How the christ does the Y Combinator work?

Fuck, I've been rereading http://mvanier.livejournal.com/2897.html for the past several hours and it might as well be written in Esperanto. Am I just not cut out for EXPERT PROGRAMMING‽

>>21
The difference is that your recursive case uses f(f, arg-1) where the recursive case with a real Y combinator would be f(arg-1), abstracting out finding the fixed point from computing the factorial. Having Y proves constructively that every function has at least one fixed point (in the context of untyped lambda calculus).