Le 15-août-07, à 17:00, David Nyman a écrit :


>
>> What comp (by UDA+FILMED-GRAPH) shows, is that, once the digitalness 
>> of
>> your local relative description is taken seriously, you can no more
>> distinguish the comp stories existing below your comp substitution
>> level.
>
> So, 'materiality' - for you - can consist in effect only of what is at
> or above this level?


Yes. The visible will appear as a sum of the invisible.



>
>> Eventually the laws of physics will be the law of what remains
>> or emerges as observable in all computations.
>
> Again - for all observers - what emerges at or above their 
> substitution level?


This is exactly what we will have to compute.



>
>> From inside this has to
>> interfere statistically (by UDA).
>
> That is, from inside comp reality, not inside 'matter'?  Then, given
> this, statistical interference leads to first person indeterminacy.


I would say the contrary. The first person indeterminacy comes from the 
fact that (relative) computational histories can diverge, and does 
diverge in case of self-differentiation or bifurcation like in the WM 
duplication experiment. Then the statistical interference emerges from 
the first (plural, hopefully) indeterminacy. If you drop a pen, to 
compute EXACTLY what will happen in principle, you have to consider all 
comp histories in UD* (the complete development of the UD) going 
through your actual state (the higher level description of it, which 
exists by comp, but which is actually not knowable by you. Of course 
this cannot be used in practice, but has to be used to derive the more 
usable laws of physics.



>
>> How? I would say by self-measurement relatively to their most probable
>> (or credible ...) comp histories. There is always an infinity of them.
>
> How does 'self-measurement' lead to the observables of physics?  By
> 'most probable' I assume you mean the convergence of first person
> experience on such histories.  Is this what you mean by
> 'self-measurement' (i.e. the convergence by self-sampling on a
> first-personal 'measure')?


Yes. And after the 8th step of the UDA, you should understand that the 
"physical implementation of the UD" is not relevant, because a UM 
cannot distinguish "reality" ("real" or virtual) from purely 
arithmetical reality,


>
>> You can see my thesis either as a the showing that comp necessitates 
>> to
>> generalize Everett embedding of the subject into the physical world.
>> (Cf also Rossler endophysiocs). Indeed comp forces us to embed the
>> arithmetician (or any memory machine) in numberland (something for
>> which we will never have a complete unification).
>
> Is comp therefore in effect a 'many minds' view?  In this case, do the
> 'many worlds' emerge as the observables contingent on the povs of the
> many minds (from the background of numberland)?


I would say yes. I have often used the expression "many dreams" where a 
dream is an infinite set of (non interacting or independent) infinite 
computations. Logicians, like modal logicians are using the term 
"world" as something primitive and indefinite: a world is just an 
element of a set. They uses it intechangeably with "states", "points", 
"elements" etc. Does the many dreams generates anything like a singular 
physical world: well probably not. Does the many dreams generate a 
quantum multiverse? Well, if comp (and my reasoning) is correct then it 
has to do that. Does it, up to now yes (Again I anticipate).


>
>> I said in Siena, and already in this list, that for Plato, what *you*
>> see (observe, measure) is the border of what *you* don't see. In the
>> universal machine context this can lead to a recursive but solvable
>> equation where physical reality is a sort of border of the comp-
>> indeterminacy or the comp intrinsical ignorance.
>
> When you refer to the observables as the border of what you don't see,
> or the border of the comp indeterminacy, are you again referring to
> the indistinguishability of what lies below one's substitution level?


Absolutely.



> If so, would this not imply the potential existence of an infinity of
> levels of observables, or physics(s), depending on the substitution
> levels of classes of observers?

All right, but note that we have no choice concerning our level of 
substitution. And the physics (observables) will be a "sum" on all 
possible fine grained histories consistent with your actual state. If 
comp is really at the origin of the quantum empirical interference, the 
"reason" why "an electron" can go through two holes simultaneously, is 
that the electron "choice" has no impact at all, even in principle, 
with your actual and successor  comp histories.
Empirically we can expect that the 'substitution level" is more related 
to a notion of "isolation" than of scaling. Nevertheless, we cannot 
really use this here, given that we have to extract quantum physics 
from the existence of that "level".


>
>> In a nutshell, you cannot use Godel incompleteness to show that we are
>> not machine (or that we are not lobian), but you can use Godel
>> incompleteness to argue that IF we are sound lobian machine then we
>> cannot know which machine we are, still less which computations 
>> support
>> us. It gives the arithmetical origin of the first person comp
>> indetermincacy, which you are supposed to have already intuitively
>> swallow from the UDA, OK?
>
> OK.  However, I still have in reserve my question about how we are
> supposed to think about the relation between, say, our minds and some
> observable version of our brains.


