Stephen P. King (stephenk1@home.com)
Sat, 17 Apr 1999 09:55:02 -0400
Dear Hitoshi,
I forgot something. The following should read in my last post to you:
I am reading Brown & Harre's "Philosophical Foundations of Quantum Field
Theory", it is very interesting. I see Cau's discussion of Gauge
theory... very helpful, but that strange notion I have of gauge
covariance is still there: "[Weyl's theory implies] ... spectral lines
with definite frequencies do not exist" This cries
out to me! What does "definite" mean? Is this not a term with meaning
that is implicit only in finite observation and meaningless when related
to the Totality? Is it that easy to forget that the "in-itselfness" of
any aspect of U, be it any LS or U itself, is always unknowable, for it
is everything simultaneously. Why is there such a need for the thought
what one person observes to be imposed on *all possible* observers? Are
we not "alone" in our minds, and thus our particular observations need
not be identical to all other's? Is it not sufficient that a small
finite subset of the totality be capable of being communicated about in
order to construct a translational bridge connecting one observer's
precepts and those of another?
I have this beautiful picture of spheres within spheres, each finite on
the outside and infinite on the inside; but I am afraid that I am a poet
trying to talk mathematics to physicists. If you only understood the
concept of "bisimulation". Please, Hitoshi, I beg you, read Peter's
paper http://www.cs.brown.edu/~pw/papers/math1.ps. Think of how an LS is
a computational system or an agent. An LS is a "black box" to any other
LS! How do they model each other's internal behavior?
"Bisimulation"!!!!! The act of communicating is the indefinite
connection; it is *not* a priori!
The key idea is how an LS "approximates" certainty, this is an
interactive computation! Remember your mention of how numbers are
constructed from 'nothingness' [time 231]? What is important is the
boundary separating one aspect from the other, the Cut. I am asking for
attention to *how it is that completion is reached*; how do we
"complete" the "natural numbers, we assume 0 (zero) is defined as an
empty set, and define 1 as {0}, 2 as {0,1}, 3 as {0,1,2}, ...," to get
the Reals? Let us think of Cantor's diagonalization (which ironically is
also Goedel's tool!) as the method of completing -think "computing!"-
them. I see that this completion is an aspect of Time! "Everything can
not happen simultaneously" This is obvious!
I understand that I am making noise from the point of view of an
observer that only can only see crisply defined symbol structures! :(
But the symbols are post hoc (after the fact) to the idea!
One final poetic question: Can we think of a "boundary" as an
equivalence class of mappings?
I have to go to work now. :(
Onward!
Stephen
This archive was generated by hypermail 2.0b3 on Sun Oct 17 1999 - 22:31:52 JST