Pythagoreanism

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Pythagoreanism is the body of teaching ascribed to Pythagoras of Samos, who in the sixth century BCE settled at Croton in southern Italy and gathered around himself a community of followers bound by shared belief and a common way of life. The difficulty stated at the outset is that Pythagoras left no writings, and almost nothing reported of him can be traced to his own mouth. What survives is what later authors said the Pythagoreans held — Aristotle chief among them, writing nearly two centuries on, already trying to sort the master from the school.

At the heart of the reports stands a single claim: that number is the principle of all things. The Pythagoreans, Aristotle records, held that the elements of number were the elements of everything, and that the cosmos itself was a harmony and a number. The intuition seems to have grown from a real discovery — that musical intervals correspond to simple ratios of string length, so that what the ear hears as concord is, underneath, plain arithmetic. From that they reasoned outward to a universe ordered by ratio, including the doctrine later called the harmony of the spheres: the heavenly bodies, in their motions, sounding a music too constant to be heard.

Alongside the mathematics ran a doctrine of the soul. The Pythagoreans taught the transmigration of souls — that the soul outlives the body and is reborn into others, human and animal alike — and from this followed their asceticism: dietary restraints, rules of purity, silence imposed on newcomers, and a daily discipline of self-examination. Ancient sources already divided the followers into two strands, the akousmatikoi, who kept the precepts as oral rule, and the mathematikoi, who pursued the reasoning behind them. Modern scholarship treats much of the surviving life of Pythagoras as legend accreted over centuries, and disputes how much of the later “Pythagorean” mathematics he could have known.

The school’s afterlife outweighs its history. Plato absorbed the number-cosmology — the Timaeus builds its world-soul from musical ratios — and through Plato the conviction that mathematical form underlies the sensible world entered the Western mainstream. In the Roman era a self-conscious Neopythagoreanism revived the master as a sage and miracle worker, and fed directly into Neoplatonism, where the One and the procession of being carry an unmistakably Pythagorean stamp. Later esotericism kept the thread alive in its own key, treating numbers as bearers of hidden virtue.

The resemblance between that ancient arithmetic and the number-mysticism of later traditions is real, and easily overdrawn. What the Pythagoreans appear to have meant was something exact: that the order of things is, at bottom, ratio and proportion — a claim the sciences would later make in their own language, having forgotten where they first heard it.

→ In the library: Plato — Timaeus (Jowett) · Plotinus — The Enneads (MacKenna): On Numbers · Westcott — Numbers: Their Occult Power and Mystic Virtues (1911)

→ Related: Neoplatonism · The One · Nous · Emanation