Republic’s discussion of philosopher-kings and the form of the ideal just man occurs at the centre of the dialogue. Comparisons between the dialogues shows that passages describing the divine wisdom and justice of the ideal philosopher often recur near the centre."

    And: "Side-by-side comparisons of passages at the same relative locations shows that concepts with negative valuations within the dialogues, like disease, dishonesty, Hades, the body, difference, and negation, tend to cluster in definite ranges and at a definite locations, such as around and between the points ten and eleven twelfths of the way through the dialogues."

    I don't feel qualified to judge these statements or their significance. But it seems to me as if the surprise value is pretty high, and that Kennedy's article deserves to be thoroughly probed and tested in the scholarly literature. An exciting prospect!

    Reply
  6. Justin Vlasits

    It should be noted that Kennedy doesn't really mean that Plato wrote poetry (which at the time meant metered verse), although the selections posted here might give that impression. In the more complete version of the paper, he makes it clear that he is only looking at lines of 35 letters, which had become standard in the production of written texts because that is the average length of a line of Homeric hexameter. Plato's writing doesn't scan or anything like that and the "poetry" would have to be considered on a metaphorical level.

    Reply
  7. Ben

    It sounds a bit like John Bigelow's view about what he calls "The Platonic Table." See http://arts.monash.edu.au/philosophy/staff/jbigelow.php.

    Reply
  8. Mohan Matthen

    I don't mean to be live-blogging my reading (or rather scanning) this article. But it is an amazing piece of fun, or perhaps a fun piece of amazing. Read this:

    "Stichometric measurements bring a new datum to [the debate over whether the Divided Line in the Republic is meant to be divided at the Golden Mean]. The numerical value of the Golden Mean is, to three places, 0.618, and thus a unit length divided at the Golden Mean will be divided at 61.8 percent. Surprisingly, the Republic’s discussion of the Divided Line begins at 61.7 percent of the way through the text. By itself, this could be a coincidence, but the other dialogues typically contain allusions to the Golden Mean near 61.8p. . . References to the mean or middle occur in other dialogues near 61.8p" (and here he cites Symposium 203e5 and 204b1 and 5, Phlb 45e1, and Phdr 259a2, 6 and d8).

    It's possible that the kinds of allusions to the mean at these places are so generic that they can be found anywhere at all. But not at first glance.

    Reply
  9. Philippe Lemoine

    I have two questions about this story, maybe someone can answer them. First, has Dr. Kennedy bothered to show that one can't find patterns analogous to those he found in Plato's books in any text whatsoever, as soon as it's long enough? Indeed, if he has not, then he didn't prove that there was anything intentional in the patterns he found in Plato's dialogues, which is essential if one is to learn something about Plato's esoteric doctrines from such patterns. Second, even if Dr. Kennedy has indeed provided some evidence that these patterns are intentional, I'm not sure I understand how this discovery could be of any help in learning something about Plato's hidden doctrine. This last question has also been asked by Marcus and Aaron Boyden, at least I think so, therefore I take it that I'm not the only one puzzled about this. Finally, I would like to note that, while this is certainly unfortunate in other respects, there is at least one positive thing to say in favor of having illiterate politicians, it is that one doesn't have to bother about hiding one's doctrine, they won't read one's books anyway…

    Reply
  10. Ralph Wedgwood

    1. We know almost nothing about the 5th- or early 4th-century Pythagoreans. (I seem to recall that Jonathan Barnes once spoke of the "black pit" of early Pythagorean studies.) We also know almost nothing about Plato's esoteric doctrines (although we do know that he did have some doctrines that he did not include in his dialogues). This is why many reputable scholars have concluded that speculation about these questions is fruitless, while it is already a quite sufficiently challenging and rewarding task to try to understand the overt meaning of Plato's dialogues.

    2. Admittedly, we know from the _Republic_ that Plato sometimes liked to play around with numerology (e.g. in his "proof" that the philosopher-king is 729 times happier than the tyrant); and we also know that many of Plato's works are extremely carefully-wrought and elaborate texts.

