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Pythagoras (570?-495? BC) |
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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? 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)
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:
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