Dear Bruno,
I realized something this morning, as I was
ruminating over your response below, that if my thesis is true so is your take
on comp! But only in one sense. ;)
Do you the Calude et al paper, discussing
the idea of embedding quantum logics into classical logics and the other paper
by Calude et al that discusses how an Quantum comp, with a Hamiltonian of
infinite degrees of freedom, can solve the Halting problem?
My realization is this, that if we consider
the case of the Calude system, classical comp would be isomorphic or something
similar to an infinite classical machine, such as your Universal Dovetailer. But
this is where our views, I think, diverge. Your argument, to me, resembles that
of Julian Barbour for the "nonexistence of time" in his celebrated book and a
similar one by Stuart Kauffman and Lee Smolin, as discussed here:
My difficulty is that the assumption of
timelessness at the level of the totality of existence does not necessitate that
timelessness prevails within all aspects of existence. Prof. Hitoshi Kitada,
with Lance Fletcher, wrote a paper discussing this:
I have found independent reasoning by
Michael C. Mackey, within the study of thermodynamics, that lead to the
same conclusion.
So, what does this have to do with comp?
Let me first quote something your wrote below:
"If a machine can
believe something, it will be hard for her to believe in comp and in its
consequences, until she realizes that indeed if a machine can believe something,
it will be hard for her to believe in comp and in its consequences, until she
realizes that indeed if a machine can believe something, it will be hard for her
to believe in comp and in its consequences until she realizes that indeed
if ...."
This situation is almost identical to that
occurs in the "bisimulation" hypothesis that I have been working on IFF one
assumes that the computational system has infinite computational resources. For
example:
System A can simulate A
simulating A simulating A ...
System A can simulate system B simulating A
simulating B ....
System A can simulate system B simulating
system C ....
One can easily avoid this regress by
requiring that the computational resources and/or "power" of the systems be
finite.
What I am thinking is that your own notion
of "it is hard to believe in comp, until she realizes that indeed if a
machine can believe something" implicitly involves a duration and/or
distinction between the state of "believing" and the state of "realizing" that
can not be shrunk to zero and retain its meaningfulness.
What the various forms of realisms that
introduce Platonic realms to "support" their necessary structure is that they
seem to want to retain the meaningfulness of numbers, AR in your case, all the
while removing the necessity for distinguishing such. One can not have one's
cake and eat it too!
Barbour would have us believe that the
computational complexity involved in his "best matching" scheme is obviated by
the mere postulation that all of the possible ways that the world could be
coexist in Platonia. The experience of time is merely an illusion that follows
from seeing the time capsules from the inside.
The trouble is that it is inconsistent to
allow for the mere possibility of belief, or computations in
general, if time is just in an illusion. As Lucas likes to say, such
reasoning is SelfStultifying! I see the same situation in your attempt to make comp "Popperian
falsifiable".
Your seem to try to avoid this pathology
with the assumption of "digital substitutability" but I see this as akin to
allowing for the existence of perpetual motion machines, in that for a classical
system to simulate faithfully my mind, it would have to also simulate every
possible experience that I could have, including any experiment that I might
perform involving explicitly "weird" QM behavior. Thus it must, de facto, be
able to simulate a QM system and it has been shown that this is only possible in
the case of systems with infinite resources.
We find ourselves unable to get to an
explanation of the "illusion" of time, and physicality in general!
My main criticism is that this problem
"goes away" if we shift from thinking of existence as a timeless and static
"Being" and use, instead, a thinking of Existence as an eternal "Becoming". We
can have our UDA and isomorphism between Quantum comp and Classical comp at the
Totality of existence level, but this indistiguishability breaks down when we
consider finite comp systems.
Am I making any sense so far?