    3. Now, I haven't read Kennedy's research; but on reading the summary by Julian Baggini in the _Guardian_, I couldn't help remembering the notorious "Bible code" claims that appeared in the journal _Statistical Science_ in the 1990s. The "Bible code" hypothesis was most convincingly refuted when other mathematicians proved that it was equally possible to find similar hidden messages in a Hebrew translation of Tolstoy's _War and Peace_! It would be good to have it shown that Kennedy's results cannot be replicated for contemporary authors like Xenophon or Demosthenes (where the hypothesis of a secret Pythagorean structure would be vastly less plausible, to say the least…).

    4. Finally, it is surely intrinsically implausible, it seems to me, that an author like Plato, who was constantly exploring slightly different approaches to the philosophical problems that concerned him, would use the same kind of mathematical structure in all his works, from _The Apology_ to _The Laws_. By the time we get to _The Laws_, his prose style is markedly different, he no longer uses Socrates as his principal character, and he is attempting something that he never tried to do before, to give a system of actual legislation for a community; but according to Kennedy, he still has the same obsession with multiples of 12 that he had when he wrote _The Apology_ perhaps 40 or even 50 years earlier. … Is this really an intrinsically plausible hypothesis?

    Reply
  11. anon

    This reminded me of the Bible Code nonsense from years ago. My guess is that Kennedy's "discovery" will turn out to be a statistical artifact. (For e.g., selecting various values for D will allow for a good deal of wiggle-room when looking for possible codes in the Dialogues.) Would this get by the editors of Statistical Science?

    Reply
  12. D.M. Hutchinson

    Not having read the article in Apeiron, I cannot assess it directly. However, if this turns out to be correct I would not be as "astonished" as others. Some important points:

    First, we DO know a lot more about pythagoreanism with the publication of Kahn's work on the pythagoreans and Huffman's works on Philolaus and Archytas.

    Second, Plato draws on numerous pythagorean themes in his works such as the Phaedo and the Timaeus.

    Third, even though the unwritten doctrines aren't fashionable in modern scholarship they were enormously influential on Plato's successors and the development of Platonism.

    Fourth, neopythagorean philosophers in late antiquity held that Plato was deeply influenced by Pythagoras and many held that Plato's philosophy was in some sense derived from Pythagorean philosophy.

    So why not give Kennedy a chance instead of framing his article that something even straussians would be astonished by? I am neither a straussian nor a follower of the Tubingen school of interpretation, but I have read lots of Plato and lots of later Platonists and I take seriously what the Neopythagoreans had to say about Plato.

    If it turns out to be wrong, then so be it. But as a specialist in Neoplatonism I would hardly dismiss it as implausible without assessing it directly.

    Reply
  13. Alan Gilbert

    Kennedy has done some apparently (have read the article once quickly) very promising work on the mathematical structure of the dialogues and Greek music. These are obviously deep and important problems suggested by the surface of the dialogues, notably the Republic, and his work on it, while a bit formal, is rather entrancing. Several thoughts: first, Plato focused on mathematics (it was this that the tyrant Dionysius the second would have none of, in the Seventh Letter). As Ralph Wedgwood suggests above, he says in the Republic that a philosopher is 729 times as happy as a tyrant. I have fooled around with this number which is 3 to the power of 4 or 9 to the power of 3, and thought it must be connected to the Pythagoreans for there is no argument that explains the comment in the Republic. One obvious problem for Kennedy's attempt to divide texts into twelfths: 729 is not a power of 12 or divisible into 12ths, but the music of someone with eudaimonia would probably be some divine harmony (see his comments about justice and a kind of divinity in the center of dialogues). This suggests only, however, some greater diversity in Pythagoreanism and perhaps Plato's forms of organization than Kennedy envisions. Second, the thought that everything has a mathematical structure is visible in the Timaeus on the surface of the argument. Kennedy can be taken to have shown something interesting about this in Plato and his students. The idea that the universe has a mathematical structure is a powerful one and serves to explicate some of Plato's "Socrates's" none too clear references to the ideas and the pretty mystical idea of the good (in the Seventh Letter and the Republic which mirror each other in this regard). Third, Plato's Phaedrus speaks of the difference between writings that are like statues (if you ask them a question, they have "no father" to defend them, and anyone may misinterpret them, and dialogues which to a certain kind of reader yield a great happiness and one which will link them into eternity, Fourth, there are many kinds of hidden arguments and levels of argument in Plato. Plato is a magically complex writer. One which I have worked on, for instance, is the notion that a tyrant of a certain kind becomes a philosopher-king. That argument I have discovered was reported by Aristotle in book 5 of the Politics (see Do Philosophers counsel tyrants? Constellations, March, 2009 or at my blog: democratic-individuality.blogspot.com

    Reply
  14. Tad Brennan

    Dr. Kennedy's paper looks to be great fun and I'm glad that he wrote it up, and glad the Apeiron crew decided to publish it.

