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Hilbert's Inferno: Time Travel for the Damned


  • Many thanks to Hud Hudson, Roy Sorensen and an anonymous referee for Ratio for comments on earlier versions of this paper. A preliminary version of this paper was produced during a year-long sabbatical which was supported by a research award from the Arts and Humanities Research Council, to whom I owe many thanks.


Combining time travel with certain kinds of supertask, this paper proposes a novel model for Hell. Temporally-closed spacetimes allow otherwise impossible opportunities for material kinds of damnation and reveal surprising limitations on metaphysical objections to Hell. Prima facie, eternal damnation requires either infinite amounts of time or time for the damned to speed-up arbitrarily. However, spatiotemporally finite ‘time travel’ universes can host unending personal torment for infinitely many physical beings, while keeping fixed finite limits on rates of temporal passage. Such ‘Hilbert's Inferno’ spacetimes suggest neither materialism nor the finitude of time and space need forbid Hell. A material Hell can be spatiotemporally finite yet eternal for its inhabitants. Hilbert's Inferno also sheds light on Hell's location and accessibility, and shows that some spacetimes are intrinsically better suited to punishment than reward.