On 16/08/07, Bruno Marchal <[EMAIL PROTECTED]> wrote: > OK. I will come back on this too.

I'm away until next Thursday, so I'll continue to think about - and reserve my response to - your last post until I return. I've received Albert, Cutland, and Franzen, so I've got plenty of bed-time reading :-) 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/ > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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