Ours was the biggest problem ever, vastly larger than any astronomical calculation done to that date on hand computers, and it needed the most advanced electronic equipment available. By then von Neumann's Princeton MANIAC was functioning and a duplicate version was being built in Los Alamos under the direction of Metropolis.
Still Teller kept on hinting that not enough work was being done on his original scheme for the ignition of the "super." He kept insisting on certain special approaches of his own. I must admit that I became irritated by his insistence; in collaboration with my friend Everett one day I decided to try a schematic pilot calculation which could give an order of magnitude, at least, a "ballpark" estimate of the promise of his scheme.
Before we started this calculation of' the progress of a thermonuclear reaction (burning in a mass of deuterium or deuterium-tritium mixture), Everett and I had done a lot of work on probability questions connected with the active assemblies of uranium and with neutron multiplications. We worked out a theory of multiplicative processes, as we called it. (Now the preferred name is "branching processes.") This work followed the ideas developed in the report on branching processes written with David Hawkins during the war. But it elaborated, deepened, and extended them very greatly. The report of Hawkins and myself conisted of a few pages. The results of several months' work with Everett were contained in three large reports of a hundred pages or more. The latter became the basis for much subsequent work, some of it done later independently by Russian and Czech scientists.
Within the formal organization of the laboratory, I was the leader of Group T-8, and Everett was its only member. Every day, in his office adjoining mine, we had done quite a lot of other mathematical work not necessarily connected with the current programmatic questions of Los Alamos and we would discuss the "universe" (Johnny's expression), mathematical or otherwise.
Now we started to work each day for four to six hours with slide rule, pencil, and paper, making frequent quantitative guesses, and managed to get approximate results much more quickly than the gigantic problem, which was progressing slowly. Much of our work was done by guessing values of geometrical factors, imagining intersections of solids, estimating volumes, and estimating chances of points escaping. We did this repeatedly for hours, liberally sprinkling the guesses with constant slide-rule calculations. It was long and arduous work, the results of which gave a rather discouraging picture of the feasibility of the original "super" scheme. Our calculation showed its enormous practical difficulties and threw grave doubts on the prospects of Edward's original approach to the initial ignition conditions of the "super."
We proceeded something like this: each morning I would attempt to supply several guesses as to the value of certain coefficients referring to purely geometrical properties of the moving assembly involving the fate of the neutrons and other particles going through it and causing, in turn, more reactions. These estimates were interspersed with stepwise calculations of the behavior of the actual motions. The reader should realize that the real times for the individual computational steps were short, each less than a "shake," and the spatial subdivisions of the material assembly very small in linear dimensions. Each step took a fraction of a "shake." A "shake" was the name given in Los Alamos during the war to the time interval of 10-8 seconds. Another unit was that of a cross section called a "barn''; it was 10–24 of a square centimeter, a terribly small area. The number of individual computational steps was therefore very large. We filled page upon page of calculations, much of it done by Everett. In the process he almost wore out his own slide rule, and when our results were achieved, after several months of work, Everett joked that "the grateful government could at least offer to buy him a new slide rule." I do not know how many man-hours were spent on this problem.
To write the reports we enlisted the help of professional computers, Josephine Elliott among them. Even Françoise was pressed into service, grinding out untold numbers of arithmetical operations on desk calculators.
Lengthy as this process was, the work was finished several months before the Princeton electronic computer's results started coming in. This so-to-speak homespun part of the H-bomb development was described in many official and popular accounts. It caught the public eye probably because of the certain appeal of its "man versus machine" element.
As our calculation progressed it naturally attracted quite a lot of attention among the physicists Teller was trying to interest in the "super" project, and also among those Bradbury had already enlisted for this work. Distinguished visitors would appear periodically to see how the calculations were going. John Wheeler's first visits to Los Alamos date from about this period.
One day Fermi and Rabi came to our office, and we showed them the results which pointed to the mediocre progress of the reaction. These results could only be indicative and were by no means certain because of the crude approximations and guesses which we used in the place of voluminous numerical operations.
When it appeared that the technical difficulties of Teller's original ideas could justify some of the scientific and political objections of certain physicists, and even perhaps the reluctance of the General Advisory Committee, Hans Bethe evidenced a renewed interest in the whole project and came to visit Los Alamos more often. With his wonderful virtuosity in mathematical physics and with his ability to solve analytical problems of nuclear physics he helped significantly. After all, it was Bethe who first suggested (Weizsäcker in Germany had reached the same conclusion independently) that nuclear reactions in the interior of the sun could be responsible for the sun's energy generation and thus explain the radiation emitted by the sun and by other stars. Their original "carbon reaction mechanism" has been found not to be quite so exclusively responsible for the energy generation in all stars as was originally thought.
Teller was not easily reconciled to our results. I learned that the bad news drove him once to tears of frustration, and he suffered great disappointment. I never saw him personally in that condition, but he certainly appeared glum in those days, and so were other enthusiasts of the H-bomb project. Subdued and depressed, he would visit our offices periodically, and would attempt to prove us wrong by trying to find mistakes. Once he said, "There is a mistake here by a factor 104." This especially annoyed Everett who did not have much self-confidence as a physicist but who, as a mathematician, amazingly enough never made mistakes. He used to say, "I never make mistakes" and this was true in that he never used a wrong sign or made simple numerical mistakes, as mathematicians often do. But each time he tried, Edward had to admit that it was he who was at fault in his arithmetic.
As the results of the von Neumann-Evans calculation on the big electronic Princeton machine slowly started to come in, they confirmed broadly what we had shown. There, in the course of the calculation, in spite of an initial, hopeful looking "flare up," the whole assembly started slowly to cool down. Every few days Johnny would call in some results. "Icicles are forming," he would say dejectedly.
These computations were the best one could do theoretically in those days. Because the existing experimental values for the constants which had to be applied in the calculations for the cross sections were uncertain, the project was still alive, but it was necessary to search for alternative approaches to ignition.
All along Johnny was emotionally involved in favor of the construction of an H-bomb. He hoped that in one way or another a good scheme would be found, and he never lost heart even when the mathematical results for the original approach were negative.