**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Wed, 26 May 1999 07:57:27 +0300 (EET DST)*

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On Tue, 25 May 1999, Stephen P. King wrote:

*> Dear Matti,
*

*>
*

*> I would like to explore my thinking of information and the "modeling of
*

*> subjectivity" a bit more closely. :) I believe that we are using
*

*> different paradigms (ways of thinking) and misunderstand each other. :(
*

*>
*

*> Matti Pitkanen wrote:
*

*> snip
*

*>
*

*> > Quantum histories are quantum superpositions of these spacetime surfaces
*

*> > and moments of consciousness (observations) give conscious information
*

*> > about them and create 'I', the illusion about observer as continuous
*

*> > stream of consciousness.
*

*>
*

*> What is "information" to you? I see is as a quality that is *what
*

*> symbols or configurations represent*; it is "meaning" in-tself! To
*

*> identify "physical states" with the "meaning of symbols" would, to me,
*

*> imply that the symbols are a priori synthetics. This is, IMHO, not even
*

*> wrong, it is meaningless. I can understand that spacetime
*

*> [hyper]surfaces do encode information and consciousness is definable as
*

*> sequences (or ensembles?!) of mappings between such. And, yes, the
*

*> "observer as continuous stream of consciousness" is a concept I agree
*

*> with! It is "how" the "illusion" is generated that I am talking about
*

*> and I think you are also!
*

[MP]

I see the concept of information as the source of problems. Is it

needed really. As I explained in previous post, various

candidates for measures of information or information gain

have turned out to be something else (negentropy gain in quantum jump

as 'catchiness' of potential conscious experience,

the negative of Kahler function as 'intelligence quotient', the

density of cognitive spacetime sheets on material spacetime sheet

defining the resolution of sensory experiencing). So my

cautious suggestion is that perhaps we should throw the concept of

information into paper basket and consider only physical systems which

quantum simulate each other and have conscious experiences when jumping

from simultation to another one.

On the other hand, I am ready to identify quantum histories as

Platonic Idea's: what does 'Idea' mean. Something fundamental

not reducible to anything else? Could the concept of 'Idea' replace

information as basic concept? Or could it be just information?

By the way, the previous posting inspired me to consider the problem

'What one can say about contents of conscious experience when initial

and final quantum histories are known?'. It is not possible to

express conscious experience using closed formula but it is possible

to say something. For instance, information contents (I caught myself

using that dangerous word!!) correspond to region where nondeterminism is

concentrated). Interpretation as quantum measurement suggests that

measured observables correspond to 'qualia', selection between final

states corresponds to experience choice,.... Could it be that the

mathematical philosophy ('conduction' instead of induction) you talked in

your last message could apply in this problem.

BTW, how do you define information precisely?

*>
*

*> [SPK]
*

*> > > > > We need to carefully consider what is computation! I see these
*

*> > > > > "associations" as an example of computation! It is the identification of
*

*> > > > > *output* by a given physical process with some *input*. We think of
*

*> > > > > "input" as data or equations and variables or signals from arbitrary
*

*> > > > > sources or ... and "output" as patterns or solutions or messages or ..
*

*> [MP]
*

*> > > > In this sense you could regard classical time evolution of physical
*

*> > > > system as computation. But quantum jumps is not a computation: it is
*

*> > > > not modellable. Or so I believe....
*

*> > >
*

*> [SPK]
*

*> > > Not modelable in a Turing Machine (TM) sense, yes, but it is modelable
*

*> > > in an Interaction Machine (IM) sense! The property of
*

*> > > "nonserializability" of MIMs (see section 10 of Peter's paper) speaks
*

*> > > directly to this point! :) The key idea is that these "quantum jumps",
*

*> > > as experiences, are _*NOT*_ a priori synthetics! They are constructed by
*

*> > > finite local systems in an "on the fly" way! This is a direct
*

*> > > contradiction to the LaPlacean vision of a 4-dimensional frozen
*

*> > > universe! Please read Peter's paper. ;)
*

*> > > also: http://hume.ucdavis.edu/kant/pap1comm.htm for comments on a priori
*

