In computer science, supertask has a different, unrelated meaning to the meaning in mathematics and philosophy. See [1].

In 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 the philosopher James F. Thomson.

Examples of supertasks:

• Thomson'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. Of course, this would be in contradiction with the Church-Turing thesis.

References

• Thomson, J., 1954-55, ‘Tasks and Super-Tasks’, Analysis, XV, pp. 1-13.

External links

• Article on Supertasks in Stanford Encyclopedia of Philosophy