Monday, June 28, 2010

Plato and stichometry

Jay Kennedy at the University of Manchester has an interesting piece coming in Apeiron applying a musical analysis to the construction of Plato's dialogues.  There's an introduction to his work here and the pdf of the proof of the article is here.

No one will deny, I think, that Plato was a careful writer.  But just how careful and for what end?


Monte said...

Guardian article here:

It is nice to see ancient philosophy getting wide coverage. As Kennedy says at the end of the Kennedy article, it is going to take years, or more, to sort this out.


James Warren said...

Sure, I think, all publicity is good publicity, but I have various thoughts about this.

They are not necessarily consistent.

1. If this does describe a genuine phenomenon, then why is it there? I'm not sure I buy the coded dangerous mathematised cosmology stuff because there were plenty of other weirder cosmologies around and lots of mathematics-type stuff around too.

2. If this does describe a genuine phenomenon then does it hold only of Plato? Let's try it on Homer and see what the divide-into-12 stuff does there. Or Herodotus. I remember vaguely a piece pulling apart the Bible Code stuff by showing you can do the same trick in, say, Moby Dick. There's something here:

So I would want to know that this is a phenomenon peculiar to Plato and then we can find a Plato-specific rationale for it.

3. I'm not sure about the +ve bits/-ve bits suggestion about the texts at the various harmonic and dissonant points. This at the least depends on an interpretative view of what the general thrust of each dialogue is.

So, lots to ponder, for sure.

Matthew Duncombe said...

I've had a quick look at the paper and I'm pretty sceptical. As with your objections, if this is a genuine phenomenon, then it needs some explaining. But I'm not sure that it is a genuine phenomenon.

Kennedy has various arguments and pieces of evidence, the main one of which is that in some of Plato's dialogues, important set pieces (speeches, arguments rhetoric) come at points in the dialogue that are multiples of 1/12th of the way through.

First, there is a weird way of counting 1/12th of the dialogue (1/12 of the number of 'hexameter' lines, where one line is 35 greek letters. Thin evidence that Plato in his autograph would have counted in this way). Second, there is heavy confirmation bias in the piece (he only looks at one dialogue, the Symposium, in detail, and mentions no more than 6 others, some of them in irrelevant ways, and only records points where his thesis is confirmed). Third, he allows himself a fairly broad construal of '1/12th' where an important argument doesn't fit exactly into 1/12th. There are other problems with his methodology, but I think these are the main ones.

But laying aside such methodological objections,there is a mathematical fact about the number 12 that explains a lot of this: namely that it has many factors: 1 , 2, 3, 4 and 6. Other numbers around there, say 10, have fewer factors: 1, 2 and 5. Actually it has the most factors of any number between 1 and 24 (which has 12 as a factor). So what? Well, that means that lots of common ratios can be expressed as proportions of 12: 1/12, 1/6=2/12, 1/4=3/12, 1/3=4/12, 1/2=6/12 and 12/12=1. So if anything philosophically exciting happens at any point around a twelth or a sixth or a quarter or a third or a half or two thirds or three quarters or 5 sixths or 11 12ths of the way through a dialogue, he can say 'ah-ha! Plato's numerological composition!'. But it would be shocking if such a thing did not occur: Plato is not full of waffle! If Kennedy tried another number, with fewer factors, it wouldn't work so well.

So, I bet, as you say, if you did the same thing with Homer, using 1/12 as the counting unit, you would find all sorts of this stuff. But its purely because of 12.

James Warren said...

Some more: