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Supertask

From Academic Kids

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

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

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