Dear Robert and friends,

At 09:36 PM 12/20/98 -0800, you wrote:

>Dear Stephen,

> I have a lot to do today, so bear with my terse remarks.

>

>> Here goes attempt number two. My system crashed while I was composing

>> this.. :( I have a terrible cold and my voice is gone… :(

>>

>> >From Game.html

>>

>> "If one tries to represent an event in terms of sequential-time, one has in

>> principle infinite precision on the time axis. But events can only be

>> determined to have existed in the past, or present or future based on a

>> memory of previous events. This memory is the sequential-time equivalent of

>> the sliding window which spectral-time uses, except that in the

>> sequential-time representation it is assumed that this duration of memory

>> window can be made arbitrarily large or small. The information of past and

>> present events in this memory are used to make predictions of future events."

>>

>> Key point: "…events can only be determined to have existed in the past, or

>> present or future based on a memory of previous events."

>>

>> The "past, present, future" speaks to a history-logical-consistency

>> ordering (or scheduling). The memory, to me, refers to the information

>> storage capacity of the finite number of *"internal"* configurations of

>> local systems (building from Hitoshi's model).

>> This leads to the conclusion that there is no *unique a priori* time

>> ordering that one can "slide a window" on. This is a refutation of the old

>> Newtonian identification (isomorphism) of an absolute time with R^1. This

>> should already be obvious when we consider how many possible concatenations

>> of points (the most general definition of curves) can be defined in any

>> space with a dimension greater than 0. Even 1 dimensional spaces, as sets,

>> can be ordered in many ways, thus the assumption of time as isomorphic to

>> R^1 is naive at best!

>

> Makes sense. The history of memory is a specific ordering or scheduling

>of the data. We can say mathematically history is an arbitrary parameterization

>of the data and in this sense "history as a narrative" is unavoidable

>as Norbert Wiener points out in Cybernetics.

>> That is referred to as "past events" is merely present memory content with

>> some historical/logical/consistency ordering/labeling that is *actual* in

>> the local present, which can be separate like a FAT on a computer's

>> harddrive. [Stop the presses! Thinking about this as I write, it occurs to

>> me that the FAT acts like an ordering metric for the data but it itself is

>> data… What general relationship exists between the two independent of

>> ordering, context, history, etc.?]

>

> Good point!! the FAT appears like a hypnotic suggestion. The elements

>of the fat are correlated but stored scattered about the hard disk's

>"subconscious mind" and difficult to access in sequence. Sleep is like

>running Norton's Speeddisk to organize the correlated data into a compressed

>form which speeds up access, and creates more continuity of access making

>it easier to bring the data into the forefront of the "conscious mind" of

>the central processor.

Building on that "correlated yet scattered" point: Local systems are not convex with respect to each other if we could see them from an "outside" perspective, much like the elements of the FAT. Internally, they are convex.

I think of this in terms of many immiscible incompressible fluids stirred together. This is a situation usually described using disjoint sets, such that A \intersection B = {0}, A and B being different fluids. Look at Schroeder’s book Fractals,… pg. 199-200. What we are looking at when we generalize this to fuzzy sets A \intersection B =\= {0} is equivalent to altering to allowing the miscibility to vary and parametrizing this using the fuzzy subsethood.

I think that this last idea might help us understand how Local Systems interact along their respective surfaces! Surfaces are allowed to "interpenetrate, yet be separate." This also might bridge over to Prigogine’s ideas! :) We have been looking for a better understanding of how quantum mechanical operators work, and I think that this idea might help a lot!

>Thought. Look into "Hashing" and "collision avoidance" algorithms as

>paradox resolution (Turing Omnibus, network protocols etc).

>How does TCPIP resolve datagram collisions which are paradoxes ?

>Really these are aliasing problems, and aliasing is the frequency

>domain version of interference in the time-domain. So QM is not

>that mysterious in terms of building up interference from single

>particles since this is just a building up of aliasing in the frequency-

>domain. No paradoxes, just aliasing and/or interference. Think of

>what "non-orthogonality" means in the time domain and the corresponding

>meaning in the frequency domain.

