All of these details concerning the origins of the hydrogen bomb, to the extent that we can put them together from declassified information, underscore Ulam as far more influential than has previously been known. Not only was he the first to dismantle the earlier Super concept which had been so inflexibly proposed for many years, he provided the key idea that resolved the difficulties of both ignition and propagation. In this instance, more than any other in Ulam's scientific career, he demonstrated "how a few scribbles on a blackboard or on a sheet of paper" have quite radically and irreversibly changed the course of human affairs."
In view of the impact that the arsenal of nuclear weapons has had on world affairs, it is intriguing that Ulam returns in his autobiography several times to discuss the mindset and social role of weapons scientists who sequester themselves in top secret laboratories to invent and construct instruments of potential mass destruction. Most of the scientists who worked at Los Alamos during World War II were shocked by the annihilation of Japanese cities and elected to return to academic life after the war. It is likely that many of those who stayed on at Los Alamos or returned later were inherently apolitical and, like Ulam, were "mainly interested in the scientific aspects of the work," having "no qualms about returning to the laboratory to contribute to further studies of the development of atomic bombs." Although Ulam later felt that the stockpile of nuclear weapons had grown larger than necessary in his view there was nothing intrinsically "bad" about the mathematics or the laws of nature used in creating new weapons. Knowledge itself is without moral content. In particular, Ulam ''never had any questions about doing purely theoretical work" on nuclear weapons, leaving to others their construction and application to political and military ends.
Ulam makes a curious distinction between the acquisition of knowledge concerning new instruments of mass destruction by scientists and its wider dissemination: "I sincerely felt it was safer to keep these matters in the hands of scientists and people who are accustomed to objective judgments rather than in those of demagogues or jingoists, or even well-meaning but technically uninformed politicians." However, in a government-funded laboratory such as Los Alamos, the symbiosis that exists between weapons technology and political decisions is inescapable. While Ulam insists that "one should not initiate projects leading to possibly horrible ends," it would nevertheless be "unwise for the scientists to turn away from problems of technology" since ''this could leave it in the hands of dangerous and fanatical reactionaries." In spite of these apparent contradictions, Ulam's justifications of his role in weapons development provide us with one of the few insights into the personal attitudes of a Los Alamos scientist toward the end products of his work.
By virtue of his defense work at the Los Alamos Laboratory, Ulam enjoyed many advantages not available to academic scientists. Chief among these was his early access to the most powerful and fastest computers in existence. For several decades after the war, the computing facilities at the national weapons labs far exceeded those available to university scientists working on non-classified research. This was an advantage that Ulam exploited in a variety of remarkable ways.
The growth of powerful computers was initially driven by the war effort. At the beginning of World War II there were no electronic computers in the modern sense, only a few electromechanical relay machines. During the war, scientists at the University of Pennsylvania and at the Aberdeen Proving Ground in Maryland developed the ENIAC, the Electronic Numerical Integrator and Computer, which had circuitry specifically designed for computing artillery firing tables for the Army. By modern standards, this early computer was extremely slow and elephantine: the ENIAC operating at the University of Pennsylvania in 1945 weighed thirty tons and contained about eighteen thousand vacuum tubes with 500,000 soldered connections. While on a visit to the University of Pennsylvania in 1944, John von Neumann was inspired to design an electronic computer that could be programmed in the modern sense, one which could be instructed to perform any calculation and would not be restricted to computing artillery tables. The new computer would have circuits that could perform sequences of fundamental arithmetic operations such as addition and multiplication. Von Neumann desired a more flexible computer to solve the mathematically difficult A-bomb implosion problem being discussed at Los Alamos. The first electronic computer at Los Alamos, however, known as the MANIAC (Mathematical Analyzer, Numerical Integrator and Computer), was not available until 1952.
One of Ulam's early insights was to use the fast computers at Los Alamos to solve a wide variety of problems in a statistical manner using random numbers, a method which has become appropriately known as the Monte Carlo method. It occurred to Ulam during a game of solitaire that the probability of various outcomes of the card game could be determined by programming a computer to simulate a large number of games. Newly selected cards could be chosen from the remaining deck at random, but weighted by the probability that such a card would be the next selected. The computer would use random numbers whenever an unbiased choice was necessary. When the computer had played thousands of games, the probabilty of winning could be accurately determined. In principle the probability of solitaire success could be rigorously calculated using probabilty theory rather than computers. However, this approach is impossible in practice since it would involve too many mathematical steps and exceedingly large numbers. The advantage of the Monte Carlo method is that the computer can be efficiently programmed to execute each step in a particular game according to known probabilities and the final outcome can be determined to any desired precision depending on the number of sample games computed. The game of solitaire is an example of how the Monte Carlo method can be used to solve otherwise intractable problems with brute computational power.
An early application of the Monte Carlo method using high speed computers was to study the propagation of neutrons in fission bombs. This was accomplished by randomly picking the position of a radioactive nucleus that would release a neutron, then randomly selecting the neutron's energy, its direction of motion, and the distance the neutron would travel before either escaping or colliding with the nucleus of another atom. In the latter event, the neutron would either be scattered, absorbed, or could induce nuclear fission according to probabilities again selected with random numbers. In this manner, after many neutron life experiences had been calculated, it was possible to determine the number of neutrons at any energy moving in a particular direction at any position in the apparatus. The Monte Carlo method is also well-suited to computing the equilibrium properties of materials, in estimating the efficiency of radiation or particle detectors having complicated geometries, and in simulating experimental data for a wide variety of physical problems.