|
In computer science, supertask has a different, unrelated meaning to the meaning in mathematics and philosophy. See [1] (http://www.cs.unc.edu/~anderson/papers/euro03b.pdf).
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 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. Hence, all propositions of arithmetic would be decidable.
References
- Thomson, J., 1954-55, Tasks and Super-Tasks, Analysis, XV, pp. 1-13.
External links
|
