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Randomness and Undecidability in Physics
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Algorithmic physics is the field in which physical systems are identified with computation processes. This book contains a brief outline of algorithmic physics, in particular of algorithmics, automata theory coding and information theory, as well as algorithmic information theory. The author relates physical entities to concepts in computer science, logic and mathematics, and introduces the concept of a theoretical model "from within" an artificial computer world and "from the outside". Chaos is characterized by both algorithmic undecidability and randomness. Godel incompleteness is translated into physical undecidability and unpredictability. It is shown that the behaviour of deterministic processes is generally impossible to predict even if their evolution law and initial states are exactly known. Several mathematical concepts of randomness are discussed with respect to their applicability for a characterization of chaotic, physical motion.
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