The influence of attention on number and magnitude estimation: Evidence from a reproduction task Author Accepted Manuscript

Approximate Number System (ANS) theory assumes that humans are born with a number system where the non-numerical features of objects are normalized and number is a primary dimension. In contrast, Sensory Integration System (SIS) theory suggests that number sense is not innate and numerosity is derived from non-numerical quantitative features like area, density, etc. Perceptual Interdependence (PI) theory occupies a middle ground, recognizing number as a real dimension, but acknowledging its dependence on other magnitudes when attention is not focused on differentiating them, without claiming any one dimension is more fundamental than another. We designed a task requiring participants (N = 64, collected in 2021) to estimate the number, cumulative area, and average dot size of the same stimuli by reproducing respective dimensions. Participants were informed of the target dimension before or after stimulus presentation. Results showed that cue timing affected the percentage estimation error of number, cumulative area and average dot size, as well as the absolute percentage estimation error of number. The distinct impact of attention on three dimensions is suggestive of differences in underlying representations and processing mechanisms. Additionally, the correlation between number and area estimations did not vary reliably by cue timing. Although these findings appear more consistent with the PI theory, any inferences based on the present results should only be considered tentative, as the analyses are exploratory and data-driven in nature.