Pythagoras and Pythagoreans
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Pythagoras (582 B.C.E. – 496 B.C.E., 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 B.C.E. Because legend and obfuscation cloud his work even more than with the other pre-Socratics, 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.
Biography
Pythagoras was born on the island of Samos, off the coast of Asia Minor. He was born to Pythais (a native of Samos) and Mnesarchus (a merchant from Tyre). As a young man he left his native city for Crotona in Southern Italy, to escape the tyrannical government of Polycrates. Many writers credit him with visits to the sages of Egypt and Babylon before going west; but such visits feature stereotypically in the biographies of many Greek wise men, and are likely more legend than fact.
Upon his migration from Samos to Crotona, Pythagoras established a secret religious society very similar to, and possibly influenced by, the earlier Orphic cult.
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 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.
The Pythagorean theorem that bears his name was known much earlier in Mesopotamia and Egypt, but no proofs have been discovered before the proofs offered by the Greeks. Whether Pythagoras himself proved this theorem is not known as it was common in the ancient world to credit to a famous teacher the discoveries of his students.
Pythagoreans
Main articles: Pythagoreans, Pythagoreanism
Pythagoras' followers were commonly called "Pythagoreans." They were mostly philosophers, mathematicians and geometricians who had an influence on the beginning of Euclidian geometry.
The Pythagoreans well known for their teachings of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. They had performed purification rites and followed ascetic, dietary and moral rules which they believed would enable their soul to achieve a higher rank among the gods. Consequentially, they expected they would be set free from the wheel of birth.
The Pythagoreans had also believed that sexes as equal; all slaves were treated humanely, and to respect animals as creatures with souls. The highest purification of the soul was "philosophy," Pythagoras has been credited with the first use of the term.
They had discovered the relationship between musical notes could be expressed in numerical ratios. The Pythagoreans elaborated on a theory of numbers. Ironically, the exact meaning is still disputed by scholars. For a short while, they taught that all things were numbers. Essence of everything is a number. All relationships, even the abstract concepts, could be expressed numerically.
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 B.C.E. Indian mathematicians were aware of special cases (at least) of the theorem as early as the 8th century B.C.E. (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].
See also
- Hippasus
- Pythagoreans
- Pythagoreanism
- Pythagorean comma
- Pythagorean theorem
- Sacred geometry
ReferencesISBN links support NWE through referral fees
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, which in turn reference the lost work Successions of Philosophers by Alexander Polyhistor) — Pythagoras, Translation by C.D. Yonge
- 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
- Pythagoreanism Web Site
- Pythagoras, Internet Encyclopedia of Philosophy
- Pythagoras of Samos, The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University of St Andrews, Scotland
- Pythagoras and the Pythagoreans, Fragments and Commentary, Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of History
- The Complete Pythagoras, an on-line book containing all survived biographies and Pythagorean fragments.
- Pythagoras and the Pythagoreans, Department of Mathematics, Texas A&M University
- Pythagoras and Pythagoreanism, The Catholic Encyclopedia
- Pythagoreanism Web Article
- Pythagoreanism Discussion Group
- Occult conception of Pythagoreanism
- Pythagoras of Samos
- Stanford Encyclopedia of Philosophy entry
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