On 30 Dec 2009, at 17:39, John Mikes wrote:

> Bruno,
> I still wait for the reasoning of the 'primitive'  in your:
>
> "...if this physical universe can be captured by a program (a  
> number) or even by a mathematical structure. It is not a primitive  
> structure. It has a reason linked to a
> statistics on computations.-..."
> What primitive(?) structure serves the computation?

The additive and multiplicative structure of the positive integers.  
This defines a "canonical" universal dovetailing, describing all the  
computations.

But there is no reason a priori why a physical universe would be  
computable, or generated by the UD, because we are multiplied  
infinititely many times, and the results of that infinite  
multiplication this is not a priori computably generable.





> (Statistics is a nono for me:
> the choice of identification (exactly what definition of elements to  
> pick) and of the domain-boundaries (what to include into our  
> 'picking' territory) make the 'statistical results' arbitrary). I  
> may have missed your explanation on that, when the question came up.

Church thesis defines the domain of indeterminacy "all the you*  
accessed by the UD. You are not aware of the number of steps made by  
the UD, and your indeterminacy is on an infinite set.



>
> And: where do you take the 'mechanism' FROM,  if you consider the  
> numbers primitive?

 From addition and mulitiplication. It is not so easy to show that,  
but it is more long and tedious, than conceptually difficult.




> Does your parenthesis (above) mean that "a number" is a program?


With respect to the choice of a phi_i or of a universal machine or  
language (like arithmetic, comobinator, java,n c++, etc.).



> I assume you mean the "very long" number (with their mathematical  
> structure?) to express anything - being considerable like a program,  
> but do you indeed mean it that way?

Not to express anything. Only the expressible things, by machines.



> Also the mathematical alteration of the numbers bothers me: if  
> addition, etc. are included, why not express just the final number?  
> - It is too long anyway, so it is a thought-experiment at best.

Because universal machine can also search for a number having some  
property (always defined by addition and multiplication), sometimes  
such a search can not stop, and we never know some final number.
By church thesis some computable function are undefined, and tha  
machine computing them does not stop, and nobody can infer from the  
structure of the machine if it will stop or not.



>
> Is such an unexpectably long number more understandable than a  
> semanic meaning?

It may be, if you mean understandable by some universal machine. Even  
this very post will be translated into a long number before your  
computer interpret it, for you, as a electronic mail.




> Granted, it is not easy to 'manipulate' semantic meanings, but with  
> a better computing (e.g. fully analogue) it is imaginable, (an  
> analogue mechanism) - maybe more so than a number-substitute (oops:  
> the other way around: the analog meaning expression substituting for  
> the (primitive?) number-based expression).

May be. But analogue machine knows today are Turing emulable, or does  
not compute anything, but one phenomenon.
If they use all the digits of real number in actual time, then we are  
no more in the digital (comp) theory. No problem.

>
> I asked earlier, but the response did not make me wiser: is there a  
> place where I could read a (not more than a short paragraph-long)  
> identification for UD(A) and AUDA? The texts that appeared are too  
> long for my limited capabilites.


UDA = Universal Dovetailer Argument. It is an argument which is  
supposed to show that if we take seriously the idea that "we" are  
digitally emulable, then we have to take seriously the idea that  
physics is a branch of number theory. Intensional number theory  
(number can serves as code for other numbers and functions: it is  
theoretical computer science, also).

AUDA = Arithmetical UDA. Instead of asking humans, I ask universal  
machine, or the Peano Arithmetic machine. It is the Escherichia Coli  
of the self-referentially correct (Löbian) machine.



>
> Happy New Year (I will try to be smarter in 2010).


Happy New Year,

Bruno


>
>
>
> On Wed, Dec 30, 2009 at 10:59 AM, Bruno Marchal <marc...@ulb.ac.be>  
> wrote:
> Hi Mindey,
>
> On 29 Dec 2009, at 15:07, Mindey wrote:
>
>
> > I was just wondering, we are talking so much about universes, but  
> how
> > do we define "universe"? Sorry if that question was answered
> > somewhere, but after a quick search I didn't find it.
>
> What do you mean by "universe"? Do you mean, like many, the physical
> universe (or multiverse), or do you mean the ultimate basic reality
> (the third person everything)?
>
> I think that if we assume mechanism, then it is absolutely undecidable
> if there is anything more than positive integers + addition and
> multiplication. Ontologically, if you want.
>
> All the rest belongs to the epistemology of numbers, or, put it
> differently, of the inside views of arithmetic. The physical universe
> becomes the sharable (first person plural) ignorance of the universal
> numbers. It is an open question if this physical universe can be
> captured by a program (a number) or even by a mathematical structure.
> It is not a primitive structure. It has a reason linked to a
> statistics on computations. Matter is sort of derivative of the
> (machine's) mind. Cf the UDA reasoning, if you have followed.
>
> There is a Skolem like paradox. Arithmetic, from outside, is infinite,
> but it is a relatively small and simple mathematical structure. Yet,
> as seen from inside, it escapes the whole of mathematics, because it
> looks *very* big for inside. So big that such a bigness is not even
> nameable by any of the creatures which live there.
>
> There is a need of some amount of mathematical logic and computer
> science to give sense on all this. Especially for expression like "as
> seen from inside", etc.
>
> Bruno Marchal
> http://iridia.ulb.ac.be/~marchal/
>
>
>
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