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

LectureGregory 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)

Mapping Bateson's Epistemology to Boolean Dynamic System: 1. The Emergence of Dynamic Form & 2. Hierarchies Form.

LectureGregory Bateson (e.g., 2002, p. 85ff; 2000, p. 457-460) construed knowledge to be the propogation of "difference" in a complex network, noting (2000 p. 460) that "the transform of difference travelling in a circuit is an elementary idea." The idea of difference is coded as 0 and 1 in Boolean systems. Kauffman (1993) developed NK Boolean computer simulations as a way explore how the structure of genomes might self-organize into emergent form (see Kauffman, 1995, p. 76 for a simple, concrete example). The N in NK Boolean systems refers to the number (N) of abstract entities called Nodes; in Kauffman's simulations N was very large, as high as 100,000 (1995, p. 83). The K refers to the number of inputs (from other nodes in the network) that each node has. Kauffman states that "While this is surely an idealization, we can extend it to networks of genes and their productrs interacting with one another in enormous webs of regulatory circuitry," (1995, p. 99). This reasoning parallels Bateson's idea of mental process. Indeed Bateson includes genetic activity as a part of mental process, stating that "the phenomena we call thought, evolution, ecology, life, learning and the like occur only in sytems that satisfy these criteria," (2002, p. 86). Mind and nature are, as his book title (Bateson 2002) states, are a necessary unity

Prerequisites to Batesonian Epistemology

LectureThe Logic of Metaphor maps sets of relations from one realm to another realm generating tautologies in the logic of logic

Emergence of dynamic form through phase relations in dynamic systems

ManuscriptGregory Bateson construes mental process as the flow and transforms of differences in a system. Stuart Kauffman uses NK Boolean systems to model the emergence of order in biological evolution. Because the Boolean base (0, 1) maps to Bateson's idea of difference, we simulate Bateson's epistemology with a Boolean system. Following Bateson's idea that knowledge emerges from the relations among multiple (at least two) descriptions, where a description is here defined as a systematic process that encodes relations between two such descriptions. The first description is retinal activity, which here is modeled as a discrete dynamic system that falls into different attractor cycles with simulation model we also propose a second, representational, description. Dynamic from perception emerges from the phase relations between the frequencies of the two descriptions. Moreover, two classes of forms, fundamental and derived, emerge from these phase relations

Design and Testing of Off Axis Illumination Filters for a 248nm DUV Exposure System

This study involves the design and testing of off axis illumination apertures for an ASML 5500/90 248nm DUV stepper. X and V slot pole apertures based on dipole theory were designed, fabricated out of aluminum, and inserted into the optical column of the stepper. Test patterns consisting of vertically oriented features were printed with and without dipole illumination, exposed, and compared to determine their effectiveness. As expected, features which were to small to print under standard illumination imaged exceptionally well using the x slot pole aperture. The y slot pole aperture delivered the same results as standard illumination which was also expected. 0.24μm features were printed clearly and consistently under the off axis illumination scheme on a system specified to print a minimum feature size of 0.35μm with a numerical aperture of 0.5

Utah Virtual Lab: JAVA interactivity for teaching science and statistics online

Journal ArticleThe Utah on-line Virtual Lab is a JAVA program run dynamically off a database. It is embedded in Stat-Center (www.psych.utah.edu/ learn/statsampler.html), an on-line collection of tools and text for teaching and learning statistics. Instructors author a statistical virtual reality that simulates theories and data in a specific research focus area by defining independent, predictor, and dependent variables and the relations among them. Students work in an on-line virtual environment to discover the principles of this simulated reality: They go to a library, read theoretical overviews and scientific puzzles, and then go to a lab, design a study, collect and analyze data, and write a report. Each student's design and data analysis decisions are computer-graded and recorded in a database; the written research report can be read by the instructor or by other students in peer groups simulating scientific conventions

Difference to Inference: teaching logical and statistical reasoning through on-line interactivity

Journal ArticleDifference to Inference is an on-line JAVA program that simulates theory testing and falsification through research design and data collection in a game format. The program, based on cognitive and epistemological principles, is designed to support learning of the thinking skills underlying deductive and inductive logic and statistical reasoning. Difference to Inference has database connectivity so that game scores can be counted as part of course grades

Logic of logic and the logic of dreams.

LectureFor Bateson explanation is the mapping of description onto tautology. "An explanation has to provide something more than a description provides, and in the end, an explanation appeals to a tautology, which as I have defined it, is a body of propositions so linked together that the links between the propositions are necessarily valid. A tautology in its simplest form is ‘If P is true, then P is true.'" Tautologies can be very elaborate including, for example, systems of nonlinear dynamical equations. Descriptions include all the data (field notes and measurements) that scientists take when studying some phenomena. This mapping of formal models onto observable data can yield powerful insights and is what ateson defines as explanation. The tautological relations within the mathematical model are mapped to relations observed in nature

Online Homework/Quiz/Exam Applet: Freely available Java software for evaluating performance online

Journal ArticleThe Homework/Quiz/Exam applet is a freely available Java program that can be used to evaluate student performance on line for any content authored by a teacher. It has database connectivity so that student scores are automatically recorded. It allows several different types of questions. Each question can be linked to images and detailed story problems. Three levels of feedback are provided to student responses. It allows teachers to randomize the sequence of questions and to randomize which of several options is the correct answer in multiple-choice questions. The creation and editing of questions involves menu selections, buttonpresses, and the typing of content; no programming knowledge is required. The code is open source in order to encourage modifications that will meet individual pedagogical needs