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

*Mon, 16 Aug 1999 14:30:46 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 556] Re: [time 553] Re: [time 535]Modeling change with nonstandard numbers"**Previous message:**Stephen P. King: "[time 554] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"**In reply to:**Matti Pitkanen: "[time 553] Re: [time 535]Modeling change with nonstandard numbers"

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...

Later,

Stephen

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.
*

snip

*> > > 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
*

*> >
*

**Next message:**Matti Pitkanen: "[time 556] Re: [time 553] Re: [time 535]Modeling change with nonstandard numbers"**Previous message:**Stephen P. King: "[time 554] Re: [time 553] Modeling change with nonstandard numbers & the Computation of Actuality"**In reply to:**Matti Pitkanen: "[time 553] Re: [time 535]Modeling change with nonstandard numbers"

*
This archive was generated by hypermail 2.0b3
on Sat Oct 16 1999 - 00:36:29 JST
*