Writing this reminds me of a feeling I once had when I visited the cyclotron in Chicago with Fermi. He took me around and made me walk through an incredibly heavy door, which he said "would flatten you into a piece of paper were it closed on you." We walked between the poles of the magnet, and I reached into my pocket for the penknife with which I sometimes play. Suddenly it was jerked out of my hand when I touched it. The power of the vacuum! This made me physically conscious of the reality of "empty" space.
Feynman was also interested in many purely mathematical recreations not related to physics. I remember how he once gave an amusing talk about triangular numbers and managed to entertain everybody with his humor. At the same time, he was doing mathematics, and showing the foolishness of excessive cleverness and the irrationality of such strange interests.
One day he recited to me the following:
and so on.
It all depends on where you put the intonation, conveying a different meaning in every case. He did it marvelously in five or six styles, each with different stresses, as it were, most humorously.
Physically, Los Alamos consisted of a collection of two-and four-apartment buildings, temporary Army structures which turned out to be sturdy enough to survive for many years after the end of the war. To his everlasting credit, Oppenheimer insisted that they be laid out along the contours of the land, retaining as many trees as possible, instead of in the monotonous rectangular pattern of army camps and company towns. Still they were rather primitive, equipped with coal furnaces and coal stoves in the kitchens. People griped about the inadequacies of the housing situation, and wives had all sorts of complaints. But I found Los Alamos on the whole quite comfortable. The climate of New Mexico — Los Alamos in particular, at an elevation of seventy-two hundred feet — was one of the best I have ever lived in.
Placzek, a physicist who joined the project after the war, felt that east of the Rocky Mountains the United States was on the whole climatically uninhabitable, "unbewohnbar." This is true especially for Europeans who are not accustomed to hot and muggy summers or to penetrating winter cold. In Cambridge, I used to tell my friends that the United States was like the little child in a fairy tale, at whose birth all the good fairies came bearing gifts, and only one failed to come. It was the one bringing the climate.
Soon after my arrival in Los Alamos I met David Hawkins, a young philosopher from Berkeley, one of the people Oppenheimer had brought with him to staff the administration of the Laboratory. We hit it off intellectually right away.
Hawkins is a tallish, blue-eyed, blond descendant of early New Mexico settlers. His father, Judge Hawkins, was a famous figure at the turn of the century. He was a lawyer and an official of the Territory, important in the Santa Fe Railroad operations. David was brought up in the small community of La Luz, in the southern part of the State. I mention this because later, when the bomb was exploded in the Jornada del Muerte desert near Alamagordo, David worried that blinding flashes or the heat and shock phenomena might be dangerous for people living in La Luz, some thirty or forty miles away, where his sister had her home.
Hawkins is a man of wide interests, with great breadth of knowledge, very good education, and a very logical mind. He regards scientific problems not as a narrow specialist, but from a general epistemological and philosophical point of view. To top it off, he is the most talented amateur mathematician I know. He told me that at Stanford he took some courses from Ouspenski, the Russian émigré specialist in probability and number theory, but he has not had any extensive training in mathematics. He has a very great natural feeling for it and a talent for manipulation. He is the most impressive of the non-professional mathematicians or physicists I have met anywhere in the world.
We discussed problems of neutron chain reactions and the probability problems of branching processes, or multiplicative processes, as we called them in 1944.
I was interested in the purely stylized problem of a branching tree of progeny from one neutron which may multiply, into zero (that is, the death of a neutron by absorption), or one (that just continues itself), or two or three or four (that is, causes the emergence of new neutrons), each possibility with a given probability. The problem is to follow the future course and the chain of possibilities through many generations.
Very early Hawkins and I detected a fundamental trick to help study such branching chains mathematically. The so-called characteristic function, a device invented by Laplace and useful for normal "addition" of random variables, turned out to be just the thing to study "multiplicative" processes. Later we found that observations to this effect had been made before us by the statistician Lotka, but the real theory of such processes, based on the operation of iteration of a function or of operators allied to the function (a more general process), was begun by us in Los Alamos, starting with a short report. This work was strongly generalized and broadened in 1947, after the war, by Everett and myself after he joined me in Los Alamos. Some time later, Eugene Wigner brought up a question of priorities. He was eager to note that we did this work quite a bit before the celebrated mathematician Andrei N. Kolmogoroff and other Russians and some Czechs had laid claim to having obtained similar results.
I liked Hawkins's general curiosity, his almost unique knowledge of the fundamentals of several scientific theories — not only in the conceptual elements of physics but in biology and even economics. I liked his interest and genuinely original work in what was to become known as "information theory" after it became formalized by Wiener and especially by Claude Shannon. David applied to economic problems the mathematical ideas of von Neumann and Morgenstern in game theory.
Hawkins has since written several interesting papers and an excellent book on the philosophy of science, or rather on the philosophy of rational thinking, called The Language of Nature.
Hawkins's position in Los Alamos at first was as a liaison between Oppenheimer's office and the military. Some years later he wrote two volumes, since declassified, about the organization and the scientific history from the early days of Los Alamos until the end of the war. I did not know it at the time (and it was not obvious from conversations with him) that in the nineteen thirties he had been involved on the West Coast with communist sympathizer groups. That caused him great trouble before and during the McCarthy era, including hearings in Washington. He came out of it completely vindicated.
His wife, Frances, an extremely interesting person, became friendly with Françoise, and we saw each other a great deal. At the time of my illness in California in 1946, the Hawkinses were immensely helpful to us in caring for our daughter Claire, who was then an eighteen-month-old infant.
Hawkins left Los Alamos after the end of the war to take the post of professor of philosophy at the University of Colorado in Boulder, where he is today.
The Los Alamos community was completely different from any where I had ever lived and worked. Even Lwów, which had a dense concentration of people and where the mathematicians and university people were in daily contact and spent much time together in restaurants and coffee houses, did not have the degree of togetherness of Los Alamos. It was even more pronounced there because of the isolation and the smallness of the town, and the proximity of all the buildings. People visited each other constantly at all hours after work. What was novel to me was that these were not mathematicians (except von Neumann and two or three younger persons), but physicists, chemists, and engineers — psychologically quite different from my more inward-oriented mathematical colleagues. The variety and richness of the physicists was interesting and delightful to observe. On the whole, theoreticians and experimentalists differed in temperament.