A Bitter Ending

Daniel Kahneman and Amos Tversky changed the way we think about thinking. Beginning in the late ’60s, the Israeli psychologists collaborated on a series of studies that showed how our intuitions can lead us astray. Their findings reshaped established fields and gave rise to new ones, like behavioral economics, and eventually led to a Nobel prize in economic science (though Tversky, who died in 1996, wouldn’t be around to share in that honor). Their partnership, the focus of a new book by Michael Lewis, The Undoing Project (W.W. Norton), is among the most successful in academic history. Here’s how that success drove a wedge between them.

A mos Tversky was in Israel on a visit in 1984 when he received the phone call telling him that he’d been given a MacArthur “genius” grant. The award came with $250,000, plus $50,000 for research, a fancy health-care plan, and a press release celebrating Amos as one of the thinkers who had exhibited “extraordinary originality and dedication in their creative pursuits and a marked capacity for self-direction.” The only work of Amos’s cited in the press release was the work he’d done with Daniel Kahneman. It didn’t mention Danny.

Amos disliked prizes. He thought that they exaggerated the differences between people, did more harm than good, and created more misery than joy, as for every winner there were many others who deserved to win, or felt they did. The MacArthur became a case in point. “He wasn’t grateful for that prize,” said his friend Maya Bar-Hillel, who was with Amos in Jerusalem shortly after the prize was announced. “He was pissed. He said, ‘What are these people thinking? How can they give a prize to just one of a winning pair? Do they not realize they are dealing the collaboration a death blow?’”

Amos didn’t like prizes, but he kept on getting them anyway. Before the MacArthur grant, he had been admitted into the American Academy of Arts and Sciences. Soon after the MacArthur, he received a Guggenheim Fellowship and an invitation to join the National Academy of Sciences. That last honor was seldom bestowed on scientists who weren’t U.S. citizens — and it wasn’t bestowed upon Danny. There would follow honorary degrees from Yale and the University of Chicago, among others. But the MacArthur was the prize Amos would dwell upon as an example of the damage caused by prizes. “He thought it was myopic beyond forgiveness,” said Bar-Hillel. “It was genuine agony. He wasn’t putting on a show for me.”

Along with the prizes came a steady drizzle of books and articles praising Amos for the work he had done with Danny, as if he had done it alone. When others spoke of their joint work, they put Danny’s name second, if they mentioned it at all: Tversky and Kahneman. “You are very generous in giving me credit for articulating the relationship between representativeness and psychoanalysis,” Amos wrote to a fellow psychologist who had sent Amos his new journal article. “These ideas, however, were developed in discussions with Danny so you should mention both our names or (if that appears awkward) omit mine.” An author of a book credited Amos with noticing the illusory sense of effectiveness felt by Israeli Air Force flight instructors after they’d criticized a pilot. “I am somewhat uncomfortable with the label the ‘Tversky effect,’ " Amos wrote to the author. “This work has been done in collaboration with my longtime friend and colleague, Daniel Kahneman, so I should not be singled out. In fact, Daniel Kahneman was the one who observed the effect of pilots’ training, so if this phenomenon is to be named after a person it should be called the ‘Kahneman effect.’ "

The American view of his collaboration with Danny mystified Amos. “People saw Amos as the brilliant one and Danny as the careful one,” said Amos’s friend and Stanford colleague Persi Diaconis. “And Amos would say: ‘It’s exactly the opposite!’ "

Amos’s graduate students at Stanford gave him a nickname: Famous Amos. “You knew that everyone knew him, and you knew everyone wanted to hang out with him,” said the Brown University psychologist Steven Sloman, who studied with Amos in the late 1980s. The maddening thing is that Amos seemed almost indifferent to the attention. He happily ignored the ever-growing media requests. (“You probably won’t be better off after you have appeared on TV than before,” he said.) He tossed out as many invitations, unopened, as he acknowledged. None of this arose from a sense of modesty. Amos knew his own value. He didn’t need to make a point of not caring what people thought of him; he actually just didn’t care all that much. The deal Amos offered the encroaching world was that people’s interactions were to be on his terms.

And the world accepted the deal. Congressmen called him for advice on bills they were drafting. The National Basketball Association called to hear his argument about statistical fallacies in basketball. The Secret Service flew him to Washington so that he could advise agents on how to predict and deter threats to the political leaders under their protection. The North Atlantic Treaty Organization flew him to the French Alps to teach leaders about how people made decisions in conditions of uncertainty.

