Humans have precise knowledge of familiar geographical slants.

Whereas maps typically depict the two-dimensional layout of an environment, the vertical dimension is generally encountered only directly. The possible importance of inclines as an orienting landmark in the environment (Nardi & Bingman, 2009), as well as the energetic significance of hills (Kammann, 1967; Proffitt, Bhalla, Gossweiler & Midgett, 1995) suggests that detailed memory of this aspect of the environment might be quite useful for navigation and route planning. Geographical slant refers to surface slant relative to horizontal (Sedgwick, 1986). Previous studies of memory for geographical slant have focused primarily on newly-observed outdoor surfaces (Creem & Proffit, 1998) or on small indoor surfaces (Haun, Allen & Wedell, 2005), and each has reported biases in memory using both verbal and manual estimates. Creem and Proffitt reported evidence of additional exaggeration in memory, whereas Haun et al. reported a categorical bias toward 45° for both types of measure. What has not been investigated experimentally is whether extremely familiar locomotor surfaces (e.g., paths frequently taken in daily life) are subject to similar memory distortions. We sought to assess the precision of the information in memory about the geographical slant of a familiar environment (a small college campus). Our principal question is not one of representational accuracy. It is well documented that geographical slant is overestimated (Kammann, 1967; Li & Durgin, 2010; Proffitt, Bhalla, Gossweiller & Midgett, 1995; Ross, 1974). Rather, our question is of representational precision. The distinction between accuracy and precision is fundamental to measurement. Precision is usually measured in terms of variability, or uncertainty, whereas accuracy is measured in terms of signed error or bias. If one's perception of a hill is consistent, but highly biased, accuracy could be poor even while precision is good. In fact, precise coding is more crucial than accurate coding for controlling action because, so long as actions and perceptions are coded in the same scale, actions themselves can be accurate (i.e., effective) without the representations that guide them being veridical. This allows action control to be able to adapt to distorted visual input, such as adaptation to wedge prisms that offset the perceived location of a target to the left. When wearing such prisms, skilled reaching to grasp an object quickly adapts so that although the object still appears to be displaced (e.g., to the left of one's midline) ballistic reaching becomes successful because one's proprioception of hand position comes to be shifted as well (Harris, 1980). So long as there is opportunity for calibration of action to visual experience, the success of action control depends on the precision rather than the accuracy of the perception. A recent theoretical account of the exaggeration of geographical slant argues that angular perceptual variables are systematically biased (coded on an expanded scale) in order to retain greater coding precision (Durgin & Li, 2011). For similar reasons, memory representations of surface layout ought to be most informative if they are scaled similarly to perception. Moreover, the precision of such memory representations is of particular interest. One would expect that estimates from newly-formed memories would be more variable (less precise) than those from perception and thus more open to categorical bias. That is, judgmental biases have greater impact on estimates when estimate uncertainty is high (precision is low). But memory variability might decline to something quite close to the limits available in perception for familiar hills. Indeed, given that a familiar slope might have been observed from many different perspectives, it is possible that a memory representation of a familiar surface could be even richer than that obtained by perceptual experience from a single vantage point. On a small campus with a single dining hall, students may become experts not only at 2D route knowledge, but also at knowing the apparent 3D shape of the terrain they are frequently traversing. Haun et al. (2005) proposed that memory errors in slant judgments might be due to categorical distortions and biases. For example, memory for position is biased toward categorical locations (e.g., Engbretson & Huttenlocher, 1996; Huttenlocher, Hedges & Duncan, 1991) and memory for angles (Fisher, 1968), graphs and figures also show systematic distortion (Tversky & Schiano, 1989) so that errors in slant memory may be quite general. But one might nonetheless expect that highly familiar surfaces would be remembered as they actually appear to us. There have been many investigations of spatial memory biases for the 2D layout of real environments and maps (e.g., Bahrick, 1979; Byrne, 1979; Tversky, 1981). However, most of these studies address novel layouts or long periods of storage. The one study conducted by Creem and Proffitt (1998) for familiar hills (Experiment 3) was non-experimental in that all participants were tested only in the memory condition and were then compared to perceptual estimates previously collected by Proffitt et al. (1995) under different circumstances. We therefore sought to conduct a full experimental comparison of memory and perception for familiar slants. We used a small liberal arts college campus as the stimulus for our study. Swarthmore College is situated in a variably inclined environment that provides a shared locomotor experience for its students. There is a single dining hall, for example, that is commonly exited by ascending a somewhat steep extended path to the main academic area of the campus. The campus is relatively small, so students are familiar with most of its paths. But, how familiar are they with their slopes? That is, how precise are their memory representations and how similar are they to their perceptual experience? We compared slant estimates obtained when students directly observed each of several paths with estimates obtained when other students recalled the same paths from memory. To anticipate the results, students differentiated the various slopes of the tested paths equally well both in perception and in memory and there were no salient differences between estimates made from memory and from perception. This suggests that incidental memory representations of the vertical dimension of a familiar locomotor environment can be quite rich. Perception and memory for familiar paths The front of the campus of Swarthmore College features an extended broad hillside, of variable slope, at the center of which extends a tree-lined path (Magill Walk) leading up to the central college building (Parrish Hall) from the train station and town center. We selected for study five well-travelled campus paths in this region of campus ranging from nearly flat (0.5°) to the steepest extended section of path (8.6°) in this part of campus. Images of the steeper paths, and the locations of all the tested paths are illustrated in Figure 1. Figure 1 The locations of the five slanted paths used in the study on a campus map. “Routes” refers to the 5 different orders used in both the perception condition and in the memory condition. Below, the three steeper paths are shown in frontal ...