The machinery of the collapse: on Republic VIII

I link together the nuptial number, that ‘whole geometric number', represented as the areas of two distinct figures -- a square and a rectangle -- with the ‘triangles in ascending order'. I locate an indeterminancy in the conditions for the production of the ‘divine creature', which I take to be a philosopher (and not the cosmos), and suggest a new interpretation of the breakdown of the eugenics programme. I try to show how and why that breakdown is metaphysically necessary. I argue that Plato uses mathematical indeterminancy not only to suggest that the decline is necessary, but also to issue an epistemic warning to us, to the effect that we should avoid trying to come to a philosophical understanding of forms by focusing on even very fine particulars.