supertasks physically impossible. Super Turing machines The impact of supertasks on theoretical computer science has triggered some new and interesting work, for example Hamkins and Lewis "Infinite Time Turing Machine". Prominent supertasks Ross–Littlewood paradox Suppose there is a jar capable of containing infinitely many marbles and an infinite collection of marbles labelled 1, 2, 3, and so on. At time t = 0, marbles 1 through 10 are placed in the jar and marble 1 is taken out. At t = 0.5, marbles 11 through 20 are placed in the jar and marble 2 is taken out; at t = 0.75, marbles 21 through 30 are put in the jar and marble 3 is taken out; and in general at time t = 1 − 0.5n, marbles 10n + 1 through 10n + 10 are placed in the jar and marble n + 1 is taken out. How many marbles are in the jar at time t = 1? One argument states that there should be infinitely many marbles in the jar, because at each step before t = 1 the number of marbles increases from the previous step and does so unboundedly. A second argument, however, shows that the jar is empty. Consider the following argument: if the jar is non-empty, then there must be a marble in the jar. Let us say that that marble is labeled with the number n. But at time t = 1 − 0.5n - 1, the nth marble has been taken out, so marble n cannot be in the jar. This is a contradiction, so the jar must be empty. The Ross–Littlewood paradox is that here we have two seemingly perfectly good arguments with completely opposite conclusions. Benardete's paradox There has been considerable interest in J. A. Benardete’s “Paradox of the Gods”: Grim Reaper paradox Inspired by J. A. Benardete’s paradox regarding an infinite series of assassins, David Chalmers describes the paradox as follows: It has gained significance in philosophy via its use in arguing for a finite past, thereby bearing relevance to the kalam cosmological argument. Davies' super-machine Proposed by E. Brian Davies, this is a machine that can, in the space of half an hour, create an exact replica of itself that is half its size and capable of twice its replication speed. This replica will in turn create an even faster version of itself with the same specifications, resulting