April 9, 2005
What is the relation of your Principle of Computational Equivalence with chaos and complexity theory?
Chaos theory is really about a very specific phenomenon: that sensitive dependence on initial conditions can lead to randomness. And what one finds in the end is that the only way to get randomness out of this phenomenon is just to put randomness in, in the initial conditions. What I’ve found is that simple programs can actually produce randomness—and complexity—without it ever being put in. It’s a much more powerful phenomenon.
Complexity theory has a very confused history, some of which starts with my early work on cellular automata. But to my regret, it’s mostly concentrated on trying to use rather traditional scientific methods to find simple features of complex phenomena—not on understanding the core phenomena and origins of complexity itself, which is what NKS now lets us address.