*> > > synthetics...
*

*> [MP]
*

*> > I think I understand you point here. My belief (we are
*

*> > now in dangerous zone(;-)) is that the basic property of subjective
*

*> > experience is nonmodellability but I could be wrong.
*

*>
*

*> It is obvious that a mathematical model of subjectivity can not have an
*

*> intentional stance or "be aware" of anything. So I agree with your
*

*> statement that "the basic property of subjective experience is
*

*> nonmodellability", but I am trying to discuss how to deal with the
*

*> subject-object dichotomy itself as a object of a model.
*

[MP]

I realize that my statement about nonmodellability might be misleading.

It is possible to say something about conscious experience and I am

definitely saying as became clear above.

*> When an observer
*

*> A observes another observer B and attempts to model B's subjective
*

*> stance, A is modeling B's point of view, but A's model of B's point of
*

*> view is not B's point of view unless A = B and thus when A =/= B, we
*

*> have to conclude that A's observations and B's observations are at least
*

*> non-Hausdorf in their classes of observations. In other words, we can
*

*> say that A and B can have similar observations, but the subjective
*

*> observation of A by B and B by A are not the same topologically set
*

*> point wise.
*

I did not understand the argument leading to non-Hausdorf although the

argument had the stimulating flavour of self-reference in it!

In any case it is interesting exercise (form me at least(;-)))

to see whether my own linguistic machinery could be capable of expressing

what you are talking about.

a) In TGD framework all possible conscious experiences/observations are

formed by all allowed initial-final quantum history pairs, which should

form quite well defined space possessing, for instance Hermitian metric

induced by Hilbert space inner product.

b) Each initial-final state pair defines subsystem-complement

decomposition: in p-adic context one can say that universe decomposes

into union of even finite sub-universes and one obtains union

of subsystem-complement pairs.

c) By adding cognitive spacetime sheets simulating not only matter

but also other cognitive spacetime sheets one should be able to

generate arbitrary complicated simulations.

This was just an exercise.

*> Umm, all of this wording tacitly assumes a third observer C, here me
*

*> writing these words, and this is one of the reasons why this issue is so
*

*> difficult! A third observer C observing the behavior of A and B
*

*> perceives them as systems with some dynamics and is only capable of
*

*> modeling them as objects separate from itself.
*

*> One of the actions that we, as conscious observers, do is to jump from
*

*> on "vantage point" to another, much like, I think, you mean with your
*

*> talk of "quantum jumps". If we do not explicitly take into account this
*

*> nonmonotonic (if this is the correct term) property we get lost!
*

The illusory 'observers' represent different vantage points.

Different side personalities as different vantage points. Left and

right brain hemispheres as different vantage points,

especially so for split brain patients. Our society

as badly split super brain, which has rather few moments of collective

consciousness. On the other hand, the splitting to two different vantage

points is also a good thing: it is known that problems which

are trivial when brain halves work as separate units of consciousness

are hopelessly difficult for brain working as single unit of

consciousness.

*>
*

*> > If quantum jump is modellable, the model must
*

*> > explain why only a discrete subset of all
*

*> > possible final states (eigenstates of 'measured' observables)
*

*> > and predict correctly the probabilities of various outcomes.
*

*> > Here is formidable challenge for IM.
*

*>
*

*> Is it explaining "why only a discrete subset of all possible
*

*> eigenstates" is experienced by any given observer?
*

[MP] Your probably mean 'only eigenstates forming a discrete subset of

all possible *final states*'. If one wants explain this selection

dynamically one must have extremely nonlinear dynamics but

quantum mechanics is linear. This is the problem.

*> I can only say
*

*> "whatever happens happens because it was the easiest given the
*

*> circumstances", e.g. the Principle of Least Action. But, I am thinking
*

*> of such as an "action", like a verb. I see this as a problem or an
*

*> equation that the Universe is trying to solve. This "solving" is what I
*

*> mean by "computation"! The solutions do not exist in a way that is
*

*> accessible without constraints; this is an assumption of Classical
*

*> thinking, that knowledge is obtainable without a price. We see the
*

*> subtleties of this in the study of Maxwell's Demon:
*

*> http://members.home.net/stephenk1/Outlaw/maxdemon.html I have been
*

*> trying to speak about this in my previous posts but it seems that I am
*

*> not understood. :( Also, to say that "this as a problem or an equation
*

*> that the Universe is trying to solve" is a figure of language, I mean it
*

*> metaphorically, but I do intend the meaning! :)
*

[MP] Universe trying to understand itself.