Amos seemed able to walk into any problem, however alien to him, and make the people dealing with it feel as if he grasped its essence better than they did. The University of Illinois flew him to a conference about metaphorical thinking only to have him argue that a metaphor was actually a substitute for thinking. “Because metaphors are vivid and memorable, and because they are not readily subjected to critical analysis, they can have considerable impact on human judgment even when they are inappropriate, useless, or misleading,” said Amos. “They replace genuine uncertainty about the world with semantic ambiguity. A metaphor is a cover-up.”

Danny couldn’t help noticing the new attention Amos was receiving for the work they had done together. Economists now wanted Amos at their conferences, but then so did linguists and philosophers and sociologists and computer scientists — even though Amos hadn’t the faintest interest in the PC that came with his Stanford office. (“What could I do with computers?” he said, after he’d declined Apple’s offer to donate 20 new Macs to Stanford’s psychology department.) “You get fed up with not being invited to the same conferences, even when you would not want to go,” Danny confessed to the Harvard psychiatrist Miles Shore. “My life would be better if he weren’t invited to so many.”

In Israel, Danny had been the person whom real-world people came to when they had some real-world problem. The people in real-world America came to Amos, even when it wasn’t obvious that he had any reason to know what he was talking about.

By the 1980s, the ideas that Danny and Amos had hatched together were infiltrating places the two had never imagined them entering. Success created, among other things, a new market for critics. “We started this unknown field,” Amos told Miles Shore in the summer of 1983. “We were shaking trees and challenging the establishment. Now we are the establishment. And people are shaking our tree.”

Those people tended to be self-serious intellectuals. Upon encountering Danny and Amos’s work, more than a few academics experienced the sensation that a person feels when a total stranger walks up and begins a sentence, “Don’t take this the wrong way, but … " Whatever might follow, you just know that you’re not going to like it.

At a conference back in the early 1970s, Danny was introduced to a prominent philosopher named Max Black and tried to explain to the great man his work with Amos. “I’m not interested in the psychology of stupid people,” said Black, and walked away.

Danny and Amos didn’t think of their work as the psychology of stupid people. Their very first experiments, dramatizing the weakness of people’s statistical intuitions, had been conducted on professional statisticians. For every simple problem that fooled undergraduates, Danny and Amos could come up with a more complicated version to fool professors. At least a few professors didn’t like the idea of that. “Give people a visual illusion and they say, ‘It’s only my eyes,’ " said the Princeton psychologist Eldar Shafir. “Give them a linguistic illusion. They’re fooled, but they say, ‘No big deal.’ Then you give them one of Amos and Danny’s examples and they say, ‘Now you’re insulting me.’ "

T he first to take their work personally were the psychologists whose work it had trumped. Amos’s former teacher Ward Edwards had written the original journal article in 1954 inviting psychologists to investigate the assumptions of economics. Still, he’d never imagined this — two Israelis walking into the room and making a mockery of the entire conversation.

In late 1970, after reading early drafts of Amos and Danny’s papers on human judgment, Edwards wrote to complain. In what would be the first of many agitated letters, he adopted the tone of a wise and indulgent master speaking to his naïve pupils. How could Amos and Danny possibly believe that there was anything to learn from putting silly questions to undergraduates? “I think your data collection methods are such that I don’t take seriously a single ‘experimental’ finding you present,” wrote Edwards. These students they had turned into their lab rats were “careless and inattentive. And if they are confused and inattentive, they are much less likely to behave more like competent intuitive statisticians.” For every supposed limitation of the human mind Danny and Amos had uncovered, Edwards had an explanation. The gambler’s fallacy, for instance. If people thought that a coin, after landing on heads five times in a row, was more likely, on the sixth toss, to land on tails, it wasn’t because they misunderstood randomness. It was because “people get bored doing the same thing all the time.”

Amos took the trouble to answer, almost politely, that first letter from Edwards. “It was certainly a pleasure to read your detailed comments on our papers and to see that, right or wrong, you have not lost any of your old fighting spirit,” he began, before describing his former professor as “not cogent.” “In particular,” Amos continued, “the objections you raised against our experimental method are simply unsupported. In essence, you engage in the practice of criticizing a procedural departure without showing how the departure might account for the results obtained. You do not present either contradictory data or a plausible alternative interpretation of our findings. Instead, you express a strong bias against our method of data collection and in favor of yours. This position is certainly understandable, yet it is hardly convincing.”

