Composition

This chapter is a composition on the theme of binding and composition. The binding problem-the investigation of the mechanisms used by the brain to bind with each other the representations of different parts or features of an object-has motivated a number of studies in recent years. In particular, attention has been given to the possible role of accurate temporal structure of multi-neuron spike trains in cortex [1-3]. The present paper uses linguistic examples to suggest that the mental material that is operated upon by the establishment of dynamical bonds largely consists, in itself, of dynamical bonds. Further, using the construction game Lego as a metaphor for compositional symbol systems, we stress the role of cooperativity among elementary bonds. We use the term map to refer to a coherent system of bonds, i.e., a system where elementary bonds cooperate with each other. We propose to view the fundamental operation of mental composition as consisting of the doing and undoing of maps between maps ... between maps. Cooperative binding in Lego can be characterized mathematically as the establishment of commutative mapping diagrams, and we outline an approach to language in which the construction of meaning consists of the establishment of recursively embedded commutative mapping diagrams. Drawing from these considerations, we suggest that the mechanism the brain uses to achieve recursive composition may consist of the cooperative binding of complex spatio-temporal patterns. Particularly interesting in this context is the synfire-chain model proposed by Abeles [4] to explain the accurately timed events in cortex reported by him and his group. This model offers a simple and plausible example of a system of recursively bound spatio-temporal neural activity patterns. Moreover, in this model, the interpretation of cooperative binding as the establishment of commutative mapping diagrams is straightforward, and consistent with the generally accepted principle of Hebbian plasticity.