Pythagoras

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Pythagoras

(pĭthăg`ərəs), c.582–c.507 B.C., pre-Socratic Greek philosopher, founder of the Pythagorean school. He migrated from his native Samos to Crotona and established a secret religious society or order similar to, and possibly influenced by, the earlier Orphic cult. We know little of his life and nothing of his writings. Since his disciples came to worship him as a demigod and to attribute all the doctrines of their order to its founder, it is virtually impossible to distinguish his teachings from those of his followers. The Pythagoreans are best known for two teachings: the transmigration of soulstransmigration of souls
or metempsychosis
[Gr.,=change of soul], a belief common to many cultures, in which the soul passes from one body to another, either human, animal, or inanimate.
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 and the theory that numbers constitute the true nature of things. The believers performed purification rites and followed moral, ascetic, and dietary rules to enable their souls to achieve a higher rank in their subsequent lives and thus eventually be liberated from the "wheel of birth." This belief also led them to regard the sexes as equal, to treat slaves humanely, and to respect animals. The highest purification was "philosophy," and tradition credits Pythagoras with the first use of the term. Beginning with the discovery that the relationship between musical notes could be expressed in numerical ratios (see Greek musicGreek music,
the music of the ancient and modern inhabitants of Greece. Ancient Greek Music

The music of ancient Greece was inseparable from poetry and dancing. It was entirely monodic, there being no harmony as the term is commonly understood.
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), the Pythagoreans elaborated a theory of numbers, the exact meaning of which is still disputed by scholars. Briefly, they taught that all things were numbers, meaning that the essence of things was number, and that all relationships—even abstract ethical concepts like justice—could be expressed numerically. They held that numbers set a limit to the unlimited—thus foreshadowing the distinction between form and matter that plays a key role in all later philosophy. The Pythagoreans were influential mathematicians and geometricians, and the theorem that bears their name is witness to their influence on the initial part of Euclidian geometry. They made important contributions to medicine and astronomy and were among the first to teach that the earth was a spherical planet, revolving about a fixed point. At the end of the 5th cent. B.C. the Pythagoreans were forced to flee Magna Graecia when people grew enraged at their interference with traditional religious customs; many were killed. A short-lived Neo-Pythagoreanism developed at the beginning of the Christian era; it borrowed some elements from Jewish and Hellenistic thought and greatly emphasized the mystical element in Pythagorean ideas.

Bibliography

See biographies by P. Gorman (1978) and T. Stanley (1988); D. J. O'Meara, Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (1989).

Enlarge picture
An illustration of Pythagoras, considered by some to be the first pure mathematician. From Jacopo Guarama, 1792. Reproduced by permission of Fortean Picture Library.

Pythagoras

(religion, spiritualism, and occult)

Pythagoras, a Greek philosopher, mathematician, and astronomer, lived from approximately 580 to 500 b.c.e. Pythagoras was the first to conceive of the heliocentric theory of the universe (the notion that Earth and the planets revolve around the Sun), a notion that did not catch on until Copernicus. Pythagoras and his followers also developed basic mathematical notions, such as the concepts of equation and proportion.

Pythagoras is said to have searched widely for wisdom and is believed to have introduced the idea of reincarnation to the Western world. One of his teachings regards the “music of the spheres,” the notion that the intervals between the planets correspond to musical tones and that the movements of the planets produce an ethereal music. Pythagoras’s significance for astrology is that he clearly formulated the notion that the human being is a miniature version (microcosm) of the larger universe (macrocosm). The microcosm and the macrocosm are linked by—and affect each other through—certain correlations. This notion is basic to ancient astrology.

Pythagoras

 

Born circa 570 B.C. on the island of Samos; died circa 500 B.C. Ancient Greek thinker, religious and political figure; founder of Pythagoreanism.

It is difficult to separate the meager facts about the life and teachings of Pythagoras from the legends that represent him as a demigod, perfect sage, heir to the knowledge of antiquity and the Near East, thaumaturgist, and magician. Pythagoras left his native Samos in protest against the tyranny of Polycrates. He may have visited Egypt and Babylonia during his travels—recent writers have suggested that Pythagoras was initiated into various secret doctrines of the Eastern priests. At a mature age (according to tradition, at 40), he settled in the southern Italian city of Croton, where he founded a strictly closed society of his followers, who already during his lifetime venerated him as a higher being. The doctrines and discoveries of Pythagoras that were preserved in the oral traditions of the Pythagorean society cannot be separated from the ideas of his followers, who often ascribed to him their own intellectual initiatives.

In mathematics, Pythagoras is credited with the systematic introduction of proofs into geometry, the construction of the plane geometry of rectilinear figures, the origination of the theory of similitude, the proof of the theorem that bears his name (the Pythagorean theorem), and the construction of certain regular polygons and polyhedrons. Also associated with Pythagoras are theories of odd and even numbers, prime and composite numbers, figúrate numbers, and perfect numbers and theories of arithmetic, geometric, and harmonic proportions and means.

