Posts Tagged ‘ mathematics ’

Historian claims Plato’s manuscripts are mathematically ordered according to 12-note scale

Julian Baggini in The Guardian:

It may sound like the plot of a Dan Brown novel, but an academic at the University of Manchester claims to have cracked a mathematical and musical code in the works of Plato.

Jay Kennedy, a historian and philosopher of science, described his findings as “like opening a tomb and discovering new works by Plato.”

Plato is revealed to be a Pythagorean who understood the basic structure of the universe to be mathematical, anticipating the scientific revolution of Galileo and Newton by 2,000 years.

Kennedy’s breakthrough, published in the journal Apeiron this week, is based on stichometry: the measure of ancient texts by standard line lengths. Kennedy used a computer to restore the most accurate contemporary versions of Plato’s manuscripts to their original form, which would consist of lines of 35 characters, with no spaces or punctuation. What he found was that within a margin of error of just one or two percent, many of Plato’s dialogues had line lengths based on round multiples of twelve hundred.

The Apology has 1,200 lines; the Protagoras, Cratylus, Philebus and Symposium each have 2,400 lines; the Gorgias 3,600; the Republic 12,200; and the Laws 14,400.

Kennedy argues that this is no accident. “We know that scribes were paid by the number of lines, library catalogues had the total number of lines, so everyone was counting lines,” he said. He believes that Plato was organising his texts according to a 12-note musical scale, attributed to Pythagoras, which he certainly knew about.

“My claim,” says Kennedy, “is that Plato used that technology of line counting to keep track of where he was in his text and to embed symbolic passages at regular intervals.” Knowing how he did so “unlocks the gate to the labyrinth of symbolic messages in Plato”.

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Brutally Hard Math Is Its Own Reward

Jordan Ellenberg in Slate:

The New York Times recently reported that reclusive Russian geometer Grigory Perelman has apparently proved the century-old Poincaré conjecture. The Times calls Poincaré “a landmark not just of mathematics, but of human thought.” But just whyit’s so significant is left a bit hazy. Big mathematical advances often generate the same kind of lofty but content-free rhetoric found in political speeches about “the family.” Like the family, math is a subject everyone agrees is very important without being able to specify exactly why.

I’m here to help. (With the Poincaré conjecture. As for the family, you’re on your own.)

Poincaré conjectured that three-dimensional shapes that share certain easy-to-check properties with spheres actually arespheres. What are these properties? My fellow geometer Christina Sormani describes the setup as follows:

The Poincaré Conjecture says, Hey, you’ve got this alien blob that can ooze its way out of the hold of any lasso you tie around it? Then that blob is just an out-of-shape ball. [Grigory] Perelman and [Columbia University’s Richard] Hamilton proved this fact by heating the blob up, making it sing, stretching it like hot mozzarella, and chopping it into a million pieces. In short, the alien ain’t no bagel you can swing around with a string through his hole.

That’s zingier than anything theTimes will run, but may still leave you without a clear picture of Perelman’s theorem. Indeed, it’s pretty hard to give an elementary account of the statement that Poincaré conjectured and that Perelman seems to have confirmed. (If that’s what you’re after, Sormani’s home page links to a variety of expositions, including one in the form of a short story.) Instead, I’ll try to explain why Perelman’s theorem matters without explaining what it is.

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