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Object Identity, Apparent Motion, Transformation Geometry

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Object Identity, Apparent Motion, Transformation Geometry Current Research in Psychology 1 (1): 35-52, 2010 ISSN 1949-0178 © 2010 Science Publications Object Identity, Apparent Motion, Transformation Geometry Felice L. Bedford and Birgitta E. Mansson Department of Psychology, University of Arizona, Tucson AZ 85721 Abstract: Problem statement: A classic question in cognition was addressed on how two glimpses separated in time are determined to refer either to the same object or to two different objects, without which coherent perception of the world is not possible. Approach: A general solution was offered in which observers exploit an entire family of geometries. It was argued that a geometry hierarchy is an attractive candidate for a solution because it is can be used on glimpses not only from different times, but from different spatial locations, different eyes, and different modalities. The theory was applied to the phenomenon of apparent motion, a time-honored paradigm for uncovering rules of object or numerical identity. Results: It was found that there was a preference to map a figure onto the “same form” (isometric transformation) when available (Exp. 1), despite controversy about form and apparent motion in the literature. When the same form was not available, next preferred was a similarity transformation (“different size”; Exps. 2 and 3) when the perceptual system was given a choice. Finally, it was found that a figure even matched to an extreme topological transformation (“plastic deformation”; Exp. 4) when that was the lowest-level geometric choice available. Conclusions/Recommendations: The experiments supported a hierarchical structure of unconscious perceptual preferences in object identity which importantly explains how the exact same pair of stimuli can sometimes be judged to refer to the same object, but sometimes not. It was also suggested that the inherent flexibility of this solution resolves contradictions in the literature concerning the relevance of form in apparent motion and that the hierarchy satisfyingly captures intuitions about what is "similar" in perception while pointing to dangers of relying exclusively on such intuition. Key words: Cognition, perception, mathematics, numerical identity, similarity, topology INTRODUCTION One approach for uncovering the fundamental rules of object identity is based on development. If relevant Object identity, apparent motion, transformation knowledge is available early, then in some sense it is a geometry: A squirrel runs behind a tree and moments primary solution to identity. Elizabeth Spelke and later a squirrel emerges. Is it the exact same squirrel or colleagues (Spelke et al ., 1995; Spelke and van de merely a cousin? Achieving numerical or object Walle, 1993) have argued that even very young infants identity-knowing whether or not the two glimpses do or know that objects travel on paths that are continuous in do not refer to the same object-is a challenge for space and in time such that violations are informative of observers at all processing levels. Frequent movement numerosity. For instance, if a green ball goes behind a of observers virtually guarantees that a single object screen and a green ball comes out another screen that is will lead to different retinal projections from one instant separated from the first, then 3 month old infants will in time to the next. For instance, the same parked car behave as if there are two green balls. They have viewed head on casts a different image than the car suggested this is because of early knowledge that one viewed from an angle. Likewise, changes to the objects object cannot not magically jump the gap between the themselves produce glimpses that are not identical. The screens. Older infants know that a member of one car can be driven from one location to the next; the category of object (e.g., elephant) cannot turn into squirrel can be crouching before darting behind the tree, another (e.g., truck) even there is only single screen yet emerge on its hind legs. Human observers are without a spatial gap, behind which one enters and the remarkably good at knowing when we have encountered other emerges (Xu and Carey, 1996; Wiggins, 1980). the exact same object even though we rarely have the Knowledge about properties specific to some categories benefit of the exact same stimulus, either rationally, of objects but not others allow more refined judgments perceptually or cognitively. The issue of object identity is (Narter, 1998). If you return home after a month, a a classic one in perception and philosophy. bigger squirrel in your yard could be the same squirrel, Corresponding Author: Felice L. Bedford, Department of Psychology, University of Arizona, Tucson AZ 85721 35 Current Research in Psychology 1 (1): 35-52, 2010 but a bigger car in your garage could not be. Even more The core of object identity will consist of criteria detailed knowledge can be useful in special