> Would you formalise that by the total (defined everywhere) functions
> from N to N, or do you accept the partial computable functions as
> well? And why would you not accept also the functions computable
> relatively to the halting problem? They correspond naturally to the
> function computable in the limit and are quite usefull if you accept
> infinite histories ...
Hmmm... As you can probably tell, I'm not big on proofs or expressing things
formally, so maybe it will be safer if I continue to talk plainly.
When devising a Theory of Everything, anything goes, except you must be able
to demonstrate the universe in action. At least the beginning part.
You must specify, exactly, what the initial conditions are, and what the
procedure is for transforming the initial conditions into the future states.
Following the instructions you specify, we should be able (in principle) to
see everything we see now. The ground, the sky, the sea, people, plants,