Feynman's rainbow [The search for beauty in physics and in life] Leonard Mlodinov

“(Im)perfect chance: how chance rules our lives” Leonard Mlodinov (translated by O. Dementievskaya)

"(Im)Perfect Randomness: How Randomness Governs Our Lives"

Leonard Mlodinov

(translated by O. Dementievskaya)

(Im)perfect accident. How chance rules our lives

Dedicated to the three wonders of chance:

Olivia, Nikolai and Alexei ...

and also Sabina Yakubovich

How chance rules our lives

Several years ago, a Spaniard won the national lottery; his ticket number ended with the number 48. Proud of his “achievement,” the Spaniard spoke about how he managed to get so rich. “Seven nights in a row I dreamed of a seven,” he said, “and seven is seven and there are forty-eight” (1). Those who remember the multiplication table better will probably grunt: the Spaniard made a mistake, but we all form our own vision of the world, through which we pass our sensations, process them, fishing out meaning from the ocean of information in everyday life. And at the same time we often make mistakes, and our mistakes, although not as obvious as those of this Spaniard, are no less significant.

It was known as early as the 1930s that intuition was of little use in a situation of uncertainty: researchers noticed that people were not able to build a sequence of numbers that would fit mathematical criteria of randomness, nor to say for sure whether a series of numbers was chosen randomly. Over the past decades, a new scientific discipline has emerged that studies the formation of a person's judgment, his decision-making in conditions of incomplete, insufficient information. Studies have shown that when it comes to chance, the human thought process misfires. The most diverse branches of knowledge were involved: from mathematics to traditional sciences, from cognitive psychology to behavioral economics and modern neuroscience. But although the results of the research were recently awarded the Nobel Prize (in economics), on the whole they did not become public knowledge, did not go beyond the academic circles. This book is an attempt to rectify the situation. It will talk about the principles that underlie randomness, about their development, about how they affect politics, business, medicine, economics, sports, leisure and other areas of our lives. In addition, the book talks about exactly how a person makes his choice, about the processes that force a person in a situation of chance or uncertainty to come to an erroneous judgment and make stupid decisions based on it.

The lack of data unwittingly gives rise to conflicting explanations. This is why it has been so difficult to confirm the fact of global warming, this is the reason why drugs sometimes are first declared safe and then declared out of the game, and most likely because of this, not everyone will agree with my observation: chocolate milkshakes - an integral part of a heart-strengthening diet. Unfortunately, the misinterpretation of data leads to numerous negative consequences, both large and small. For example, both doctors and patients often misunderstand statistics on the effectiveness of drugs and the importance of medical trials. Parents, teachers, and students misjudge the importance of exams as something like a test of learning ability, and wine tasters make the same mistakes when evaluating wines. Investors, based on the performance of mutual funds over a certain period, come to the wrong conclusions.

There is a widespread belief in the world of sports, based on intuitive experience of correlation, that the victory or defeat of a team largely depends on the professional qualities of the coach. As a result, after the team loses, the coach is often fired. However, recent mathematical analysis suggests that, by and large, these layoffs do not affect the nature of the game - minor improvements achieved by changing coaches are usually offset by random changes in the game of individual players and the whole team (2). The same thing happens in the world of corporations: it is believed that the CEO has superhuman abilities, can create or destroy a company, but in the example of such companies as Kodak, Lucent, Xerox, you are convinced again and again that power is deceptive . In the 1990s Gary Wendt was considered one of the most successful business people, he managed General Electric Capital, headed by Jack Welch. When Wendt was hired by Conseco to improve the company's dire financial situation, he asked for $45 million, putting pressure on his reputation. During the year, the company's shares tripled - investors were full of optimism. Two years later, Wendt suddenly quit, Conseco went bankrupt, and the shares sold for next to nothing (3). What, Wendt got an impossible task? Maybe he lost interest in the case, suddenly caught fire with the desire to become the first among bowling professionals? Or was Wendt crowned on dubious assumptions? Based, for example, on the fact that a manager has almost absolute ability to influence the company. Or that a single success in the past serves as a reliable guarantee of achievements in the future. Be that as it may, it is impossible to give unambiguous answers to these questions without owning the whole situation. I will return to this example later, and, more importantly, I will talk about what is needed to recognize signs of randomness.

