Putting the world in mind: The case of mental representation of quantity

A reoccurring question in cognitive science concerns the way the world is represented. Cognitive scientists quantify the contribution of a physical attribute to a sensation and try to characterize the underlying mechanism. In numerical cognition, the contribution of physical properties to quantity perception in comparison tasks was widely demonstrated albeit leaving the underlying mechanism unclear. Furthermore, it is unclear whether this contribution is related solely to comparison tasks or to a core, general ability. Here we demonstrate that the shape of the convex hull, the smallest convex polygon containing all objects in an array, plays a role in the transfer function between quantity and its mental representation. We used geometric probability to demonstrate that the shape of the convex hull is correlated with quantity in a way that resembles the behavioral enumeration curve of subitizing and estimation. Then, in two behavioral experiments we manipulated the shape of the convex hull and demonstrated its effect on enumeration. Accordingly, we suggest that humans learn the correlation between convex hull shape and numerosity and use it to enumerate.