Re: Is the universe computable

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Mon, 19 Jan 2004 15:24:15 +0100

At 17:36 16/01/04 +0100, Eugen Leitl wrote:

>On Fri, Jan 16, 2004 at 02:28:27PM +0100, Bruno Marchal wrote:
>
> > of brain and the like. I of course respect completely that opinion; but I
> > point on the fact
> > that once you make the computationnalist hypothesis then it is the reverse
> > which becomes
> > true: even if locally pi is a production of the human brain, globally the
> > laws of physics logically
> > develop on the set of all possible beliefs of all possible universal and
> > immaterial (mathematical)
> > machines embedded in all possible computations (computationnal histories).
>
>I respect that opinion,

Actually it is more a theorem than an opinion. But I don't want to insist on
this at this stage, I guess it would be premature.


>I'm just interested in theories which are
>instrumental in solving this universe's problems. You know, trivial stuff:
>wars, famines and death. A TOE which says: universe is information, every
>possible pattern exists, observers which can observe themselves will, is a
>bit sterile in that respect.

That's my point: the comp hyp is popper falsifiable, because it put
very strong constraint on any possible measure on the set of all
computational histories (as seen from any possible sound first person).
Unfortunately the notion of first person is hard to make precise without
going into the modal logics.




>There's a little problem with some practical relevance I don't have an
>answer, though, which I'd like to have your opinion on.
>
>We have a finite system, iteratively evolving along a trajectory in state
>space.
>We have observers within that system, subjectively experiencing a flow of
>time.
>
>I have trouble alternating between the internal and the external observer
>view. So we have a machine crunching bits, sequentially falling from state to
>state. This spans a continous trajectory. We can make a full record of that
>trajectory, eliminating a time axis. When does the subjective observation of
>existence assemble into place? The first time the computation was made?

The type of approach advocated in this list makes indeed possible to answer
such a question. Of course I will ask you, if only for the sake of the
argument,
to accept that idea that all arithmetical true propositions are true in a
atemporal
way (and a-spatial way too btw). Now a computation can be described as a
purely arithmetical object (to make this precise you need Church thesis
aswell).
Such computation are never run, they exist like the decimals of PI once and
forall (by Arithmetical realism of course). The subjective observation as such
will then also exists out of space and time, and will be felt as a time
ordered,
or as a space-time structured scenario only from the point of view of the
observer
which is related to that computation. If you want, from each instant an
observer
can think, that instant is now. In philosophy such a treatment of
subjective time is
called an indexical. This is counterintuitive because people (including many
defender of comp) are used to believe in the following psycho-physical
relation:

    (the sensation of pain/pleasure) at space-time point (x,t)

is associated with

    the physical state of some device at space-time (x,t)

But comp precludes this and forces instead:

    the sensation of (pain/pleasure at space-time point (x,t))

is associated with

a (infinite set of equivalent) relative computational state(s).

That is the space-time qualia is completely part of the sensation.






>I have trouble seeing my subjective observer experience as a sequence of
>frames, already computed.

No problem. It is totally unbelievable. As it should be in case it is true.
*that*
can be proved. Such unbelievable but true proposition belongs to the family
of undecidable but true arithmetical propositions.


>Is the first run magical, and the static record
>dead meat? I'm confused.

The static record (here it is the set of all true arithmetical proposition) is
similar to any "block universe" view in which time is internal. Note that
this is
the case for quantum cosmology where time disappears from the fundamental
equation without precluding internal time to be defined. Remember the
DeWitt Wheeler equation H = 0. With comp, space itself is "illusion", although
that word is misleading in the sense that comp justify the solidity and
stability of such
illusion. Actually this has not yet be shown, but It has been shown how to
translate
that problem into a mathematical question. In case the math leads to not enough
stability, that will give a falsification of comp.



>Let's bring a little dust into the run. Let's say we use a HashLife approach,
>which assembles the flow from lightcone hashes. Does this screw up the
>subjective experience? If yes, how?


I don't think this will screw up the subjective experience. The illusion of
time
makes part of the relativeness of the computational states.



>What about computing a record of all possible trajectories? Is enumerating
>all possible states sufficient to create an observer experience?


It is not even necessary (I really assume comp implicitly). The only think
which is needed is the existence, in some logical sense, of all those relative
states.




>I haven't spent much time on this, so maybe you can bring some light into the
>matter.


I hope I have not been to short. You can tell me if you grasp the idea or
perhaps
if you grasp at least the intention of the idea, perhaps.

Bruno
Received on Mon Jan 19 2004 - 09:24:35 PST