Abstract Body, Abstract Machine: Alan Turing's Drama of Difference

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Mann-O'Donnell, Sarah. 2005. Abstract Body, Abstract Machine: Alan Turing's Drama of Difference. Sociology Working Papers, pp. 1-18. [Article]

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In order to prove that mathematics cannot be exhausted by a finite set of procedures, Alan Turing conceives, in 1936, of an abstract machine 1. The machine makes its debut in “On Computable Numbers with an application to the Entscheidungsproblem,” his first major mathematical paper 2. A close reading of this machine’s dynamic will show that Turing’s thought in the field of mathematics is a consciously embodied thought that contemplates its own incompleteness. By examining Turing’s machine through the lens of incompleteness, this project will reveal how, through his extension into abstraction, Turing engages in a paradoxically intensive movement that reveals his body as inextricably enfolded in thought. To understand this radical act of contemplation, Turing must be situated within a history of thinkers working against totality, because in thinking his own incompleteness, he refutes the idea that systems are defined by completeness, or that the unfolding of something is circumscribed by that something as goal. This constellation of thinkers includes Kurt Gödel, before Turing, with his Incompleteness Theorem 3;
it also includes Gilles Deleuze, with his
explanation of how meaning gets made in The Logic of Sense ,4 and Michel Foucault, with his formulation of meaning’s dissolution in “The Thought of the Outside.”5 Brian Massumi then ushers this tradition into the present by defining the limit of a human being as immanent to that being in Parables for the Virtual.6 Massumi grounds his theory in Deleuzeian and Foucauldian concepts, themselves built from Turing’s legacy of lived thought, which in turn is grounded in Gödel’s theorem. Explaining these writers’ relation to Turing’s work on incompleteness will reveal the way in which systems of meaning are always torn between their own constitution and dissolution; this state of being torn will clarify, in turn, the movement of Turing’s mathematical body.

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