On 16/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:

> 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.

I hope this will become clearer as we proceed.

> 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".

I don't understand this yet.

> 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.

Do you mean here that: there exists a 'state that [increases] the
probability that you will be able to manifest....etc.' and that the
3-brain 'is a local and relative "description"' of such a state?

> Can you explain why the set of all binary sequences *is* closed
> for diagonalization

Because any additional members generated by diagonalisation must also
be binary sequences?

> and why any *enumerable* set of binary sequences
> is *not* close for diagonalization?

Because new members can always be generated by diagonalisation that go
outside the original enumerable set (as distinct from the larger set
of *all* sequences)?

> 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?

Could you please elucidate "functions from A to {0,1}" ?

David

>
>
> 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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