On 12 Jan 2009, at 17:24, Mirek Dobsicek wrote:

> Thank you for a quick answer! I'll take a look at it, my curiosity
> approves additional items on my TODO list :-)

Manage keeping finite your todo list :)

I have finished the reading of the paper I mentioned (Deutsch's  
Universal Quantum Turing Machine revisited) and I see they have very  
similar problems, probably better described. The paper mentions (but  
does not tackle) an old problem already described by Shi 2002, which  
made me think at the time that the notion of Universality is a bit  
dubious in the quantum realm.

To sum up: is there a (never stopping) quantum counting algorithm? I  
think I can build a Quantum UD from it, well in case the Shi problem  
is not too much devastating.
But here, and now, I got a feeling there is just no quantum counting  
algorithm ...



PS Note that AUDA (the arithmetical UDA) is in principle already able  
to solve completely that problem. It is still possible that "the  
material hypostases" of the self-observing *classical* universal  
machine lacks both the kestrels and the starlings, and their  
descendant combinators in which case comp predicts that physics is NOT  
Turing Universal. Comp would predict that not all natural numbers are  
in any possible nature or physics!
"in principle" only because the translation in arithmetic leads to  
very complex arithmetical formula (bounded by PI_1 IN Arithmetical  
Truth, if you know a bit of degrees of unsolvability. I will perhaps  
explain a bit of this, but take it easy for not making explode the  
todo list :).
Note the beauty of comp: even if there are no physical universal  
machine in the physical universe (including the physical universe(s)),  
*you* (and other persons) are and remains universal machine.
We do not live in physical universes, we just traverse them to be able  
to chat some bits, perhaps. The first persons would be spiraling  
through an infinite sequence of rotations, if said through an image.


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