Future, Present, & Past:

~~ Giving itself latitude and leisure to take any premise or inquiry to its furthest associative conclusion.
Critical~~ Ready to apply, to itself and its object, the canons of reason, evidence, style, and ethics, up to their limits.
Traditional~~ At home and at large in the ecosystem of practice and memory that radically nourishes the whole person.

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Monday, June 28, 2010

Plato and the music of the text

Having put up two papers now where I argue that Plato (1) meant for his musico-mathematical to be taken seriously and (2) drew on a long-standing and widespread cross-cultural inheritance in using it, I should now pass on this news item arguing that (3) there's a lot more of it than we usually think.

Jay Kennedy is a professor of at the University of Manchester, whose research (some of which was just published in the journal Apeiron) has put forward an argument about Plato that will doubtless remind many of the fracas a decade and a half or so ago over the Bible Codes. Kennedy argues that Plato's dialogues are structured along mathematical and musical lines, not just in their arguments or in occasional examples, but in the very rhythm of their composition. His audacity is pretty apparent: "This is a true discovery, not simply reinterpretation," he says. He claims to have the statistics to back it up, and apparently the peer-review process at Apeiron agrees. This is worth paying attention to.

Kennedy's claim is not completely original. He notes that in antiquity, it was commonplace to read Plato with an eye and ear to what was hidden, and many neoplatonists expressly invoked music in their interpretations (see below on Thrasyllus). More recently, John Bremer has already argued in his study of the Republic that Plato divided this dialogue into 240 equal units; he found, moreover, that reading the dialogue on a particular day of the year in a particular spot near Athens puts decisive moments of the dialogue at sundown and sunrise. Big deal, you might say-- there's a lot of days in a year and a of places in the world. But the argument gets more interesting when Bremer asserts that the time and place in question is the setting for the dialogue. There is a very small taste of this argument here (some of the links from this page are now dead, however), and (alas, behind a paywall) a more full argument by Bremer himself here. (See too Bremer's Plato’s Ion: Philosophy as Performance.)

Bremer's argument is based in part on the counting of syllables and lines. This apparent finickiness looks odd to our eyes; it's easy to think of it as a dogged pursuit of evidence where there is none. But it is well justified by ancient practice. The number of lines would be one of the things the author would know, as surely as the author of a modern academic article keeps to the editor-specified word-count. Why? Because scribes, on whom the reproduction of the text depended, were paid by the line. (Message, meet the medium.) This book-keeping has preserved for us some sense of the magnitude of an ancient writer's oeuvre; Diogenes Laertius, for instance, says there were 146 works of Aristotle, and remarks that "all of them together are 445,270 lines." This practice of enumerating totals of lines is well-attested late into the Christian era; the Patriarch of Constantinople, Nicephorus, compiled a list sometime in the early years of the 9th century, which preserves for us the length, in lines, of numerous Christian writings both scriptural and post-. (Interestingly, the totals are in nice round numbers, except for "The Book of the prophet Elias" which is counted at 316 lines.) Wikipedia offers a good introduction to what we know; a more full exposition is Harris' Stichometry.

Kennedy starts with a similar premise, and pursues it further with the aid of computer programs to calculate the number of characters in a line (he uses an average of 35), and thus the total lines per any dialogue. Then he looks at the significant turns in the dialogue's plot--characters' entrances or exits, significant speeches, important themes. His results, which he considers statistically strongly indicative, are that Plato took great pains to shape his dialogues, rounding different sections to lengths that would stand in proportion to other sections in musical ratios. In particular, he finds, with remarkable regularity, the division of a dialogue into twelfths. (Socrates chides Thrasymachus: "You ask someone what twelve is, and then you forbid them to say it's twice six or three times four.") Kennedy suggests that one-twelfth is the fundamental unit in a Platonic dialogue, in part because the musical octave divides (in Pythagorean terms) into twelve semitones. Plato uses this twelve-fold scale as a scaffold for the emotional highs and lows of his argument, and paying attention to this can even give us a clue as to where authorial sympathies lie. For instance, he notes that in the Symposium, the buffoonish, the silly,or the too-simple arguments come at the most disharmonious intervals in the scale: e.g., Agathon's over-wrought rhetoric near the tritone, and Alcibiades' drunken interruptions at the note we would call Ti (a note which was left out of a good deal of medieval music, precisely because it made a tritone with the fourth). By contrast, Aristophanes' myth is by this reckoning at the fourth, and Socrates' speech begins at the fifth.

As far as I know, Kennedy does not cite Bremer, nor the interpretation of Ernest McClain which also strongly emphasizes the musical import of Plato's myths, parables and numbers, but his findings clearly intersect with their research. Kennedy also claims that this exegesis would have been far more obvious to a student closer to Plato's own day. He indeed presents a fair case that this was at least partly understood by neoplatonic readers, citing in particular Theon of Smyrna's book On the mathematics required for understanding Plato, which expressly appeals to Thrasyllus (the 1st-century editor of Plato who among other things is credited with the division of Plato's works into tetralogies) in expounding a musical scale with twelve regularly-spaced notes. As Kennedy notes, Theon's book is a compilation of a good deal of mathematical material, but not very obviously connected to Plato. It has not occurred to most readers to wonder whether the mathematics was "required" not because it was in some way presupposed by Plato (the way algebra might be "required" for pre-trig), but rather because this was the sort of mathematics Plato used to arrange, and to conceal, his meanings.