I need to understand this well. I am very exited by your knowledge of DSP, since it is a much better paradigm than what I have been using up to now! :) I just got in Information Flow by Barwise and Seligman, AWESOME! It defines and applies the infamous "infomorphism" that Peter Wegner uses in his paper. I am investigating the possibility of connecting fuzzy subsethood with hypersets, i.e. fuzzy mutual entropy between streams of information. I also need to see if we can relate the above idea of schedules to streams; I’ll ask Peter… :)

>> Moving on, the past is not some absolute "out there" entity, it is

>> "internal-contextual." The "present" is not definable in any absolute

>> external terms. It is an arbitrary origin of a basis, which is defined by

>> internal (Quantum mechanical) relations. Much like Hitoshi discusses how

>> "the past and the future do not exist unless one fixes a time coordinate.

>> The Big Bang "is an imagination under the $presumption$ that [one's

>> arbitrarily chosen time coordinate] … exists *a priori*."

>

> I see. The present represent a casually related next step of the

> arbitrary history, so it too must be arbitrary. Wingmakers has a similar

> idea in terms of BST. It describes how one might take the ensemble of

> the arbitrary presents, and shift us into another one with its associated

> past without our knowing it. *The causal chain of that new present and

> its past, will seem logical, and we will not be aware of the change since

> we notice no causal discrepancy.*

and Pratt’s ratmech.ps

But overall, I agree with your statement; since the possible information implementable by any given local system is finite, and thus susceptible to error, the "shifting" of the "present" is bounded by logical consistency and necessity (again remember that this term is NOT a universal, it is local, e.g. each LS has its own "present" as it has its own clock). This is the whole point of Pratt’s idea that Logic is dual to time. Each LS, being bounded in information content (ensemble of possible "presents" or moments), has its own consistency chaining from one present to the next and like you said: "one might take the ensemble of the arbitrary presents, and shift us into another one with its associated past without our knowing it. The causal chain of that new present and its past, (it will always seem logical) and we will not be aware of the change since we notice no causal discrepancy."

I frame this idea as: "observers always perceive their universe as Minkowskian."

>> Thus: "This memory is the sequential-time equivalent of the sliding

>> window which spectral-time uses, except that in the sequential-time

>> representation it is assumed that this duration of memory window can be

>> made arbitrarily large or small. The information of past and present events

>> in this memory are used to make predictions of future events" shows that

>> the "predictions" are subjective (e.g. "internal to LS") transitive (?)

>> relations/mappings between information structures… Umm that last is not

>> quite right, I need to find and re-read that Past-Future Complementarity

>> paper (the Difficult one). :)

>

> Given the above, the prediction seems arbitrary due to the arbitrary

> nature of the past and present. But the arbitrary past and present

> are not completely arbitrary, there is a constraint on how arbitrary

> they are. A sound signal can depend on how we parametrize it. Therefore

> the historical sequence that we record of it, determines constraints

> on the predictability of future sounds. This is what IIRs seem to overcome by

> looking for contextual information across all the possible ensembles

> of parameterizations. If we parametrize the past randomly it is very

> difficult but not completely impossible to reassemble the whole.

YES! :) We can "reassemble" or reconstruct or simulate past states to the degree that we can recover contextual information. The same should apply "forwards." The simulation / constructability / prediction of future states is equally dependent on contextual information.

A footnote from Information Flow: "If information about the future is possible, as it seems to be, then information travels faster than the speed of light." Pg. 3. :)

> See for instance topological sorting. I think Knuth gives and example:

> If we extend from coast to coast all the people in the US and have

> each one write on a piece of paper their (unique) name and the name of the

> person standing next to them on the western side, then take all the

> pieces of paper and mix them up completely, we can topologically sort

> these papers and regain the initial ordering. So randomness with enough

> contextual information can be ordered. Determinism from apparent

> non-determinism with a little context. In this case the context is

> very small: diagrams (length of window =2).

Can we understand entropy, both Shannon and Boltzmann, in this context? I say that they are dual to each other in that their respective contexts transform contravariantly, e.g. the more precisely the physical context is defined the smaller the number of possible messages can be inferred (decoded) from it, and dually; the more precise a message can be specified the fewer ways it can be encoded in matter. Bremermann’s limit is the "best of both worlds" situation…

I think that your idea might help us understand how we can recover determinism in the limit of large contexts. I believe that this is Peter’s premise in his conjecture that quantum non-determinism is "caused" by secondary observers, but we need to be sure that the statistics involved satisfy the Bell theorem violation of QM.

>> Further comments on quotes from your paper:

>>

>> "If one tries to represent an event in terms of spectral-time, one has in

>> principle no more temporal precision than the length of the window. In this

>> sense the window represents an event horizon. All events within this window

>> are considered concurrent, so "Eastern" languages express temporal events

>> verbally without tense. Temporal precision is expressed in terms of sliding

>> this window along the time axis continuously."

