Experiment 6: Distances to Afterimages on the Sky It was considered possible that Ss might not only see a difference in the sizes of after...
Experiment 6: Distances to Afterimages on the Sky It was considered possible that Ss might not only see a difference in the sizes of afterimages projected at different elevations in the sky (King & Gruber, 1962), but they might also see a difference in apparent distances, thus providing data directly relevant to the applicability of Emmert's law in this situation. Each S was asked to fixate foveally and binocularly a small white square, subtending 1.3 deg of visual arc, pasted on a very dark blue field. He was then asked to observe the dark afterimage of the square in the sky both over the horizon and at 45 deg elevation (as defined by S). The sky was a homogeneous gray-blue field with the sun located over the shoulders on both days the data were collected. The S was then asked in half of the cases which image was larger, and then larger by what percent. Following another fixation period, these Ss were asked to determine which image was farther away, and by what per cent. For the other half of the Ss the two questions were reversed in order.
RESULTS The index which seemed to provide the most comparability across the experiments was the ratio of apparent vertical distance to apparent horizontal distance. For example, a mean apparent VIH distance ratio of 1.65 would mean that, on the average, a particular vertical distance seemed to be 65 percent greater than a physically equal horizontal distance in that situation. In Experiment 1 the' mean apparent v/n ratio was given directly by (a) the distance of the chosen ceiling plate from the wall, or (b) the distance the S stood from the wall-divided by the distance from the wall which would correctly match the distance to the ceiling. In Experiments
2, 3, and 4, the S was not presented with physically equal vertical and horizontal distances so the data had to be corrected by the physical ratio actually presented. In the cases of the slopes of hills (Experiments 3 and 4), the estimated and physical v/a ratios were defined by the tangents of the estimated and correct angles, respectively. Finally, in Experiment 6 the ratio given could be called the mean E/H ratio since it represented apparent distance to a 45 deg elevated target as compared with the apparent distance to a target just over the horizon; no vertical distance was involved. The results, according to the sex of the Ss, are given in Table 1; the formulas for calculating the VIH ratios are given in the footnotes. It can be seen that in every case both males and females showed vertical overestimation, statistically significant in all but one case which had too small an N. Furthermore, in every case except that of the afterimages in the sky (Experiment 6), the females showed a greater amount of vertical overestimation, which was statistically significant in Experiments 1 to 5. The percent of judgments in all situations which were underestimations, correct, and overestimations were 4.2, 6.4, and 89.4 for males, respectively, and 0.0, 2.5, and 97.5 for females, respectively. In Experiments 1 and 2 (vertical distances upward and downward) there remained the possibility that the Ss were not using the eyes as a reference point for vertical distance, although the instructions emphasized this point. However, if the Ss used some point nearer their feet as a reference point, it would reduce the calculated illusion in Experiment I, but it would increase it in Experiment 2. In order to interpret the data from Experiments 3 and 4, both involving estimates of slope,iUs necessary Table 1. Mean Apparent Vertical/Horizontal Distance Ratios in Five Experimentsa Males Females Signi!. Experiment Situation N V/H Ratio N V/H Ratio t(sex) Level 10. Ceiling with paper plates 15 1.42** 15 1.52" 1.05 N.S. b. Ceiling without plates 15 1.62** 15 1.94" 3.20 .01 2 22.9 ft. bridge b 4 1.28 12 1.69" 2.34 .05 3 34° hill slope c 66 1.65" 13 2.12" 3.53 .001 40. 25° streetC 78 1.71" 92 2.31" 5.04 .001 b. 17.5° street (SF)C 4 2.48* 6 4.46** 2.12 N.S. 6. Images in the skyd 7 1.48" 8 1.28* 2.07 N.S. a. V/H ratios significantly different by t test from a ratio of 1.00 are marked * for the .05 level and" for the .001 level. b. In experiment 2 the mean estimated V/H ratio was divided by .80. the physical.v/H ratio presented to the S. c. In Experiments 3 and 4 the V/H ratio is the tangent of the mean estimated angle divided by the tangent of the correct or maximum ang le of slope (34°. 