joining
Argand
This is my joining post!
I am a lecturer in mathematics and physics at a senior school in
England
my background is B.Sc and Master of Philosophy degrees in mathematical
physics, the latter was by research in cosmology and general
relativity - but this was some time ago. I have published a few
papers which relate to physical eschatology, particularly the
simulation argument of Bostrom and the Omega point theory of Tipler.
I am interested in how these ideas, along with the many worlds
interpretation could fit together in the quantum theory of immortality.
Russell Standish
--
----------------------------------------------------------------------------
A/Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052 hpc...@hpcoders.com.au
Australia http://www.hpcoders.com.au
----------------------------------------------------------------------------
Hal Ruhl
I have at last found a opportunity to start looking at your
book. Thanks for the cite.
My view has been that the Nothing is incomplete because it contains
no ability to answer meaningful questions about itself and there is
one it must answer and that is its duration. This question is always
asked and must be answered. To answer it the Nothing must acquire
information and become a Something.
Most initial Something landing pads - so to speak - will also be
incomplete and continue the quest for completeness. Such a quest
must exhibit a monotonic increase in information in that Something.
Therefore the initial observation of an incomplete and unstable
Nothing has within it the imposition of an ordered sequence of
compatible states for a Something each containing more information
than the last - that is the imposition of time.
Each step of the quest has an equal but opposite twin and so to
minimize selection a Something bifurcates at each one.
The Everything contains enough Nothings [meaningful question: How
many more Nothings beyond 1 are in the Everything? Minimum selection
response: unlimited.] so that all paths to completeness are followed
over and over forever.
Hal Ruhl
John Mikes
I read your post with appreciation (did not follow EVERY word in it
though) - it reminded me of my "Naive Ode (no rhymes) of Ontology"
dating back into my "pre-Everythinglist" times, that started something
like:
"...In the Beginning there was Nothingness ( - today I would add:
observer of itself). When it realized that it IS nothingness, that was
providing this information - making it into a Somethingness. The rest
is history. (Chris Lofting would say: it went alongside
Differentiation and Integration).
A minor remark: I would not denigrate Mama Nature by using the word
'bifurcation' - indicating that "only 2" chances in the impredicative
unlimited totality.
As a second (even more minor) remark: "All possible states" sounds to
me as being restricted to the level "WE" find possible. Since
cave-times (I don't go further) we have encountered many things that
looked like impossible. I wonder if Bruno's unlimited Loebian Machine
considers anything 'iompossible'?
Have a good 2008
John M
John Mikes
Do you seriously mean "How many Nothings"?
John
Hal Ruhl
At 12:12 PM 1/7/2008, you wrote:
>Hal,
>
> I read your post with appreciation (did not follow EVERY word in it
>though) - it reminded me of my "Naive Ode (no rhymes) of Ontology"
>dating back into my "pre-Everythinglist" times, that started something
>like:
>
>"...In the Beginning there was Nothingness ( - today I would add:
>observer of itself). When it realized that it IS nothingness, that was
>providing this information - making it into a Somethingness. The rest
>is history. (Chris Lofting would say: it went alongside
>Differentiation and Integration).
>
>A minor remark: I would not denigrate Mama Nature by using the word
>'bifurcation' - indicating that "only 2" chances in the impredicative
>unlimited totality.
I agree that there can be a multiplicity of simultaneous
splits. This was a mistake I realized later.
>As a second (even more minor) remark: "All possible states" sounds to
>me as being restricted to the level "WE" find possible. Since
>cave-times (I don't go further) we have encountered many things that
>looked like impossible. I wonder if Bruno's unlimited Loebian Machine
>considers anything 'iompossible'?
What I indicated was all paths to completion. I suspect that there
may be sequences within the Everything that would not be on such paths.
Yes I did mean an unlimited number of Nothings in the
Everything. For the Everything to contain just one copy of the
information in it would be a selection. Rather it needs to contain
an unlimited number of copies.
>Have a good 2008
Thanks, you too.
Hal Ruhl
Hal Ruhl
The dynamic starts with and continues a pattern - a path to completeness.
The path is not deterministic because most states would be multiply
incomplete so any two successive states will differ by some
fractional reduction in this incompleteness and that fraction can not
be selected prior to the transition [minimal selection].
However, this fraction is nevertheless composed of information that
reduces an incompleteness that started in a logic observation -
responses to meaningful questions - and should remain in this venue.
There would be only one possible maximum size transitions and many
possible small ones.
In this approach large transitions that resemble White Rabbits would
be uncommon and patternless White Rabbit events should not exist.
Hal Ruhl
John Mikes
on our humanly limited language (however infiltrating into the
'meaning' of texts):
HR:
"...> What I indicated was all paths to completion."
JM:
does anything like 'completion' make sense in speaking about an
unlimited totality? Furthermore: are 'copies' considerable substantial
items, or simply our figment of looking from different angles into
different angles - at the same item?
I try to 'cut' my human incompleteness (didn't claim success) when
using a totality-vocabulary (way above my head) and all that may be in
it.
1. If there is -a- 'nothingness' does it multiply when we in our
human logic detect "it" again?
2. Do we assign qualia to nothingness? of course not.
- I am inclined to sort nothingness with infinity: we can talk about
it but have no (human) reason-based meaning - understanding - about
its essence. Georg Cantor tried it for the "infinity" - what
I still consider a mathematical game of details - not the end.
Parlance: nothingness is different from nothing. Saying about a
construct "there is nothing in it about the storch" does not mean a
storch-restricted nothingness included as part of the construct.
So if there appears innumerable nothingness-occasions in the
everything - it may be our detection of the ONE - existing there
(=found?) many times over.
Would it jibe with your vocabulary?
John M
Gevin Giorbran
> JM: does anything like 'completion' make sense in speaking about an
> unlimited totality? Furthermore: are 'copies' considerable substantial
> items, or simply our figment of looking from different angles into
> different angles - at the same item?
> human logic detect "it" again?
> 2. Do we assign qualia to nothingness? of course not.
> - I am inclined to sort nothingness with infinity: we can talk about
> it but have no (human) reason-based meaning - understanding - about
> its essence. Georg Cantor tried it for the "infinity" - what
> I still consider a mathematical game of details - not the end.
simple way that I unite nothing and infinity in my own book which is I
suppose is fundamentally about nothing and everything.
There is a real existing "nothing" and there is a concept nonexistence
and they should never be confused. The real nothing is common,
"nothing in the refrigerator", a white canvas, empty space (the ideal
or direction toward i.e., expansion). The real nothing is simply
balance, uniformity, perfect symmetry. It isn't a cancellation of
properties or existence, it is a unification or synthesis into a
single form, which we see as nothing. Cook everything in the frig
together and you end up with one thing with far fewer properties. That
property-less "one" in mathematics is zero. In a simple examination of
zero it appears to contain all other numbers, as x + -x equals zero.
However, zero mathematically refers to "no things" or cancellation,
and so we say the sum of all reals is indefinite. However, as I
explain in my book there are two mathematical systems not one. It is
all or nothing. Zero can either represents no things, or zero
represents all things. If zero is all things, zero becomes infinite,
and as a result all numbers become infinite. +1 becomes all numbers
except -1 is excluded, etc etc. Suddenly instead of counting things,
numbers represents fragments of the everything of zero. The radical
consequence of this is that the value or content of numbers decreases
rather than increases. Five is a larger infinity than four, since more
has been removed, it is a smaller fragment of the whole of a zero
everything. 5 billion is a much smaller value and as we count into
greater numerals our value or content is decreasing and even
converging toward an infinitely small value. What we are doing is
fragmenting zero, we are slicing it up into parts, and since our
numerical value is converging rather than diverging we can recognize a
smallest number, positive infinity, an exact division or fragmentation
made of zero, which in this system is an actual value, no less
definite and completed than the whole of zero, and so this infinity
not merely a never ending or unlimited process. I call this number
Proto, and the negative Elea. So where we are used to not having a
mathematical value to represent everything, and used to being caught
up in incomprehensible indefinite infinities, in this math the overall
infinity of mathematical values is bounded by extremes. There is an
all positive half, an all negative half, and the whole of zero. In the
same way there exists infinite fractions between zero and one, this
math system is infinite yet bounded by extremes, and note there is no
nothing in this system, or rather nothing and everything are the same
thing...zero.
