Re: Introduction (Digital Physics)

From: Fred Chen <flipsu5.domain.name.hidden>
Date: Tue, 26 Jun 2001 19:25:27 -0700

Hi Scerir. Thanks for your explanation of Godel's theorem.

> Goedel's argument does not prove the existence of absolutely
> unprovable (arithmetical) truths.
>
> Its conclusion is relative to some first-order axiom system
> (of elementary arithmetic), and proves only that there is a true
> proposition unprovable in that system.
>
> But there are plenty of other systems in wich that proposition
> is provable (mechanically too).

If we exclude ourselves from the part of the universe we attempt to
simulate, I think we can avoid the self-referential paradox brought up by
Godel. This is probably okay for simulating unconscious phenomena, like in
physics or biology or engineering. But if we include our consciousness in
the simulation, I imagine we would surely have a problem describing our
thought processes, especially the thought of how to simulate the thought
process, etc.
>
> The existence of a proposition unprovable in a given system
> requires, also, that the system is consistent.

I am indeed assuming the universe is consistent.

> But how is a computer supposed to know that?
>
> Does the universe know Goedel's theorems?
>
> - Scerir
>
Well, we know Goedels' theorem, so if we include our knowledge into the
universe simulation, then we have this barrier.

Despite this, Godel does not bar us from stumbling upon a truth without
proving it.

Fred
Received on Tue Jun 26 2001 - 21:11:48 PDT