 Constructing and using a relativistic hypercomputer is challenging. The first question is whether our spacetime is Malament-Hogarth. The answer is currently unknown. Even if our spacetime is not Malament-Hogarth globally, it might still contain regions that have the Malament-Hogarth property locally. An example of such a region is a huge, rotating black hole; there is evidence that our universe contains such black holes (Etesi and Németi 2002). But even if there are Malament-Hogarth regions in our universe, there remain considerable obstacles. For starters, (i) the huge, rotating black hole that is closest to us is probably out of our reach as well as our descendants’ reach, (ii) completing an infinite computation requires an unbounded memory, which might require an unbounded amount of matter, and (iii) a machine that requires an unbounded amount of matter running for an infinite amount of time will malfunction with probability 1, rendering it useless (Button, 2009, 779). The latter challenge might be addressable by employing multiple self-reproducing and self-correcting machines that check one another’s computations instead of a single machine (Andréka et al. 2018), although that seems to exacerbate the need for unbounded resources (see also Németi and Dávid 2006, Andréka, Németi, and Németi 2009).