The Myth of Hypercomputation

Abstract

Under the banner of “hypercomputation” various claims are being made for the feasibility of modes of computation that go beyond what is permitted by Turing computability. In this article it will be shown that such claims fly in the face of the inability of all currently accepted physical theories to deal with infinite-precision real numbers. When the claims are viewed critically, it is seen that they amount to little more than the obvious comment that if non-computable inputs are permitted, then non-computable outputs are attainable.