The notion of geometrical symmetry in Art and in Nature is a familiar one. In Modern Physics, this notion has evolved to include symmetries of an abstract kind. These new symmetries play an essential part in the theories of the micro structure of matter. The basic symmetries found in Nature seem to originate in the mathematical structure of the laws themselves — laws that govern the motions of the galaxies on the one hand and the motions of quarks in nucleons on the other.
In the Newtonian era, the laws of Nature were deduced from a small number of imperfect observations by a small number of renowned scientists and mathematicians. It was not until the Einsteinian era, however, that the significance of the symmetries associated with the laws was fully appreciated. The discovery of space-time symmetries has led to the widely-held belief that the laws of Nature can be derived from symmetry, or invariance, principles. Our incomplete knowledge of the fundamental interactions means that we are not yet in a position to confirm this belief. We therefore use arguments based on empirically established laws and restricted symmetry principles to guide us in our search for the fundamental symmetries. Frequently, it is important to understand why the symmetry of a system is observed to be broken.
