16. The Role of Symmetry in Event Perception

Ernst Cassirer (1944), in his article discussing the role of group theory in perception, asserts that the primitive form of understanding is that of the intuitive concept of a group. The usefulness of the group concept in contemporary mathematics and theoretical physics offers strong support to the validity of this insight. One of the chief functions of group theory in mathematics and physics has been to describe what properties of objects, events, or even natural laws remain invariant, or symmetrical, across different domains, or under modification by transformations. In geometry, Felix Klein, in pursuing his Eriangen program, succeeded in showing that different geometries can be represented by specific groups of tra~sformations which leave only certain geometric properties of objects invariant when applied. Consequently, Herman Weyl provided a very simple definition of the term "invariant, " indicating that it is merely a synonym of the term "symmetrical, " namely, that a thing is symmetrical i f there is something we can do to it so that after we have done it, it appears the same as it did b e f ~ r e. ~ The precise statement of what the thing is, an