Perfect Symmetries

While empirical symmetries relate situations, theoretical symmetries relate models of a theory we use to represent them. An empirical symmetry is perfect if and only if any two situations it relates share all intrinsic properties. Sometimes one can use a theory to explain an empirical symmetry by showing how it follows from a corresponding theoretical symmetry. The theory then reveals a perfect symmetry. I saywhat this involves and why it matters, beginning with a puzzle that is resolved by the subsequent analysis. I conclude by pointing to applications and implications of the ideas developed earlier in the paper.