Visual Illusions Help Reveal the Primitives of Number Perception

The human perceptual system is responsive to numerical information within visual and auditory scenes. For example, when shown 2 displays of dots, observers can instantly, albeit approximately, identify the set that is more numerous. Theories in perceptual and cognitive psychology have focused on 2 mechanisms for how vision accomplishes such a feat: Under the domain-specific encoding theory, number is represented as a primary visual feature of perception, much like motion or color, while under the domain-general theory, the visual system represents number indirectly, through a complex combination of features such as the size of the dots, their total cluster, and so forth. Evidence for the latter theory often comes from "congruency effects:" the finding that participants frequently select the side where the dots on the screen are denser, larger, or brighter, rather than the side that is actually more numerous. However, such effects could also stem from response conflicts between otherwise independent dimensions. Here, we test these 2 competing accounts by embedding numerical displays within visual illusions that create large conflicts between number and other non-numeric dimensions-including contour length, convex hull, and density-and contrast participants' performance on a number discrimination task (i.e.. "Which side has more dots?") against a number estimation task (i.e.. "How many dots are there?"), which should eliminate response conflicts. Across 3 experiments, we find that while contour length illusions only affect number perception in discrimination tasks, the influences of convex hull and density on number perception persist in both discrimination and estimation tasks, supporting a more domain-general account of number encoding.