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

[Andrej Bauer]

Antonino Drago wrote:
>> 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.
> 
> This example is questioned; the mathematical space is cumbersome more 
> than the due.

Let me reiterate: I did NOT claim that Pour-El and Richards example is physically realistic.
I too agree that their  example is problematic. I used the example to demonstrate the fact that
the original claim by Hendrik was not at all obvious:

> hendrik at topoi.pooq.com wrote:
> Nothing prevents the numerical analyst from computing arbitrarily close approximations except
> time and effort.

So please forget about Pour-El and Richards example since it is obviosly causing a confusion (and
we all agree that it is problematic).

We have two people claiming seemingly mutually opposing things:

1. Henrik says that "nothing prevents the numerical analyst from computing arbitrarily
close approximations except time and effort".

2. Antonio says that "almost each differential equation belonging to theoretical physics
presents some undecidable solutions".

Which is why I would prefer to pass from idle chatting to claims supported by references and
slightly more carefully phrased statements.

For example, I am _guessing_ that Antonio's "undecidable solutions" really mean "non-computable
solutions" with the implicit assumption that initial data is computable.

Best regards,

Andrej