On the Structure of Semantic Number Knowledge

This doctoral thesis present the results of five distinct projects which all share a common focus - the structure of cognitive number processing. Two of the projects employ psychophysical methods to (a) establish some perceptual constraints on the processing of very large numbers (or very long digit strings) and (b) demonstrate a doissociation between subjects' sensitivities to these (large) numbers' holistic content from their sensitivities to the numbers' single-digit components. The other three projects are primarily computational; each proposes a novel model-building method, then applies it to a problem of relevance to numerical cognition. The results include (a) a novel proposal for the format of semantic number knowledge, which is supported by recent neurophysiological data, (b) a model-space analysis which suggests that this new format may be more effective than its conventional counterparts in driving models of multi-digit number comparison, and (c) a demonstration of model-building with minimal assumptions, which captures the optimal and near-optimal features of neural information processing in a well-known decision problem.