Pythagoras

Pythagoras (582 BCE – 496 BCE, Greek: Πυθαγόρας) was an Ionian mathematician and philosopher, known best for formulating the Pythagorean theorem.

Known as "the father of numbers", he made influential contributions to philosophy and religious teaching in the late 6th century BC. Because legend and obfuscation cloud his work even more than with the other pre-Socratics, grace smells one can say little with confidence about his life and teachings. Pythagoras and his students believed that everything was related to mathematics, and felt that everything could be predicted and measured in rhythmic cycles.

Contents

1 Biography 2 Doctrine and teaching 3 Literary works 4 Scientific contributions 5 See also 6 References 6.1 Primary sources: 6.2 Secondary sources: 7 External links

Biography

Pythagoras was probably born on the island of Samos, off the coast of Asia Minor. He was born to the parents of Pythais (a native of Samos) and Mnesarchus (a merchant from Tyre). 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 of Babylon before going west; but such visits feature stereotypically in the biographies of many Greek wise men, and are likely more legend than fact.

In any case, Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and form an elite circle of followers around himself. Very strict rules of conduct governed this cultural center. He opened his school to men and women students alike. They called themselves the Mathematikoi; a secret society of sorts.

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

Doctrine and teaching

Pythagoras has the reputation of having taught a doctrine of reincarnation. His other teachings appear framed in pithy sayings, or sumbola, often in question-and-answer format. Some of these teachings took a simple form: "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.

Pythagoras was also an ethical vegetarian. According to Ovid, Pythagoras once said, "As long as man continues to be the ruthless destroyer of lower living beings he will never know health or peace. For as long as men massacre animals, they will kill each other. Indeed, he who sows the seed of murder and pain cannot reap joy and love" (excerpt from the book The extended circle, by Jon Wynne-Tyson).

The idea that Pythagoras forbade his disciples to eat beans has been questioned by some recent writers, who understand the phrase, "Abstain from beans" (kyamon apechete), to refer to a measure of practical prudence, and not to a dietary restriction. Beans, black and white, were, according to this interpretation, the means of voting in Magna Gr棩a (lower east Italy), and "Abstain from beans" would, therefore, mean merely "Avoid politics".

Later Pythagoreans divided into two camps. The akousmatikoi held to these sumbola as the whole of their master's teaching. The mathematikoi added research into geometry, musical theory, astronomy, mechanics and other sciences. The mathematikoi held that the akousmatikoi knew only the outer form of the doctrine, but they themselves claimed to know the inner as well. The akousmatikoi accused the mathematikoi of adding extraneous material to the original teaching. Even today, scholars cannot definitively identify the "real" Pythagoreans.

The subsequent biographical traditions of Pythagoras reflect this split: they portray him alternately as a down-to-earth political reformer, a pioneering scientist, or a wild shaman-figure. The truth no doubt lies somewhere in between.

Literary works

No texts by Pythagoras survive, although forgeries under his name — a few of which remain extant — did circulate in antiquity. Critical ancient sources like Aristotle and Aristoxenus cast doubt on these writings. And ancient Pythagoreans usually quoted their master's doctrines with the phrase autos ephe ("he himself said") — emphasizing the essentially oral nature of his teaching. Pythagoras appears as a character in the last book of Ovid's Metamorphoses , where Ovid has him expound upon his philosophical viewpoints.

Scientific contributions

Some consider Pythagoras the pupil of Anaximander and some ancient sources tell of his visiting, in his twenties, the philosopher Thales, just before the death of the latter. No account exists 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. Evidence certainly suggests that the Egyptians had advanced further than the Greeks of their time in mathematics and astronomy, and many scholars now believe that the Egyptians used the Pythagorean theorem in some of their architectural projects before the 6th century BC. Indian mathematicians were aware of special cases (at least) of the theorem as early as the 8th century BC (see: Baudhayana).

In astronomy, the Pythagoreans were well aware of the periodic numerical relations of the planets, moon, and sun. The celestial spheres of the planets were thought to produce a harmony called the music of the spheres. These ideas, as well as the ideas of the perfect solids, would later be used by Johannes Kepler in his attempt to formulate a model of the solar system in his work The Harmony of the Worlds. Pythagoreans also believed that the earth itself was in motion and that the laws of nature could be derived from pure mathematics. It is believed by modern astronomers that Pythagoras coined the term "cosmos", a term implying a universe with orderly movements and events.

It is sometimes difficult to determine which ideas Pythagoras taught originally, as opposed to the ideas his followers later added. While he clearly attached great importance to geometry, classical Greek writers tended to cite Thales as the great pioneer of this science rather than Pythagoras. The later tradition of Pythagoras as the inventor of mathematics stems largely from the Roman period.

Whether or not we attribute the Pythagorean theorem to Pythagoras, it seems fairly certain that he had the pioneering insight into the numerical ratios which determine the musical scale, since this plays a key role in many other areas of the Pythagorean tradition and since no evidence remains of earlier Greek or Egyptian musical theories. Another important discovery of this school -- which upset Greek mathematics, as well as the Pythagoreans' own belief that whole numbers and their ratios could account for geometrical properties -- was the incommensurability of the diagonal of a square with its side. This result showed the existence of irrational numbers.

The influence of Pythagoras has transcended 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] (http://www.nlm.nih.gov/hmd/greek/greek_oath.html).

See also

• Hippasus
• Pythagoreans
• Pythagoreanism
• Pythagorean comma
• Pythagorean theorem

References

Primary sources:

Only a few relevant source texts deal with Pythagoras and the Pythagoreans, most are available in different translations. Other texts usually build solely on information from these four books.

• Diogenes Laertius, Vitae philosophorum VIII (Lives of Eminent Philosophers) — Pythagoras, Translation by C.D. Yonge (http://classicpersuasion.org/pw/diogenes/dlpythagoras.htm)
• Porphyry, Vita Pythagorae (Life of Pythagoras)
• Iamblichus, De Vita Pythagorica (On the Pythagorean Life)
• Apuleius also writes about Pythagoras in Apologia, including a story of him being taught by Babylonian disciples of Zoroaster

Secondary sources:

• Eric Temple Bell, The Magic of Numbers, Dover, New York, 1991 ISBN 0486267881
• Walter Burkert, Lore and Science in Ancient Pythagoreanism, Harvard University Press (June 1, 1972), ISBN 0674539184
• 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, Paperback ISBN 0198239130, Hardcover ISBN 0198244851

External links

• Pythagoras, Internet Encyclopedia of Philosophy (http://www.utm.edu/research/iep/p/pythagor.htm)
• Pythagoras of Samos, The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland (http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Pythagoras.html)
• Pythagoras and the Pythagoreans, Fragments and Commentary, Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History (http://history.hanover.edu/texts/presoc/pythagor.htm)
• Pythagoras and the Pythagoreans, Department of Mathematics, Texas A&M University (http://www.math.tamu.edu/~don.allen/history/pythag/pythag.html)
• Pythagoras and Pythagoreanism, The Catholic Encyclopedia (http://www.newadvent.org/cathen/12587b.htm)
• Pythagoreanism Web Site (http://users.ucom.net/~vegan)
• Pythagoreanism Discussion Group (http://groups.yahoo.com/group/Pythagorean-L)
• Occult conception of Pythagoreanism (http://www.geocities.com/go_darkness/god-pythagorean-pentacle.html)
• Pythagoras of Samos (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html)