Abstract
We expose and discussPenrose's thesis: “Nature produces harnessable noncomputable processes, but none at the classical level.” We then suggest a partial counterexample to it, based on aGedanken experiment about an undecidable family of integrable Hamiltonian systems that could lead to a sort of idealized solution to the Halting problem for Turing machines.
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1. Partially supported by a Fulbright/CNPq-Brazil grant. Permanent address after November 5, 1990: Center for the Study of Mathematical Theories of Communication, IDEA/School of Communications, Federal University of Rio de Janeiro, Av. Pasteur 250, 22290 Rio de Janeiro, RJ Brazil.
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da Costa, N.C.A., Doria, F.A. Classical physics and Penrose's thesis. Found Phys Lett 4, 363–373 (1991). https://doi.org/10.1007/BF00665895
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DOI: https://doi.org/10.1007/BF00665895