John von Neumann's Dangerous Game

Von Neumann was a key member of the Manhattan Project team. Members of this gifted scientific gathering often relied on his mathematical judgment and eventually put him in charge of the mathematical calculations upon which all their theories depended. Later, as the director of the Atomic Energy Commission and an influential member of the ICBM Committee, he ended up a key policy-maker in the fields of nuclear power, nuclear weapons, and intercontinental ballistic weaponry. Von Neumann not only used his scientific expertise to hasten and accelerate the development of nuclear weapons and computer-guided missiles, but counseled military and political leaders to think about using these new American inventions against the USSR in a "preventive war." In an article published shortly after he died, von Neumann was quoted as saying: "If you say why not bomb them tomorrow, I say, why not today. If you say at five o'clock, I say why not one o'clock" (Blair, 1957, p. 96).

His contributions to the science of calculation in the late forties and early fifties were preceded by even earlier theoretical work that led to the notion of mechanical computation. In the 1940's, von Neumann learned about an Army project called ENIAC that was soon to produce a device that would be capable of performing mathematical calculations at phenomenal speeds. He was one of the principal participants in both of the lines of thought that converged into the construction of ENIAC: mathematical logic and ballistics. John von Neumann's role in the invention of mechanical computation, however, began nearly twenty years before the ENIAC project.

Von Neumann first established himself by offering models and explanations of quantum mechanics. He attempted to explain away the probabilistic elements that Heisenberg introduced into the understanding of what occurs on the sub-atomic level. He later developed this preliminary work into Mathematical Foundations of Quantum Mechanics (1955). Although he never found a complete alternative, it was totally unacceptable to von Neumann that we could know where an electron might be at any given moment only in statistical terms. In an attempt to describe human motives and behaviors in mathematical and logical terms, von Neumann formulated — and later codified in Theory of Games and Economic Behavior (1944) — the discipline of game theory. He was driven to create this discipline out of frustration at the success of Gödel's Theorem, which problematized the ideal of a consistent and complete set theory, a project towards which von Neumann had been working with Hilbert. Gödel's Theorem, like Heisenberg's Principle, represented another telling defeat for strict determinism. Even so, when humans were involved — as in game theory applied to economic strategies — von Neumann treated all the elements of a system as if they could be described through formal logic. His mathematical method seemed driven by deeper impulses than the sheer power of logic. For him, the struggle between chance and determinism seemed like an elemental duel between good and evil. Von Neumann's commitment to logic and mathematics formed a religious faith wherein science and math transcend time and space (Heims, pp. 141-162). From that perspective he helped formulate a principle that has had powerful consequences and many followers.

Von Neumann was particularly interested in mathematical questions involving turbulence. He was also engaged in new mathematical methods for modeling complex phenomena like global weather patterns and the passage of radiation through matter. Future progress in these fields was severely limited by the human inability to process the enormous number of consequent calculations or the results of the most interesting equations. By the 1940's, von Neumann's expertise in the mathematics of hydrodynamic turbulence and the management of very large calculations took on unexpected importance; these two specialties were particularly applicable to the dynamics of explosions and implosions. The designers of the first fission bomb knew that mathematical problems in both areas had to be solved before any of the elegant equations of quantum physics could be transformed into the fireball of a nuclear detonation. As von Neumann already suspected, the mathematical work involved in designing nuclear and thermonuclear weapons created an overwhelming amount of calculations.

The War Department's desire for raw calculating power led von Neumann to travel to Los Alamos in 1943 to work on the problems of unleashing and harnessing nuclear energy. His contribution is one that made it possible to create the bombs dropped on Hiroshima and Nagasaki. Due to his history of fleeing anti-Semitism, it is likely that his motives for working on the atom bomb were political. At the same time, he was driven by an equally deep, personal, and even more persistent struggle for certitude. The predominant characteristic of von Neumann's mathematical approach was his desire to describe nature in the terms of strict logical determinism untainted by incompleteness or uncertainty. At Los Alamos, he faced a particularly difficult problem for which he attempted to develop a way of simulating atomic events. His solution has had momentous fallout.

When any sufficiently large nuclear explosion occurs within a container, unless the radioactive material is properly contained and the timing of triggering explosions perfect, neutrons stream out of one side of the container. This leak causes an asymmetrical, much weaker, and more unpredictable blast. In order to make the most potent blast possible, a series of complex events must be modeled so that the radioactive material explodes symmetrically. This research appears under the hygienic guise of solving the "neutron diffusion problem." Until 1943, when von Neumann and Stanley Ulam worked on the neutron diffusion problem, there were essentially only two sorts of modeling employed by scientists and mathematicians to describe complex events: deterministic methods (which are essentially applied mathematics) and variations on stochastic techniques (which were known simply as simulation).

To get around the apparently inevitable incorporation of the random, von Neumann devised a third kind of simulation called the "Monte Carlo" in homage to the games of luck he enjoyed in the gambling capital of Europe. He held that random elements in simulations were unacceptable, a form of contamination tantamount to cheating at cards. Indeed, his aversion to stochastic modeling and his appreciation of rule-based games is at the heart of his epistemology. In the Monte Carlo simulation, Von Neumann devised a non-stochastic formula for approximating the stochastic operators in non-trivial simulations. Essentially, he had found a deterministic way to model random events. At the same time, he had rigged the game in the house's favor. When the Monte Carlo simulation worked, it suggested not only that we could describe nature without relying on randomness or chance, but that nature itself was deterministic.

Von Neumann's obsession with how Heisenberg introduced the element of randomness into science's view of the universe at its most atomic level — in the orbit of an electron around a nucleus — was further articulated in game theory as an attempt to further model human motives and actions in carefully circumscribed arenas. If, he reasoned, one could simulate and express fully all human actions in formal rational terms, one could eliminate the random from the quantum world. Von Neumann's game theory essentially created an infinite matrix upon which all possible actions by potential actors were mapped. By correlating the choices of each actor, potential outcomes could be determined with formal certainty.

Following his work with simulation, von Neumann proposed the prototypical architecture of the computer. His work, The Computer and The Brain (1958), clarified what he and others had done prior to the War in computational design. Contemporaneously, von Neumann applied what he had learned about eliminating chance to describing the human mind. Von Neumann outlined an entire programmatic for the science previously contemplated by Alan Turing; what we now know as artificial intelligence. In the simple coupling of von Neumann's title — The Computer and the Brain — he proposed a dual metaphor: the computer as brain and the brain as computer. In truth the book is only partially devoted to designing computational technologies. The second half outlines a mechanical view of individual neurons and how they transmit information. This claim is premised entirely on what is called cellular automata, the assumption that neurons are binary (like the "logical switches" von Neumann proposed as the basis for some of the first giant computers including ENIAC, EDVAC, MANIAC, and JONIAC and the "gates" proposed by Turing for his Universal Machine). Von Neumann was moving from a metaphor founded on pure conviction — the nerve as a binary switch — to embrace a model that has enjoyed prominence ever since.

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