Using Occam's razor and Bayesian modelling to compare discrete and continuous representations in numerosity judgements

Spicer, Jake; Sanborn, Adam N.; Beierholm, Ulrik R.

Abstract

Previous research has established that numeric estimates are based not just on perceptual data but also past experience, and so may be influenced by the form of this stored information. It remains unclear, however, how such experience is represented: numerical data can be processed by either a continuous analogue number system or a discrete symbolic number system, with each predicting different generalisation effects. The present paper therefore contrasts discrete and continuous prior formats within the domain of numerical estimation using both direct comparisons of computational models of this process using these representations, as well as empirical contrasts exploiting different predicted reactions of these formats to uncertainty via Occam’s razor. Both computational and empirical results indicate that numeric estimates commonly rely on a continuous prior format, mirroring the analogue approximate number system, or ‘number sense’. This implies a general preference for the use of continuous numerical representations even where both stimuli and responses are discrete, with learners seemingly relying on innate number systems rather than the symbolic forms acquired in later life. There is however remaining uncertainty in these results regarding individual differences in the use of these systems, which we address in recommendations for future work.

Citation

Spicer, J., Sanborn, A. N., & Beierholm, U. R. (2020). Using Occam's razor and Bayesian modelling to compare discrete and continuous representations in numerosity judgements. Cognitive Psychology, 122, Article 101309. https://doi.org/10.1016/j.cogpsych.2020.101309

• Journal Article Type: Article
• Acceptance Date: May 23, 2020
• Online Publication Date: Jul 3, 2020
• Publication Date: 2020-11
• Deposit Date: May 28, 2020
• Publicly Available Date: Jul 2, 2021
• Journal: Cognitive Psychology
• Print ISSN: 0010-0285
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 122
• Article Number: 101309
• DOI: https://doi.org/10.1016/j.cogpsych.2020.101309
• Public URL: https://durham-repository.worktribe.com/output/1263615