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

*Mon, 16 Aug 1999 14:04:49 -0400*

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Dear Matti and Friends,

Did you read the whole paper? Do you understand what Calude's

"Lexicons" are?

Matti Pitkanen wrote:

*>
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*> On Mon, 16 Aug 1999, Stephen P. King wrote:
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*>
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*> > Dear Matti,
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*> >
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*> > Please read this paper!
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*> >
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*> > http://www.cs.auckland.ac.nz/CDMTCS//researchreports/089walter.pdf
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*>
*

*> The paper seems that it is about Zeno paradox. I think
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*> that I have read some popular article about solution of Zeno paradox
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*> in terms of infitesimal numbers for year or so ago.
*

Zeno's paradox is the framing of the problem... I am not saying that I

agree with Calude's conclusion, I am just pointing it out. I have a

surprise, but you need to understand What Dr. Meyerstein is saying about

Chris Calude's result to understand a notion that I have been working on

for a very long time! :-)

*> The introduction of infinite primes forces automatically also the
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*> introduction of infinitesimals. All predictions of the
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*> p-adicized quantum TGD for infinite p:s would be series containing also
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*> powers of infinitesimals and only the finite part is interesting from our
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*> point of view: two lowest orders in pinary expansion would give the exact
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*> result.
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What are the axioms that define infinite primes? Can we think of them

as additional postulates for the set theory (Frakel-Zernelo (spelling?))

theory?

*> It seems that the testing of our theories with accuracy of
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*> infinitesimals is a rather remote possibility: and perhaps un-necessary:
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*> we cannot even agree on basic philosophy! Perhaps those God like
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*> creatures in the hierarchy of selves, which are labelled by infinite
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*> primes, are busily constructing physical models in accuracy
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*> O((1/infinite P)^n) and performing the needed high resolution
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*> experimentation and reporting various errors using infinitesimals(;-).
*

What space-time do you think that these creatures exist "in" or do

they, as I suggest, generate their space-times by the very act of

constructing models and performing experiments? What determines the

material structure of the "matter" (and energy) involved? Remember, a

space-time is, literally, an empty and meaningless notion independent of

Local Systems or observer! [quotes are from the paper]

The "lexicon" numbers "Any $finite$ sequence can be unambiguously

coded in binary (or decimal) and thus corresponds exactly to some

rational number"... "on the other hand, real numbers are infinite

sequences of digits (in whatever chosen code or $base$)" "Is there a

real number that with certainty contains the word w? ... Yes ... and

there exists a real number that contains $every possible "word"$. That

is, that contains $everything that can be explicitly stated, coded,

communicated$. ... It can be shown that this special number not only

contains, by construction, every possible finite linear sequence, say

William Shakespeare's complete works, but also that it contains every

possible linear sequence $infinitelt many times$!"

Calude and Zamfirescu have shown that there "exist real numbers that

represent this remarkable property $independent of the employed code or

alphabet$ (binary, decimal, or, for instance, all the symbols on a

computer keyboard). These are the Lexicons. ... The amazing result is:

almost every real number is, both geometrically and

measure-theoretically, a Lexicon! In particular, if you put al the reals

in an urn, and blindly pick one, with almost certainty it will be a

Lexicon."

I see these Lexicons as encoding descriptions of material systems, e.g.

what Local Systems "observe", to be specific! The trick I see is that if

we consider that for every finite sequence there exists a configuration

of matter (in a finitely bounded or closed space-time!) such that the

finite sequence or "word" describes it, given some code or base.

We then ask: By what procedure are "configurations of matter" matched

up with "words" such that their "meaning" can be communicated and

decoded by another LS?

Let us take a long hard look at what Pratt is telling us!

Onward!

Stephen

**Next message:**Stephen P. King: "[time 555] Re: [time 554] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"**Previous message:**Matti Pitkanen: "[time 553] Re: [time 535]Modeling change with nonstandard numbers"**In reply to:**Stephen P. King: "[time 551] Re: [time 535]Modeling change with nonstandard numbers"**Next in thread:**Matti Pitkanen: "[time 557] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"

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