Hi Mirek,

On 12 Jan 2009, at 15:36, Mirek Dobsicek wrote:

>
> Hello Bruno,
>
>>>> I think you are correct, but allowing the observer to be  
>>>> mechanically
>>>> described as obeying the wave equation (which solutions obeys to  
>>>> comp),
>>>
>>> Hmm well if you have a basis, yes; - but "naked" infinite- 
>>> dimensional
>>> Hilbert Space (the "everything" in QM)?
>>
>>
>> You put the finger on a problem I have with QM. I ill make a  
>> confession:
>> I don't believe QM is "really" turing universal.
>> The universal quantum rotation does not generate any interesting
>> computations!
>
> Could you please elaborate a bit on the two above sentences. I am
> missing a more context to understand where "really" points to.



"really" was just some emphases. Also I should have said instead: I  
don't understand how QM can be really Turing Universal.
This could be, and probably is, due to my incompetence. It is due to  
the fact that I have never succeed in programming a clear precise  
quantum Universal dovetailer in a purely unitary way. The classical  
universal dovetailer generates easily all the quantum computations,  
but I find hard to just define *one* unitary transformation, without  
measurement, capable of generating forever greater computational  
memory space. Other problems are more technical, and are related to  
the very notion of universality and are rather well discussed in the  
2007 paper:


Deutsch's Universal Quantum Turing Machine revisited.
http://arxiv.org/pdf/quant-ph/0701108v1




> And with
> the second sentence, I simply don't understand it.


Me too. Forget it. Let me try to remember what I did have in the mind.  
I guess I did have wanted to say that a universal unitary  
transformation (what I meant by Universal Quantum rotation) cannot  
generate infinite complexity, although I have a good idea why a  
"sufficiently big or rich" unitary transformation can generate any  
long (but finite) simulation of any universal Turing machine. This is  
again related to my lack of success in just programming the Universal  
quantum Dovetailer. If you have any idea how to do that, let me know.  
I am not sure I am saying deep things (here :), just that I have not  
enough practice in quantum computing to make all this clear, and when  
I consult the literature on quantum universality it makes things worse  
(see the paper above).

I could relate this with technical problem with the BCI combinator  
algebra, that is those structure in which every process are  
reversible, and no cloning are possible (cf the No Kestrel, No  
Starling summary of physics(*)). Those algebra are easily shown being  
non turing universal, and pure unitarity seems to me to lead to such  
algebra.

This leads to the prospect that a sort of Everything-structure could  
exist, yet not be Turing universal. Computers would just not exist, in  
the sense that the universe, in that case, would not been able to  
provide the extendable memory space without which universality does  
not exist. This would not make the UDA (AUDA) reasoning false, but it  
would make the ultimate physics still much more constrained. Physical  
reality would be essentially finite.


I was pointing on place where I am a bit lost myself, which means that  
I am the one who would like a bit more explanation.

Could you implement with a quantum computer the "really infinite"  
counting algorithm by a purely unitary transformation? The one which  
generates without stopping 0, 1, 2, 3, ... That would already be a big  
help.

Bruno

(*) Marchal B., 2005, Theoretical computer science and the natural  
sciences, Physics of Life Reviews, Vol. 2 Issue 4 December 2005, pp.  
251-289.


>
>
>> I am open, say, to the idea that quantum universality needs  
>> measurement,
>> and this could only exists internally. So the "naked"  
>> infinidimensional
>> Hilbert space + the universal wave (rotation, unitary  
>> transformation) is
>> a simpler ontology than arithmetical truth.
>> Yet, even on the vaccum, from inside its gives all the non  
>> linearities
>> you need to build arithmetic ... and consciousness.
>
> Cheers,
> mirek
>
> >

http://iridia.ulb.ac.be/~marchal/




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