In the perception of distance, depth, and visual motion, a single property is often represented by two or more stimuli. Two instances of such redundant stimulation are discussed. (a) the various stimuli that represent visual motion and (b) the two forms of stimulation by which binocular parallax evokes stereoscopic depth perception. In the case of visual motion, simultaneous operation of redundant stimulation has unexpected consequences and raises interesting problems. Experiments are briefly described that suggest that some redundant stimuli owe their existence to learning. Evidence is reviewed that shows that binocular parallax causes stereoscopic depth by means of two different perceptual processes. During the last 30 years evidence that space perception can be rapidly altered by perceptual learning has been accumulating. Adaptation to displaced visual direction involves, under certain conditions, a visual change, and there are other ways in which the relation between the position of the eyes and perceived visual direction can be altered. When subjects turn their heads from side to side while they observe a visual environment that moves left and right dependent on those head movements, an adaptation develops within minutes. It involves changes in the evaluation of eye movements that compensate for head movements and in the evaluation of eye positions as measured by pointing tests (Wallach & Bacon, 1977). In stereoscopic depth perception, the relation between retinal disparity and the extent of perceived depth can be rapidly changed. In such experiments, tridimensional shapes are viewed through a mirror arrangement that enhances the disparities with which their depth is given so that they are perceived with greater than normal depth. When these shapes are rotated, information about their true depth is provided, which disagrees with the enhanced stereoscopic depth that the mirror arrangement causes. Exposure to this conflict between two different kinds of stimulation that both represented the depth of the same object resulted in adaptation; stereoscopic depth perception was temporarily altered so that it partly compensated for the enhanced depth that the mirror arrangement provided (Wallach, Moore, & Davidson, 1963; see also Wallach & Barton, 1975). Convergence and accommodation function as cues for viewing distance for a great majority of observers. The relation between these oculomotor cues and perceived distance can be greatly changed in 20 minutes by having subjects wear spectacles that force the eye to view objects with oculomotor adjustments that normally represent, for instance, smaller distances. The presence of other distance cues that are not affected by the spectacles results in a rapid change in the perceived distances that result from the oculomotor cues. What happens in this case is easily explained. The distance cues that are not affected by the spectacles result in veridical perceived distances, and the altered oculomotor cues caused by the spectacles become contiguous with these correctly perceived distances and become connected with them. These new connections and the normal evaluations of oculomotor adjustments that the subject brings to the experiment add up to partial adaptation (Wallach, Frey, & Bode, 1972; see also Wallach & Halperin, 1977). Demonstrations of such rapid adaptations do not prove that the evaluation of eye position, of retinal disparity, or of oculomotor adjustments is originally learned, but they make it likely. Moreover, original learning may resemble what goes on in adaptation. Convergence and accommodation are being adjusted for distance whether they function as distance cues or not, because they are necessary for single vision and optimal acuity. Therefore, they are present when other distance cues result in perceived distance, and they may thus become connected to the perceived distances. Forming such connections may be favored when we move and when viewing distances change. Oculomotor adjustments and perceived distances will then vary together, and this covariance may provide the signal that brings such heterogeneous matters as oculomotor adjustment and distance perception in contact with each other. Redundant St imulat ion in Motion Percept ion Learned stimulation also seems to play a large role in motion perception, and it raises interesting probApril 1985 • American Psychologist Copyright 1985 by the American Psychological Association, Inc. 0003-066X/85/$00.75 Vol. 40, No. 4, 399-404 399 lems. It has been known for more than 50 years that three major conditions of stimulation mediate the motion of objects in the environment. Two of them represent the change in the visual direction of the moving object, a subject-relative change. A subject-relative change is either given by pursuit movements when the eyes track the object or by displacement of the object's image on the retina when the eyes are fixed on a stationary point. A third stimulus condition represents the changing configuration in the vicinity of the moving object, caused by its changing position relative to other field contents. This changing configuration is given as such, as a change in the pattern of images on the retina. This so-called object-relative stimulus condition is redundant; the information it carries does not add to the information that either one of the subject-relative stimuli provides. Because it is redundant, the function of configurational change as a stimulus in motion perception can be demonstrated only because it operates in a peculiar manner. Primarily it registers only the relative displacement between the moving object and its stationary surround, and it becomes veridical only through the operation of an additional rule that says that in such a relative displacement the surrounded object is seen to move. This rule transforms the relative displacement that is actually given into absolute motion and was first formulated by Duncker (1929). We know about configurational change only because the relativity of object-relative stimulation and Duncker 's rule can lead to a misperception that will occur when the surrounded object is actually at rest and the surround moves. The stationary surrounded object will then often be seen to move, although subject-relative conditions of stimulation represent it as stationary. This experience is called induced motion, and it is used when the effect of configurational change in motion perception is being investigated. Such investigations have shown that configurational change is a potent stimulus condition, about as potent as image displacement and much more effective than ocular pursuit (Wallach, O'Leary, & McMahon, 1982). The operation of redundant stimuli in motion perception raises interesting questions. When we see an object move in a well-lit scene, and its motion is This article was originally presented as a Distinguished Scientific Contributions Award address at the meeting of the American Psychological Association, Toronto, Canada, August 1984. Award addresses, submitted by award recipients, are published as received except for minor editorial changes designed to maintain American Psychologist format. This reflects a policy of recognizing distinguished award recipients by eliminating the usual editorial review process to provide a forum consistent with that employed in delivering the award address. Requests for reprints should be sent to Hans Wallach, Department of Psychology, Swarthmore College, Swarthmore, Pennsylvania 19081. given simultaneously by configurational change and perhaps by ocular pursuit, what is t h e object's experienced motion based on? It could be based either on ocular pursuit or on the configurational change, or it might be based on both. In the latter case, the different processes that result from the different stimuli would have to combine at some level of perceptual processing, although they start out quite differently, one with an evaluation of an eye movement and the other as a matter of form perception. We know several instances in which the different processes clearly combine. In one such instance, a pattern of long vertical lines moved horizontally in reciprocating motion and caused horizontal induced motion in a dot located near its center. The dot moved up and down, reversing its motion at the same moments when the line pattern reversed its motion. Because the lines presented no landmarks for the vertical motion of the dot, the dot's real motion was given only subject relatively. But it also moved horizontally, an induced motion, that resulted from the configurational change in the dot-line arrangement. But neither one of the two motions was perceived as such. The two motion processes, one due to subject-relative stimulation and the other due to configurational change combined into a single unified motion. The dot was always seen to move on an oblique path. In an experiment where the extent of the vertical motion of the dot and of the horizontal motion of the lines were equal, this oblique path formed a mean angle of 45 ° with the vertical, when the vertical motion of the dot was given by ocular pursuit. The mean motion path was steeper, 23 °, when the dot motion was given as image displacement. Apparently, when it was in conflict with the vertical dot motion that was given aS image displacement, induction was not fully effective (Wallach et al., 1982). A straight motion path that is the resultant of two simultaneous motions in different directions is the simplest instance o f a Lissajous figure. (Lissajous figures are the resultants of two simultaneous simple harmonic motions.) But in the Wallach et al. (1982) experiment, the path was not an ordinary Lissajous figure, and was not a physical resultant. It was the combination of two nervous processes; it might be called a psychological Lissajous figure. We found that we could produce more complex psychological Lissajous figures by changing the phase relation be
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