The Undoing Project: A Friendship That Changed Our Minds

by Michael Lewis

Occasionally, people who watched Amos in action sensed that he was more afraid of being thought unmanly than he was actually brave. “He was always very gung ho,” recalled Uri Shamir. “I thought it was maybe compensation for being thin and weak and pale.” At some point it didn’t matter: He compelled himself to be brave until bravery became a habit. And as his time in the army came to an end he clearly sensed a change in himself.

To those who knew Amos best, Amos’s stories were just an excuse to enjoy Amos. “People who knew Amos could talk of nothing else,” as one Israeli woman, a friend of long standing, put it. “There was nothing we liked to do more than to get together and talk about him, over and over and over.” There were—for starters—the stories about the funny things Amos had said, usually directed at people whom he found full of themselves. He had listened to an American economist talk about how so-and-so was stupid and so-and-so was a fool, then said, “All your economic models are premised on people being smart and rational, and yet all the people you know are idiots.” Much later, he heard Murray Gell-Mann, a Nobel laureate in physics, hold forth on seemingly every subject under the sun. After Gell-Man was done, Amos said, “You know, Murray, there is no one in the world who is as smart as you think you are.”

There was—to take just one example—the time that Tel Aviv University threw a party for a physicist who had just won the Wolf Prize. It was the discipline’s second-highest honor, and its winners more often than not went on to win the Nobel. Most of the leading physicists in the country came to the party, but somehow the prizewinner ended up in the corner with Amos—who had recently taken an interest in black holes. The next day the prizewinner called his hosts to ask, “Who was that physicist I was talking to? He never told me his name.” After some confusing back-and-forth, his hosts figured out that the man meant Amos, and they told him that Amos wasn’t a physicist but a psychologist. “It’s not possible,” the physicist said, “he was the smartest of all the physicists.”

The Princeton philosopher Avishai Margalit said, “No matter what the topic was, the first thing Amos thought was in the top 10 percent. This was such a striking ability. The clarity and depth of his first reaction to any problem—any intellectual problem—was something mind-boggling. It was as if he was right away in the middle of any discussion.” Irv Biederman, a psychologist at the University of Southern California, said, “Physically he was unremarkable. In a room full of thirty people he’d be the last one you’d notice. And then he’d start to talk. Everyone who ever met him thought he was the smartest person they had ever met.”

A lot of things that most human beings would never think to do, to Amos simply made sense. For instance, when he wanted to go for a run he . . . went for a run. No stretching, no jogging outfit or, for that matter, jogging: He’d simply strip off his slacks and sprint out his front door in his underpants and run as fast as he could until he couldn’t run anymore. “Amos thought people paid an enormous price to avoid mild embarrassment,” said his friend Avishai Margalit, “and he himself decided very early on it was not worth it.” What all those who came to know Amos eventually realized was that the man had a preternatural gift for doing only precisely what he wanted to do. Varda Liberman recalled visiting him one day and seeing a table with a week’s worth of mail on it. There were tidy little stacks, one for each day, each filled with requests and entreaties and demands upon Amos’s time: job offers, offers of honorary degrees, requests for interviews and lectures, requests for help with some abstruse problem, bills. When the new mail came in Amos opened anything that interested him and left the rest in its daily pile. Each day the new mail arrived and shoved the old mail down the table. When a pile reached the end of the table Amos pushed it, unopened, off the edge into a waiting garbage can. “The nice thing about things that are urgent,” he liked to say, “is that if you wait long enough they aren’t urgent anymore.” “I would say to Amos I have to do this or I have to do that,”...

Amos’s three children have vivid memories of watching their parents drive off to see some movie picked by their mother, only to have their father turn up back at their couch twenty minutes later. Amos would have decided, in the first five minutes, whether the movie was worth seeing—and if it wasn’t he’d just come home and watch Hill Street Blues (his favorite TV drama) or Saturday Night Live (he never missed it) or an NBA game (he was obsessed with basketball). He’d then go back and fetch his wife after her movie ended. “They’ve already taken my money,” he’d explain. “Should I give them my time, too?” If by some freak accident he found himself at a gathering of his fellow human beings that held no appeal for him, he’d become invisible. “He’d walk into a room and decide he didn’t want anything to do with it and he would fade into the background and just vanish,” says Dona. “It was like a superpower. And it was absolutely an abnegation of social responsibility. He didn’t accept social responsibility—and so graciously, so elegantly, didn’t accept it.”

