[nobodyandproud]

The point of the article was that we don’t have a way of predicting the position at a point in time, without calculating all of the interim steps.

An analogy would be the ancient mathematicians aversion to infinites (Calculus); also, being unable to imagine non-Euclidean planes.

There may be better tools out there that we haven’t considered, because it’s so far removed from our intuition.

Edit: Was it a Vernor Vinge book, where humans had a small (but great) advantage over more established, space-faring aliens because of their ability to handle infinites (calulus)? Whereas all aliens relied on numerical/computional approximations.

[i_cannot_hack]

> The point of the article was that we don’t have a way of predicting the position at a point in time, without calculating all of the interim steps.

Sure. But that is true for most linear systems of PDEs as well. It has very little to do with nonlinearity. And my point is that it does not contradict universality as defined in the article, as was claimed by the author.

[nobodyandproud]

Aren’t chaotic systems non-linear?

It’s the non-linear PDEs that get interesting, and one is reduced to iterative approximation or computational methods, way back when I went to school for this stuff.

[i_cannot_hack]

You are more often than not reduced to iterative numerical approximations for very simple linear PDEs as well.

Consider a simple linear PDE such as the heat equation du/dt = Δu + f(t). On a square or a circle you can solve this analytically in the frequency domain using separation of variables. But as soon as you consider an arbitrary domain (say, shaped like an elephant) you can no longer solve it in the frequency domain and need to use iterative numerical approximations.