Theme and Variations
The great mathematician Hermann Weyl wrote a book, Symmetry, to make the point that visual symmetry is a special case of the concept known as invariance.(An invariant is something that does not change under a set of transformations. Invariance is the property of being an invariant. Some felt that Einstein's relativity theory should be called Invariantentheorie, "theory of invariants.")
However you rearrange the quadrants of the diamond figure, the result has some ordinary or color-interchange symmetry:
So the diamond figure illustrates how symmetry itself can be invariant under a set of tranformations.This would be of little interest unless this invariance of symmetry can be generalized. Fortunately, it can.
-- Steven H. Cullinane
Page created April 28, 2004
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