Plato's Lambda

In the Timaeus the Demiurge blends the soul of the world and then divides it according to a precise series of numbers: first 1, then the doubles 2, 4, 8, and the triples 3, 9, 27. Later commentators arranged these on the two arms of the Greek letter lambda (Λ) — the even doubles descending one side, the odd triples the other, with the monad at the apex — and the figure became one of the most meditated diagrams in the Platonic tradition.

The two arms end in 8 and 27, the first cube of the even and of the odd: soul is thus given the full dimensionality of body — line, plane, solid — before body exists, which is why soul can pervade and govern body. The Demiurge then fills each interval with harmonic and arithmetic means, generating the ratios 4:3, 3:2, and 9:8 — the musical fourth, fifth, and tone — so that the World Soul is literally tuned, and the harmony of the spheres follows as its outward song.

For the Neoplatonists the passage was inexhaustible: Proclus' commentary devotes hundreds of pages to it, reading the psychogonia not as chronology but as the eternal articulation of soul's essence by number. It is the supreme instance of the Pythagorean conviction that the deepest truths are delivered arithmetically.