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Welton became the fourth physicist in the group Feynman headed, now formally known as T-4, Diffusion Problems. As a group leader Feynman was ebullient and original. He drove his team hard in pursuit of his latest unorthodox idea for solving whatever problem was at hand. Sometimes one of the scientists would object that a Feynman proposal was too complex or too bizarre. Feynman would insist that they try it out, computing in groups with their mechanical calculators, and he had enough unexpected successes this way to win their loyalty to the cause of wide-ranging experimentation. They all tried to innovate in his fashion—no idea too wild to be considered. He could be ruthless with work that did not meet his high standards. Even Welton experienced the humiliation of a Feynman rebuke—“definitely ungentle humor” to which “only a fool would have subjected himself twice.” Still Feynman managed to build esprit. He had taught himself to flip a pencil in one motion from a table into his hand, and he taught the same trick to his group. One day, amid a typical swirl of rumors that military uniforms were going to be issued to scientists working in the technical area, Bethe walked in to talk about a calculation. Feynman said he thought they should integrate it by hand, and Bethe agreed. Feynman swiveled around and barked, “All right, pencils, calculate!”

A roomful of pencils flipped into the air in unison. “Present pencils!” Feynman shouted. “Integrate!” And Bethe laughed.

Diffusion, that faintly obscure and faintly pedestrian holdover from freshman physics, lay near the heart of the problems facing all the groups. Open a perfume bottle in a still room. How long before the scent reaches a set of nostrils six feet away, eight feet away, ten feet away? Does the temperature of the air matter? The density? The mass of the scent-bearing molecules? The shape of the room? The ordinary theory of molecular diffusion gave a means of answering most of these questions in the form of a standard differential equation (but not the last question—the geometry of the containing walls caused mathematical complications). The progress of a molecule dependedon a herky-jerky sequence of accidents, collisions with other molecules. It was progress by wandering, each molecule’s path the sum of many paths, of all possible directions and lengths. The same problem arose in different form as the flow of heat througha metal. And the central issues of Los Alamos, too, were problems of diffusion in a newguise.

The calculation of critical mass quickly became nothing more or less than a calculation of diffusion—the diffusion of neutrons through a strange, radioactive minefield, where now a collision might mean more than a glancing, billiard-ball change of direction. A neutron might be captured, absorbed. And it might trigger a fission event that would give birth to new neutrons. By definition, at critical mass the creation of neutrons would exactly balance the loss of neutrons through absorption or through leakage beyond the container boundaries. This was not a problem of arithmetic. It was a problem of understanding the macroscopic spreading of neutrons as built up from the microscopic individual wanderings.

For a spherical bomb the mathematics resembled another strange and beautiful diffusion problem, the problem of the sun’s limb darkening. Why does the sun have a crisp edge? Not because it has a solid or liquid surface. On the contrary, the gaseous ball of the sun thins gradually; no boundary marks a division between sun and empty space. Yet we see a boundary. Energy diffuses outward from the roiling solar core toward the surface, particles scattering one another in tangled paths, until finally, as the hot gas thins, the likelihood of one more collision disappears. That creates the apparent edge, its sharpness more an artifact of the light than a physical reality. In the language of statistical mechanics, the mean free path—the average distance a particle travels between one collision and the next—becomes roughly as large