# RE: The limit of all computations

```Hi Everyone:

Unfortunately I have been unable to support a post reading/creation activity
on this list for a long time.```
```
I had started this post as a comment to one of Russell's responses [Hi
Russell] to a post by Stephen [Hi Stephen].

I have a model (considerably revised here) that I have been developing for a
long time and was going to use it to support my comments.   However, the
post evolved.

Note:
The next most recent version of the following model was posted to the list
on Friday, December 26, 2008 @ 9:28 PM as far as I can reconstruct events.

A brief model of - well - Everything

SOME DEFINITIONS:

i) Distinction:

That which enables a separation such as a particular red from other colors.

ii) Devisor:

That which encloses a quantity [none to every] of distinctions. [Some
divisors are thus collections of divisors.]

MODEL:

1) Assumption # A1: There exists a set consisting of all possible divisors.
Call this set "A" [for All].

"A" encompasses every distinction. "A" is thus itself a divisor by (i) and
therefore contains itself an unbounded number of times.

2) Definition (iii): Define "N"s as those divisors that enclose zero
distinction.  Call them Nothings.

3) Definition (iv): Define "S"s as divisors that enclose non zero
distinction but not all distinction.  Call them Somethings.

4) An issue that arises is whether or not an individual specific divisor is
static or dynamic. That is: Is its quantity of distinction subject to
change? It cannot be both.

This requires that all divisors individually enclose the self referential
distinction of being static or dynamic.

5) At least one divisor type - the "N"s, by definition (iii), enclose no
such distinction but must enclose this one.  This is a type of
incompleteness.  That is the "N"s cannot answer this question which is
nevertheless meaningful to them.  [The incompleteness is taken to be rather
similar functionally to the incompleteness of some mathematical Formal
Axiomatic Systems - See Godel.]

The "N" are thus unstable with respect to their initial condition.  They
each must at some point spontaneously enclose this static or dynamic
distinction.  They thereby transition into "S"s.

6) By (4) and (5) Transitions exist.

7) Some of these "S"s may themselves be incomplete in a similar manner but
in a different distinction family.  They must evolve - via similar
incompleteness driven transitions - until "complete" in the sense of (5).

8) Assumption # A2: Each element of "A" is a universe state.

9) The result is a "flow" of "S"s that are encompassing more and more
distinction with each transition.

10) This "flow" is a multiplicity of paths of successions of transitions
from element to element of the All.  That is (by A2) a transition from a
universe state to a successor universe state.

Consequences:

a) Our Universe's evolution would be one such path on which the "S" has
constantly gotten larger.

b) Since a particular incompleteness can have multiple resolutions, the path
of an evolving "S" may split into multiple paths at any transition.

c) A path may also originate on any incomplete "S" not just the "N"s.

d) Observer constructs such as life entities and likely all other constructs
imbedded in a universe bear witness to the transitions via morphing.

e) Paths can be of any length.

f) Since many elements of "A" are very large, large transitions could become
infrequent on a long path where the particular "S" gets very large.  (Few
White Rabbits if both sides of the transition are sufficiently similar).

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

So far I see no "computation" in my model.

However, as I prepared the post and did more reading of recent posts and
thinking I found that I could add one more requirement to the model and thus
make it contain [but not be limited to] comp as far as I can tell:

Add to the end of (5):

Any transition must resolve at least one incompleteness in the relevant "S".
Equate some  fraction of the incompleteness of SOME relevant "S"s to a
snapshot of a computation(s) that has(have) not halted.

The transition path of such an "S" must include (but not limited to)
transitions to a next state containing the next step of at least one such
computation.

Thus I see the model as containing, but not limited to, comp.

Well, the model is still a work in progress.

Hal Ruhl

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