Edwards was not pleased, but he kept his anger to himself for a few years. “No one wanted to get in a fight with Amos,” said the University of Southern California psychologist Irv Biederman. “Not in public! I only once ever saw anyone ever do it. There was this philosopher. At a conference. He gets up to give his talk. He’s going to challenge heuristics. Amos was there. When he finished talking, Amos got up to rebut. It was like an ISIS beheading. But with humor.”

Edwards must have sensed, in any open conflict with Amos, the possibility of being on the painful end of an ISIS beheading, with humor. And yet he needed to say something.

In the late 1970s he finally found a principle on which to take a stand: The masses were not equipped to grasp Amos and Danny’s message. The subtleties were beyond them. People needed to be protected from misleading themselves into thinking that their minds were less trustworthy than they actually were. “I do not know whether you realize just how far that message has spread, or how devastating its effects have been,” Edwards wrote to Amos in September 1979. “I attended the organizational meeting of the Society for Medical Decision Making one and a half weeks ago. I would estimate that every third paper mentioned your work in passing, mostly as justification for avoiding human intuition, judgment, decision making, and other intellectual processes.” Even sophisticated doctors were getting from Danny and Amos only the crude, simplified message that their minds could never be trusted. What would become of medicine? Of intellectual authority? Of experts?

Edwards sent Amos a working draft of his assault on Danny and Amos’s work and hoped that Amos would leave him with his dignity. Amos didn’t. “The tone is snide, the evaluation of evidence is unfair and there are too many technical difficulties to begin to discuss,” Amos wrote, in a curt note to Edwards. “We are in sympathy with your attempt to redress what you regard as a distorted view of man. But we regret that you chose to do so by presenting a distorted view of our work.”

In his reply, Edwards did a fair impression of a man who has just realized that his fly is unzipped as he backpedals off a cliff. He offered up his personal problems — they ranged from serious jet lag to “a decade’s worth of personal frustrations” — as excuses for his failed paper, and then went on to more or less concede that he wished he’d never written it. “What especially embarrasses me is that after working so long as I did on trying to put this thing together I should have been as blind to its many flaws as I was,” he wrote to both Amos and Danny, before saying how he intended to entirely rewrite his paper and hoped very much to avoid any public controversy with them.

Not everyone knew enough to be afraid of Amos. An Oxford philosopher named L. Jonathan Cohen raised a small philosophy-sized ruckus with a series of attacks in books and journals. He found alien the idea that you might learn something about the human mind by putting questions to people. He argued that because man had created the concept of rationality, he must, by definition, be rational. “Rational” was whatever most people did. Or, as Danny put it in a letter that he reluctantly sent in response to one of Cohen’s articles, “Any error that attracts a sufficient number of votes is not an error at all.”

Cohen labored to demonstrate that the mistakes discovered by Amos and Danny either were not mistakes or were the result of “mathematical or scientific ignorance” in people, easily remedied by a bit of exposure to college professors. “We both make a living by teaching probability and statistics,” Stanford’s Persi Diaconis and David Freedman, of the University of California at Berkeley, wrote to the journal Behavioral and Brain Sciences, which had published one of Cohen’s attacks. “Over and over again we see students and colleagues (and ourselves) making certain kinds of mistakes. Even the same mistake may be repeated by the same person many times. Cohen is wrong in dismissing this as the result of ‘mathematical or scientific ignorance.’”

But by then it was clear that no matter how often people who were trained in statistics affirmed the truth of Danny and Amos’s work, people who weren’t would insist that they knew better.

U pon their arrival in North America in 1977, Amos and Danny had published a flurry of papers together. Mostly it was stuff they’d had in the works when they’d left Israel. But in the early 1980s what they wrote together was not done in the same way as before. Amos wrote a piece on loss aversion under both their names, to which Danny added a few stray paragraphs. Danny wrote up on his own what Amos had called “The Undoing Project,” titled it “The Simulation Heuristic,” and published it with both their names on top, in a book that collected their articles, along with others by students and colleagues. (And then he set out to explore the rules of the imagination not with Amos but with his younger colleague at the University of British Columbia, Dale Miller.) Amos wrote an article, addressed directly to economists, to repair technical flaws in prospect theory. “Advances in Prospect Theory,” it was called, and though Amos did much of the work on it with his graduate student Rich Gonzalez, it ran as a journal article by Danny and Amos. “Amos said that it had always been Kahneman and Tversky, and that this had to be Kahneman and Tversky, and that it would be really strange to add a third person to it,” said Gonzalez.

