Computation, hypercomputation, and physical science
type: Item
instance of: scholarly article
title: Computation, hypercomputation, and physical science
zbMATH Open document ID: 1167.03002
author: Konstantine Arkoudas
published in: Journal of Applied Logic
publication date: 2008-12-11T00:00:00Z
review text: In this logico-philosophical paper, the author (1) investigates, in great detail, the role of the Church-Turing Thesis in computability theory and (2) criticizes the works of several people on their interpretations of the Church-Turing Thesis. He especially argues against some of the results of B. J. Copeland, who holds that the Church-Turing Thesis is widely misunderstood by philosophers and cognitive scientists. The overall conclusion of the paper under review is that prospects for a scientific theory of hypercomputation are very poor, since ``physical science does not have the wherewithal to investigate computability or to discover its ultimate `limit'.'' However, in the reviewer's opinion, physical theory does have the capability to move toward an ultimate `limit' with (nondeterministic) quantum systems using entropy flow as a measure of information flow in pico-computers. That is, for every calculable function there exists a quantum computer/stochastic automaton (not necessarily subject to the Church-Turing Thesis) that computes it. The computational capability of quantum computers can be identified with hypercomputation. The physical science used to develop quantum computers is a well-understood part of quantum theory being used by several physicists.
reviewed by: Albert A. Mullin
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03D10
Mathematics Subject Classification ID: 03D20
Mathematics Subject Classification ID: 68Q01
Mathematics Subject Classification ID: 68Q05
Mathematics Subject Classification ID: 68T01
Mathematics Subject Classification ID: 81P68
zbMATH DE Number: 5380972
zbMATH Keywords: Church-Turing thesis
zbMATH Keywords: Gandy's thesis
zbMATH Keywords: hypercomputation
zbMATH Keywords: quantum computers
zbMATH Keywords: quantum computability
zbMATH Keywords: Turing limit
describes a project that uses: ALGOL 60
MaRDI profile type: Publication
full work available at URL: j.jal.2008.09.007
OpenAlex ID: W2169365145
cites work: The B-Book
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DOI: 10.1016/J.JAL.2008.09.007
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description: scientific article; zbMATH DE number 5380972