Computation, hypercomputation, and physical science
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.
scientific article; zbMATH DE number 5380972
scientific article