A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly kno… - John von Neumann

A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.

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.

The very last stage of any memory hierarchy is necessarily the outside world — that is, the outside world as far as the machine is concerned, i.e. that part of it with which the machine can directly communicate, in other words, the input and the output organs of the machine. These are usually punched paper tapes or cards, and on the output side, of course, also printed paper.

Since I am neither a neurologist nor a psychiatrist, but a mathematician, the work that follows requires some explanation and justification.