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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.
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The psychophysics of number arise from resource-limited spatial memory
People can identify the number of objects in small sets rapidly and without error but become increasingly noisy for larger sets. However, the cognitive mechanisms underlying these ubiquitous psychophysics are poorly understood. We present a model of a limitedcapacity visual system optimized to individuate and remember the location of objects in a scene which gives rise to all key aspects of number psychophysics, including error-free small number perception and scalar variability for larger numbers. We therefore propose that number psychophysics can be understood as an emergent property of primitive perceptual mechanisms — namely, the process of identifying and representing individual objects in a scene. To test our theory, we ran two experiments: a change-localization task to measure participants’ memory for the locations of objects (Experiment 1) and a numerical estimation task (Experiment 2). Our model accounts well for participants’ performance in both experiments, despite only being optimized to efficiently encode where objects are present in a scene. Our results demonstrate that the key psychophysical features of numerical cognition do not arise from separate modules or capacities specific to number, but rather from lower-level constraints on perception which are manifested even in non-numerical tasks
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- Award ID(s):
- 2000759
- PAR ID:
- 10275753
- Date Published:
- Journal Name:
- Cognitive Science Society
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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