In mathematics “curvature” is described in various ways, but perhaps the most common is as a rate of spatial attitude. Such a definition is similar to the deviation from flatness, where flatness might again be understood (in various ways) in terms of congruence. In classical physics the notion of curvature occurs in kinematics and in the theory of elastic continuous media. The latter aspect is perhaps closest to what might be the notion of “curvature as a gut feeling.” It is least likely that hands-on experience with elastic materials in visuomotor interaction was at the root of the curvature as a proto-concept. One guesses it developed roughly in parallel with the development of spoken language, although “curvature” no doubt was present as a quality of experience with the Neanderthal, say. I consider relations between the very diverse notions of “curvature.” Curvature as a gut feeling survives even today in artistic intuition, it applies to most of us who appreciate sculpture.