Symmetry, invariance, harmony

Abstract

“How nice and symmetrical,” we often say or think to ourselves. The associations that the word awakens in us depend on the experiences in our past that have established its meaning for us. The term ‘symmetry’ can have three separate types of meaning, as a phenomenon, a concept, or an operation. The phenomenonis what we consider to be symmetrical on the basis of our experience or of knowledge we have learned. The concept is what circumscribes all such phenomena. The operation is what gives rise to the phenomenon or makes it possible.