>>

>> Note that such "continuousness" is alien to actual DSP and physical

>> situations! It is tied, IMHO, to the "t = R^1" assumption.

>

> Somewhat, in DSP a sliding window is quite natural as are moving

> averages, and the sliding of a window a fraction of a sample is

> not common. But I think such continuity is effectively achieved, virtually, by

> multi-rate sampling, and "up-sampling" (in which the sample rate is

> increased virtually) Up-sampling pretends to have more information than

> it really does, and DSP engineers can actually make use of this.

> I'll look into this some more.

I think that you are right! When we look at how continuity is defined using the topology of open sets, multi-rate sampling sets up a situation that allows for the appearance of continuity to be constructed, much like how 30 fps shifting of images in a film creates the illusion of continuous motion. But, I should point out that since we are dealing with concurrent and, possibly, asynchronous mutual mappings between local systems, things are a bit more complex.

etc.

The use of "virtual information" is interesting. This could be seen as guessing or consulting oracles…

>> "In this manner temporal precision is tied to the small increment with

>> which the window moves through time. A Hopi Native American therefore

>> expresses temporal precision by "explaining" or "observing" when some

>> single event enters into this window of perception, but this is considered

>> a spatial event not a temporal one.

>> Whorf shows this in terms of two observers observing the same event,

>> temporal precision is expressed by two ways of describing the observed

>> event; if the event is observable by both observers, or if the event is

>> observable only by one of the observers. In this way grammatical tense is

>> avoided. Events are therefore described not in terms of tense, but in terms

>> of whether they are uniquely, jointly or generally observable within event

>> horizons."

>>

>> So we have something like set theory relations between "event horizons" as

>> complementary to temporal tense orderings among LSs! This is what I have

>> been thinking about with regards to relations "between" Local Systems! :)

>

> Event horizons morphing into each other, as a fuzzy overlap?

WOW! This guy is too cool!

etc.

>> Thus my questions about mutual entropy, subsethood, inclusions, etc.!

>> This also ties to Pratt's definition of interaction via residuation (in the

>> binary K=2 case): "…event a $necessarily precedes$ event b when every state

>> x $witnessing$ the occurrence of b also witness a." and "the dual

>> calculation… $permits$ a transition from state x to state y when every

>> event a $impressing$ itself on x does also on y. That is, any transition is

>> permitted just so long as it forgets no event." (pg. 3 ratmech.ps)

>>

>> What we need here is to be able to translate Pratt's terminology into

>> Whorf's and vise versa, particularly the italicized ($…$) words. Pratt

>> relates left residuation (a -> b) to <Phi|Psi>, the inner product in an

>> Hilbert Space, and the left residuation (x ->y) |Psi><Phi| , the outer

>> product in an Hilbert Space.

>

> Inner and outer products have more simple meanings although one has to

> be careful since in QM their meaning is different from Euclidean geo.

> Hestenes makes a big point of this.

> If my memory serves me correctly:

> |a><a| = FFT^-1(FFT(a)a*)

> where FFT(a)a* is just the power spectrum.

Could you explain power spectra a bit more?

etc.

> Also, there are simpler more intuitive representations in terms

> of auto-correlation and cross-correlation. See "Chaos Theory Tamed"

> by Garnett P. Williams which is a very good book:

I’ll order it from the library…

> variance = 1/N * \sigma_{t=1}^N (x_t - mean(x))^2

> autocovariance = 1/N*\sigma_{t=1}^{N-m) (x_t - mean(x)) (x_{t-m} - mean(x))

> autocorrelation = autocovariance / variance

>

> As I wrote Pratt earlier, <a|a> and |a><a| seem to morph into each other

> as a degenerative case. I can't seem to find that email right now.

Did he reply?

>> Further thoughts:

>>

>> At 06:22 PM 7/10/98 -0700, you wrote:

>> >BREMERMANN'S LIMIT

>> >

>> >"No data-processing system whether artificial or living can process more

>> than 2*10^47 >bits/sec per gram of its mass."

>> >

>> >This idea amuses me but I don't understand it.

>> >It goes like this:

>> >

>> >Information must be represented by some kind of marker.

>>

>> I call this "marker" a physical implementation.

>>

>> >If energy levels are used as markers then there are at most

>> >

>> > n = E_max/delta_E

>> >

>> >distinguishable markers in E_max.

>

> In the frequency domain, each frequency bucket has a

> discrete number of possible energy values. The total

> energy in the spectrum is discrete.