    That said, a few quick glances suggest to me that there may be problems on the interpretive side, as well as any problems that turn up on the statistical side.

    E.g., in support of the claim that "the other dialogues [sc. in addition to the Republic] typically contain allusions to the Golden mean near 61.8p", Kennedy offers us four examples: Parmenides, Symposium, Philebus, and Phaedrus.

    First, he gives Euclid's definition of the Golden Mean as the section which divides a line into two parts such that whole line is to the greater part as the greater part is to the lesser part. (i.e. the line A+B is divided into a greater A and a lesser B such that A+B/A = A/B).

    He then looks at roughly 61.8% of the way through the Parmenides, and finds this:

    "The One is equal and greater and less than itself … And if greater and less and equal, it would be of equal measures and more and less than itself … and in number less and more …" [151b5-c7].

    The trouble is that the Parmenides passage really says nothing about the Golden Section, despite the presence of the words "greater" and "less". The One here in the Parmenides is not cut into two parts, such that the One is to the greater part as the greater part is to the lesser part. Indeed, the One here is not cut into any parts at all. Nor is it being said to be "greater and less" than some of its parts; rather, it is being said to be "greater and less" than itself. But the line in Euclid's Golden Section is not greater and less than itself. Furthermore, the discussion of "greater than and less than" has been going on in this stretch of the Second Hypothesis since 149d, a fair bit earlier.

    So this piece of evidence that other dialogues talk about the Golden Mean just where the Golden Mean of word-count occurs, turns out to be nothing more than some unrelated talk about "greater and less". That's not a problem of statistics so much as a problem of evidence-gathering.

    Second example: in the Symposium, Eros is said to be "in the middle", and this occurs at 61.0% of the way through. All right–I'm happy to give him the 0.8% so as to locate it at the Golden Section of word count. But what's the reference to the Golden Section in the text? "Eros is in the middle between wisdom and ignorance." That's all it says at 203e5, the passage that Kennedy cites. Why does that count as a reference to the Golden Section, i.e. (1+root5)/2? There are no references here to ratios, to parts, to irrationals, to any one intermediate position rather than another. All that we learn is that Eros is somewhere in between wisdom and ignorance–he might be 61.8 percent of the way across (which way?), or 50%, or 99%; the text just doesn't say. Furthermore, the idea that Eros is "in the middle" already was broached back at 202d11 with the claim that he is between gods and mortals. Should we take *that* passage to mean that he was 61.8% of the way between gods and mortals, too?

    Third piece of evidence: Philebus 45e7, just 61.8% of the way through the dialogue, quotes the Delphic slogan 'nothing too much'. And, as Kennedy notes, "[t]he Delphic Oracle was a temple to Apollo, a deity important to the Pythagoreans." Yes; the Pythagoreans liked Apollo, and Apollo disliked excess (or so he claimed). But what does this have to do with any particular ratio?

    Final piece of evidence at Phaedrus 259a2, which is just a hair past 61.8%, Socrates mentions that it's noon time. Thats right: it's the middle of the day!

    I'm afraid I really don't see that any of these pan out as clear references to the Golden Section located at the Golden Section of the dialogues in question.

    Still, that's only a first reaction after a quick dip. I'm looking forward to reading the paper thoroughly, and again I'm grateful to Dr. Kennedy for writing up his researches and to Apeiron for publishing them. It should stimulate lots of interesting discussions!

    Reply
  15. Michael Drake

    I don't think we'll ever really know what Plato was up to until someone finds out his astrological sign. And maybe his favorite color.

