As for myself, after this first work on Edward's problem, I spread out my interests to other related questions, one being the problem of statistics of neutron multiplication. This was more tangible for me from the purely mathematical side. I discussed such problems of branching and multiplying patterns with David Hawkins. We wrote a report on multiplicative branching processes, which had some practical application and relevance to the problem of the initial detonation of the bomb by a few neutrons. This problem was also studied by Stan Frankel and by Feynman, in a more technical and classical way. Our paper could be considered the beginning of what would come to be known in mathematics as branching processes theory, a sub-field of probability theory.
I also talked a lot with von Neumann and Calkin about problems of hydrodynamics, especially those concerning the process of implosion. Somewhat to my surprise I found my purely abstract intellectual habits as a mathematician immediately useful in the work with these more practical, special, and tangible problems. I have never felt the "gap" between the mode of thinking in pure mathematics and the thinking in physics, on which many mathematicians place so much stress. Anything amenable to mental analysis was congenial for me. I do not mean the distinction between rigorous thinking and more vague "imaginings"; even in mathematics itself, all is not a question of rigor, but rather, at the start, of reasoned intuition and imagination, and, also, repeated guessing. After all, most thinking is a synthesis or juxtaposition of advances along a line of syllogisms — perhaps in a continuous and persistent "forward'' movement, with searching, so to speak "sideways," in directions which are not necessarily present from the very beginning and which I describe as "sending out exploratory patrols" and trying alternative routes. It is all a multicolored thing, not very easy to describe in a way that a reader can appreciate. But I hope this kind of personal analysis of thinking in science is one of the possible interests of this book.
A discussion with von Neumann which I remember from early 1944 took several hours, and concerned ways to calculate the course of an implosion more realistically than the first attempts outlined by him and his collaborators. The hydrodynamical problem was simply stated, but very difficult to calculate — not only in detail, but even in order of magnitude.
In particular, the questions concerned values of certain numbers relating to compression versus pressure, and such. These had to be known, let us say within ten per cent or better, but the simplifications made in the outline of the calculations were of such a nature that they could not guarantee accuracy within a factor of two or three. All the ingenious shortcuts and theoretical simplifications which von Neumann and other mathematical physicists suggested, and which he tried to execute with the help of Calkin, seemed inadequate to me. In this discussion I stressed pure pragmatism and the necessity for attempting to get a heuristic survey of the general problem by simpleminded brute force — that is, more realistic, massive numerical work. At that time, in 1944, with the available computing facilities, the accuracy of the necessary numerical work could not be satisfactory. This was one of the first reasons for pressing for the development of electronic computers.
One of the charms and great attractions of life in Los Alamos in those days was the lunches at the Lodge, in the midst of friends. I was very surprised to find there and gradually to meet so many famous persons I had heard about.
Los Alamos was a very young place. At thirty-four, I was already one of the older people. What impressed me most was the very great competence of the younger people and the variety of their fields of specialization. It was almost like having an encyclopedia to look at, something that I so much like to do. I had the same feeling when talking to the young scientists around the laboratory. It is not the right expression perhaps but, roughly speaking, they were more accomplished in depth than in breadth. The older men, many of whom were European-born, had a more general knowledge. Yet science had become so ramified, specialization had proceeded so far, that it was quite difficult to retain knowledge of all the details and the overall view at the same time.
The younger scientists showed a lot of common sense in their own fields, but in general a great hesitation to engage in speculation outside their areas. Perhaps this stemmed from a fear of not being "absolutely right." Many displayed a certain anti-philosophical spirit — not anti-intellectual, but anti-philosophical. This was perhaps because of the pragmatic nature of American attitudes.
I was also struck by the well-known American talent for cooperation, the team spirit, and how it contrasted with what I had known in continental Europe. I remembered how Jules Verne had anticipated this when he wrote about the collective effort needed for the organization of his "Voyage to the Moon." People here were willing to assume minor roles for the sake of contributing to a common enterprise. This spirit of team work must have been characteristic of life in the nineteenth century and was what made the great industrial empires possible. One of its humorous side effects in Los Alamos was a fascination with organizational charts. At meetings, theoretical talks were interesting enough to the audience, but whenever an organizational chart was displayed, I could feel the whole audience come to life with pleasure at seeing something concrete and definite ("Who is responsible to whom," etc.). Organization was and perhaps still is a great American talent, although this is written at a time when the so-called energy crisis appears to me to be more a crisis of momentum than of energy (a crisis of enterprise, solidarity, common spirit, determination, and cooperation for the common good).
It is difficult to describe for the general reader the intellectual flavor, the feeling, of a scientific "atmosphere." There is no specific English word for this impression. Odor and smell have unpleasant connotations; perfume is artificial; aura is suggestive of mystery, of the supernatural. The younger scientists did not have much of an aura, they were bright young men, not geniuses. Perhaps only Feynman among the young ones had a certain aura.
Six or seven years younger than I, he was brilliant, witty, eccentric, original. I remember one day Bethe's laughter shook the corridor walls, making me rush out of my office to see what was so funny. Three doors down in Bethe's office, Feynman was standing — talking and gesticulating. He was telling the story of how he had failed his draft physical examination, re-enacting his now famous gesture: when a doctor asked him to show his hands, he chose to stretch them in front of him one with palm up, the other palm down. The doctor said, "The other side!" and he reversed both hands. This and other incidents of his physical examination had caused an explosion of laughter on the entire floor. It was on the first or second day in Los Alamos that I met Feynman, and remarked to him about my surprise that E = mc2 — which I of course believed in theoretically but somehow did not really "feel" — was, in fact, the basis of the whole thing and would bring about a bomb. What the whole Project was working on depended on those few little signs on paper. Einstein himself, when he was first told before the war about radioactive phenomena showing the equivalence of mass and energy, allegedly replied, "Ist das wirklich so? ist das wirklich so?" (Is that really so?)
Jokingly I told Feynman, "One day people will discover that a cubic centimeter of vacuum is really worth ten thousand dollars — it is equivalent to so much energy." He immediately agreed and added, "Yes, but of course it will have to be pure vacuum!" Indeed, people now know about the polarization of vacuum. The force between two electrons or two protons is not e2/r2, but an infinite series of which this is the first term. It works on itself, like two almost-parallel mirrors, which show a reflection of a reflection of a reflection, ad infinitum.