situations. that are applicable to all domains with the same formal Teresa Wilcox (1999) has argued that instructions about structure. The purpose of the present article is to test the an “electric warmer” hidden behind a screen that turns applicability of a potentially general set of core criteria green objects into red ones changes will change identity for object identity to the phenomenon of apparent outcomes for young observers. Children will now motion. First the role of identity in apparent motion will believe that a green ball that disappeared behind that be noted, then the proposed criteria will be introduced, screen is the same ball as a red one that emerged from followed by the predictions of the criteria in the apparent the other side, but would not without those instructions. motion paradigm and finally by the experiments. Developmentally relevant solutions to object Apparent motion: Apparent motion is a classic identity emerged in consideration of a single problem: (Wertheimer, 1961; Korte, 1915) readily manipulable identity across gaps in time, often spatio-temporal gaps. laboratory phenomenon that is well-accepted to depend However, consideration that the problem of object upon an object identity judgment (e.g., Rock, 1983; identity is much broader than this prototypic situation Shepard, 1984; Kahneman et al ., 1992; Ullman, 1979; points to a different kind of fundamental solution for Warren, 1977; Xu and Carey, 1996). As such, it is an object identity. Bedford (2001; 1999; 2007) argues that ideal candidate for testing the criteria of object identity. the same object identity problem must be solved not In apparent motion, a stimulus is shown in one location only for samples that come from different times, but for a brief period of time and is replaced by a second also when the samples do not come from different times stimulus in a different location a short time later. The at all. That is, samples can also come from different sequence is usually repeated a number of times and modalities, eyes, or spatial locations. How do you know observers see a stimulus moving back and forth between that the pen you are seeing and the pen you feeling are the two locations. Rock (1983) and Shepard (1984) argue the exact same pen? Or that the pen you are feeling and that although intermediate positions are not detected on the cup of coffee you are eyeing are different objects? the retina, an interpretation of a single object moving Asked generally, the question is how does the observer back and forth between the two locations is preferable to determine when any two non-identical samples, s1 and accepting the coincidence that two identical or similar 2, arise from the same object? Bedford argues object looking objects are appearing and disappearing in identity may play a role in nearly all perceptual alternation. The phenomenon hinges on misidentifying accomplishments, including tracking objects over time, the two stimuli as two different glimpses of the same cross-modal perception, stereopsis and perceptual object at two different times. If the two samples are organization across space, as well as in laboratory judged to refer to one object, one object in motion is phenomena of apparent motion, prism adaptation, experienced. If the two samples are judged to refer to two ventriloquism, priming and Gestalt grouping, since objects, then two objects flashing on and off are correctly much of perceiving the world involves taking in seen and there is no impression of motion. information from non-identical samples. A compelling demonstration that destroying the The same formal problem in different domains one-object assumption destroys apparent motion comes invites the possibility of a common solution (Dennett, from Sigman and Rock (1974); Rock, (1983). At one 1996). Task-specific knowledge of electric warmers, or time, there is a small black dot in position A and a big even that animals and plants can grow, can be used for screen covering position B and a short time later, the identity but they are not applicable to all domains and screen covers position A and there is a small black dot thus cannot constitute the core solution to object in position B. Observers do not see the small black dot identity. Categorization of objects into their kinds moving from A to B, as they would without the screen. (elephants/trucks) also cannot be relied upon Rather, the display looks as if there is a screen moving exclusively because object identity is achieved even back and forth to successively occlude and reveal two when we cannot recognize the objects involved (Bloom, dots, one on each side. The addition of the screen 2000). Spatial-temporal continuity is general, but often invites a different explanation of the mysterious sensory that is the problem, not the solution: Did discrete appearance and disappearance of two dot stimuli: samples s1 and 2 result from a singe object Rather than one object moving back and forth, a screen continuously transforming from one state to the other is moving back and forth in front of two objects.
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