    Reply
  16. Edward Song

    I am not a scholar of ancient philosophy, but Kennedy's argument almost makes me wish I was. The debate as it has shaken out so far reminds of a similar debate that followed the work of the German musicologist, Helga Thune, who suggested that Bach's famous Chaconne contained hidden chordal allusions to Bach's own sacred music–specifically to some of Bach's Easter hymns concerning death and resurrection. Thune, argued that the Chaconne was a kind of musical epitaph to his wife who had died just before Bach wrote the Chaconne (Bach, in fact, was out of town when his wife had died and returned to discover that she had been dead and buried for several weeks). Hidden references–musical allusions, inside jokes, numerological codes–are well known in Bach's work, but no one in three hundred years had ever suggested that the Chaconne had this specific interpretation. Lots of scholars immediately argued that Thune's discoveries were just statistical aberrations and that one could likely invent similar "insights" into any piece of music if one looked hard enough. Interestingly, a recording was produced in which a choral ensemble sings the choral allusions in concert with the solo violin. It musically puts the theory to the test. Whatever you think about Thune's argument, it is an astonishing recording.

    Kennedy's argument needs to be evaluated. How regular are these patterns? Does every harmonic "note" in the text accompany a discussion with positive valence? Is every dissonant note associated with something negative? Does every text easily divide into twelthes? Does every discussion of the golden mean occur 61.8% through the text? But at the end of the day, I expect, as with Thune, that the proof of the pudding is going to be in the eating. That is to say, what kind of philosophical illumination does the insight bring to the text? Some people seem skeptical about this, but it seems way too early in the game to make any predictions. Who is to say what kind of payoff there will be?

    But what an exciting time to be a scholar of ancient philosophy! This is what seems truly extraordinary to me. How often is it, in any academic field, that one gets a genuinely original scholarly contribution that opens up entirely unexplored tracts of intellectual territory. We will see how useful this all is and perhaps it will all come to nothing, but as a political philosopher I am envious of the opportunity. I wish someone would discover similar hidden messages in say, Rawls.

    Reply
  17. Kris

    Someone ask Kripke if he can rewrite Wittgentsein on Rules and Private Language or Naming and Necessity (okay, it's a transcribed lecture) but this time with coded messages implying that he's actually Francis Bacon or that the world will end in 2012.

    Sounds pretty impossible to me.

    Reply
  18. A Facebook User

    I admit that my describing this as poetry is based on modern standards of what counts as poetry, which does cast doubt on my hypothesis that this should affect our reading of Plato's passages about poetry. On the other hand, Kennedy argues for connections between Plato's stylistic choices and musical traditions, and I thought Plato saw music and poetry as interconnected, so I don't think it's impossible that he might have had a broader view of poetry than simply metered verse.

    Reply
  19. Duncan

    Regarding the remarks about the Golden Mean it occurs to me that while it's relatively complicated (and not obvious to the reader) to start a topic 61.8% into a modern paged text it's fairly trivial with a continuous scroll. Would the dialogues have been written in scroll or tablet form?

    Reply
  20. Sean Halsey

    MM McCabe points me to a recent episode of the BBC Radio 3 programme Night Waves in which she discusses this with Dr Kennedy – it can be heard for the next five days here: http://www.bbc.co.uk/programmes/b00sv7cf (perhaps only by UK residents). The relevant portion of the show is at 29:00.

    Reply
  21. Eric Schliesser

    I agree with remarks above that suggest that the methodology followed has a risk of confirmation bias.
    I have some more literary musings on this topic at another blog (thank you Brian for self-promotion):
    http://itisonlyatheory.blogspot.com/2010/07/on-pythagorean-structures-and-summer.html

    Reply
  22. Patrick Lee Miller

    First the Bible Code, then the DaVinci Code, and now the Plato Code. I haven't yet read this article, nor do I presume to know whether its conclusions are true or false. What interests me is our present culture's fascination with these secret codes.

    Reply
  23. James Harold

    I'm concerned about confirmation bias as well. Here are a few questions. First, would a reader who was unaware of the hypothesis read the passages in the way that Kennedy requires? Suppose we asked some qualified readers to look at the passages located at 1/12 intervals through the texts, and asked for their independent characterizations of those passages. What would they come up with? How similar would their conclusions be to Kennedy's? Second, suppose we took the same texts, and divided them into different intervals, say sevenths, or tenths. Could a reader who is directed to look for similarities find parallels between the dialogues at those intervals also? Third, as Philippe Lemoine suggested above, what if we were to divide up texts by other authors into twelfths, and look for patterns? We might come up with some apparently striking parallels.

