Waterhouse is thinking about cycles within cycles. He’s already made up his mind that human society is one of these cycles-within-cycles things and now he’s trying to figure out whether it is like Turing’s bicycle (works fine for a while, then suddenly the chain falls off, hence the occasional world war) or like an Enigma machine (grinds away incomprehensibly for a long time, then suddenly the wheels line up like a slot machine and everything is made plain in some sort of global epiphany or, if you prefer, apocalypse) or just like a rotary airplane engine (runs and runs and runs; nothing special happens; it just makes a lot of noise).