"Kurt Gödel's achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible … - John von Neumann

It is a well known phenomenon in many branches of the exact and physical sciences that very great numbers are often easier to handle than those of medium size. An almost exact theory of a gas, containing about 1025 freely moving particles, is incomparably easier than that of the solar system, made up of 9 major bodies; and still more than that of a multiple star of three or four objects of about the same size. This is, of course, due to the excellent possibility of applying the laws of statistics and probabilities in the first case.

In the deceptively modest volume you are now holding, von Neumann articulates his model of computation and goes on to define the essential equivalence of the human brain and a computer. He acknowledges the apparently deep structural differences, but by applying Turing’s principle of the equivalence of all computation, von Neumann envisions a strategy to understand the brain’s methods as computation, to re-create those methods, and ultimately to expand its powers.

Thus all sorts of sophisticated order-systems become possible, which keep successively modifying themselves and hence also the computational processes that are likewise under their control.