Perceiving geographical slant

DENNIS R. PROFFITT 0 1 2 MUKUL BHALLA 0 1 2 RICH GOSSWEILER 0 1 2 JONATHAN MIDGETT 0 1 2 0 This research was supported by NIMH Grant MH5240-01 and NASA Grant NCC2-5074 to the first author. The authors are very grateful for the assistance provided by Marco Bertamini. Bennett Bertenthal , Sarah Creern, Jim Durbin, Frank Durgin, Jane Joseph, and Shahwar Qureshi. The development of our ideas benefitted greatly from numerous con versations with Jack Loomis. Nicola Bruno, William Ittelson, and Johan Wagernans provided valuable criticism on an earlier version of this D. R. Proffitt, Department of Psychology , Gilmer Hall, University of Virginia , Charlottesville, VA 22903-2477 ( 1 University oj Virginia , Charlottesville, Virginia 2 PROFFITT, BHALLA, GOSSWEILER, AND MIDGETT People judged the inclination of hills viewed either out-of-doors or in a computer-simulated virtual environment. Anglejudgments were obtained by having people (1) provide verbal estimates, (2) adjust a representation of the hill's cross-section, and (3) adjust a tilt board with their unseen hand. Geographical slant was greatly overestimated according to the first two measures, but not the third. Apparent slant judgments conformed to ratio scales, thereby enhancing sensitivity to the small inclines that must actually be traversed in everyday experience. It is proposed that the perceived exaggeration of geographical slant preserves the relationship between distal inclination and people's behavioral potential. Hills are harder to traverse as people become tired; hence, apparent slant increased with fatigue. Visuallyguided actions must be accommodated to the actual distal properties of the environment; consequently, the tilt board adjustments did not reflect apparent slant overestimations, nor were they influenced by fatigue. Consistent with the fact that steep hills are more difficult to descend than to ascend, these hills appeared steeper when viewed from the top. - By east coast standards, Virginia is a mountainous state, and many of its roads appear quite steep, especially to midwestern visitors. Yet by law, roads in the state can be inclined no more than 9 from the horizontal, and 9 is a much smaller angle than the inclination that most people estimate these steep roads to have. This is an example of a pervasive phenomenon: Hills appear to be steeper than they actually are. The first purpose of this paper is to pro vide a normative description of this overestimation in ge ographical slant perception. As we will show, a 5 hill is typically judged to be al most 20 in slant; however, when walking up a 5 hill, we do not raise our feet to accommodate a 20 incline and thereby stumble as we begin the ascent. The visual guid ance oflocomotion shows no evidence of slant mispercep tion. The second purpose of this paper is to show that a motoric index of geographical slant shows little evidence of the overestimations manifest in visual awareness. The paper's third purpose may be introduced with an anecdote. Not long ago, I (Proffitt) was riding in a l-day, 100-mile, bicycle tour, with the finish-line only a couple of miles ahead. The tour had traversed a number ofsmall mountains in a circuit that began and ended at a site in the rolling hills of the Virginia piedmont. The final hill before the finish seemed incredibly steep, and as I passed another rider I commented on how organizers of these affairs always seemed to arrange for the steepest hills to be located just before the finish. The other rider muttered an oath as she bemoaned what a cruel joke it was to make us climb this hill so late in the ride. (It would have been an even crueler joke to have informed her that the incline of this hill was only about r.) Now the hill in question was relatively steep, but it was far less so than many that we had previously en countered during this day of cycling. The third purpose of this paper is to show that the apparent steepness of this hill was due, in part, to our state ofphysical fatigue. Hills do, in deed, look steeper when we are tired than when we are not. We interpret these findings to imply that our conscious perceptions of geographical slant are highly exaggerated. Moreover, we argue that these perceptions are distorted in a manner that is well suited for the purposes of guiding lo comotion in the environment. For most of us who live out side of San Francisco, the effective range of slopes that we walk up and down is between 0 and 10. A 10 hill is quite difficult to climb for any distance, and it looks very steep to us. A 30 hill is about the limit of what we can walk up, and it is too steep to walk down without risk of slipping and falling. The top of a 30 hill is a dangerous place. We will show that, unlike smaller inclines, such hills look steeper from the top than from the bottom. We will argue that geographical slant perception relates the actual phys ical slant of inclines to our behavioral potential. For this reason, steep hills look steeper from the top and all hills look steeper when we are fatigued. In this regard, we will suggest that we perceive the affordances of slopes as op posed to their purely distal characteristics. Finally, we will suggest that the reason that people can locomote skillfully in the context of gross overestimations of slant is related to the separation of visual pathways that support conscious perception versus motoric action. Geographical Slant Geographical slant refers to the inclination of surfaces relative to the environmentally specified horizontal. There are three different ways in which surface slant can be de fined, depending on which ofthree reference frames is se lected. Relative slant specifies the orientation of one sur face with respect to the reference frame provided by another. Optical slant is specified in relation to the line of sight from the point of observation to the surface in ques tion. Finally, geographical slant is specified in relation to a fixed environmental frame of reference, typically the horizontal ground plane (Gibson & Cornsweet, 1952). As examples of these three slant representations, imagine a book being held during normal reading and consider the slant of the page that is being read. The relative slant of this surface with respect to the facing page would be about 170, its optical slant would be approximately 0, and its geographical slant would be around 45. In this paper, we are concerned with geographical slant-slant specified in relation to the horizontal plane of the ground. Geographical slant is independent of viewpoint. Its magnitude is specified in relation to the horizontal, as can be seen in Figure 1. The intersection of a surface with a horizontal plane defines a line. From any point on this line, perpendicular lines can be drawn along both the surface and the horizontal plane. Slant is defined by the smaller of the two supplementary angles formed by the intersection ofthe latter two lines. With respect to a Carte sian r (...truncated)