An Incompleteness Theorem for Calculating the Future
AbstractThis 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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Bibliographic InfoPaper provided by Santa Fe Institute in its series Working Papers with number 96-03-008.
Date of creation: Mar 1996
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- Koppl, Roger, 2010. "Some epistemological implications of economic complexity," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 859-872, December.
- 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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