Minds and Machines 13 (1):115-153 (2003)

Abstract
Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently close computable approximations. In addition to considering the nature of computability relative to any given physical theory, we can consider the relationship between versions of computability corresponding to different models of physics. Deutsch and Penrose have argued on mathematical grounds that quantum computation and Turing computation have equivalent formal power. We suggest this equivalence is invalid when considered from the physical point of view, by highlighting a quantum computational behaviour that cannot meaningfully be considered feasible in the classical universe.
Keywords Church–Turing thesis  computability  hypercomputation  recursion  scientific method  super-Turing machine
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Reprint years 2004
DOI 10.1023/A:1021341202779
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References found in this work BETA

Tasks and Supertasks.James Thomson - 1954 - Analysis 15 (1):1--13.
The Church-Turing Thesis.B. Jack Copeland - 2008 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.

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Citations of this work BETA

Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
Superminds: People Harness Hypercomputation, and More.Mark Phillips, Selmer Bringsjord & M. Zenzen - 2003 - Dordrecht, Netherland: Springer Science & Business Media.
Uncomputable Numbers and the Limits of Coding in Computer Science.Paweł Stacewicz - 2019 - Studia Semiotyczne—English Supplement 30:107-126.

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