Thus they maintained the illusion that they were still working together, much as before, even as the forces pulling them apart gathered strength. The growing crowd of common enemies failed to unite them. Danny was increasingly uneasy with the attitude Amos took toward their opponents. Amos was built to fight. Danny was built to survive. He shied from conflict. Now that their work was under attack, Danny adopted a new policy: to never review a paper that made him angry. It served as an excuse to ignore any act of hostility. Amos accused Danny of “identifying with the enemy,” and he wasn’t far off. Danny almost found it easier to imagine himself in his opponent’s shoes than in his own. In some strange way, Danny contained within himself his own opponent. He didn’t need another.

Amos, to be Amos, needed opposition. Without it he had nothing to triumph over. And Amos, like his homeland, lived in a state of readiness for battle. “Amos didn’t have Danny’s feeling that we should all think together and work together,” said Walter Mischel, who had been the chair of Stanford’s psychology department when it hired Amos. “He thought, ‘Fuck you.’”

That sentiment must have been passing through Amos’s mind in the early 1980s even more often than it usually did. The critics publishing attacks on his work with Danny were the least of it. At conferences and in conversations, Amos heard over and over from economists and decision theorists that he and Danny had exaggerated human fallibility. Or that the kinks in the mind that they had observed were artificial. Or present only in the minds of undergraduates. Or … something. A lot of people with whom Amos interacted had big investments in the idea that people were rational. Amos was perplexed by their inability to admit defeat in an argument he had plainly won. “Amos wanted to crush the opposition,” said Danny. “It just got under his skin more than it did mine. He wanted to find something to shut people up. Which of course you can never do.”

Toward the end of 1980, or maybe it was early 1981, Amos came to Danny with a plan to write an article that would end the discussion. Their opponents might never admit defeat — intellectuals seldom did — but they might at least decide to change the subject. “Winning by embarrassment,” Amos called it.

Amos wanted to demonstrate the raw power of the mind’s rules of thumb to mislead. He and Danny had stumbled upon some bizarre phenomena back in Israel and never fully explored their implications. Now they did.

Danny was of two minds about this new project, and about Amos. From the moment they had left Israel, they’d been like a pair of swimmers caught in different currents, losing the energy to swim against them. Amos felt the pull of logic, Danny the tug of psychology. Danny wasn’t nearly as interested as Amos in demonstrations of human irrationality. His interest in decision theory ended with the psychological insight he brought to it. “There is an underlying debate,” said Danny later. “Are we doing psychology or decision theory?” Danny wanted to return to psychology.

The paper, published in the October 1983 issue of Psychological Review, was another hit. Danny had misgivings, however. The new work was jointly written, but it was, he said, “joint and painful.” He no longer had the feeling that he and Amos were sharing a mind. Danny was uneasy with the feeling that the paper was less an exploration of a new phenomenon than the forging of a new weapon, to be used by Amos in battle. “It’s very Amos,” he said. “It’s a combative paper. We’ll provoke you with this. And we’ll show you that you can’t win this argument.”

By then their interactions had become fraught. It had taken Danny the longest time to understand his own value. Now he could see that the work Amos had done alone was not as good as the work they had done together. The joint work always attracted more interest and higher praise than anything Amos had done alone. It had apparently attracted this genius award. And yet the public perception of their relationship was now a Venn diagram, two circles, with Danny wholly contained by Amos. The rapid expansion of Amos’s circle pushed his borders further and further away from Danny’s. Danny felt himself sliding slowly but surely from the small group Amos loved to the large group whose ideas Amos viewed with contempt. “Amos changed,” said Danny. “When I gave him an idea, he would look for what was good in it. For what was right with it. That, for me, was the happiness in the collaboration. He understood me better than I understood myself. He stopped doing that.”

