Physically-relativized Church–Turing Hypotheses: Physical foundations of computing and complexity theory of computational physics

We turn the physical Church–Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent controversies and causes for misunderstanding concerning the state of the Church–Turing Hypothesis (CTH), it is sug...

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Bibliographic Details
Published in:	Applied mathematics and computation 2009-10, Vol.215 (4), p.1431-1447
Main Author:	Ziegler, Martin
Format:	Article
Language:	eng
Subjects:	Church–Turing Hypothesis Exact sciences and technology Logic and foundations Mathematical analysis Mathematical logic, foundations, set theory Mathematics Numerical analysis Numerical analysis. Scientific computation Recursion theory Sciences and techniques of general use Structuralism in physics
Online Access:	Get full text
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Summary:	We turn the physical Church–Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent controversies and causes for misunderstanding concerning the state of the Church–Turing Hypothesis (CTH), it is suggested to study the CTH ‘sharpened’ relative to an arbitrary but specific physical theory – rather than vaguely referring to “nature” in general. For this purpose we apply, and emphasize the utility of, concepts from philosophy: physical structuralism, ontological commitment, and constructivism. This general approach is then illustrated with some exemplary results on computability and complexity theory in computational physics.
ISSN:	0096-3003 1873-5649