Hi Nick,

Oops, soory. I sent an empty answer.

Actually I agree with all you say here, so an empty comment was a good  
comment!

I think all this becomes simpler once you grasp that a computation, in  
the math sense, is a very well defined object.
If a computation exists, it can be proved to exist in elementary  
arithmetic.

And it exists there with a relative measure. This can not necessarily  
prove in arithmetic (but init can be proved for arithmetic in set  
theory). But here Stathis' intuition is correct, we don't have to  
prove in arithmetic the existence of the measure to be able to "live"  
it, and develop a first person perspective.

An hardwareless computer is well defined mathematical notion.  
Conceptually, it is even difficult and not yet solved problem to  
define an hardware computer (despite its common use could give you the  
contrary feeling).
Without the rize of quantum computation, I am not sure I would have  
ever believed in a notion of physical computation.
Cf also, the Mallah implementation problem.

Bruno


On 03 Jan 2010, at 14:55, Nick Prince wrote:

> Thank you Stathis
> This has helped move me on a bit. “The hardwareless computer” has been
> giving me some real problems.  Let me replay my understanding of what
> you said back just to check it is on the right lines.
> As a possible example of one of these “lurking computations” we could
> consider the one which begins with no-thing and think of the null set
> as made of it phi ={ } and then associating it with the number 0. Then
> imagine the set { phi} associating it with 1, then    { phi,{phi }}
> associating this with 2, then { phi, { phi} , { ,{phi }} },
> associating it with 3 etc. Hence we get an infinite sequence of
> abstract (platonic) entities which can conjure up (compute) the
> natural numbers and the implied successor function simply from the
> abstract (platonic) notion of a set and an association rule (also a
> platonic relation). More and more structure can be built up until - as
> you say - the entire structure of the computation contained in the
> mapping can be envisioned. Now although no external observers might be
> able to access these computations, the computations might just create
> conscious observers – bootstrapped into existence by the special class
> of computations which these (internal) observers (if they believed in
> comp) would naturally consider as non trivial.  As you say the entire
> structure of the mapping which describes the computation is a platonic
> object too – hence the world comes from nothing and computation.
> Have I got this roughly right? I would be grateful for any critical
> comments from you, Bruno (or anyone).
> Many thanks
> Nick
>
>
> On Jan 3, 11:05 am, Stathis Papaioannou <stath...@gmail.com> wrote:
>> 2010/1/3 Nick Prince <m...@dtech.fsnet.co.uk>:
>>
>>
>>
>>
>>
>>> HI Bruno
>>> Thank you so much for your answers to my queries so far.  I really
>>> need to do some more thinking about all that you have said so far  
>>> and
>>> to understand why I am having difficulty replacing a real physical
>>> universal machine existing in the future (like Tipler suggests) or a
>>> great programmer existing now (like schmidhuber suggests) with your
>>> arithmetical realism.  I also need to search some previous posts to
>>> make use of past discussion topics that are relevant. Perhaps my
>>> background makes me a physicalist who can currently accept a milder
>>> form of comp.  However, I want to explore your position because I
>>> think it makes sense in so far as I think it is less vulnerable to  
>>> the
>>> threat of infinite regressions like in  Schmidhuber’s great  
>>> programmer
>>> (or even the greater programmer that programmed him).  Your  
>>> version of
>>> computationalism would still be valid if either or both of the two
>>> options above were true. Herein lies its appeal to me (both
>>> fundamental and universal).
>>> I would like to read up on logic and computation as you suggest. I
>>> have read about all the books you recommend . However, can you  
>>> suggest
>>> topic areas within these texts which I can  focus on to help me  
>>> get up
>>> to speed with the problems I have regarding arithmetical realism  
>>> with
>>> the UDA?  There is much that could perhaps be left out on a first
>>> reading and to my untrained eyes, it’s difficult to know what to  
>>> omit
>>> (for example what would godels arithmetisation technique come under?
>>> (Googling it brings not much up).  Sorry but I haven’t ordered any
>>> books yet so I can’t look into them.
>>> Is there an English translation of your Ph.D. thesis yet?  Sorry  
>>> but I
>>> can’t do French. My thanks and best wishes.
>>
>> My justification for the hardwareless computer is the fact that any
>> computation can be mapped onto any physical process, in the same way
>> that any English sentence can be mapped onto any string of symbols.
>> Such a post hoc mapping would be useless to an observer trying to
>> extract meaning from the symbols or the result of a calculation from
>> the computer, since he would have to figure out the mapping himself
>> and he would have to know the answer he wants before doing this. With
>> the right key Bruno's PhD thesis contains an account of next week's
>> news, but so what? If you look at it the right way the dust swept up
>> by a storm is implementing a Turing machine calculating the digits of
>> pi, but what good does that do anyone? The claim that codes and
>> computations lurk hidden all around us could be taken as true but
>> trivial, or perhaps defined away as untrue on account of its
>> triviality. However, there is a special class of computations to
>> consider: computations that give rise to conscious observers in
>> virtual universes that do not interact with the environment at the
>> level of the substrate of implementation. If such computations are
>> possible (i.e. if comp is true) then it doesn't matter that no
>> external observers have access to the mapping that would allow them  
>> to
>> recognise them, for these computations create their own observers,
>> bootstrapping themselves into non-triviality. The physical process
>> "sustaining" the computation need not even be as complex in structure
>> as the computation: the computation could be mapped for example  
>> onto a
>> repetitive process, the idle passage of time, even a single instant  
>> of
>> time implementing the parts of the computation in parallel. And if we
>> get that far, it's obvious that the physical process does nothing,  
>> and
>> we may as well map the computation onto the null set. It is obvious
>> that the entire structure of the computation is contained in the
>> mapping, and the mapping is a platonic object, not dependent on being
>> written down or even understood in the mind of an external observer.
>>
>> --
>> Stathis Papaioannou- Hide quoted text -
>>
>> - Show quoted text -
>
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