It is not easy to swim against the current of human intuition. We will see that the human mind is arranged in a certain way - for each event, he is looking for a very specific reason. And it is difficult for him to take into account the influence of factors that are not correlated or random. Thus, the first step is to realize that success or failure is sometimes not the result of exceptional ability or lack of it, but, as the economist Armen Alchian put it, "accidental circumstances" (4). And although random processes underlie the structure of nature and wherever they are found, most people do not understand them and simply do not attach importance to them.

The title of the last chapter of the book, "Drunken Walk," comes from a mathematical term describing random trajectories, such as the spatial motion of molecules constantly colliding with their fellows. It's a kind of metaphor for our lives, our journey from college up the career ladder, from single life to family life, from the first hole on the golf course to the nineteenth. Surprisingly, this metaphor is also applicable to mathematics - the mathematics of random walks and methods of its analysis can be useful in everyday life. My task is to shed light on the role of chance in the world around us, to demonstrate how you can recognize its action in order to penetrate deeper into the essence of being. I hope that after this journey into the world of chance, the reader will see life in a new light and understand it better.

UNDER A LIGHT OF RANDOMNESS

I remember as a teenager during Shabbat I looked at the yellow flames - they danced randomly over the white cylinders of paraffin candles. I was too young to think of any kind of romance by candlelight, but still the flame was fascinating - its flickering gave rise to all sorts of bizarre images. Images shifted, merged, grew and dwindled, all without an obvious reason or plan. Of course, I suspected a certain rhythm, a design, a certain pattern, which scientists are able to predict and explain with the help of mathematics, at the basis of the movements of the flame. “Life is completely different,” my father told me then. “Sometimes things happen that you can’t predict.” My father told me about those times when he was in Buchenwald, a Nazi concentration camp. The prisoners were kept starving; one day my father stole a loaf of bread from a bakery. At the insistence of the baker, the Gestapo gathered everyone who could commit such a crime, lining up in a row. "Who stole the bread?" asked the baker. No one confessed, and then the baker told the guards to shoot one after the other - until they shot everyone or until someone confessed. And the father, saving the others, stepped forward. Telling, he did not try to present himself as a hero at all - he was threatened with execution in any case. But the baker unexpectedly left his father alive, moreover, he made him his assistant, and this is a warm place. “Accident, nothing more,” my father told me. “And it has nothing to do with you, but if everything had turned out differently, you would never have been born.” Then it occurred to me: it turns out that I owe my existence to Hitler - the Nazis killed my father's wife and two younger children, destroying his past. If not for the war, my father would not have emigrated to America, would not have met my mother in New York, who was also a refugee, and would not have produced me and my two brothers.

(Im)perfect accident. How chance rules our lives Leonard Mlodinov

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Title: (Im)perfect accident. How chance rules our lives

About the book “(Im)perfect accident. How Chance Governs Our Life Leonard Mlodinov

In the book “(Not) perfect accident. How chance rules our life" Mlodinov easily introduces everyone to the theory of probability, the theory of random walks, scientific and applied statistics, the history of the development of these all-pervasive theories, as well as the importance of chance, regularity and the inevitable confusion between them in our daily life. .

This book is a great way to shake the old days and refresh some of the course of higher mathematics, the history of natural science, astronomy and statistics for those who studied these wondrous disciplines in universities; understandable and accessible outlined the foundations of the theory of probability and its applicability in everyday circumstances (with numerous examples) for those who were not lucky enough to study them specially; finally, a professional and friendly tipster gnawing at the granite of the relevant sciences at the moment.

On our site about books, you can download the site for free without registration or read the online book “(Not) perfect accident. How Chance Governs Our Life” by Leonard Mlodinov in epub, fb2, txt, rtf, pdf formats for iPad, iPhone, Android and Kindle. The book will give you a lot of pleasant moments and a real pleasure to read. You can buy the full version from our partner. Also, here you will find the latest news from the literary world, learn the biography of your favorite authors. For novice writers, there is a separate section with useful tips and tricks, interesting articles, thanks to which you can try your hand at writing.

Quotes from the book “(Not) perfect accident. How Chance Governs Our Life Leonard Mlodinov

A fascinating lesson in probabilistic forecasting.

