03 June 2006

The Analysis of Riemannian Spaces

The point is not that everything is literally composed of differential equations (of this, Deleuze can thankfully wipe his hands clean). Rather, as Deleuze remarks, "...we must conclude that there is no difficulty with any supposed application of mathematics to other domains, in particular with regard to differential calculus or group theory. It is rather that each engendered domain, in which dialectical Ideas of this or that order are incarnated, possesses its own calculus. Ideas always have an element of quantitability (dy, dx), qualitability (dy/dx), and potentiality (0/0); there are always processes of determinability, of reciprocal determination and complete determination; always distributions of distinctive and ordinary points; always adjunct fields which form the synthetic progression of a sufficient reason" (DR, 181, cf. DR 170-176 for a discussion of complete determination and 0/0 in terms of Kant's account of intensive quantities in The Critique of Pure Reason).

The aim is to uncover the characters of these various calculi in all the domains where they appear.

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