Amos liked to say that stinginess was contagious and so was generosity, and since behaving generously made you happier than behaving stingily, you should avoid stingy people and spend your time only with generous ones.

Amos had his own theory, which he called “features of similarity.”† He argued that when people compared two things, and judged their similarity, they were essentially making a list of features. These features are simply what they notice about the objects. They count up the noticeable features shared by two objects: The more they share, the more similar they are; the more they don’t share, the more dissimilar they are. Not all objects have the same number of noticeable features: New York City had more of them than Tel Aviv, for instance. Amos built a mathematical model to describe what he meant—and to invite others to test his theory, and prove him wrong.

“Similarity increases with the addition of common features and/or deletion of distinctive features.”

Otherwise Amos was unchanged: the last to go to bed at night, the life of every party, the light to which all butterflies flew, and the freest, happiest, and most interesting person anyone knew. He still did only what he wanted to do. Even his new interest in wearing a suit was more peculiarly Amos than it was bourgeois. Amos chose his suits only by the number and size of the jacket pockets. Along with an interest in pockets, he had what amounted to a fetish for briefcases, and acquired dozens of them. He’d returned from five years in the most materialistic culture on the face of the earth with a desire only for objects that might help him impose order on the world around him.

That was another thing colleagues and students noticed about Danny: how quickly he moved on from his enthusiasms, how easily he accepted failure. It was as if he expected it. But he wasn’t afraid of it. He’d try anything. He thought of himself as someone who enjoyed, more than most, changing his mind. “I get a sense of movement and discovery whenever I find a flaw in my thinking,” he said. His theory of himself dovetailed neatly with his moodiness. In his darker moods, he became fatalistic—and so wasn’t surprised or disturbed when he did fail. (He’d been proved right!) In his up moments he was so full of enthusiasm that he seemed to forget the possibility of failure, and would run with any new idea that came his way. “He could drive people up the wall with his volatility,” said fellow Hebrew University psychologist Maya Bar-Hillel. “Something was genius one day and crap the next, and genius the next day and crap the next.” What drove others crazy might have helped to keep Danny sane. His moods were grease for his idea factory.

They were seeking to understand not whether the eye played tricks on the mind, but if the mind also played tricks on the eye. Or, as they put it, how “intense mental activity hinders perception.” They found that it wasn’t just emotional arousal that altered the size of the pupil: Mental effort had the same effect. There was, quite possibly, as they put it, “an antagonism between thinking and perceiving.”

Amos presented research done in Ward Edwards’s lab that showed that when people draw a red chip from the bag, they do indeed judge the bag to be more likely to contain mostly red chips. If the first three chips they withdrew from a bag were red, for instance, they put the odds at 3:1 that the bag contained a majority of red chips. The true, Bayesian odds were 27:1. People shifted the odds in the right direction, in other words; they just didn’t shift them dramatically enough. Ward Edwards had coined a phrase to describe how human beings responded to new information. They were “conservative Bayesians.” That is, they behaved more or less as if they knew Bayes’s rule. Of course, no one actually thought that Bayes’s formula was grinding away in people’s heads. What Edwards, along with a lot of other social scientists, believed (and seemed to want to believe) was that people behaved as if they had Bayes’s formula lodged in their minds.

And yet, to Danny, the experiment that Amos described sounded just incredibly stupid. After a person has pulled a red chip out of a bag, he is more likely than before to think the bag to be the one whose chips are mostly red: well, duh. What else is he going to think?

In Danny’s view, people were not conservative Bayesians. They were not statisticians of any kind. They often leapt from little information to big conclusions. The theory of the mind as some kind of statistician was of course just a metaphor. But the metaphor, to Danny, felt wrong. “I knew I was a lousy intuitive statistician,” he said. “And I really didn’t think I was stupider than anyone else.”

Which was odd when you thought about it. Most real-life judgments did not offer probabilities as clean and knowable as the judgment of which book bag contained mostly red poker chips. The most you could hope to show with such experiments is that people were very poor intuitive statisticians—so poor they couldn’t even pick the book bag that offered them the most favorable odds. People who proved to be expert book bag pickers might still stumble when faced with judgments in which the probabilities were far more difficult to know—say, whether some foreign dictator did, or did not, possess weapons of mass destruction. Danny thought, this is what happens when people become attached to a theory. They fit the evidence to the theory rather than the theory to the evidence. They cease to see what’s right under their nose.

