Pythagorean Order Study Portal

TL;DR

Kosmos (κόσμος) originally means order — an arrangement, an adornment, a whole whose parts are in their right places — and the Pythagorean wager is that the universe deserves that name: its order is real, discoverable, and mathematical, and a human life can be brought into tune with it the way a lyre string is brought into tune. This is one claim doing two jobs at once. As cosmology it says the structure of things is ratio, and it was vindicated when the Pythagoreans found that the consonant musical intervals correspond to the simple whole-number ratios 2:1, 3:2 and 4:3 — the first demonstration in the Western record that a qualitative experience has an exact quantitative cause. As ethics it says a soul, like a string, can be in tune or out of tune, and that the disciplines of the community at Croton — silence, diet, shared property, and above all the nightly review of the day's conduct — are the tuning. Everything difficult about the school follows from taking both jobs seriously at once: the irrationality of √2 was a mathematical result and a spiritual emergency, because the ethics had been resting on the assumption that proportion is always a ratio of whole numbers.