J. B. Kennedy proposes that Plato organized his dialogues in mathematical form. His argument is mostly found in 'Plato's Forms, Pythagorean Mathematics, and Stichometry', but there is some interesting additional material in his site, and, apparently, a planned book on the subject. The story has found its way to the popular press, without, unfortunately, a lack of journalistic hyperbole thrown in.I was first suspicious of the notion of a Plato Code, as the name itself reminds one of the discredit Bible Code, but Kennedy proposes something more down-to-earth, namely that Plato used Pythagorean musical principles in the organization of his dialogues. Three main claims stand out: (i) that dialogues have an internal organization in which high points are placed in 1/12ths, corresponding to notes of a musical scale, (ii) that positive and negative turns of the dialogue correspond to consonant intervals of the scale, and this may allow us to discover what Plato "really thought" in open-ended dialogues, and (iii) that different dialogues have a different length of their 1/12th unit, which stretch from 100 lines for the Apology to 1000 lines for the Republic and 1200 lines for the Laws. Kennedy makes several interesting observations on his material, including an apparent lack of this mathematical structure in some of the Platonica that are universally acknowledged to be spurious.
Is it plausible that Plato went into all this trouble? Kennedy cites some pieces of evidence in favor of his Platonic stichometry thesis. In my opinion, the thesis is plausible: the "secret structure" may sound like a conspiracy theory, yet Plato himself (in the 7th epistle) argued against revealing the highest doctrines to the polloi, and (in the Republic) proposed that the advanced study of geometry and astronomy should be revealed -after preparation- to the guardian class. The idea that Plato had a secret mathematical doctrine, discussed only within the walls of the Academy, also finds support in Aristotle, who recounts the tale of Plato's Lecture on the Good, which ended in disaster when Plato attempted to present his geometrical arguments about the One to a lay audience. And, the relationship between the world created by the demiurge, music, and mathematical proportion is famously presented in the Timaeus.
Could it be that as the Timaean demiurge looked at the eternal model of number and proportion to fashion the universe as an expression of a musical scale, so did Plato, as the demiurge of his philosophical universe? It is an intriguing idea.
Even though Kennedy's thesis does not sound like a simple case of quackery, and circumstantial evidence lends it a level of initial credibility, the main weakness of the paper is its lack of statistical elaboration, and its reliance on expert judgments.
Perhaps there is evidence that key themes coincide with 1/12ths, but how many key themes are placed in-between notes? A thorough breakdown of the dialogues based on who is speaking, the topic of discussion, the tone, etc. would allow us to better appreciate whether or not the proposed structure actually exists.
In support of this idea, there is quite a bit of intentional, almost numerological structure to modern screen plays. There are places in TV and movie scripts where climaxes and subclimaxes are expected in industry formulas adhered to rather slavishly down to plus or minus factions of a minute.
ReplyDeleteIn TV, this is, in part, a product of the rather mundane need for commercial breaks, but a good share of it is just applies psychology. The sense of what worked developed long before the formulas were canonized. But, someone actually did write a book spelling the formula out, and once that was done, it was followed slavishly by the major studios and has become a formalistic rule that greatly enhances the chances that a script will be produced if followed.
In the same way, the Golden ratio was used intuitively in art and architecture long before it was formally recognized as a design principle, and the rules of musical harmony and form (e.g. Sonatas, the Blues) were derived from examples of great composers before they were taught as formalistic rules for musical composition.
While Plato would be a more likely figure to have some hidden form than many, given his philosophy, and much of Greek writing at the time was explicitly lyric and fit a poetic structure (in part of meomonic reasons), it is easy to find coincidences. A null hypothesis of an internal structure driven by rhetorical intuition rather than conscious mathematical structure seems at least as plausible.
Andrew,
ReplyDeleteHere is an article you might find interesting about the history of musical tuning:
http://www.slate.com/id/2250793/
Here's a nice discussion paper:
ReplyDeleteMeans, Meaning, and Music: Pythagoras, Archytas, and Plato (Scott Makeig)
http://www.ex-tempore.org/means/means.htm
In support of this idea, there is quite a bit of intentional, almost numerological structure to modern screen plays. There are places in TV and movie scripts where climaxes and subclimaxes are expected in industry formulas adhered to rather slavishly down to plus or minus factions of a minute.
ReplyDeleteAncient drama had its own mathematical structure (acts, chorals, etc). I don't find it unbelievable that just as modern screenwriters compute the time of a movie as about a minute/script page, the ancient dramatists whose plays were performed in religious festivals must've organized their material temporally in some way.
Plato was a poet before he famously burned his poems and became a student of Socrates, and he would be well versed in the mathematical intricacies of Greek poetry (syllables per verse, verses per act, etc.). Given his own mathematical bent, it's not unlikely that he might have done something like what Kennedy proposes.
Would he have thought it worthwhile to go into all that trouble? It's hard to tell, but many of the dialogues have substantial internal cross-references ("we will get to this later", or "as we said") and evidences of structure, so it's a good guess that they were planned and were not written spontaneously.
The key is the statistical evidence.
"Could it be that as the Timaean demiurge looked at the eternal model of number and proportion to fashion the universe as an expression of a musical scale, so did Plato, as the demiurge of his philosophical universe?"
ReplyDeleteSure. I'd also like to see the analysis to support J.B. Kennedy's proposal.
Whether or not Plato did this, what interests me is that Plato and his contemporaries had grabbed onto the fact that frequency mattered beyond just music. They headed in the direction of inserting numerology in their writings, which is rather inconsequential in the grand scheme of things. Still, they (and we) were on our way to developing a framework for understanding frequency and harmony.
I wonder not so much how far they got with literature, but how far they got with architecture, astronomy, and water in applying this idea.
"The key is the statistical evidence."
ReplyDeleteStatistical evidence wouldn't distinguish between honed intuition and intentional form.
Intentional form would be better shown by exact correspondences, particularly if they actually differ from some more natural measure, like recitation time for the same passages, or by contortions in composition (e.g. regrouping ideas to unnatural break points) to fit the form.