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Pythagoras (570?-495? BC)

 

Greek pre-Socratic mathematician and spiritual teacher, a semi-mystical figure, whose ideas has survived, as quotations, in writings of his successors. Pythagoras himself apparently did not record his philosophy in writing, but The Golden Verses, commonly dated to the fourth century B.C., constitute an important source of ancient Pythagoreanism.

"First the Immortal Gods as ranked by law / Honor, and use an oath with holy awe. / Then honour Heroes which Mankind excell, / And Daemons of the earth, by living well." (in The Golden Verses, tr. John Norris)

Little is known of Pythagoras' life, or what he originally said. And there so are many legends and anecdotes about him, that modern scholars have concluded that Pythagoras acted more like a religious leader than a scientist, mathematician or systematic philosopher. However, at that time these different roles were not contradictory. Pythagoras was born in Samos, Greece, about 570 BC. A legend tells that he was the son of Hermes. At the beginning of the tyranny of Polycrates, he left Samos. The natural philosopher Thales adviced him to go to Egypt, to study under the priests of Memphis and Zeus.

Pythagoras probably traveled in Egypt and perhaps in Asia, for the purpose of acquiring knowledge. In Samos he set up a school, but lived outside the city in a cave, where he carried out his mathematical research. About 530 BC he settled at Croton, a Greek colony in Southern Italy. Around him formed a philosophical school, a group of 300 persons, male and female. The inner circle was known as mathematicoi, the outside circle as akousmatics. To join the commune as probationers, his students had to give up all all personal possessions and maintained silence for five years. It appears that the members had some secret conventional symbols, perhaps the six-pointed star of interlocking triangles, by which they could recognize each other.

Porphyry (233-c.305 BC) stated in his Vita Pythagorae: "What Pythagoras said to his associates there is no one who can tell for certain, since they observed a quite unusual silence." Pythagoras' teaching methods provided later a model for Hugh of St. Victor (c.1097-1141), who mentioned them in The Didascalion, a guide for the study of texts: "for seven years, according to the number of the seven liberal arts, no one of his pupils dared ask the reason behind statements made by him; instead, he was to give credence to the words of the master until he had heard him out, and then, having done this, he would be able to come at the reason of those things himself." As a result, it is very difficult to separate Pythagoras' original ideas from those of his followers and later commentators.

The Pythagorean Order was largely a mystical organization. Its members followed a strict way of life. They practiced asceticism and vegetarianism, with one exception in their diet: "do not eat beans" - this was connected to purification of the soul. Iambichus of Chalcis (c.250-c.325 AD)  tells in The Life of Pythagoras, that as a result, Pythagoras' "sleep was short, his soul pure and vigilant, and the general health of his body was invariable." According to Pythagorean teaching, "both the universe and man, the macrocosm and microcosm, are constructed on the same harmonic proportions."

It is said that Pythagoras married at the age of sixty one of his disciples, a young girl named Theano. During political and social disturbances, the temple in which the Pythagoreans assembled was set on fire. Some of Pythagoras' companions migrated about 495 BC to Metapontum in Lucania. A legend tells that Pythagoras starved there himself to death. Some say he perished in the temple with his disciples. In exile, the brotherhood developed the teachings of Pythagoras and missionaries spread his thought. Pythagoras' successors were Philolus of Croton (c.470-390 BC) and Archytas of Tarentum (fl. 400-350 BC), who was a mathematician. The brotherhood virtually disappeared at the end of the fourth century BC.

Pythagoras had a profound influence on Plato (c.427.-c.347 BC), later philosophers, and musicians, and artist. Even the Swiss psychiatrist Carl Jung (1885-1961) was interested in Pythagoras' thought in his youth. Heraclitus (fl. c.500 BC), a younger philosopher, said that Pythagoras "practised investigation most of all men, and having chosen out these treatises, he made a wisdom of his own - much learning and bad art." Plato wrote in Republic, that Pythagoras "wasn't only held inextremely high regard for his teachings during his lifetime, but his successors even now call their way of life Pythagorean". Plato's close friend, Archytas of Talentum, a statesman and thinker, was a Pythagorean. Likely he was one of the inspirations for Plato's "philosopher-kings". Aristotle's work on the Pythagoreans, which has not survived, was based on Philolus' book. In the first century BC Publius Nigidus Figulus founded the Neopythagoreanist school of philosophy.

