Danny was also training Air Force flight instructors to train fighter pilots. (But only on the ground: The one time they took him up in a plane he vomited into his oxygen mask.) How did you get fighter pilots to memorize a series of instructions? “We started making a long list,” recalled Zur Shapira. “Danny says no. He tells us about ‘The Magical Number Seven.’” “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information” was a paper, written by Harvard psychologist George Miller, which showed that people had the ability to hold in their short-term memory seven items, more or less. Any attempt to get them to hold more was futile. Miller half-jokingly suggested that the seven deadly sins, the seven seas, the seven days of the week, the seven primary colors, the seven wonders of the world, and several other famous sevens had their origins in this mental truth.
At any rate, the most effective way to teach people longer strings of information was to feed the information into their minds in smaller chunks. To this, Shapira recalled, Danny added his own twist. “He says you only tell them a few things—and get them to sing it.” Danny loved the idea of the “action song.” In his statistics classes he had actually asked his students to sing the formulas. “He forced you to engage with problems,” said Baruch Fischhoff, a student who became a professor at Carnegie Mellon University, “even if they were complicated problems without simple solutions. He made you feel you could do something useful with this science.”
A lot of the problems Danny threw at his students felt like pure whim. He asked them to design a currency so that it was hard to counterfeit. Was it better for bills of different denominations to resemble each other, as they did in the United States, thus leading anyone accepting them to examine them closely; or should they have a wide variety of colors and shapes so that they were harder to copy? He asked them how they would design a workplace to make it more efficient. (And of course they must be familiar with the psychological research showing that some wall colors led workers to be more productive than others.) Some of Danny’s problems were so abstruse and strange that the student’s first response was, Um, we’ll need to go to the library and get back to you on that. “When we said that,” recalled Zur Shapira, “Danny responded—mildly upset—by saying, ‘You have completed a three-year program in psychology. You are by definition professionals. Don’t hide behind research. Use your knowledge to come up with a plan.’”
But what were you supposed to say when Danny brought in a copy of a doctor’s prescription from the twelfth century, sloppily written, in a language you didn’t know a word of, and asked you to decode it? “Someone once said that education was knowing what to do when you don’t know,” said one of his students. “Danny took that idea and ran with it.” One day Danny brought in a stack of those games in which the object is to guide a small metal ball through a wooden maze. The assignment he gave his students: Teach someone how to teach someone else how to play the game. “It would never occur to anyone that you could teach this,” recalled one of the students. “The trick was to break it down into the component skills—learning how to hold your hand steady, learning how to tilt slightly to the right, and so on—then teach them separately and then, once you’d taught them all, put them together.” The guy at the store who sold the games to Danny found the whole idea of it hysterical. But to Danny, useful advice, however obvious, was better than no advice at all. He asked his students to figure out what advice they would give to an Egyptologist who was having difficulty deciphering a hieroglyph. “He tells us that the guy is going slower and slower and getting more and more stuck,” recalled Daniela Gordon, a student who became a researcher in the Israeli army. “Then Danny asks, ‘What should he do?’ No one could think of anything. And Danny says; ‘He should take a nap!’”
Danny’s students left every class with a sense that there was really no end to the problems in this world. Danny found problems where none seemed to exist; it was as if he structured the world around him so that it might be understood chiefly as a problem. To each new class the students arrived wondering what problem he might bring for them to solve. Then one day he brought them Amos Tversky.
5
THE COLLISION
Danny and Amos had been at the University of Michigan at the same time for six months, but their paths seldom crossed; their minds, never. Danny had been in one building, studying people’s pupils, and Amos had been in another, devising mathematical approaches to similarity, measurement, and decision making. “We had not had much to do with each other,” said Danny. The dozen or so graduate students in Danny’s seminar at Hebrew University were all surprised when, in the spring of 1969, Amos turned up. Danny never had guests: The seminar was his show. Amos was about as far removed from the real-world problems in Applications of Psychology as a psychologist could be. Plus, the two men didn’t seem to mix. “It was the graduate students’ perception that Danny and Amos had some sort of rivalry,” said one of the students in the seminar. “They were clearly the stars of the department who somehow or other hadn’t gotten in sync.”
Before he left for North Carolina, Amnon Rapoport had felt that he and Amos disturbed Danny in some way that was hard to pin down. “We thought he was afraid of us or something,” said Amnon. “Suspicious of us.” For his part, Danny said he’d simply been curious about Amos Tversky. “I think I wanted a chance to know him better,” he said.
Danny invited Amos to come to his seminar to talk about whatever he wanted to talk about. He was a little surprised that Amos didn’t talk about his own work—but then Amos’s work was so abstract and theoretical that he probably decided it had no place in the seminar. Those who stopped to think about it found it odd that Amos’s work betrayed so little interest in the real world, when Amos was so intimately and endlessly engaged with that world, and how, conversely, Danny’s work was consumed by real-world problems, even as he kept other people at a distance.
Amos was now what people referred to, a bit confusingly, as a “mathematical psychologist.” Nonmathematical psychologists, like Danny, quietly viewed much of mathematical psychology as a series of pointless exercises conducted by people who were using their ability to do math as camouflage for how little of psychological interest they had to say. Mathematical psychologists, for their part, tended to view nonmathematical psychologists as simply too stupid to understand the importance of what they were saying. Amos was then at work with a team of mathematically gifted American academics on what would become a three-volume, molasses-dense, axiom-filled textbook called Foundations of Measurement—more than a thousand pages of arguments and proofs of how to measure stuff. On the one hand, it was a wildly impressive display of pure thought; on the other, the whole enterprise had a tree-fell-in-the-woods quality to it. How important could the sound it made be, if no one was able to hear it?