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Bruce Bridgeman; Optical Illusions on the Slopes of Hills. Journal of Vision 2011;11(15):29. doi: https://doi.org/10.1167/11.15.29.
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Observers are known to overestimate the slopes of hills, and estimates of slope are significantly greater when estimated verbally than with a proprioceptive measure. Since neurons in the premotor cortex have been found to respond differently to objects within arm's reach, we hypothesized that slope estimations might show a break where distances are no longer reachable. A second hypothesis assumes that observers take into account the effort that would be needed to climb the hill to the required distance, predicting a linear increase in apparent slope. We tested apparent slope at a range of distances on a hill of constant real slope. Verbal measures greatly overestimated the actual slope, and increased logarithmically with distance from the observer, while proprioceptive estimates were more accurate but still increased logarithmically. The results also fit exponential functions. Thus neither of the original hypotheses was supported. The results can be interpreted as an implicit slope, previously measured only in darkness, modulated by depth cues available at near distances. Observers use a transformation of the angle between the line of sight and the surface of the hill to inform their estimates.
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