Topology, Metric and Dynamics of Social Systems

Structurally orientated sociologists tend to neglect the dynamical aspects of social systems, whereas theorists of social systems emphasize systems dynamics but only rarely analyze structural features of their domains. The aim of this paper is to integrate dynamical and structural approaches by means of the analysis of particular artificial systems, namely logical or Boolean networks, and their geometry. It is well known that the dynamics of Boolean networks and the logically similar cellular automata are governed by control parameters. Less well known is the fact that the geometry of these artificial systems, understood as their topology and metric, also contain specific control parameters. These "geometrical" control parameters can be expressed using graph theoretical concepts such as the density of graphs or geodetical properties. Further, the dynamics of those artificial systems depend on the values for the geometrical parameters. These mathematical investigations are quite important for social research: On the one hand, social dynamics and social structure appear to be two closely related aspects of social reality; on the other hand, a general hypothesis may be drawn from our results, namely that social structural inequality yields simple dynamics whereas social equality gives rise to complex dynamics. Therefore the dynamical complexity of modern democratic societies may be in part due to their democratic structures.