Sistemi Combinatori - L’Ordine nel Comportamento Collettivo

This study aims to present the Combinatory Systems Theory, a simple theory which is able to describe, interpret and explain many collective phenomena and their observable effects. The Combinatory Systems Theory was recently formalized by my book Combinatory Systems Theory, published by Springer in 2017. I was partly inspired by it to prepare this paper. A Combinatory System is a “collectivity” (plurality, population, species, group, etc.) of non-organized relatively similar agents (men, animals, bacteria and so on) which produce relatively analogous micro behaviors (changes in micro-states), that lead to observable (or definable) micro effects. Combined together, the micro behaviors/effects produce an emergent macro behavior (changes in the macrostate), which is not included in advance in the operating program of the agents’ behavior, but is instead attributed to the “collectivity” as a whole, regarded as a Unitary System (hence the name of Combinatory Systems). This collectivity’s macro behavior in turn conditions the subsequent micro behaviors/effects of the agents. This reciprocal agents-collectivity relationship is defined as micro-macro feedback and represents a necessary and sufficient condition for a combinatory system to exist as it guarantees the maintenance over time of the system’s macro behavior and continuously updates the micro behavior When the system starts up “by chance”, it then maintains its behavior “by necessity”, as if an “invisible hand”, a Supreme Authority regulated its time path and produced the observable effects and patterns. Combinatory Systems can produce many relevant phenomena four of which 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 agents’ micro behaviors. A very relevant fifth effect, which ncludes the others, is the interdependent dynamics of individual improvement and collective progress in the overall state of a collectivity (defined in opportune ways).