This is like the quantum atom having a discrete number of electron orbits at each level of energy…

>> This partitions physical configurations in terms of their energy…

>>

>> >>From

>> >E=mc^2,

>>

>> We should use the full equation that includes momentum since most bodies

>> are in some relative motion relative to each other:

>>

>> E^2 = m_0^2c^4 + c^2p^2

>>

>> (I'm re-reading Bohm's The Special Theory of Relativity)

>>

>> >and

>> >delta_E* delta_t>= hbar

>>

>> The Heisenberg uncertainty…how would the Fourier uncertainty be defined here?

>>

>

> phase vs. quantum number uncertainty ?

Umm, could you elaborate?

>> >leads to:

>> > mc^2/hbar>=n/delta_t

>

> delta_t must be the window of time for a spectrum with n quanta

> mc^2/hbar is the total energy of the spectrum / hbar

Is it the finite "duration" of a moment as we have defined such above?

>> >for which

>> > Max H = n log_2(n/2+1) = n bits

>> >is the optimal energy usage.

>>

>> "Optimal" => optimization is not a priori, it must be computed locally…

>>

>> >This leads to Bremermann's limit:

>> > mc^2/hbar ~ 2m * 10^47 bits/sec

>> >per gram of mass.

>

> Which is "mass equivalent" of the information that is contained in a spectrum

> of represented in a temporal window of duration delta_t.

I am missing your point here… :( Could you expand a bit? I think I am grokking it a little… :) If I am not mistaken, you are restating the idea about matter/info duality!

> Maybe in terms of the spectra of a closed system a Maxwell daemon acts on,

> the rate (velocity) of entropy ? This is why the non-relativistic energy

> (rest energy) is used ?

Well, one would use the rest energy since each LS is "at rest" with respect to its horizon in any given moment… I need to understand this better…

>> >

>> >ENTROPY AND DATA COMPRESSION

>> >The information content or entropy E_i of a particular state is related to

>> the probability >p_i of that state.

>> >

>> > E_i = -log p_i

>> >

>> >The more frequent (probable) the state is, the less is its entropy.

>> >

>> >The -average- entropy of a state message is

>> > E' = sum p_i * E_i

>> >or

>> > E' = - sum p_i * log(p_i)

>> >

>> >which relates to Shannon's entropy (the entropy of the ensemble of

>> messages, or the >amount of uncertainty, on the average, that a system is

>> in a particular state)

>>

>> This assumes something! How is the basis of the probability p_i defined?

>

> ensembles. reproducibility. A certain amount of determinism of the

> system is assumed, but it is not completely deterministic otherwise

> we'd have no need to "predict" and the entropy = 0. So entropy takes

> us from non-determinism to determinism, or more specifically I think

> it takes a mixture of non-determinism and determinism and transforms

> the amount of non-deterministic information into deterministic information.

Can we think of this the other way around, e.g. from deterministic nearby to non-deterministic far away, like a distance / entropy relation? This would instantly explain the Hubble Red Shift!!!! :) That does make sense, since distance is related to time as we look out in space…and the further back in time we look the more uncertainty (non-determinism) we see in the energy content of light. This is SERIOUSLY HANDWAVING!

> Like going from a pure iterative frame of reference into a pure recursive frame.

> Same as lengthing the context/sample window/local system size,

> from 0 to infinity.

Look at what happens at the infinite length! We have an infinite context and thus a static Universe, since not local logical inconsistencies are allowed. Logical consistency of LS’s is locally bounded! For an infinite LS, there would be ZERO inconsistency. This is EXACTLY what Kosko was talking about when he said that complete binary uncertainty = infinite information wave velocities! This is way too KUHL! :)

>> There seems to be some idealistic absolute basis here. This is a big point

>> in Kosko's work! Is the possibility of "incomplete" sampling allowed for,

>> i.e. we need to be able to model situations were we can only model a

>> limited number of variables due to space/time restrictions on computation!

>> (Note that there is a space/time trade-off (complementarity) in computation

>> to begin with!)

>

> Right, the space time tradeoff is occurring as we go from the iterative

> frame into a recursive one. The pure recursive frame is that of equilibrium

> so there are no "temporal events" there in the ideal case. Like a superfluid

> all particles are completely correlated and no "event" happens which is not

> an event "seen" by all. There are no local systems within a superfluid.

> It is a local system without subsystems.

