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Clockwork or Turing U/universe? Remarks on causal determinism and computability. (English) Zbl 0944.03029

Cooper, S. Barry (ed.) et al., Models and computability. Invited papers from the Logic colloquium ’97, European meeting of the Association for Symbolic Logic, Leeds, UK, July 6-13, 1997. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 259, 63-116 (1999).
The relevance of the Turing universe as a model for complex physical situations is discussed. Some well-known arguments concerning the nature of scientific reality are related to this theoretical context. The paper compares and introduces the notions of Laplacian determinism, Shannon entropy, incomputability in nature, Mandelbrot sets, Gödel incompleteness, Chaitin’s \(\Omega\) number, Blum-Smale’s theory of computable reals, Turing degree theory, quantum processes, and the continuum hypothesis.
For the entire collection see [Zbl 0919.00039].
Reviewer: U.Schöning (Ulm)

MSC:

03D10 Turing machines and related notions
03B30 Foundations of classical theories (including reverse mathematics)
03D30 Other degrees and reducibilities in computability and recursion theory
03D35 Undecidability and degrees of sets of sentences
03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics
68Q01 General topics in the theory of computing
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
68Q30 Algorithmic information theory (Kolmogorov complexity, etc.)
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