An Incompleteness Theorem for Calculating the Future
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.
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|Date of creation:||Mar 1996|
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Web page: http://www.santafe.edu/sfi/publications/working-papers.html
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