I love these various theoretical explanations, but what would really land the plane is some suitably small unit test date doing the forward and reverse transforms.<p>This is the general grief with math: in enshrining the ideas in a single letter based formula, the mathematician has produced a kind of sculpture that makes sense to the initiate, but baffles the lay reader.<p>This is not a complaint; such sculpture filters out the riff-raff. One has to want it. And maybe filling in that unit test data is just part of the journey to understanding.