'John von Neumann and Stochastic Simulations'
John von Neumann and stochastic simulations, Understanding Society: John von Neumann was one of the genuine mathematical geniuses of the twentieth century. A particularly interesting window onto von Neumann's scientific work is provided by George Dyson in his book, Turing's Cathedral: The Origins of the Digital Universe. The book is as much an intellectual history of the mathematics and physics expertise of the Princeton Institute for Advanced Study as it is a study of any one individual, but von Neumann plays a key role in the story. His contribution to the creation of the general-purpose digital computer helped to lay the foundations for the digital world in which we now all live.
There are many interesting threads in von Neumann's intellectual life, but one aspect that is particularly interesting to me is the early application of the new digital computing technology to the problem of simulating large complex physical systems. Modeling weather and climate were topics for which researchers sought solutions using the computational power of first-generation digital computers, and the research needed to understand and design thermonuclear devices had an urgent priority during the war and post-war years. Here is a description of von Neumann's role in the field of weather modeling in designing the early applications of ENIAC (P. Lynch, "From Richardson to early numerical weather prediction"; link):
John von Neumann recognized weather forecasting, a problem of both great practical significance and intrinsic scientific interest, as ideal for an automatic computer. He was in close contact with Rossby, who was the person best placed to understand the challenges that would have to be addressed to achieve success in this venture. Von Neumann established a Meteorology Project at the Institute for Advanced Study in Princeton and recruited Jule Charney to lead it. Arrangements were made to compute a solution of a simple equation, the barotropic vorticity equation (BVE), on the only computer available, the ENIAC. Barotropic models treat the atmosphere as a single layer, averaging out variations in the vertical. The resulting numerical predictions were truly ground-breaking. Four 24-hour forecasts were made, and the results clearly indicated that the large-scale features of the mid-tropospheric flow could be forecast numerically with a reasonable resemblance to reality. (Lynch, 9)
image: (link, 10)
A key innovation in the 1950s in the field of advanced computing was the invention of Monte Carlo simulation techniques to assist in the invention and development of the hydrogen bomb. Thomas Haigh, Mark Priestley, and Crispin Rope describe the development of the software supporting Monte Carlo simulations in the ENIAC machine in a contribution to the IEEE Annals of the History of Computing (link)....MORE