YES! :) This is the same way that Hitoshi describes LSs. They are quantum systems, like superfluids, and can not be separated into non-interacting parts. This is the main message of Bohr and Bohm when discussing the EPR effect! The QM correlations are the "invisible strings" that bind the divided wholes. Your statement "all particles are completely correlated and no "event" happens which is not an event "seen" by all" also resonates Pratt’s definition of a K=2 Chu space residuation! Remember this is the crisp binary case!

> But a superfluid can be divided, but each division has no sub-local systems

> This is the essence of recursion, the whole can be divided only in a way that

> each division is just the same as the whole. There's some topology in there

> somewhere. (a recursion formula is the same for each "step")

I remember something Schroeder said… scale invariance…self-similarity… I think. Chapter 3 of his book…perfect scale invariance would imply complete compressibility of information, I think…I’ll look further… See also the Golden Mean stuff, each segment of it is "the same" as its successors…

>> >Compression tries to minimize the bits needed to transmit state messages.

>> >Shannon showed that the -average- number of bits per state message can

>> >approach E' but not be less.

>> >You can apparently have a code that beats the odds and does better than

>> >the source entropy, but not consistently. It is important here to note

>> >that the entropy is based on a probability distribution and averages apply.

>>

>> This idea seems to be implicit in my "AI Maxwell Demon"

>> gedankenexperiment. A string (or more generally, stream) of n-ary bits that

>> pair-wise matches a sequence of fluctuations/particle states/etc. can

>> exist, but can not be "modeled in zero time" since it's (is it recursive?)

>> computation is NP- Complete… man, this is still too hand-wavy! :(

>

> What NP-relations exist transforming between recursive and iterative algorithms

> and vice versa ?

> This is what we probably need to look into.

I agree! :) A friend of mine was working on the "splittance of graphs" That involved splitting a graph into an independent set and a clique.

"A split graph is a graph in which the vertices can be partitioned into two sets Q and I such that Q is a clique and I is an independent set. The major result I plan to discuss allows one to determine if a given graph is a split graph in linear time." Ted Doyle, private communication.

They have both a clique Q (completely connected subgraph) and an independent set I (set of mutually disjoint nodes); finding either in a given graph is NP Complete, but he talked about how a graph can be classified as split in linear time! Q and I and complements (dual) of each other!

>> >Arithmetic coding was born out of finding the minimal measure of

>> >distinguishability of states. Shannon noted that minimal-bit codes for

>> >each state message can be derived in terms of the cumulative probabilities

>> >in a sorted list of state probabilities.

>>

>> Note the assumption of a priori existence/model/oracle of a "sorted list."

>> We need to consider the realistic situation where the derived minimal-bit

>> codes are computed "live" in real time, e.g. constructed by bisimulations

>> (coinductions) among streams. The streams are both generated by and make up

>> systems. Systems are distinguished (as discussed in Peter's latest paper)

>> their relative coinduction of each other's behaviour, e.g. SIM observers

>> "can distinguish two systems iff they compute different sequences of

>> observations." [We are thinking here of "input-output" couplings as

>> matchings between past and future events!]

>

> Bisimulation is starting to sound to me like the tomography problem.

> Given two 2-d views of a building, can we reconstruct the building

> in 3-d ? Not. But we can get a fair picture.

Maybe, I’ll look into this…

etc.

>> See section 3 of "Mathematical Models…"

>>

>> >Later, the coding was optimized using incremental adaptive coding,

>> unsorted lists and >finite precision arithmetic in linear time.

>>

>> Exactly! :)

>>

>> >It amounts to successive subdivisions of the unit interval in a manner

>> >that is reversible. In theory, this coding produces a state message code

>> >that has the same number of bits specified by the entropy of that message

>> >-with respect to the coding model-.

>>

>> This reversibility is exact only if the information needed to reverse the

>> computation is maintained (persistently encoded) in the system. This leads

>> to the need to better understand how memory ("working tape") is

>> constructed. I think that the physical/information dualism allows us to

>> model this effectively! Matter can persistently encode information via

>> "dissipative structures"… Again we must not assume that matter is

>> persistent with out a solid reason….

>

> Matter is the paint in a picture. But the paint is moving fluidly.

> Dripping. Spinning. Mixing. Splatting. Just thinking...

:) Matter is the paint. Information is the meaning…both the paint and the meaning change (contravariantly? under ideal situations!) then the perspective of the moment (context!) is shifted…

>> >Several factors cause this performance to be slightly less than optimal:

>> >

>> > *Message termination overhead - an additional code is needed to indicate

>> the >termination of a message

>>

>> See above note!