To those close to Amos who glimpsed his interaction with Danny, the wonder wasn’t that he and Danny were falling out, but that they had ever fallen in. “Danny isn’t so easy to access,” said Persi Diaconis. “Amos was all out there. The chemistry was so deep, I don’t know if it’s describable, in a mechanistic way. Each of them was brilliant. And that they did interact, and that they could interact, was a miracle.” The miracle did not look as if it was going to survive its removal from the Holy Land.

I n 1986, Danny moved with his wife, the psychologist Anne Treisman, to the University of California at Berkeley. “I really hope the move to Berkeley will open a new era with Danny, with more everyday interaction and less tension,” Amos wrote in a letter to a friend. “I am optimistic.”

When Danny had put himself back on the job market, the year before, he’d discovered that his stock had risen dramatically. He received 19 offers, including one from Harvard. Anyone who wanted to believe that what ailed Danny was simply an absence of status outside of Israel would have some difficulty explaining what happened next: He went into a depression. “He said he wasn’t going to work again,” recalled Maya Bar-Hillel, who bumped into Danny soon after he’d moved to Berkeley. “He had no more ideas, everything was getting worse.”

Danny’s premonition of the ending of a relationship that he had once been unable to imagine ending had a lot to do with the state of his mind. “This is a marriage, a big thing,” Danny had said to Miles Shore in the summer of 1983. “We have been working for 15 years. It would be a disaster to stop. It’s like asking people why do they stay married. We would need a strong reason not to stay married.” But in three years he’d gone from trying to stay in the marriage to trying to get out.

His move to Berkeley had the opposite of the intended effect: Seeing Amos more often caused him only more pain. “We have got to the point that the very thought of telling you of ANY idea that I like (mine or someone else’s) makes me anxious,” Danny wrote to Amos in March 1987, after one meeting. “An episode such as the one we had yesterday wrecks my life for several days (including anticipation as well as recovery) and I just don’t want those anymore. I am not suggesting we stop talking, merely that we show some good sense in adapting to the changes in our relationship.”

Amos replied to that letter from Danny with a long letter of his own. “I realize my response style leaves a lot to be desired but you have also become much less interested in objections or criticism, mine or others’,” he wrote. “You have become very protective of some ideas and develop an attitude of ‘love them or leave them’ rather than trying to ‘get it right.’ One of the things I admired you for most in our joint work was your relentlessness as a critic. You discarded a very attractive treatment of regret (developed mostly by you) because of a single counter-example that hardly anyone (except me) could really appreciate the force of. You prevented us from writing up our work on anchoring because it lacks something etc. I do not see any of this in your attitude to many of your ideas recently.”

When he’d finished that letter, Amos wrote another, to the mathematician Varda Liberman, his friend in Israel. “There is no overlap between the way I see my relationship with Danny and the way he perceives me,” he wrote. “What seems to me openness between friends he takes as an insult, and what seems like correct behavior to him is to me unfriendly. It is difficult for him to accept we are different in the eyes of other people.”

Danny needed something from Amos. He needed him to correct the perception that they were not equal partners. And he needed it because he suspected Amos shared that perception. “He was too willing to accept a situation that put me in his shadow,” said Danny.

Amos may have been privately furious that the MacArthur foundation had recognized him and not Danny, but when Danny had called to congratulate him, Amos had said offhandedly, “If I hadn’t gotten it for this, I’d have gotten it for something else.” Amos might have written endless recommendations for Danny, and told people privately that Danny was the world’s greatest living psychologist, but after Danny told Amos that Harvard had asked him to join its faculty, Amos said, “It’s me they want.” He’d just blurted that out, and then probably regretted saying it — even if he wasn’t wrong to think it. Amos couldn’t help himself from wounding Danny, and Danny couldn’t help himself from feeling wounded. Barbara Tversky, Amos’s wife, occupied the office beside his at Stanford. “I would hear their phone calls,” she said. “It was worse than a divorce.”

The wonder was that Danny didn’t simply break off the relationship. By the late 1980s he was behaving like a man caught in some mysterious, invisible trap. Once you had shared a mind with Amos Tversky, it was hard to get Amos Tversky out of your mind.