My cosmological application of this system is that Proto, I claim, is
the infinitely dense (all positive) and infinitely small singularity
in our past, the extreme of all positive, and the pendulum swung all
the way to one side. (In this second system there cannot be a value
smaller than half of the whole, yet that smallest value is still
infinite). The zero of this math, or Omega, is the singularity of
empty space toward which our universe is currently accelerating
towards. It is the largest value in nature, and why the universe
expands and ultimate ends as a perfectly flat space extending
infinitely in all directions (perfect symmetry).
The most dramatic consequence of all this being the realization that
our universe is not simply becoming disordered, our universe is not
dying, rather time evolves away from one kind of order (the ultimate
grouping of all positive apart from all negative, with each having
high symmetry internally while relative to zero they are perfect
asymmetry) and time evolves towards a whole other kind of order
(unity, balance, perfect symmetry) which is actually the infinite
whole, a quantum superposition of all universes, matter and antimatter
worlds, antimatter worlds being those that travel from negative Elea
to zero.
So as to why we exist rather than nothing at all, the answer is that
nothing still exists. What we think of as nothing is really
everything, and zero is the native state of being, as non-being or
nonexistence cannot "be" (Parmenides). It simply is. We are inside the
real nothing, inside zero. Ordinary math is based upon the order of
the past, the distinction and form that results of slicing zero up,
with Proto claiming to be the great 1, the beginning, everything that
matters, more than zero. This second system, which I call symmetry
math, is certainly less functional in our everyday lives, but it is
less of an abstraction of true reality, and applies much more
effectively to cosmology, the study of the whole.
Gevin Giorbran
http://everythingforever.com
Gevin Giorbran
> My view has been that the Nothing is incomplete because it contains
> no ability to answer meaningful questions about itself and there is
> one it must answer and that is its duration. This question is always
> asked and must be answered. To answer it the Nothing must acquire
> information and become a Something.
asymmetry exists in the identity confusion of being everything and
nothing simultaneously. This produces two states, the masculine "I am
everything, you are nothing", (i.e., King of the world, all that
matters, "the self"), and the feminine "I am nothing, you are
everything" (all that matters, giving self over for family, spouse,
church, state). In the end there is the final "I am, you are
(infinity, God)" as well as "I am not, you are not (zero as nothing,
eastern emptiness)".
> Most initial Something landing pads - so to speak - will also be
> incomplete and continue the quest for completeness. Such a quest
> must exhibit a monotonic increase in information in that Something.
Bohm's implicate order. NOt just the exploring of distinct
possibilities, the slices of zero, but also a becoming of the
integrated whole, finally becoming or unifying with the everything.
> Therefore the initial observation of an incomplete and unstable
> Nothing has within it the imposition of an ordered sequence of
> compatible states for a Something each containing more information
> than the last - that is the imposition of time.
> Each step of the quest has an equal but opposite twin and so to
> minimize selection a Something bifurcates at each one.
> The Everything contains enough Nothings [meaningful question: How
> many more Nothings beyond 1 are in the Everything? Minimum selection
> response: unlimited.] so that all paths to completeness are followed
> over and over forever.
followed, with each path ending at the final state of knowing itself
as both nothing and everything, Omega, completeness, zero, oneness,
returning home to know itself for the first time.
Cool stuff Hal!
Günther Greindl
> There is a real existing "nothing" and there is a concept nonexistence
> and they should never be confused. The real nothing is common,
> "nothing in the refrigerator", a white canvas, empty space (the ideal
> or direction toward i.e., expansion). The real nothing is simply
> balance, uniformity, perfect symmetry.
Hmm - your real existing nothing is just a word without referent - like
a null pointer.
Q: "What is on the paper?"
As answer you expect that what is written.
As the paper is still blank:
A: "Nothing."
You are being returned a null pointer, not a metaphysical reference to
balance, uniformity, symmetry or whatever.
Your concept of _nonexistence_ would then be a metaphysical null
pointer. Attributing either concept some kind of "existence" is major
metaphysical error IMHO.
> It isn't a cancellation of
> properties or existence, it is a unification or synthesis into a
> single form, which we see as nothing. Cook everything in the frig
> together and you end up with one thing with far fewer properties. That
> property-less "one" in mathematics is zero.
These are all features of language. I recommend Niiniluoto's "Critical
Scientific Realism" how to resolve these issues - indeed, how they have
been resolved through diligent work of many philosophers (that does not
mean that there is no disagreement anymore ;-))
> converging toward an infinitely small value. What we are doing is
> fragmenting zero, we are slicing it up into parts, and since our
<snip>
You seem to have a certain preconception of what a number is; or at
least develop a conception which one must not naturally share.
> high symmetry internally while relative to zero they are perfect
> asymmetry) and time evolves towards a whole other kind of order
> (unity, balance, perfect symmetry) which is actually the infinite
I suppose you do not mean the heat death of the universe. But what would
perfect symmetry be but heat death?
Regards,
Günther
--
Günther Greindl
Department of Philosophy of Science
University of Vienna
guenther...@univie.ac.at
http://www.univie.ac.at/Wissenschaftstheorie/
Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org
John Mikes
thanks for your comprehensive - and very understandable - explanation about
"nothing" (no pun) and its qualia-circumstances.
My post to Hal targeted "nothingness" as differentiated from
"nothing". The concept, not the qualia or nature of its adjectival
meaning.
I regret to have missed so far your book. It must be an intresting reading.
John M
John Mikes
your reply is well to the point(s) - I feel to explain why I opened Pandora's
(empty?<G>) box of nothingness. It was long ago when we discussed
these things with Hal, I changed my views a lot since then - as well,
as Hal also developed a comprehensive theory of his own. I wrote a
macama on 'Ontology' (what I hold today as a 'model-view' of a reduced
aspect in the royaume 'existence'). In my present view ontology is a
frozen state related explanation in a (dynamic?) world of continuous
change. As we look at it today. So my recollection was just that: a
recollection.
I referred to a "starting point" what most theories shove under the
rug, mostly as some meaningless free concept to start a hazy process
(thinking of Q-science) - and at 'that' time I did not accept it. I
was 2 decades younger.
so I started with "nothingness" - and elevated it into our worldview.
As a later phase I started from an imagined 'plenitude' - perfect(!)
symmetry invariant singularity (atemporal, aspatial of course) and
deduced from my arbitrary conditions the innumerable "Bigbangs" for
the unlimited multiverse (diverse qualia, including ours) with all the
peculiarities we induce HERE. The 'universes' are lashing up and
dissipating complexity-knots (ours looks different from the inside
only).
I call this a "narrative" and accept the origination of that
'plenitude' as untouchable as any other shoved under the rug.
I write this in explanation for my not going into discussion of
details of the 'old' idea.
The closest (a bit obsolete) is included in my Karl Jaspers Forum
#TA-62MIK-2003.
John M
Hal Ruhl
At 04:01 PM 1/8/2008, you wrote:
>Hi, Hal: - Hopefully without risking strawmanship, a further remark
>on our humanly limited language (however infiltrating into the
>'meaning' of texts):
>HR:
>"...> What I indicated was all paths to completion."
>JM:
>does anything like 'completion' make sense in speaking about an
>unlimited totality?
The idea of completeness in this case is not a matter of an objects
size [amount of information within] but rather its ability to resolve
any meaningful question about itself. Low information objects can be
complete. The Nothing has too little information within to resolve
any such question but such a question exists, so it is
incomplete. Further the duration question is always eventually asked
so the Nothing must become a something which answers this particular
question. However, this initial Something may not be able to answer
all meaningful questions about itself that in fact get asked. The
Everything is complete but contains multiple answers to at least some
meaningful questions so it is inconsistent. Our particular Nothing or
origin is now gone but there is an unlimited supply in the Everything.
>Furthermore: are 'copies' considerable substantial
>items, or simply our figment of looking from different angles into
>different angles - at the same item?
>I try to 'cut' my human incompleteness (didn't claim success) when
>using a totality-vocabulary (way above my head) and all that may be in
>it.
The question appears related to: does net information need a physical
tablet upon which it is manifest in order to exist. The Everything
has no net information so needs no such tablet. I suspect that it
can not be established that sub components of the Everything
containing net information would need one.
>1. If there is -a- 'nothingness' does it multiply when we in our
>human logic detect "it" again?
This would require observers to have an effect on the amount of
content of the Everything. I see no argument to support this.
>2. Do we assign qualia to nothingness? of course not.
>- I am inclined to sort nothingness with infinity: we can talk about
>it but have no (human) reason-based meaning - understanding - about
>its essence. Georg Cantor tried it for the "infinity" - what
>I still consider a mathematical game of details - not the end.
