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.
Highlights
In many everyday tasks, we are required to make quick estimates of discrete stimuli based on noisy perceptual data: the number of people in a crowded room, or cars in a lane of traffic, for example
This is further supported by comparisons with computational models of estimation: in both experiments, behaviour was better fit by a Gaussian mixture prior over a discrete mixture prior in both the number of participants accounted for and aggregated measures of fit, providing a second source of evidence for the use of a continuous prior format
The present results offer an interesting display of the use of continuous systems even in discrete numerosity judgements: use of a continuous numerical format appears dominant in the present task despite stimuli, responses and feedback all being discrete
Summary
We are required to make quick estimates of discrete stimuli based on noisy perceptual data: the number of people in a crowded room, or cars in a lane of traffic, for example These decisions are not solely reliant on perceptual information, and use past experiences with such stimuli to guide responses: if estimating the number of people in a room, the actor may consider similar occasions where that number was later provided and use this information to inform their decision. Accurate estimates are reliant on the learning of the distribution of such figures, building representations that reflect the prevalence of these values in the real world The influence of such previous experience is in turn dependent on its representation, reflecting the different forms in which numerical information could be stored.
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