Le 20-juil.-06, à 05:31, Stathis Papaioannou a écrit :
>
> Bruno Marchal writes (quoting SP):
>
> >
> I mainly agree with you, except perhaps that I would not go so quickly
> > from
> > "any sufficiently complex physical system implements any finite
> > computation" to
> > "any computation can be mapped to any physical substrate",
> >
> I doubt long and deep (in Bennett technical sense) computation can be
> > mapped to *any* physical substrate.
>
> I admit that the latter statement does not necessarily follow from
> the former. But suppose all that exists is a single hydrogen atom in
> an otherwise empty universe, no MW, just the atom with some version of
> CI of QM. Over eternity, how many distinct physical states will this
> atom go through?
An infinity. All linear complex combination of "waves", each of which
described by 3 quantum numbers.
If you have a MAC you can visualize it (freely for a time) through
http://www.versiontracker.com/dyn/moreinfo/macosx/525&mode=feedback
If you have a PC, I think here is a PC version of that software:
http://www.tucows.com/preview/205430
I have try a long time ago to prove that just a hydrogen atom is turing
universal. I failed, and I am no more sure it could be the case. Of
course it is trivially the case if you describe (through quantum field
theory) the "whole of the hydrogen atom", that is, taking into account
explicitly the quantum vacuum into consideration. This is trivial
because the quantum vacuum is already turing universal (making btw the
quantum zero body problem already insoluble---in classical physics I
think you need at least three bodies).
> We could map one distinct computational state to one distinct physical
> state. Well, why should a transistor or valve switching on and
> off implement a certain computation but not a hydrogen atom changing
> states?
Mmmmh..... (you are driving us toward the movie-graph, but I have the
feeling you could solve this problem without it ....)
> Furthermore, given that the mapping of physical state to computation
> is arbitrary (a switch going on/off/on could be saying 1/0/1 or 0/1/0
> or even 1/1/0, the mapping changing halfway through the computation in
> the last example), we could "reuse" physical states multiple times to
> implement whatever computation we want. This is a lot of
> responsibility for one little hydrogen atom, and it seems to make more
> sense to say that in fact computation does *not* supervene on the
> physical.
Yes. (this confirms my feeling above). But note that if we were able
to show that a hydrogen atom does compute something or even anything (I
doubt that!), then after the DU argument, even without the eighth
(movie-graph) step, it would just mean we need to take into account
larger part of the UD works, those who emulate or simulate enough of
the possible implementation of the Hydrogen Atom. But with the comp
"no-cul-de-sac phenomena", even if your actual state is emulated by,
let us say, some hydrogen atom on the planet Venus (say) then you not
be directly and first person aware of that fact, and your probable
continuation will still necessitate all the apparition of that states
in all computations generated by the UD. So it will not change the
conceptual problem, it just make the practical math more difficult.
Remark: of course the quantum explanation is in advance here through
the phase randomization process which associates destructive
interferences for "aberrant" computational histories.
But the pure quantum explanation misses the G/G* gap, which explains
the first person qualia (through the theatetical definition of
knowledge).
>
> > This is important because consciousness should relie on infinite
> > computations.
>
> This may actually be the case, but why does it necessarily have to be
> the case?
Because the first person cannot be aware of any delays between the
generation of the computational states by the UD.
This is a consequence of the "big" first person indetermincacy when she
is "in front" of a real concrete UD running forever.
From this, consciousness (a first person notion) will supervene of the
infinite union of all finite histories, and the infinite histories will
"eventually" win the measure battle, just because they are much more
numerous (a continuum). Take this explanation as a non constructive
justification of the reversal. A more constructive justification is,
in fine, given by the lobian interview.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Jul 20 2006 - 10:54:19 PDT