In this fascinating book, mathematician Ed Beltrami takes a close enough look at randomness to make it mysteriously disappear. The results of coin tosses, it turns out, are determined from the start, and only our incomplete knowledge makes them look random. "Random" sequences of numbers are more elusive, but Godels undecidability theorem informs us that we will never know. Those familiar with quantum indeterminacy assert that order is an illusion, and that the world is fundamentally random. Yet randomness is also an illusion. Perhaps order and randomness, like waves and particles, are only two sides of the same (tossed) coin.
Author(s): Edward Beltrami
Edition: 1
Publisher: Copernicus
Year: 2012
Language: English
Commentary: Softcover reprint of the original 1st ed. 1999
Pages: 221
City: New York
Tags: Random; Chance; Probability; Large Numbers; Uncertainty; Entropy; Janus-Faced Randomness; Algorithmic Randomness; Algorithmic Complexity; Algorithmic Undecidability; Algorithmic Probability
[1]
The Taming of Chance 1
From Unpredictable to Lawful 2
Probability 9
Order in the Large 14
The Normal Law 18
Is It Random? 25
More About the Law of Large Numbers 30
Where We Stand Now 33
[2]
Uncertainty and Information 35
Messages and Information 36
Entropy 40
Messages, Codes, and Entropy 44
Approximate Entropy 53
Again, Is It Random? 58
The Perception of Randomness 62
[3]
Janus-Faced Randomness 65
Is Determinism an Illusion? 66
Generating Randomness 77
Janus and the Demons 82
[4]
Algorithms, Information, and Chance 91
Algorithmic Randomness 92
Algorithmic Complexity and Undecidability 102
Algorithmic Probability 109
[5]
The Edge of Randomness 117
Between Order and Disorder 118
Self-Similarity and Complexity 129
What Good is Randomness? 143
Sources and Further Readings 145
Technical Notes 153
Appendix A: Geometric Sums 179
Appendix B: Binary Numbers 183
Appendix C: Logarithims 189
References 191
Index 197