    When one reads Henry James' _Turn of the Screw_ with the idea that the governess is mad, one finds evidence for this interpretation everywhere one looks. But James never intended this reading. Or, consider the popular idea that one can find striking structural parallels between Pink Floyd's _The Wall_ and _The Wizard of Oz_ ("Dark Side of the Rainbow").

    It is easy to underestimate just how much coincidence there is in the world, and our interpretations of what we read tend to hew closely to our preconceptions.

    Reply
  24. Jonathan Birch

    Currently the most shared story on BBC News:

    http://news.bbc.co.uk/local/manchester/hi/people_and_places/newsid_8773000/8773564.stm

    I don't have anything like the scholarly expertise to evaluate this hypothesis, but having read Tad Brennan's post I'm somewhat mistrustful!

    Reply
  25. Phil Bert

    I think it's fair to say that when one has read enough of Plato, one tends to get a feel for the rhythm and flow of the dialogues. One can almost predict when a shift of mood or topic will take place. Evidence indicating that this sort of flow was rigorously designed doesn't so much shock me, as make me wonder how this remained undiscovered for such a long time.

    No, the _truly_ shocking bit, I thought, was Dr. Kennedy's admission during the BBC interview that he had never heard of the author Dan Brown before he started this work. I wouldn't have thought there's a man alive who had escaped the promotion of that drivel.

    Reply
  26. Carl

    To people who haven't read the Apeiron paper, you really should. (Kennedy also has the first two chapters for his book online. It looks like he's already typeset it himself, though he doesn't say that he's got a publisher yet — does anyone think that's odd?) Anyway, the argument is pretty well crafted, and if he's right about the data (I haven't checked any of his assertions about where passages appear when you count the way he does) then it looks like he's found some interesting results regarding the composition of Plato's dialogues. His interpretation of these patterns is much harder to support, but if you found the problem sufficiently interesting to get to this comment, you'll find the paper worth reading. Brief selections from his argument, or summaries of it, don't do it justice. It's a carefully worked out argument, and he's gone some way to anticipate criticism, as well as being very conscious of and explicit about his methods.

    Reply
  27. Tim O'Keefe

    I haven't read the article, so I won't comment on the main claim that the dialogues are structured in accordance with Pythagorean number mysticisms. However, the following claim (from the newspaper article that BL quotes above) strikes me as implausible:

    Dr Kennedy argues that Plato did not use the code for pleasure, but for his own safety. Plato's own teacher had been executed for heresy.

    Two points:

    (i) I don't see offhand why expressing some sort of Pythagorean ideas about the mathematical harmony underlying the cosmos would be particularly dangerous. In any case, Plato had characters in his dialogues explicitly express sympathy for these very ideas.
    (ii) Plato had folks in his dialogues explicitly express ideas far more likely to get him into trouble than Pythagorean number mysticism, e.g., withering criticisms of Greek popular religion and of democracy.

    Reply
  28. Phillip Horky

    I've read Kennedy's piece, and as a scholar who takes very seriously the relationship between Plato and the Pythagoreans (I'm writing a book on this now), I would like to raise some concerns.

    I'm particularly worried about something that nobody, to my knowledge, has yet discussed. Why should we assume that it is to the Pythagoreans that we should attach stichometric symbology? We have Pythagorean texts – both original texts of Philolaus and Archytas (fragmentary), as well as pseudo-Pythagorica – that do not apparently demonstrate stichometric tendencies (again, to my knowledge, but the onus of proof is on Kennedy's shoulders). Even if the latter did, it would raise a problem for Kennedy. The evidence cited from Vitruvius is late (1st Century CE). It does not account for the generally accepted view that much of the pseudo-Pythagorica were products of the Hellenistic age (post-320s BCE), a time in which riddling language – anagrams, symbols, etc. – arrived a certain level of sophistication that the Greeks had not used before (not even in texts such as the Derveni Papyrus, to which Kennedy refers). It is more likely that Vitruvius had access to these sorts of texts, rather than actual texts of Archytas, Philolaus, or others (or, at least, that he could not distinguish between the two types). Burkert's studies of Pythagorean symbols of the 5th Century BCE suggests no such sophistication – we really are starting to attach arbitrarily codes to things that appear not to warrant such encoding. Again, a healthy dose of Eco's Foucault's Pendulum (mentioned by Eric Schliesser above) is worth taking.