What Danny did, instead, was get Amos out of his sight, by leaving Berkeley for Princeton, in 1992. “Amos cast a shadow on my life,” he said. “I needed to get away. He possessed my mind.” Amos couldn’t understand this need of Danny’s to put 3,000 miles between them. He found Danny’s behavior mystifying. “Just to give you a small example,” Amos wrote to Varda Liberman in early 1994, “there’s a book on judgment that came out, and in the introduction there’s a passage that says Danny and I are ‘inseparable.’ This is, of course, an exaggeration. But Danny wrote to the author to tell him that it’s an exaggeration and added that ‘we haven’t had anything to do with each other for a decade.’ In the last 10 years we published five papers together, and worked on several other projects we never finished (mainly because of me). It’s a trivial example but gives you an idea of his state of mind.”

For the longest time, even as they went back and forth, the collaboration was over in Danny’s mind. And for the longest time, in Amos’s mind, it wasn’t. “You seem determined to make me an offer that I cannot accept,” Danny wrote to Amos in early 1993, after one of Amos’s proposals.

They remained friends. They found excuses to get together and work through their issues. They kept their troubles so private that most people assumed they were still working together. But Amos liked that fiction better than Danny. He had hopes to write the book that they had agreed to write 15 years earlier. Danny found ways to let Amos know that wasn’t going to happen. “Danny has a new idea how to get the book done,” Amos wrote to Liberman in early 1994. “We’ll stick together a few papers published recently by each of us, with no connection or structure. This strikes me as so grotesque. It’ll look like a collection of work by two people who once worked together and now cannot even coordinate chapters. … With the situation as it is I can’t find enough positive energy even to start thinking, let alone to write.”

If Amos couldn’t give Danny what he needed, it was perhaps because he couldn’t imagine having the need. The need was subtle. Danny didn’t need job offers from Harvard or genius awards from the MacArthur Foundation. Those might have helped, but only if they altered Amos’s view of him. What Danny needed was for Amos to continue to see him and his ideas uncritically, as he had when they were alone together in a room. If that involved some misperception on Amos’s part — some exaggeration of the earthly status of Danny’s ideas — well, then, Amos should continue to misperceive. After all, what is a marriage if not an agreement to distort one’s perception of another, in relation to everyone else? “I wanted something from him, not from the world,” said Danny.

I n October 1993, Danny and Amos found themselves together at the same conference in Turin, Italy. One evening they went for a walk, and Amos made a request. There was a new critic of their work, a German psychologist named Gerd Gigerenzer, and he was getting a new kind of attention. From the start, those most upset by Danny and Amos’s work argued that by focusing only on the mind’s errors, they were exaggerating its fallibility. In their talks and writings, Danny and Amos had explained repeatedly that the rules of thumb that the mind used to cope with uncertainty often worked well. But sometimes they didn’t, and these specific failures were both interesting in and of themselves and revealing about the mind’s inner workings. Why not study them? After all, no one complained when you used optical illusions to understand the inner workings of the eye.

Gigerenzer had taken the same angle of attack as most of their other critics. But in Danny and Amos’s view, he’d ignored the usual rules of intellectual warfare, distorting their work to make them sound even more fatalistic about their fellow man than they were. He also played down or ignored most of their evidence, and all of their strongest evidence. He did what critics sometimes do: He described the object of his scorn as he wished it to be rather than as it was. Then he debunked his description.

In Europe, Amos told Danny on their walk, Gigerenzer was being praised for “standing up to the Americans,” which was odd, as the Americans in this case were Israelis. “Amos says we absolutely must do something about Gigerenzer,” recalled Danny. “And I say, ‘I don’t want to. We’ll put in a lot of time. I’ll be very angry, and I hate being angry. And it’ll be a draw.’ And Amos said, ‘I’ve never asked you for anything as a friend. I’m asking you this as a friend.’ " And Danny thought: He’s never done that before. I can’t really say no.

It wasn’t long before he wished that he had. Amos didn’t merely want to counter Gigerenzer; he wanted to destroy him. (“Amos couldn’t mention Gigerenzer’s name without using the word ‘sleazeball,’ " said the UCLA professor of management Craig Fox, Amos’s former student.) Danny, being Danny, looked for the good in Gigerenzer’s writings. He found this harder than usual to do. But Danny didn’t like being angry at people, and he contrived not to feel anger toward their new critic.

Combining his peculiar handling of the evidence with what struck Danny and Amos as a willful misreading of their words, Gigerenzer gave talks and wrote articles with provocative titles like “How to Make Cognitive Illusions Disappear.” “Making cognitive illusions disappear was really making us disappear,” said Danny. “He was obsessed. I’ve never seen anything like it.”

