A quantitative-qualitative measure of information in cybernetic systems (Corresp.)

A Quantitative-Qualitative Measure of Information in Cybernetic Systems equal to the sum of the information supplied by each event separately. Let p and q be the probabilit.ies of the E and F events, respectively; the event E r\ F has a probability pq if E and F are independent, and we have the equality In order to elaborate a theory of communicat ion which could be useful for designing a great variety of transmission systems, it was necessary to find a general notion capable of abstracting the various kind of signals which can be transmitted. By neglecting the particular aspect of these signals and considering them as random abstract events, it was possible to define the quantitative aspect of information based on the probability of different events. AE a matter of fact, thii simplification of the complex aspect of information led to the first great analogy between biological and technical systems considered as information transmission systems. The cybernetic analogy between man and machine consists precisely of the fact that both are control systems. This means that information is transmitted and processed in view of a goal with regard to which control signals must be efficient. The whole activity of cybernetic systems (biological or technical) is directed toward the fulfillment of a goal. The system must then possess a qualitative differentiating criterion for the signals to be transmitted. This implies the existence of a logical block able to discriminate the quality of various signals according to a given criterion. The cybernetic criterion for a qualitative differentiation of the signals is represented by the relevance, the significance, or the utility of the information they carry with respect to the goal. The occurrence of an event removes a double uncertainty: the quantitative one related to its probability of occurrence, and the qualitative one related to its utility for the fulfillment of the goal. In the following, a general formula, taking into account the two basis concepts of probability and utility, will be established. Let E,, E,, . ., En be a finite set of events representing the possible realizations of some experiment; let pl, pi, . . . , pn be the probabilities of occurrence of these events, satisfying