Cooper, S. Barry 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) Cited in 5 Documents 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.) Keywords:Turing machine; philosophy of science; Turing universe; complex physical situations; nature of scientific reality; Laplacian determinism; Shannon entropy; incomputability in nature; Mandelbrot sets; Gödel incompleteness; Chaitin’s \(\Omega\) number; Blum-Smale’s theory of computable reals; Turing degree; quantum processes; continuum hypothesis PDFBibTeX XMLCite \textit{S. B. Cooper}, Lond. Math. Soc. Lect. Note Ser. 259, 63--116 (1999; Zbl 0944.03029)