The Concept of Symmetry

Abstract

Symmetry is immunity to a possible change, i.e., we have symmetry when it is possible to perform some change in the situation that nevertheless leaves some aspect of the situation unaffected. Then we have symmetry under the change with respect to that aspect. If some aspect of the situation is not immune to the change, then the situation is asymmetric under the change with respect to this aspect. Since a change requires the existence of a reference frame that is affected by the change, such a reference frame is necessarily asymmetric under the change. Thus, for every symmetry there exists an asymmetry. Further, it is shown that analogy is symmetry and that analogy implies and is implied by classification, which is also symmetry.