No abstract

The results of two experiments suggest that strong constraints on the ability to imagine rotations extend to the perception of rotations. Participants viewed stereographic perspective views of rotating squares, regular polyhedra, and a variety of polyhedral generalized cones, and attempted to indicate the orientation of the axis and planes of rotation in terms of one of the 13 canonical directions in 3D space. When the axis and planes of a rotation were aligned with principal directions of the environment, participants could indicate the orientation of the motion well. When a rotation was oblique to the environment, the orientation of the object to the motion made a very large difference to performance. Participants were fast and accurate when the object was a generalized cone about the axis of rotation or was elongated along the axis. Variation of the amount of rotation and reflection symmetry of the object about the axis of rotation was not powerful.The study of motion and spatial transformation has long been central in mathematics and the physical sciences, and recently it has become the focus of much work in the study of perception and spatial cognition. Rotation, for example, is a fundamental form of motion (e.g., Gibson, 1957;Shepard, 1984), and the study of mental imagery has benefited greatly from the investigation of mental imagery of rotation (see Shepard & Cooper, 1982). Across the study of spatial cognition, it has become clear that some forms of spatiotemporal structure are cognitively simple for the typical person, whereas other forms are quite complex and difficult. This distinction is familiar from work on the spatial organization of elementary forms (e.g., Garner, 1974;Palmer, 1977;Wertheimer, 1950), but it applies also to a great variety of familiar or three-dimensional (3D) structures and events (e.g., Hinton, 1979;McCloskey, 1983;Pani, 1993;Pani, Zhou, & Friend, 1995;Proffitt, Kaiser, & Whelan, 1990;Tversky, 1981).Consider simple rotational motion, the topic of this article. In simple rotation, all of the points on a rotating object move, with common angular velocity, in circles about an axis fixed in space. The planes of these circles are parallel to each other and normal to the axis (e.g., Todd, 1982). In contrast, if the axis and planes of rotation change orientation during the motion, the rotation is no longer physically simple. Fundamental parameters of simple rotation include the orientation of the axis and planes of rotation to the environment and the orientation of the rotating object to the axis and planes of rotation (see Pani, 1989,

No abstract

Physical reasoning is strongly influenced by various parameters of orientation. The authors report 3 experiments in which this phenomenon was explored for a particularly elementary transformation: the formation of a line from the intersection of 2 planes. Participants perceived pairs of planar surfaces (disks) in a variety of orientations in 3-D space and indicated the orientations of the edges that would result if the surfaces interpenetrated. The ranges of error and response time were large. Performance depended on whether the orientation of the edge that would be formed was the same as components of the orientations of the perceived surfaces, the degree to which the orientation of the edge would be canonical in the environment, and whether the angle between the surfaces would be perpendicular. The results are discussed in the context of a general approach to orientation in perception and physical reasoning.

No abstract