I define Nothing as an object [no physical structure required] that
has too little information to answer any meaningful question about
itself. I have such a question and it must be asked thus I conclude
that it is incomplete and unstable. I have no idea how little
information is required to answer the least demanding question but
the smallest amount above none seems like it might answer some such
question so I set the Nothing at no internal information to be a
content opposite so to speak of the Everything.
>Parlance: nothingness is different from nothing. Saying about a
>construct "there is nothing in it about the storch" does not mean a
>storch-restricted nothingness included as part of the construct.
>So if there appears innumerable nothingness-occasions in the
>everything - it may be our detection of the ONE - existing there
>(=found?) many times over.
>Would it jibe with your vocabulary?
The Everything is an ensemble and is a member of itself [The
definition of an object is information and equivalent to the object
itself in this venue and the Everything contains all information so
it contains itself]. As such it is divisible along the boundaries of
its members and sets of its members. The Nothing and all its copies
in the "member of itself Everything" are of course members of the
ensemble but I see "nothingness" as a multiplicity [or set] of
various other members since nothingness can have various sub texts.
Hal Ruhl
Gevin Giorbran
> Hmm - your real existing nothing is just a word without referent - like
> a null pointer.
> Q: "What is on the paper?"
> As answer you expect that what is written.
> As the paper is still blank:
> A: "Nothing."
> You are being returned a null pointer, not a metaphysical reference to
> balance, uniformity, symmetry or whatever.
return? Duality, distinction, form? The white paper displays
uniformity, sameness, identical to properties of balance i.e., balance
of color, neutrality, equilibrium. Such are real and plainly observed
properties, not metaphysical. We nullify the distinction and form of
writing on paper (A. Nothing) in response to an observation of
something else (physical uniformity).
> Your concept of _nonexistence_ would then be a metaphysical null
> pointer. Attributing either concept some kind of "existence" is major
> metaphysical error IMHO.
that the term nonexistence attempts to meaningfully reference or
identify an assumed potential that itself has no meaning. If I say non-
white I am referring to some other color, off white. If I draw or
metaphorically refer to an arrow, the arrow points to something, such
defines the meaningfulness of "arrow". What is a "metaphysical null
pointer" pointing to? Nonexistence? Something outside of the realm of
meaning? Such is not a meaningful statement or reference as there
aren't "somethings" outside of meaning. Nonexistence, metaphysical
null pointer, non-being, meaninglessness...any attempt to refer to
that which has no meaning commits a semantic error. What has no
meaning? Nonexistence or non-meaning cannot be referenced or pointed
in any use of meaning. It is a fundamental mistake simply to refer to
nonexistence, since the concept has no meaning whatsoever. Doing so is
merely a trick of language, a misnomer, a null pointer that isn't a
null pointer. We can and only refer to actual properties of nature or
real nothings: a nullification of form, a uniformity, sameness,
symmetry. Confusing nothing and nonexistence is thus is a major
"physical" error, albeit a very common one.
http://everythingforever.com/ywexist.htm
> > It isn't a cancellation of
> > properties or existence, it is a unification or synthesis into a
> > single form, which we see as nothing. Cook everything in the frig
> > together and you end up with one thing with far fewer properties. That
> > property-less "one" in mathematics is zero.
>
> These are all features of language. I recommend Niiniluoto's "Critical
> Scientific Realism" how to resolve these issues - indeed, how they have
> been resolved through diligent work of many philosophers (that does not
> mean that there is no disagreement anymore ;-))
reference to many esteemed philosophers. Eliminating the confusion
between nonexistence and real properties is made in defense of
scientific realism and actually even ends the debate.
> > converging toward an infinitely small value. What we are doing is
> You seem to have a certain preconception of what a number is; or at
> least develop a conception which one must not naturally share.
mathematics, instead it offers another way of seeing the same physical/
mathematical reality without finitivity or abstraction. However,
symmetry math is not disconnected from classical math. Our present
conclusion that the sum of all reals is indefinite is incorrect, made
in defense of classical math. In evaluation of the question, is zero
the sum of all reals?, if we don't preconceive the value of zero, and
genuinely consider zero as the sum of all reals based upon x + -x = 0,
then we are moved into the domain of symmetry math. We cannot say the
sum of all reals is only indefinite, or the sum of all physical things
is only an indefinite infinity, the sums are indefinite in cmath and
"zero" in smath.
Where the finitivity of cmath has led many to doubt the Universe is
infinite, smath and seeing the two types of order, grouping and
symmetry, reveals the interdependent relationship between finitivity
and infinity.
http://everythingforever.com/st_math.htm
> > high symmetry internally while relative to zero they are perfect
> > asymmetry) and time evolves towards a whole other kind of order
> > (unity, balance, perfect symmetry) which is actually the infinite
>
> I suppose you do not mean the heat death of the universe. But what would
> perfect symmetry be but heat death?
scenario where the universe expands endlessly without ever reaching
zero, rather a big rip type of future where time reaches a common zero
for mass, density, temperature, energy, gravity, volume, and time,
i.e., maximum entropy, equilibrium, symmetry (not maximum disorder).
Caldwell also describes the end of accelerating expansion as the
ultimate singularity. Maximum heat/energy is the pendulum swung all
the way to one side, to imbalance. Energy is a measurement or quantity
of improbability, the improbability of imbalance over balance. Entropy
always increases due to the improbability of imbalance over balance,
not the improbability of order over disorder (http://
everythingforever.com/st_order5.htm). Balance is a very powerful kind
of order, and each day in an expanding universe we move increasingly
nearer to the balance of zero and perfect symmetry. What would perfect
symmetry be? The default setting of reality, the inevitability of
being. What is classic physical reality? The fragmentations of zero,
the internal boundaries and differentations (+x, -x).
Bruno Marchal
Le 07-janv.-08, à 18:12, John Mikes wrote (to Hal Ruhl)
>
> Hal,
>
> I read your post with appreciation (did not follow EVERY word in it
> though) - it reminded me of my "Naive Ode (no rhymes) of Ontology"
> dating back into my "pre-Everythinglist" times, that started something
> like:
>
> "...In the Beginning there was Nothingness ( - today I would add:
> observer of itself). When it realized that it IS nothingness, that was
> providing this information - making it into a Somethingness. The rest
> is history. (Chris Lofting would say: it went alongside
> Differentiation and Integration).
>
> A minor remark: I would not denigrate Mama Nature by using the word
> 'bifurcation' - indicating that "only 2" chances in the impredicative
> unlimited totality.
>
> As a second (even more minor) remark: "All possible states" sounds to
> me as being restricted to the level "WE" find possible.
Who "WE"? (I guess you are used to this question by me, with me =
Bruno :)
> Since
> cave-times (I don't go further) we have encountered many things that
> looked like impossible. I wonder if Bruno's unlimited Loebian Machine
> considers anything 'iompossible'?
Be careful. The Loebian Machine is a *machine*, that is a finite
limited creature (infinitely patient though!).
Now, if you agree to modelize (at least) necessity by
provability and possibility by consistency, then the facts are that
a sound Lobian Machine can refute, and thus can show the inconsistency
of all elementary arithmetical truth.
So 1=2 is impossible (inconsistent) for a lobian machine.
More weird is the fact that there is NO propositions that a Lobian
Machine can show possible !!!
Even the arithmetical obvious fact that 1 = 1 cannot be shown possible,
that is consistent, by the sound Lobian Machine.
This is a direct consequence of Godel's second incompleteness (with
the completeness theorem in the background). No proposition beginning by
consistent, like Dt, which I have also written <>t, or ~B~f or ~[]~t,
or ~[]f)
can be proved by the sound machine (G does not prove any such
proposition,
but most are true, and peoved by G*).
>
> Have a good 2008
I wish you the best,
Hal Ruhl
view of "Dark Energy"
In my approach a Something is on a quest for completeness within the
Everything.
Based on this, the following points can be made:
1) The number of current incompleteness sites for a given Something
would be at least proportional to the surface area of its boundary
with the rest of the Everything if not proportional to its volume.
2) Thus the larger [more information content] a Something is [has]
the more such sites it has and the larger any given step in the quest can be.
3) This gives an increase in the average information influx as the
quest progresses.
4) If the universe described by that Something has a maximum finite
information packing density in its "space" then an accelerating
increase in the size of that space should be "observed" since both
the volume and surface area of a Something inside the Everything
increases as the quest progresses.
Hal Ruhl
George Levy
This topic interests me, but I find it difficult to go past the second
sentence in your post. The phrase "Something is on a quest" carries a
lot of baggage, in particular that "Something" has intention, purpose
and motivation. Either we have to assume that this intention is produced
by a fundamental "spirit" or "soul" that you have assigned to the
Something, or that the intention is emergent from a complex
consciousness simulation possibly involving Quantum Mechanics..... If
you assume a spirit or soul you are making a quasi religious assumption.