25°, 17.5°). d. The V/H ratio in Experiment 6 is the mean of the reported ratios of the distance to the 45° elevated afterimage to the distance of the horizon atterimaoe . Perception & Psychophysics, 1967, Vol. 2 (12) 587 Table 2. Reported Degrees of Angle for Six Drawn Angles a (N = 20 males, 20 females) Drawn Angles Measure 10° 20° 35° 50° 70° 90° Mean (males) 11.3- 23.5- 36.3 SO.5 73.5 90.0 Mean (females) 15.0-- 27.3-- 41.3- - 57.7- 79.0-- 90.0 S.D. (males) 2.36 4.33 5.90 4.33 8.27 0.00 S.D. (females) 3.94 3.94 4.33 10.22 3.15 0.00 VIH Ratio (males)b 1.11 1.19 1.04 1.02 1.23 V/H Ratio (females)b 1.51 1.41 1.25 1.33 1.82 t(sex diff.) 3.56 2.80 2.98 2.84 2.58 s gnif. level .001 .01 .01 .01 .05 a. Means of reported angles which are significantly different from the correct angle by t test are marked - for the .05 level and - - for the .001 level. b. The V/H ratio refers to the tangent of the mean reported angle divided by the tangent of the correct angle. to examine the results of the control study on judgments of drawn angles. The results may be seen in Table 2. It will be noted first that the data were stable enough so that even small mean deviations from the correct angle were often significant. In general, males showed a slight overestimation but only for the smaller angles, while females showed a consistent small overestimation of all angles (except 90 deg), That these differences are not based simply on a greaterIack of familiarity with angles by females is probable in that females usually showed no greater variability of judgments than males. Although both overestimation and the sex difference held for drawn angles, the degree of illusion was substantially less than that found in Experiments 3 and 4. For example, a 34 deg hill slope produced mean estimates of 48 deg and 55 deg for males and females, respectively, but a drawn angle of 35 deg produced mean estimates of only 36 deg and 41 deg, respectively. Similarly, the estimated maximum streetslope of 25 deg (with actual values perhaps in 15 deg to 20 deg range) produced recall estimates of 38 deg and 47 deg, while a drawn angle of 20 deg produced recall estimates of only 23 deg and 27 deg for males and females, respectively. All considered, the data seem to say that the illusion holds to some degree even for drawn angles, rather than seeming to say that the Ss simply don't know how to use the concept of degrees of angle. In Experiment 6 (afterimages in the sky) the size [udgments, not appearing in Table I, revealed that the images appeared larger on the horizon than at elevation, just as with the moon. The illusion for males, with a horizontal-to-elevated size ratio of 1.44, was comparable to that found by King and Gruber, but for females, it was substantially less (1.17). DISCUSSION An obvious question is whether the various judgmental tasks used in this study involved the same perceptual processes. The judgmentof distances in Experi588 ments I, 2, and 6, involved comparisons of distances along the line of sight with the observer's eyes as a point of origin. In the judgments of slopes and drawn angles the relevant distances were between external points, may have varied from parallel to perpendicular to the line of sight (as for a hill viewed from the front versus from the side), and did hot necessarily involve head tilt. The results are tentatively placed together here because of the geometric consistency by analyzing slopes into their vertical and horizontal components and because the sex difference was consistent in all situations except Experiment 6 (afterimages on the sky), Given these considerations it is less easy to find an acceptable alternative classification for the tasks. For example, the overestimation of drawn angles could be easily subsumed under the classical vertical-horizontal illusion, but this would not explain the sex differential, the virtual absence of angle overestimation by males, and the dramatically greater amount of the illusion in the other experimental situations. The probable irrelevance of head tilt for the slope and angle judgments is also not a compelling reason to classify them separately, although head tilt may remain a unique, contributing factor. An alternative explanation of the illusion covering all of the cases might be based on a transactional or behavioral coding of the visual cues for distance and length.
