Analyzing the Semantics of Point Spaces through the Topological Weighted Centroid and Other Mathematical Quantities: The Hidden Geometry of the Global Economic Order

For many spatial processes, there is a natural need to find out the point of origin on the basis of the available scatter of observations; think, for instance, of finding out the home base of a criminal given the actual distribution of crime scenes, or the outbreak source of an epidemics. In this article, we build on the topological weighted centroid (TWC) methodology that has been applied in previous research to the reconstruction of space syntax problems, for example, of problems where all relevant entities are of spatial nature so that the relationships between them are inherently spatial and need to be properly reconstructed. In this article, we take this methodology to a new standard by tackling the new and challenging task of analyzing space semantics problems, where entities are characterized by properties of a nonspatial nature and must therefore be properly spatialized. We apply the space semantics version of the TWC methodology to a particularly hard problem: the reconstruction of global political and economic relationships on the basis of a small-dimensional qualitative dataset. The combination of a small set of spatial and nonspatial sources of information allows us to elucidate some intriguing and counterintuitive properties of the inherent global economic order and, in particular, to highlight its long-term structural features, which interestingly point toward the idea of longue duree developed by the distinguished French historian Fernand Braudel.