Is this what you want? How do we explain spirit or soul? If you are
assuming a complex consciousness simulation, there is a whole layer that
needs to be explained which no one has yet fully explained yet.
Usually scientists use objective and impersonal criteria such as "energy
minimization" to explain how a reaction is driven in one particular
direction. In chemistry, for example, "Le Chatelier Principle" is used.
George
Hal Ruhl
I use the term "quest" because a Something if incomplete will have to
increase its completeness to answer meaningful questions that get
asked but it can not answer. The motivator is partly external - an
answer [mostly more than one is available] is "out there" in the
unexplored Everything and partly internal - the particular question
must be answered. There is no intent to imply some sort of choice on
the part of the Something. To use your last thoughts below the quest
is an [Everything, Something, Nothing] system induced need for a
ongoing influx of information into the particular Something from the
Everything [the boundary of the particular Something with the
Everything alters to include more of the Everything. The Something
encompasses an ever increasing portion of the Everything but it must do so.
In this case I currently see no higher level of driver for any sub
component of the Something including what one might call an
observer. I may need to reconsider when I get to that point in
Russell's book but my time restraints force me to take considerable
time doing so.
Hal Ruhl
George Levy
I cannot follow you: one the one hand you say:
Something if incomplete will have to increase its completeness to answer meaningful questions
and on the other hand you say:
There is no intent to imply some sort of choice on the part of the Something.
and on the third hand:
in which the term "need" goes back to supporting a spirit-based system.the quest is an ... system induced need for a ongoing influx of information
George
Hal Ruhl
At 09:59 PM 1/16/2008, you wrote:
Hal,
I cannot follow you: one the one hand you say:
- increase its completeness to answer meaningful questions
which implies volition and therefore spirit;
and on the other hand you say:
which denies spirit,
- the part of the Something.
and on the third hand:
in which the term "need" goes back to supporting a spirit-based system.
- ongoing influx of information
Hal Ruhl
George Levy
>
> This is an automatic process like a mass has to answer to the forces
> [meaningful questions] applied to it.
What in the psyche of the mass makes it answer to the forces?
George
Hal Ruhl
I see no motivator to any dynamics within the Everything other than
the incompleteness of some of its members and the unavoidable
necessity to progressively resolve this incompleteness.
Hal Ruhl
George Levy
Allright. You are saying that incompleteness is the (only) motivator of the members. In other words the members feel motivated by incompleteness. They do have the feeling of being incomplete that motivates their behavior. Is this correct?
George
Bruno Marchal
I send to David Nyman (the 06 Nov 2007) a little planning:
1) Cantor's diagonal
2) Does the universal digital machine exist?
3) Lobian machines, who and what are they?
4) The 1-person and the 3- machine.
5) Lobian machines' theology
6) Lobian machines' physics
7) Lobian machines' ethics
Let me summarize what has been done and what remains to be done.
1) Cantor's diagonal
I tend to consider that the point "1)" is finished. Cantor's argument
is that if there is a bijection between natural numbers, that is: 0, 1,
2, 3, 4, ..., and sequences of numbers, that is a bijection like
0 ----------- 45, 7, 8976, 4, 32, ...
1 ----------- 0, 0, 67, 78, 0, ...
2 ----------- 27, 1, 24, 24, 23, ...
3 ----------- 1, 1, 1, 345, 7, ...
...
then the "antidiagonal" sequence 46, 1, 25, 346, ... cannot be in the
list, because by construction it differs from each sequence in the
list. See below how to make explicit the contradiction.
The reasoning does not depend on the particular sequences exhibited,
and it shows that no enumerable set of sequences can be put in 1-1
correspondence with the natural numbers. The conclusion is that the set
of all sequences of natural numbers is innumerable (not enumerable, not
countable, uncountable, etc. Important concept have many synonym in
math).
Let me recall the same proof, but with usual mathematical notation.
A sequence of numbers, like f_0 =
56, 7897876, 67, 89, 1, 1, 45, ...
is really "just" a function from N to N:
f_0(0), f_0(1) f_0(2), f_0(3), f_0(4), ...
with here: f_0(0) = 56, f_0(1) = 7897876, f_0(2) = 67, f_0(3) = 89,
f_0(4) = 1, etc.
So the bijection above becomes:
0 ----------- f_0 = f_0(0), f_0(1) f_0(2), f_0(3), f_0(4), ...
1 ----------- f_1 = f_1(0), f_1(1) f_1(2), f_1(3), f_1(4), ...
2 ----------- f_2 = f_2(0), f_2(1) f_2(2), f_2(3), f_2(4), ...
3 ----------- f_3 = f_3(0), f_3(1) f_3(2), f_3(3), f_4(4), ...
...
You can see that the diagonal sequence can be described by:
f_0(0), f_1(1), f_2(2), .... f_n(n), ...
Then the "antidiagonal" sequence (function) g is given by
f_0(0)+1, f_1(1)+1, f_2(2)+1, .... f_n(n)+1, ...
That is: g(n) = f_n(n)+1 (definition of g)
Now we can make the contradiction explicit. Suppose that g is in the
list f_i. Then it exists a number k such that g = f_k. This means of
course that for all numbers n we have g(n) = f_k(n). In particular g(k)
= f_k(k). But by the definition of g: g applied on k
= g(k) = f_k(k)+1. Thus (by Leibniz identity rule):
f_k(k) = f_k(k)+1
Now, all f_i are functions from N to N, so they are defined on all
natural numbers, so f_k(k) is a number. We have seen in high school
that identical numbers can be subtract on both sides of an equation
leading to
0 = 1. (contradiction). Thus the f_i cannot enumerate all functions
from N to N. We say:
N^N is innumerable.
This was point "1)". Hope it is ok for every one. Please be sure you
get the point before proceeding.
2) Does the universal digital machine exist?
I recall the informal notion of what is an (intuitively) computable
function (from N to N). Def: A function f from N to N is computable if
we can describe in some formal language L, in a finite way, how to
compute, in a finite time, its value f(n) on each natural number n.
Def. I will call "code of f" such a description of how to compute f.
Def. A language L is said universal if all computable functions can be
described in the language.
Def. A machine is universal if she understands a universal language,
(and thus can indeed compute all computable functions from N to N, at
least in Platonia, where "Platonia" is defined by a place where you can
always ask and get more time and more space/memory: we don't put
deadline to the (universal) machine.
Church thesis is the statement that a universal language (and machine)
exists, and indeed that in particular lambda-calculus provides such a
universal language.
Church's thesis is not obvious. Indeed, when Church "defined" the
computable functions by those capable of being computed by a
lambda-expression (a symbolic expression or code written in the
lambda-calculus), Stephen Cole Kleene thought at first that a reasoning
similar to Cantor's proof of the non enumerability of N^N (see above)
could be made against Church's pretension.
Kleene's reasoning is the following, and works for any pretension that
there is a universal language (so we have not to even define what
lambda-calculus). Indeed, suppose that there is a universal machine and
thus a universal language in which all computable functions from N to N
can be given a code. Now the set of codes in the language L is
enumerable, being a subset of all possible expression written in the
language (which we have seen to be enumerable). Thus there is an
enumeration of all computable functions from N to N
f_1, f_2, f_3, f_4, f_5, f_6, f_7, f_8, f_9, ...
but then the "antidiagonal" function g defined by
g(n) = f_n(n) + 1
is computable, given that each f_n is computable, and that "+1" is a
computable operation. But g cannot be in the list, for the same reason
as above.
Now this cannot be a proof that the set of computable functions is not
enumerable, given that the set of codes is obviously enumerable. So
this looks like a proof by absurdo that there is no universal language,
and thus no universal machine.
The proof, nevertheless is wrong. It did presuppose that the universal
language compute all functions from N to N and only that
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Indeed to substract f_(k)(k) on both
side of f_(k)(k) = f_(k)(k) + 1, f_k(k) has to be a number!!!!!!!
If f_k(k) is undefined (for example the interpretation by the universal
machine of the code makes the machine non stopping) then the argument
just doesn't go through!!!!
So the possibility that there is a universal language remains intact.
But now we know that the codes written in the possible universal
language could correspond to object which are NOT function from N to N,
but from some subset of N to N. Such "function" are called strictly
partial function: they are not defined on each natural number. Such
function can make the computer crashing (looping, running forever, non
stopping, etc.). So you have to accept the universal machine can crash
if you want her to be able to be universal. As I said: you cannot have
both security and universality. Later security will play a role for the
notion of first person, and universality will play a role for the
notion of third person.
