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

Abstract

AbstractA 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 and pedodiversity are natural resources, although some consider pedotaxa to be artificial. The studies carried out to date emphasize that many pedodiversity and biodiversity spatial patterns converge at the same regularities. Many of these studies used natural resources maps and their digital databases. Information is extracted from the taxa types contained in each polygon and the areas covered. 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 undertaken. The main variables in these maps are manmade and/or combinations of natural resources data layers. Regularities detected in the geospatial information of these 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 more small things/objects than larger ones across several orders of magnitude in geographic space to be a law. Some geographers also contend that the classical “Gaussian thinking” and its statistical tools should be replaced by a “Paretian thinking” and its related statistical tools. This paper analyses the above topics as well as the lack of adequate data and types of cognitive maps we use in our modern 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.Highlights Long tail distributions, power laws and fractal‐like structures are ubiquitous in geospatial analysis. Scale invariance of natural and artificial map structures seem to be the rule. The Paretian approach appears to be more appropriate than the Gaussian approach for many purposes. Our cognitive maps and brain processing follow Paretian thinking in many instances.