Representations of Complexity: How Nature Appears in Our Theories

Abstract

In science we study processes in the material world. The way these processes operate can be discovered by conducting experiments that activate them, and findings from such experiments can lead to functional complexity theories of how the material processes work. The results of a good functional theory will agree with experimental measurements, but the theory may not incorporate in its algorithmic workings a representation of the material processes themselves. Nevertheless, the algorithmic operation of a good functional theory may be said to make contact with material reality by incorporating the emergent computations the material processes carry out. These points are illustrated in the experimental analysis of behavior by considering an evolutionary theory of behavior dynamics, the algorithmic operation of which does not correspond to material features of the physical world, but the functional output of which agrees quantitatively and qualitatively with findings from a large body of research with live organisms.

Keywords: behavior dynamics; cellular automata; complexity theory; emergence; evolutionary theory; neural networks.

Figure 1.

Time evolution of cellular automaton Rule 152 given initial conditions of 6 (left), 10 (center), and 14 (right) adjacent black cells in the first row. Rule 152 “divides by two” when the initial condition is an even number of adjacent black cells. The result is displayed as a set of diagonal black lines, or shooters, the number of which gives the result of the calculation. Adapted from McDowell and Popa's (2009) Figure 3.

Figure 2.

Material processes and functional theories about their operation. The functional theories do not incorporate the processes themselves, but they do incorporate the emergent computations the processes carry out. The question mark in the center indicates that an atom may not be the sort of material process about which facts can be stated in ordinary terms of space and time.