For example, it is possible that When, in the past, visual cues have involved head tilt up or down or involved directly perceived slope, they have represented targets which required more effort to reach and were thus coded in motor-effort units as being farther away. The Moon Illusion The data clearly show that not Emmert's law but, if anything, its reverse holds for afterimages in the sky, Kaufman and Rock (1962) and Woodworth and SChlosberg (1954) have admitted, while subscribing to Emmert's law in the situation, that the moon itself is typically experienced as not only larger, but also as closer, in its horizon setting. This phenomenal finding is explained away as a secondary effect,
a result of the size illusion itself. To understand this apparently perverse loyalty to Emmert's law in the face of contradictory data, it may be noted that the moon's image and the afterimage are alike in two respects: they both have a constant retinal size, and they both lack the ordinary visual cues to distance (except for cues that should indicate that they are not nearby). It is only parsimonious that if Emmert's law describes size and distance judgments for afterimages it should also cover size and distance jUdgments for the moon, On the other hand the demonstration that the larger appearing horizon moon must also (unconsciously) appear to be farther away as Emmert's law demands has not been accomplished. What Kaufman and Rock Perception & Psychophysics, 1967, Vol. 2 (12) have shown, for example, is that a visual context of Iearthly terrain contributes to an apparently larger moon, but if and how this visual terrain produces a hypothetically increased apparent distance remains to be shown. The one point offered to support the flattened sky assumption is that observers typically aim too low when asked to point out an elevation of n degrees (from 0 to 90) above the horizon. Since this fact can be seen to be simply another case of perceptual overestimation of vertical distance and slope, it is obvious that several well chosen assumptions are necessary to convert it into support for an opposite conclusion (see Kaufman & Rock, 1962). There is an interesting alternative to Emmert's law in understanding the size-distance interaction in these cases which was first suggested to the E by the spontaneous statements of a few of the Ss participating in the experiment on afterimages(Experiment 6). These students commented to the effect that "Of course if it is closer it should be larger," with the words "closer" and "larger" sometimes interchanged. This kind of statement is indeed a description of general daily experience, but only if the observer shifts the locus of his size judgments from external objects to retinal images, for it is the retinal image which becomes larger when an object is moved closer. To make this kind of statement the observer must abandon the assumption or construction of size constancy and behave like an introspectionist, although his choice of words hides this fact. If an observer can report changes in his retinal image size then it is also conceivable that he would suffer from biasesin his[udgment of them, For example,
Perception & Psychophysics. 1%7, \'01 (1~) if he assumed that the moon and sky afterimages were like solid objects of constant physical size, then he would expect a decrease in perceived distance to be accompanied by an increase in (retinal) size. Thus his verbal statement of the relationship might correspond with the perceptual expectancy mechanisms at work. The advantage of considering this position isthat it is consistent with the data and does not postulate contrary unconscious processes, or involve the assumption that the sky is perceived as a surface, whose distance is somehow biased by the visual terrain. None of this rules out the possibility that both the size and distance illusions could be simultaneous byproducts of some third factor, such as vestibular stimulation. Until more data are collected, however, it is difficult to specify how such simultaneous biases might arise and operate. References Kaufman, L" & Rock, I. The moon illusion. Scient. American, 1962,207,120-130. King, W. L., & Gruber, H. E. Moon illusion and Emmert's Law. Science. 1962, 135, 1125-1126. Thor, D. H.; & Wood, R. J. A vestibular hypothesis for the moon illusion. Paper presented to the Annual Meeting of the Midwestern Psychological Association in Chicago. May 5, 196p. Woodworth, R. S., & Scholosberg ,H. Experimental psychology. Henry Holt, 1954. Notes 1. Now on a one year's leave of absence to Bell Telephone Laboratories, Inc., Holmdel, New Jersey. 2. Emmert's law states that the apparent size of an afterimage is directly proportional to its apparent distance from the observor. (Accepted for publication August 16,1967.)
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