Mental Rotation, Pictured Rotation, and Tandem Rotation in Depth

摘要

The mental rotation effect in depth is qualitatively different from mental rotation in the picture plane. The magnitude of angular difference in depth that is depicted between two static shapes has been thought to predict mean response time for same-different comparisons on shapes in the mental rotation effect. The tandem rotation effect provides a counterexample to that hypothesis. Two planar shapes are depicted as separated by a small and fixed angular difference in depth; the pair of shapes is then depicted as tilted in depth. Mean response time to compare these shapes varies nearly linearly with the magnitude of the yoked rotation - though angular difference is held constant. The slope of this response time function is very close to that for single rotation in depth. The tandem effect supports a claim that mean response time varies as a function of the change in area of planar shapes that are depicted to rotate away from the picture plane, rather than as a function of the angular difference of one shape from another. The tandem rotation effect is not found to obtain for rotations in the picture plane. A conclusion drawn from these and other results is that an hypothesis of mental rotation is neither necessary nor sufficient to explain changes in response times for the simultaneous comparison of planar shapes pictured in depth. A piecewise continuous trigonometric function is proposed to describe response times for the comparison of planar shapes that are depicted to rotate in depth. The characteristic Shepard-Metzler response time function for complex solids in depth is shown to be a definite integral of that trigonometric function.