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Sunday, June 1, 2008

Pythagoras was a kind of myth-magnet?

Poor old Pythagoras is slipping away from us. He was always a shadowy figure in Western thought -- his followers were secretive and he himself wrote nothing, as far as we know. Even in his own time and place, the Greek cities of southern Italy in the seventh century B.C., Pythagoras was a kind of myth-magnet. Over time a large body of thought about him developed, though it was based on precious little evidence. Then, in the second half of the 20th century, Pythagoras became yet more mysterious.

In 1962, the Swiss scholar Walter Burkert -- using a close reading of earliest written accounts of what Pythagoras was supposed to have said to his followers -- published a monumental debunking of the Pythagorean tradition. Fellow scholars were persuaded that what little they thought they knew about Pythagoras was probably wrong.

Until then, it had been said that there were two sides to Pythagoras -- which is a little ironic, given his presumed association with triangles. He had a religious side as the miracle-working leader of a cult that believed in the transmigration of souls (that "the soul of our grandam might haply inhabit a bird," as Shakespeare's Malvolio puts it in "Twelfth Night"). And Pythagoras had a "scientific" side: He was a pioneering mathematician and philosopher who regarded geometry and numbers as the keys to the universe's harmonious structure.

Only the first side emerged intact from Burkert's scrutiny. The picture of Pythagoras as a mathematician and philosopher was a "mistake," Burkert said, an error resulting largely from the eagerness of self-styled "Pythagoreans" in later centuries to attribute their work to the master himself.

It now seems that Pythagoras did not invent the notion of mathematical proof after all. (Bertrand Russell and Arthur Koestler thought he did, which is why they both proclaimed him the West's most influential thinker.) Nor did he discover the theorem that bears his name -- that the square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. It was known a thousand years earlier in Mesopotamia. He may have noted a link between some harmonic intervals in the music of his time and certain simple numerical ratios. But there is no reason to think he was the first to do so.

Still, even if the old Greek magician himself did not have much to do with it, Pythagoreanism played a sometimes important role in Western science before Newton, especially in astronomy, as Kitty Ferguson illustrates in "The Music of Pythagoras," an engaging survey of the ideas that have been thought of as Pythagorean.

For example, Plato's "Timaeus," with its account of a creator fashioning the world out of basic geometrical shapes, reflected the ideas of Plato's friend Archytas of Tarentum, a mathematician who regarded himself as a Pythagorean. "Timaeus" was the basis for most cosmology in the West for the first 12 centuries of the Christian era.

In the early 17th century, the astronomy of Johannes Kepler was suffused with Pythagorean themes, including the Pythagorean "music of the spheres." In ancient times it was much discussed why this sound, allegedly made by the heavenly bodies as they whiz through space, cannot be heard by human ears. Aristotle wryly noted that humans cannot hear it because there is no such sound.

In general, Ms. Ferguson's theme is that Pythagoras himself is responsible for the notion that numbers reveal hidden patterns in nature and that this notion amounts to a fundamental principle in science. It is indeed likely that Pythagoras regarded simple numbers and ratios as the keys to the universe; this much survives the skeptical thrust of recent scholarship about him.

Ms. Ferguson is familiar with the scholarship, but it is not clear that she has grasped its significance. Pythagoras' interest in numbers was primarily mystical, with little scientific content. He was concerned more with numerological symbolism (four was justice, for example, and five was marriage) than with measuring things. And the hope that it is possible to provide a unified account of the universe, using quantitative tools, is fundamentally Greek rather than specifically Pythagorean. The idea is found, in crude forms, in Pythagoras' immediate predecessors, Thales, Anaximander and Anaximenes.

Ms. Ferguson closes her book with a hurried meditation on the threats to the conception of an orderly universe that are allegedly posed by 20th-century math and science. Were the Pythagoreans -- or, we might as well say, the Greeks -- correct to assume that there are comprehensible patterns in the universe? Or has that turned out to be a false hope? Ms. Ferguson skips briskly through quantum mechanics, chaos theory, set theory and more, wondering whether they show, in their sometimes surprising and always complex claims, that the universe is not rational after all.

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Posted by Ajay :: 12:05 PM :: 0 comments

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