Bruno Marchal wrote:
> On 10 Nov 2009, at 19:29, Brent Meeker wrote:
>> But this seems like creating a problem where none existed.  The
>> factorial is a certain function, the brain performs a certain function.  
>> Now you say we will formalize the concept of function in order to study
>> what the brain does and perhaps understand what is consciousness.  But
>> there is nothing that requires that you start over with all possible
>> computations.  That is like explaining the factorial function by
>> considering all possible computations that produce it (like the above).  
>> It's not wrong, but it doesn't follow from saying that the factorial is
>> a function.  That's why I say I take it as an ansatz - "Let's consider
>> all possible computations and see if we can pick out physics and the
>> brain and consciousness from them."
> Hmm... The seventh step comes after six other steps. I think you 
> confuse UDA and Tegmark or Egan speculation on the mathematical nature 
> of physics. But when we assume comp,

But it seems there is a shift the meaning of "assume comp" here.  We 
start with comp = "Consciousness is something a brain does.  A brain 
does a lot of things (metabolizes, takes up space,...) but the thing it 
does that produces consciousness is a kind of computation, i.e. 
information processing. "  Almost all scientists and philosophers think 
that is good hypothesis and one they would assume.  But then it seems 
you use comp2 = "We - our stream of consciousness - IS a computation 
that exists in the Platonic sense."  This seems slightly different.

> the physical appearance cannot be describe by *any* computation a priori:
But the main evidence for the comp hypothesis is that physics is so 
successfully described by computations.

> it *has* to be retrieve from all computation. Roughly speaking, if we 
> are universal machine,

But assuming "we are a universal machine" is assuming more than "our 
brains do computations and that produces consciousness."

> we do belong to an infinity of computation, and matter, or anything 
> below our substitution level, has to be described by "all 
> computations". It is an open problem if that sum converge toward 
> something we could describe by "one" computation.
If it is proven that it doesn't, would that refute comp2?  Would we be 
left with no explanation of the perceived unity of individual consciousness?

> It is the whole point of the reasoning. It is "theorem" in the comp 
> theory that matter emerges from all computations. From this you can 
> prove that comp implies the non-cloning of any piece of matter, like 
> it proves the existence of a strong form of indeterminacy, etc.

What's the non-cloning proof?

>>>> Could you remind me what the phi_i are?  The enumerated partial
>>>> functions?
>>> The enumerated so called "partial /computable/ functions".
>>> To get them, take your favorite universal system (fortran, lisp, c++,
>>> java, whatever), write down the grammatically correct description of
>>> function (of one argument, say, that is, from N to N). Put those codes
>>> in lexicographical order, and you get the corresponding phi_i: phi_1,
>>> phi_2, ..., and their domain W_1, W_2, W_3, ...
>>> With Church thesis, all the computable functions (having the domain N)
>>> will belong to that list, but there will be no algorithm capable of
>>> telling in advance for any phi_i if it compute partial computable
>>> function or a computable functions.
>>> Given that this is a key point for everything which will follow, I
>>> have to be sure that most people understand exactly why this has to 
>>> be so.
>> Ok, I think I understand.  It's probably not relevant here, but
>> physicist usually think of functions which can be computed approximately
>> by a uniformly convergent algorithm as computable (e.g. compute pi) but
>> I think in the above you mean computable in the Turing sense that the
>> computation stops with the answer (e.g. compute pi to 100 decimal
>> places).  Right?
> Right. There is a vocabulary problem about what is a function, and 
> unfortunately english speaker and french speaker have different 
> conventions, and sometimes I slip from one to other, and this does not 
> help. Usually a function from N to N is supposed to be defined on all 
> element of N. And thus a computable function will have an algorithm 
> which does stop on all of its input.
> But the Kleene diagonalization shows that there is no computable list 
> of all computable functions, so if a language is universal, it means 
> that the computable functions can only belong to a list of something 
> else. That something else are called partial computable function: they 
> are allowed to be not necessarily define on some natural number. So to 
> get ALL functions, in some computable way, we have to take something 
> larger: all partial functions, and to get all execution of all 
> algorithm, we will have to dovetail,
Thanks, I did understand, but sometimes I need reassurance that I've 
grasped it.

> and from the first person point of view, there is an emerging 
> continuum of computations, and it plays the role of the background 
> roots of the physical laws, below our substitution level.

But how is the "first person point of view" defined?  Can this theory 
tell me how many persons exist at a given time?

> The physical world is not just a mathematical space among mathematical 
> spaces, it is really a sort of summary of the whole border of the 
> whole set of "mathematical spaces" as seen by mean universal machines. 
> That the laws of physics seems computable is a mystery now.
> I am just showing that the comp theory reduces the mind-body problem 
> to a pure arithmetical (or combinatorial, ...) body problem.
> Bruno
> <>
> >

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