RE "One page" revisited again

From: H J Ruhl <HalRuhl.domain.name.hidden>
Date: Mon, 22 Oct 2001 21:10:58 -0700

Please allow me to try this one more time since I think I see why it did
not make it into the posted archive and I have a change to my additional
comment.

In #10 I discuss the length of the descriptive string. A better way to
state what is said there may be to indicate that I am only interested in
the structure of the finite prefix of what might be an infinite
string. The infinite tail if there is one is "invaded" for lack of a
better term as the length of the prefix increases until the prefix is
itself infinite.



This is an improved presentation of my current TOE model. Its a bit more
than one page.

I believe I see some shadow of both Juergen's approach and Bruno's approach
in it. The intermediate step has unfinished business and the lowest level
is a bit like a duplicator, transporter.


1) The single postulate is "The total system contains no information."

2) Two distinct expressions of "no information" are recognized by the model:

         a) The "Nothing" which is devoid of any information whatsoever.

         b) The "Everything" which contains all information.

      These are not identical. Rather they are antipodal in that neither
      can contain the other because of a stability issue.

3) The stability issue is the unavoidable emergence of a question of the
stability of the manifestation of either of these expressions of "no
information" should either actually become manifest. This manifestation
must either be stable or not with respect to the alternate expressions of
"no information". Thus the alternate expression must be separately
available for manifestation and the stability question must have a resolution.

4) If either expression of "No information" becomes manifest then the
resolution of the stability question represents information and violates
the postulate.

5) A way to make the total system comply with the postulate:

     a) Both the "Nothing" and the "Everything" are in a simultaneous
         partial manifestation.

      b) To avoid any information including any permanent selection in this
system
          and thus comply with the postulate the partial manifestation of
          the "Everything" is realized by the actual but temporary
          manifestation of randomly selected pieces of the "Everything" herein
          called patterns each of which has a manifestation of random duration.

6) Evolving universes are successive isomorphisms to some portion of those
patterns with overlapping manifestations.

7) Enduring evolving universes with fully deterministic rules of
isomorphism succession find no home in this model because they would find
no sustainable state to state trajectory within the random nature of the
partial manifestation of the "Everything". The rules of an enduring
universe must be partly true noise.

8) The cascade representation for state Sj(i + 1) of universe j while in
state Sj(i) is:

     (1) P'j(i + 1) = {R'j(i)[Pj(i)]} determines the group of pairs:

                          {R'jk(i + 1),Sjk(i + 1)}; k = 1 to sj(i).

Where: Pj(i) is the shortest self delimiting program that computes Sj(i).
             R'j(i) is the current full set of rules that act on the
current state
                    [represented in its compressed condition].
             sj(i) is the number of acceptable successor {rule set, state}
pairs to
                   Sj(i) due to the true noise content of R'j(i).

Pj(i) contains Rj(i) which is a deterministic derivative of R'j(i - 1) used
only to allow the compression of the data in Sj(i) and a self delimiter DeL(i).

R'j(i) is the full and partially non deterministic true noise containing
successor to R'j(i - 1).

9) The first of the {R'jk(i + 1), Sjk(i + 1)} pairs to be represented in a
sub section of one of the manifest patterns becomes the next state and its
rules [isomorphic link] of universe j as the pattern supporting the current
link loses its own manifestation.

Once this happens the precursor program P'(i + 1) is replaced with Pj(i +
1) and the applicable Sjk(i + 1) becomes Sj(i + 1). So we get:

      (2) Pj(i + 1) = {Rj(i + 1)[P(i)] + DeL(i + 1)} computes Sj(i + 1).

So operating on this with R'j(i + 1) in a manner similar to (1) gives the
next iteration to the cascade:

      (3) P'j(i + 2) = {R'j(i + 1)[Pj(i + 1)} determines the group of
pairs

                          {R'jk(i + 2),Sjk(i + 2)}; k = 1 to sj(i + 1).

and so on.

10) The model's focus on the use of a discrete point space for a universe
is due to:

      a) Notice that each successive Pj() is longer than its predecessor if
Rj() does
          not decrease in length and ultimately any such shortening of Rj()
will be
          swamped out. Over the long haul then Pj() increases in length.

      b) As the length of Pj() increases the length of the string it
computes and
          which represents Sj() must increase in length [perhaps not always
          synchronized with length changes in Pj()] if it is to maintain a
degree
          of internal correlation - an aspect which is considered necessary to
          support SAS - but nevertheless contain more complexity.

      c) Finite strings can easily increase in length by adding short strings.

Thus the string is considered finite and must describe the location of
points within any space on a grid with finite pitch.

The possibility of infinitely long highly correlated tails on the strings
that are skipped by the rules of succession is considered an unnecessary
entity.

11) Exploring the dynamics of (1), (2), and (3) is most interesting and
will be covered in later posts.

12) The most interesting space so far explored is face centered cubic.


Hal
Received on Mon Oct 22 2001 - 18:17:38 PDT