Amos was a psychologist and yet the experiment he had just described, with apparent approval, or at least not obvious skepticism, had in it no psychology at all. “It felt like a math exercise,” said Danny. And so Danny did what every decent citizen of Hebrew University did when he heard something that sounded idiotic: He let Amos have it. “The phrase ‘I pushed him into the wall’ was often used, even for conversations among friends,” explained Danny later. “The idea that everyone is entitled to his/her opinion was a California thing—that’s not how we did things in Jerusalem.”

The students who once wondered why the two brightest stars of Hebrew University kept their distance from each other now wondered how two so radically different personalities could find common ground, much less become soul mates. “It was very difficult to imagine how this chemistry worked,” said Ditsa Kaffrey, a graduate student in psychology who studied with them both. Danny was a Holocaust kid; Amos was a swaggering Sabra—the slang term for a native Israeli. Danny was always sure he was wrong. Amos was always sure he was right. Amos was the life of every party; Danny didn’t go to the parties. Amos was loose and informal; even when he made a stab at informality, Danny felt as if he had descended from some formal place. With Amos you always just picked up where you left off, no matter how long it had been since you last saw him. With Danny there was always a sense you were starting over, even if you had been with him just yesterday. Amos was tone-deaf but would nevertheless sing Hebrew folk songs with great gusto. Danny was the sort of person who might be in possession of a lovely singing voice that he would never discover. Amos was a one-man wrecking ball for illogical arguments; when Danny heard an illogical argument, he asked, What might that be true of? Danny was a pessimist. Amos was not merely an optimist; Amos willed himself to be optimistic, because he had decided pessimism was stupid. When you are a pessimist and the bad thing happens, you live it twice, Amos liked...

“Amos did not write in a defensive crouch,” he said. “There was something liberating about the arrogance—it was extremely rewarding to feel like Amos, smarter than almost everyone.”

“Belief in the Law of Small Numbers” teased out the implications of a single mental error that people commonly made—even when those people were trained statisticians. People mistook even a very small part of a thing for the whole. Even statisticians tended to leap to conclusions from inconclusively small amounts of evidence. They did this, Amos and Danny argued, because they believed—even if they did not acknowledge the belief—that any given sample of a large population was more representative of that population than it actually was.

They then went on to show that trained scientists—experimental psychologists—were prone to the same mental error. For instance, the psychologists who were asked to guess the mean IQ of the sample of kids, in which the first kid was found to have an IQ of 150, often guessed that it was 100, or the mean of the larger population of eight graders. They assumed that the kid with the high IQ was an outlier who would be offset by an outlier with an extremely low IQ—that every heads would be followed by a tails. But the correct answer—as produced by Bayes’s theorem—was 101. Even people trained in statistics and probability theory failed to intuit how much more variable a small sample could be than the general population—and that the smaller the sample, the lower the likelihood that it would mirror the broader population. They assumed that the sample would correct itself until it mirrored the population from which it was drawn. In very large populations, the law of large numbers did indeed guarantee this result. If you flipped a coin a thousand times, you were more likely to end up with heads or tails roughly half the time than if you flipped it ten times. For some reason human beings did not see it that way. “People’s intuitions about random sampling appear to satisfy the law of small numbers, which asserts that the law of large numbers applies to small numbers as well,” Danny and Amos wrote.

But then UCLA sent back the analyzed data, and the story became unsettling. (Goldberg described the results as “generally terrifying.”) In the first place, the simple model that the researchers had created as their starting point for understanding how doctors rendered their diagnoses proved to be extremely good at predicting the doctors’ diagnoses. The doctors might want to believe that their thought processes were subtle and complicated, but a simple model captured these perfectly well. That did not mean that their thinking was necessarily simple, only that it could be captured by a simple model. More surprisingly, the doctors’ diagnoses were all over the map: The experts didn’t agree with each other. Even more surprisingly, when presented with duplicates of the same ulcer, every doctor had contradicted himself and rendered more than one diagnosis: These doctors apparently could not even agree with themselves. “These findings suggest that diagnostic agreement in clinical medicine may not be much greater than that found in clinical psychology—some food for thought during your next visit to the family doctor,” wrote Goldberg. If the doctors disagreed among themselves, they of course couldn’t all be right—and they weren’t. The researchers then repeated the experiment with clinical psychologists and psychiatrists, who gave them the list of factors they considered when deciding whether it was safe to release a patient from a psychiatric hospital. Once again, the experts were a...

