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Using Occam’s razor and Bayesian modelling to compare discrete and continuousrepresentations in numerostiy judgements
Abstract
Previous research has suggested that numerosity judgements are based not just on perceptual data but also past experi-ence, and so may be influenced by the form of this stored information. The representation of such experience is unclear,however: numerical data can be represented by either continuous or discrete systems, each predicting different general-isation effects. This study therefore contrasts discrete and continuous prior formats within numerical estimation usingboth direct comparisons of computational models using these representations and empirical contrasts exploiting differentpredicted reactions of these formats to uncertainty via Occam’s razor. Both computational and empirical results indicatethat numeroisty judgements rely on a continuous prior format, mirroring the analogue approximate number system, ornumber sense. This implies a preference for the use of continuous numerical representations even where both stimuli andresponses are discrete, with learners seemingly relying on innate number systems rather than symbolic forms acquired inlater life.
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