Randomness and Undecidability in Physics

By: K Svozil

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Hardcover | 1 December 1992

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Hardcover
308 Pages

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26.04 x 17.78 x 2.54

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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.

Industry Reviews

"The interaction between computer science and physics has become more and more visible. Indeed, physical systems may be perceived as computational processes (according to some authors, physical systems exactly correspond to specific computations), and, conversely, computers are physical systems, not only in the crude sense of their hardware, but as a medium to virtual realities. Svozil's text is the first monograph devoted, in a technical sense, to this topic, and in the reviewer's opinion the author has succeeded excellently in his project. The book represents a valuable contribution toward a global understanding of computers and physics; the topic presented in its entirely and placed in perspective for researchers, students, and practitioners alike." Cristian Calude

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Non-Fiction Mathematics Applied Mathematics Stochastics Chaos Theory Science Physics Booktopia Publisher Services World Scientific Publishing

Preface
List of symbols
Algorithmic physics: the Universe as a computer	p. 1
Algorithmics and recursive function theory	p. 3
Mechanism and determinism	p. 33
Discrete physics	p. 37
Source coding	p. 45
Lattice theory	p. 51
Extrinsic-intrinsic concept	p. 73
Algorithmic information	p. 83
Computational complexity	p. 99
Undecidability	p. 107
Classical results	p. 109
Complementarity	p. 127
Extrinsic indeterminism	p. 177
Intrinsic indeterminism	p. 181
Weak physical chaos	p. 189
Randomness	p. 191
Randomness in mathematics	p. 193
Random fractals and 1/f noise	p. 203
Chaotic systems are optimal analogues of themselves	p. 215
Quantum chaos	p. 223
Algorithmic entropy	p. 231
Epilogue: Afterthoughts, speculations and metaphysics	p. 243
A Program code	p. 249
Bibliography	p. 271
Index	p. 290
Table of Contents provided by Blackwell. All Rights Reserved.

Randomness and Undecidability in Physics

At a Glance

Hardcover

Industry Reviews

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How to return your order

Defective items

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