0 1–2 3–4 5–7 8–10 11–15 16+
Then they put to those same people a second question: How many seven-letter words appeared, in that same text, of the form _ _ _ _ _ n _? Of course (of course!) there had to be at least as many seven-letter words with n in the sixth position as there were seven-letter words ending in ing, as the latter was just one example of the former. People didn’t realize that, however. They guessed, on average, that the 2,000-word text contained 13.4 words ending in ing and only 4.7 words with n in the sixth position. And they did this, Amos and Danny argued, because it was easier to think of words ending in ing. Those words were more available. People’s misjudgment of the problem was simply the availability heuristic in action.
The paper was another hit.* “The Linda problem” and “the conjunction fallacy” entered the language. 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. Amos had written two entire pages of it by himself in which he sought to define, with greater precision, “representativeness.” Danny had wanted to keep the definition vague. 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.
* * *
In 1986 Danny moved with Anne to the University of California at Berkeley—the same university that had told Danny eight years earlier that he was too old for a job. “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 nineteen offers, including an overture 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 fifteen 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 short 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 only caused him 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 recognized him and not Danny, but when Danny had called to congratulate him, he had only 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 he was the greatest living psychologist in the world, 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 occupied the office beside Amos 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 he 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 three thousand 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 ten 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 coll
aboration 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 fifteen 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. In Israel they’d each had a cucumber. Now Amos had a banana. But the banana wasn’t what was provoking Danny to hurl the cucumber in his experimenter’s face. 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.
* * *
In 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 downplayed 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 UCLA professor 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. He’d avoided even visiting Germany until the 1970s. When he finally visited, he traveled the streets entertaining a strange and vivid fantasy that the houses were all empty. But Danny didn’t like being angry at people, and he contrived not to feel anger toward their new German critic. He even found himself in some slight sympathy with Gigerenzer on one point: the Linda problem. Gigerenzer had shown that, by changing the simplest version of the problem, he could lead people to the correct answer. Instead of asking people to rank the likelihood of the two descriptions of Linda, he asked: To how many of 100 people who are like Linda do the following statements apply? When you gave people that hint, they realized that Linda was more likely to be a bank teller than a bank teller active in the feminist movement. But then Danny and Amos already knew that. They’d written as much, with less emphasis, in their original paper.
At any rate, they’d always thought that the most outrageous version of the Linda problem was superfluous to the point they were making—that people judged by representativeness. The very first experiment, like their earlier work on human judgment, showed that plainly enough, and yet Gigerenzer didn’t mention it. He had found their weakest evidence and attacked it, as if it were the only evidence they had. 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. He told Amos that they were no longer even friends. “I sort of divorced him,” said Danny.
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