The neo-Platonist Iambichus, a student of Porphyry, wrote an account of the Pythagorean way of life. He claimed that Pythagoras' innumerable miracles included "tranquillisations of the waves of rivers and seas in order that his disciples might the more easily pass over them." Jesus performed the same miracle according to the Gospel of Mark. And like Jesus, Pythagoras was  said to have performed many healings, and he reappeared to his disciples after his death. He also preached the doctrine of one God.

Pythagorean and Neopythagorean thought influenced deeply neo-Platonism. Although Diogenes Laertius' Lives and Opinions of the Eminent Philosophers from the early 3rd century AD is often dismissed as a collection of gossips and anecdotes, it offers much information about the reception of Pythagoras' teachings. Leonardo da Vinci wrote down in one of his notebooks an anecdote about Pythagoras' belief in the transmigration of the soul, but his famous drawing of the Vitruvian man can be called Pythagorean in its examination of harmony between microcosm and macrocosm.

Pythagoras believed in the kinship of all living things. It can be assumed that he was a vegetarian. The soul is immortal, doomed to a cycle of rebirth. But the soul could be liberated by means of ritual purification. Pythagoras himself claimed to be able to remember his past lives. He believed that he was the reincarnation of Euphorbus, a famous warrior. Concerning the transmigration of the soul, the Clown says in Shakespeare's Twelfth Night: "... fear to kill a woodcock least thou dispossesses the soul of thy  grandmam."

These ideas have a striking resemblance to Buddhism. Siddharta Gotama, the historical founder of Buddhism, lived c.563-c.483 BC. Pythagoras founded his order about 525 BC. It is not impossible, that Pythagoras may have been influenced by ideas from India, transmitted via Persia and Egypt. Closer sources of influence were Bacchic and Orphic mysteries. One fantastic theory claims, that Pythagoras returned in the fifth century as Merlin, then as the English philosopher Francis Bacon (1561-1626). After an incarnation as the Comte de St. Germain in the 18th century, his next life was supposedly Hermann Göring in the 20th century.

Pythagoras saw a deep connection between the natural world and numbers and mathematical relations - "all is number" was the mystical conclusion of Pythagoreans. The universe has a rational order: "Reason is immortal, all else is mortal," he claimed according to Diogenes Laertius. The first ten numbers have special importance. Together, in equilateral triangle of ten dots, they constitute the tetraktys, which become an object of religious veneration: "Nay, by him that gave us the tetractys which contains the fount and root of ever-flowing nature". Four, the tetrad, represents completion, it completes the progression 1+2+3+4; ten is a perfect number (1+2+3+4) and was recognized as fate, the universe, heaven and even God. Anticipating Nicolaus Copernicus' heliocentric hypothesis, the Pythagoreans had also a model of the universe, where every sphere in the universe revolves around a central fire. This was revealed only to the most trusted disciples. One of his students, known as Alexanamos, gained fame for being able to predict the weather.

Pythagoras is associated with mathematical discoveries involving the musical intervals of the octave, fourth and fifth - the simple ratios of the lengths of stretched strings and the pitch of their vibration. Intervals could be expressed in the numbers from 1 to 4; thus, 1:2 the sound of an octave; 2:3 the fifth; 3:4 the fourth. Aristoxemus maintained that the true method of determining intervals was by the ear, not by numeral ratio. The dominant notes of the universe are proportion, order, and harmony.

From Pythagoreans originated the doctrine of the "harmony of the spheres", a theory according to which the heavenly bodies emit constant tones, corresponding to their distances from the earth. The cosmos is thus perceived as a single lyre. The idea that "all things are numbers" and that there is a connection between the laws of music and harmony, was much later picked up by string theorists, who see that the "Mind of God represents cosmic music resonating through ten-dimensional hyperspace." (Michio Kaku in Parallel Worlds, 2005)

Pythagoras frequently sang the Homeric poems and reputedly claimed to hear the "music of the spheres" - was he suffering from tinnitus? The famous geometrical theorem (in a right angled triangle the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides), attributed to Pythagoras, was perhaps developed later by members of the Pythagorean school. Also statements closely related to the theorem were made earlier in Egypt, Babylonia, China, and India. In Euclid's Elements, book one (6th century BC), the theorem was given as the 47th proposition.

The Golden Verses, written in dactylic hexameter, was not composed by Pythagoras. However, the work gives a brief introduction to Pythagorean doctrines. It advises among others to honor first the immortal gods, avoid foolishness, and "practice a way of life that is pure, not dissipated, and guard against whatever incurs envy." In general, the instructions encourage to strengthen the "harmony" of one's soul and free it from physicality with the help of purifying exercises. "When you leave the body behind and attain to the free air, you will be immortal, and undying god, a mortal no longer."

