[time 540] Re: [time 536] Are numbers a matter of convenience?

Stephen P. King (stephenk1@home.com)
Fri, 13 Aug 1999 19:15:58 -0400

Dear Hitoshi,

Hitoshi Kitada wrote:
> Dear Stephen,
> ----- Original Message -----
> From: Stephen P. King <stephenk1@home.com>
> To: Matti Pitkanen <matpitka@pcu.helsinki.fi>; <time@kitada.com>
> Sent: Friday, August 13, 1999 4:23 PM
> Subject: [time 533] Re: [time 530] Surreal numbers
> > In Hitoshi's LS theory, the "outsides" of LS are "physical" and
> > the "insides" are "mental", I think!? We could categorize the
> > information involved in the external behavior of LS in the way you describe
> > here. :-)
> It is human's convenience to distinguish the outside and inside.
> Under this convenient method, the world (or the outside) might
> _look_ as following, e.g. pinary physics, even if it would decribe
> well the nature. But this is just a look! The primes are a notion
> very humanistic. How can one see the nature? Or How can one believe
> what he sees is what others see?
        It is said that physics is the correlation of observation with numbers
and the relationships thereof, so if the patterns of behavior that any
given observer perceives and represents with numerical relation
structure constitute a physics, we have to say that physics is
subjective. We can think of physics as "objective" only within the range
of behaviors that can be consistently communicated within a cluster of
observers that have similar enough "clockings" (Lance's term) (each Chu
space has its own time according to Pratt!). It then becomes possible to
consider what would happen if we could somehow alter the clocking
behavior of an LS!
        I agree that distinguishing the "inside" from the "outside" of an LS is
merely a conveniance, but I was writting a thought following the
description you gave in your papers of LSs. We say that LSs can only
observe the centers of mass of each other ("bodies"), this is an
"outside". It would follow that we would identify the "inside" of an LS
with the observer itself, specifically its mind. The act of
consciousness is a mapping between an internal and an external
configuration, just as the "meaning" of a symbol is given by an
identification between a physical configuration of ink or lit CTR
pixels, etc. and an information structure.
        The relationship between the two is most obvious in the context of
computers. Take for example a DVD movie; we see an obvious relationship
between the dynamics of the patterns on the monitor and the bits of
information that is encoded in the reflective spots on the DVD disk.
What I am thinking of when I say "information structure" is the logical
relational structure that denotes the entailments among the bits.
        How to explain the formal aspects given by the propagator of the
quantum mechanical system, is beyond by present ability. :-( I used to
have a paper that discussed the logical structures involved with QM
systems (I am looking frantically for it!), and am studying C. F. von
Weizacker's work about this. I hope that in the future we can look at
this more carefully! :-)
        Umm, Hitoshi, I do not understand exactly what you mean by "the primes
are a [very humanistic] notion..." :-( I can see that it is the human
ability to imagine situations that are different from those presented to
us by observations of "external" objects (e.g. imaginations) that is
involved in the very human fascination with numbering systems, but it
does seem that the property of whether a number is prime or not is
dependent only on the rules (grammar) of the numerical language.
Mathematics do seem to be as "objective" as mental objects can get
(other than Pratt's CABAs?!), and this "objectivity", while delimited by
our mutual agreement on the a set of mathematical rules, is "humanistic"
in that it is representative of the similarity of the clockings of
        You raise a question that I have been asking for a very long time! How
can we be sure that what one observer "sees" is identical to what
another "sees"? It seems that we only have the *possibility* of
agreement in communications between the observers, but it is easy to see
that this is contingent on the mutual consistency of logical structures
that each observer uses to represent their perceptions and this only
seems to be necessitated locally. I believe that the formal notions of
bisimulation and Chu spaces gives us a way to consistently model how it
is that we can form agreements in our observations of each other while
never really "touching" each other.


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