[time 555] Re: [time 554] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality

Stephen P. King (stephenk1@home.com)
Mon, 16 Aug 1999 14:30:46 -0400

Dear Youlian,

        Write now I only have a mere metaphor of an idea. I am trying to
understand if it is possible to create a consistent model of the world
(all that we can agree upon given a finite sequence of communications)
using Pratt's notions.
        I has thinking, as I hung out the laundry, where does the information
meet the matter in a Turing machine? At the reading head! What is
occuring in a read/write operation? Some matter is being changed, how?
In the instance of a read/write head and (paper) tape, the head/tape
alters its configuration. What is "really" going on?
        I am not a physicists, and have a very hard time writing explicit
equations that can be used to describe some event, so I ask for help!

Got to go. Camile, my baby needs me...



Youlian Troyanov wrote:
> Pretty close to Borges. I like your train of thought. Please elaborate
> on how you understand the Chu connection to the Lexicons.
> > > It seems that the testing of our theories with accuracy of
> > > infinitesimals is a rather remote possibility: and perhaps un-necessary:
> > > we cannot even agree on basic philosophy! Perhaps those God like
> > > creatures in the hierarchy of selves, which are labelled by infinite
> > > primes, are busily constructing physical models in accuracy
> > > O((1/infinite P)^n) and performing the needed high resolution
> > > 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
> >

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