Observing Collectivities. The Combinatory Sistems Approach in Social Sciences

Since Thomas Schelling’s attempt, in Micromotives and Macrobehavior, to offer a logical explanation of why collective macro behaviour derives from the micro behaviours of intelligent agents and Conway’s discovery of the fantastic world of Life, the study of the behaviour of collectivities has been a very complex subject of study, and for this reason a fascinating and interesting one as well. If observed from a certain distance collectivities appear distinct with respect to the individuals that compose them and, due to the interactions of the micro behaviours, seem capable of producing interesting macro behaviours to which many relevant collective phenomena of self-organization may be associated; four of these processes are: the accumulation of objects, the spread of features or information, the pursuit or exceeding of a limit, and the attainment and maintenance of an order among the micro behaviours. To understand, explain and, to a certain extent, control these collective phenomena I have formalized the simple Theory of Combinatory Systems. In plain words, by Combinatory System I mean any unorganized collectivity made up of a plurality of similar agents producing analogous micro behaviours; the macro behaviour of the system, as a whole, derives from the combination of the analogous micro behaviours (hence the name Combinatory System); but, on the other hand, the macro behaviour directs the subsequent micro behaviours according to a feedback relation. The action of a set of recombining and necessitating factors guarantees the maintenance over time of the dynamics of the system, so that when the system starts up “by chance” it then maintains its behaviour “by necessity”, as if an invisible hand regulated its time path and produced the observable effects and patterns. This paper presents the fundamental ideas and mechanisms that underlie these systems, along with some models that illustrate the self-organization activity in collectivities.