Limits for a growing complexity system

The debate on the Limits to Growth is most often focused on the constraints posed by the finiteness of the material and energy resources available on earth. These constraints are indeed rigid and impending, however there are also more subtle but equally looming constraints posed by the growing complexity of a growing socio-economic system. The complexity of a system is somehow measured by the number or relations (which are in fact material and information exchange relations) among the elements of the system. A human economy is indeed a system of exchange relations among individuals and organized groups of individuals. Our contemporary worldwide economy places all hopes of precarious stability on continuous material growth. The pursued material growth implies and produces both a growth of the system (the number of elements in the system) and of the volume of material and immaterial exchanges among the elements of the system. Every single element of the system tends to be involved in a growing flux of information, however any element has, for physical reasons, a finite management capacity of the information flow. In practice, as it happens with computers (and multicellular biologic organisms), there is a maximum governable size of the system, above which it splits into smaller controllable domains. In other words a growing complexity system tends to go out of the possibility of a rational unified control, and to assume a chaotic behavior. Another aspect related to the growth of complexity has to do with the security and the actual wealth production. The growth of the number of active relations implies a corresponding growth of the cost of unavoidable inconveniencies related to the material exchange. In order to keep the security level stable, increasing costs for the improvement of technologies are required. Finally the diminishing returns law, together with the material growth, leads to a decreasing balance between global wealth and security costs. All this may be cast in mathematical terms using the formalism and concepts of statistical thermodynamics. Complete examples with realistic numbers will be worked out and presented.