[kragen]

The article incorrectly describes the equations of kinematics of the double pendulum as describing its dynamics. They do not; describing its dynamics requires taking time into account and considering how its angles and positions change over time.

It also considers the existence of a general theory of nonlinear mathematics. There's a famous quote to the effect that this makes as much sense as the study of non-elephant mammals. And I think the argument that our everyday experience is linear is very weak; our bodies are made of non-Newtonian fluids, fluid friction is nonlinear, everyday physical phenomena like solid bodies coming into contact with one another are wildly nonlinear.

So in a sense I would criticize this article in the same way it criticizes Deutsch's book: it's flawed and weak, but still thought-provoking. Even if we can't predict the double pendulum's position several Lyapunov times in the future with any degree of certainty, are there things we can say about it that haven't yet been said? Is there a way we can look at things (or that some physical system could look at things) that would enable useful cognition?