On 28 Jul 2009, at 02:56, David Nyman wrote:

>
> 2009/7/27 Bruno Marchal <marc...@ulb.ac.be>:
>
>> Actually, the real axiom is a self-duplicability principle. According
>> to the duplicability, you will have the whole of AUDA remaining
>> correct and even complete, at the propositional level, for many
>> "gods" (non emulable entities). The theology of the machine van be
>> lifted to almost all "self-duplicable" entities (but the proofs get
>> more complex). It applies to most of the "gods" I mentioned in some
>> post. You have to go very near the big unnameable for getting rid of
>> the completeness of G/G* propositional theology. This was seen by
>> Solovay (with other terms).
>> Or you have to postulate we are much less than universal machine,
>> which is just "obviously false", imo.
>> This is a weakness, it means we can only test a very general
>> principle. Most gods have similar physical realities, they have the
>> same observable. Physics become a very strong invariant, it is stable
>> for many non recursive permutations. But it is real hard math to
>> handle all this material.
>> Actually, comp itself has a huge spectrum according to the choice of
>> substitution level. Transfinite weakenings of the notion of
>> substitution level can help to extend most comp consequence on those
>> weakenings. But this could be only of academical interest, I don't  
>> know.
>> I am not sure I would say "yes" to a doctor who does propose me an
>> actual infinite brains.
>
> Actually, I find much of the above VERY hard to follow except in a
> vague way.

The problem is that the negation of COMP is a very vague and multiple  
notion.
All what I say is that most of the consequence of COMP remains true  
for most precise technical weakening of the comp hyp.
Unless you weaken so much comp that you lost the self-duplicability  
property: you say no to all possible doctors.




> Would it be possible, as an accompaniment of your
> step-by-step exposition of the UD in detail, to also give a
> step-by-step storyline of the above, but with the absolutely
> irreducible minimum of reliance on the deeper (i.e. very hard for
> ingnorami like me to access) technicalities.  You could say, for
> example, at any point "to go further you would need a deeper grasp of
> x, but for now, it has this or that role or function in the overall
> story" - or something like that.  I'd be very grateful - and
> attentive.

I think that you have already understood that this will just lead back  
to an unsolved mind-body problem.


>
>
> We talked in the past of a grandmother version or roadmap - do you
> recall?  I've got a feeling that you sometimes wonder if you may let
> us - or yourself - down by *not* going into all the detail all the
> time, but the problem - at least for me - is that my memory isn't
> retentive enough to retain the pivotal elements of the narrative
> whilst we charge off on the next - no doubt essential - safari into
> the logical-mathematical jungle.  But could we try grandma's version
> again?  Even heroic failure would teach us something.


Let me define two notions of first person indeterminacies.

There is the local one, when your current state is duplicated  
relatively to earth, or me (say) . This is done in the first sixth  
steps of the UD reasoning.
 From some of your post I can suspect that there is something perhaps  
still unclear there.

In the Washington/Moscow duplication, the *you* arriving in Moscow  
(resp. Washington) provably cannot understand why he is the one  
arriving in Moscow (Washington). It is the same question as the one  
you asked me: "why am I me and not my brother". It is trivial, with  
comp. No program can predict which backup, among two, will be the one  
being re-instantiated, relatively to its most probable history/ 
computation.


Then there is the global first person indeterminacy, which appears at  
step 7, although it is "definitely there" with the step 8. It is the  
indeterminacy of your immediate subjective future "in front" of a  
never ending universal dovetailing. At that step, assuming (or not  
with step 8) a concrete universal dovetailing in the universe (or in  
arithmetic) you should understand that you are duplicated " at each  
instant", so that your future subjective instant is determined by an  
infinity of computations: all those (existing in the U dovetailing)  
going through your actual states. So, in order to attach your mind to  
a physical appearance, you have to justify the physical appearances  
from an infinite set of computational histories. OK?
The physical reality can no more be just a mathematical structure  
among others. There may or may not exist such a structure, but in any  
case this structure or quasi-structure has to result from the  
statistical "interference" of an infinity of computations.

AUDA illustrates the consistency of such an idea, and provides a  
technical way to extract already the logic of the observable events.  
But AUDA is far more demanding in logico-mathematical technicalities.

AUDA is UDA, where the "yes doctor" is replaced by a "direct"  
interview of a correct self-introspecting universal machine.

Somehow, what I am saying in AUDA is that, thanks to the work of  
Gödel, Löb, Solovay, etc., we can already have a talk with the  
universal machine and ask her opinion, and what "her" physics looks  
like.

Then it is a rather technical point to show that by adding non  
computational power to such a universal machine will not change the  
AUDA interview, unless you bring necessarily vague ad hoc "non comp"  
feature build for changing the interview. If a universal machine bet  
that God create earth and heaven in six days and that she is not  
duplicable, well, it becomes hard to even argue if the AUDA physics  
will change or not.

Hope this "heroic failure" can help the grandma a little bit,

Bruno





http://iridia.ulb.ac.be/~marchal/




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