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Pythagoras

From Wikipedia, the free encyclopedia.

Pythagoras (582 BC - 496 BC, Greek: Πυθαγόρας) was a Greek mathematician and philosopher, known best for the Pythagorean Theorem.

Bust of Pythagoras

Pythagoras, "the father of numbers," was an influential Greek philosopher and religious teacher of the late 6th century BC. Because he is clouded with even more legend and obfuscation than even the other pre-Socratics, it is difficult to say very much with confidence about his life and teachings.

Pythagoras was born on the island of Samos off the coast of Asia Minor. As a young man, he left his native city for Croton in Southern Italy to escape the tyrannical government of Polycrates. Many writers credit him with visits to the sages of Egypt and Babylon in between; but these are stereotypical items in the biographies of Greek wise men, and may be purely legendary.

In any case, Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and forming an elite circle of followers around himself. The doctrines of this cultural center were bound by very strict rules of conduct. His school was open to men and women students alike.

According to Iamblichus, the Pythagoreans followed a structured life of common meals, exercise, reading and philosophical study. We may infer from this that some degree of wealth and leisure was required to join the inner circle. Music was an essential organizing factor of this life: the disciples would sing hymns to Apollo together regularly; the lyre was used to cure illness of the soul or body; poetry was recited before and after sleep to aid the memory.

Pythagoras Pythagoras as portrayed on Roman coins from Samos

Pythagoras is known to have taught the doctrine of reincarnation. His other teachings were framed in pithy sayings, or sumbola, often in question-and-answer format. Some of these teachings were simple: "What is wisest?" "Number"; "What is truest?" "Most men are bad." Others were more cryptic: "What is the Delphic oracle?" "The tetraktys, in which the Sirens sing." Other sumbola related to sexual, dietary and other taboos, including the proper way to stir a fire or place one's shoes before going to sleep.

Later Pythagoreans were divided into two camps. The akousmatikoi held to these sumbola as the whole of their master's teaching. The mathematikoi added in addition research into geometry, musical theory, astronomy, mechanics and other sciences. The mathematikoi held that the akousmatikoi knew only the outer form of the doctrine, and they the inner as well. The akousmatikoi accused the mathematikoi of adding extraneous material to the original teaching. Even today, scholars are not sure who were the "real" Pythagoreans.

The subsequent biographical tradition about Pythagoras reflects this split: he may be portrayed alternately as a down-to-earth political reformer, a pioneering scientist, or a wild shaman-figure. For example, all three major biographers agree that Pythagoras spent time in a cave before leaving Samos. Iamblichus holds that he was pursuing study of geometry and astronomy. Porphyry contends that he was holding cousel among his follower. But in Diogenes Laertius, he is apparently involved in mystical study with the seer Epimenides of Knossos. The truth no doubt lay somewhere in between, but it is not always easy to say exactly where. What we can infer from the divergent traditions, however, is the immense mystical awe in which an early Greek thinker like Pythagoras might have held number, and also his immediate impulse to connect this insight with the political world around him. Other pre-Socratics had similar tendencies, but none took them so far as Pythagoras.

There are no surviving texts by Pythagoras, although forgeries under his name - a few of which are extant - did circulate in antiquity. Critical ancient sources like Aristotle and Aristoxenus cast doubt on these writings. And the usual way for ancient Pythagoreans to quote their master's doctrines was 'autos ephe', "he himself said" - emphasizing the essentially oral nature of his teaching.

Pythagoras is sometimes considered to be the pupil of Anaximander and is reputed by some ancient sources to have visited Thales in his twenties, just before Thales died. There is no account of the specifics of the meeting, other than the report that Thales recommended that Pythagoras travel to Egypt in order to further his philosophical and mathematical training. There is certainly evidence that the Egyptians had advanced further than the Greeks of their time in mathematics and astronomy and it is now widely believed that Egyptians used the Pythagorean Theorem in some of their architectural projects before the 6th century BC.

It is sometimes difficult to determine which ideas are original to Pythagoras and which are latter additions by his followers. While it is clear that he attached great importance to geometry, classical Greek writers were more prone to cite Thales as the great pioneer of this science than Pythagoras. The later tradition of Pythagoras as inventor of mathematics is largely a product of the Roman period.

Whether or not the Pythagorean theorem may be safely attributed to Pythagoras, his pioneering insight into the numerical ratios which determine the musical scale is fairly certain, since this plays a key role in many other areas of the Pythagorean tradition and since there is no evidence of earlier Greek or Egyptian musical theories.

The pentagram (five-pointed star) was an important religious symbol used by the Pythagoreans. It was called "health".

Pythagoras is also said to have devised an alternative discrete presentation of geometry know today as Figurate numbers.

Diogenes Laertius (about 200 AD) quotes Alexander's (about 100 BC) book Successions of Philosophers (and according to Diogenes Alexander has access to a book called The Pythagorean Memoir) in his account of how the pythagorean cosmology was constructed (Diogenes Laertius, Vitae philosophorum VIII, 24):

The principle of all things is the monad or unit; arising from this monad

(It should be noted that Diogenes, although one of our only sources for early Greek philosophy, is highly unreliable. Among other faults, he is given to recasting older ideas into the language of his own day, very often mangling it one the way.)

This cosmology also inspired the arabic gnostic Monoimus to combine this system with monism and other things to form his own cosmology.

The influence of Pythagoras has not been limited to the field of mathematics, and the Hippocratic Oath - with its central commitment to First do no harm - has its roots in the oath of the Pythagorean Brotherhood [1].

In some European medieval texts his name is written as Pitagora.

References

• Primary sources:

There are just a few relevant source texts to consult about Pythagoras and the pythagoreans, most are available in different translations. Other texts usually build solely on these three books.

• Diogenes Laertius, Vitae philosophorum VIII (Lives of Eminent Philosophers)
• Porphyry, Vitae pythagorae (Life of Pythagoras)
• Iamblichus, Life of Pythagoras

• Secondary literature:
  • Eric Temple Bell, The Magic of Numbers, Dover, New York, 1991
  • Walter Burkert, Science and Lore in Ancient Pythagoreanism
  • K. L., Guthrie (Ed.), The Pythagorean Sourcebook and Library, Phanes,
  • Grand Rapids, 1987 ISBN 0-933999-51-8
  • Dominic J. O'Meara, Pythagoras Revived, Clarendon Press, Oxford, 1989

External links

• Pythagoreanism website

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