`Stephen Paul King wrote:`

Dear George,

Interleaving,

----- 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

U can find it here:

http://www.qubit.org/people/david/Articles/ItFromQubit.pdf

`Deutsch does not discuss the ordering issue. I haven't seen anyone discuss it, but I have not been reviewing much literature on the subject. No one in this group has tackled it to my knowledge. I think ordering in infinite sets is an essential component in the discussion of measure.`

I do not agree with David's arguements because of its appearent

physicalist assumptions

I agree with you

I agree with you

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]

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.

`"sufficient" implies "minimum," I think so you may delete minimum from the above sentence. I certainly believe the necessary condition - it is the anthropic principle. The "sufficient" condition appears to be some from of Occam razor condition. Together, they seem to relate to the mirror idea I discussed earlier. "Logically speaking, the world is a mirror of ourselves." However, what do you mean by observer and reality. I think we may have to restrict ourselves to the "logical" domain, not to specifics such as the earth has one moon, or the name of my cat is Sandy. On the other hand.... see below....`

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?

This relates to my relativistic point of view: observers sharing the same "frame or reference" experience the same objective reality. By frame of reference I mean logical model not specific mental states like "my name is George," and by objective reality I mean physical laws, not specific instances like "one moon."

This relates to my relativistic point of view: observers sharing the same "frame or reference" experience the same objective reality. By frame of reference I mean logical model not specific mental states like "my name is George," and by objective reality I mean physical laws, not specific instances like "one moon."

`Hmmm.... after some reflection I am now inclined to say that if two observers share the same logical model as well as the same particular mental states, then the objective reality should be the same both in physical laws and in physical instances. Well, I suppose the degree of divergence between two observers should be reflected by divergence in their physical reality.`

[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/

`This is a lot of homework.... I'll give it a shot.`

`George`