Hilbert’s Inferno

hilbert-inferno-omni-magazine“Hell may be the most interesting part of Dante’s famous poem, but its physical existence has always been a topic of debate among philosophers and theologians. If either space or time is finite—a distinct possibility in our current theories of cosmology—how can there be room for a potentially infinite number of sinners for eternity? In what he admits is a speculative proposal, University of Edinburgh philosopher Alasdair Richmond suggests that a hell large enough for an infinite number of the damned could be contained within the boundaries of a finite space, and could provide infinitely-long punishment, even if time itself is finite—but only with the help of time travel. The quite literally devilish trick is a kind of time loop, but not an exact loop. (That would mean that the damned merely suffer through the same experience over and over, without any awareness of the eternal nature of their plight—which is not suffering enough for the traditional idea of Hell.) If the loop shifts and the gap shrinks just the tiniest bit each time around, you end up with an ever-tightening time spiral. You can fit an infinite number of spirals in a tiny amount of space the same way an infinite number of points lie between any two other points on a line. This hell, which Richmond calls ‘Hilbert’s Inferno’ (for pioneering mathematician David Hilbert), might deliver truly eternal torment to an infinite population of sufferers, while the non-suffering and temporally finite universe moves steadily onward, toward its own non-judgmental doom.” — Omni Magazine (December 12, 2017)

Richmond’s 2013 paper can be accessed in the Wiley Online Library (institutional login required).

Pascal’s Wager 2.0


“[…] But the ethical value is a matter of my own judgment, independent of religious authority. And the understanding may be only a partial illumination that does not establish the ultimate truth of the ideas that provide it, as, for example, both Dante and Proust help us understand the human condition, despite their conflicting intellectual frameworks. None of this will interfere with a commitment to intellectual honesty. […]”    –Gary Gutting, The New York Times, September 28, 2015