Thursday, July 1, 2010

On Pythagorean structures and Summer musings

The Leiter Report has been abuzz with discussion about the Pythogorean structures discerned within Plato's texts by Jay Kennedy, a scholar with HPS background. (For the discussion and further links, see:

This post and the links associated with it brought back wonderful memories to one of my undergraduate teachers at Tufts University, the noted Milton scholar Michael Fixler (1928-2007), who was a well known character on campus and around the philosophy department. Fixler was near retirement when I took his seminars on Milton, the Metaphysical poets, and Wallace Stevens with him--all these courses were extended commentaries on Plato (and his role in Derrida, then very popular among English professors much to Fixler's annoyance). At the time Fixler's abiding interest were structures encoded in poetry. In particular, he would call attention to how the *Phaedrus, *Symposium*, and the *Republic* deploy and thematize Pythagorean threefold and fourfold structures that were discerned and transformed by later poets (and, I should add, philosophers). [In that context the opening line of the Timaeus becomes a wonderful joke.] At his death he was still working on three (of course!) enormous books on the topic.

Anyway, As a scholar I sometimes bump into these Pythagorean structures and games, especially in Early Modern Alchemists and natural philosophers with Platonizing tendencies (Kepler most famously). For example, I am probably not the first to have noticed that Newton's Lemma 2 and Scholium (of Book 2, section 2), in which he discusses the calculus in the Principia (it's also the place where he states that he had discussed this earlier with Leibniz in the form of a concealed anagram [something removed in the third edition of the Principia!]), are placed exactly in the middle of the book, if this is measured by numbered Theorems.

Now, I am slowly getting to the point. Christian Huygens had a youthful (Keplerian) flirt with neo-Platonism, especially because after his discovery of Titan he thought the number of potential planets was limited on mathematical grounds. While Huygens quickly learned the error of his ways, I am convinced that Spinoza had him in mind when he wrote that "Indeed there are philosophers who have persuaded themselves that the motions of the heavens produce a [mathematical] harmony" (Appendix 1, Ethics). A century later Huygens would still be explicitly lampooned for his Platonism in Colin MacLaurin's influential Account of Sir Isaac Newton's Discoveries (a text well known to Hume, Adam Smith, and Maxwell).

Recently, I noticed that if we establish the middle of the Principia by the middle proposition of the middle book (that is the propositions in section 6 of book 2), we find a marvelous set of propositions about isochronous simple pendulums in resisting media. (These should not be confused with the propositions in section 10 of book 1, where Pythagorean theorem is used to prove crucial aspects of the properties of an oscillating pendulum which are crucial to Newton's ability to recover and use Galileo's and Huygens' results.) It made me wonder if the placement of these propositions wasn't Newton's Pythagorean homage to Huygens (whom he praises throughout the Principia). After all, Huygens wrote the book on the pendulum.

Anyway, somebody who did se the connection between Plato's pythagoreanism and the Huygens pendulum, is Robert Pirsig (of Zen and motorcycles Fame). Just check out page 301 of his second novel *Lila: An Inquiry Into Morals*. It was a passage that Fixler much appreciated. Anyway, all of this has been explored more elegantly and seriously by Umberto Eco in Foucault's Pendulum, so my time is up here.

No comments:

Post a Comment