The Mathematics of Communication

Abstract

HOW do men communicate, one with another? The spoken word, either direct or by telephone or radio; the written or printed word, transmitted by hand, by post, by telegraph, or in any other way—these are obvious and common forms of communication. But there are many others. A nod or a wink, a drumbeat in the jungle, a gesture pictured on a television screen, the blinking of a signal light, a bit of music that reminds one of an event in the past, puffs of smoke in the desert air, the movements and posturing in a ballet—all of these are means men use to convey ideas. The word communication, in fact, will be used here in a very broad sense to include all of the procedures by which one mind can affect another. Although the language used will often refer specifically to the communication of speech, practically everything said applies equally to music, to pictures, to a variety of other methods of conveying information. In communication there seem to be problems at three levels: 1) technical, 2) semantic, and 3) influential. The technical problems are concerned with the accuracy of transference of information from sender to receiver. They are inherent in all forms of communication, whether by sets of discrete symbols (written speech), or by a varying signal (telephonic or radio transmission of voice or music), or by a varying twodimensional pattern (television). The semantic problems are concerned with the interpretation of meaning by the receiver, as compared with the intended meaning of the sender. This is a very deep and involved situation, even when one deals only with the relatively simple problems of communicating through speech. For example, if Mr. X is suspected not to understand what Mr. Y says, then it is not possible, by having Mr. Y do nothing but talk further with Mr. X, completely to clarify this situation in any finite time. If Mr. Y says “Do you now understand me?” and Mr. X says “Certainly I do,” this is not necessarily a certification that understanding has been achieved. It may just be that Mr. X did not understand the question. If this sounds silly, try it again as “Czy pan mnie rozumie?” with the answer “Hai wakkate imasu.” In the restricted field of speech communication, the difficulty may be reduced to a tolerable size, but never completely eliminated, by “explanations.” They are presumably never more than approximations to the ideas being explained, but are understandable when phrased in language that has previously been made reasonably clear by usage. For example, it does not take long to make the symbol for “yes” in any language understandable. The problems of influence or effectiveness are concerned with the success with which the meaning conveyed to the receiver leads to the desired conduct on his part. It may seem at first glance undesirably narrow to imply that the purpose of all communication is to influence the conduct of the receiver. But with any reasonably broad definition of conduct, it is clear that communication either affects conduct or is without any discernible and provable effect at all. One might be inclined to think that the technical problems involve only the engineering details of good design of a communication system, while the semantic and the effectiveness problems contain most if not all of the philosophical content of the general problem of communication. To see that this is not the case, we must now examine some important recent work in the mathematical theory of communication.