Combinatory system theory: a theory for understanding and controlling collective phenomena

The collectivity can be interpreted as a unit formed by a plurality of distinct elements, and characterized by an autonomous behaviour. These units, however, produce collective phenomena which do not refer to the single elements, even if they are necessarily generated by the behaviour of the latter. We define as combinatory those systems whose elements are relatively similar, each of which produces a micro behaviour similar to that of the others. The macro behaviour of the system, as a unit, derives from the combination of the analogous behaviours of its similar elements, according to a feedback relation. A necessary and sufficient condition for a collectivity (observable or hypothesized) to be considered a combinatory system is the existence of a feedback between the micro behaviour of the individuals and the macro behaviour of the collectivity. The Theory of Combinatory Systems searches for the conditions that produce the macro behaviours and builds models to interpret the collective phenomenon. If we classify combinatory systems according to their macro behaviour (or their macro effect), despite the variety of phenomena produced we can determine five fundamental types of combinatory systems, the most important of which are: 1. systems of accumulation, whose activity involves an accumulation of objects, of behaviours, of states or of effects of some kind; 2. systems of diffusion, which have as their macro effect the diffusion of an «object» (of a feature, a particularity, or a «state») from a limited to a greated number of elements of the system; 3. systems in pursuit, which produce a behaviour consisting in a gradual shift of the system toward an objective, a limit, a target, just as if the system, as a single entity, were pursuing a goal or trying to move towards ever more «advanced» states; 4. systems of order, which produce a phenomenon that can be interpreted as the attainment or maintainment of an arrangement, an ordered disposition, or a form of some kind, among the elements that form the system 5. systems of improvement and progress: their effect is to produce progress (according to commonly accepted value judgments) in the overall state of a collectivity in which the individuals pursue their search for individual improvement (that is, an increase in some parameter judged to be useful or favorable).