A partial list of the rules of the Pythagorean school:

One must not eat beans
One must not pick up what is fallen
One must not touch a white cock
One must not break bread
One must not step over a crossbar
One must not stir the fire with iron
One must not eat from a whole loaf
One must not pluck a garland
One must not sit on a quart
One must not eat the heart
One must not walk on highways
One must not allow swallows share one's roof
One must not look in a mirror beside a light

For further reading: A History of Philosophy by Thomas Stanley (1687) The Life of Pythagoras, with His Symbols and Golden Verses. Together with the Life of Hierocles, and His Commentaries upon the Verses by André Dacier (1707); Pythagorean Politics in Southern Italy Kurt von Fritz (1940); Early Pythagorean Politics in Practice and Theory by Edwin L. Minar (1942); Greek Philosophy, Vol. 1, ed. C.J. de Vogel (1952); Greek Mathematics, Vol. 1, by Ivor Thomas (1952); The Presocratic Philosophers by Geoffrey S. Kirk and John E. Raven (1962); Was Pythagoras Chinese?: An Examination of Right Triangle Theory in Ancient China by T.I. Kao, Frank J. Swetz (1977); Pythagoras: Lover of Wisdom by Ward Rutherford (1984); Iamblichus' Life of Pythagoras, or, Pythagoric Life by Thomas Taylor (1986); On the Pythagorean Life by Iamblichus by Gillian Clark (1989); Pythagoras: An Annotated Bibliography by Luis E. Navia (1990); Pythagoras Revived: Mathematics and Philosophy in Late Antiquity by Dominic J. O'Meara (1991); The Pythagorean Sourcebook and Library: An Anthology of Ancient Writings Which Relate to Pythagoras and Pythagorean Philosophy, ed. Kenneth Sylvan Guthrie, et al. (1991); The Harmony of the Spheres: A Sourcebook of the Pythagorean Tradition in Music, ed. Joscelyn Godwin (1993); Looking for Pythagoras: The Pythagorean Theorem by Glenda Lappan, et al. (1997); Piety and Pythagoras in Renaissance Florence: the Symbolum Nesianum by Christopher S. Celenza (2001); Pythagoras and the Pythagoreans: A Brief History by Charles H. Kahn (2001); The Beautiful Shape of the Good: Platonic and Pythagorean Themes in Kant's Critique of the Power of Judgment by Mihaela C. Fistioc (2002); Divine Harmony: The Life and Teachings of Pythagoras by John Strohmeier & Peter Westbrook (2003); Pythagoras: His Life, Teaching, and Influence by Christoph Riedweg (2005); Pythagoras: His Life and Teachings (by Thomas Stanley, ed. James Wasserman and J. Daniel Gunther, 2010)   

Editions:

  • Opus aureum et scholasticvm, in qvo continentvr Pythagorae Carmina aurea, Phocylidis, Theognidis & aliorum poëmata, 1577 (edita omnia stvdio & cura Michaëlis Neandri)
  • De providentia & fato; una cum Fragmentis ejiusdem; et Lilii Gyraldi interpretatione Symbolorum Pythagorae; notisque Merici Casauboni ad Commentarium Hieroclis in Aurea carmina, 1673 (2 vols., London: Printed by J. R. for F. Williams)
  • Hierocles upon the Golden Verses of the Pythagoreans, 1682 (tr. John Norris)
  • The Life of Pythagoras, with His Symbols and Golden Verses. Together with the Life of Hierocles, and His Commentaries upon the Verses, 1701 (tr. N. Rowe)
  • The Golden Verses of Pythagoras, in The Judgment of Hercules, a Poem by Robert Lowth, 1746 (tr. Mr. Rowe)
  • Die goldnen Sprüche des Pythagoras, 1786
  • The Golden Verses of Pythagoras. And Other Pythagorean Fragments, 1904 (selected and arranged by Florence M. Firth, with an introduction by Annie Besant)
  • The Golden Verses of Pythagoras Explained and Translated into French, by Antoine Fabre d'Olivet, 1917
  • Les vers d'or. Commentaire sur les Vers d'or des Pythagoriciens / Hiéroclès, 1931 (by Mario Meunier)
  • The Golden Verses of the Pythagoreans; A new Translation; Commentary by the Editors of the Shrine of Wisdom, 1952
  • Golden Verses of Pythagoras, in Cavafy as I Knew Him by Memas Kolaitis, 1980
  • Golden Verses of Pythagoras by Hierocles, 1983 (preface by Raghavan Iyer)
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