Recent work on the fundamental processes of regulation in biology (Ashby, 1956) has shown the importance of a certain quantitative relation called the law of requisite variety. After this relation had been found, we appreciated that it was related to a theorem in a world far removed from the biological—that of Shannon on the quantity of noise or error that could be removed through a correction-channel (Shannon and Weaver, 1949; theorem 10). In this paper I propose to show the relationship between the two theorems, and to indicate something of their implications for regulation, in the cybernetic sense, when the system to be regulated is extremely complex. Since the law of requisite variety uses concepts more primitive than those used by entropy, I will start by giving an account of that law.
The design of a complex regulator often includes the making of a model of the system to be regulated. The making of such a model has hitherto been regarded as optional, as merely one of many possible ways. In this paper a theorem is presented which shows, under very broad conditions, that any regulator that is maximally both successful and simple must be isomorphic with the system being regulated. (The exact assumptions are given.) Making a model is thus necessary. The theorem has the interesting corollary that the living brain, so far as it is to be successful and efficient as a regulator for survival, must proceed, in learning, by the formation of a model (or models) of its environment.
Cybernetics is here defined as “the science of control and communication, in the animal and the machine”-in a word, as the art of steersmanship; and this book will interest all who are interested in cybernetics, communication theory and methods for regulation and control. W. Ross Ashby (1903-1972) was an English psychiatrist and a pioneer in cybernetics, the study of complex systems. His two books, “Design for a Brain” and “An Introduction to Cybernetics,” were landmark works. They introduced exact and logical thinking into the nascent discipline and were highly influential. Contents include: What is new — Change — The Determinate Machine — The Machine with Input — Stability — The Black Box — Quantity of Variety — Transmission of Variety — Incessant Transmission — Regulation in Biological Systems — Requisite Variety — The Error-controlled Regulator — Regulating the Very Large System — Amplifying Regulation