Experimentally, this is what happens for lambda-calculus, FORTRAN,
JAVA, C++, Lisp, SK-combinators, game-of-life, etc. With those language
each corresponding g functions, will indeed crash the corresponding
universal machine (codes, expressions) when applied on their own code.
All known universal language have been shown equivalent: they define
always exactly the same class of computable functions.
From this you can infer immediately unsolvability and incompleteness of
any effective theory about machines (and numbers). Indeed if L is
universal, then you can enumerate the codes (and thus the corresponding
partial functions) written in L:
f_1, f_2, f_3, f_4, f_5, f_6, f_7, f_8, f_9, ...
But here the f_i denotes partial functions. That is a mixture of
strictly partial function and of total functions (partial function
where the domain-definition subset is N itself and thus total = defined
on all n, or put in another way they belongs to N^N.
Absolute unsolvability result:
There is no machine capable of deciding when, given a description of a
code in L, if that code is for a strictly partial functions or a total
partial function.
Proof. If such a code exists then you can used it to extract
mechanically from the enumeration
f_1, f_2, f_3, f_4, f_5, f_6, f_7, f_8, f_9, ...
a "sub-enumeration" of the total partial functions. But then you obtain
an enumeration of all total computable function and only
those!!!!!!!!!!!!
But this leads to a (always the same) contradiction (see above). QED.
(Relative) Incompleteness result.
There is no correct theories about machines in which all statements can
be proved.
Proof: if there was such a theory, you would be able to use it to
construct a machine capable of deciding totality/strict-partiality of
codes in L, contradicting the absolute unsolvability result. QED.
Note in particular that this means that for *any* correct theory T
there will be a particular true statement with the shape "the ith
expression in language L does code a total partial function" which is
undecidable in that theory. This explains why incompleteness is
relative, because in the theory T', which is T'+ (as new axioms) the
preceding true statement, obviously the statement becomes provable in
one line (by a proof saying "see the axiom". There is no equivalent of
Church's thesis for provability!
So you see that the first incompleteness theorem of Gödel is a simple
consequence of Church thesis. Incompleteness is proved by a direct
Cantor diagonalization done in the realm of computable partial
functions.
A question: what if we want, for some reason, be sure the universal
computer will not crash. After all we could ask for security. I will
not answer that question now, but thinking on this question will lead
to a notion of first person, and will give a notion of
sub-universality. Sub-universality is somehow the nearer you can go
near universality without loosing security.
More remains to be said, here of course. In particular, both in this
list and in a course I'm giving at ULB(*) I have begun to provide
example of universal language. It seems to help a lot some students.
- Cutland-Shepherdson-Sturgis coffee-bar language
- SK-combinators
- Diophantine Polynomials
- Robinsonian (and Lobian) Machine
- LISP
Let me summarize roughly the other points:
3) Lobian machines, who and what are they?
Here I have to explain the fundamental nuances between computability
and provability. We have already seen, just above, a very big
difference. For computability we have a "Church's thesis" and thus a
notion of universality, but we have none for provability. Having a
theory, we can always build a more powerful theory. No theories can be
provability-universal.
Now, nothing prevent *some* theory of being computability-universal,
and indeed we can build such a theory from any formal logical
specification of a universal language.
Such specifications will give our "absolute ontic TOE", and defines
the absolute measure on the Observer Moments from which we will derive
the physical laws (just to test such theories with the empirical
facts).
But the physics will not belong to the "absolute ontic TOE". Physics
will appears to belong to the "categorie de l'entendement"' would say
Kant, I mean physics appears as a particular view by internal observers
appearing in the "absolute ontic TOE".
We thus need an observer notion (if only to get the "Observer Moments),
and, as most of you already know, the observer will be the Lobian
Machine. A lobian machine will be a universal machine knowing (in some
weak sense) that she is universal. Such a machine will known to be
incomplete and will (a bit like Hal Ruhl try to say currently to
George) begin to build an (infinite path) toward completion. Much more
on this later.
BTW, Torkel Fraenkel's other book, on inexhaustibility, is a good
introduction for those autonomous progressions (as they are called in
the literature), but we will need only the fact that some modal logics
(the hypostases) remains invariant in those progressions for making the
comp-physics , and all hypostatses, stable and recoverable. More later
...
4) The 1-person and the 3- machine.
They are not the same, and they will fight against each other
"forever". In case you worry: they can make progress so that such fight
is less and less painful, or more and more civilized, that is by
discussing around a table instead than with bombs and bloody war, but
the tension between those two different view is not eliminable. Never,
unless comp is false.
5) Lobian machines' theology
The 1-person and the 3-person (3-machine) are just two arithmetical
interpretation of the Plotinian hypostases. Those who have followed
older posts, or have read my Plotinus paper, knows that there is 8
hypostases. Later we will see that some of those hypostases (=
points-of-view) will still be multiplied, indeed I expect some of them
to lead to some graded algebra describing some quantum computer, ...
For each machine, its arithmetical hypostases defines its theology.
Propositional (self) "theology" is given primarily by the modal logic
G*.
Propositional (self) "science" is given primarily by the modal logic G.
Pure propositional theology is given by G* minus G.
6) Lobian machines' physics
Just particular hypostases corresponding intuitively to the way matter
has to emerge as explained in the universal dovetailer argument.
7) Lobian machines' ethics
Not so difficult, assuming comp. I will indeed only consider the ethics
of the computationalist Lobian machine. One key is that the TRUTH of
"yes doctor" entails the RIGHT of saying NO to the doctor.
Computationalism *is* a religion somehow, and it can explain why it has
to be a "religion", and why it just cannot be used coercively on
people.
Alas, some NON-comp people could not tolerate the comp-people, and
this will give rise to future conflicts, ...
Then computationalism is not (at all) an ethical panacea, and I will
say some word of the type of conflicts occuring (in Platonia) between a
large variety of comp-people.
OK, I send this before putting it in the trash ... I expect to correct
and complete this post slowly but surely, and your remarks could help,
thanks.
Hal Ruhl
I see no "feeling" of anything in a Something. There is only an absence of the information needed to answer meaningful questions that are asked and must is be answered.
Hal Ruhl
George Levy
Ok, there is no feeling but there is motivation. There is no feeling of motivation and there is motivation without feeling. This is totally alien or the English language is broken.
John Mikes
Why does a "question" emerge? Why does it 'imply' to be answered? (I
avoid 'why do we feel') Where did 'incompleteness' occur from?
All these are very 'human' concepts and we impersonate them into a wider sense.
"WE" (as Bruno asked: who is that? and I replied 'humanly thinking
machines') still 'think' in our restricted human terms - cannot do
otherwise - using that incomplete primitive tool (brain function)
which in Self-reflection (consciousness? I hate that term) realizes
its own incompleteness and projects it towards the targets of its
thinking.
So the question itself does not 'emerge': it 'imerges in our thinking.
"Something" stands for the unidentified content - a challenge (human that is).
And - George - yes, the English language IS broken (as are all other
ones, maybe the English - as a mixed artifact - a bit more) because it
stands for unclear symbols and their communication with the pretension
of clarity. Words are restrictive tools of a restrictive
brainfunction.
Sorry for the holiday-breaking denigration
John
Hal Ruhl
In my post:
"I see no motivator to any dynamics within the Everything other than
the incompleteness of some of its members and the unavoidable
necessity to progressively resolve this incompleteness."
I used "motivator" in the sense that a gas engine is a motivator of dynamics.
I use incompleteness in the sense of a lack of information.
The initial "meaningful" question concerns the duration of a
particular Nothing.
This question is inevitable and must be answered ["unavoidable
necessity"], but the Nothing can answer no questions so is incomplete
so it becomes a Something to gain information.
A Something is a sub set of the members of the Everything and is
defined by its current boundary with the Everything.
The same question will apply to Somethings: What is the duration of
the current boundary? If a Something can not answer this question it
must change its boundary [expand it into the Everything]. This is a
new Something and the expansion may not have encompassed a sufficient
general answer to this question and so the process repeats
["progressively resolve this incompleteness"].
I currently see no other dynamic motivator/process within the
Everything or in/of any of its sub sets.
Hal Ruhl
John Mikes
">... I used "motivator" in the sense that a gas engine is a motivator
of dynamics...." <
Indeed? does a gas engine 'work' without dynamics - what is supposed
to be motivated by its activity?
