Beauty

I was plodding through some notes on relativity and electrodynamics and flipping through Jackson's tome on the subject when I had a flashback of Riemannian geometry and everything began to make sense.  If I have interpreted everything correctly (i.e. I could be dead wrong), these silly Lorentz transformations are just a Lie group (some subgroup of SO(4), I think).  Because they act on vectors in Minkowski space--a manifold!--the group of Lorentz transformations are, in fact, a Lie group action on Minkowski space, under which the Minkowski metric is (bi-?)invariant.  Hence the entire edifice of special relativity is reduced to one particular Lie group action on a rather boring Riemannian 4-manifold.  While I know absolutely no general relativity, this conception of the special case meshes well with the fact that (as I have heard) general relativity can be realized entirely in terms of Riemannian geometry.