**Stephen P. King** (*stephenk1@home.com*)

*Mon, 30 Aug 1999 09:12:17 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 645] Re: [time 644] Re: [time 636] Worlds as Lexicon -> Possible Worlds of Kripke structure?"**Previous message:**Hitoshi Kitada: "[time 643] Re: [time 640] Quotes from the Tao Te Ching"**In reply to:**WDEshleman@aol.com: "[time 640] Quotes from the Tao Te Ching"**Next in thread:**Stephen P. King: "[time 645] Re: [time 644] Re: [time 636] Worlds as Lexicon -> Possible Worlds of Kripke structure?"

Dear Bill,

I have been thinking hard about your ideas! It occurred to me that you

may be really on to something. I am sorry to hear of Paul's plight. :-(

I do not earn a living from my philosophizing so I can risk being a

heretic, but we must remember Bruno!

WDEshleman@aol.com wrote:

*>
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*> In a message dated 8/25/99 8:01:08 PM Eastern Daylight Time,
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*> stephenk1@home.com writes:
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*>
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*> > Are "close copies" a minority or majority? Well, there measure
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*> > theoretic properties of real valued labeled worlds is "measure one", in
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*> > other words it is certain that if we picked a pair of worlds out of an
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*> > urn that they would look almost alike! The article by F.W. Meyerstein
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*> > (http://www.cs.auckland.ac.nz/CDMTCS//researchreports/089walter.pdf) is
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*> > a good discussion of this!
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*> >
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*> Stephen,
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*> I have read the paper now; I sure like short papers. At first, one may
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*> think that infinite sums are Lexicons, then it becomes apparent that
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*> infinite sums of infinite sums are really the Lexicons; that is if each
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*> inner sum represents the same information as the outer sum.
*

I like them little papers too, short and to the point...

We could discover if this were true if we could compare the two sums to

each other, but simple isomorphism would not work since it is blind to

ordering. Umm, this looks like it requires cohomorphism testing, which

tests the topology to see if it is simply or multiply connected. The

former shows that the space of points (= sums) is commutative and has

"no holes" and the latter is non-commutative, as if the space has knots

or wormholes in it. (Oh, BTW, Pratt has something about that in his

papers!)

Since I am trying to advance the idea that our individual realities

(read space-times) are constructions, it follow that the topology of

such follows from some aspect of the process. More on this later. For a

preview read:

http://math.ucr.edu/home/baez/week40.html

http://boole.stanford.edu/pub/ph94.ps.gz

http://boole.stanford.edu/pub/tppp.ps.gz

*> This is where infinite products surface (sums of sums are products).
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*> I had not thought of a product as a Lexicon, but it makes sense if
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*> a Lexicon must have near copies of itself coded into its parts.
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*> The infinite products of my study have parts (factors) that differ
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*> from the the total product only by very small amounts of information.
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Have you thought about how the concept of neighborhood could be defined

using infinite products? Since I see everything visually, this

immediately popped up. :-) I noticed that the notion that "infinite

products of my study have parts (factors) that differ from the the total

product only by very small amounts of information" would imply that

there is some variational principle derivable from the way that the

products differ in their information content. (I am seeing your ideas in

light of Pratt's!) Can we think of a metric (or ultrametric!) to measure

how far apart a pair of factors are?

*> I am interested to read some of your ideas on this Lexicon topic.
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*> To understand my approach to infinite products, all you need to
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*> know is some algebra, and simple rules of logarithms. What may
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*> appear as complex at first, is really quite simple in concept
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*> accessible (probably) to philosophers and high school kids too. :-)
*

I am thinking of how the lexicons relate to states of Mind qua

information structures and how causality is defined in a "branching

time" or "lazy binding" way. This is important as it allows for

observers to "chance their mind", which I will argue is necessary and

sufficient to allow free will.

Pratt says in ratmech.ps pg.9 paragraph 8: "...we find that two events

or two states ... communicate with each other by interrogating all

entities [read worlds!] of the opposite type. Thus event a deduces that

it precedes event b not by broaching the matter with b directly, but

instead by consulting the record of every state to see if there is any

state volunteering a counterexample [a contrafactual of "has this been

experienced before"?]. When none is found, the precedence is

established. Conversely, when a Chu space is in state x and desires to

pass to state y, it inquires as to whether this would undo any event

that has already occurred. If not then the transition is allowed."

Note the phrase "communicate with each other by interrogating all

entities of the opposite type". I added the "[other worlds]" since I am

trying to point out how causality is an active process and it is

necessary to consider all possible variations when considering even the

simple process of motion! In your thinking, Bill, what do you see as the

role or purpose of the infinite products?

You make a good point about "keep it simple!" :-)

Onward,

Stephen

**Next message:**Stephen P. King: "[time 645] Re: [time 644] Re: [time 636] Worlds as Lexicon -> Possible Worlds of Kripke structure?"**Previous message:**Hitoshi Kitada: "[time 643] Re: [time 640] Quotes from the Tao Te Ching"**In reply to:**WDEshleman@aol.com: "[time 640] Quotes from the Tao Te Ching"**Next in thread:**Stephen P. King: "[time 645] Re: [time 644] Re: [time 636] Worlds as Lexicon -> Possible Worlds of Kripke structure?"

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