Hi Bruno, John, Liz, and everyone:
Bruno:
Your comments helped me to refine my thoughts about my model and the model
itself.
See below.
Thank you.
I believe my model as clarified below has convinced me that Comp to the
degree I may understand it and to the degree it is “machine” is at least
one component of a correct and complete description of our observer
experience. This because I believe it to be a different expression part of
if not all of my approach. There may be other components but this may be
TBD.
On 01 Apr 2014, at 01:48, Hal Ruhl wrote:
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?
-----------
*I am not very strong on computer science but just an MSEE minted in 60’s,
however I think my answer would be a qualified yes with the following
qualifications:*
*a) I take your “predicate” to be the subject number itself.*
*b) The program for the machine is in that number.*
*c) The rest of the number is the data for the machine.*
*d) Not all numbers, such as maybe zero, can be distinctions since they
encode an incomplete machine and or incomplete data.*
-----------
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).
--------
*By definition “ii” regarding “divisors” I merely give a relevant short
name to a subset of numbers.*
*Also by “ii” some divisors contain zero distinctions [the “N”s by
definition “iii”] but nevertheless can contain numbers that contain
incomplete code. *
*Further some divisors can contain numbers that are distinctions and some
that are not because such numbers encode incomplete machines or data or
both.*
*Notes:*
*I need to clarify definition “ii” per the underlined words above*
*Here I have tried to structure the clarifications so that there is no need
to resort to a machine that is external to a divisor.*
--------
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,
--------------
*I am not sure I understand. Some numbers [+integers] are excluded from
being distinctions in the above because they contain incomplete codes. *
*However the full set of distinctions [call it “d”] should still be [I
think] a countable infinite set of integers. *
*Divisors include all subsets of the set {“d” Union [the set of all
integers that are not distinctions - call this set “I”]}*
* This I think makes “A” - the set of all divisors - an uncountable
infinite powerset of {“d” U “I”}. So by your comment I think both {“d” U
“I”} and “A” are computable (perhaps some with the aid of a random oracle.
*
--------------
by accepting that some code will not output any answer for some predicate
("distinction")
---------------
*I think the above covers that.*
--------------
No machine can distinct the totally distinguishable from the non
distinguishable.
--------------------------------------
*I do not think this applies, but I think my clarifications may help
decide the issue.*
*Many incomplete codings [machine, data or both] should produce output
which is at least partly a guess on some of the incomplete coding [output
of a random oracle]. I would identify this as the transition from an
incomplete divisor [a universe state by assumption A2] to a successor
divisor [universe state] which itself may be incomplete – a trace in “A” is
started, continued or terminated [on a complete divisor]. *
--------------
Since I think any number can be 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.
---------------
*See the clarification of “Divisor” above.*
----------------
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).
--------------
*See my last comment below.*
--------------
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.
------------------
*Well I do think I have built a machine out of numbers alone.*
*Thanks *
*For a rather long time I have commented that I thought we were on or
nearly on the same page.*
--------------------------------------------------------------------------------------------------------------
John:
*1) Assumption # A1: There exists a set consisting of all possible
divisors. Call this set “A”.*
*“A” encompasses every distinction.*
Possible as per what? our present inventory of knowledge, or including what
we would deem impossible today? How about the presently unknown/unknowable
but included into "Everything" (A?) as additional items, qualia, functions
and divisors we have not the faintest idea about in today's inventory of
our knowledge?
---------------------------
*Given my comments above I intend to remove the word “possible” from this
sentence.*
*Thanks*
------------------------------
Liz:
Could you perhaps give some examples of how your model works?
-----------------------
*I hope the above helps.*
As to my comments on life I was looking for an explanation for why the
numerous warnings regarding the nature of the current course of human
civilization produced so little response.
I was not looking for new revelations about life but looked for an answer
to the question in the common physics of the issue.
I concluded that life [except for a few behavioral outliers] will never
depart from the path dictated by its origins as I saw them – namely being a
cog in the machine [see above] component that increases entropy.
To comment please read my post at
*http://arobustfuturehistory.wordpress.com/*<http://arobustfuturehistory.wordpress.com/>
Thanks to all
Hal Ruhl
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