Non-Turing Computers and Non-Turing Computability*

Various examples of Malament-Hogarth (hereafter, M-H) spacetimes are given in Hogarth (1992), but the following artificial example from Earman and Norton (1993) is perhaps the simplest. Start with Minkowski spacetime (R4, η) and choose a scalar field Ω on M such that Ω=1 outside a compact set C⊂M and Ω tends rapidly to infinity as a point r∈C is approached. The spacetime (R4-r, Ω2η), depicted in Figure 1, is then M-H. (Although the region inside C appears quite small, it is in fact as large as the complement of C.)