1 Representation in Dynamical Systems

The brain is often called a computer and likened to a Turing machine, in part because the mind can manipulate discrete symbols such as numbers. But the brain is a dynamical system, more like a Watt governor than a Turing machine. Can a dynamical system be said to operate using “representations”? This paper argues that it can, although not in the way a digital computer does. Instead, it uses phenomena best described using mathematic concepts such as chaotic attractors to stand in for aspects of the world. We can trace the roots of the current state of cognitive science back to Plato and his fundamental separation of mind and matter, a theory today known as substance dualism. With little science available to incorporate physical reality and experiential qualia, Plato turned away from such problems and regarded the abstract forms of the mind as the true Reality. Such a framework has directed philosophies and sciences of the mind and brain for the past 2,400 years. Another substance dualist, Descartes, strengthened the assumptions behind the still-dominant computational paradigm. In the 17th Century he based his system of knowledge upon the self-awareness of the soul, and its own intrinsic powers of deduction. According to Descartes, “[the soul] was, after all, a rational soul with a scheme of innate representations, and principles of logic were the principles of its dynamics” (P.S. Churchland, 243). He understood central mental capacities merely to be processes of reasoning. According to van Gelder, “the prior grip that this Cartesian picture has on how most people think about mind and cognition makes the computational conception intuitively attractive to many people.” (1995, 379). Since the time of Aristotle we have been able to describe logical operations explicitly and formulaically. Such operations act upon symbolic structures, which also can be described explicitly and formulaically. These abilities have lead to the modern theories of computation, developed in parallel by computer scientists and cognitive scientists. Digital computers provide physical mechanisms for implementing symbolic computations, and in the computationalist paradigm the human brain is thought to be a special type of digital computer. Our knowledge and belief structures are static representations of internal or external states, and cognition takes place when abstract rules of computation are applied to such representations. Fodor (1975) calls this compositional format of cognitive computation the “Language of Thought” hypothesis. The most powerful and versatile method of representing knowledge that we know of is through symbols. Therefore the brain must compute symbolically. A particularly well formulated version of this theory appears in Newell & Simon (1976) under the name of “the physical symbol system hypothesis.” Interaction with the world takes place through peripheral input and output mechanisms that translate messy external physical states into