Re: Key Post 1, toward Church Thesis and Lobian machine
But thanks to that crashing, *Church thesis remains consistent*. I would just say An existence of a universal language is not ruled out. I am ok with you. Consistent (in math) means basically not rule out. Formally consistent means not formally ruled out, or not refutable. That is: Consistent(p) is the same as ~ Provable(~ p) ~ = negation like Provable(p) is equivalent with ~ Consistent( ~ p) All right... Now, let me just rephrase few points of the key post one more time. I will try to be picky with wording. Points which are not mentioned - I fill comfortable with. 1\ There is no language/algorithm/procedure/machine which can describe/execute all total computable functions. 2\ There exists non-empty set of all machine computable functions (inevitably includes both total and strict partial functions). Let us call this set MC (machine computable). 3\ Church himself *defined* the set of so-far-known-computable-functions as those computable by lambda calculus. 4\ What we use to call a *Church thesis* today says, that MC is in fact equal to the set of functions computable by lambda calculus. 5\ Church thesis is refutable. * * * Something else: to us verify MM = SII(SII) does crash the system: SII(SII) = I(SII)(I(SII)) = SII(SII) = I(SII)(I(SII)) = SII(SII) = I(SII)(I(SII)) = SII(SII) = I(SII)(I(SII)) = SII(SII) = ... (crashing). Working with SK combinators, I had a bit problems with omitted parenthesis. Also it was not clear to me what is the meaning of eg. (SKK) since S is expected to take three arguments. What helped me was the unlambda language (http://www.madore.org/~david/programs/unlambda/) So here is my crashing sequence (yep, yours is shorter) (I don't expand the I term to keep it short) SII(SI(S(KI)I)) a reference implementation in unlambda: ```sii``si``s`kii the ` stands for 'apply' operation, aka left parenthesis. with a small modification ```sii``si``s`k.ui we can achieve the computer to print u in an endless loop. .u is a special function with a side effect of printing the character u. Best, Mirek --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Properties of observers
Hal,
I lost you 2) - 13): I cannot squeeze the philosophical content into a
physicalist-logical formalism. The 'terms' are naturally vague to me,
cannot follow them 'ordered. The words in your perfect schematic are
(IMO) not adequate for the ideas they are supposed to express: our
language is inadequate for the (my?) advanced thinking.
I am for total interconnection, no separable divisions etc. Aspects,
no distinctions.
I am not ready to make a conventional scientific system out of the
inconventional. I am not an 'engineer': I am a dreamer.
Maybe if I learned your entire vocabulary?(I cannot - it
interferes with mine).
Thanks for your effort, it was counterproductive FOR ME.
I appreciate your way as your way.
John M
On Sat, Feb 9, 2008 at 10:55 PM, Hal Ruhl [EMAIL PROTECTED] wrote:
Hi John and Tom:
Below is a first try at a more precise expression of my current model.
1) Assume [A-Inf] - a complete, divisible ensemble of A-Inf that
contains its own divisions.
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].
{Therefore [A-Inf] is a member of itself, and 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) mQ(p) intersect S(p).
{mQ(p) are meaningful questions for S(p)}
6) umQ(r) should intersect S(r) but do not, or should intersect N(r)
but can not.
{umQ(r) are un-resolvable meaningful questions}.
7) Duration is a umQ(t) for N(t) and makes N(t) unstable so it
eventually spontaneously becomes S(t).
{This umQ(t) bootstraps time.}
8) Duration can be a umQ(v) for S(v) and if so makes S(v) unstable so
it eventually spontaneously becomes S(v+1)
{Progressive resolution of umQ, evolution.}
9) S(v) can have a simultaneous multiplicity of umQ(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 umQ(v) of S(v) and
can have new umQ(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.
Well its a first try.
Hal Ruhl
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Re: Properties of observers
Hi John:
My intent is to eventually back fill the compacted description with
additional discussion once I think it is OK. Perhaps that will
help. In that regard I currently want information to be a divisor
and packets of divisors to be a division of the [A-Inf]. I am trying
to avoid the central use of the words information and
meaning. I redid the compact form along these lines and I put it
below for easy reference. I am also attempting to avoid or at least
minimize appeal to math such as that associated with sets. I hope
there will not be much more to revise before I attempt a slightly
longer discussion.
I am an engineer but I will try to make the added discussion more
universal if that is the right word. However, I am looking for a
lattice upon which to build that discussion.
Interconnection is a main theme since the S(i) are intersected or
should be [incompleteness] by the Q(i).
Are aspects also types of distinctions? Information could be
called a distinguisher I suppose, but I currently prefer divisor as
in that which lies between, or outlines distinguishables.
