Le 25-janv.-07, à 12:25, Stathis Papaioannou a écrit :
>
>
> Bruno Marchal writes:
>
>> Le 23-janv.-07, à 06:17, Stathis Papaioannou a écrit :
>>
>>> Searle is not a computationalist - does not believe in strong AI -
>>> but
>>> he does
>>> believe in weak AI. Penrose does not believe in weak AI either.
>>
>> Yes. In that way Searle is "not even wrong".
>
> Meaning what? I thought you agreed his position was coherent.
In the sense that if you predict that weak AI is possible and strong AI
is not, then he can no more be refuted. At least Penrose can be refuted
by a success of weak AI, at least in principle. Now you can note that
both Penrose and Searle are coherent with respect to comp (called
"strong AI" by Searle) in the sense that they are aware of some
difficulty between comp and materialism. Of course they are both
materialist and so believes that comp must be abandoned. I prefer to
abandon materialism which I have practically always suspect of
incoherence even before I learned about QM (which I take as confirming
that the notion of primary matter is at least not well defined).
Just to be clear on vocabulary:
COMP = I am a digital machine (roughly)
STRONG AI = digital machine can have qualia/subjective life
WEAK AI = digital machine can behave exactly like if they does have
qualia/subjective life.
A lot of people confuse COMP and STRONG AI. But obviously, it is
logically possible that a digital machine could have subjective
experience, without me being a machine. Of course if machine can
think, this could be taken as an inductive inference argument for
*guessing* that I could be a machine myself, but deductively "Machine
can think" does not entail that *only* machine can think, perhaps
angels and supergods could too, or whatever. So COMP => STRONG AI =>
WEAK AI, but in principle none of those arrows are reversible.
>
>> <snip: see my preceding post to you>
>>
>>
>>> If there are more arbitrary sequences than third person computations,
>>> how
>>> does it follow that arbitrary sequences are not computations?
>>
>>
>> I guess I miss something (or you miss your statement?). Is it not
>> obvious that "if there are more arbitrary sequences than third person
>> computations, then some (even most) arbitrary sequences are not
>> computations".
>
> OK, but my concern was to find room in the arbitrary sequences for all
> computations, not the other way around (perhaps I didn't make this
> clear).
> Every rational number is also a real number.
We certainly agree on that. And all computable sequences are indeed
contained in the set of all sequences.
>
>> Let us define what is a computable infinite sequence. A sequence is
>> computable if there is a program (a machine) which generates
>> specifically the elements of that sequence in the right order, and
>> nothing else. The set of programs is enumerable, but by Cantor theorem
>> the set of *all* sequences is not enumerable. So the set of computable
>> sequences is almost negligible compared to the arbitrary one.
>>
>> Does it mean there is no program capable of generating a non
>> computable
>> sequence?
>>
>> Not at all. A universal dovetailer generates all the infinite
>> sequences. The computable one, (that is, those nameable by special
>> purpose, specific, program) and the non computable one (how? by
>> generating them all).
>>
>> I give another example of the same subtlety. One day a computer
>> scientist told me that it was impossible to write a program of n bits
>> capable of generating an incompressible finite sequence or string of
>> length m with m far greater than n. I challenge him.
>> Of course, what is true is that there is no program of n bit capable
>> of
>> generating that m bits incompressible string, AND ONLY, SPECIFICALLY,
>> THAT STRING.
>> But it is really easy to write a little program capable of generating
>> that incompressible string by letting him generate ALL strings: the
>> program COUNT is enough.
>>
>> I think this *is* the main line of the *everything* list, or a
>> miniature version of it if you want.
>
> Yes, and there are many related examples, like Borges' library; I
> would include
> the computations that might be hiding in noise as another such example.
We will have to go back on this. I would compare the Borges' library
(or its countable infinite generalization) as equivalent with the
counting algorithm. It generates all (finite) strings, and a lot of
computations can be considered as being embedded in those strings.
Still I consider that the counting algorithm is not equivalent with a
universal dovetailer. I will try to explain the difference with some
details, but roughly speaking, what the UD does, and what neither the
rock nor the counting algorithm really do, is that the UD generates
both the program codes and their finite and infinite running. Saying
that all computations are generated by the counting algorithm makes
sense only if we add a universal interpreter in the description.
I can anticipate that you will say this does not change anything from
inside. But remember that once we abandon the "physical" supervenience
thesis, we will replace it by the computational supervenience thesis
which ask us to be precise of what is a mathematical computations. We
can no more relate on notion of time space, energy, etc.
The easy way to do that consists in defining in some axiomatics what
will be necessary for both the existence of computations and the
existence of internal observer related to those computations. In that
case a counting algorithm is just equivalent to the first three axiom
of Peano Arithmetic. This is provably not enough to define or execute
all programs. It appears that by adding the definition of addition and
multiplication (and order) you get the turing universal level (and then
with the induction axioms you get the internal lobian observer.
Everything will emerge from (mathematical interrelation between those
beings).
