Supertask
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In philosophy, a supertask is a task involving infinitely many steps completed in a finite amount of time. The term supertask was coined by philosopher James F. Thomson.
Examples of supertasks:
- Thomson's lamp: consider a lamp that 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?
- Hilbert's paradox of the Grand Hotel: how many guests can be added to an infinitely large hotel that is already full?
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. This would, however, be in contradiction with the Church-Turing thesis.
External links
- Article on Supertasks in Stanford Encyclopedia of Philosophy (http://plato.stanford.edu/entries/spacetime-supertasks/)
References
- Thomson, J., 1954-55, ‘Tasks and Super-Tasks’, Analysis, XV, pp. 1-13.
In computer science, supertask has a different meaning, unrelated to its meaning in mathematics and philosophy. [1] (http://www.cs.unc.edu/~anderson/papers/euro03b.pdf).sl:supernaloga