From Turing and von Neumann to the Present

The notion of automata in the sense of machines that operate on their own from encoded instructions is very ancient, and one might say that mechanical clocks and music boxes fall under this category. The idea of computing machines is also very old. For instance. Pascal and Leibnitz outlined various schematics for such machines. In the latter part of the 18th century Baron de Kempelen built what was alleged to be the first chess-playing machine. Remarkable as it appeared. alas, it was a fake operated by a person hidden within it! The modern theory of automata can be traced to two giants in the field of mathematics. Alan Turing and John von Neumann. These two men laid much of the logical foundation for the development of present-day electronic computers, and both were involved in the practical design of real computing machines. Before World War II Turing had proved the logical limits of computability and on the basis of this work had designed in idealized terms a universal computer, a machine that could perform all possible numerical computations. This idealized machine is now known as a Turing machine. (All modern computers have capabilities equivalent to some of the universal Turing machines.) During World War H Turing successfully applied his logical talent to the real and urgent problem of breaking the Nazi intelligence code. a feat that played a crucial role in the Allied victory. Prior to World War II von Neumann was aware of Turing’s work on computing machines and realized how useful such machines would be for investigating nonlinear problems in mathematical physics, in particular. the fascinating problem of turbulence. Numerical calculations might, for example, elucidate the mysterious role of t h e R e y n o l d s n u m b e r i n t u r b u l e n t phenomena. (The Reynolds number gives roughly the ratio of the inertial forces to the viscous forces. A flow that is regular becomes turbulent when this number is about 2000.) He was convinced that the best mathematics proceeds from empirical science and that numerical calculation on electronic computers might provide a new kind of empirical data on the properties of nonlinear equations. Stan Ulam suggests that the final impetus for von Neumann to work energetically on computer methods and design came from wartime Los Alamos, where it became obvious that analytical work alone was often not sufficient to provide even qualitative answers about the behavior of an atomic bomb. The best way to construct a computing machine thus presented a practical as well as a theoretical problem. Starting in 1944 von Neumann formulated methods of translating a set of mathematical procedures into a language of instructions for a computing machine. Before von Neumann’s work on the logical design of computers, the few existing electronic machines had to be rewired for each new problem. Von Neumann developed the idea of a fixed “flow diagram” and a stored “code,” or program, that would enable a machine with a fixed set of connections to solve a great variety of problems. Von Neumann was also interested, as was Turing, in discovering the logical elements