Dear Bruno,
 
    Let me put to the most salient part of your reply:
 
> My feeling Stephen is just that you don't like comp, and I have no problem with that. Some people takes my
> work to be a beginning of refutation of comp, and perhaps they are right. I want just illustrate that this is not
> obvious, and the tiny part of physics I have extracted from comp is for me just very weird (and no more so I
> estimate we are still far from a real reductio ad absurde of comp).
[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 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 weirdness is the many world like feature of any comp reality, the non computability of the physical
> processes in any reality compatible with comp, and a sort of quantum logic weaker than usual quantum logic. Is > that so weird? Certainly no more weird than quantum weirdness.
[SPK]
 
    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. ;-)
 

> If you are really interested in my reasoning, I would dare to insist going from step to step. If you prefer not
> studying the consequences of comp because you don't have the taste for it, I will not insist at all. My point is
> just that comp (that is
>         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.
 

>         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.
 

>         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.
 
    I will go through your thesis step by step again and see if I can wrestle my prejudices down into some reasonableness. ;-)
 
Kindest regards,
 
Stephen
 

Bruno
 
----- Original Message -----
Sent: Wednesday, January 28, 2004 9:27 AM
Subject: Re: Is the universe computable

At 11:57 27/01/04 -0500, Stephen Paul King wrote:



    Thank you for this post. It gives me a chance to reintroduce one problem that I have with your model. Like you, I am very interested in comments from others, as it could very well be that I am misunderstanding some subtle detail of your thesis.
 
    You wrote:
 
"... remembering the comp 1-indeterminacy, that is that if you are duplicate
into an exemplary at Sidney and another at Pekin, your actual
expectation is indeterminate and can be captured by some measure,
let us say P = 1/2,  and this (capital point) independently of the time
chosen for any of each reconstitution (at Pekin or Sidney), giving that the
delays of reconstitution cannot be perceived (recorded by the first person))."
 
    Now my problem is that IF there is any aspect of perception and/or "observers" that involves a quantum mechanical state there will be the need to take the "no-cloning" theorem into account. For example, we find in the following paper a discussion of this theorem and its consequences for teleportation:
 
http://arxiv.org/abs/quant-ph/0012121



This is a question people ask me often. But not only the cloning theorem is not a problem with the comp hyp, but actually it is highly plausible the non-cloning theorem is a direct consequence of comp. Remember that, with comp, physicalities emerges from an average of an infinity of computationnal histories: it is a priori hard to imagine how we could clone that. This is no more amazing than the fact the white rabbit. remember that with comp, from inside things look a priori not computable. The apparant computability of the laws of physics is what is in need to be explain with comp. We should perhaps come back when you have accept all the steps in uda step by step.




    As a possible way to exploit a potential loop hole in this, I point you to the following:
 
http://www.fi.muni.cz/usr/buzek/mypapers/96pra1844.pdf
 
 
    My main question boils down to this: Does Comp 1-determinacy require this duplication to be exact? Is it sufficient that
approximately similar copies could be generated and not exact duplicates?




It must be exact if the duplication is done exactly at the right level of substitution (which exits by hypothesis), and can be approximate if some lower level of duplication is chosen instead.





    How would this affect your ideas about measures, if at all?
 
    I understand that you are trying to derive QM from Comp and thus might not see the applicability of my question, but as a reply to this I will again point your to the various papers that have been written showing that it is impossible to embed or describe completely a QM system (and its logics)  using only a classical system (and its logics), if that QM system has more that two Hilbert space dimensions associated. Start with the Kochen-Specker theorem...
 
http://plato.stanford.edu/entries/kochen-specker/




I'm afraid you make a confusion of level here. What KS showed is that you cannot put a boolean algebra of values to quantum observable pertaining to some systems. But this is exactly what comp predict for matter and time notion. That is why we get quantum logics for the first person verifiable proposition. Nowhere I pretend to recover a classical logic in which quantum measurement value can be embedded, quite the contrary with comp classical logic is plainly false for all verifiable 1-notion right at the beginning. BTW, even if KS was a threat, your argument does not follow because KS is a theorem in quantum mechanics, and as you say, I just show that the physics is derivable from comp; if KS is false in the physics derived from comp then KS would indeed be a problem, but I insist it is not. It is only the apparent computability of the universe which still remains the miracle.

My feeling Stephen is just that you don't like comp, and I have no problem with that. Some people takes my work to be a beginning of refutation of comp, and perhaps they are right. I want just illustrate that this is not obvious, and the tiny part of physics I have
extracted from comp is for me just very weird (and no more so I estimate we are still far from a real reductio ad absurde of comp).
The weirdness is the many world like feature of any comp reality, the non computability of the physical processes in any reality compatible with comp, and a sort of quantum logic weaker than usual quantum logic. Is that so weird? Certainly no more weird than quantum weirdness.

If you are really interested in my reasoning, I would dare to insist going from step to step. If you prefer not studying the consequences of comp because you don't have the taste for it, I will not insist at all. My point is just that comp (that is
         1) there is level of description of me such that I cannot be aware of functional digital substitution made at that level.
         2) Church thesis
         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 ...

Bruno

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