SOURCES

Diels, H. Fragmente der Vorsokratiker, 9th ed., vol. 1. Edited by W. Kranz. Berlin-Neuköln, 1960. Chapter 14.
Iamblichus. De vita Pythagorica. Edited by A. Nauck. St. Petersburg, 1884.
Diogenes Laertius. Lives of Eminent Philosophers, vol. 2, London-Cambridge (Mass.), 1958. Book 8, sections 1–50.

REFERENCE

Kerényi, K. Pythagoras und Orpheus, 3rd ed. Zürich, 1950.

S. S. AVERINTSEV

Pythagoras

?580--?500 bc, Greek philosopher and mathematician. He founded a religious brotherhood, which followed a life of strict asceticism and greatly influenced the development of mathematics and its application to music and astronomy

Pythagoras

(person)
(Pythagoras of Samos, Ionia; about 569-475 BC) The Greek mathematician who founded a philosophical and religious school in Croton (now Crotone) in southern Italy.

Pythagoras is most famous for Pythagoras's Theorem but other important postulates are attributed to him, e.g. the sum of the angles of a triangle is equal to two right angles.
References in periodicals archive ?
Tanto Croton como Pitagoras, aunque probablemente son personas reales, son asimismo figuras con biografias reelaboradas miticamente, tambien en lo que se refiere a su parentesco y estrecha amistad y colaboracion.
La tradicion sostiene que fue Pitagoras el primero en valerse de los terminos filosofia/filosofo, con el fin de dar a conocer la forma de vida que lo caracterizaba: "Pitagoras, habiendo sido interrogado acerca de su oficio, respondio que no sabia ningun arte, sino que era, simplemente, filosofo; y comparando la vida humana a las fiestas olimpicas, a las que unos concurrian por el negocio, otros para participar en los juegos, y los menos, en fin, por el puro placer de ver el espectaculo, venia a concluir que solo estos eran los filosofos" (Millan, 1962, p.
Pero no nos vamos a inventar cuentos sacados de la numerologia de esta guisa: que el 25 es la suma de 1 + 3 + 5 + 7 + 9 = 25 (los primeros primos--excepto el 9--, o al menos los primeros numeros impares antes del divino 10, !la Tetraktys!, exclamaran los que ya se lo han pillado), que es tambien como decir que si los primeros primos los sumamos nos da 16, es decir, 42, y entonces [3.sup.2] + [4.sup.2] = [5.sup.2] = 25 (!el teorema de Pitagoras!).
Quiza porque en el Platon dio un nuevo sentido al universo harmonico extremadamente sensitivo de Pitagoras, sin pruebas empiricas y sin conocimiento musical a priori, sino solo con las matematicas, confinandolo en los limites establecidos matematicamente de cuatro octavas y una sexta mayor (12).
Los testimonios doxograficos antiguos preservan los viajes de Orfeo, Pitagoras y Platon a tierras egipcias.
El segundo es un fragmento extraido de los apuntes del conservatorio musical que explica como Pitagoras, a traves de un monocordio, establecio las primeras leyes de la armonia y de la acustica musical.
El paquete accionario de control de Kroton Educacional es ejercido, a traves de distintos vehiculos societarios (Pitagoras Administracion e Participacoes, Neiva Participacoes, Samos Participacoes, Julio Fernando Cabizuca y Citissimo Participacoes) en partes iguales por los accionistas originales de la sociedad Pitagoras y el Fondo de Inversiones, Brasil Gestao e Participacao, un fondo de inversion administrado por Advent International Corporation.
A experiencia de socializacao do conhecimento, alimentada pelas solidas experiencias de conhecimento que sao compartilhadas, encontra uma ligacao com um dos discursos do consultor Pitagoras: "[...] crio situacoes desafiadoras que induzem os colaboradores a procurar a minha ajuda, observar como eu faco a atividade.
Pitagoras cede la cuerda y la armonia, a el debemos las octavas.
Pese a que el termino nervosa se atribuye a Richard Morton (1689), se revisan en este articulo sus verdaderos origenes, los que pueden remontarse a Empedocles de Agrigento, y mas atras a Alcmeon de Crotona, discipulo de Pitagoras. La revision etimologica del mencionado termino arroja luz sobre los fascinantes inicios de esta palabra, indefectiblemente ligada a la bulimia y la anorexia.
Desde los estudios de Pitagoras en el siglo VI a.C.
Divide estas teorias en tres grupos: la filosofia sofistica (Aristoteles, que aplica dialectica a la naturaleza); la filosofia "empirica" (para Bacon el trabajo de Gilbert, el teorico del magnetismo, es producto de poca y estrecha observacion, carente de metodo); y la filosofia supersticiosa (Platon y Pitagoras, teoricos de doctrinas que acaban siendo meramente "teologicas").