Anyway, he spent most of his time indoors, talking to Amos. They installed themselves in an office in the former Unitarian church, and continued the conversation they’d started in Jerusalem. “I had the sense, ‘My life has changed,’” said Danny. “We were quicker in understanding each other than we were in understanding ourselves. The way the creative process works is that you first say something, and later, sometimes years later, you understand what you said. And in our case it was foreshortened. I would say something and Amos would understand it. When one of us would say something that was off the wall, the other would search for the virtue in it. We would finish each other’s sentences and frequently did. But we also kept surprising each other. It still gives me goose bumps.” For the first time in their careers, they had something like a staff at their disposal. Papers got typed by someone else; subjects for their experiments got recruited by someone else; money for research got raised by someone else. All they had to do was talk to each other.

When they sat down to write they nearly merged, physically, into a single form, in a way that the few people who happened to catch a glimpse of them found odd. “They wrote together sitting right next to each other at the typewriter,” recalls Michigan psychologist Richard Nisbett. “I cannot imagine. It would be like having someone else brush my teeth for me.” The way Danny put it was, “We were sharing a mind.”

Their first paper—which they still half-thought of as a joke played on the academic world—had shown that people faced with a problem that had a statistically correct answer did not think like statisticians. Even statisticians did not think like statisticians. “Belief in the Law of Small Numbers” had raised an obvious next question: If people did not use statistical reasoning, even when faced with a problem that could be solved with statistical reasoning, what kind of reasoning did they use? If they did not think, in life’s many chancy situations, like a card counter at a blackjack table, how did they think?

“Subjective probabilities play an important role in our lives,” they began. “The decisions we make, the conclusions we reach, and the explanations we offer are usually based on our judgments of the likelihood of uncertain events such as success in a new job, the outcome of an election, or the state of a market.” In these and many other uncertain situations, the mind did not naturally calculate the correct odds. So what did it do? The answer they now offered: It replaced the laws of chance with rules of thumb. These rules of thumb Danny and Amos called “heuristics.” And the first heuristic they wanted to explore they called “representativeness.” When people make judgments, they argued, they compare whatever they are judging to some model in their minds. How much do those clouds resemble my mental model of an approaching storm? How closely does this ulcer resemble my mental model of a malignant cancer? Does Jeremy Lin match my mental picture of a future NBA player? Does that belligerent German political leader resemble my idea of a man capable of orchestrating genocide? The world’s not just a stage. It’s a casino, and our lives are games of chance. And when people calculate the odds in any life situation, they are often making judgments about similarity—or (strange new word!) representativeness. You have some notion of a parent population: “storm clouds” or “gastric ulcers” or “genocidal dictators” or “NBA players.” You compare the specific case to the parent population.

group. “Our thesis,” they wrote, “is that, in many situations, an event A is judged to be more probable than an event B whenever A appears more representative than B.” The more the basketball player resembles your mental model of an NBA player, the more likely you will think him to be an NBA player.

“Our thesis,” they wrote, “is that, in many situations, an event A is judged to be more probable than an event B whenever A appears more representative than B.” The more the basketball player resembles your mental model of an NBA player, the more likely you will think him to be an NBA player.

For instance, in families with six children, the birth order B G B B B B was about as likely as G B G B B G. But Israeli kids—like pretty much everyone else on the planet, it would emerge—naturally seemed to believe that G B G B B G was a more likely birth sequence. Why? “The sequence with five boys and one girl fails to reflect the proportion of boys and girls in the population,” they explained. It was less representative. What is more, if you asked the same Israeli kids to choose the more likely birth order in families with six children—B B B G G G or G B B G B G—they overwhelmingly opted for the latter. But the two birth orders are equally likely. So why did people almost universally believe that one was far more likely than the other? Because, said Danny and Amos, people thought of birth order as a random process, and the second sequence looks more “random” than the first.