Theories of "normal accidents".

Historians-traditionalists and historians-socialists.

© 2008, Leonard Mlodinow

© 2009, Studio Art. Lebedev

© 2013, Livebook

© 2009, O. Dementievskaya, translation

All rights reserved. No part of the electronic version of this book may be reproduced in any form or by any means, including posting on the Internet and corporate networks, for private and public use, without the written permission of the copyright owner.

©The electronic version of the book was prepared by Litres (www.litres.ru)

Dedicated to three miracles of chance: Olivia, Nikolai and Alexei ... and also Sabina Yakubovich

Several years ago, a Spaniard won the national lottery; his ticket number ended with the number 48. Proud of his “achievement,” the Spaniard spoke about how he managed to get so rich. “Seven nights in a row I dreamed of a seven,” he said, “and seven is seven and there are forty-eight.” Those who remember the multiplication table better will probably grunt: the Spaniard made a mistake, but we all form our own vision of the world, through which we pass our sensations, process them, fishing out meaning from the ocean of information in everyday life. And at the same time we often make mistakes, and our mistakes, although not as obvious as those of this Spaniard, are no less significant.

It was known as early as the 1930s that intuition was of little use in a situation of uncertainty: researchers noticed that people were not able to build a sequence of numbers that would fit mathematical criteria of randomness, nor to say for sure whether a series of numbers was chosen randomly. Over the past decades, a new scientific discipline has emerged that studies the formation of a person's judgment, his decision-making in conditions of incomplete, insufficient information. Studies have shown that when it comes to chance, the human thought process misfires. The most diverse branches of knowledge were involved: from mathematics to traditional sciences, from cognitive psychology to behavioral economics and modern neuroscience. But although the results of the research were recently awarded the Nobel Prize (in economics), on the whole they did not become public knowledge, did not go beyond the academic circles. This book is an attempt to rectify the situation. It will talk about the principles that underlie randomness, about their development, about how they affect politics, business, medicine, economics, sports, leisure and other areas of our lives. In addition, the book talks about exactly how a person makes his choice, about the processes that force a person in a situation of chance or uncertainty to come to an erroneous judgment and make stupid decisions based on it.

The lack of data unwittingly gives rise to conflicting explanations. This is why it has been so difficult to confirm the fact of global warming, this is the reason why drugs sometimes are first declared safe and then declared out of the game, and most likely because of this, not everyone will agree with my observation: chocolate milkshakes - an integral part of a heart-strengthening diet. Unfortunately, the misinterpretation of data leads to numerous negative consequences, both large and small. For example, both doctors and patients often misunderstand statistics on the effectiveness of drugs and the importance of medical trials. Parents, teachers, and students misjudge the importance of exams as something like a test of learning ability, and wine tasters make the same mistakes when evaluating wines. Investors, based on the performance of mutual funds over a certain period, come to the wrong conclusions.

There is a widespread belief in the world of sports, based on intuitive experience of correlation, that the victory or defeat of a team largely depends on the professional qualities of the coach. As a result, after the team loses, the coach is often fired. However, recent mathematical analysis suggests that, by and large, these layoffs do not affect the nature of the game - minor improvements achieved by changing coaches are usually offset by random changes in the game of individual players and the whole team. The same thing happens in the world of corporations: it is believed that the CEO has superhuman abilities, can create or destroy a company, but in the example of such companies as Kodak, Lucent, Xerox, you are convinced again and again that power is deceptive . In the 1990s Gary Wendt was considered one of the most successful business people, he managed General Electric Capital, headed by Jack Welch. When Wendt was hired by Conseco to improve the company's dire financial situation, he asked for $45 million, putting pressure on his reputation. During the year, the company's shares tripled - investors were full of optimism. Two years later, Wendt suddenly quit, Conseco went bankrupt, and the shares sold for next to nothing. What, Wendt got an impossible task? Maybe he lost interest in the case, suddenly caught fire with the desire to become the first among bowling professionals? Or was Wendt crowned on dubious assumptions? Based, for example, on the fact that a manager has almost absolute ability to influence the company. Or that a single success in the past serves as a reliable guarantee of achievements in the future. Be that as it may, it is impossible to give unambiguous answers to these questions without owning the whole situation. I will return to this example later, and, more importantly, I will talk about what is needed to recognize signs of randomness.

