Tuesday, May 6, 2008

The History of Civilization

Chapter Twelve: Pythagoras

Crotona was a Greek colony founded in southern Italy around 710 BC. It had the closest natural harbor north of Sicily, and enough trade to give the citizens a comfortable prosperity. It was here that Pythagoras founded his famous school, where he taught hundreds of pupils including both men and women.
He was born in Samos around 580 BC. During his youth he traveled, we are told, to Arabia, Syria, Egypt, India, and Gaul. Returning to Samos he found the oppressive dictatorship of Polycrates, and so migrated to Crotona.

Pythagoras established rules which nearly turned the school into a monastery. The members swore an oath of loyalty to Pythagoras and one another. They were not to eat meat, eggs, or beans. Wine was also forbidden, possibly because they believed in reincarnation and were wary of eating their ancestors.
To purify the soul they maintained celibacy, and observed many peculiar religious taboos. They would not touch a white rooster, walk on highways, or use iron to stir a fire.

The Pythagoreans were the first to divide numbers into odd and even, and into prime and factorable. They noticed that if you pluck a string, then halve its length, it plays the same note but an octave higher. Nature, it was believed,  was filled with these sorts of hidden mathematical codes, which were the key to understanding how the Universe works.
Pythagoras and his pupils made their imprint not only on mathematics, but also on philosophy. In fact, the very word philosophy is thought to be one of his creations.
The universe, he said, is a living sphere with the earth at its center. The earth, too, is a sphere, revolving with the other planets from west to east. Pythagoras was one of the first who considered the earth a sphere.

Surely his most famous contribution is the Pythagorean Theorem, which says that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the remaining sides, expressed as:
A2 + B2 = C2
Pythagoras was said to be so overjoyed by this theorem that he sacrificed an ox to celebrate its discovery, although this seems unlikely considering he was a life-long vegetarian.

The Pythagoreans were the first to appreciate the very concept of numbers, and sought to employ numbers to explain every aspect of the physical world. Legend says that when one of them discovered irrational numbers, which cannot be expressed as a decimal or fraction, the others threw him overboard into the Mediterranean out of fear and revenge.

No one is certain what became of this great mind or his academy in the long run. In one story he starves himself to death, perhaps feeling that eighty years old was old enough. In another version he is captured by rivals because he refused to escape by walking across a field of beans. His society survived for three centuries in scattered groups throughout Greece.
His theorem of right triangles is learned by everyone in high school geometry. Pythgoras was the founder, as far as we know, of both science and philosophy in Europe, an impressive achievement for any man.

To be continued...

For my previous posts on civilization, click here.

If you're interested in Pythagoras and the development of early math, check out Mathematics for the Nonmathematician, by Morris Kline. It's got a great chapter on the Pythagoreans, and it will redefine how you think of numbers and arithmetic.

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