*> "Predict correctly the probabilities of various outcomes" seems to
*

*> imply, to my thinking, that it is somehow possible to compute the
*

*> outcome of a given equation "faster" than it takes Nature to generate
*

*> it! This is why I say that observations qua experiences are
*

*> constructions! It is well known that it is impossible to simulate most
*

*> phenomena "faster" that Nature makes them happen. (the NP-Completeness
*

*> issue)
*

You seem to define simulation as computation. I define it as physical

interaction. Cognitive spacetime sheet interacts with wormhole

contacts with material spacetime sheets: oscillatory processes

on material spacetime sheets are mapped to oscillatory processes

at cognitive spacetime sheet. Radio receiver is excellent example

metaphor for this. I have problems with my age old radio receiver,

but these problems have nothing to do with NP-completeness issue!

Of course, in my simplest model simulation is bound to happen

in 'real time'.

*> This last point speaks to two issues that at first do not appear to be
*

*> related: 1) the finite "speed" of signals and 2) the "why" one thing
*

*> happens rather than another (Leibnitz's Principle of Sufficient Reason).
*

*> But I don't wish to get into this thorny line of thinking directly here
*

*> and now. :)
*

*> We could say that what we experience is the Universes simulation, but
*

*> we must understand the subject-object duality better. I say that the
*

*> subject-object relation is a duality because, well, to think of one
*

*> without at least tacitly assuming the existence of the other is
*

*> impossible and it is obvious that they are not ontologically identical.
*

*>
*

[MP] But what if one gives up the idea of subject and object.

No continuous streams of consciousness? Only different vantage points?

The moments of consciousness of subject and object as different vantage

points?

