In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time.
Thus it follows, according to Zeno, that motion (travelling a non-zero distance in finite time) is a supertask.
Common sense seems to decree that Achilles will catch up with the tortoise after exactly 1 second, but Zeno argues that this is not the case.
While these distances will grow very small, they will remain finite, while Achilles' chasing of the tortoise will become an unending supertask.
[5] Paul Benacerraf believes that supertasks are at least logically possible despite Thomson's apparent contradiction.
Benacerraf agrees with Thomson insofar as that the experiment he outlined does not determine the state of the lamp at t = 1.
[citation needed] Most of the modern literature comes from the descendants of Benacerraf, those who tacitly accept the possibility of supertasks.
For example, McLaughlin claims that Thomson's lamp is inconsistent if it is analyzed with internal set theory, a variant of real analysis.
If supertasks are possible, then the truth or falsehood of unknown propositions of number theory, such as Goldbach's conjecture, or even undecidable propositions could be determined in a finite amount of time by a brute-force search of the set of all natural numbers.
Some have argued this poses a problem for intuitionism, since the intuitionist must distinguish between things that cannot in fact be proven (because they are too long or complicated; for example Boolos's "Curious Inference"[6]) but nonetheless are considered "provable", and those which are provable by infinite brute force in the above sense.
However, such a design would ultimately fail, as eventually the distance between the contacts would be so small as to allow electrons to jump the gap, preventing the circuit from being broken at all.
The impact of supertasks on theoretical computer science has triggered some new and interesting work, for example Hamkins and Lewis – "Infinite Time Turing Machine".
A. Benardete’s “Paradox of the Gods”:[9] A man walks a mile from a point α.
Grim reaper 2 is disposed to kill you with a scythe at 12:30 pm, if and only if you are still alive then, taking 15 minutes about it.
[12]It has gained significance in philosophy via its use in arguing for a finite past, thereby bearing relevance to the Kalam cosmological argument.
This replica will in turn create an even faster version of itself with the same specifications, resulting in a supertask that finishes after an hour.
However, Davies also points out that – due to fundamental properties of the real universe such as quantum mechanics, thermal noise and information theory – his machine cannot actually be built.