Six experiments were conducted to test the hypothesis that overestimation of vertical distance is a pervasive phenomenon. The experiments i...
Six experiments were conducted to test the hypothesis that overestimation of vertical distance is a pervasive phenomenon. The experiments involved judgments of: (a) vertical distance looking upward; (b) vertical distance looking downward; (c) the slope of a real hill; (d) the recalled slopes of streets; (e) the magnitudes of angles drawn on paper; rn the distances to afterimages projected into the sky. The results showed that a very strong illusion of overestimation of both vertical distance and slope occurred in all situations except for the judgments of drawn angles by males. Furthermore, in five of the six experiments females showed a greater amount of the iIIusion than males. The discussion pointed out the difficulty of explaining the moon illusion by the assumptions of a flattened sky surface and Emmert's law in light of the data.
At present there exist two tenable theories of the moon illusion which. however. make opposite assumptions about the perception of distances in vertical or elevated directions. The theory of Kaufman and Rock (1962) assumes that. perceptually speaking. the sky is a surface which has the shape of a "flattened dome." This phrase indicates that the sky surface is perceived to be farther away at the horizon than when it is overhead as a result of the visible terrain. The larger apparent size of the moon (or sun) at the horizon is derived from this greater apparent distance. by the logic of Emmert's law for afterimages.2 This same argument was advanced by King and Gruber (1962) who showed that the size illusion also held for negative afterimages projected into the sky at the jlorizon and at 45 deg elevation. However.
Thor and Wood (1966) have taken the position that vertical distances are typically overestimated relative to horizontal distances. This "heightened arch" view of visual space implies that targets at high elevations in the sky are seen as farther away. as well as smaller. which is a direct reversal of the positive correlation of size and distance as given in Emmert's law. Since the sky is not. in fact. a surface with normal cues to its distance, it is not necessary that Emmert's law should apply. even for afterimages. Furthermore. Thor and Wood reported vertical distance overestimation in experiments in both a lighted and darkened room.
They concluded from their investigation that the moon illusion is one case of visual distortion produced by stimulation coming from the vestibular system accompanying the tilting of the head. The purpose of this paperis to report several experiments which were designed to find out how pervasive is the tendency, as suggested by the Thor and Wood hypothesis, for observers to overestimate vertical distances. The present studies examined vertical distance judgments in both upward and downward directions. the perceived and recalled slopes of hills. the magnitudes of drawn angles, and the apparent distances to afterimages projected into the sky. The data were analyzed by the sex of the subject in each situation. Since each experiment measured an apparent vertical distance relative to an apparent horizontal distance, it would be equally possible to call the phenomenon horizontal underestimation, although some anecdotal data couldbe offered to support the term chosen. METHODS In all of the six experiments run. the Ss were undergraduate students at Oakland University. and except for five female Ss who participated in Experiments 2. 3, and 6, no Ss were used in more than one experimental condition. In all experiments requiring target perception. the S was free to use binocular vision under normal indoor or outdoor lighting conditions. Experiment 1: Distance Upward The purpose of this experiment was to replicate and quantify the Thor and Wood report thatthe distance to the ceiling of a room is overestimated relative to the distance to the wall. The room used had a ceiling height of 13.4 it (the front of a small classroom auditorium) with cream colored walls and ceiling. In the first version (a) of the experiment. the S was first shown a plain white paper plate suspended at eye level on the far wall. Directly above this on the ceiling. in a line perpendicular to the wall was mounted a row of eleven identical paper plates. These plates ran from .90 it from the wall. at 1.74 it intervals. to a final distance of 18.30 it for the 11th plate. The S was asked to walk back and forth beneath the row of ceiling plates until he found one to stand under such that the distance from his eyes to the wall plate was equal to the distance from his eyes (emphasized) to the chosen plate on the ceiling. At that time his eye height was measured. and with .10 ft added to compensate for the upward tilting of the head, the actual distance from eyes to ceiling could be obtained by subtracting the corrected eye height from the total room height. If the S chose a paper plate which was farther from the wall than the distance from eyes to ceiling, he was said to overestimate the vertical distance accordingly. In the second version (b) of the experiment, all paper Perception & Psychophysics. 1967, Vol. 2 (12) Copuruih! 1967, Peuctionomic Prcs«, Goleta, Calif. .. 21.7' Fig. 1. Diagram of Ute physical situation for Ute vertical-horizontal distance comparison in Experiment 2, and of Ute slope judged in Experiment 3. plates were removed and a path perpendicular to the wall was marked by two chalk lines on the floor. Again each S was asked to walk back and forth in the path until he found a place to stand such that the eye-wall distance matched the eye-ceiling distance. In this case it was necessary to measure not only the S's eye height but also the distance from the wall to his eyes. A different sample of Ss was used in each version of the experiment. Experiment 2:
Distance Downward This study examined vertical distance judgments in which the S had to look downward instead of upward. Each S was stationed near the center of a bridge walkway leading from a 19.2 ft hill to the third floor of the Van Wagoner dormitory. The situation is shown in Fig. 1. The S was asked to bend over until his eyes were level with the bridge railing and to observe the distance from his eyes to the ground below (which was level). He was then asked to straighten up and observe the distance to the E who had taken a position at the open end of the bridge. Ss were encouraged to look down and forth again and then to report which distance was greater. After a choice was made, they were asked "greater by what per cent?"
The actual distance from eyes to ground was 22.9 ft and the distance to the E was 28.7 ft, for a physical vertical-horizontal distance ratio of .80. Experiment 3: The Slope of a 34°Hill It followed that if the Ss overestimated the vertical distance from the bridge to the ground in Experiment 2, they should also overestimate the slope of the 34 deg grass hill which fell from bridge level to ground level underneath the forward section of the bridge (Fig. 1). In order to ensure that the S understood the judgmental task, he was first shown a line diagram of two hills of 30 deg and 60 deg, each labeled only by an arrow and the symbol 9 which identified the angle of interest. 586 For further anchoring, a 0 deg hill was verbally defined as level ground with no slope and a 90 deg hill as a straight up and down cliff wall. The S was then asked to walk wherever he wished and to report back with his best estimate of the slope of the hill in degrees. No S reported difficulty in understanding the task. Experiment 4:
Memory for Steep Streets In order to ensure that the resultsfrom Experiment 3 would not be peculiar to that visual scene, a questionnaire was distributed to an introductory psychology class during the first week of the course. The questionnaire showed a line diagram of a hill with the 45 deg angle under the hill numerically labeled. The verbal definitions of 0 deg and 90 deg slopes as in Experiment 3 were included. The questionnaire asked the Ss to report, in degrees, the steepest streets they had ever driven on, walked on, and seen, with the location of the streets requested in each case. Only the data from steepest streets ever driven on are reported here; these data show the least amount of overestimation of the three questions. In order to calculate the amount of overestimation, it was necessary to decide upon some maximum feasible slope as a baseline, for which purpose 25 deg was decided to be a generous estimate after an examination of several highway engineering manuals which made no reference to grades above 15 deg. Furthermore, it was established through the San Francisco Bureau of Engineering, Divtston of Grades, that the steepest segment of passable street in that city was 17.5 deg, Those sa who located their steepest street experiences in San Francisco were then used as a subsarnple for comparison with this more objective baseline
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