On a formal definition of organization

Abstract

A mathematic definition is proposed to account for the intuitive features of what is usually meant by organization. To account for both functional and structural aspects of organization the rate at which information content of a system changes in time is examined. It can be shown that Shannon's expression for ambiguity in a channel has two different meanings according to whether one is interested in the information transmitted in the channel or in the information transmitted to the observer from a whole system in which the channel is a part of a redundant communication network. This was applied in a previous work to show that the effects of noise on the information content H of a system result in two kinds of ambiguities, “autonomy-producing” and “destructive” leading to increase and decrease in H, respectively. By making use of this observation and Shannon's definition of redundancy R, a single equation for dH dt is proposed to define organization on the basis of a kinetics of change of information content of a system under the effects of environmental noise-producing factors accumulated in time. It is shown how these factors, obviously responsible for a decrease in H, i.e. a “disorganizing” effect, can be responsible also—under certain conditions and up to a certain time or “dose” of noise—for an initial increase in H interpreted as a process of “self”-organization. The autonomy-producing ambiguity is expressed by a term of decrease in redundancy, while a second term in the equation, of decrease in maximum-non-redundant-information content expresses the destructive ambiguity. A given organization is defined at least by three parameters, which determine the main features of its characteristic function H(t). One of them is the initial information content H 0 and has a structural meaning. A second parameter, with a dimension of time, has the meaning of a functional reliability, related to the overall resistance of the system to noise-producing factors. The third parameter, namely the initial redundancy R 0, is both structural and functional in character, since structural redundancy is known to help insure reliability. Various conditions on these parameters lead to various kinds of organizations, with and without self-organizing properties.