Londoners in the Second World War thought that German bombs were targeted, because some parts of the city were hit repeatedly while others were not hit at all. (Statisticians later showed that the distribution was exactly what you would expect from random bombing.) People find it a remarkable coincidence when two students in the same classroom share a birthday, when in fact there is a better than even chance, in any group of twenty-three people, that two of its members will have been born on the same day. We have a kind of stereotype of “randomness” that differs from true randomness. Our stereotype of randomness lacks the clusters and patterns that occur in true random sequences.

The average heights of adult males and females in the U.S. are, respectively, 5 ft. 10 in. and 5 ft. 4 in. Both distributions are approximately normal with a standard deviation of about 2.5 in.§ An investigator has selected one population by chance and has drawn from it a random sample. What do you think the odds are that he has selected the male population if 1. The sample consists of a single person whose height is 5 ft. 10 in.? 2. The sample consists of 6 persons whose average height is 5 ft. 8 in.? The odds most commonly assigned by their subjects were, in the first case, 8:1 in favor and, in the second case, 2.5:1 in favor. The correct odds were 16:1 in favor in the first case, and 29:1 in favor in the second case. The sample of six people gave you a lot more information than the sample of one person.

A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. As you know, about 50 percent of all babies are boys. The exact percentage of baby boys, however, varies from day to day. Sometimes it may be higher than 50 percent, sometimes lower. For a period of 1 year, each hospital recorded the days on which more than 60 percent of the babies born were boys. Which hospital do you think recorded more such days? Check one: — The larger hospital — The smaller hospital — About the same (that is, within 5 percent of each other) People got that one wrong, too. Their typical answer was “same.” The correct answer is “the smaller hospital.” The smaller the sample size, the more likely that it is unrepresentative of the wider population.

The frequency of appearance of letters in the English language was studied. A typical text was selected, and the relative frequency with which various letters of the alphabet appeared in the first and third positions of the words was recorded. Words of less than three letters were excluded from the count. You will be given several letters of the alphabet, and you will be asked to judge whether these letters appear more often in the first or in the third position, and to estimate the ratio of the frequency with which they appear in these positions. . . . Consider the letter K Is K more likely to appear in ____the first position? ____the third position? (check one) My estimate for the ratio of these two values is:________:1 If you thought that K was, say, twice as likely to appear as the first letter of an English word than as the third letter, you checked the first box and wrote your estimate as 2:1. This was what the typical person did, as it happens. Danny and Amos replicated the demonstration with other letters—R, L, N, and V. Those letters all appeared more frequently as the third letter in an English word than as the first letter—by a ratio of two to one. Once again, people’s judgment was, systematically, very wrong. And it was wrong, Danny and Amos now proposed, because it was distorted by memory. It was simply easier to recall words that start with K than to recall words with K as their third letter. The more easily people can call some scenario to mind—the more avai...

“In assessing the profit of a given company, for example, people tend to assume normal operating conditions and make their estimates contingent upon that assumption,” they wrote in their notes. “They do not incorporate into their estimates the possibility that these conditions may be drastically changed because of a war, sabotage, depressions, or a major competitor being forced out of business.” Here, clearly, was another source of error: not just that people don’t know what they don’t know, but that they don’t bother to factor their ignorance into their judgments.

The stories people told themselves, when the odds were either unknown or unknowable, were naturally too simple. “This tendency to consider only relatively simple scenarios,” they concluded, “may have particularly salient effects in situations of conflict. There, one’s own moods and plans are more available to one than those of the opponent. It is not easy to adopt the opponent’s view of the chessboard or of the battlefield.” The imagination appeared to be governed by rules. The rules confined people’s thinking. It’s far easier for a Jew living in Paris in 1939 to construct a story about how the German army will behave much as it had in 1919, for instance, than to invent a story in which it behaves as it did in 1941, no matter how persuasive the evidence might be that, this time, things are different.

Amos liked to say that if you are asked to do anything—go to a party, give a speech, lift a finger—you should never answer right away, even if you are sure that you want to do it. Wait a day, Amos said, and you’ll be amazed how many of those invitations you would have accepted yesterday you’ll refuse after you have had a day to think it over.

