Traditional equations involve just the rather specific kinds of rules that are built into ordinary human mathematics. But programs can involve much more general kinds of rules. It is those more general rules that nature seems to be using a lot of the time.

The crucial discovery from the 1930s is that it’s possible to make universal systems that can compute anything, if they’re given appropriate input. And it was that discovery that launched the computer revolution. But we normally assume that universal systems have to be pretty complicated—like the CPUs in our practical computers. What I’ve now discovered is that even very simple systems are very often universal. This means that lots of systems in nature are likely to be universal too.