Supertask

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 [1].

External References

• Article on Supertasks in Standford Encyclopedia of Philosophy