It is not easy to swim against the current of human intuition. We will see that the human mind is arranged in a certain way - for each event, he is looking for a very specific reason. And it is difficult for him to take into account the influence of factors that are inconsistent or random. Thus, the first step is to realize that success or failure is sometimes not the result of exceptional ability or lack thereof, but, as the economist Armen Alchian puts it, "accidental circumstances." And although random processes underlie the structure of nature and wherever they are found, most people do not understand them and simply do not attach importance to them.

The title of the last chapter of the book, "Drunken Walk," comes from a mathematical term describing random trajectories, such as the spatial motion of molecules constantly colliding with their fellows. It's a kind of metaphor for our lives, our journey from college up the career ladder, from single life to family life, from the first hole on the golf course to the nineteenth. Surprisingly, this metaphor is also applicable to mathematics - the mathematics of random walks and methods of its analysis can be useful in everyday life. My task is to shed light on the role of chance in the world around us, to demonstrate how you can recognize its action in order to penetrate deeper into the essence of being. I hope that after this journey into the world of chance, the reader will see life in a new light and understand it better.

I remember as a teenager during Shabbat I looked at the yellow flames - they danced randomly over the white cylinders of paraffin candles. I was too small to think about some kind of romance by candlelight, but still the flame was fascinating - its flickering gave rise to all sorts of bizarre images. Images shifted, merged, grew and dwindled, all without an obvious reason or plan. Of course, I suspected a certain rhythm, a design, a certain pattern, which scientists are able to predict and explain with the help of mathematics, at the basis of the movements of the flame. “Life is completely different,” my father told me then. “Sometimes things happen that you can’t predict.” My father told me about those times when he was in Buchenwald, a Nazi concentration camp. The prisoners were kept starving; one day my father stole a loaf of bread from a bakery. At the insistence of the baker, the Gestapo gathered everyone who could commit such a crime, lining up in a row. "Who stole the bread?" the baker asked. No one confessed, and then the baker told the guards to shoot one by one until everyone was shot or until someone confessed. And the father, saving the others, stepped forward. Telling, he did not at all try to present himself as a hero - he was threatened with execution in any case. But the baker unexpectedly left his father alive, moreover, he made him his assistant, and this is a warm place. “An accident, nothing more,” my father told me. “And she has nothing to do with you, but if everything had turned out differently, you would never have been born.” Then it occurred to me: it turns out that it was Hitler that I owe my existence to - the Nazis killed my father's wife and two younger children, destroying his past. If not for the war, my father would not have emigrated to America, would not have met my mother in New York, who was also a refugee, and would not have produced me and my two brothers.

Leonard Mlodinov.

(Im)perfect accident. How chance rules our lives

© 2008, Leonard Mlodinow

© 2009, Studio Art. Lebedev

© 2013, Livebook

© 2009, O. Dementievskaya, translation

All rights reserved. No part of the electronic version of this book may be reproduced in any form or by any means, including posting on the Internet and corporate networks, for private and public use, without the written permission of the copyright owner.

©The electronic version of the book was prepared by Litres (www.litres.ru)

Dedicated to three miracles of chance: Olivia, Nikolai and Alexei ... and also Sabina Yakubovich

Prologue. How chance rules our lives

Several years ago, a Spaniard won the national lottery; his ticket number ended with the number 48. Proud of his “achievement,” the Spaniard spoke about how he managed to get so rich. “Seven nights in a row I dreamed of a seven,” he said, “and seven is seven and there are forty-eight.” 1
Stanley Meisler, “First in 1763: Spain Lottery – Not Even War Stops It”, Los Angeles Times, December 30, 1977.

Those who remember the multiplication table better will probably grunt: the Spaniard made a mistake, but we all form our own vision of the world, through which we pass our sensations, process them, fishing out meaning from the ocean of information in everyday life. And at the same time we often make mistakes, and our mistakes, although not as obvious as those of this Spaniard, are no less significant.

