Geometric categories in cognition

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Description: In this project, we discover that two categories of special angles in formal geometry, parallels and perpendiculars, are robustly reflected in adults’ basic angle discrimination. Our results both characterize the psychophysical properties of angle discrimination, which has been debated in prior literature, and also link vision research to the conceptual, formal, and school-relevant spatial understanding that supports abstract mathematics At the scale in which we live, space is continuous. Nevertheless, our perception and cognition parse the world into categories, whether physical, like scene or object, or abstract, like infinitesimal point or seven. The present study focuses on two categories of special angles in planar geometry, parallels and perpendiculars, and we evaluate how these categories might be reflected in adults’ basic angle discrimination. In the first experiment, participants were most precise when detecting two parallel or perpendicular lines among other pairs of lines at different relative orientations. Detection was also enhanced for two connected lines whose angle approached 90°, with precision peaking at 90°. These patterns emerged despite large variations in the scales and orientations of the angle exemplars. In the second experiment, the enhanced detection of perpendiculars persisted when stimuli were rotated in depth, indicating a capacity to discriminate shapes based on perpendicularity in three dimensions despite large variation in angles’ two-dimensional projections. The results suggest that two categorical concepts which lie at the foundation of Euclidean geometry, parallelism and perpendicularity, are reflected in our discrimination of simple visual forms, and they pave the way for future studies exploring the developmental and evolutionary origins of these cognitive categories.

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