> >I can only suggest that they failed to propose "what else it
> >could have been, if not mathematics".
> >
>
> Well, the short answer would be non-mathematical :). Surely
> a mathematical universe would have to be a special case.
>
> What comes to mind first is the plasticity of metals.
Hmm, that is a good example. Not just plasticity, but all solid state
physics: phonons, exitons, spinons, etc. and propogation of fractures,
catastrophic failures, diffusion-limited aggregation, percolation,
critical points, etc.
I agree ... one gets the feeling that there will soon be as many
formulas as there are atoms in the material itself.
A tradionalist would argue that this merely shows how rich the
behaviours are for a collection of atoms. Someone whose head
hurts might argue that this is math approaching disaster.
However, I don't see a way out: nature will not suddenly become
simple. Nore do I see any way of making a prediction without math.
For plasticity of metals, you are still asked to make a prediction.
How can you possibly make a prediction that's not anchored in math?
Literlly, there appears to be no alternative, even if one is forced
to discard a seemingly infinte number of theories, or to use
formlas so incredibly complex that no one human can understand all of
the terms, and only computers can generate some-what suspect
simulations. What else can one do? Arguably, you are right:
math broke down. But what to replace it with?
--linas