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An Incompleteness Theorem for Calculating the Future

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  • David H. Wolpert

Abstract

This paper proves that one can not build a computer which can, for any physical system, take the specification of that system's state as input and then correctly predict its future state before that state actually occurs. Loosely speaking, this means that one can not build a physical computer which can be assured of "processing information faster than the universe." This result holds even if one restricts one's attention to predicting the states of systems which are finite, purely classical, and obey dynamics which is not chaotic, and even if one uses an infinitely fast, infinitely dense computer. Key words. uncompatibility, incompleteness, time-series analysis, indecidability.

Suggested Citation

  • David H. Wolpert, 1996. "An Incompleteness Theorem for Calculating the Future," Working Papers 96-03-008, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:96-03-008
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    Cited by:

    1. Koppl, Roger, 2010. "Some epistemological implications of economic complexity," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 859-872, December.
    2. Koppl, Roger G., 1996. "It is high time we take our ignorance more seriously," International Review of Financial Analysis, Elsevier, vol. 5(3), pages 259-272.

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