Exploring the scaling law of geographical space: Gaussian versus Paretian thinking

Abstract

A debate has occurred concerning the laws of scale and the fractal nature of geographical space. Biodiversity and pedodiversity studies show the emergence of fractal structures such as taxa-area relationships. Biodiversity andpedodiversity are natural resources, although some consider pedotaxa to beartificial. The studies carried out to date emphasize that many pedodiversityand biodiversity spatial patterns converge at the same regularities. Many ofthese studies used natural resources maps and their digital databases. Information is extracted from the taxa types contained in each polygon and the areascovered. However, the structure of the maps (number, area, fragmentation, etc.) has rarely been a matter of study. When map structure was studied,intriguing similarities were observed in pedodiversity and biodiversity analyses. To understand whether these similarities also appear in other types of spatial entities that are more artificial, a review of geospatial analyses that studied topics such as urban maps, land system maps, etc., was under taken.The main variables in these maps are manmade and/or combinations of natural resources data layers. Regularities detected in the geospatial information ofthese latter topics also seem to conform to results obtained when analysing natural resources maps such as soils, rock types, landforms, plant communities, etc. Thus, some geographers consider the idea that there are far moresmall things/objects than larger ones across several orders of magnitude ingeographic space to be a law. Some geographers also contend that the classical“Gaussian thinking”and its statistical tools should be replaced by a“Paretianthinking”and its related statistical tools. This paper analyses the above topicsas well as the lack of adequate data and types of cognitive maps we use in ourmodern scientific society, supporting the conjecture that that we should include Paretian thinking in our research at least in the same way we use Gaussian thinking