Order and Chaos in Combinatory Systems. A different approach to Collective Behaviour

My paper deals with a particular view of synergetics applied to social phenomena produced by collectivities, and aims to demonstrate that collectivities of non-interconnected similar agents which develop analogous micro behaviours can also show very interesting forms of self-organization that lead to ordered or chaotic macro behaviour. I have called these collectivities combinatory systems since, on the one hand, the macro behaviour of the system as a whole derives from the combination of the analogous micro behaviours or effects of the agents and, on the other, the macro behaviour determines, conditions, or directs the subsequent micro behaviours. This internal micro-macro feedback produces a self-organization effect as if an Invisible Hand or Internal Organizer regulated its time path and produced the observable effects and patterns. Combinatory systems are not easily recognizable; nevertheless they are widely diffused and produce most of the social and economic collective phenomena involving the accumulation of objects, the spread of features or information, the pursuit of a limit, and the achievement of general progress as the consequence of the individul pursuit of particular interests. My second aim is to illustrate – with the aid of simple combinatory automata – phenomena as intriguing as they are emblematic: the voice-noise effect in organizations; the clustering and swarming effects in economics; the unjustified raising of retail prices; the stock exchange dynamics deriving from the micro-macro feedback between stockbroker decisions and the stock index. We will see that the joint action of crossed and multi-level micro-macro feedback makes it not unthinkable that “a butterfly can cause the collapse of the stock exchange”.