RANDOMNICITY: Rules and Randomness in the Realm of the Infinite

by Tsonis, Anastasios A.

• ISBN13: 9781848161979
• ISBN10: 1848161972
• Format: Hardcover
• Copyright: 2008-11-30
• Publisher: World Scientific Pub Co Inc

Summary

"This unique book explores the definition, sources and role of randomness. A joyful discussion with many non-mathematical and mathematical examples leads to the identification of three sources of randomness: randomness due to irreversibility which inhibits us from extracting whatever rules may underlie a process, randomness due to our inability to have infinite power (chaos), and randomness due to many interacting systems. Here, all sources are found to have something in common: infinity. The discussion then moves to the physical system (our universe). Through the quantum mechanical character of small scales, the second law of thermodynamics and chaos, randomness is shown to be an intrinsic property of nature - this is consistent with the three sources of randomness identified above. Finally, an explanation is given as to why rules and randomness cannot exist by themselves, but instead have to coexist. Many examples are presented, ranging from pure mathematical to natural and social processes, that clearly demonstrate how the combination of rules and randomness produces the world we live in."--BOOK JACKET.

Table of Contents

Preface	p. vii
Acknowledgements	p. ix
The Three Parts of Everything	p. 1
Gödel Visits Escher's Studio	p. 3
Gödel's Theorem	p. 10
Slippery Road	p. 19
Fuller than Full	p. 27
Cantor Would Have Been Pleased	p. 34
Sources of Randomness	p. 39
A Private Lesson a Long, Long Time Ago	p. 41
The Five Faces of Order	p. 47
Randomness of the First Kind	p. 55
Randomness of the Second Kind	p. 59
Randomness of the Third Kind	p. 65
Randomness in the Universe	p. 69
From Aristotle to Einstein	p. 71
The World According to an Electron	p. 76
Chaos	p. 86
The Supreme Law	p. 91
Randomness of the Fourth Kind?	p. 98
Connections	p. 102
Allowed Behaviors	p. 107
The Emergence of Real World	p. 109
The Fractal Character of Nature	p. 111
Physics Plus Randomness	p. 129
Stochastic Processes	p. 135
Self-Organization	p. 138
The Blueprint of Life	p. 140
Human Products and Social Phenomena	p. 144
The Principle of Minimum Energy Consumption	p. 159
The Role of Randomness	p. 161
Efficiency, Paradoxes and Beauty	p. 163
In Closingà	p. 173
Notes and References	p. 175
Index	p. 189
Table of Contents provided by Ingram. All Rights Reserved.