*> What I am trying to do here is to see if there is an algebra that can
*

*> be represented symbolically. One thing that see as lacking in other
*

*> attempts to construct such kinds of algebra is that they tend to only
*

*> allow
*

*> for a single set of observables. There does appear to be an identity and
*

*> an operation and an inverse, but there is also something else! There is
*

*> not an equality, there is an equivalence that I see explained well by
*

*> the concept of observational equivalence. I will try to get to the
*

*> detail of Peter's discussion in a future post.
*

*> I found an interesting paper that discusses these issues:
*

*> http://xxx.lanl.gov/abs/quant-ph/9901013
*

*> Later,
*

*>
*

*> Stephen
*

MP

*>
*

*> PS, I am pasting a letter that discusses these issues:
*

*>
*

*> ***
*

*>
*

*> Subject: Re: Consciousness
*

*> Date: Tue, 18 May 1999 09:07:43 -0400
*

*> From: "Stephen P. King" <stephenk1@home.com>
*

*> Organization: OutLaw Scientific
*

*> To: SOMMEB@mail.modot.state.mo.us
*

*>
*

*> Dear Frater Rex,
*

*>
*

*> SOMMEB@mail.modot.state.mo.us wrote:
*

*> >
*

*> > >Ahh, yes! "recursion"!
*

*> > >I have to ask some questions... You know what a time series and an
*

*> > >ensemble is, in that statistics, and/or a Fourier transform is? I have
*

*> > >been working on a thought experiment to illustrate what we are both
*

*> > >talking about! :)
*

*> >
*

*> > Yes. I have been studying the Fourier series lately to better
*

*> > understand holography. Since I'm no mathematician, it is
*

*> > slow going. What's the gist of your thought experiment?
*

*>
*

*> A local friend has also. :) The idea is to consider that the
*

*> relationship between a time series of observations and an ensemble of
*

*> observations as a Fourier transform. (I think!)
*

*>
*

*> http://uss-macran.com/Procs/ensav.htm
*

*> http://karlsberg.usask.ca/~andreas/thesis/node26.html
*

*> http://www.cv.nrao.edu/adass/adassVI/vityazevv2.html
*

*>
*

*> What I am trying to do is to see if it is possible to model
*

*> space and
*

*> time in terms of the way discrete time systems (that have time varying
*

*> over Z) can sample each others events as isomorphisms into some
*

*> multivalued subset
*

*> of their phase space. Umm, the math is a mess. The problem here is that
*

*> there is no natural (english) language to explain what I am thinking.
*

*> :( I will try to build up to it as we correspond, if you put up with my
*

*> rantings! :)
*

*>
*

*> > >Is it assumed that information *is* the configurations of
*

*> > >matter/energy?
*

*> >
*

*> > Well, I think in reference to what you write further down
*

*> > in this note, that information equates more to the Platonic
*

*> > realm. I think there is much merit in Rupert Sheldrake's
*

*> > morphogentic field theory. One thing that I asked my
*

*> > biology professor in college was "How can an organism
*

*> > take a certain form when each cell contains the same
*

*> > genetic coding, i.e., there is no "master cell." You have
*

*> > many copies of a software program which are identical,
*

*> > each one capable of producing the whole (as with
*

*> > cloning). But if this is so, how do you get tissue
*

*> > differentiation? What tells this group of cells to start
*

*> > becoming muscle, these cells bone, etc., and to
*

*> > begin growing and stop growing at point x, if each cell
*

*> > contains identical information? Of course, he didn't
*

*> > have a clue.
*

*>
*

*> I have read all of Sheldrake's book that I have been able to
*

*> find and I
*

*> think that he was (I don't know if he is still "into it...) onto a good
*

*> idea. The way that cell differentiation occurs is a strange thing
*

*> indeed. I have read the chemical signal + number of cell divisions
*

*> theory, but I am a bit agnostic on the issue. There are some very subtle
*

*> processes going on! But, I will say that if the information/matter
*

*> duality holds, effects such as that Sheldrake describes are more likely
*

*> derivable!
*

*>
*

*> > >I have found Berkeley's idealism (mental monist) to
*

*> > >suffer from the same incompleteness as that of the material monist. :(
*

*> >
*

*> > Yes, I agree, as I've written before, that he failed to see that there is
*

*> > no distinction between the two, and sought the exclusivity of one
*

*> > (ideal). I was afraid to bring him up, but I think he does give a good
*

*> > refutation of qualia being inherent characteristics of an object rather
*

*> > than mental constructs.
*

*>
*

*> I agree. It is easy to see from QM that qualia, qua definite
*

*> properties, are not inherent, but rather selected by observation...
*

*>
*

*> > >They both can not deal with the fact that knowledge presupposes a
*

*> > >standard against which propositions can be decided against. Problem is
*

*> > >that the validity of a standard that can be encoded into a finite set of
*

*> > >configurations of matter/energy is not decidable by any algorithm
*

*> > >encodable in the dynamics of the matter/energy.
*

*> >
*

*> > Are you talking about Roger Penrose's algorithmic argument against the
*

*> > ability of a machine to be conscious?
*

*>
*

*> Sort of, I had not consciously considered Penrose's argument
*

*> when I was writing, but I
*

*> have read all his papers and books so I could except some influence. :)
*

*> I was thinking more in terms of Goedel Incompleteness from Calude and
*

*> Svozil's work:
*

*> http://www.cs.auckland.ac.nz/~cristian/
*

*> http://tph.tuwien.ac.at/~svozil/w1.html
*

*>
*

*> > >This line of thought is mute if one is convinced that matter/energy
*

*> > >*is* information and vise versa at all levels of recursion. The mind can
*

*> > >be seen as pure information, once we understand that information has
*

*> > >dynamics "of its own" independent of any particular motion of
*

*> > >matter/energy. And, dually, we see that a particular motion of
*

*> > >matter/energy can be described by many different pattern of shifting
*

*> > >information.
*

*> >
*

*> > The very word "information" or "in-form-ation" implies that it is
*

*> > a process whereby form is given to something which was previously
*

*> > formless. It would seem to me that information is the raw potential
*

*> > which mind operates on, i.e., the rules of thought (mind) which
*

*> > then process this raw potential to "in form" an object.
*

*>
*

*> Yes, that makes sense, but this argument does not categorically
*

*> distinguish mind from information! Mind is structured information, but
*

*> not is a static sense; it orders and correlated bits. Web weaving is a
*

*> good analogy. :) Information, in it-self is just as meaning-less as
*

*> matter in it-self is property-less.
*

*>
*

*> > >The idea that I am talking about does not consider matter/energy and
*

*> > >information as different in essence, as Decartes at al posited, they are
*

*> > >the Forms of subject and object, in the Platonic sense (if that means
*

*> > >something to you. ;) ) in that they are necessary aspects of
*

*> > >consciousness that are a priori to any particular "initial" act of such.
*

*> >
*

*> > I would say that information and certain aspects of
*

*> > mind are a priori, but not matter. The reason I state that certain aspects
*

