Search for: All records

Humans and other animals are able to perceive and represent a number of objects present in a scene, a core cognitive ability thought to underlie the development of mathematics. However, the perceptual mechanisms that underpin this capacity remain poorly understood. Here, we show that our visual sense of number derives from a visual system designed to efficiently encode the location of objects in scenes. Using a mathematical model, we demonstrate that an efficient but information-limited encoding of objects’ locations can explain many key aspects of number psychophysics, including subitizing, Weber’s law, underestimation, and effects of exposure time. In two experiments (N = 100 each), we find that this model of visual encoding captures human performance in both a change-localization task and a number estimation task. In a third experiment (N = 100), we find that individual differences in change-localization performance are highly predictive of differences in number estimation, both in terms of overall performance and inferred model parameters, with participants having numerically indistinguishable inferred information capacities across tasks. Our results therefore indicate that key psychophysical features of numerical cognition do not arise from separate modules or capacities specific to number, but rather as by-products of lower level constraints on perception. 

Many models of intuitive physical reasoning posit some kind of mental simulation mechanism, yet everyday environments frequently contain far more objects than people could plausibly represent with their limited cognitive capacity. What determines which objects are actually included in our representations? We asked participants to predict how a ball will bounce through a complex field of obstacles, and probed working memory for objects in the scene that were more and less likely to be relevant to the ball’s trajectory. We evaluate different accounts of relevance and find that successful object memory is best predicted by how frequently a ball’s trajectory is expected to contact that object under a probabilistic simulation model. This suggests that people construct representations for mental simulation efficiently and dynamically, on the fly, by adding objects “just in time”: only when they are expected to become relevant for the next stage of simulation. 

The approximate number system (ANS) has attracted broad interest due to its potential importance in early mathematical development and the fact that it is conserved across species. Models of the ANS and behavioral measures of ANS acuity both assume that quantity estimation is computed rapidly and in parallel across an entire view of the visual scene. We present evidence instead that ANS estimates are largely the product of a serial accumulation mechanism operating across visual fixations. We used an eye-tracker to collect data on participants’ visual fixations while they performed quantity-estimation and -discrimination tasks. We were able to predict participants’ numerical estimates using their visual fixation data: As the number of dots fixated increased, mean estimates also increased, and estimation error decreased. A detailed model-based analysis shows that fixated dots contribute twice as much as peripheral dots to estimated quantities; people do not “double count” multiply fixated dots; and they do not adjust for the proportion of area in the scene that they have fixated. The accumulation mechanism we propose explains reported effects of display time on estimation and earlier findings of a bias to underestimate quantities.