Observing Collectivities as Simplex Systems: The Combinatory Systems Approach

My paper aims to present a particular class of complex systems made up of collectivities of non- interconnected similar agents, acting on the basis of global information which they directly produce and update by the combination of their analogous micro behaviours, and that directs the subsequent micro behaviours as a result of a micro-macro feedback that produces self-organization in the agents’ micro behaviours. Due to their operative logic these systems can in general be called Combinatory Systems. I have provocatively defined the simplest class of them as Simplex Systems, since the similarity of the agents and the micro behaviours, the absence of direct interactions among the agents, and the simplicity of their structure and operative logic make these collectivities a particular simplified class of complex systems, as usually conceived. If we accept the traditional definition of self-organization as the macro behaviour of a collectivity of agents in which the micro behaviours appear to be directed, or organized, by an Invisible Hand, or Supreme Authority, in order to produce the emerging phenomenon represented by the formation of ordered structures, or recognizable patterns, then it is easy to recognize the synergetic effect of a micro-macro feedback action (or circular causality) acting between the agents’ micro behaviours and a global system’s macro behaviour or effect.