A human being who finds himself stuck at some boring meeting or cocktail party often finds it difficult to invent an excuse to flee. Amos’s rule, whenever he wanted to leave any gathering, was to just get up and leave. Just start walking and you’ll be surprised how creative you will become and how fast you’ll find the words for your excuse, he said. His attitude to the clutter of daily life was of a piece with his strategy for dealing with social demands. Unless you are kicking yourself once a month for throwing something away, you are not throwing enough away, he said.

Dick is a 30 year old man. He is married with no children. A man of high ability and high motivation, he promises to be quite successful in his field. He is well liked by his colleagues. Then they ran another experiment. It was a version of the book bag and poker chips experiment that Amos and Danny had argued about in Danny’s seminar at Hebrew University. They told their subjects that they had picked a person from a pool of 100 people, 70 of whom were engineers and 30 of whom were lawyers. Then they asked them: What is the likelihood that the selected person is a lawyer? The subjects correctly judged it to be 30 percent. And if you told them that you were doing the same thing, but from a pool that had 70 lawyers in it and 30 engineers, they said, correctly, that there was a 70 percent chance the person you’d plucked from it was a lawyer. But if you told them you had picked not just some nameless person but a guy named Dick, and read them Danny’s description of Dick—which contained no information whatsoever to help you guess what Dick did for a living—they guessed there was an equal chance that Dick was a lawyer or an engineer, no matter which pool he had emerged from. “Evidently, people respond differently when given no specific evidence and when given worthless evidence,” wrote Danny and Amos. “When no specific evidence is given, the prior probabilities are properly utilized; when worthless specific evidence is given, prior probabilities are ignored.”*

Biederman had been friends with Amos at the University of Michigan and was now a member of the faculty at the State University of New York at Buffalo. The Amos he knew was consumed by possibly important but probably insolvable and certainly obscure problems about measurement. “I wouldn’t have invited Amos to Buffalo to talk about that,” he said—as no one would have understood it or cared about it. But this new work Amos was apparently doing with Danny Kahneman was breathtaking. It confirmed Biederman’s sense that “most advances in science come not from eureka moments but from ‘hmmm, that’s funny.’”

In the course of our personal and professional lives, we often run into situations that appear puzzling at first blush. We cannot see for the life of us why Mr. X acted in a particular way, we cannot understand how the experimental results came out the way they did, etc. Typically, however, within a very short time we come up with an explanation, a hypothesis, or an interpretation of the facts that renders them understandable, coherent, or natural. The same phenomenon is observed in perception. People are very good at detecting patterns and trends even in random data. In contrast to our skill in inventing scenarios, explanations, and interpretations, our ability to assess their likelihood, or to evaluate them critically, is grossly inadequate. Once we have adopted a particular hypothesis or interpretation, we grossly exaggerate the likelihood of that hypothesis, and find it very difficult to see things any other way. Amos was polite about it. He did not say, as he often said, “It is amazing how dull history books are, given how much of what’s in them must be invented.” What he did say was perhaps even more shocking to his audience: Like other human beings, historians were prone to the cognitive biases that he and Danny had described. “Historical judgment,” he said, was “part of a broader class of processes involving intuitive interpretation of data.” Historical judgments were subject to bias.

After the trip, Fischhoff went back and asked the same people to recall the odds they had assigned to each outcome. Their memories of the odds they had assigned to various outcomes were badly distorted. They all believed that they had assigned higher probabilities to what happened than they actually had. They greatly overestimated the odds that they had assigned to what had actually happened. That is, once they knew the outcome, they thought it had been far more predictable than they had found it to be before, when they had tried to predict it. A few years after Amos described the work to his Buffalo audience, Fischhoff named the phenomenon “hindsight bias.”†

In his talk to the historians, Amos described their occupational hazard: the tendency to take whatever facts they had observed (neglecting the many facts that they did not or could not observe) and make them fit neatly into a confident-sounding story: All too often, we find ourselves unable to predict what will happen; yet after the fact we explain what did happen with a great deal of confidence. This “ability” to explain that which we cannot predict, even in the absence of any additional information, represents an important, though subtle, flaw in our reasoning. It leads us to believe that there is a less uncertain world than there actually is, and that we are less bright than we actually might be. For if we can explain tomorrow what we cannot predict today, without any added information except the knowledge of the actual outcome, then this outcome must have been determined in advance and we should have been able to predict it. The fact that we couldn’t is taken as an indication of our limited intelligence rather than of the uncertainty that is in the world. All too often, we feel like kicking ourselves for failing to foresee that which later appears inevitable. For all we know, the handwriting might have been on the wall all along. The question is: was the ink visible?

