Physical Hypercomputation and the Church–Turing Thesis

  • Authors:
  • Oron Shagrir;Itamar Pitowsky

  • Affiliations:
  • Department of Philosophy, The Hebrew University of Jerusalem, Israel/ E-mail: shagrir@cc.huji.ac.il;Department of Philosophy, The Hebrew University of Jerusalem, Israel/ E-mail: itamarp@vms.huji.ac.il

  • Venue:
  • Minds and Machines
  • Year:
  • 2003

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Abstract

We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy's thesis.