It was known as early as the 1930s that intuition was of little use in a situation of uncertainty: researchers noticed that people were not able to build a sequence of numbers that would fit mathematical criteria of randomness, nor to say for sure whether a series of numbers was chosen randomly. Over the past decades, a new scientific discipline has emerged that studies the formation of a person's judgment, his decision-making in conditions of incomplete, insufficient information. Studies have shown that when it comes to chance, the human thought process misfires. The most diverse branches of knowledge were involved: from mathematics to traditional sciences, from cognitive psychology to behavioral economics and modern neuroscience. But although the results of the research were recently awarded the Nobel Prize (in economics), on the whole they did not become public knowledge, did not go beyond the academic circles. This book is an attempt to rectify the situation. It will talk about the principles that underlie randomness, about their development, about how they affect politics, business, medicine, economics, sports, leisure and other areas of our lives.

In addition, the book talks about exactly how a person makes his choice, about the processes that force a person in a situation of chance or uncertainty to come to an erroneous judgment and make stupid decisions based on it.

The lack of data unwittingly gives rise to conflicting explanations. This is why it has been so difficult to confirm the fact of global warming, this is the reason why drugs sometimes are first declared safe and then declared out of the game, and most likely because of this, not everyone will agree with my observation: chocolate milkshakes - an integral part of a heart-strengthening diet. Unfortunately, the misinterpretation of data leads to numerous negative consequences, both large and small. For example, both doctors and patients often misunderstand statistics on the effectiveness of drugs and the importance of medical trials. Parents, teachers, and students misjudge the importance of exams as something like a test of learning ability, and wine tasters make the same mistakes when evaluating wines. Investors, based on the performance of mutual funds over a certain period, come to the wrong conclusions.

There is a widespread belief in the world of sports, based on intuitive experience of correlation, that the victory or defeat of a team largely depends on the professional qualities of the coach. As a result, after the team loses, the coach is often fired. However, the results of a recent mathematical analysis suggest that, in general, these dismissals do not affect the nature of the game - minor improvements achieved by changing coaches are usually offset by random changes in the game of individual players and the whole team. 2
About basketball: Michael Patrick Allen, Sharon K. Panian, and Roy E. Lotz, “Managerial Succession and Organizational Performance: A Recalcitrant Problem Revisited”, 24, no. 2 (June 1979): 167–80; about football: M. Craig Brown, “Administrative Succession and Organizational Performance: The Succession Effect”, Administrative Science Quarterly 27, no. 1 (March 1982): 1–16; about baseball: Oscar Grusky, “Managerial Succession and Organizational Effectiveness”, 69, no. 1 (July 1963): 21–31, and William A. Gamson and Norman A. Scotch, “Scapegoating in Baseball”, American Journal of Sociology 70, no. 1 (July 1964): 69–72; about American football: Ruud H. Koning, “An Econometric Evaluation of the Effect of Firing a Coach on Team Performance”, Applied Economics 35, no. 5 (March 2003): 555–64.

The same thing happens in the world of corporations: it is believed that the CEO has superhuman abilities, can create or destroy a company, but in the example of such companies as Kodak, Lucent, Xerox, you are convinced again and again that power is deceptive . In the 1990s Gary Wendt was considered one of the most successful business people, he managed General Electric Capital, headed by Jack Welch. When Wendt was hired by Conseco to improve the company's dire financial situation, he asked for $45 million, putting pressure on his reputation. During the year, the company's shares tripled - investors were full of optimism. Two years later, Wendt suddenly quit, Conseco went bankrupt, and the shares sold for next to nothing. 3
James Surowiecki, The Wisdom of Crowds(New York: Doubleday, 2004), pp. 218–19.

What, Wendt got an impossible task? Maybe he lost interest in the case, suddenly caught fire with the desire to become the first among bowling professionals? Or was Wendt crowned on dubious assumptions? Based, for example, on the fact that a manager has almost absolute ability to influence the company. Or that a single success in the past serves as a reliable guarantee of achievements in the future. Be that as it may, it is impossible to give unambiguous answers to these questions without owning the whole situation. I will return to this example later, and, more importantly, I will talk about what is needed to recognize signs of randomness.

It is not easy to swim against the current of human intuition. We will see that the human mind is arranged in a certain way - for each event, he is looking for a very specific reason. And it is difficult for him to take into account the influence of factors that are incommensurable or random. Thus, the first step is to realize that success or failure is sometimes not the result of exceptional ability or lack thereof, but, as the economist Armen Alchian puts it, “accidental circumstances.” 4
Armen Alchian, “Uncertainty, Evolution, and Economic Theory”, Journal of political economy 58, no. 3 (June 1950): 213.

