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 "non-existence of time" in his celebrated book and a similar one by Stuart Kauffman and Lee Smolin, as discussed here:
http://www.edge.org/3rd_culture/smolin/smolin_p2.html
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:
http://www.kitada.com/timeV.html
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 co-exist 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 Self-Stultifying! 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 -----
From: Bruno Marchal
To: Stephen Paul King ; everything-list.domain.name.hidden ; complex-science.domain.name.hidden
Cc: time.domain.name.hidden
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 3-determinacy 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 not-comp. 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 everything-list 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 n-1 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/
Received on Mon Feb 02 2004 - 19:34:36 PST