Establishment of a Complementary Bilateral
Hierarchical Entity-Ecosystem Rationality

Willy Ranson, Ron Cottam & Roger Vounckx

Abstract

            At first sight, the hierarchical aspects of nature appear to be most comprehensively described by a specification hierarchy which is constructed between the complementary extremes of nonlocality and localization. This approach results in a layered structure which alternates between the "simple" and the "complex" in such a manner that dimensionality of the layers progressively reduces through the hierarchy from nonlocality towards localization. "Simple" layers correspond to Newtonian potential wells, where low-dimensional representations approximate locally to an underlying high-dimensional phase space. "Complex" layers correspond to regions of those "irrationalities" which are unavoidably associated with change in dimensionality. Many otherwise isolated models then find place in the overall description as reduced-dimensional forms of a higher-order complementarity of rationality and causal chaos.

            However, the complementary nature of the overall description is lost in the direct relationships between adjacent simple and complex layers, and the establishment of stability-supporting simplification of these inter-layer relationships is less than evident. We propose that a more all-inclusive hierarchy can be built by associating local simple-complex pairs in the form of complementarily-complete entities, where the "complex" plays the role of an ecosystem "within" which the "simple" survives, and in relation to which its stability can be reinforced in relation to the more global context.

            Careful evaluation of the way in which the globalities of both the "simple" and the "complex" layers change through the hierarchy leads to the realization that the entire structure can be replaced by an interlocking complementarity of complementary systems of rationality. One system consists of the progression from "perfect" localization to its complement of "least perfect" localization, the other of the progression from "perfect" non-localization to its complement of "least perfect" non-localization.

            Both systems of rationality are hierarchical, and they interlock in such a way that the layering is now … system1 - system2 - system1 … , which corresponds to the original single-rationality sequence of … simple - complex - simple … . It should be noted that, because of evolutionary aspects of the hierarchical structure, "least perfect" localization is not coincident with "perfect" non-localization, it is adjacent to it, and the two form one of the complementarily-complete entities we refer to above. This "association of complementary entity-ecosystem pairs" corresponds to the local establishment of a Peircian semiosis, and the resultant filiated hierarchy of complementarily-complete entities corresponds to the extension of a Peircian semiosis to a hierarchially-stabilized global system.
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