Pythagoras
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 BC., constitute an important source of ancient Pythagoreanism.

"Pythagoras . . . was intellectually one of the most important men that ever lived, both when he was wise and when he was unwise. Mathematics, in the sense of demonstrative deductive argument, begins with him, and in him is intimately connected with a peculiar form of mysticism." (History of Western Philosophy by Bertrand Russell, second impression, 1947, p. 48)

Little is known of Pythagoras' life, or what he originally said. There are many amazing but untrue legends and anecdotes about him. 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 complementary. Pythagoras was born in Samos, Greece, about 570 BC. A legend tells that he was the son of Hermes. Some occultists claim that he was a student of Abaris, a Scythian magician, who was said to have lived without eating or drinking. Pythagoras supposedly stole his golden arrow. (An Encyclopedia of Claims, Frauds, and Hoaxes of the Occult and Supernatural by James Randi, 1995, p. 1)

At the beginning of the tyranny of Polycrates, Pythagoras left Samos. The natural philosopher Thales adviced him to go to Egypt, to study under the priests of Memphis and Zeus. Egypt was the place to go to learn about the mystery of life after death. Maybe he traveled in Egypt and perhaps in Asia, for the purpose of acquiring knowledge; his ideas of rebirth were alien to Greek tradition.

In Samos he set up a school, but lived outside the city in a cave (or so it is told), 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, who fully submitted to Pythagoras' teachings. The inner circle was known as mathematicoi, the outside circle as akousmatics. To join the community, the novices had to give up all all personal possessions. It appears that the full members had some secret symbol, 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." ('Pythagorean Philosophy before Plato' by Charles H. Kahn, in The Pre-Socratics: A Collection of Critical Essays, edited by Alexander P.D. Mourelatos, 1993, pp. 164-165) Pythagoras' teaching methods provided later a model for Hugh of St. Victor (c.1097-1141), who mentions them in The Didascalion: "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." (The Didascalicon of Hugh of St. Victor: A Medieval Guide to the Arts, translated from the Latin with an introduction and notes by Jerome Taylor, 1961, p. 87)

It is very difficult to separate Pythagoras' original ideas from those of his followers and later commentators, among them Hierocles of Alexandria (died around 431/2 AD), who wrote Commentary on the Golden Verses of the Pythagoras. Pythagoras was an oral teacher, fond of lecturing at night. He did not write: he must have had a great faith in his own spoken word.

"First the Immortal Gods as ranked by law / Honour and use an oath with holy awe. / Then honour Heroes which Mankind excell, / And Daemons of the earth, by living well." (in Hierocles upon the Golden Verses of the Pythagoreans, translated by John Norris, 1682)

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. Very likely Pythagoras derived his doctrine from Egypt. Herodotus tells in his History, Book II, that "beans—which none of the Egyptians ever sow, or eat, if they come up of their own accord, either raw or boiled—the priests will not even endure to look on, since they consider it an unclean kind of pulse." (The History of Herodotus: A New English Version, translated by George Rawlinson, 1862, p. 56)

Iambichus of Chalcis (c.250-c.325 AD) tells that as a result of Pythagoras' abstinence from wine and meat, his "sleep was short, his soul pure and vigilant, and his body confirmed in a state of perfect and invariable health." (Iamblichus' Life of Pythagoras or Pythagoric Life, translated from the Greek by Thomas Taylor, 1818, p. 9) According to Pythagorean teaching, "both the universe and man, the macrocosm and microcosm, are constructed on the same harmonic proportions." (Spiritual and Demonic Magic: From Ficino to Campanella by Daniel Pickering Walker, 2003, p. 14) Noteworthy, there was no place for the Gods of Olympus in Pythagorean cosmology.

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. According to another story, 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), a a statesman and mathematician, who solved the geometrical problem of doubling the cube. Around 450 BC toleration toward the school came to an end and it was broken up. The brotherhood had virtually gone out of existence when the fourth century BC closed. A later revival by the Neopythagoreans took place from at least the first century BC. This movement was eventually incorporated into the neo-Platonists.

Herodotus termed Pythagoras "by no means the feeblest of the Greek sages". (Pythagoras: His Lives and the Legacy of a Rational Universe by Kitty Ferguson, p. 4, 2011) He 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, son of Mnesarchus, practiced investigation most of all men, and having chosen out these treatises, he made a wisdom of his own—much learning and bad art." (The Fragments of the Work of Heraclitus of Ephesus on Nature, translated from the Greek text of Bywater by G.T.W. Patrick, 1889, p. 88) Plato stated that Pythagoras "wasn't only held in extremely high regard for his teaching during his lifetime, but his successors even now call their way of life Pythagorean and somehow seem to stand out from all other people." (Republic by Plato, translated with an introduction and notes by Robin Waterfield, Oxford Universaity Press, 1993, p. 351) Archytas of Tarentum was one of the inspirations for Plato's "philosopher-kings".

