Eye movements reveal distinct encoding patterns for number and cumulative surface area in random dot arrays

Humans can quickly and intuitively represent the number of objects in a scene using visual evidence through the Approximate Number System (ANS). But the computations that support the encoding of visual number-the transformation from the retinal input into ANS representations-remain controversial. Two types of number encoding theories have been proposed: those arguing that number is encoded through a dedicated, enumeration computation, and those arguing that visual number is inferred from nonnumber specific visual features, such as surface area, density, convex hull, etc. Here, we attempt to adjudicate between these two theories by testing participants on both a number and a cumulative area task while also tracking their eye-movements. We hypothesize that if approximate number and surface area depend on distinct encoding computations, saccadic signatures should be distinct for the two tasks, even if the visual stimuli are identical. Consistent with this hypothesis, we find that discriminating number versus cumulative area modulates both where participants look (i.e., participants spend more time looking at the more numerous set in the number task and the larger set in the cumulative area task), and how participants look (i.e., cumulative area encoding shows fewer, longer saccades, while number encoding shows many short saccades and many switches between targets). We further identify several saccadic signatures that are associated with task difficulty and correct versus incorrect trials for both dimensions. These results suggest distinct encoding algorithms for number and cumulative area extraction, and thereby distinct representations of these dimensions.