## 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

**the book details :**

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