[FOM] Godel's First Incompleteness Theorem as it possibly relatesto Physics

[Andrej Bauer]

hendrik at topoi.pooq.com wrote:
> Only intractable in the sense that there isn't a neat formula 
> that solves it -- there's just a differential equation.  Nothing 
> prevents the numerical analyst from computing arbitrarily close 
> approximations except time and effort.  Isn't that more or less the 
> definition of computable reals?

It's not quite that simple, so I would like to see a reference for the
above claim (namely that the n-body problem has computable, albeit
chaotic solutions).

For example Pour-El and Richards have an example of a wave equation
whose initial condition (time t=0) is computable but the solution is not
computable at time t=1. In their particular example it can be argued
that the example does not present a physically realistic setup, but my
point stands: things are not that simple.

Best regards,

Andrej