Dear George, Interleaving,

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----- Original Message ----- From: "George Levy" <[EMAIL PROTECTED]> To: "Everything List" <[EMAIL PROTECTED]> Sent: Friday, June 13, 2003 4:21 PM Subject: Re: are we in a simulation? > HI Stephen > > Stephen Paul King wrote: > [SPK] > >>> Does computational complexity (such as NP-Completeness, etc.) > >>>and computational "power" requirements factor into the idea of > >>>simulated worlds? > >>> > >>>[GL] > >>It may. Also important is the issue that Tegmark raised in the > >>Scientific American article about the ordering of an infinite set. The > >>probability of the occurence of an element of any subset (say the even > >>numbers) can be altered depending on how the element of the set (say the > >>natural numbers) are ordered. > >> http://arxiv.org/abs/quant-ph/0101077 http://www.sciam.com/article.cfm?articleID=000F1EDD-B48A-1E90-8EA5809EC5880000 > >> > > > >[SPK] > > > > Is this related to what D. Deutsch mentions regarding the "measure on > >the ensemble" in his paper "It From Qubit"? > > > I don't know. I haven't read his paper [SPK] U can find it here: http://www.qubit.org/people/david/Articles/ItFromQubit.pdf I do not agree with David's arguements because of its appearent physicalist assumptions but he does raise some interesting points to counter those of Tegmark. > [SPK] > >It might also be related to the > >Burali-Forti paradox? > > > >>From http://www.andrew.cmu.edu/~cebrown/notes/vonHeijenoort.html : > > > >"The Burali-Forti paradox deals with the "greatest ordinal"--which is > >obtained by assuming the set of ordinals is well-ordered [and, of course, > >that it is a set!]--which must be a member of the set of ordinals and > >simultaneously greater than any ordinal in the set." > > > >[GL] > >>So if we assume that the multiworlds are an infinite set, to compute the > >>probability of any event we need to know how the multiwords are ordered. > >>I conjecture that the ordering should be anthropy related. > > > >[SPK] > > Do you mean "entropy"? > > > >[GL] > No, I mean "anthropic-principle." I just shortened it out of lazyness to > anthropy which I know is not an accepted word. Sorry. On the other hand > maybe we should just coin the word. It seems useful. I meant that the > ordering of the multiworlds should affect the measure of the world we > observe which is itself anthropic-principle related. [SPK] Oh, ok. I have my own version of the anthropic principle: The content of a first person "reality" of an observer is the minimum that is necessary and sufficient for the existence of that observer. I am trying to include observer selection ideas in my definition of "anthropy". ;-) I conjecture that the "third-person" aspect could be defined in terms of a so-called "communication" principle: An arbitrary pair of observers and only communicate within the "overlap" or set theoretic intersection of their first person "realities". Does this make sense? Do you see any way of generalizing it? [GL] > I don't know how the Burali-Forti paradox comes into play. When I talked > about the ordering of the multiworlds, I made a comparison with ordering > of a set. However, we don't know if the multiworlds or perhaps more > generally, the plenitude, is a set. Probalby not. > [SPK] Well, if we want to consider the ability of our observers to "speculate" about the plenitude we will eventually be forced to deal with this question in a definite manner. I guess this would be a form of meta-metaphysics. ;-) [GL] > >>Let's consider a double slit diffraction experiment. The multiworlds are > >>ordered according to the output diffraction pattern. Since the phases > >>add up to produce this pattern, it seems that the process is linear, > >>(thus simplifying computation) so computational complexity and > >>computational power do seem to be of relevance. > >> > > > >[SPK] > > > > I am still struggling with my intuitions regarding how to think of the > >liner superposition of QM states as "multiple worlds". > >[GL] > I also do not understand either the connection between the philosophical > concept of the plenitude with the quantum idea of phase and conjugate > quantities. > [SPK] This should be explained in Everett's original paper on the Relative State interpretation, but I have not seen much discussion of it. :_( [SPK] > >For one thing, > >nowhere does there seem to be a place to embed the notion of an observer > >other than the notion of the observable itself, but we don't have a formal > >(or even informal!) way of defining the idea of a relation between and > >"observer" and observables. Do you have any ideas? > >[GL] > The observer can only observe "anthropy" related worlds. Each > consciousness is the fundamental filter in the selection of what it, > itself, observes out of the plenitude. I believe that it is no accident > that the world "makes sense." The world is rational in exactly the same > extent that we are (or maybe that we could be in an ideal situation) > Logically speaking, the world is a mirror of ourselves. To paraphrase a > much earlier saying, "We are made in the world's image." > [SPK] This is reflected in the Anthropy definition I gave above. But it seems that this is not sufficient for a model of observers. I suspect that we need to figure out how to define the mapping functions and their inverses between the Boolean representations of the particular observations of an arbitrary observer and the QM versions. I suspect that the work of Karl Svozil, et al, (http://tph.tuwien.ac.at/~svozil/ ) and Chris Isham, et al, (http://www.mmsysgrp.com/QuantumGravity/topos.htm ) on Kochen-Specker might be a good start. But, all that aside, I favor Hitoshi Kitada's formulation of QM systems to ground the notion of an observer. See: http://www.kitada.com/ Kindest regards, Stephen