Hal Ruhl
At 09:02 AM 2/11/2008, you wrote:
Hal,
I lost you 2) - 13): I cannot squeeze the philosophical content into a
physicalist-logical formalism. The 'terms' are naturally vague to me,
cannot follow them 'ordered. The words in your perfect schematic are
(IMO) not adequate for the ideas they are supposed to express: our
language is inadequate for the (my?) advanced thinking.
I am for total interconnection, no separable divisions etc. Aspects,
no distinctions.
I am not ready to make a conventional scientific system out of the
inconventional. I am not an 'engineer': I am a dreamer.
Maybe if I learned your entire vocabulary?(I cannot - it
interferes with mine).
Thanks for your effort, it was counterproductive FOR ME.
I appreciate your way as your way.
John M
1) Assume [A-Inf] - a complete, divisible ensemble of divisors and
its own divisions.
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].
{[A-Inf] contains itself.}{i ranges from 1 to infinity} {N(i) is the
ith Nothing and E(i) is the ith Everything.}
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}.
{incompleteness}
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.
Hal Ruhl
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Re: Properties of observers
Stephen, your concerns echoed in my mind my reply to Hal's ordering the unknowable in my reply to him today. [SPK] Does this inability need to be, itself, Complete? I would not think so: that would require omniscience. I also do not rely on 'Leibnitz' or other past geniuses, because since their time we acquired SOME additional epistemic enrichment added to our thinking so we may 'reflect' to their wisdom, but not 'use' it as applicable today. Dictionaries also use past distinctions, mostly in the sense of conventional thinking. * Jamie's in-between-ness stems in my opinion from our incomplete (present-human) views of how we imagine a change in space-time thinking. I cannot offer a better one but it would be important for developing 'meaningfulness' in the new worldview of the total interconnectedness, which implies continuum in idea-changes. * I cannot fit 'randomness' into the totality: it would fragment it into irrelevant portions which I find controversial in the overall interconnectedness of Everything. As Russell wrote once: maybe a random - 2nd order (as the product of his random generator). Regards John M - Original Message - From: Tom Caylor [EMAIL PROTECTED] To: Everything List [EMAIL PROTECTED] Sent: Wednesday, February 06, 2008 12:42 AM Subject: Re: Properties of observers On Feb 3, 11:46 am, Hal Ruhl [EMAIL PROTECTED] wrote: The following discusses observer properties under my model of the Everything. I take the list of observer properties I discuss below from what I have so far found in Russell's Theory of Nothing. One property - Giving meaning to data [number 5 on the list] - does not seem to be supportable under a description of the Everything as containing all information. Hi again between my being too busy to converse here in a while. Surprise, surprise, that the crux of the matter ends up in yet another circumstance being the mystery of where meaning comes from. Alas, this single unsolved problem has a viral effect to the rest of any theory of everything. See below. As indicated in earlier posts, within my model of the Everything is a dynamic which consists of incomplete Nothings and Somethings that progress towards completeness in a step by step fashion. At each step they grow more complete by encompassing more of the information in the Everything. The incompleteness is not just that of mathematical systems but is more general. It is the inability to resolve any question that is meaningful to the particular Nothing or Something. Some such questions may be of a sort that they must be resolved. The one I focus on in this regard is the duration of the current boundary of the particular Nothing or Something with the Everything. Without the ability to give meaning to anything, how can there be a meaningful question? [SPK] Does this inability need to be, itself, Complete? It seems to me that meaning per say is relational and more of a sort of how much of X is expressed in Y. A Complete resolution of a question such as this would be like unto a exact equality between X and Y. We could use Leibniz' principle of the Indentity of Indiscernables here. http://en.wikipedia.org/wiki/Identity_of_indiscernibles A Something will of course be divisible into subsets of the information it contains. Many of these subsets will participate in the incompleteness of the Something of which it is a subset. At each step wise increase in the information content of that Something many of its subsets will receive information relevant to the resolution of their local un-resolvable meaningful questions. [SPK] Consider how a word in a dictionary is defined in terms of a web of relations with other words... How would we quantify this amount of Incompleteness? Resultant observer properties: 1) Prediction of the future behavior of the Something of which they are a subset [of their particular universe]: The subsets share some of the incompleteness of their Something and participate in the progressive resolution of this incompleteness. The current local incompleteness [part of the current state of an observer] can serve as a predictor of the Something's evolution since it is a target of the progressive influx of information. How can there be any meaningful progressive resolution without meaning? [SPK] Maybe because there is no meaningfulness in absense of a relationship. Meaning would arise just as the notion of between-ness. (This idea comes from James N. Rose) 2) Communication between subsets: There is no requirement that the subsets be disjoint or have fixed intersections. There are no restrictions on the number of copies of a given packet of information contained within in a Something and no restrictions on the copy function. A Something