Kindest regards,
Stephen
 Original Message 
Sent: Friday, January 30, 2004 6:48
AM
Subject: Re: Is the universe
computable
Dear Stephen,
[SPK] No, Bruno, I
like Comp, I like it a LOT! I just wish that it had a support that was
stronger than the one that you propose ... [BM]
Where do I give a support to comp? I don't remember. No doubt that I am
fascinated by its consequences, and that I appreciate the so deep modesty and
silence of the Wise Machine. But the reason why I work on comp is just that
it makes mathematical logic a tool to proceed some fundamental question I'm
interested in.
and that in addition
to your 1 and 3determinacy that there would be a way to shift from the
Dovetailer view (the "from the outside" view) to the "inside" view such that
some predictiveness would obtain when we are trying to predict, say the
dynamics of some physical system. Otherwise, I claim, your theory is merely
an excursion into computational Scholasticism. The
whole point of my work consists to show (thanks to math) that comp is indeed
popper falsifiable. It is just a matter of work and time to see if the logic
of observable proposition which has been derived from comp gives a genuine
quantum logic and ascribes the correct probability distribution to the
verifiable facts. The weakness of the approach is that it leads to hard
mathematical question.
I
am sanguine about QM's "weirdness"! I see it as implying that there is much
more to "Existence" than what we can experience with our senses.
;) I agree with you. Now comp shows much more easily
that it *must* be so. You know Bohr said that someone pretending to
understand QM really does not understand it. The same with comp, it can
even be justified. If a machine can believe something, it will be hard for
her to believe in comp and in its consequences, until she realizes that indeed
if a machine can believe something, it will be hard for her to believe in comp
and in its consequences, until she realizes that indeed if a machine can
believe something, it will be hard for her to believe in comp and in its
consequences until she realizes that indeed if .... (apology for
this infinite sentence).
[BM] > comp
= > 1) there is level
of description of me such that I cannot be aware of functional digital
> substitution made at that level. [SPK] Here we
differ as I do not believe that "digital substitution" is possible, IF such
is restricted to UTMs or equivalents.
No
consistent machine can really "believe" that indeed. But this does not mean a
consistent machine will believe notcomp. The point is: are you willing to
accept it for the sake of the reasoning.
> 2) Church
thesis [SPK] I have problems with Churches thesis because it,
when taken to its logical conclusion, explicitly requires that all of the
world to be enumerable and a priori specifiable. Peter Wegner, and others,
have argued persuasively, at least for me, that this is simply is not the
case.
Church thesis entails that the partial
(uncontrolable a priori) processes are mechanically enumerable. AND Church
thesis entails that the total (controlable) processes are NOT mechanically
enumerable. In each case we face either uncontrolability or non
enumerability. It is Church thesis which really protects comp from
reductionnism. That was the subject of one thesis I propose in the seventies.
Since then Judson Webb has written a deep book on that point. (Webb 1980, ref
in my thesis, url below). See my everythinglist posts "diagonalisation"
for the proof of those facts.
> 3)
Arithmetical Realism) > makes the physical science eventually
secondary with respect to number theory/computer science/machine >
psychology/theology whatever we decide to call that fundamental field ...
[SPK] I have
no problem with AR, per say, but see it as insufficient, since it does not
address the "act" of counting, it merely denotes the list of rules for doing
so.
Certainly not. AR is the doctrine that
even in a case of absolute catastrophe killing all living form in the
multiverse, the statement that there is no biggest prime will remain true. It
has nothing to do with axioms and rules of formal system. Indeed by Godel's
incompleteness theorem Arithmetical truth extends itself well beyond any set
of theorem provable in any axiomatizable theory. Now, what do you mean by
AR is insufficient? AR just say that arithmetical truth does not depend on us.
It does not say that some other truth does not exist as well (although as a
*consequence* of comp plus occam they do indeed vanish). Don't confuse AR with
"Pythagorean AR" which asserts explicitely "AR and no more". We got P.AR as a
consequence of comp, but we do not postulate it in the comp hyp.
I will go through your thesis step by step again
and see if I can wrestle my prejudices down into some reasonableness.
;)
OK. Be sure to go to step n only if you manage
to go to step n1 before. Don't hesitate to ask question if something is
unclear. Be sure you accept the hypotheses (if only for the sake of the
argument).
Best Regards,
Bruno
http://iridia.ulb.ac.be/~marchal/