This question came in as an initiator to my reply, since 'dynamics' is
bound to a process in time (maybe I misunderstand it). You also
mention several times "duration" - a definitely time-related concept.
Do you consider "time", - that hard-to-identify term, the coordinate
"WE" use in THIS universe (together with space) to get a hold on
occurrences which otherwise would overstep our mental (?)
capabilities - as fundamental at the Nothing - Something - Everything
discussion? If so, what is the origo? Is it in nothing or in
everything? How does it proceed from zero to nonzero?
*
"... duration of a particular Nothing..."
Does "nothing" carry qualia like 'duration'? Indirectly maybe, if you
compare identified 'somethings' to be cocurrent with 'nothing' and
then those 'somethings' WHEN you find no 'nothing connected.
It still would not mark the duration of 'nothing', only the duration
of its detection. I am weary of considering 'nothing' as a "physical"
system. By ANY attribute it becomes a something. Sorry, I may be
one-sided and ignorant, but I am stubborn.
*
Why "must {anything} be answered {as an} ["unavoidable
> necessity"],..."?
Our questions stem from our ignorance. With more mental power we
probably would know all the answers and have no questions.
I try to visualize (again the wrong view) "mental scales" and fear the
comparisons between concepts on different scales of ideation. (Cf:
quantized scale transition in chaos-thinking). We cannot overstep our
restricted level of [human] mental power just as Abbott's Mr 2D could
not think 3D.
*
I see your 'Something' point, not differentiated (all the way) to
Everything, when it becomes impredicative and unspecifiable.
I try to use the same concept locally in the R. Rosen type
'complexity', applied (mostly) to 'our world' (this universe).
Regards
John
Hal Ruhl
I discussed time origins in an earlier post on 1/9/2008.
I see no need for a "physical" grounding.
No entity is required to ask the question, it is asked by the mere
fact that Nothings are members of the "member of itself" nested Everything.
It is the question itself and the inability to respond that is the
key not any possible response.
I see no way for any sub set of the Everything including itself to
avoid this question and responding to it. An Everything is the only
member sure to have a response and a Nothing is the only member sure
to not have one. Somethings would be diverse on the issue.
Hal Ruhl
Mirek Dobsicek
> Title: SUMMARY (was: OM = SIGMA_1)
>
> I send to David Nyman (the 06 Nov 2007) a little planning:
>
> 1) Cantor's diagonal
> 2) Does the universal digital machine exist?
> 3) Lobian machines, who and what are they?
> 4) The 1-person and the 3- machine.
> 5) Lobian machines' theology
> 6) Lobian machines' physics
> 7) Lobian machines' ethics
>
>
> Let me summarize what has been done and what remains to be done.
Hi Bruno,
just want to let you know that I am still following your CT posts. I
hope to send my comments and/or 'OK' sign :-) on Monday.
Nice weekend to everyone,
Mirek
Bruno Marchal
Le 25-janv.-08, à 21:10, Mirek Dobsicek a écrit :
>
> Bruno Marchal wrote:
>> Title: SUMMARY (was: OM = SIGMA_1)
>>
>> I send to David Nyman (the 06 Nov 2007) a little planning:
>>
>> 1) Cantor's diagonal
>> 2) Does the universal digital machine exist?
>> 3) Lobian machines, who and what are they?
>> 4) The 1-person and the 3- machine.
>> 5) Lobian machines' theology
>> 6) Lobian machines' physics
>> 7) Lobian machines' ethics
>>
>>
>> Let me summarize what has been done and what remains to be done.
>
> Hi Bruno,
>
> just want to let you know that I am still following your CT posts.
Thanks for saying. Don't hesitate to ask anything in case some points
are unclear.
> I
> hope to send my comments and/or 'OK' sign :-) on Monday.
Take it easy. There is no deadline on the list.
>
> Nice weekend to everyone,
Best,
David Nyman
David
Bruno Marchal
Please take your time. As I said to Mirek we have all the time on this
list. I know that your motivation consists in clarifying the notion and
role of the "first person" in the unravelling of "everything", and I
feel a bit uneasy that I have to go back on Cantor and most importantly
on Kleene's diagonal argument for explaining that.
You can also ask me to go back on the motivations in case I am too
technical or in case you loose the main line, which is something easy
to do in a long multi-conversation.
What I have to do, before getting the math of the 1-person, is to
explain the nuance between computability and provability, and then the
nuance between provability which, like computability, is a third
person notion, and many 1-person (singular and/or plural) notions like
knowability, observability and sensibility or sensitivity (I am still
searching some words). And I have to make clear that all those notions
are quite different from the notion of "truth".
But thanks telling me that you are still thinking on my posts, despite
your short-of-time-ness (hmmm... that's not english).
I will perhaps give soon the solution of how to write a combinator
which makes the system looping, though. It is not necessary to
understand this to get the main point, but it is helpful for some
people in providing example of universal system/language.
Have a good day,
Bruno
Le 28-janv.-08, à 18:16, David Nyman a écrit :
Mirek Dobsicek
Hi Bruno and everybody,
>> I
>> hope to send my comments and/or 'OK' sign :-) on Monday.
>
> Take it easy. There is no deadline on the list.
Making a declaration helps me to get things done. Yet I'm late. Whenever
you see such sentences in my posts, you can skip it, they are mostly for
me :-)
---------------
I'll try to write a summary in my own words. Let's see how much I did
understand.
Prepositions:
A .... finite alphabet
A* .... finite words over A (it is enumerable, moreover effectively
enumerable)
L ..... a language over A.
E .... a subset of A*, a set of valid expressions in L (obviously, it
is at least enumerable)
M ..... a machine which understands to L
f ..... a total function from N to N.
Goal: I want to develop a universal language L which describes all
and only all functions f. Given an expression from E, M computes the
result in finite time. Given the restrictions on L, the result is a
number and nothing else.
The set of all functions f from N to N is not enumerable (by Cantor's
diagonal). Thus there is no bijection to E. Thus, I have to find a
smaller set of functions. I will call this set a set of computable
functions, C. Inevitably, this is computability by definition, by
definition of L. So L should be 'really good' in order to encompass as
much functions f from N to N as possible.
Now, I think of a bijection between E and C.
0 --- E_0 ~ f_0
1 --- E_1 ~ f_1
2 --- E_2 ~ f_2
3 --- E_3 ~ f_3
....
....
Since E are efficiently enumerable, C are efficiently enumerable as
well. Yes, it might happen that f_i = f_j for i != j, but is does not
matter as long as all unique f_i are in the enumeration.
Time for the Kleene diagonal argument. Opps, a language L that I dreamt
of does not exist. I have to relax from the condition that M on E_i
always return a number in a finite time. Well, what to return if not a
number ... nothing -> M experiences an infinite loop.
What a world, ok, my language has to describe total functions from N to
N and as well as strict partial functions from N to N. And it is clear
that I cannot know whether E_i corresponds to a total function or a
strict partial function. f' stands for any function descriable by L.
0 --- E_0 ~ f'_0
1 --- E_1 ~ f'_1
2 --- E_2 ~ f'_2
3 --- E_3 ~ f'_3
....
....
N, E and C are enumerable, moreover obviously effectively enumerable.
Any subset of C is at least enumerable. A subset of C corresponding to
total functions is no effectively enumerable. It cannot be.
Well, a language L which describes both total and strict partial
functions and hereby defines a set of computable functions is not
refuted by Kleene's diagonal.
It is not obvious to me how strong sort of evidence that universal L
exists, it is to survive Kleene's diagnonal. Droping an apple on the
floor is in favor of Newton's law but not very convincing :-)
Oh, now I realize that my question is actually weird. Since the set of
computable functions is defined by L, and L is said to be universal if
it describes exactly these functions - it is simple to develop a trivial
L -> it defines a set of computable functions ... and of course
universal L exists.
In this sence a universal language L always exists. So I write it rather
like this:
If we develop many sufficiently different programming languages and they
turn out to be all equivalent, it might convince me that the set of
'computable functions' is fixed. Although, written like this I can think
of educated (math) people who will tell me: This is all you have????
So, what are like 2-3 most direct consequences of CT which make CT to
seem rock-solid? Here I assume that CT basically says that the set of
functions descriable by the lambda calculus is all what I can ever compute.
-------------
Regarding points 3)-5) of your summary, I am lost on terms such as
Absolute ontic TOE, Observer Moments, Aristotelian principles, Machine
theology, ...
-------------
I wrote down a list of short-term goals on what I would like to have
some background/knowledge with a help from this list:
1\ I saw somewhere a sentence saying approximately this:
".... so universe is performing a computation. Is then universe a big
computer? No."
