I thank everyone again for their questions. Below is a new accumulated and
corrected statement of my approach for easy reference.
POSTULATE:
All counting numbers exist with countably infinite copies in a seething
foamy fractal.
Call this fractal Everything.
In this fractal every universe Uj is isomorphic to a non deterministicly
self sorting sequence Uj(i) of these numbers that, upon chance encounters
between numbers, they self sort according to:
1) pj(i) = {Rj(pj(i - 1)) + PLj(i)} is the compressed form of Uj(i).
where Rj(pj(i - 1)) is the fixed rule set of a particular universe acting
on the previous Uj(i) and the underlying FAS structure is:
a) It has a single axiom unique to a particular family of universes which
is in pj(1), it serves as pj(0) and initiates the recursion.
b) It has a fixed set of rules = Rj
c) It has an alphabet = differently sequenced strings of bits I call types
of "regions". Each region type is isomorphic to a physical structure that
has existence such that the location of a discrete space point inside a
small fixed portion of a grid is coded by each region type. [In our case I
believe the grid to be 3D and most likely Face Centered Cubic.] The axiom
contains the entire initial alphabet for a particular universe.
Uj(i) contains a theorem of this FAS giving a specific arrangement of
regions - a configuration of a particular universe.
2) Uj(i) grows in length [number of bits] randomly to avoid Chaitin's limit
on how much information you can put into an N-bit number. Since pj(i) can
not yield pj(i) unless pj(i -1) is empty and each pj(i) is clearly longer
than pj(i - 1) the sequence can not stop on a finite number. To sustain
this growth in complexity of Uj(i) the FAS - again as per Chaitin - must
also increase in complexity - randomly adding additional alphabet elements
- new types of regions.
3) When Uj(i) gets to have a countably infinite number of bits the sequence
ends. From Turing [limits to FAS size] and Hilbert [Mathematical
existence]- See Tegmark Section II.
The numbers in the fractal non deterministicly self sort upon encounters
because of (2) and Uj(i -1) contains Rj and recognizes any PLj(i) suitably
higher valued than its own PLj(i -1) - i.e. Uj(i -1) picks the first good
number it encounters out of a countably infinite set of potential successors.
(2) and (3) may not be independent of (1).
The fractal contains all universes potentially an infinite number of times.
Alternate beginning: No numbers exist. This is unstable logically. It
contains no answer to its own stability. It decays into the above fractal
which is sufficient to contain the answer.
Once Nothing becomes Everything to answer its own stability, the question
of the stability of Nothing is no longer meaningful to Everything neither
is "Nothing?" itself, so Everything is now stuck as Everything.
What I just wrote down is just spontaneous self replication with mutation,
in another word Life - it is a potential in every universe.
Additional considerations and comments:
First Person:
My equation is life. Each universe is an "I". Some sub strings of a
universe's Uj(i) may carry the illusion of an individual "I". See also
Tegmark, footnote # 2 - each of my universes is its own SAS.
Nothing:
My point in having an alternate initiation, as I have said many times, is a
logical one - you can not prove a postulate. In this case - if we have
arrived at the correct conclusion - Everything exists - [or at least
someone's concept of Everything] there must be more than one postulate that
results in the same conclusion. Neither will have an argument that can
exclude the other otherwise it amounts to a proof. This seems only straight
forward.
Deterministic vs non deterministic:
Please note that my equation is piecewise computational. Each
computational run in Uj(i) is separated from another by non deterministic
jumps. In a way it unifies both views.
Note:
My fractal:
My fractal is more than the usual description of "Everything" that I have
seen. It has no selection at all up to the Hilbert/Turing limit [Which copy
of all copies would a person select to form the usual version of the "All
strings exist." approach?], and it is dynamic in the sense that it is
overall not deterministic from the point of view of a particular "I" - a
particular Uj(i). This "I" is not a selection either since there would be a
countable infinity of identical "I"'s and so too for the sub string
illusions of "I". Each string at a given "i" has a fixed history, but an
uncertain future. Each universe "j" has no interaction with another.
As to not going to a continuum in my fractal I do not see how that can
satisfy Hilbert - i.e. consistency - given Turing - i.e. no proofs beyond a
countably infinite number. In my opinion consistency has no application
beyond Turing's limit to "proof".
A suitable metaphor for my equation.
Think of a very tall highly branched bush.
On the lower levels ants wink into existence and start climbing the bush.
At each junction of the bush an ant must select a single up-going branch.
At each selection the ant morphs - grows more hair or something.
When the ant gets to the top it winks out.
Wherever the ant goes on the bush there are ants ahead of it and ants
behind it.
There is a countably infinite number of kinds of bushes each with a
countably infinite number of copies each with a countably infinite number
of ants.
Individual ants randomly jump to other bush types that are identical to
their current bush below their current position but differ above.
When it comes to no selection you have to get serious.
The remarkable thing is there is an equation for it.
How I see "regions" making up our particular universe can be found in my
papers posted at:
http://www.connix.com/~hjr/model01.html
though the current version needs much work to inject the above much neater
version of my core model.
Hal
Received on Fri Nov 24 2000 - 17:13:16 PST