And although random processes underlie the structure of nature and wherever they are found, most people do not understand them and simply do not attach importance to them.

The title of the last chapter of the book, "Drunken Walk," comes from a mathematical term describing random trajectories, such as the spatial motion of molecules constantly colliding with their fellows. It's a kind of metaphor for our lives, our journey from college up the career ladder, from single life to family life, from the first hole on the golf course to the nineteenth. Surprisingly, this metaphor is also applicable to mathematics - the mathematics of random walks and methods of its analysis can be useful in everyday life. My task is to shed light on the role of chance in the world around us, to demonstrate how you can recognize its action in order to penetrate deeper into the essence of being. I hope that after this journey into the world of chance, the reader will see life in a new light and understand it better.

Chapter 1

I remember as a teenager during Shabbat I looked at the yellow flames - they danced randomly over the white cylinders of paraffin candles. I was too small to think about some kind of romance by candlelight, but still the flame was fascinating - its flickering gave rise to all sorts of bizarre images. Images shifted, merged, grew and dwindled, all without an obvious reason or plan. Of course, I suspected a certain rhythm, a design, a certain pattern, which scientists are able to predict and explain with the help of mathematics, at the basis of the movements of the flame. “Life is completely different,” my father told me then. “Sometimes things happen that you can’t predict.” My father told me about those times when he was in Buchenwald, a Nazi concentration camp. The prisoners were kept starving; one day my father stole a loaf of bread from a bakery. At the insistence of the baker, the Gestapo gathered everyone who could commit such a crime, lining up in a row. "Who stole the bread?" the baker asked. No one confessed, and then the baker told the guards to shoot one by one until everyone was shot or until someone confessed. And the father, saving the others, stepped forward. Telling, he did not at all try to present himself as a hero - he was threatened with execution in any case. But the baker unexpectedly left his father alive, moreover, he made him his assistant, and this is a warm place. “An accident, nothing more,” my father told me. “And she has nothing to do with you, but if everything had turned out differently, you would never have been born.” Then it occurred to me: it turns out that it was Hitler that I owe my existence to - the Nazis killed my father's wife and two younger children, destroying his past. If not for the war, my father would not have emigrated to America, would not have met my mother in New York, who was also a refugee, and would not have produced me and my two brothers.

My father rarely mentioned the war. I didn’t realize why then, but over time I realized that every time my father talked about the horrors he endured, he did not do it to enlighten me, he tried to tell me something much more about life. War is an event of an extreme nature, but chance does not manifest itself at all in moments of extremes. The contours of our lives, like the flame of a candle, are constantly changing, being affected by a variety of random events that, together with our reactions to them, determine our destinies. It turns out that the course of life is difficult to predict and explain. About the same, looking at the Rorschach spot 5
Swedish psychiatrist. He invented a test named after him, which consists in interpreting a set of ink spots of various configurations and colors that have a certain meaning for diagnosing hidden attitudes, motives, and character traits. (Here and below - approx. Transl.)

You will see the Madonna, and I will see the platypus. Information business, legal, medical, sports, printed publications, the same assessments of your third grader can be understood in different ways. And yet, unlike the Rorschach stain, interpreting the role of chance, you can go the right way and the wrong way.

Often, in a situation of uncertainty, a person evaluates or makes a choice due to the intuitive processes involved. From the point of view of evolution, these processes are an unconditional step forward: a person had to hastily decide whether the saber-toothed tiger smiles, full and satisfied, or grins from hunger, looking at the person in front of him as a potential dish for lunch. But in the modern world, the alignment of forces is different, and these very intuitive processes are stalling. When a person is faced with modern "tigers", their usual ways of thinking may turn out to be far from optimal, if not completely inappropriate. This is not surprising to those who study the brain's reactions to uncertainty: numerous studies indicate a close connection between the areas of the human brain responsible for assessing the situation of uncertainty, and the areas responsible for reactions that are often considered the most irrational - emotions. For example, functional magnetic resonance imaging shows that risk and expected reward are assessed by subsystems of the brain's dopaminergic system, a mediator system that plays an important role in driving motivational and emotional processes. 6
Kerstin Preuschoff, Peter Bossaerts, and Steven R. Quartz, “Neural Differentiation of Expected Reward and Risk in Human Subcortical Structures”, Neuron 51 (August 3, 2006): 381–90.

