Hypercomputation, Frege, Deleuze: Solving Thomson's Lamp

We present the first known solution to the original supertask, the Thomson Lamp Paradox. Supertasks, or infinite operations, form an integral part of the emerging study of hypercomputation (computation in excess of classical Turing machine capabilities) and are of philosophical interest for the paradoxes they engender. We also offer preliminary resources for classifying computational complexity of various supertasks. In so doing we consider a newly apparent paradox between the metrical limit and the ordinal limit. We use this distinction between the metrical and ordinal limits to explain the shortcomings both of Thomson's original formulation of the Lamp Paradox and Benacerraf's consequent critique. We resolve this paradox through a careful consideration of transfinite ordinals and locate its ambiguity as inherent to the identity relation under logic with a close reading of Frege's Begriffsschrift. With this close reading in hand we expose how the identity relation is counter-intuitively polyvalent and, with supertasks, how the logico-mathematical field operates on the basis of Deleuzian point-folds. Our results combine resources from philosophy, mathematics, and computer science to ground the field of hypercomputation for logically rigorous study.