I would like to know in a broad sense what it tries to say a why one
shoud rather accept it or reject.
2\ Bruno, you recently wrote that you do not agree with Wolfram's
Principle of Computational Equivalence. As I understand to that
principle, Wolfram says that universe is a big cellular automata. What
is the evidence that it is unlikely this way?
Sincerely,
Mirek
Mirek Dobsicek
> Time for the Kleene diagonal argument. Opps, a language L that I dreamt
> of does not exist. I have to relax from the condition that M on E_i
> always return a number in a finite time. Well, what to return if not a
> number ... nothing -> M experiences an infinite loop.
>
> What a world, ok, my language has to describe total functions from N to
> N and as well as strict partial functions from N to N. And it is clear
> that I cannot know whether E_i corresponds to a total function or a
> strict partial function. f' stands for any function descriable by L.
>
> 0 --- E_0 ~ f'_0
> 1 --- E_1 ~ f'_1
> 2 --- E_2 ~ f'_2
> 3 --- E_3 ~ f'_3
> ....
> ....
>
> N, E and C are enumerable, moreover obviously effectively enumerable.
> Any subset of C is at least enumerable. A subset of C corresponding to
> total functions is no effectively enumerable. It cannot be.
Correction:
N and E are enumerable, moreover obviously effectively enumerable.
C is enumerable and thus any subset of C is at least enumerable.
A subset of C corresponding to total functions is not effectively
enumerable. It cannot be. Neither C as such is effectively enumerable.
It cannot be.
Mirek
Bruno Marchal
Le 30-janv.-08, à 13:42, Mirek Dobsicek a écrit :
>
>
> Hi Bruno and everybody,
>
>>> I
>>> hope to send my comments and/or 'OK' sign :-) on Monday.
>>
>> Take it easy. There is no deadline on the list.
>
> Making a declaration helps me to get things done. Yet I'm late.
> Whenever
> you see such sentences in my posts, you can skip it, they are mostly
> for
> me :-)
Am I suppose to skip this one too? :)
> Since E are efficiently enumerable, C are efficiently enumerable ...
I guess you want to say "effectively enumerable". Typo error.
> ... as well. Yes, it might happen that f_i = f_j for i != j, but is
> does not
> matter as long as all unique f_i are in the enumeration.
>
> Time for the Kleene diagonal argument. Opps, a language L that I dreamt
> of does not exist. I have to relax from the condition that M on E_i
> always return a number in a finite time. Well, what to return if not a
> number ... nothing -> M experiences an infinite loop.
>
> What a world, ok, my language has to describe total functions from N to
> N and as well as strict partial functions from N to N.
OK.
> And it is clear
> that I cannot know whether E_i corresponds to a total function or a
> strict partial function.
Clear for you, apparently. Is it clear for everybody? This follows from
the Diagonal argument applied on the "programs" in L.
> f' stands for any function descriable by L.
>
> 0 --- E_0 ~ f'_0
> 1 --- E_1 ~ f'_1
> 2 --- E_2 ~ f'_2
> 3 --- E_3 ~ f'_3
> ....
> ....
>
> N, E and C are enumerable, moreover obviously effectively enumerable.
> Any subset of C is at least enumerable. A subset of C corresponding to
> total functions is no effectively enumerable. It cannot be.
>
> Well, a language L which describes both total and strict partial
> functions and hereby defines a set of computable functions is not
> refuted by Kleene's diagonal.
OK. I guess that you see now that is by allowing a universal machine to
do infinite task which makes CT consistent (possible). OK?
>
> It is not obvious to me how strong sort of evidence that universal L
> exists, it is to survive Kleene's diagnonal. Droping an apple on the
> floor is in favor of Newton's law but not very convincing :-)
Because the diagonal argument is *the* tool for demolishing the idea
that such or such set is universal or complete, but then it does not
work on language like Lambda, Turing, etc. This entails a strong form
of incompleteness.
Then, Judson Webb, argued that Godel's incompleteness confirmed such
incompleteness, and thus CT, and thus Mechanism, Comp ...
>
> Oh, now I realize that my question is actually weird. Since the set of
> computable functions is defined by L, and L is said to be universal if
> it describes exactly these functions - it is simple to develop a
> trivial
> L -> it defines a set of computable functions ... and of course
> universal L exists.
OK, but this is due to your "definition" above of the set of computable
functions. Recall that we do have some starting intuition of what is an
intuitively computable functions. Church thesis is the assertion that
LAMBDA (or FORTRAN, or whatever programming system you love) does
capture that starting intuition. CT is both philosophical (linking an
epistemic concept with a mathematical class of functions) and
scientific (refutable in Popper sense: CT would be refuted in case we
find a clearly humanly computable function which would be uncomputable
in Lambda (and thus in Turing, Java, or any modern all-purpose
computer, etc.).
>
> In this sence a universal language L always exists. So I write it
> rather
> like this:
>
> If we develop many sufficiently different programming languages and
> they
> turn out to be all equivalent, it might convince me that the set of
> 'computable functions' is fixed.
Yes, and that is the case. I guess (from your thesis) that you are very
well aware that the quantum computer itself does not compute more
functions than FORTRAN, LISP, JAVA, PYTHON, Billiard Ball, Games of
Life, etc.
> Although, written like this I can think
> of educated (math) people who will tell me: This is all you have????
>
> So, what are like 2-3 most direct consequences of CT which make CT to
> seem rock-solid? Here I assume that CT basically says that the set of
> functions descriable by the lambda calculus is all what I can ever
> compute.
Of course, the power of *evidences* could depend on your own
background. Personally, the fact that the collection of partial
computable functions is closed for the diagonalization procedure seems
to me to be a very powerful reason to believe in CT. Of course it is
not enough, you could try as exercise to build a class of functions
closed for the diagonalization, yet not Turing-universal!. The evidence
comes from the empirical facts that all attempts have lead to the same
class, *together* with the fact that that the diagonal does not lead
outside the defined set, + some particularly good analysis of what is a
computation, mainly, imo, like the Turing's arguments, Church's one,
Emil Post's one.
> -------------
> Regarding points 3)-5) of your summary, I am lost on terms such as
> Absolute ontic TOE, Observer Moments, Aristotelian principles, Machine
> theology, ...
All right, all right .... that was an anticipation, at least relatively
to the current thread. We will come back on this, but to give you some
food I could say this:
Absolute Ontic Toe: that concerns the (minimal) ontological commitment,
i.e. what I will take as existing independently of me, or (because this
is just a question of phrasing) the set of sentences that I consider
being true independently of me or of any observer whatsoever.
I can explain that on,ce we accept comp (if only for the sake of the
conversation) then ontically we need not more than the number
theoretical truth (this is perhaps not obvious, but it should be
obvious that this follows from the UD Argument).
Observer Moment is a key informal "everything-list" concept. It has
been introduced by Nick Bostrom in together with the notion of
Self-Sampling Assumption, but the term is defensible in the comp
context, with the condition to be clear on the distinction between
states and the first person perspective. We can go back on this: I
argue that if comp is true, then the physical world in an internal view
of number theory as seen from inside. I like to paraphrase Kronecker:
God created the numbers, all the rest are inventions by ... numbers.
Aristotelian principle: well, concerning matter it is just the quite
common idea that there is a substancial world, made of "matter" ... I
call that sometimes weak materialism: the belief in a notion of primary
matter. Physicalism is very close to that idea: the dea that physics is
the fundamental science.
Machine theology: once you assume Church's thesis, it is easy to show
that most truth ABOUT machines can be written as relations between
numbers. Those relations are either true or false. The theology ABOUT
machine M is the set of all true relations among numbers which can be
interpreted as relations about the machine (albeit not necessarily so
by the machine). Due to the incompleteness phenonemon, this set is
different of the set of provable (by M) relations among numbers
(including again those relations bearing on the machine). In a
nutshell: theology is the science of truth (about machines, and other
entities), science itself corresponds to the provable relations. See my
Plotinus paper for more. We have to go back on this in due time.
> -------------
> I wrote down a list of short-term goals on what I would like to have
> some background/knowledge with a help from this list:
>
>
> 1\ I saw somewhere a sentence saying approximately this:
> ".... so universe is performing a computation. Is then universe a big
> computer? No."
>
> I would like to know in a broad sense what it tries to say a why one
> shoud rather accept it or reject.
>
> 2\ Bruno, you recently wrote that you do not agree with Wolfram's
> Principle of Computational Equivalence. As I understand to that
> principle, Wolfram says that universe is a big cellular automata. What
> is the evidence that it is unlikely this way?
