Non-Turing Computers are the New Non-Euclidean Geometries
Mark Hogarth
It is argued that recent work on non-Turing computability suggests a picture of computability analogous to that of modern geometry, and that in this picture there is no fundamental (absolute) boundary between the computable and the uncomputable. If correct, a conjecture about this fictional boundary’s precise location would merely reflect a misunderstanding. The Church-Turing thesis is just such a conjecture.
Keywords: Hypercomputation, non-Turing, spacetime, Malament-Hogarth, Church-Turing, supertasks.