In mathematics and philosophy, a supertask is a task involving an infinite number of steps, completed in a finite amount of time. The term supertask was coined by Thompson.
Examples of supertasks:
- Thompson's lamp -- a lamp can be either on or off. Begin with it on at time t = 0. At time t = 1/2, switch it off; at time t = 1/2 + 1/4, switch it on again; and so on. Is the lamp on or off at time t = 1?
- the addition of new guests to Hilbert's Grand Hotel.
Some philosophical issues of supertasks include:
- what is a supertask? There is a dispute whether the running of Achilles, in Zeno of Elea's paradox, constitutes a supertask.
- are supertasks physically possible?
If supertasks are physically possible, then the truth or falsehood of unknown propositions of number theory
, such as Goldbach's conjecture
, could be determined in a finite amount of time by a brute force search of the set
of all natural numbers
. Hence, all propositions of arithmetic
would be decidable.
In computer science, it has a different, unrelated meaning .