Randomnicity: Rules And Randomness In The Realm Of The Infinite

by Anastasios A Tsonis

Overview

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.

Product Details

ISBN-13:	9781848162051
Publisher:	Imperial College Press
Publication date:	09/24/2008
Pages:	204
Product dimensions:	5.90(w) x 8.80(h) x 0.60(d)

Table of Contents

Preface vii

Acknowledgements ix

Part I The Three Parts of Everything 1

1 Gödel Visits Escher's Studio 3

2 Gödel's Theorem 10

3 Slippery Road 19

4 Fuller than Full 27

5 Cantor Would Have Been Pleased 34

Part II Sources of Randomness 39

6 A Private Lesson a Long, Long Time Ago 41

7 The Five Faces of Order 47

8 Randomness of the First Kind 55

9 Randomness of the Second Kind 59

10 Randomness of the Third Kind 65

Part III Randomness in the Universe 69

11 From Aristotle to Einstein 71

12 The World According to an Electron 76

13 Chaos 86

14 The Supreme Law 91

15 Randomness of the Fourth Kind? 98

16 Connections 102

17 Allowed Behaviors 107

Part IV The Emergence of Real World 109

18 The Fractal Character of Nature 111

19 Physics Plus Randomness 129

20 Stochastic Processes 135

21 Self-Organization 138

22 The Blueprint of Life 140

23 Human Products and Social Phenomena 144

24 The Principle of Minimum Energy Consumption 159

Part V The Role of Randomness 161

25 Efficiency, Paradoxes and Beauty 163

In Closing . . . 173

Notes and References 175

Index 189