Steps to an Ecology of Emergence

How might we take steps toward understand ing emergent hierarchies in a mental ecology? To answer that question we outline an epistemological framework which begins with two fundamental assumptions from the methodology of transformational grammar in linguistics—the centrality of human judgment based on direct experience and the proposition that the systematic nature of human behavior is algorithmically driven. We then set a double criteria for the understanding of any formalism such as emergence: What is formalism X that a human may know it; and what is human knowledge that a human may know formalism X? In the cybernetic sense, the two are defined in relation to each other. In answer to the first question, we examine emergence as a formalism, using Turing’s work as a defining case and an N, K Boolean system as a specific working model. In answer to the second question, we frame the knowing of emergence in a broad Batesonian epistemological approach informed by modern developments in neural nets and discrete dynamic systems models. This epistemology specifies mental process as the transformation of differences across a richly connected network. As the relational reference point which integrates the two sides of the cybernetic question, we use human judgments of perceptual similarity to link emergent hierarchies formally found in an N, K Boolean model to hierarchies of perceptual similarity based on direct experience. Steps to an Ecology of Emergence 12/12/03 3 I have said that what gets from territory to map is transforms of differences and that these (somehow selected) differences are elementary ideas. But there are differences between differences. Every effective difference denotes a demarcation, a line of classification, and all classifications are hierarchic. In other words, differences are themselves to be differentiated and classified. In this context I will only touch lightly on the matter of classes of difference, because to carry the matter further would land us in the problems of Principia Mathematica. Let me invite you to a psychological experience, if only to demonstrate the frailty of the human computer. First note that differences in texture are different (a) from differences in color. Now note that differences in size are different (b) from differences in shape. Similarly ratios are different (c) from subtractive differences. Now let me invite you... to define the differences between "different (a)," "different (b)," and "different (c)" in the above paragraph. The computer in the human head boggles at the task. --Gregory Bateson (1972), pp. 463, 464. In 1952 Alan Turing published a groundbreaking paper that laid the foundation for the concept of emergence. Within the constraints of a formal mathematical symbol system, he derived insights into how form self-organizes from the interactions among well-defined processes. He found that forms observed in nature (dappled patterns, radial whorls seen in leaves around stems) resulted naturally from the interplay of coupled equations that themselves had no hints of the higher order characteristics of the emergent forms. His insight required, in his words, “a good deal of mathematics, some biology, and some elementary chemistry.” These prerequisites for understanding this early formal example of emergence (not a word he used) were a substantial barrier; and for fifteen years it was largely ignored (Keller, 2002). Now, fifty years later Turning’s paper has become among the most seminal of the twentieth century (Keller, p. 108). And penetrating and extensive insights can be easily understood through more accessible formalisms, often derived from the languages of computing (e.g., Holland, 1998, p. 103, p. 125). For example, the gliders, generated by simple rules, in Conway’s cellular automaton, Life (e.g., Holland 1998, p. 138, Malloy, www.psych.utah.edu/dysys ), skate across a computer screen, transforming and reforming as they interact. Gliders have become a canonical example of emergence. The distinction between the level of generating processes and the level of wholes that emerge is the basis of the idea of emergent hierarchies. If interacting processes produce wholes with novel characteristics not found in those lower level processes and if the wholes are themselves processes that can interact and so produce even higher level wholes with yet again novel characteristics, then we have an outline of a process for emergent hierarchies. Emergence was a fundamental process in Bateson’s epistemology (1979, chapter 3), although he did not use that term. The case of difference, that “there must be two entities such that the difference between them... can be immanent in their relationship,” is particularly relevant to this discussion. Prime examples discussed by Bateson of what is now called emergence are binocular vision, beats and moiré patterns. Steps to an Ecology of Emergence 12/12/03 4 To examine in detail how emergent levels develop in a model and, more critically, how those model-defined levels relate to human perception of emergent levels we will use a computer simulation, E42. E42 is an N, K Boolean simulation program (Kauffman, 1993) that generates discrete dynamic systems. N, K Booleans systems are computer simulations of the behavior of a net of N entities (nodes) each of which is connected to (i.e., takes input from) K other nodes in the network. These systems are Boolean because each node has only two possible states (0 or 1) and therefore the system is based on difference and the transforms of difference through a network. As such, N, K Boolean systems create a simulation context consistent with several of Bateson’s criteria of mental process (e.g., differences, transformations of difference across a network, complex chains of determination, and, as we will propose, emergent hierarchies). Kauffman used his program to investigate the processes of biology; in contrast, E42 (Malloy & Jensen, 2002) is designed to explore the processes of human epistemology wherein the genesis of form and its apprehension is a central issue. More details on N, K, Boolean systems can be found in Kauffman (1993, 1995) and at Malloy (www.psych.utah.edu/dysys ). Under very broad constraints the reverberation of difference in N, K Boolean systems falls into repetitive cycles called basins. This falling into cycles is what Kauffman (1995) calls “order for free.” That is, if biology is construed as a vast network of transformations of difference, then under certain general conditions it will selforganize into complex cyclic patterns. Figure 1 shows static snapshots of basin patterns from two small discrete dynamic systems generated pseudo-randomly by E42. Panels (a) through (d) are all from the same dynamic system. Panel (e) shows one basin from a different pseudo-randomly generated system; it is included merely to show that there are many systems, many ways to getting the appearance of striped camouflage. An interesting aside, and one that Kauffman links to genes and evolution, is that the four patterns of zebra stripes shown in (a) through (d) can shift, one to another, based on changing the state (0 to 1 or 1 to 0) of one or very few nodes on a particular iteration. The trick is knowing which nodes and which iteration.