Patterns, Biology & Everything

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Wed, 13 Dec 2000 17:55:38 -0800

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.

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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 consisting of Uj discrete sub objects u 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 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 - 15:08:33 PST