Amos was now what people referred to, a bit confusingly, as a “mathematical psychologist.” Non-mathematical 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 non-mathematical 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?

After the seminar, Amos and Danny had a few lunches together but then headed off in separate directions. That summer Amos left for the United States, and Danny for England, to continue his study of human attention. He had all these ideas about the possible usefulness of this new interest of his. In tank warfare, for instance. Danny was now taking people into his research lab and piping one stream of digits into their left ear and another stream of digits into their right ear, to test how quickly they could switch their attention from one ear to the other, and also how well they blocked their minds to sounds they were meant to be ignoring. “In tank warfare, as in a Western shootout, the speed at which one can decide on a target and act on that decision makes the difference between life and death,” said Danny later. He might use his test to identify which tank commanders could best orient their senses at high speed—who among them might most quickly detect the relevance of a signal, and focus his attention upon it, before he got blown to bits.

Dual Personalities

By the fall of 1969, Amos and Danny had both returned to Hebrew University. During their joint waking hours, they could usually be found together. Danny was a morning person, and so anyone who wanted him alone could find him before lunch. Anyone who wanted time with Amos could secure it late at night. In the intervening time, they might be glimpsed disappearing behind the closed door of a seminar room they had commandeered. From the other side of the door you could sometimes hear them hollering at each other, but the most frequent sound to emerge was laughter. Whatever they were talking about, people deduced, must be extremely funny. And yet whatever they were talking about also felt intensely private: Other people were distinctly not invited into their conversation. If you put your ear to the door, you could just make out that the conversation was occurring in both Hebrew and English. They went back and forth—Amos, especially, always switched back to Hebrew when he became emotional.

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 soulmates. “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 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 Danny made a stab at informality, it 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 to say. Once when you worry about it, and the second time when it happens. “They were very different people,” said a fellow Hebrew University professor. “Danny was always eager to please. He was irritable and short-tempered, but he wanted to please. Amos couldn’t understand why anyone would be eager to please. He understood courtesy, but eager to please—why?” Danny took everything so seriously; Amos turned much of life into a joke. When Hebrew University put Amos on its committee to evaluate all Ph.D. candidates, he was appalled at what passed for a dissertation in the humanities. Instead of raising a formal objection, he merely said, “If this dissertation is good enough for its field, it’s good enough for me. Provided the student can divide fractions!”