    I admire Kennedy's attention to and serious consideration of the Neoplatonic/Neopythagorean traditions that followed, and, in my mind, there are many sorts of cases that can be made to support a reading of Plato as having a Pythagorean complex (pace Doug Hutchinson above, with whom I have shared many ideas about these issues), but I'm afraid that I'm not convinced that Kennedy has proven the Pythagorean provenance of this apparent "code" in Plato's writing (see Tad Brennan's comments above). That we might consider Kennedy's approaches to reading Plato is a topic that would require a more thorough discussion of stichometric practices and norms, with careful analysis of philosophical papyri from antiquity (such as those preserved from Philodemus' library at the Officina dei Papiri in Naples).

    Reply
  29. Mohan Matthen

    Tad Brennan's reservations are well-taken. What we need is to compare the probability of some word connoting "middle" occurring at 61.8% with the probability of its occurring elsewhere — e.g. at 48%.

    But there is a problem in investigating questions of that type. Kennedy's analysis is performed on a specially redacted corpus designed to mimic papyri. Plus, some emendations from OCT etc are incorporated. You can't do it on Stephanus page and line numbers. I didn't get the impression that the corpus on which the analysis was performed was public property.

    One more thing. In the radio panel, MM McCabe rightly points out that there is no divergence between the doctrines that are directly expressed by the meaning of the Platonic text, and the Pythagorean doctrines allegedly buried in the formal/musical structure. When asked, she said that the Apeiron article was not "path-breaking". (The word was not hers but the talk-show host's, and she was responding to a demand for a yes-no answer. MM is anything but rude.) This is of a piece with some of the comments in this thread.

    But I should point out that the Apeiron article does not make a detailed case for hidden doctrines. It lays out a way of dividing the text into parts, and makes the claim that when you read various dialogues, you find certain things happening at the same place. For example: "concepts with negative valuations within the dialogues, like disease, dishonesty, Hades, the body, difference, and negation, tend to cluster in definite ranges and at a definite locations, such as around and between the points ten and eleven twelfths of the way through the dialogues." This is a claim about the formal structure of the dialogues, not (primarily) about content. In the interview, Kennedy says that the code and hidden doctrines are laid out in the book he is writing. But the question of whether the paper in Apeiron is path-breaking or not has to rest on the importance of the formal analysis.

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  30. AN

    To Mohan Matthen's point about the versions of the texts Kennedy used not being publicly available:

    Kennedy says on his personal page here http://personalpages.manchester.ac.uk/staff/jay.kennedy/ that he will send people the analyzable versions of the files, as well as the Python program he used to do the analyses, upon request. He notes that these are "not user-friendly packages and probably require some familiarity with compiling and running programs". (I'm not at all equipped to do this so haven't asked for them, but it sounds like they're available if one has the required skill to use them.)

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  31. D.M. Hutchinson

    I am happy to be confused with a scholar as fine as Doug Hutchinson (who often goes by D.S. Hutchinson) but I am D.M.Hutchinson (which is short for Danny Munoz-Hutchinson)!

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  32. John Bremer

    The fact of a mathematical atructure to Plato's dialogues was first enunciated in my 1984 book "On Plato's Polity" and a detailed analysis of the Republic in matheamatical/harmonical terms was given in my 2002 "Plato and the Founding of the Academy". A brief account of my methods (open to anyone to verify)and some of its findings are contained in an article in the University of Dublin's HERMATHENA, No. 169, Winter 2000.
    While I admire and respect the work of Jay Kennedy, it cannot claim the priority for this discovery.
    Platonic studies suffer because scholars are not prepared to master what Plato had mastered and they often write, quite unashamedly, that they are ignorant of bothe mathematics and music, fields in which Plato was incomparable.
    One final note, even if Jay Kennedy and myself have understood something of the mathematuical structure of Plato's dialogues, there remains the question that Plato is always asking: How does this effect the way a man should live? Or what is its relation to the Good? If we don't face those questions, we might as well do crossword puzzles.

