A general framework for the explanation of perceptual phenomena as internalizations of external regularities was developed by R. N. Shepard. A particular example of this framework is his account of perceived curvilinear apparent motions. This paper contains a brief summary of the relevant psychophysical data, some basic kinematical considerations and examples, and several criticisms of Shepard's account. The criticisms concern the feasibility of internalization of critical motion types, the roles of simplicity and uniqueness, the contrast between classical physics and kinematic geometry, the import of perceived path curvilinearity, and the relation of perceptual and scientific knowledge.