*> > of mind are a priori and others not is because I see the a priori aspect
*

*> > of mind as the rules which determine how the information is going to
*

*> > be explicated as object. However, sensation is not a priori, and
*

*> > sensation is an aspect of mind. Is this a sublte form of dualism? I
*

*> > don't think so because if mind can be roughly equated with a program,
*

*> > then sensation would be the identification of certain information from
*

*> > the implicate realm (to borrow a phrase from Bohm) and using this
*

*> > to form constructs which are themselves, of course, information, but
*

*> > in explicate form, i.e, the information has been given form. The form
*

*> > that this information takes will be determined by the a priori rules
*

*> > of mind. It is this explicate form that we call matter.
*

*>
*

*> umm, I don't take Bohm that way. I see his explicate and
*

*> implicate as
*

*> identical to my existence and actualize concepts. Explication is the
*

*> process of selecting out one particular set of properties from the
*

*> infinitude just as actualization, and both are relative to observational
*

*> contexts.
*

*> Well, I found this: http://www.qedcorp.com/book/tsld005.htm which back
*

*> you up...
*

*> This paper is excellent:
*

*> http://www.island.net/~dbruiger/doc_html/entire_doc.html
*

*> The matter/information duality is different as I see it. I see
*

*> matter
*

*> as categorically different from information in that they are co-defining
*

*> substances, information requires some substance that is not information
*

*> to be actualized and matter requires some substance that is not matter
*

*> to label its properties. Vaughan Pratt, as I interpret him, shows that
*

*> it is the dynamics of each that distinguishes their substanceness. They
*

*> have opposite arrows of entropy! For matter we identify time's direction
*

*> with the arrow of thermodynamic entropy and for information we identify
*

*> the logic's direction of implication with the arrow of Fisher
*

*> information.
*

*> When we look at the situation in the limit of infinity, we see
*

*> that
*

*> their "motions" exactly cancel leaving us with the no-thing-ness of the
*

*> grundlagen of Totality. Thus, to get mystical, we can echo A. Crowley's
*

*> assertion that 0 = 2 = |1| + |-1| :)
*

*>
*

*> > >But, to think of them, like the physicists do, as aspects of some
*

*> > >"pre-spacetime" vacuum from which the Big Bang "singularity" inflated.
*

*> > >(Oh, BTW, I do think that the Big Bang is a giant optical illusion!)
*

*> >
*

*> > Do you propose a steady-state theory or something else?
*

*>
*

*> The Universe is only "static" en toto, any finite observational
*

*> frame
*

*> will have the appearance of expansion due to the increase in information
*

*> encoded in an observer as their time goes on. Think of this as how any
*

*> given observer has its own finite actuality - their own universe- as we
*

*> allow (within the model) for increasing information content of the
*

*> knowledge base, e.g. increasing experience, there must also be a
*

*> proportional increase in the material content to encode such
*

*> information.
*

*> Equivalently, we can think of increases in the efficiency of
*

*> compressing the knowledge base of the observer, but we trade off space
*

*> for time. Either way, if we think of the subsets of the Totality, a
*

*> subset of which are us, are being aspects of the Universe experiencing
*

*> itself, we must consider the consequences of knowledge increases! :)
*

*>
*

*> > >The key is that interchanging subject and object is equivalent to
*

*> > >turning one into the other, such that their mutual 'motions' are
*

*> > >unobservable. I am trying to see if this can be modeled mathematically,
*

*> > >but you do make a good point below...
*

*> >
*

*> > I don't follow what you mean by interchanging subject and object?
*

