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Matthew Jordan, Yuval Hart, Moira Dillon; Pathing judgment on planes and spheres: Accurate intuitions about shortest paths. Journal of Vision 2018;18(10):505. doi: https://doi.org/10.1167/18.10.505.
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© ARVO (1962-2015); The Authors (2016-present)
Humans alone are capable of formal geometry, like the one outlined in Euclid's Elements. We can conceive of points of no size and lines of infinite length. How do we conceive of such points and lines without ever perceiving them? We examined adults' (N=48) capacity to judge the shortest path between two points (i.e., linearity) on pictures of planes and spheres (Fig. 1). Our primary analysis focused on whether participants' success depended on three factors: surface (plane vs. sphere); planar linearity (i.e., a line vs. curve); and spherical linearity (i.e., a geodesic vs. arc). While participants were more successful at judging the shortest paths on planes vs. spheres (P < .001; Fig. 2), they were nevertheless above chance (.50) when judging geodesics that were also either lines (P < .001) or curves (P < .001). Indeed, participants modulated their responses based on the surface (Surface X Planar Linearity, P < .001; Surface X Spherical Linearity, P < .001). Nevertheless, participants were more accurate at judging geodesics that were also lines vs. geodesics that were also curves (P < .001, holm-corrected). Finally, spherical judgments were more accurate with smaller spheres, longer paths, and paths closer to the poles (all Ps < .001). Participants' success with geodesics is surprising because prior work has shown a planar bias in adults' commonsense geometric reasoning (e.g., Izard et al., 2011) and because formal spherical geometry is rarely taught in school. Future work may examine how human and animal navigation may underlie such accurate path judgments (e.g., Jeffery et al., 2013; Urdapilleta et al., 2015), and how such judgments may depend on development of visual form processing (e.g., Ons & Wagemans, 2011). Ultimately, this work aims to bridge our perception of spatial entities to our conception of geometric formalisms.
Meeting abstract presented at VSS 2018
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