Hi Stephen:
In response to your post I have revised my previous post.
I made division equal information and rewrote (1) and (2).
I replaced "meaningful" with "compulsatory" in various places at least for now.
The result is below.
As for associating randomness with creativity Russell argues this in
his book and I was showing that my model has randomness and thus was
not in conflict with his argument at least at this level.
As to degrees of incompleteness I do not see how this can be
routinely measured. Arithmetic may be known to be infinitely
incomplete but for other structures the resolution of an
incompleteness may lead to additional incompleteness.
1) Assume [A-Inf] - a complete, divisible ensemble of divisions.
{[A-Inf] contains itself.}
2) [N(i):E(i)] are two component divisions of [A-Inf] where i is an
index [as are j, k, p, r, t, v, and z below] and the N(i) are empty
of any [A-Inf] and the E(i) contain all of [A-Inf].
{i ranges from 1 to infinity}
3) S(j) are divisions of [A-Inf] that are not empty of [A-Inf].
{Somethings}
4) Q(k) are divisions of [A-Inf] that are not empty of [A-Inf].
{Questions}
5) cQ(p) intersect S(p).
{cQ(p) are compulsatory questions for S(p)}
6) ucQ(r) should intersect S(r) but do not, or should intersect N(r)
but can not.
{ucQ(r) are un-resolvable compulsatory questions}.
7) Duration is a ucQ(t) for N(t) and makes N(t) unstable so it
eventually spontaneously becomes S(t).
{This ucQ(t) bootstraps time.}
8) Duration can be a ucQ(v) for S(v) and if so makes S(v) unstable so
it eventually spontaneously becomes S(v+1)
{Progressive resolution of ucQ, evolution.}
9) S(v) can have a simultaneous multiplicity of ucQ(v).
{prediction}
10) S(v+1) is always greater than S(v) regarding its content of [A-Inf].
{progressive resolution of incompleteness} {Dark energy?} {evolution}
11) S(v+1) need not resolve [intersct with] all ucQ(v) of S(v) and
can have new ucQ(v+1).
{randomness, developing filters[also 8,9,10,11], creativity, that
is the unexpected, variation.}
12) S(z) can be divisible.
13) Some S(z) divisions can have observer properties [also S
itself??]: Aside from the above the the S(v) to S(v+1) transition can
include shifting intersections among S subdivisions that is
communication, and copying.
Perhaps one could call [A-Inf] All Information [all divisions].
Well its a first try.
Hal Ruhl
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