Pythagoreanism

Pythagoras is one of the most famous names in the history of thought and one of the least recoverable people in it. He wrote nothing. No text by him was known even in antiquity. The earliest references to him, within a century or so of his death, are brief and largely hostile: Heraclitus calls him a practitioner of inquiry who made his own wisdom out of other people's writings; Xenophanes tells a story about him recognising the soul of a dead friend in a beaten puppy, which is mockery, but which is also the earliest evidence that he taught the transmigration of souls; Herodotus mentions him in passing. The detailed accounts (the golden thigh, the appearance in two cities at once, the taming of a bear, the catalogue of dietary rules), come from biographies written seven or eight centuries later by Porphyry and Iamblichus, who were Neoplatonists with a case to make.

Between those two bodies of evidence sits the problem. The later material is abundant, vivid and almost entirely untestable; the early material is meagre but contemporary. Modern scholarship, following Walter Burkert's study of 1962, has generally taken the early evidence as controlling, and the resulting picture is of a charismatic religious authority rather than a scientist: a man known for teaching what happens to the soul after death, for founding a community with a rule of life, and for a personal authority so complete that his followers were said to settle arguments by saying that he himself had said so.

Two things can be attributed to him with reasonable confidence. He taught metempsychosis, the passage of the soul into other bodies including animal ones, which is what Xenophanes is mocking. And he founded a society at Croton that lived by a shared discipline and became politically significant enough to be violently suppressed.

Almost everything else is contested, including the item everyone knows. The relation between the sides of a right triangle was in use in Mesopotamia a thousand years before him, there is no early evidence connecting him to a proof, and the attribution appears only in late sources. The famous prohibition on beans is reported in antiquity, but it is reported alongside mutually exclusive explanations, which is usually a sign that the reason had been forgotten while the rule survived.

The doctrine that things are numbers is the most influential idea associated with Pythagoreanism, and the earliest good witness to it is Aristotle, writing in the fourth century BCE about people he calls the so-called Pythagoreans rather than about Pythagoras himself. On his account they held that the principles of number are the principles of all things, that the elements of number are the odd and the even, and that the whole heaven is a harmony and a number.

Behind this lies a genuine discovery about musical intervals: that the concordant intervals correspond to simple ratios of string length, the octave as two to one, the fifth as three to two, the fourth as four to three. Whether Pythagoras made the discovery cannot be established, and the anecdote about him hearing the ratios in the sound of hammers in a forge is physically wrong. But the observation itself is correct and consequential. It showed that something as immediate as consonance is governed by exact proportion, and it made plausible the far larger claim that proportion governs everything.

From that came the harmony of the spheres: the heavenly bodies move at speeds standing in ratios to one another and therefore produce sound, unheard because it has been constant since birth. Philolaus of Croton, in the later fifth century, built the first cosmology of this kind that can be attributed to a named person, and it is genuinely radical, the earth is not at the centre but moves, along with the sun, moon, planets and a counter-earth, around a central fire. This is not heliocentrism, but it removed the earth from the middle of things nearly two thousand years before Copernicus, who cited Philolaus by name.

The tetractys, the triangular arrangement of ten points in rows of one, two, three and four, functioned as a symbol of the whole scheme, containing the ratios of the musical concords in its rows. Oaths were reportedly sworn by it.

A separate tradition holds that a Pythagorean, usually named as Hippasus, discovered incommensurability, that the diagonal of a square has no common measure with its side, and was drowned for revealing it. The mathematical result is real and belongs to this milieu. The drowning is a good story with no early evidence behind it, and it is told in several incompatible versions.

Pythagoreanism was, before it was anything else, a way of living. The community at Croton had entrance requirements, common property in at least some accounts, a period of silence for initiates, and a body of oral precepts called acousmata, things heard. These were terse and often cryptic: do not step over a yoke, do not stir the fire with a knife, do not eat the heart, help a man to load a burden but not to unload it. Some are plainly ethical, some ritual, some unintelligible, and ancient writers already disagreed about what they meant.

The foundation of the discipline was metempsychosis. If the soul passes from body to body, including into animals, then kinship extends across species and the boundary between human and animal is porous. Some form of dietary restriction follows, and the sources report it, though they disagree about its extent: whether all meat was refused, or only certain animals or certain parts, and whether the rule bound the whole community or only an inner group. The prohibition on beans is reported consistently enough to be taken seriously as a rule, but the explanations offered in antiquity are incompatible with one another, which suggests they are later rationalisations of a practice whose original reason had been lost.

The purpose of the discipline was purification. The soul is fallen into the body and works its way out over successive lives, and the rule of life, together with study, is the instrument. This makes Pythagoreanism structurally similar to Orphism, with which ancient writers frequently associated it, and it is the point at which it is most clearly a religion rather than a school of philosophy.

Two features are worth noting because they were unusual. Women appear as members of the community in the sources, which is not the norm for Greek philosophical groups; the tradition names Theano in connection with Pythagoras, though the writings ascribed to her are late. And the community was political. Pythagoreans held office and exercised influence in several cities of southern Italy, and the destruction of the movement in the fifth century was a political event rather than a religious persecution.

Later revivals kept the name and changed the content. Neopythagoreanism, from the first century BCE, produced numerology, ascetic ideals and a large literature of forgeries attributed to Pythagoras and his circle, and it is from this layer, transmitted through Neoplatonism, that most popular impressions of Pythagoreanism derive.