On the affine structure of perceptual space

Affine geometry is a generalization of Euclidean geometry in which distance can be scaled along parallel directions, though relative distances in diff erent directions may be incommensurable. This article presents a new proced ure for testing the intrinsic affine structure of a psychological space by having subjects perform bisection judgements over multiple directions. If t hose judgements are internally consistent with one another, they must satis fy a theorem first proved by Pierre Varignon around 300 years ago. In the e xperiment reported here, this procedure was employed to measure the perceiv ed structure of a visual ground surface. The results revealed that observer s' judgements were systematically distorted relative to the physical enviro nment, bu that the judged bisections in different directions had an interna lly consistent affine structure. Implications of these findings for other p ossible response tasks are considered.