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  33. Howard Isaacs

    On the general topic of patterned structure in (mostly) ancient texts, I'd also suggest a look at the late Mary Douglas's last book, 'Thinking in Circles: An Essay on Ring Composition.' For an independent precursor, there is the title essay in Eva Brann's 'The Music of the Republic: Essays on Socrates' Conversations and Plato's Writings.'

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  34. Stephen Menn

    I was surprised to see that there is a discussion of Kennedy's article by Yoel Matveyev in the July 16-22 issue of the Forverts, page 8 (in Yiddish). I wasn't immediately able to find it in their online edition, so can't give a link. As for the comments about Plato and Kabbalah in the last paragraph, well, naturally the Forverts will be interested in the particular relevance of Kennedy's article to Jewish culture. I think the description of Apeiron as a scholarly journal in which various alternative theories are often published which have not been accepted in mainstream academic circles is just intended as a description of what scholarly journals in humanistic subjects are like, rather than as a criticism of Apeiron. Matveyev does immediately add that nonetheless they are based on serious evidence.

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  35. David Wolfsdorf

    The idea that Plato was a Pythagorean is not news, as far as I'm concerned- although it is not so easy to clarify precisely what it means for him or anyone to be a Pythagorean. Specifying his Pythagorean commitments would be helpful. For example, it seems clear from the conjunction of Phaedo and Timaeus that he was committed to metempsychosis. It also seems clear from various dialogues that he was committed to the idea that the pursuit of sophia was a kind of psychic purification.

    Of course, it would be news to learn that all his dialogues were constructed in twelfths according to principles of Pythagorean musical theory. It is questionable whether this would be philosophical news or rather intellectual historical news. But it would be news.

    Among other things it might help authenticate or confirm as spurious dialogues such as Alcibiades I, Epinomis, Cleitophon. Kennedy claims that these dialogues are also composed in twelfths, which lends support to their authenticity. However, Kennedy doesn't venture to use this evidence to support their authenticity since he admits that another Academic-Pythagorean could have composed the texts. Still, with the other evidence out there to support a positive conclusion, this would weigh heavily, I think.

    One of the basic difficulties I see with the attempt to dis/confirm Kennedy's main thesis relates to the initial task of counting the lines of Plato's works. Must this proceed as if Plato had written in the standard epic verse form of dactylic hexameter? Counting meters in this case is not completely straightforward even in the case of Homer. But the real problem is that the manuscripts for Plato's dialogues give thousands of alternative readings. If every syllable counts, what standard text is one to use?

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  36. Dennis Des Chene

    There's a basic difficulty in Kennedy's interpretation. His "Pythagorean" scale consists in twelve intervals in arithmetic progression. Set aside the fact that Greek scales typically consisted of eight notes (two tetrachords juxtaposed), not twelve.

    In general, scales, Greek or not, consist of intervals in geometric, not arithmetic, progression. (That's because the Weber-Fechner Law applies to pitch perception.) See, for example, http://www.midicode.com/tunings/Tuning10102004.pdf.

    A scale consisting of twelve intervals in arithmetic progression looks like this (these are ratios to the base frequency, so that for example if the base frequency is 100Hz, then the next pitch would be about 13/12*100=108Hz): 1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/12.

    Any musicologist would tell you that these are pretty funky intervals, because of the relatively large prime numbers involved (11, 17, 19, 23). The Pythagoreans limited themselves to powers of 2 and 3 in numerator and denominator. Later theorists (e.g. Ptolemy) included 5.

    Thus it is unlikely that a scale consisting of arithmetically equally spaced intervals would have been adopted by Plato, and if he had adopted such a scale, it almost certainly wouldn't have been Pythagorean.

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  37. Sarah B. Reichart

    I am surprised and disappointed that no one here has referred to "The Pythagorean Plato" by musician Ernest G. McClain. This study, published in 1978, is a detailed discussion of the "Just" tuning in the allegory of Plato's Republic.
    One may also find here discussions of Pythagorean Tuning for Athens and an "Archytas"tuning for the city of Magnesia (in laws).

    Reading this book is a requirement for anyone proposing to have discovered a new musical code in Plato, or who doubts the extent of Plato's understanding of musical tuning systems.

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