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EmergenceContemporary Readings in Philosophy and Science$
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Mark A. Bedau and Paul Humphreys

Print publication date: 2008

Print ISBN-13: 9780262026215

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262026215.001.0001

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Undecidability and Intractability in Theoretical Physics

Undecidability and Intractability in Theoretical Physics

Chapter:
(p.387) 21 Undecidability and Intractability in Theoretical Physics
Source:
Emergence
Author(s):

Stephen Wolfram

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262026215.003.0025

This chapter explores some fundamental consequences of the correspondence between physical process and computations. Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be considered formally undecidable. The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation that reproduce the outcome without tracing each step. Computational irreducibility is common among the systems investigated in mathematics and computation theory, but it may well be the exception rather than the rule, since most physical questions may be answerable only through irreducible amounts of computation.

Keywords:   physical process, computation, physical system, theoretical physics, calculation, computational irreducibility, computation theory

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