Aristotle's study on the Pythagoreans, which has not survived, was based on a book by the pre-Socratic philosopher Philolus. This work, composed about 370 BC, may have been the first writing by a Pythagorean. 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 "a tranquillization of the waves of rivers and seas, in order that his disciples might easily pass over them." (Iamblichus' Life of Pythagoras or Pythagoric Life, translated from the Greek by Thomas Taylor, 1818, p. 98) 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. 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. Shakespeare ridiculed Pythagoras and the doctrine of transmigration in Twelfth Night:

CLOWN: What is the opinion of Pythagoras concerning wild fowl?

MALVOLIO: That the soul of our grandam might haply inhabit a bird.

CLOWN: What thinkest thou of his opinion?

MALVOLIO: I think nobly of the soul, and no way approve his opinion.

CLOWN: Fare thee well. Remain thou still in darkness. Thou shalt hold the opinion of Pythagoras ere I will allow of thy wits, and fear to kill a woodcock, lest thou dispossess the soul of thy grandam. Fare thee well.

( Act 4, Scene 2)

It is not impossible, that Pythagoras may have been influenced by ideas from India, transmitted via Persia and Egypt. Siddharta Gautama, the historical founder of Buddhism, lived c.563-c.483 BC. Pythagoras founded his order about 525 BC. 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 the Beatles' guru Maharishi Mahesh Yogi 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. (Lives of Eminent Philosophers by Diogenes Laertius, with an English translation by R.D. Hicks, in two volumes, II, MCMXXV, p. 347) 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: "No, I swear by him who gave the tetractys to our head, which has the source and root of everlasting nature." (Pythagoras and the Early Pythagoreans by Leonid Zhmud, translated from the Russian by Kevin Windle and Rosh Ireland, 2012, p. 301)

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 like Albert Einstein that the "Mind of God represents cosmic music resonating through ten-dimensional hyperspace." ('Listen! It's Alive' by Paul Kingsbury, in Soundscapes of Wellbeing in Popular Music, edited by Paul Kingsbury, Gavin J. Andrews and Robin Kearns, 2014, p. 93)

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, think before acting, and "Keep closed thine eye and ear 'gainst prejudice; Of others the example fear; think always for thyself".(The Golden verses of Pythagoras, Explained and Translated into French . . . by Fabre d'Olivet, Done into English by Nayán LouiseRedfield, 1917, p. 117) In general, the instructions encourage to strengthen the "harmony" of one's soul and free it from physicality with the help of purifying exercises. "So that, ascending into radiat Ether, / Midst the Immortals, thou shalt be thyself a God." (Ibid., p. 121)

Some rules of the Pythagorean way of life:

1. To abstain from beans.

2. Not to pick up what has fallen.

3. Not to touch a white cock.

4. Not to break bread.

5. Not to step over a crossbar.

6. Not to stir the fire with iron.

7. Not to eat from a whole loaf.

8. Not to pluck a garland.

9. Not to sit on a quart measure.

10. Not to eat the heart.

11. Not to walk on highways.

12. Not to let swallows share one’s roof.

13. When the pot is taken off the fire, not to leave the mark of it in the ashes, but to stir them together.

14. Do not look in a mirror beside a light.

15. When you rise from the bedclothes, roll them together and smooth out the impress of the body.

(Early Greek Philosophy by John Burnet, second edition, 1908, p. 106)

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); Hierocles of Alexandria by H.S. Schibli (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); An Archaeology of Disbelief: the Origin of Secular Philosophy by Edward Jayne; edited by Elaine Anderson Jayne (2018); Music by the Numbers: from Pythagoras to Schoenberg by Eli Maor (2018); Pythagoras' Legacy: Mathematics in Ten Great Ideas by Marcel Danesi (2020); 'Pythagoras and the cult of personality', in Past Mistakes: How We Misinterpret History and Why It Matters by David Mountain (2020); Brill's Companion to the Reception of Pythagoras and Pythagoreanism in the Middle Ages and the Renaissance, edited by Irene Caiazzo, Constantinos Macris, Aurélien Robert (2022); The Life and Philosophy of Pythagoras by Manly Palmer Hall (2023)

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)

The Golden Verses of Pythagoras: And Other Pythagorean Fragments, 2007 (publisher: Forgotten Books)

Some rights reserved Petri Liukkonen (author) & Ari Pesonen. 2008-2024.