Visual perception as invariance.

The railroad tracks stretch straight and far away from me over the desert and on to the horizon. I stand squarely between them, looking along them to the horizon, and I observe both that they converge as distance gets greater and also that they are at every distance equidistant. This is the perceptual paradox of converging parallels. Every one has the experience, and Blumenfeld (1, pp. 323-346) found it under the controlled conditions of his alley'experiment. The convergence, when you have regard to it, is irresistible, and it is much less than the convergence of the retinal image that underlies the perception. That image might converge as much as the legs of an isosceles triangle that is almost equilateral. The base of the triangle, the tracks at your right and left, would be at the top of your inverted retinal image, and the lines of the image for the tracts would come together quickly, meeting at the fovea, on which would be the image of the vanishing point at the horizon. It is thus plain that the perceptual pattern is not the pattern of the retinal image nor any form topographically equivalent to it.