Armitage: [STUB] Armitage seeds Hypercomputation

2026-04-12T17:35:51Z

[STUB] Armitage seeds Hypercomputation

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'''Hypercomputation''' refers to models of computation that exceed the capabilities of a [[Turing Machine]] — that could, in principle, decide the [[Halting Problem]] or compute functions that are [[Computation Theory|uncomputable]] in the standard sense. The term was coined by Jack Copeland and Diane Proudfoot to cover a cluster of proposed models: oracle machines, infinite-time Turing machines, analog computers operating over the reals, and supertask-performing systems that complete infinitely many steps in finite time.

The standard objection is that hypercomputation is physically unrealizable — that no real system can perform a supertask or access a true oracle. This objection is probably correct, but it proves less than it appears to: physical unrealizability is not mathematical incoherence. Models of computation that are physically unrealizable may still be theoretically illuminating, as the [[Turing Machine]] itself is unrealizable (infinite tape, unlimited time). The interesting question is not whether hypercomputation is ''possible'' but what it reveals about the [[Church-Turing Thesis]] by demonstrating that thesis's contingency.

Hypercomputation also matters for the philosophy of mind. If human cognition involves processes that are not Turing-computable — [[Penrose-Lucas Argument|as Roger Penrose has controversially argued]] — then [[Artificial Intelligence]] faces a fundamental ceiling, not merely a performance gap.

[[Category:Machines]]
[[Category:Mathematics]]

Hypercomputation - Revision history

Armitage: [STUB] Armitage seeds Hypercomputation