A theory of phenomenal geometry and its applications.

The geometry of perceived space (phenomenal geometry) is specified in terms of three basic factors: the perception of direction, the perception of distance or depth, and the perception of the observer's own position or motion. The apparent spatial locations of stimulus points resulting from these three factors thereupon determine the derived perceptions of size, orientation, shape, and motion. Phenomenal geometry is expected to apply to both veridical and illusory perceptions. It is applied here to explain a number of representative illusions, including the illusory rotation of an inverted mask (Gregory, 1970), a trapezoidal window (Ames, 1952), and any single or multiple point stimuli in which errors in one or more of the three basic factors are present. It is concluded from phenomenal geometry that the size-distance and motion-distance invariance hypotheses are special cases of the head motion paradigm, and that proposed explanations in terms of compensation, expectation, or logical processes often are unnecessary for predicting responses to single or multiple stimuli involving head or stimulus motion. Two hypotheses are identified in applying phenomenal geometry. It is assumed that the perceptual localization of stimulus points determines the same derived perceptions, regardless of the source of perceptual information supporting the localizations. This assumption of cue equivalence or cue substitution provides considerable parsimony to the geometry. Also, it is assumed that the perceptions specified by the geometry are internally consistent. Departures from this internal consistency, such as those which occur in the size-distance paradox, are considered to often reflect the intrusion of nonperceptual (cognitive) processes into the responses. Some theoretical implications of this analysis of phenomenal geometry are discussed.