The Semantics of Symmetry, Invariance, and Structure

Abstract

Symmetry carries the connotation of beauty. Mathematized, it is a deep and reoccurring theme in the Book of Nature. Many unexpected properties of reality are uncovered by it. A key concept related to symmetry is invariance, the simple property of a system to remaining unchanged under manipulations. Invariance has the power to unlock fundamental knowledge. Level of mathematical formality: high (however, the mathematically involved parts are encapsulated and demarcated by the tags, hence easily bypassed).