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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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Examining Limits of Small Multiples: Frame Quantity Impacts Judgments with Line Graphs
Small multiples are a popular visualization method, displaying different views of a dataset using multiple frames, often with the same scale and axes. However, there is a need to address their potential constraints, especially in the context of human cognitive capacity limits. These limits dictate the maximum information our mind can process at once. We explore the issue of capacity limitation by testing competing theories that describe how the number of frames shown in a display, the scale of the frames, and time constraints impact user performance with small multiples of line charts in an energy grid scenario. In two online studies (Experiment 1 n = 141 and Experiment 2 n = 360) and a follow-up eye-tracking analysis (n = 5), we found a linear decline in accuracy with increasing frames across seven tasks, which was not fully explained by differences in frame size, suggesting visual search challenges. Moreover, the studies demonstrate that highlighting specific frames can mitigate some visual search difficulties but, surprisingly, not eliminate them. This research offers insights into optimizing the utility of small multiples by aligning them with human limitations.
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- Award ID(s):
- 2238175
- PAR ID:
- 10503942
- Publisher / Repository:
- IEEE Transactions on Visualization and Computer Graphics
- Date Published:
- Journal Name:
- IEEE Transactions on Visualization and Computer Graphics
- ISSN:
- 1077-2626
- Page Range / eLocation ID:
- 1 to 12
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TVCG.2024.3372620