*>
*

*> I am thinking of the "involution", we change an object into a
*

*> subject
*

*> and vise versa.
*

*>
*

*> > >I mean the "reflection"; of course that which Perceives, (P), can not
*

*> > >be that which P is not, e.g. (~P), e.g. (P) = (~P); or can it?! Ever
*

*> > >hear of the Liar's Paradox? Ever heard of fuzzy set theory? I do not
*

*> > >mean to be arrogant or whatever, it is just that I need to understand
*

*> > >your background to understand that you "mean" with these words used. I
*

*> > >have experience how even simple ideas can be terribly misunderstood. :(
*

*> > >So I try to be sure that I am making sense in my arguments by trying to
*

*> > >be sure I understand your thinking.
*

*> >
*

*> > P observes itself by becoming false to itself, e.g., by splitting itself
*

*> > into subject and object. So in this sense, P is ~P. I think most
*

*> > physicists would agree that everthing came from nothing, that or
*

*> > everthing has always existed. How does everyting come from
*

*> > nothing? Because no-thing is the ultimate level of reality, that level
*

*> > which exists beyond dualism, beyond subject and object, beyond the
*

*> > created world of thingness. When you keep tracing matters back
*

*> > far enough, it gets strange by anyone's standards, and the ultimate
*

*> > question is why there is something rather than nothing, and how
*

*> > this could occur. Anyone who thinks talk of "that which perceives" is
*

*> > muddy headed new age nonsense hasn't really come to grips with
*

*> > how bizarre this subject is (obviously I'm not stating that YOU are
*

*> > such a person, since you have obviously though of it a lot !)
*

*>
*

*> You do cut to the quick! ;) This property of "P observes itself
*

*> by
*

*> becoming false to itself" is what I would consider the essential
*

*> property of consciousness! The distinguishability of Self from not-Self
*

*> via negation can be considered as a sequence of questions that act to
*

*> asymptotically to select properties. This is the act of actualization.
*

*> Thus we affirm that actualization is the act of selecting a finite set
*

*> of properties out (via negation) from the infinitude of possibilities.
*

*> The renormalization procedure in physics work the same way! For example
*

*> http://socrates.berkeley.edu/~jqwu/paper3/node1.html#SECTION00010000000000000000
*

*>
*

*> > > What is it that is observing your thoughts? That is the
*

*> > > level of Absolute Subjectivity which cannot itself be an
*

*> > > object of perception, and it is this level that I believe
*

*> > > Erwin Schrodinger and others have written of, one perceiver
*

*> > > "multitasking" through many nodes, the One looking at
*

*> > > itself through an infinite number of conscious beings
*

*> > > which in fact only exist by virtue of the One dividing
*

*> > > itself up infinitely through the creation of subject/object
*

*> > > duality, which relates back to your statement that in a
*

*> > > sense duality doesn't exist, but is a necessary "artificial"
*

*> > > splitting up in order for any awareness to even be
*

*> > > possible.
*

*> >
*

*> > >Absolute Subject-ivity necessitates Absolute Object-ivity, problem is
*

*> > >that the very attempt to talk about "subject" makes it an object. It is
*

*> > >not unlike me responding to your post here, I am responding to my mental
*

*> > >version (VR) of what you wrote and your response to my post with follow
*

*> > >the same pattern. There is thinking of this type of idea running
*

*> > >throughout Peter Wegner's work...
*

*> >
*

*> > This I would have to strongly disagree with. Absolute subjectivity is subject
*

*> > without object. It is utterly unconscious, unaware, it is pure being. There is no
*

*> > absolute objectivity, which is not a contradiction since there is no
*

*> > awareness at the level of absolute subjectivity, and hence no objectification.
*