It wasn’t just sports announcers and political pundits who radically revised their narratives, or shifted focus, so that their stories seemed to fit whatever had just happened in a game or an election. Historians imposed false order upon random events, too, probably without even realizing what they were doing. Amos had a phrase for this. “Creeping determinism,” he called it—and jotted in his notes on...

They had been gripped by “The Decision to Seed Hurricanes,” a paper coauthored by Stanford professor Ron Howard. Howard was one of the founders of a new field called decision analysis. Its idea was to force decision makers to assign probabilities to various outcomes: to make explicit the thinking that went into their decisions before they made them.

Redelmeier had actually co-written an article about that: “Elevator Buttons as Unrecognized Sources of Bacterial Colonization in Hospitals.” For one of his studies, he had swabbed 120 elevator buttons and 96 toilet seats at three big Toronto hospitals and produced evidence that the elevator buttons were far more likely to infect you with some disease.

Lung cancer proved to be a handy example. Lung cancer doctors and patients in the early 1980s faced two unequally unpleasant options: surgery or radiation. Surgery was more likely to extend your life, but, unlike radiation, it came with the small risk of instant death. When you told people that they had a 90 percent chance of surviving surgery, 82 percent of patients opted for surgery. But when you told them that they had a 10 percent chance of dying from the surgery—which was of course just a different way of putting the same odds—only 54 percent chose the surgery. People facing a life-and-death decision responded not to the odds but to the way the odds were described to them.

Many sentences popped out of Amos’s mouth that Redelmeier knew he would forever remember: A part of good science is to see what everyone else can see but think what no one else has ever said. The difference between being very smart and very foolish is often very small. So many problems occur when people fail to be obedient when they are supposed to be obedient, and fail to be creative when they are supposed to be creative. The secret to doing good research is always to be a little underemployed. You waste years by not being able to waste hours. It is sometimes easier to make the world a better place than to prove you have made the world a better place.

Basketball experts seized on random streaks as patterns in players’ shooting that didn’t exist. Arthritis sufferers found patterns in suffering that didn’t exist. “We attribute this phenomenon to selective matching,” Tversky and Redelmeier wrote.† “. . . For arthritis, selective matching leads people to look for changes in the weather when they experience increased pain, and pay little attention to the weather when their pain is stable. . . . [A] single day of severe pain and extreme weather might sustain a lifetime of belief in a relation between them.”

By the fall of 1973 it was fairly clear to Danny that other people would never fully understand his relationship with Amos. The previous academic year, they’d taught a seminar together at Hebrew University. From Danny’s point of view, it had been a disaster. The warmth he felt when he was alone with Amos vanished whenever Amos was in the presence of an audience. “When we were with other people we were one of two ways,” said Danny. “Either we finished each other’s sentences and told each other’s jokes. Or we were competing. No one ever saw us working together. No one knows what we were like.” What they were like, in every way but sexually, was lovers. They connected with each other more deeply than either had connected with anyone else. Their wives noticed it. “Their relationship was more intense than a marriage,” said Barbara. “I think they were both turned on intellectually more than either had ever been before. It was as if they were both waiting for it.” Danny sensed that his wife felt some jealousy; Amos actually praised Barbara, behind her back, for dealing so gracefully with the intrusion on their marriage. “Just to be with him,” said Danny. “I never felt that way with anyone else, really. You are in love and things. But I was rapt. And that’s what it was like. It was truly extraordinary.”

The distinction between judgment and decision making appeared as fuzzy as the distinction between judgment and prediction. But to Amos, as to other mathematical psychologists, they were distinct fields of inquiry. A person making a judgment was assigning odds. How likely is it that that guy will be a good NBA player? How risky is that triple-A-rated subprime mortgage–backed CDO? Is the shadow on the X-ray cancer? Not every judgment is followed by a decision, but every decision implies some judgment. The field of decision making explored what people did after they had formed some judgment—after they knew the odds, or thought they knew the odds, or perhaps had judged the odds unknowable. Do I pick that player? Do I buy that CDO? Surgery or chemotherapy? It sought to understand how people acted when faced with risky options.