The World Is Built On Probability
This book begins with a talk between myself and an imaginary reader about the role of chance and ends with another talk about the relationship between randomness and symmetry. The text is divided into two major parts. The first is on the concept of probability and considers the various applications of probability in practice, namely, making decisions in complicated situations, organizing queues, participating in games, optimizing the control of various processes, and doing random searches. The basic notions of cybernetics, information theory, and such comparatively new fields as operations research and the theory of games are given. The aim of the first part is to convince the reader that the random world begins directly in his own living room because, in fact, all modern life is based on probabilistic methods.
The second part shows how fundamental chance is in Nature using the probabilistic laws of modern physics and biology as examples. Elements of quantum mechanics are also involved, and this allows me to demonstrate how probabilistic laws are basic to microscopic phenomena. The idea was that bypassing from the first part of the book to the second one, the reader would see that probability is not only around us but is at the basis of everything. patterns.
Contents:
Part One
Introduction 9
Tamed Chance 17
Chapter 1
Mathematics of Randomness 18
Probability 18
Random Numbers 26
Random Events 30
Discrete Random Variables 34
Continuous Random Variables 42
Random Numbers 26
Random Events 30
Discrete Random Variables 34
Continuous Random Variables 42
Chapter 2
Decision Making 44
These Difficult Decisions 46
Random Processes with Discrete States 50
Queueing Systems 55
Method of Statistical Testing 63
Games and Decision Making 69
These Difficult Decisions 46
Random Processes with Discrete States 50
Queueing Systems 55
Method of Statistical Testing 63
Games and Decision Making 69
Chapter 3
Control and Self-control 79
The Problem of Control 79
From the "Black Box" to Cybernetics 81
Information 84
Selection of Information from Noise 94
From the "Black Box" to Cybernetics 81
Information 84
Selection of Information from Noise 94
On the Way to a Stochastic Model of the Brain 99
part two
Fundamentality of the Probability Laws 105
Chapter 4
Probability in Classical Physics 106
Thermodynamics and Its Puzzles 106
Molecules in a Gas and Probability 115
Pressure and Temperature of an ideal Gas 124
Fluctuations 127
Entropy and Probability 132
Entropy and Information 138
Fluctuations 127
Entropy and Probability 132
Entropy and Information 138
Chapter 5
Probability in the Microcosm 142
Spontaneous Micropro-
cesses 1 42
From Uncertainty Relations to
the Wave Function 149
Interference and Summing Prob-
ability Amplitudes 154
Probability and Causality 160
the Wave Function 149
Interference and Summing Prob-
ability Amplitudes 154
Probability and Causality 160
Chapter 6
Probability in Biology 164
Introduction 164
The Patterns After the Random Combination of Genes in Cross-breeding 169
Mutations 176
The Patterns After the Random Combination of Genes in Cross-breeding 169
Mutations 176
Evolution Through the Eyes of Geneticists 179
A Concluding Conversation 184
Recommended Literature 189
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