070 Categorical System Theory

Having gone through the preceding discussions, we can now simply say that a natural system is a set of „qualities“ on which different definite relations can be imputed. A perceptible quantity of a natural system is obviously what we call an observable, and relations among them are linkages. The study of natural systems is precisely the specification of its observables, and the characterization of the manner in which they are linked. Thus it becomes clear that the category S we looked at in Section III is the appropriate mathematical (formal) tool to be used to study (static models of) natural systems. Next we have to recognize that (almost by definition) natural systems are dynamic objects and their changes cause a modification in our percepts. Most of the changes in natural systems are of course from their mutual interactions, and in fact the changes in our percepts (these are „observables“) can be considered as the result of interactions with other natural systems. So if an interaction between two natural systems causes some change, then the vehicle responsible for the change in one is an observable of the other. This leads us to the discussions of meters and dynamics, and dynamical systems in general, of Section IV. So the category D can be used to model the dynamical aspects of natural systems. We can express these considerations succinctly in a diagram:


In this section we shall be concerned with these models of natural systems. The categories S and D will be amalgamated into the „category of natural systems“, denoted by N.