Developmental Psychology1988, Vol. 24, No. 4, 512-521Copyright 1988 by the American Psychological Association, Inc.0012-1649/88/$0O.75Geometric Complexity and Object Search in InfancyBarbara LandauColumbia UniversityElizabeth SpelkeCornell UniversityIn four experiments we investigated the role of geometric path type in infants' ability to make spatialinferences about the location of a hidden object after they themselves had been moved through space.Nine-month-old infants were moved along geometrically simple paths of rotation (Experiments 1and 2) or translation (Experiment 3) or along geometrically complex paths of combined rotation andtranslation (Experiment 4). In all but the fourth experiment, infants were able to retrieve an objecthidden before they were moved, as long as the object was not located behind them at test time. Directcomparisons among the conditions showed that moving infants along geometrically simple paths ledto significantly better performance than moving them along geometrically complex paths. We foundthe length of a path, the time needed to traverse it, and the likelihood of fixation of die target to beunrelated to the infants' performance. These findings are discussed in the context of theories of thedevelopment of spatial knowledge.After moving through space adults can usually relocate stableobjects and positions even if the objects are not visible and theirpositions are not marked by distinctive landmarks. We can de-termine the location of an object by using knowledge of its origi-nal position and of our path of movement. Given the distanceand direction of the object relative to our starting point and ofour starting point relative to our final position, we can infer theobject's distance and direction from our final position. Suchinferences about location follow logically from geometric prin-ciples relating spatial positions; they are similar to logical de-ductions, although they are neither conscious nor effortful. Theability to make such inferences is fundamental to human spatialactivities, allowing humans both to relocate invisible objectsand to plot new paths toward invisible goals. This ability is alsoof theoretical interest, because inferences require premises, thatis a body of principles concerning geometric objects and geo-metric relationships that has been termed "spatial knowledge"(Landau, Spelke, & Gleitman, 1984).In this article, we focus on the developmental origins of spa-tial knowledge in infancy. Although spatial inferences of thesort discussed above come quite naturally to adults and evento 2-year-old children (Landau et al., 1984; Rieser & Heiman,1982), studies of infants have revealed some significant diffi-culties in relocating objects after self-movement (Acredolo,1978). In the absence of rich external landmarks, for example,6- and 11-month-old infants have been found to search for ahidden object at egocentrically defined locations, ignoring theeffects of their own displacements. Such results have been takenThis work was supported in part by a Social and Behavioral SciencesResearch Award from the National Foundation, March of Dimes to LilaGleitman and Barbara Landau.A portion of this work was presented at the 4th Biennial Conferenceon Infant Studies, New \brk, April 1984. We thank Marcia Glicksman,Lenora Knapp, and Crystal Norris for assistance in data collection.Correspondence concerning this article should be addressed to Bar-bara Landau, Department of Psychology, 315 Schermcrhorn Hall, Co-lumbia University, New \ork, New \brk, 10027.to imply that infants are incapable of performing the sort ofspatial inferences that are the foundations of spatial knowledge(Acredolo, 1978). It is possible, however, that infants make in-ferences about object location under certain circumstances butfail to do so if the geometric problem that they must solve be-comes sufficiently complex. One intriguing possibility is thatinfants, like adults, are affected by the geometric nature of thepath that they travel or the consequent complexity of the changein their own position. We focus on this possibility here.Path types can be divided into three categories in accordancewith their geometric properties: rotations, translations, and ro-tation-translation combinations (Gans, 1969). In rotations, theorientation of the subject changes relative to every stable object,but the subject's distance relative to the objects is constant. Intranslations, the subject maintains a constant orientation butmoves a certain distance to a new location. In rotation-transla-tion combinations, the subject both changes orientation andmoves to a new location. Rotations and translations are geomet-rically simple in that each of them involves a change in a singleparameter, orientation or location, whereas rotation-transla-tion combinations bring changes in both parameters. If geomet-ric complexity affects infants' performance, then movements ofthe observer along complex paths might produce more errors inan object-relocation task than movements along simple paths.Informal observation suggests that adults may be affected bygeometric complexity. Certain paths that combine rotation andtranslation—for example, a zigzag path or a series of curves—seem to result in total disorientation of the observer. For exam-ple, camera movements along such paths disorient viewers ofmotion picture films (Hochberg, personal communication,1986). If variations in path type affect adults' ability to relocatea stable object, infants might be affected as well.Existing studies are consistent with the hypothesis that geo-metric complexity affects infants1 ability to relocate objects af-ter self-movement. Acredolo (1978) trained 6- and 11-month-old infants to look toward their right or left in anticipation ofan event at a constant position. The infants then underwent acombined rotation-translation in which they were moved512GEOMETRIC COMPLEXITY AND OBJECT SEARCH513around a circular table to a new location and orientation severalfeet away and at a 180° rotation from their original position.The infants appeared not to update their position, continuingto search for the event in the egocenirically defined direction oftraining. In contrast, infants have been found to relocate objectssuccessfully after a self-movement of pure rotation. McKenzie,Day. and Ihsen (1984) reported that 8-month-old infants lookedtoward the correct place of an expected event over rotations ofup to 90° around the body axis after they had