Francis E. Low, writing in his 1967 book Symmetries and Elementary Particles, says:
A symmetry principle can usually be formulated as a statement about the impossibility of knowing something. Thus translation invariance states that all points in space-time are equivalent—there is no way of knowing where you are. Any inhomogeneity observed so far has always been accounted for by identifying a field which produces it. Thus translational invariance applies to an isolated system.
Vincent Icke, a Dutchman, says in his 1995 book The Force of Symmetry:
If you wanted to organize a universe, you could compile a whole book full of rules, a long list of entries that say ‘Thou shalt not this,’ ‘Thou shalt not that.’ But if your universe consisted of a possibly infinite multitude of inhabitants, which could do an infinite multitude of things at an infinite number of points in time and space, then such a rule book would surely be multiply infinite. . . .
Alternatively, you could lump together a large (possibly infinite) number of rules in a single all-encompassing one. Thus, you might write in the Constitution of your universe, ‘Do unto others as thou wouldst others do unto thee’, or even more briefly, ‘Love thy neighbour as thyself’. Such an overall rule, that summarizes a multitude of individual possibilities, is called a symmetry. The symmetry just mentioned is between you and your neighbor. You are surely familiar with social symmetries: you and your neighbour have the same rights, even though you are certainly not the same, and may differ as to age, race, sex, creed, ethnic origin, and what not. It turns out that the symmetries that govern the quantum world are of a very special type, called a symmetry group by mathematicians. . . .
