Building on an idea by Pitowsky (1990), David Malament (private communications), Hogarth (1992) and Earman and Norton (1993) have shown how it is possible to perform computational supertasks—that is, an infinite number of computational steps in a finite span of time—in a kind of relativistic spacetime that Earman and Norton (1993) have dubbed a Malament-Hogarth spacetime.
Definition 1 A spacetime (M,g) is Malament-Hogarth just when there is a future endless curve with past endpoint and a point q∊M such that .
(Hereafter, the symbols “q” and “λ” are assumed to have the properties they have in Definition 1.1 shall also speak of a “λ-curve”.)
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.