Symbols, neurons, soap-bubbles and the neural computation underlying cognition

Abstract

A wide range of systems appear to perform computation: what common features do they share? I consider three examples, a digital computer, a neural network and an analogue route finding system based on soap-bubbles. The common feature of these systems is that they have autonomous dynamics — their states will change over time without additional external influence. We can take advantage of these dynamics if we understand them well enough to map a problem we want to solve onto them. Programming consists of arranging the starting state of a system so that the effects of the system's dynamics on some of its variables corresponds to the effects of the equations which describe the problem to be solved on their variables. The measured dynamics of a system, and hence the computation it may be performing, depend on the variables of the system we choose to attend to. Although we cannot determine which are the appropriate variables to measure in a system whose computation basis is unknown to us I go on to discuss how grammatical classifications of computational tasks and symbolic machine reconstruction techniques may allow us to rule out some measurements of a system from contributing to computation of particular tasks. Finally I suggest that these arguments and techniques imply that symbolic descriptions of the computation underlying cognition should be stochastic and that symbols in these descriptions may not be atomic but may have contents in alternative descriptions.