Imaging also shows that the amygdala, among other things associated with the emotional state of a person, turns on when a person makes decisions in a situation of uncertainty. 7
Benedetto De Martino et al., “Frames, Biases, and Rational Decision-Making in the Human Brain”, Science 313 (August 4, 2006): 684–87.

The mechanisms for analyzing a situation with elements of uncertainty are quite difficult to understand and arose in the process of evolution and not without the influence of a specially arranged human brain, his personal experience, knowledge and emotions. In fact, the human response to uncertainty is so complex that sometimes different structures in the brain come to different conclusions and appear to be in conflict with each other, contesting dominance. For example, every three times out of four when you eat delicious shrimp, your face swells five times against its normal state; in this case, the "logical" left hemisphere of your brain will try to deduce a pattern. On the other hand, the “intuitive” right hemisphere simply commands: “Stay away from the shrimp!”. At least, that's what the researchers came to as a result of less painful experiments. This exciting activity is called probabilistic forecasting. Instead of fiddling with shrimp and histamine, you are shown a set of flashcards or light signals: green or, say, red flashes. Everything is arranged in such a way that the colors appear in random order, but in any case without any regularity. For example, red may light up twice as often as green, in a sequence like: red-red-green-red-green-red-red-green-green-red-red-red, etc. The subject's task is to in order to guess, after some time of observation, whether each subsequent flash will be red or green.

There are two main strategies that can be used in the game. One is to always name the color that you think appears most often. This method is preferred by rats and other animals not related to humans. If you adopt this strategy, you are guaranteed success to a certain extent, but at the same time you agree that you will not show the best results. For example, if green lights up at 75% and you choose to always say that color, your answers will be 75% correct. Another strategy is to "calculate" the ratio of green to red based on your observations. If green and red signals appear in a certain sequence, and you manage to calculate this sequence, this strategy will allow you to guess correctly every time. However, if the signals appear without any sequence, it is safer to stick to the first strategy. If green lights up 75% of the time, the second strategy will only guess correctly about 6 out of 10 times.

Usually a person tries to calculate a certain sequence; if it is not there, then the rats are better at this game. But there are people with certain postoperative brain lesions in which the interaction of the right and left hemispheres is excluded. If you set up an experiment with their participation and at the same time they see a color signal or a card only with their left eye, and answer only with their left hand, the right hemisphere of the brain will be involved. If during the experiment the subjects use the right eye and right hand, the left hemisphere is involved. As a result of such experiments, the researchers found that in the same subject, the right hemisphere more often guessed the color that lit up, and the left hemisphere tried to calculate a certain sequence of signals.

Few people have the skill of correct analysis and the right choice. However, like any skill, it can be improved with practice. Next, I will consider the role of chance in the world around us, ideas that have been formed for centuries and thanks to which this role is understandable, as well as factors that often lead us astray. The English philosopher and mathematician Bertrand Russell wrote:

“We all start with 'naive realism',” that is, with the doctrine that things are as they seem. We believe grass is green, rock is hard, and snow is cold. However, physics says that the greenness of grass, the hardness of stone and the coldness of snow are not the greenness, hardness and coldness that we know from our own experience, but something completely different. 8
Bertrand Russell, An Inquiry into Meaning and Truth. Tot. scientific ed. and note by E. E. Lednikov. - M .: Idea-Press: House of Intellectual Books, 1999

I propose to look through the magnifying glass of chance - it will become clear that many events in our lives actually look a little different than we might think.

In 2002, scientist Daniel Kahneman became the winner of the Nobel Prize in Economics. Economists these days are doing all sorts of things: they explain why teachers get such low salaries, why football teams are so expensive, how the data on physiological functions correct the size of pig farms (a pig defecates two to five times more than a human, so a pig farm in thousands of heads of waste are often more than from neighboring settlements) 9
Matt Johnson and Tom Hundt, “Hog Industry Targets State for Good Reason”, Vernon County (Wisconsin) Broadcaster, July 17, 2007

Despite the enormous amount of research done by economists, the 2002 Nobel Prize was notable in that Kahneman, who received it, was not an economist. He is a psychologist and for decades, together with the already deceased Amos Tversky, debunked all sorts of erroneous ideas about the theory of chance, which in turn gave rise to common misconceptions. They will be discussed in this book.