'course, this is tricky and quite counterintuitive: a third person 
description of a brain (what we usually call "brain") is most probably 
a relative comp state with respect to (relative) comp histories. The 
3-brain is just not a physical device for producing consciousness, it 
is a local and relative "description" of a state making greater the 
probability that you will be able to manifest your first person 
experience relatively to some "dream", itself being an infinite set of 
histories.




> For example, how are we supposed to
> account for how changes to some version of our brains seem to
> correlate with changes of mind, or how the physical evolution of
> brains relates to that of minds?
>
>> Where a layman says: the temperature in Toulouse is 34.5,  the 
>> logician
>> says:   temperature(Toulouse) = 17.
>
> Is it colder for logicians?


No, just one of the false sentences I was talking about. Just to see if 
your are not sleeping (if you mind that kind of deformed teacher bad 
joke :)


>
>> So an arbitrary function from n-tuple to number will
>> be denote by f(x_1, x_2, ..., x_n). Exactly like in the definition of
>> an arbitrary derivative in calculus: the limit, if it exists, for h
>> going near zero of the quotient f(x + h) - f(x) with h. OK?
>
> OK, thanks.
>
>> I propose to go, from the Cantor non-enumerability of the reals (or
>> things equivalent) to Kleene non recursive enumerability of the
>> recursive reals, by Church thesis. Comp, both in the UDA, and in the
>> arithmetical UDA, is mainly Church thesis. I want to show you how
>> strong and deep that thesis is. OK?
>
> OK
>
>> Now diagonalization will appear to be a sort of "transcendental
>> operation". Its main use is for going outside some set, and I would
>> like to convey why the fact that the set  "programmable functions" is
>> closed for diagonalization is truly a miracle! (to borrow Godel's
>> expression). It is really that miracle which makes the set of
>> programmable or computable function fitting so well the search for
>> universal everything theory.
>
> I think I see what you mean - i.e. that extensions to the set by
> diagonalisation are also programmable functions, which makes the set
> in effect a closed but infinite universe.


Yes. Can you explain why the set of all binary sequences *is* closed 
for diagonalization, and why any *enumerable* set of binary sequences
is *not* close for diagonalization?
A set is said enumerable if there is a bijection between that set and 
the set of natural numbers. A bijection from a set A to B is a function 
b from A to B such that for any x in A, b(x) is defined and is in B, 
all element of B are equal to some b(x) with x in A, and if x is 
different from y in A, then b(x) is different from b(y).

A bit more difficult: can you show that for any set A, the set of 
functions from A to {0,1} is bigger than A? and BTW, do you see that 
there is a bijection between the set of functions from A to {0,1} and 
the sets of parts of the set A. (A set S is said to be part of B, i.e. 
S is included in B, i.e.  we have for all x that (x belongs to S 
implies x belongs to B). Can you see why this entails that the empty 
set {} is included in all sets).

Sorry for those little exercise. The one a bit more difficult is know 
as Cantor theorem. I give the solution when you ask, even just for 
comparing with your answer, which you don't have to put on the list (we 
are *not* at school here ...).

All this should help some others, and of course, they are free and even 
invited to ask if they have a problem.

Is it ok for everybody that:

The union of A and B is equal to the set of x such that x belongs to A, 
OR x belongs to B.
The intersection of A and B is equal to the set of x such that x 
belongs to A, AND x belongs to B.
The complement of A in B is equal to the set of x such that x belongs 
to B and does NOT belongs to A.

The first line can be written A U B = {x : x is-in A OR x is-in B}   
non exclusive OR.

OK?  (It would be too bad people loose the real difficulty because of 
notation trouble, so let us take the time to revise a bit those 
things).




>
>> Well, ok, sorry. Instead of "the non enumerability of the subset of 
>> N",
>> read "the non enumerability of the set of subsets of N".
>> Have you take a look on my old diagonalization post which I send to
>> Lennart?
>
> Yes, thanks.

I will come back on this.


>
>> Did this post helped? I want you to understand Church thesis, before
>> the description of some formal language. This will economize work, and
>> help you disentangle the rigorous from the formal. In our setting,
>> "formal" will always mean "output by a machine". Don't believe that
>> formal = rigor. That would be equivalent to believe that all machines
>> are correct (a nonsense).  OK?
>
> Yes, very helpful.


OK. I will come back on this too.



Bruno



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


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