| Summary: | This article continues the exploration of the antagonistic ternary logic of S. Lupasco in the geographic field. It examines its contribution to the issue of systems of cities, relying on the works of A. Bretagnolle and D. Pumain [2010] which consider these systems as "a progressive construction founded on a variety of spatialized interactions between heterogeneous entities in co-evolution". This affirmation is in agreement with the ternary logico-geographical theorizing proposed by H. Reymond [2009, 2011] and provides the opportunity to reflect on the concept of co-evolution, a reflection in three parts. The first part studies the role of a logico-mathematical coupling in the dynamics of co-evolution, using the Lotka-Volterra model and the idea of permanent "society-biosphere" coupling expressed by A. Berque’s mediance concept. The second part underlines that the logico-mathematical consistency that ensues allows its generalization to a geocartographic reasoning anchored in antagonistic ternary formalization. In the third part, this reasoning allowed us to test the transdisciplinary transfer of nomadic concepts coupling biology and geography: the growth in size of animals and that of systems of cities both present energy consumptions raised to the same 0.75 power. The conclusion puts forward the idea of a coupled "energy-density" deployment: the medial action of human societies in the construction of systems of cities follows dynamics coupling idiosyncratic local morphologic solutions to the nomothetic limits which require that the "energy-density" ratio be organized in a framework permitting the necessary flow circulation. The resulting couplings do not seem to contradict the tested hypothesis: they developed along a negative allometry varying around the 0.75 power. Finally, this value, which still needs to be validated, seems to correspond to sociobiological constraints whereas increasing allometrics appear to reflect the socioeconomic adjustments of the urban spread of human populations around the globe.
|
|---|
