(a blog post of today, x-posted here as it seems relevant)
I’ve never come away from any of Deleuze’s texts feeling that I understood any more (about) mathematics than I did when I started. There’s enough in Deleuze about differential calculus, Riemannian manifolds and so on to make you think that there ought, at some point, to be a settling of accounts with mathematical formalization; but the settlement never arrives, and the reader who undertakes (like Manuel DeLanda) to put things in some sort of scientific order must wrestle with the fact that Deleuze’s texts frequently resist such organization through a combination of willed incoherence and masterful pronouncements about the “nomadic” untameability of the matter at hand. They do so with the fine, pleasant and anti-dogmatic intention of evoking a virtual, problematic field behind every conceptual solution or actualization, so that the reader might not be enslaved by a system or held captive by an image of truth. But what is sacrificed by this approach is any experience of what Lacan called the impasse of formalization (Valéry: “Une difficulté est une lumière. / Une difficulté insurmountable est un soleil.”). It would be illuminating for example to be shown just why the “arborescent” cannot fully comprehend the “rhizomatic”, by means of a demonstration of the exact limit of its ability to do so. As it is, one is sometimes left feeling that some of the most stirring passages of “Capitalism and Schizophrenia” amount to little more than the varied and passionate affirmation of an emotional commitment to untidiness.
There is, nevertheless, something still troubling about Deleuze’s faintly hauntological harping on about old mathematical problematics curtly “obsoleted” by the inhabitants of Cantor’s paradise. Rather than a scientifically normalizing move, DeLanda’s projection of Deleuze’s concerns into the (now not quite so especially) brave new world of chaos and complexity theory can be seen as an attempt to show how science at its very frontiers remains receptive to the Event, continually developing “abnormal” concepts in response to the perennial problems of change, flux and turbulence. Badiou’s account of the (recent, European) history of mathematics is one in which the generation of mathematical novelty occurs through a series of formal impasses resolved by the setting of new foundations: the heroes of this history are the geniuses (collective as may be) who boldly posit new axioms and faithfully elaborate the systems of thought that unfold from them. But the beginnings of chaos theory, as narrated in James Gleick’s tremendously readable Chaos, were to be found in a new assemblage of heterogeneous mathematical techniques, advances in computer technology, problems thrown up by natural science and somewhat maverick metaphorical thinking (e.g. Mandelbrot’s “How long is the coastline of Britain?”). One cannot without distortion represent this development as a militant truth procedure faithful to the vanished trace of an ontological infraction; it seems much closer to Deleuze’s “minor science”, an abnormal enterprise, attending to the little embarrassments of normal theory, that only later submits to regulation by the “royal science” of axiomatics.
I’m reminded here of Lyotard’s suggestion, in The Postmodern Condition, that postmodernity precedes modernity, as the generating matrix of new modernisms. Every modernism is a new foundationalism, albeit often in the guise of a radical undermining of existing foundations; but the postmodern moment is that in which thought and language drift or err away from foundations, forsaking correctness as a criterion in favour of productivity or what Lyotard called “legitimation through paralogy”. It seems that even Badiou, in his call for an “experimental” politics pending the next great foundational upheaval, acknowledges the role of the postmodern moment or modality in the gestation of new modernisms; but for him the role of that moment is precisely to act as a fils conducteur leading towards the revolutionary instant. Deleuze’s “lines of flight”, for better or worse, seem to lead nowhere of the sort.