Hi Hal,
On 01 Apr 2014, at 01:48, Hal Ruhl wrote:
Hi Bruno:
Reintroducing some mathematical terms to my model:
A distinction is a description of a boundary between two things see
definition "i". As a description it is a number - I suppose [a
positive integer ?].
Do you mean the code of a program computing a predicate P(x), that is
a function from N to {0, 1}, so that some digital machine can
distinguish if some number, of finite input, verifies or not that
property?
This makes a divisor - a collection of distinctions by definition
"ii" - a collection of numbers.
Why use "divisor", where "x is divisor of y" already means Ez(z*x =
y), (i.e. it exists a number z such that z times x is equal to y).
The collection of numbers (codes of the total computable predicates)
will not be a computable set of numbers, but you can compute a
superset of them, by accepting that some code will not output any
answer for some predicate ("distinction")
No machine can distinct the totally distinguishable from the non
distinguishable.
Since I think any number can be a description and thus a member of a
divisor, "A" since it contains all divisors by assumption A1
contains all numbers. I consider "A" to be the Everything.
It works with the superset above. I think. As you are a bit unclear, I
take the opportunity to understand you in the frame which makes
already some sense to me (mainly the mechanist hypothesis).
To get a dynamic in the "A" - one of my personal goals - I point to
the incompleteness of a subset of divisors.
A universe [see assumption A2] needs to answer all meaningful
questions relevant to it, so it must eventually become complete in
this sense.
Thus a trace from state to state is created within "A" for each
universe. The trace eventually ends on a complete divisor.
I see "A" and its traces as a UD.
It is, if you take the superset above. If you take only the total
predicates, you get a sort of "god", which means a non Turing emulable
entity. This one is not even emulable with the halting oracle. But the
UD makes clear we don't have to assume it in the ontology once we
assume mechanism.
As for the issue of the nature of life please see my draft at:
http://arobustfuturehistory.wordpress.com/
It is a pleasure to converse with you again.
Thanks, you are welcome back,
Bruno
On Monday, March 31, 2014 4:12:08 AM UTC-4, Bruno Marchal wrote:
Hi Hal,
I read and try to understand. I am not sure life is inherently self-
destructive. It is more inherently self-replacing.
Can you define the A of your assumption more specifically? Your
notion of divisors is quite vague for me.
Best,
Bruno
On 31 Mar 2014, at 01:21, Hal Ruhl wrote:
Hi everyone:
I am currently interested in two questions:
Does my model of why there are dynamic universes within the
Everything [latest version is below] include Bruno's Comp? Hi Bruno.
If life is inherently self destructive under any reasonable
definition of life [see some of my recent posts], then how does
this impact the Everything since I see it as a restriction
[selection] on the scope of possible universes?
Comments welcome.
Thanks
Hal Ruhl
DEFINITIONS:
i) Distinction:
That which enables a separation such as a particular red from other
colors.
ii) Devisor:
That which encloses a quantity [zero to every] of distinctions.
[Some divisors are thus collections of divisors.]
iii): Define "N"s as those divisors that enclose zero
distinction. Call them Nothing(s).
iv): Define "S"s as divisors that enclose a non zero number of
distinctions but not all distinctions. Call them Something(s).
MODEL:
1) Assumption # A1: There exists a set consisting of all possible
divisors. Call this set "A".
"A" encompasses every distinction. "A" is thus itself a divisor by
definition (i) and therefore contains itself an unbounded number of
times ["A" contains "A" which contains "A" and so on.
2) 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.
3) At least one divisor type - the "N"s, by definition (iii),
enclose no such distinction but by (2) they must enclose this one.
This is a type of incompleteness. [A complete divisor can answer
any self meaningful question but not necessarily consistently i.e.
sometimes one way sometimes another] 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 stability
distinction. They thereby transition into "S"s.
4) By (3) Transitions between divisors exist.
5) Some of the "S"s resulting from "N"s [see (3)] may themselves be
incomplete in a similar manner but perhaps in a different
distinction family. They must evolve - via similar incompleteness
driven transitions - until "complete" in the sense of (3).
6) Assumption # A2: Each element of "A" is a universe state.
7) The result is a "flow" of "S"s most of which are encompassing
more and more distinction with each transition.
8) 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.
9) Our Universe's evolution would be one such path on which the "S"
constantly gets larger.
10) Since incompleteness can have multiple resolutions the path of
an evolving "S" may split into multiple paths at any transition.
11) A path may also originate on an incomplete "S" not just the "N"s.
12) Observer constructs such as life entities and likely all other
constructs imbedded in a universe bear witness to the transitions.
13) Transition paths ["traces" may be a better term] can be of any
length.
14) A particular transition may not resolve any incompleteness of
the subject evolving "S".
15) White Rabbits: Since many elements of "A" are very large, large
transitions could become infrequent on a long path [trace] whereon
the particular "S" itself gets large. (Also few White Rabbits if
both sides of the divisors on either side of the transition are
sufficiently similar in size).
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