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

Area of Science:

• Cognitive Psychology
• Neuroscience
• Mathematical Cognition

Background:

• Numeric estimates integrate perceptual data with past experience.
• Stored numerical information can be represented by continuous analogue or discrete symbolic systems.
• The representation format influences generalization effects in numerical tasks.

Purpose of the Study:

• To investigate whether numeric estimates utilize continuous analogue or discrete symbolic prior formats.
• To contrast computational models and empirical data for both representations.
• To determine the preferred numerical representation system in estimation.

Main Methods:

• Computational modeling comparing discrete and continuous prior formats.
• Empirical testing exploiting differential predictions of uncertainty.
• Analysis using Occam's razor to favor simpler explanations.

Main Results:

• Both computational and empirical results favored a continuous prior format.
• Numeric estimates commonly rely on the analogue approximate number system ('number sense').
• A preference for continuous representations exists even with discrete stimuli/responses.

Conclusions:

• Learners appear to utilize innate number systems (continuous) over acquired symbolic systems (discrete).
• Continuous representations are preferred in numerical estimation tasks.
• Further research is needed to address individual differences in system use.