The most serious obstacle to understanding the role of chance in life is this: the basic principles of chance follow from everyday logic, and many of the consequences of these principles turn out to be counterintuitive. The research of Kahneman and Tverskoy was initiated by chance. In the mid 1960s. Kahneman, then an associate professor of psychology at the Hebrew University, agreed to do the rather boring job of lecturing Israeli Air Force instructors on the conventional wisdom on behavior modification as applied to the psychology of flight training. Kahneman argued that rewarding good behavior makes sense, but punishing mistakes does not. One of the listeners interrupted Kahneman and expressed his opinion, thanks to which Kahneman had an insight, and he delved into research for decades. 10
Kevin McKean discover, June 1985, pp. 22–31.

“Often I praised pilots for perfectly executed maneuvers, and what do you think? The next time they did much worse, - said the instructor. - I shouted at those who performed the maneuvers poorly - the next day they did much better. So don't tell me fairy tales about how rewards improve performance and punishment doesn't. I know from experience that this is not the case." Other instructors agreed with him. To Kahneman, the words of the instructor seemed not without meaning. At the same time, Kahneman trusted the results of experiments on animals, which showed that rewards can achieve more than punishment. He began to reflect on this apparent paradox. And then it dawned on him: the cry preceded the punishment, but, despite the obvious, did not cause it.

How is this possible? The answer to this question is the phenomenon of "regression to the mean". The bottom line is that in any series of random events, an out-of-the-ordinary event, most likely and by pure chance, will be followed by an ordinary event. The mechanism is this. Every pilot, to some extent, has the skill of flying a fighter aircraft. The improvement of this skill depends on many factors, including long-term training. Thus, although pilots slowly increase in skill during training, they will not achieve much in one flight. And any particularly successful or unsuccessful flight will depend heavily on luck. So if the pilot landed the car perfectly, as they say, jumped above his head, it is likely that his next flight will take place at a level much closer to his personal norm, that is, it does not matter. If the instructor, after the first flight, praised his ward, the results of the next flight will prove that the praise did not seem to benefit. However, if a pilot has an exceptionally bad landing—say, a car veers off the runway and hits a cafe, crashing into a cauldron of corn soup—the chances are high that next time he flies off much closer to his personal norm, that is, better. If the instructor, out of habit, yells at a bad flyer - they say that he should not control the plane, but turn the steering wheel of the truck - it will seem as if the suggestions had an effect. Thus, a very obvious picture emerges: the pilot flew well, he is praised, and the next flight is no good; the pilot flew off unimportantly, the instructor tells him everything he thinks about him, he corrects himself on the next flight. The instructors who came to Kahneman's lecture were sure that if you yell at the pilot properly, it will only benefit him. In fact, such a teaching technique does not change anything.

Such an intuitive error prompted Kahneman to think. He wondered: how common are such misconceptions? Do we, like those instructors, believe that harsh criticism has an educational effect on our children, increases the productivity of our subordinates? Are we delusional when faced with uncertainty? Kahneman knew that a person habitually tends to simplify a task that requires making a certain conclusion, and that the representation of probabilities on an intuitive level plays an important role in this process. Will you get sick after eating the fresh-looking seafood toast you bought at that stall over there? After all, you don’t connect your consciousness, going over in your mind similar stalls in which you often bought food, and counting how many times you then had to stay up at night, swallowing pills for indigestion. You do not give the result in numerical value. All work is done at the level of intuition. However, research in the 1950s and early 60s proved: in such situations, when it comes to chance, intuition fails. So Kahneman asked himself: How common are these misconceptions about uncertainty? And how does this affect a person's ability to make decisions? Several years have passed; once Kahneman invited junior teacher Amos Tversky to one of his seminars to give a lecture. Later, over dinner, Kahneman shared some of his thoughts with Tversky. Over the next thirty years, Tversky and Kahneman found out that when it comes to random processes - even if they are related to such difficult areas as military science, sports, business, medicine - beliefs, intuitions of people often fail.