Tuesday, 11 July 2006

The Fractal Mind of Pedologists (Soil Taxonomist and Soil Surveyors).

Juan Jose Ibanez, CIDE, CSIC-UV, Valencia, Spain, Rufino Pérez, ETSI Topografía, Geodesia y Cartografía (Universidad Politécnica de Madrid), Ctra Valencia Km 7.5., Madrid, 28031, Spain, and Robert Ahrens, National Soil Survey Center; NRCS-USDA, 100 Centennial Mall, North, rm 152, Lincoln, NE 68508.

There has been little work in science dealing with the organizational, political and scientific layering of database structures as well as classifications and surveys of natural resources. Currently, information infrastructures are of paramount importance in the new wave of how the science must work in order to solve societal demands. There is disagreement among the most reputed scientific thinkers that the taxonomies are invented (human-made constructs) not discovered (“natural” structures), with independence of the discipline involved. Thus, as scientists we must begin to study the nature of the taxonomies from different points of view. We should answer the following questions: are there common features in the whole of the taxonomic systems?; are these neutral?; how are classifications and data collection (surveys)  linked? It is also accepted that the social and political work that the classification systems were doing institutionally (nationally biased) and in terms of practical land management demands. As pedologists we must answer these questions about our taxonomies and soil survey products.


The most recent studies show that the USDA Soil Taxonomy has the same mathematical structure as the biological ones, which conform to the physical laws that dictate and optimize the information flow in a user friendly retrieval system. Furthermore, cognitive studies show that, in general, the taxonomic architectures do not exceed our cognitive channel capacity in terms of information.


Most pedologists recognise that this taxonomy, as other soil classification has a strong cartographic bias (among others). In this paper we show that the multifractal nature of the USDA Soil Taxonomy is strongly linked with conventional soil survey practices. In fact good survey practice cannons are packed with power law distributions in different ways, such as: (i) map scale-area surveyed; (ii) standard line density-scale dependency; (iii) sampling density-mapped area; (iv) hierarchic taxonomic level used according to the scale map; (v) minimum polygon size fits the functions to the map scale; (vi) soil survey effort depending of the scale map: (iv) boundary density-scale map relationship, and so on, as Beckett and Bie, as among others showed previously (CSIRO Aust. Div. Soils, Technical Pap. N.º 33, 1988). Therefore a plethora of power law appears one after another in soil survey activities, and also in soil taxonomies. Because both activities are strongly linked it seems the minds of soil surveyors and soil taxonomist make fractal structures. Fractals objects and power laws are scale invariant mathematical constructs, and the products delivered by the experts are also fractal in many aspects. For example, this process could be the reason that all maps devoid of legends and other information have a high resemblance and information content, and with independence of scales, a clear fractal signature. If it was not the case, the soil survey activities, as well as the users interpretation will be much more difficult (different scale maps carry out from different criteria, demand much more training and mental work).  


Summarising, the system used by soil surveyors and soil taxonomist as a whole has (or works) a fractal structure. The latter is a subconscious activity of the human brain as some of us show in other contributions to this International Congress (“The magical Numbers of the Soil Taxonomy”). Thus, against the opinion of many experts the fractals are not outrageous products of nature, but are common both to the nature and our way to process and represent the information. For example layman's interprets better an isopleth map than an isarithm one.


Because the standards of many natural resource maps are similar to the soil ones, we conjecture that this scale-invariance information processing is intuitive to the human being. A rigorous formalization of the survey-taxonomy architecture system must help practitioners to understand deeply their activities and constructs, and improve these.

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