Le 26-janv.-07, à 11:11, Stathis Papaioannou a écrit :

> It seems to me that abstract machines have been created for our 
> benefit, rather like mathematical notation or human language. That is, 
> they allow us to think about algorithms and to consider how we might 
> build a physical machine to carry them out, even if this is not 
> actually done in practice.

I could agree that mathematical notation are our own invention, unlike 
number, OK?
Now, and I know I have to come back on this with more details, if you 
get what really is CHURCH'S THESIS, I can explain that "abstract 
machine" are mathematical object like numbers, having objective and 
general mathematical properties which does not depend on the choice of 
language or notation. There is an intrinsical, machine independent 
computer science.

> If you do away with the possibility of physical implementation and if 
> you consider only first person experience, what purpose is served by 
> an abstract machine?

But I do not consider only first person experiences. I consider the 
0-person (roughly: truth), the 3-person (roughly: provability), the 
1-person captured by the conjunction of provability and truth, the 
first person plural or "intelligible matter" (conjunction of 
provability and consistency) and the "sensible matter" (conjunction of 
provability, consistency and truth). This makes five notion of person 
points of view.
And thus it makes 10 such notion when you distinguish machine discourse 
on them and divine (true) discourse on them (you can do that by using G 
and G*). And then, for technical but important reason, two of them 
collapse, so in reality there are 8 hypostases.
I don't either do completely away with the physical implementation, 
only they are "abstract" or "immaterial" themselves, by relating 
"abstract machine state" with their possible abstract computational 
"most probable" continuations.

> The quotient of two numbers does not depend on a long division 
> algorithm, or any algorithm running on any  machine; it simply *is*.

Yes, but with Church thesis, the many abstract machine computing the 
quotient simply *are*, too. And the first person observer, if he 
believe in comp, know that if he want to take localise himself in its 
most probable computational history has to take those many machine into 
considerations. The UD compute the quotient in all possible way (a 
little bit like an electron who follows all possible path).

> > 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.
> Communicating with the outside world changes everything, but we can 
> put a box around the whole system and declare it closed. This closed 
> system (which may contain many interacting conscious entities) exists 
> somewhere in the Library of Babel, in the output of the "count" 
> program, in noise, in the decimal expansion of pi, etc., and even 
> though we outside the the system cannot find it or interact with it, 
> its inhabitants are going about their business regardless.

Yes but, after the UDA, unless we abandon comp, we just cannot refer to 
an outside world so easily, nor can we reify any piece of matter. Then 
if comp allows such rich piece of matter, embedding interacting 
consciousness (which I doubt) will be relevant only as far as they 
perturb the relative first person (plural) SSA measure.

> > 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).
> OK, I think I understand why you can see all the arbitrary sequences 
> from inside the UD but not the outside (it relates to the irrelevance 
> of delays from the inside), but I don't see why these extra sequences 
> should be more likely to encode white rabbit universes than the 3rd 
> person observable ones.

Because the arbitrary sequences are much more numerous (a continuum) 
than the computable one. Matter, Nature and Life "occur" on the 
boundary of the computable and the uncomputable, where the first person 
view and the third person view get conflicting. Frankly, here computer 
science provides many (subtle and counterintuitive) clues.

>  Also, I still don't understand how you will avoid the white rabbits.

By extracting the physical laws from some 1-person machine measure. 
This one can be extracted from some interview of an honest 
self-observing machine. Well, to be sure, I'm saying this since 1973 
but it is only in 1991 that I have find a "formal" clue of the reason 
why the rabbits could disappear: the logic of certainty, corresponding 
to the godelian sort of undeterminateness, allows a formal quantization 
of the true Sigma_1 propositions (= those corresponding to the 
accessible state of the UD). This is by far NOT enough for already 
pretending that comp will avoid the white rabbits, but, imo, it is 
enough to make very plausible they can disappear through purely number 
theoretical reason, so that we don't have to rely on some material 
assumption, which puts the mind body problem (my basic motivation) 
under the aristotelian rug.

But sure, the disappearance of white rabbits with comp is still an open 
problem. Brent seems to believe it is yet open in QM too, which is 
coherent with the fact that most MWI relies implicitly or not on some 
comp assumption. I sum up this sometimes by saying that decoherence + 
MWI avoids 3-person rabbits, but not the 1-person one. Actually I have 
argue that ASSA does the same. Some bayesian stuff seems to be able to 
eliminate the 3-rabbits (or the first plural person one), but hardly 
the first person one (I refer to my oldest post to this list, but I can 
repeat, especially when encouraged, the subject matter is tricky).


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