The shortest answer is that you cannot simulate "in real time" a
quantum computer with a classical cellular automata. OK?
Also: what does that mean that the universe is a big cellular automata?
Now the main reason to find that unlikely is that such a vison is based
on the idea that pour consciousness and experiences are related to the
actual running of a machine/brain. This is shown just epistemologically
unlikely through the UD Argument.
Your points 1) and 2) are related. I maintain that if comp is true,
then the physical or observable "universe" cannot be a computational
object: i.e. it cannot be the output of a program nor can it be related
to the running of a special program, except in some very weak sense.
Why? that is really all what the UDA is about. And then the interview
of the lobian machine will consist in making a rough, (but highly non
trivial) arithmetical translation of UDA in the language of the
(universal, even Lobian) machine. A Loebian machine is mainly an
enlightened machine: a universal machine which knows that it (she ...)
is a universal entity.
The reason why, IF we are digitalizable machines, then the physical
world cannot a priori be a machine, nor a product of a machine, comes
from the fact that we cannot know which computations does actually go
through our local states, and there is an infinity of such
computations. To predict our local and relative "future" we have to
take into account *all* such computations. Comp predicts that if I
observe myself at a level below the level of substitution (where I
survive substitution by comp), then I will observe the trace of many
parallel computations. I take QM (without collapse) as a confirmation
of this.
Did you grasp the first-person indeterminacy? Are you ok with the idea
that comp makes us duplicable, at some level, and if we are duplicable
(at that level) then if we are actually duplicated (copy and
annihilated in Brussels, say, and reconstituted in Sidney and Beijing
(say), do you accept that in Brussels we cannot predict with any
certainty which places we will feel to be there?
I must go and perhaps comment your other post later (about ordinal, I
will have the opportunity to give some effective use of them related to
the notion of universality).
Bruno
Hal Ruhl
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.
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.
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.
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.
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 containing any number
of copies of part or all of itself is just as incomplete as if it
contained just one copy.
3) Evolution:
The progressive resolution of the incompleteness is an evolution.
4) Developing filters [re: white rabbit density]:
The shifting incompleteness of a subset constitutes a shifting filter
that is founded in the history of the dynamic for that Something. [I
mentioned white rabbits in this regard in another post.]
5) Giving meaning to data [symbol strings][generation of information?]:
The Everything is considered information. A symbol string seems to
be just a link between the set of all possible meanings that
particular string can have. It is just a boundary within the
Everything enclosing the associated set of meanings. It is a
definition, definitions are information [meaning] and thus part of
the Everything. How can an evolving Something and its subsets give
more meaning to a meaning? This property seems unsupportable in an Everything.
6) Necessity of "Time":
As I mentioned in a earlier post the meaningful question I use
bootstraps time and thus the dynamic.
7) Life:
The characteristics of life [evolution, copy, variation] are just
part of the ensemble of potential meaningful questions - some
un-resolvable - that can apply to some subsets of a Something and
seem covered by the other discussions herein.
8) Randomness:
Each step in the progression towards completeness provides a
resolution to a random set of the open meaningful questions.
9) Self awareness, consciousness:
The Something subset boundary dynamics/allowances described above
appear to cover these varieties of subset evolution.
10 Creativity:
See #8 - randomness.
Subsets of evolving Somethings in my model appear to have the
properties of observers mentioned above that also seem supportable by
an Everything - all but giving meaning to data.
There is so far no subset based spontaneous influence on the
progression of the dynamic. All aspects of the information dynamic
appear to originate from the history of the dynamic for a particular
Something and its resultant current incompleteness.
Hal Ruhl
John Mikes
that is quite a description... - especially if one dos not abide
inside your terminology.
I feel it is based on somewhat 'humanized' thinking (...prediction of
future...etc.) and 'subsets' (a humanly visualized hierarchy) with
'communication' as we understand it. Evolution fits my version, in a
more general wording (would be long to compare here).
Information (=everything) is fine, I just add in MY terminology (not
said as preferable!) an "acknowledged difference" which is not
contradictory vs. 'realizing the everything'. (Acknowledged means ANY,
maybe phenomenological imbibing or 'structural' absorption)
[I don't exclude the 'humanized' versions of the more general meanings].
I give less validity to 'data' - maybe I look at them too narrowly as
quatiz(able) markers.
I like your 'symbol string' as boundary, giving 'meaning' to inside
the boundary-s - what I call a model, topically distinct and
identifiable domain within the totality (everything?).
I am still strygglin with thinking 'atemporaneously', maybe I should
pick on your 'bootstrap time'.
Interesting view on 'randomness' as a result rather than random generational.
Consciousness, self-awareness I mix into reflexive relations, not
resolved so far. Creativity ditto, a relational game.
Hal, please excuse my rambling about words I picked and indeed did not
comprehend. Your system is way above the level I could follow. I
scribbled the above reflections as an example from a different mindset
and vocabulary as I 'glanced' at your post.
Not argumentatively at all.
My 'system' is NO system, just ideas in a heap.
If you find something addressable in the above, please do let me know,
I speculate on imported suggestions to resolve that vast amount of
unresolved points in that heap.
John Mikes
Tom Caylor
> 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.
>
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.
>
"meaningful question"?
> 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.
>
> 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.
>
meaning?
> 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 containing any number
> of copies of part or all of itself is just as incomplete as if it
> contained just one copy.
>
> 3) Evolution:
> The progressive resolution of the incompleteness is an evolution.
>
> 4) Developing filters [re: white rabbit density]:
> The shifting incompleteness of a subset constitutes a shifting filter
> that is founded in the history of the dynamic for that Something. [I
> mentioned white rabbits in this regard in another post.]
>
> 5) Giving meaning to data [symbol strings][generation of information?]:
> The Everything is considered information. A symbol string seems to
> be just a link between the set of all possible meanings that
> particular string can have. It is just a boundary within the
> Everything enclosing the associated set of meanings. It is a
> definition, definitions are information [meaning] and thus part of
> the Everything. How can an evolving Something and its subsets give
> more meaning to a meaning? This property seems unsupportable in an Everything.
>
> 6) Necessity of "Time":
> As I mentioned in a earlier post the meaningful question I use
> bootstraps time and thus the dynamic.
>
> 7) Life:
> The characteristics of life [evolution, copy, variation] are just
> part of the ensemble of potential meaningful questions - some
> un-resolvable - that can apply to some subsets of a Something and
> seem covered by the other discussions herein.
>
> 8) Randomness:
> Each step in the progression towards completeness provides a
> resolution to a random set of the open meaningful questions.
>
> 9) Self awareness, consciousness:
> The Something subset boundary dynamics/allowances described above
> appear to cover these varieties of subset evolution.
>
> 10 Creativity:
> See #8 - randomness.
>
That's the crux of the matter.
> Subsets of evolving Somethings in my model appear to have the
> properties of observers mentioned above that also seem supportable by
> an Everything - all but giving meaning to data.
>
> There is so far no subset based spontaneous influence on the
> progression of the dynamic. All aspects of the information dynamic
> appear to originate from the history of the dynamic for a particular
> Something and its resultant current incompleteness.
>
> Hal Ruhl
reductionism, if everything is information.
As I've said before in other discussions here, you can't get there
solely with (impersonal) information. There needs to be a personal
aspect to the foundations of everything. Hal, I think you were
touching on a personal aspect earlier with your word "quest" in your
dark energy post.
Tom
Hal Ruhl
I am thinking about your posts.
Hal Ruhl
Hal Ruhl
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
Stephen Paul King
I hae been following Hal's work for quite some time. Some comments...
[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)
[SPK]
COuld it be that a "random set" is just a stand in for some collection
chosen without a pre-established "rule"? Again, consider a dictionary and
the sequensing of words in a paragraph or a string of symbols.Given a notion
of a grammar, do the words/symbols follow necessarily monotonically from a
fixed one-to-one and onto type of rule? No. Just because a rule may exist
that could generate a given string, it does not follow that said string was
in fact thus generated.
>> Subsets of evolving Somethings in my model appear to have the
>> properties of observers mentioned above that also seem supportable by
>> an Everything - all but giving meaning to data.
>>
>> There is so far no subset based spontaneous influence on the
>> progression of the dynamic. All aspects of the information dynamic
>> appear to originate from the history of the dynamic for a particular
>> Something and its resultant current incompleteness.
>>
>> Hal Ruhl
snip
Onward,
Stephen
Hal Ruhl
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].
John Mikes
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
John Mikes
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
Hal Ruhl
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