Sets of Transformations as Criteria of Diversity within Sets of Objects

A set of transformations acting within a domain may serve as a standard in judging the diversity within any subset of that domain. We distinguish two possible outcomes of such a comparison (upper vs. lower bound to diversity), highlight some basic properties of both concepts, and illustrate them with examples. In the concluding section we indicate reasons of importance of such a “transformational approach to diversity”, by referring to the process of “transformation induction” and to problems in vision psychophysics.