You are right, Nigel, but as I said earlier, to convert the method into a mathematical proof needs a few more powerful tools that would obscure the heart of idea, which is easy to grasp for a non-mathematician. This is essentially the same problem that crops up again and again in science and mathematics (and, indeed history and many other subjects): to teach something you often have to simplify it so much that you know is not strictly true. Alternatively, you can stick to truth (or I should say our best current understanding), and present something that is so convoluted and complex it is, quite literally, incomprehensible.

You may remember that there was a TV show a looooong time ago called 'That was the week that was'. The intro varied each week, but on one occasion it contained the couplet "One eye open wide, one eye closed. And between the two the picture gets composed'. I've often thought that is one of the wisest remarks I've ever heard from a television program. And it applies here.