It may be useful to describe some of the peculiarities of cybernetic explanation.

Causal explanation is usually positive. We say that billiard ball B moved in such and such a direction because billiard ball A hit it at such and such an angle. In contrast to this, cybernetic explanation is always negative. We consider what alternative possibilities could conceivably have occurred and then ask why many of the alternatives were not followed, so that the particular event was one of those few which could, in fact, occur. The classical example of this type of explanation is the theory of evolution under natural selection. Ac-cording to this theory, those organisms which were not both physiologically and environmentally viable could not possibly have lived to reproduce. Therefore, evolution always followed the pathways of viability. As Lewis Carroll has pointed out, the theory explains quite satisfactorily why there are no bread-and-butter-flies today.

In cybernetic language, the course of events is said to be subject to restraints, and it is assumed that, apart from such restraints, the pathways of change would be governed only by equality of probability. In fact, the “restraints” upon which cybernetic explanation depends can in all cases be regarded as factors which determine inequality of probability. If we find a monkey striking a typewriter apparently at random but in fact writing meaningful prose, we shall look for restraints, either inside the monkey or inside the typewriter. Perhaps the monkey could not strike inappropriate letters; perhaps the type bars could not move if improperly struck; perhaps incorrect letters could not survive on the paper. Somewhere there must have been a circuit which could identify error and eliminate it.

Ideally—and commonly—the actual event in any sequence or aggregate is uniquely determined within the terms of the cybernetic explanation. Restraints of many different kinds may combine to generate this unique determination. For example, the selection of a piece for a given position in a jigsaw puzzle is “restrained” by many factors. Its shape must conform to that of its several neighbors and possibly that of the boundary of the puzzle; its color must conform to the color pattern of its region; the orientation of its edges must obey the topological regularities set by the cutting machine in which the puzzle was made; and so on. From the point of view of the man who is trying to solve the puzzle, these are all clues, i.e., sources of information which will guide him in his selection. From the point of view of the cybernetic observer, they are restraints.

Similarly, from the cybernetic point of view, a word in a sentence, or a letter within the word, or the anatomy of some part within an organism, or the role of a species in an ecosystem, or the behavior of a member within a family—these are all to be (negatively) explained by an analysis of restraints.

The negative form of these explanations is precisely comparable to the form of logical proof by reductio ad absurdum. In this species of proof, a sufficient set of mutually exclusive alternative propositions is enumerated, e.g., “P” and “not P,” and the process of proof procedes by demonstrating that all but one of this set are untenable or “absurd.” It follows that the surviving member of the set must be tenable within the terms of the logical system. This is a form of proof which the nonmathematical sometimes find unconvincing and, no doubt, the theory of natural selection sometimes seems unconvincing to nonmathematical persons for similar reasons—whatever those reasons may be.

Another tactic of mathematical proof which has its counterpart in the construction of cybernetic explanations is the use of “mapping” or rigorous metaphor. An algebraic proposition may, for example, be mapped onto a system of geometric coordinates and there proven by geometric methods. In cybernetics, mapping appears as a technique of explanation whenever a conceptual “model” is invoked or, more concretely, when a computer is used to simulate a complex communicational process. But this is not the only appearance of mapping in this science. Formal processes of mapping, translation, or transformation are, in principle, imputed to every step of any sequence of phenomena which the cyberneticist is attempting to explain. These mappings or trans-formations may be very complex, e.g., where the output of some machine is regarded as a transform of the input; or they may be very simple, e.g., where the rotation of a shaft at a given point along its length is regarded as a transform (albeit identical) of its rotation at some previous point.

The relations which remain constant under such transformation may be of any conceivable kind.

This parallel, between cybernetic explanation and the tactics of logical or mathematical proof, is of more than trivial interest. Outside of cybernetics, we look for explanation, but not for anything which would simulate logical proof. This simulation of proof is something new. We can say, however, with hindsight wisdom, that explanation by simulation of logical or mathematical proof was expectable. After all, the subject matter of cybernetics is not events and objects but the information “carried” by events and objects. We consider the objects or events only as proposing facts, propositions, messages, percepts, and the like. The subject matter being propositional, it is expectable that explanation would simulate the logical.