Thursday, 13 July 2006 - 10:15 AM

The Magical Numbers of the USDA Soil Taxonomy:Towards an Outline of a Theory of Natural Resource Taxonomies.

Juan Jose Ibanez1, Richard Arnold2, and Juan Sanchez-Diaz1. (1) CIDE, CSIC-UV, Valencia, Spain, (2) USDA-NRCS (retired), 9311 Coronado Terrace, Fairfax, VA 22031-3835

Recently, a mathematical analysis of the USDA Soil Taxonomy structure showed that biological and pedological classifications have the same topological structure in terms of entropic, statistical distribution, fractal, and multifractal models. The structure also conforms to the Mayr criterion, Willis curve, and the MaxEnt (Maximum Entropy) Principle. These results indicate that both biological and pedological taxonomies are organized in a manner that optimizes (maximum efficiency) the flow of information as retrieval information systems taking into account their respective initial and boundary conditions. Both systems tend to have fractal structures, whereas, geographical, purpose oriented classifications (agronomic), and cognitive bias divert them toward multifractal structures. These analyses, however, only take into account their mathematical architecture and the so-called “Roch prototype effect”: a cognitive bias type that takes into account the human being capacities to process the information. In 1956 Miller, a reputed cognitive psychologist hypothesized that there is an upper limit on our mental potential to process information on simultaneously interacting elements with reliable accuracy and correctness. The limit proposed by Miller, after compiling the results of a multitude of psychological studies, was seven plus or minus two elements. The “Miller Conjecture” has been corroborated in the fields of cognitive computing and chaos (complexity) sciences. There is empirical evidence from cognitive studies of indigenous populations carrying out folk taxonomies and other types of categorization processes that are in agreement with the above mentioned “magic number”. Folk and scientific classifications often initially break natural continuums into less than 7 plus or minus two hierarchical levels. In both the USDA Soil Taxonomy and the FAO 1988 Revised Legend most of the number of subtaxa (classes) per taxa of a given category fall in this range 7 ± 2, although some contain less subtaxa per taxon. In this respect the FAO 1988 Revised Legend corroborates better the Miller conjecture than the USDA Soil Taxonomy. The Miller conjecture explains that separating a continuum under consideration into more that 9 classes causes mental confusion and generates mistakes in the populations tested. In other words, it is not suitable that a taxon have a lot of subtaxa. This cognitive or memory constraint (cognitive span), also termed channel capacity by Miller indicates that the human mind has a sense for numbers that is primitive and predates conscious counting, and likely dictates our ability to tell the difference among groups of different number of objects. Obviously this magical number may be a constraint in teaching classical taxonomies. Insofar as this is true, it would be of interest in future modifications or development of soil taxonomies not to exceed, as far as possible, our innate capacities to simultaneously handle information. Folkbiology studies shows also that while the best trained native people (in strong contact with the nature around them) detect “generic species” (the equivalent to the scientific species and genera) as the core of their taxonomies. Those with less direct interaction with nature recognize and classify better using life forms than “species”. The latter ones could be considered as pedological analogies of the older soil classifications that were based on soil forming factors. With this background in mind it is possible to try to construct a framework of an ideal soil taxonomic scheme: (i) taxonomy with 7 ± 2 hierarchical structures; (ii) a iterative fragmentation of higher hierarchical categories into 7 ± 2 subcategories; (iii) a generated branching system that is as symmetric as possible; (iv) a final fractal structure; (vi) the content of the taxonomic information (entropy) must not exceed 5 bits, and so on. Such a scheme would not have initial and boundary constraints. Thus, it would be expected to divert from a hypothetical optimal one in some features as a consequence. As far as practical and scientifically sound, it is recommended that any given taxon not contain many taxa, and that the number of taxa with a single subtaxa be kept to a minimum.

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