HI Stephen

Stephen Paul King wrote:


Does computational complexity (such as NP-Completeness, etc.) and computational "power" requirements factor into the idea of simulated worlds?




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.



[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

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."



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"?



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.
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.


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.

George.



[SPK]


I am still struggling with my intuitions regarding how to think of the
liner superposition of QM states as "multiple worlds".


I also do not understand either the connection between the philosophical concept of the plenitude with the quantum idea of phase and conjugate quantities.

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?

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."


George





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