Gigerenzer came to be identified with a strain of thought known as evolutionary psychology, which had in it the notion that the human mind, having adapted to its environment, must be very well suited to it. It certainly wouldn’t be susceptible to systematic biases. Amos found that notion absurd. The mind was more like a coping mechanism than it was a perfectly designed tool. “The brain appears to be programmed, loosely speaking, to provide as much certainty as it can,” he once said, in a talk to a group of Wall Street executives. “It is apparently designed to make the best possible case for a given interpretation rather than to represent all the uncertainty about a given situation.” The mind, when it dealt with uncertain situations, was like a Swiss Army knife. It was a good enough tool for most jobs required of it, but not exactly suited to anything — and certainly not fully “evolved.” “Listen to evolutionary psychologists long enough,” Amos said, “and you’ll stop believing in evolution.”

Danny wanted to understand Gigerenzer better, perhaps even reach out to him. “I was always more sympathetic than Amos to the critics,” said Danny. “I tend to almost automatically take the other side.” He wrote to Amos to say that he thought the man might be in the grip of some mind-warping emotion. Perhaps they should sit down together and see if they might lead him to reason. “Even if it were true you should not say it,” Amos shot back, “and I doubt that it is true. An alternative hypothesis to which I lean is that he is much less emotional than you think, and that he is acting like a lawyer trying to score points to impress the uninformed jury, with little concern for the truth. … This does not make me like him more but it makes his behavior easier to understand.”

Danny agreed to help Amos “as a friend,” but it wasn’t long before Amos, once again, was making him miserable. They wrote, and rewrote, drafts of a response to Gigerenzer but at the same time wrote and rewrote the dispute between each other. Danny’s language was always too soft for Amos, and Amos’s language too harsh for Danny. Danny was always the appeaser, Amos the bully. They could agree on seemingly nothing. “I am so desperately unhappy at the idea of revisiting the GG postscript that I am almost ready to have a chance device (or a set of three judges) decide between our two versions,” Danny wrote to Amos. “I don’t feel like arguing about it, and what you write feels alien to me.”

Four days later, after Amos had pressed on, Danny added, “On a day on which they announce the discovery of 40 billion new galaxies we argue about six words in a postscript. … It is remarkable how ineffective the number of galaxies is as an argument for giving up in the debate between ‘repeat’ and ‘reiterate.’ " And then: “Email is the medium of choice at this stage. Every conversation leaves me upset for a long time, which I cannot afford.” To which Amos replied, “I do not get your sensitivity metric. In general, you are the most open minded and least defensive person I know. At the same time, you can get really upset because I rewrote a paragraph you like, or because you chose to interpret a totally harmless comment in an unintended negative way.”

One night in New York, while staying in an apartment with Amos, Danny had a dream. “And in this dream the doctor tells me I have six months to live,” he recalled. “And I said, ‘This is wonderful because no one would expect me to spend the last six months of my life working on this garbage.’ The next morning I told Amos.” Amos looked at Danny and said, “Other people might be impressed, but I am not.” Even if you had only six months to live, I’d expect you to finish this with me.

Not long after that exchange, Danny read a list of the new members of the National Academy of Sciences, to which Amos had belonged for nearly a decade. Once again, Danny’s name wasn’t on the list. Once again, the differences between them were there for all to see. “I asked him, why haven’t you put me forward?” said Danny. “But I knew why.” Had their situations been reversed, Amos would never have wanted to be given anything on the strength of his friendship with Danny. At bottom, Amos saw Danny’s need as weakness. “I said, ‘That’s not how friends behave,’ " said Danny.

And with that, Danny left. Walked out. Never mind Gerd Gigerenzer or the collaboration. Danny told Amos that they were no longer even friends. “I sort of divorced him,” said Danny.

Three days later Amos called Danny. He’d just received some news. A growth that doctors had discovered in his eye had just been diagnosed as malignant melanoma. The doctors had scanned his body and found it riddled with cancer. They were now giving him, at best, six months to live. Danny was the second person he’d called with the news. Hearing that, something inside Danny gave. “He was saying, ‘We’re friends, whatever you think we are.’ "

Michael Lewis is the author of The Undoing Project: The Friendship That Changed Our Minds (W.W. Norton), from which this article is adapted.