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“No, there are not!” Henry said.

Feynman said he could prove it. “Name a number.”

“One million.”

Feynman said, “Two million.”

“Twenty-seven!”

Feynman said, “Fifty-four,” and kept on countering with the number that was twice Henry’s, until suddenly Henry saw the point. It was his first real encounter with infinity.

For a while, because Feynman did not seem to take his work seriously, neither did Dyson. Dyson wrote his parents that Feynman was “half genius and half buffoon” (a description he later regretted). Just a few days later Dyson heard an account from Weisskopf, visiting Cornell, of Schwinger’s progress at Harvard. He sensed a connection with the very different notions he was hearing from Feynman. He had begun to see a method beneath Feynman’s flash and wildness. The next time he wrote his parents, he said:

Feynman is a man whose ideas are as difficult to make contact with as Bethe’s are easy; for this reason I have so far learnt much more from Bethe, but I think if I stayed here much longer I should begin to find that it was Feynman with whom I was working more.

A Half-Assedly Thought-Out Pictorial Semi-Vision Thing

By the physicists’ own lights their difficulties were mathematical: infinities, divergences, unruly formalisms. But another obstacle lay in the background, rarely surfacing in the standard published or unpublished rhetoric: the impossibility of visualization. How was one to perceive the atom, or the electron in the act of emitting light? What mental picture could guide the scientist? The first quantum paradoxes had so shattered physicists’ classical intuitions that by the 1940s they rarely discussed visualization. It seemed a psychological issue, not a scientific one.

The atom of Niels Bohr, a miniature solar system, had become an embarrassingly false image. In 1923, on the tenth anniversary of Bohr’s conception, the German quantum physicist Max Born hailed it: “the thought that the laws of the macrocosmos in the small reflect the terrestrial world obviously exercises a great magic on mankind’s mind”—but already he and his colleagues could see the picture fading into anachronism. It survived in the language of angular momentum and spin—as well as in the standard high-school physics and chemistry curriculums—but there was no longer anything plausible in the picture of electrons orbiting a nucleus. Instead there were waves with modes of resonance, particles that smeared out probabilistically, operators and matrices, malleable spaces with extra dimensions, and physicists who forswore the idea of visualization altogether. Bohr himself had set the tone. In accepting the Nobel Prize for his atomic model, he said it was time to give up the hope of explanations in terms of analogies with everyday experience. “We are therefore obliged to be modest in our demands and content ourselves with concepts which are formal in the sense that they do not provide a visual picture of the sort one is accustomed to require… .” This progress had not been altogether free of tension. “The more I reflect on the physical portion of Schrödinger’s theory, the more disgusting I find it,” was Heisenberg’s 1926 comment to Pauli. “Just imagine the rotating electron whose charge is distributed over the entire space with axes in 4 or 5 dimensions. What Schrödinger writes on the visualizability of his theory … I consider trash.” As much as physicists valued the conceptualizing skill they called intuition, as much as they spoke of a difference between physical understanding and formal understanding, they had nevertheless learned to mistrust any picture of subatomic reality that resembled everyday experience. No more baseballs, artillery shells, or planetoids for the quantum theorists; no more idle wheels or wavy waves. Feynman’s father had asked him, in the story he told so many times: “I understand that when an atom makes a transition from one state to another, it emits a particle of light called a photon… . Is the photon in the atom ahead of time? … Well, where does it come