Obviously, this is an argument that intersects with Straussian exegesis (and Kennedy does indeed argue that Plato used these methods in order to protect himself). It also dovetails nicely with the claim, starting with Aristotle and repeated over the centuries, that Plato taught "secret" or "unwritten" doctrines. Depending on one's disposition, this might appeal to you or turn you off. But leaving that aside, is it even plausible? Could it be just a matter of sifting Plato long enough to find what you're looking for?

I see a few points that leave me wondering. Greek tuning systems are not the same as modern equal temperament, and I may have misunderstood some of Kennedy's arguments, but I don't quite follow all of his exposition on the way harmonic and disharmonic themes are supposed to align with analogous intervals, for instance. Occasional qualifiers like "about" and "[very] close to" raise my eyebrows. And of course the inevitable question arises--could one find this sort of pattern in, say, Aristotle, or Homer, or Aristophanes?

Kennedy does have some control cases--for instance, spurious dialogues attributed to Plato but whose authenticity is generally rejected by scholars, in which he finds no significant correlations between numbers and themes. And he presents a good deal of supporting evidence, both circumstantial and direct. At the end of the day, for all the rhetoric of "proof," I think this may come down to disposition to believe. To many, it's bound to look to many like playing with numbers and wishful thinking ("you can prove anything with statistics"), the Greek equivalent of equidistant letter-skips. (In fact, this isn't so damning in my opinion--I have no truck with accounts of supernatural influence over the precise shape of the Masoretic Text either, but I do believe the Hebrew editors and scribes were perfectly capable of laying in plenty of such "codes", and I consider a few examples quite well-enough established [amid a lot of nonsense, of course].) To others, including myself, it just sounds right. This isn't a reason to wholeheartedly endorse it, but I am certainly staying (ahem) tuned. I don't know whether Kennedy's research will re-shape the entire field of Plato scholarship, as he claims; but it matches very well what I have come to expect from Plato.

[Update: Kennedy was interviewed on PRI concerning his findings; click here to listen.]

[Update 2: Several fair points made (both enthusiastic and skeptical) in the comments on this story on Leiter Reports]


  1. I hope that you will indeed stay 'tuned'. What you are proposing may make the conventional scholars come over all faint but it is completely commonplace within all, without exception, esoteric systems. A book The Vedas written by Sri Chandrashekharendra Saraswati (aka The Sage of Kanchi) goes into great detail about the vibratory aspects of vedic chanting. You don't have to understand Sanskrit for mantras to be effective but it must be pronounced correctly. Because one doesn't know that the Platonic dialogues are pulsed in a certain manner does not mean that there is no effect.

    I am not sure that the occasional rounding up or down of the brute data is an indication of apophrenia any more than the actual interactions of pendulums and oxygen having to be corrected to an 'ideal' form to deliver their truth is an indication of fiddling the results. Maybe in the end we have to leave the realm of the ideal and descend into chaos, mystery and the cloud of unknowing.

  2. Wow! This is important. Your friend Ernest G. McClain was talking about Plato, math and music. As was, in his way, Badiou. Bryan, wouldn't it be amazing if Nietzsche (another musician) played similar games in his Zarathustra? (I do not believe he had the math...)

    However, the exact significance of this (i.e., Kennedy's argument) is debatable. For instance, dividing the Republic into Twelths of the Greek Harmonic Scale and finding that some form of 'twelve' appears in the text at each turn might be little more than an applause sign at the 'harmonic' points.

    Plato had no 'stage instructions' for his dialogue-plays, and I have no doubt scholars will argue that is all this is. Notes (in this case, to the audience, not the actors) of what is to be emphasized as important and what is not.

    Of course, Mr. Kennedy will counter that his whole argument lies in the fact that these notes are for the "audience", not the actors. (And most peculiarly, an audience of readers!) My question is - how much of this would've been obvious to a Greek (reader) of Plato's time?

  3. ombh~~ I quite agree that a degree of "tuning" approximation is admissible. I simply regard a certain moderate skepticism here as indispensable, as Kennedy's claims are so "right down my alley" that I should guard against embracing them too readily. You are right about the Vedas; indeed, it was reflecting about the Vedic meters that first made me reflect upon the likelihood that it is in poetry, even today, that the unconscious tendency of our culture to revert to the sampads (equivalences) still manifests. One can see this, e.g., in Baudelaire. But this is a matter for a full post or three.

    Joe~~ As it is likely (well, plausible) that the dialogues were to be read aloud, and perhaps in groups, in the Academy, the distinction between reader/actor may be blurred somewhat--which is part of the "tuning" and approximation too. As to how much would have been obvious-- is not the whole point the (navigable) distinction between what appears and what withdraws?

  4. One of Yeats' late poems The Statues discusses the Pythagorean influence on Greek sculpture. In his opinion it was as important as Salamis in keeping Asia out of the Mediterranean world.