The Computer and the Brain

From the Author's Introduction Since I am neither a neurologist nor a psychiatrist, but a mathematician, the work that follows requires some explanation and justification. It is an approach toward the understanding of the nervous system from the mathematician's point of view. However, this statement must immediately be qualified in both of its essential parts. First, it is an overstatement to describe what I am attempting here as an "approach toward the understanding"; it is merely a somewhat systematized set of speculations as to how such an approach ought to be made. That is, I am trying to guess which of the---mathematically guided--lines of attack seem, from the hazy distance in which we see most of theme a priori promising, and which ones have the opposite appearance. I will also offer some rationalizations of these guesses. Second, the "mathematician's point of view," as I would like to have it understood in this contexts carries a distribution of emphases that differs from the usual one: apart from the stress on the general mathematical techniques, the logical and the statistical aspects will be in the foreground. Furthermore, logics and statistics should be primarily, although not exclusively, viewed as the basic tools of "information theory." Also, that body of experience which has grown up around the planning, evaluating, and coding of complicated logical and mathematical automata will be the focus of much of this information theory. The most typical, but not the only, such automata are, of course, the large electronic computing machines. Let me note, in passing, that it would be very satisfactory if one could talk about a "theory" of such automata. Regrettably, what at this moment exists---and to what I must appeal--can as yet be described only as an imperfectly articulated and hardly formalized "body of experience." Lastly, my main aim is actually to bring out a rather different aspect of the matter. I suspect that a deeper mathematical study of the nervous system --"mathematical" in the sense outlined above--- will affect our understanding of the aspects of mathematics itself that are involved. In fact, it may alter the way in which we look on mathematics and logics proper. I will try to explain my reasons for this belief later.