Mapping Gregory Bateson's epistemology to nonlinear dynamic systems theory: dynamic form and hierarchies of knowledge

Gregory Bateson construes mental process as the flow and transform of differences in a system whether the system be a single human or a complex ecology. Stuart Kauffman uses NK Boolean systems to model the self-organization of order in biological evolution. Because the Boolean base (0, 1) maps to Bateson's idea of difference, we are able explore new implications of Bateson's epistemology using a Boolean system. This paper will map Bateson's difference-based epistemology to nonlinear dynamic systems theory (NDS); more specifically we will use a Boolean simulation model (E42) to examine and extend his deep pistemological insight that the relations between double (multiple) descriptions generate new knowledge where, following Bateson's definition of mental process, a "description" is a specific flow of differences in a network. This connects Bateson to mathematical developments in NDS theory and makes explicit implications derived from Bateson's work. We will present perceptual demonstrations of how the relations between double descriptions generate knowledge in two very different realms: Form perception and hierarchies of knowledge. In the first realm, we will propose a perceptual model in which dynamic visual form self-organizes from the phase relations between two such descriptions. Using Java applets generated by the freely available, open-source E42 simulation software, we will demonstrate perceptually how dynamic form perception emerges from the phase relations between what can be called systemic processes (the flow of differences in the system itself) and representational processes (the flow of differences that generate perceptual experience of the system's behavior). Moreover the relations between systemic and representational processes will be of two kinds: visual forms that code fundamental characteristics of the system itself versus visual forms that arise solely from the relationship of systemic process and representational process; the latter are not map-able to any characteristics of the system per se. We will call the first kind of form "fundamental forms" and the second "derivative forms." Regarding the second realm, Bateson proposes that differences themselves differ and that categorizing the differences in differences produces a hierarchy of knowledge. We will demonstrate that taking differences in differences in the flow of differences in a Boolean system results in perceptual hierarchies in visual perception. In this second realm, the first description is defined as any flow of differences in a system while the second description is defined as the flow of differences that are generated by taking the differences in the differences in the first flow. The perceptual hierarchies (in the context of the Boolean model) will allow us to define precisely the distinction between ideas about the evolutionary processes that generate the emergence of biological forms in evolution and ideas about the mental processes that generate the hierarchies we use to categorize those biological forms (e.g. Chordata, Aves, Corvidae, Ravens).