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.
Bibliographical noteFunding Information:
21The paper was read before the logic group at the Hebrew University, Jerusalem, and at the workshop on Hypercomputation at University College, London. We thank the participants for stimulating discussion. We are grateful to Carl Posy for his assistance in formulating answers to the objections, and to Jack Copeland for helping to clarify various issues. This research was supported by the Israel Science Foundation.
- Church-Turing thesis
- Effective computation
- Gandy's thesis
- Physical hypercomputation