Abstract We suppose that the visual nervous system possesses compensatory rectifying mechanisms by means of which it achieves “constancy” of visual recognition despite variation in physical appearance of the stimulus object. Using geometric rotations, reflections, and other transformations of text as the physical variation, we studied the recognizability of the texts and the influence that practice in reading one type of transformation exerted on the recognition of others. The mathematical structure of the training set was used as a clue to the perceptual mechanisms mediating transfer, isolating perceptual functions involving a geometric transformation and an ordinal operator. The main feature of the theory is its emphasis upon a dialogue or interaction between ongoing problem-solving processes in visual rectification and the sample being recognized. The theory developed is contrasted with other theories of pattern recognition in which concepts such as stimulus generalization, tuned detectors, and preprocessing play major roles. A relation of this theory to problems encountered among disabled readers (“dyslexics”) is also brought out.