Patterns, Biology & Everything

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Wed, 13 Dec 2000 19:34:53 -0800

I hope this fixes the mailer coding errors.

The following is a improved incorporation of the idea of "patterns" into
the existing approach of my model. The result looks even more like biology.

-------------------------------

In concert with an "Everything" style TOE this work is an effort to show
that our particular physical universe [universe "j" out of the countably
infinite many in an Everything I call a Superverse S] can be modeled as
being a compound object Uj [bold italic] consisting of Uj [bold no italic]
discrete sub objects u [bold] that are actually isolated points that form
the spatial component of its discrete space-time. The "time" dimension is
subjective to the particular universe. Each successive configuration [its
geometric pattern] of this universe is isomorphic to a finite length string
of bits Uj(i) which is an expression of a particular "nested" N-bit,
finite, consistent Formal Axiomatic System [N-bit, fc-FAS]. By "nested" I
mean that the FAS is contained within the strings Uj(i) in a manner not
unlike the way some researchers consider all the information necessary to
express DNA is in the DNA. As I see it DNA knows the necessary external
chemistry in a manner similar to the way we are trying to "know"
the Everything".

I build this discrete universe Uj [bold italic] while incorporating a
method for avoiding the construction of an automaton. This is a way of
inducing something like Schmidhuber's "noise" into the system.


                                       TOE SUMMARY:

My model is based essentially on just the following:

1) N-bit binary strings are viable representations of "suitable pieces"
that help form a suitable Everything.

2) To avoid a static "selected" Everything the "suitable pieces" circulate
at random within the Everything.

3) While circulating the "suitable pieces" can associate into sequences
according to fixed rules of membership internal to that sequence.

4) The rules can have a non deterministic content. This is not a
probability distribution, but rather a random encounter with a viable
successor that then joins the sequence. The rules define the family of
viable successors with a procedure that can be partially "do not
care". They say nothing further as to the chance of encountering a
particular one. Due to the structure of the Superverse S the chance of
encountering a given pattern is equal for all patterns. This is the source
of the "noise" content of the sequencing.

5) Some "suitable pieces" are actually "states of universes".

6) Some rules sequence "states of universes" into "suitable cascades".

7) "Suitable cascades" can not stop while isomorphic to a finite N-bit
binary string.

8) "States of universes" that can have a valid successor in "suitable
cascades" are isomorphic to finite N-bit binary strings.

9) Chaitin's incompleteness.

10) There are only 2^N N-bit strings.

11) Our universe is a "suitable cascade".

12) Our universe is one whose rules are partially non deterministic.

13) I prefer to call the "suitable pieces" "patterns" to avoid confusion
with "number" and "string" and most importantly because I currently believe
"pattern" to be the correct concept as a component of the Everything.

Definitions:

14) Pattern: A pattern is a geometric structure that could vary in at least
one characteristic from location to location within the pattern. Patterns
must be at least a set of more than two zero dimensional points.

I propose that a given state of a physical universe can be precisely a
pattern consisting of such a set of zero dimensional points. The varying
characteristic in this case is the relative spacing of the points from
location to location within a pattern.

The entire process is not unlike the replication of DNA in a soup of amino
acids with mutation. The strand being copied is the current state and the
soup of amino acids is a little like the circulating collection of viable
successors.

Hal
Received on Wed Dec 13 2000 - 16:50:30 PST