A slippery slope: estimated slant of hills increases with distance.

Abstract

The slopes of hills tend to be greatly overestimated. Previous studies have found that slope estimates are significantly greater when estimated verbally than with a proprioceptive measure. It has yet to be determined whether these estimates are made for the entire extent of the slope, or whether the estimates in closest proximity are estimated using a different process. Since some parietal cortex neurons respond differently to objects within arm's reach, short-distance slope estimation may utilize these or analogous neurons. Alternatively, greater implied effort might make longer slopes seem steeper. We determined that both verbal and proprioceptive reports of slope are overestimates that increase logarithmically with distance from the observer, contradicting both theories. Consistent with previous work, proprioceptive estimates were more accurate at all ranges. Our results can be interpreted as a function of the angle between the observer's gaze and the plane of the hill, modified by depth cues available at only near distances.