Numerosity and cumulative surface area are perceived holistically as integral dimensions.

Abstract

Human and non-human animals have the remarkable capacity to rapidly estimate the quantity of objects in the environment. The dominant view of this ability posits an abstract numerosity code, uncontaminated by non-numerical visual information. The present study provides novel evidence in contradiction to this view by demonstrating that number and cumulative surface area are perceived holistically, classically known as integral dimensions. Whether assessed explicitly (Experiment 1) or implicitly (Experiment 2), perceived similarity for dot arrays that varied parametrically in number and cumulative area was best modeled by Euclidean, as opposed to city-block, distance within the stimulus space, comparable to other integral dimensions (brightness/saturation and radial frequency components), but different from separable dimensions (shape/color and brightness/size). Moreover, Euclidean distance remained the bestperforming model, even when compared to models that controlled for other magnitude properties (e.g., density) or image similarity. These findings suggest that numerosity perception entails the obligatory processing of non-numerical magnitude.

A theory of perceptual number encoding.

“…Aulet and Lourenco (2021b) found that, for both the categorization and match-to-sample tasks, participants’ perceived similarity for the visual displays was best modeled by Euclidean distance, suggesting that number and area are integral dimensions, akin to other integral dimensions such as brightness/saturation and radial frequency components (Gottwald & Garner, 1975; de Beeck et al, 2003). That is, participants’ responses reflected the similarity of the joint space rather than each component dimension separately.…”

“…In this section, we describe recent research designed to dissociate between the possibility of separate, perceptually-independent representations of magnitude, versus integral, perceptually-interdependent representations, in which number and other magnitudes are encoded together. Using classic, quantitative measures of similarity (i.e., city-block and Euclidean distance), Aulet and Lourenco (2021b) tested whether numerical and nonnumerical magnitudes are better characterized as separable or integral dimensions. In this study, the non-numerical magnitude of interest was cumulative surface area, and thus, only number and area were directly manipulated.…”

Numerosity perception is tuned to salient environmental features

“…The site of numerosity adaptation is still debated. Several authors (e.g., Aulet and Lourenco, 2021 ; Dakin et al., 2011 ; Durgin, 2008 ) have suggested that number is represented at an early stage of visual processing, together with size and other low-level features. Durgin (2008) specifically claimed that adaptation to the number is also early, occurring early in processing, possibly mediated by adaptation to texture.…”

Perceived number is not abstract

“…Our own research suggests that number and area are perceived holistically as integral dimensions (Aulet & Lourenco, 2021a). In Aulet and Lourenco, we found that perceived similarity for dot arrays, which varied parametrically in number and cumulative area, was best modeled by Euclidean, as opposed to city-block, distance within the stimulus space (Garner, 1974;Shepard, 1964), comparable to classically integral dimensions (e.g., brightness and saturation) but different from separable dimensions (e.g., shape and color).…”