*> > Absolute subjectivity, as opposed to "regular" subjectivity, is unconscious!
*

*> > This is why I make the distinction between consciousness and absolute
*

*> > subjectivity. Otherwise, you fall into infinite regress.
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*>
*

*> Well, I agree when it is put that way! :) But one could argue
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*> that
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*> absolute objectivity has exactly the same properties of "utterly
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*> unconscious, unaware, it is pure being"! So we are left with relative
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*> subjectitivy/objectivity! Relative to finite "local" standards with
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*> which actualization may occur. These finite standards relate to clocks,
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*> rods and orderings that each observer has as the categories (filters)
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*> with which to distinguish qualia. But note that in the big picture,
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*> these standards are only asymptotically accurate up to the limit of
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*> infinite certainty at which point subject-object distinguishability
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*> vanishes.
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*>
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*> > >YES! :) We are on the same wavelength! What I am arguing is that since
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*> > >there are more than one "way" that the "frames" in the film can be
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*> > >ordered in such a way that is consistent, e.g. ... frame(1) -> frame (2)
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*> > -> ... frame (N) -> frame (N+1) ... Thus we must understand that where
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*> > >is *not* just One Film with its One Now within Existence at any finite
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*> > >order of complexity. The key point is that there is no absolute
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*> > >"initiality", there is no way of uniquely ordering all possible
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*> > >(nonenumerable) number of possible events. There are many finitely
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*> > >consistent orderings. Only at the Infinite level is there one unique
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*> > >ordering, but, such is unknowable! To Know something is to be able to
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*> > >represent it is some way within one's repertoire of possible finite
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*> > >experiences.
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*> >
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*> > Right.
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*>
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*> Ok, then given that line of thinking, we realize that the
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*> notions of
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*> causality and logical implication are tied into the notion of
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*> constructed orderings. Question: We say "a priori" to denote a property
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*> that exists "from the beginning", what word would we use to denote a
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*> property that is actualized relative to some finite observational
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*> context? We can associate an ordering with a particular observer's
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*> "history" but with the caveat that such histories are NOT experienciably
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*> a priori but ongoing constructions such that they can be altered within
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*> the limits of the observer's ability to distinguish differences. Again,
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*> Peter Wegner discusses this better in his later papers...
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*> http://www.cs.brown.edu/~pw/papers/bcj1.pdf
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*>
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*> > >I think of events as finite actualizations and since the Universe is
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*> > >infinite, in it-self, it contains all possible possible actualizations
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*> > >or observations of itself. If we assume a finite Universe we can not
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*> > >escape the contradiction of infinite regress, since any finite Universe
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*> > >would have to include all possible subsets of itself *and* all possible
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*> > >information encoding the difference between the subsets and such
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*> > >introduces a diagonalization. I do not have time to work through the
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*> > >proof tonight... :( Got to go soon!
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*> >
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*> > Please do comment further on this!
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*>
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*> We start with a set X (representing a finite universe) with N
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*> different
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*> states that can encode 2^N bits of information. We can see that we can
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*> also construct a set X' that has N+1 different states and thus encode
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*> 2^N+1 bits of information which can simulate all possible behavior of X
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*> but X can't simulate all of X's repertoire. We then see that we can
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*> construct an endless sequence of sets X </= X' </= X" </= X"' </= ...
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*> with N </= N+1 </= N+2 </= ... such that each includes the prior's
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*> behavior in its repertoire and encode 2^N+... information.
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*> The question then becomes: Is there an X^oo that includes all of
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*> these
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*> as subsets? If we are going to assume the potential experienciability of
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*> any X we also must allow for the existence of X^oo (and its 2^oo bits of
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*> information encodable) that includes it; either it exists via a priori
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*> reasons or it exists via construction. I am here distinguishing
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*> "potential" from "actual".
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*> There is more involved, of course, but lets see what your
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*> response
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*> is... :)
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*> > Yours,
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*> >
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*> > Frater Rex
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*> Onward to the Unknown,
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*>
*

*> Stephen
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*>
*

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