This is absolutely fascinating, but I'm having trouble really grokking the principle behind this. I understand fixed points of mathematical functions with numbers, but my mind seems to explode in the transition to functions of functions. Is there a really clear explanation anywhere of the idea behind all this? Or is it the kind of thing where this is simple as it gets, and I just need to put in more work to get it?
The best I've managed is this: http://qntm.org/fib
I find that removing all mention of Y combinators made the whole thing a lot easier to read.