I'm afraid I'm not clear, and I will think how to make this clearer
without going to much into the technics.
> The
> significant thing in all these cases is that from the third person
> perspective, the
> information or computation is inaccessible. You need to have the book
> you want
> already before you can find it in the Library of Babel. However, if
> computations
> (or books) can be conscious, then they will still be conscious despite
> being unable
> to communicate with the world at the level of their implementation.
> The first person
> perspective makes these situations non-trivial.
OK, but as far as they can communicate from their inside points of view
(btw: thanks for the spelling!) you are adding implicitly some addition
and multiplication laws. Once we stop to take for granted what exists
or not, such little nuance have some importance, especially for
deriving concretely physics from something else.
>
>> Now, when you run the UD, as far as you keep the discourse in the
>> third
>> person mode, everything remains enumerable, even in the limit.
>> But from the first person point of view, a priori the uncountable
>> stories, indeed generated by the UD, take precedence on the computable
>> one: thus the continua of white rabbits. This results from the lack of
>> any possibility from the first person point of view to locate herself
>> into UD*. Somehow the first person belongs to 2^aleph_zero histories
>> at
>> the start.
>
> Can you explain again why only the countable stories appear to the 3rd
> person
> but the 1st person sees the uncountable ones as well? Also, why should
> the
> white rabbits prefer the uncountable habitat?
The computable stories can be said to be generated by programs, and
thus are enumerable (countable).
But the UD generates not only all programs and their execution, it
generates also all data, including all streams, all oracle, etc.
Of course he never generates a complete streams in one strike, but by
dovetailing on the reals (which can be defined by a finite subroutine,
he can present such real streams through finite but enough big portion
to some program who "want to read them".
Now, for an external observer everything at any time (or number of
steps of the running of the UD) is countable. We can see finite portion
of the stream to be generated with some advance and then presented to
the program, then we have to wait a billion years (say) to see the
"same program" getting a larger portion of its stream datum.
Now, put yourself in front of a concrete UD, like in step 7 of the
version of UDA in 8 steps.
cf the pdf slide:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004Slide.pdf
To predict your "future history", and taking into account the first
person is unaware of delays of computation introduced by the UD (due to
its dovetaling), and taking into account that the UD generates all
programs infinitely often (necessarily), and taking into account that
the "probability measure" cannot bear on the computational states but
only on the (infinite) computational histories: all that entails that
you have to take into account ALL computational histories going through
your current state. Well, now take just into account the infinite
dumbness of the UD, which is that for all programs it will generate its
execution on all streams, and thus on all arbitrary sequences
(including first person descrition of white rabbits) which makes a non
countable set (!!!, by Cantor) then, well, then it *seems* we cannot
avoid white noise and flying pigs and all slight variants, etc... OK ?
(don't hesitate to say NO, I'm quick and it is not easy). Are you OK
with any "taking into account" described above?
Of course, such measure is a bit too much intuitive: a priori all
probabilities of histories add up, and we could a bit naively take this
as a refutation of comp. What refrains us to jump toward that
conclusion, is that such intuitive probabilities have not enough taken
into account the difference between the points of view, something any
self-referentially correct universal machine can be shown to be able to
do, thanks, not really to incompleteness, but thanks to the fact that
machine can reason about their own incompleteness (leading to the
arithmetical points of view/hypostases). This motivates then the AUDA
(Arithmetical version of UDA, ... or of Plotinus, actually).
>
>> A similar "explosion of stories" appears with quantum mechanics,
>> except
>> that here the physicist as an easy answer: white rabbits and Potter
>> universe are eliminated through phase randomization (apparently).
>>
>> I am not satisfied by this answer if only because my motivation is to
>> understand where that quantum comes from.
>>
>> Is complex randomization of histories the only way to force normal
>> nature into the shorter path?
>>
>> Well, my point is that if we take comp seriously, we have to justify
>> the absence of rabbits from computer science. In case too much white
>> rabbits remains, comp would be false, and this would be an argument in
>> favor of materialism. But, when you interview a universal machine on
>> this question you can realize at least that this question is far from
>> being settled.
>
> If QM emerges from comp, does that solve the problem?
As far as QM is confirmed by nature, if QM can be justified by comp, it
would mean nature confirms comp, and thus its immateriality. In this
sense the problem would be solved: materialism would be false. If QM is
confirmed by nature (an infinite process, note) and if comp predicts
something different, then it will depend. Some circumstances could lead
to argument in favor of materialism. I mean I can speculate about this.
>
>> Hope you don't mind I continue to comment your post tomorrow,
>
> I appreciate that you are taking the time to reply to my posts; even
> though
> you are probably repeating yourself, I think I understand things a
> little better
> every time.
Thanks for saying. Don't hesitate to ask precisions. When I reread
myself I am not just ashamed of my spelling, I realize I forget
arguments or points, or, often, that I miss the relevant emphasis.
Things will be clearer when I will describe the UD in term of the Fi
and Wi.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Thu Jan 25 2007 - 11:32:16 PST