Minds and Machines

, Volume 21, Issue 1, pp 83–96

On the Possibilities of Hypercomputing Supertasks

Authors

    • ACT Department of Humanities and Social SciencesAnatolia College
Article

DOI: 10.1007/s11023-011-9222-6

Cite this article as:
Müller, V.C. Minds & Machines (2011) 21: 83. doi:10.1007/s11023-011-9222-6
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Abstract

This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with “Zeno-machines”, i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though non-effective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation.

Keywords

ComputingComputabilityHypercomputingEffective computingSupertaskChurch-Turing thesisCopelandBenacerrafThomsonZenoZeno-machineAccelerated Turing machine

Copyright information

© Springer Science+Business Media B.V. 2011