>

> Closure of continuity and paradox, discreteness as a necessary.

> Motion as a paradox, Zeno. Closure of a recursive algorithm.

> An infinite recursion has no closure.

It has greatest fixed points?…

this last one is AWESOME!

>> > *The use of finite precision instead of infinite precision arithmetic.

>>

>> Look at Kosko's identification of arithmetic (addition of real numbers)

>> with the fuzzy mutual entropy of some fuzzy set F. (Theorem 12.1 pg. 404,

>> Fuzzy Engineering)

>>

>> > *Normalization of probabilities.

>>

>> This is a big one! When we normalize probabilities we are considering that

>> all the probabilities involved in the sampling (window) sum to 1, so we

>> assume completeness.

>

> And closure. We force closure whenever we derive "information" from

> the infinite streams. Information needs discreteness to be communicated

> otherwise we have infinite context and communication of the information

> is instantaneous and complete. We, do not have infinite context, so

> information travels discretely, in time.

Centroid Defuzzification, approximation, bounded consistency – contextual definiteness! :) It is here that we realize that Plato’s realm of absolute ideals is just that, ideal, not Real! Reality is local and thus bounded and finite and thus uncertain to some degree! This goes back to the key idea that each local system is maximally (not absolutely) consistent information-wise.

>> >One problem in sequential adaptive coding is that of context.

>>

>> Absolutely!

>>

>> >The zero-frequency problem arises in a probability space so that

>> <initially, the amount of that space to reserve for a state message out of

>> >an unknown number of possible states cannot be determined. For instance,

>> >Pierce points out that this leads to a paradox (similar to the Monty Hall

>> >problem) where a particular state can be assigned different probabilities

>> >dependent on the context of its observation. During a statistical window

>> >some known possible messages do not occur at all and receive

>> >zero-probabilities.

>>

>> I think that this is the essence of Hitoshi's problem with statistics! We

>> can not claim that there exist an *a priori* state (information datum)

>> defining the size of the sampling window ("number of cells needed to

>> reserve/encode"?) that is needed to assure 100% accuracy or truth value of

>> any given observation! This is implicit in uncertainty relations!

>

> Increase the context of the window (energy) and you decrease "time".

> You increase a local system's "absolute time" (window) at the expense of

> "relative time". The local system engulfs all other local systems and

> there is no more relative time, only an absolute time which cannot be

> measured since there are no local systems left. There are no clocks in

> equilibrium.

:) This "absolute time" is "no time" since it, like the pre-relativistic ether, is not ever measurable. Its existence is reduced to mere necessity. When I say "All is Flux," the "flux" is this absolute time.

>> I am interested in how Nature computes the optimal matchings between

>> possible messages and statistical windows such that accuracy is maximal.

>> Umm, I need to better understand David's "sharpness"… I think it relates

>> to this…

>>

>> >The context of a single state in a history of states can be used to reduce

>> the entropy of >that state's message (representation).

>>

>> Can we translate this to a "possible world" in a Kripke structure to tie

>> it into Pratt's terms?

>

> I'll have to read Kripke.

>>

>> >But a large context has a large space of possible aggregates of state

>> >messages, and so it takes a long time (history) in order to benefit from

>> >that knowledge.

>>

>> Could you elaborate on how a larger space of state messages (powerset

>> cardinality?) means "in order to benefit…"?

>

> You cannot know a book, without reading it completely word by word.

> A book is distinguished from another book only by reading the whole book

> (large history and context). One character difference could distinguish

> the books from each other, so you need complete context on the book

> to completely distinguish (orthogonalize) it from others.

Agreed!

>> >A short context provides a faster convergence to some particular state

>> message coding >but the reduction of entropy for those codes is less.

>>

>> Umm, "faster convergence"… -> slower convergence -> time needed ->

>> computational steps required -> relationship between time and information

>> defined in terms of the relationships between thermodynamic and information

>> entropies. Umm, I may be reading too much into this, like seeing faces in

>> the grain of wood. I need to show necessity and consistency of this

>> relation.

>

> Data compression is faster with less context, but not optimal.

>

>> >A blending of context lengths is usually employed. But not one method

>> >stands out as superior just as no one method of dealing with the

>> >zero-probability problem stands out and no one method of determining a

>> >power spectrum.

> Multi-rate resolution.

Can we explore this concept further? It something like Doppler radar?

>> Thus this may speak to the "freedom of choice" that one has in defining

>> meaning since meaning is relative to context! Since there is no ABSOLUTE

>> gauge or metric or ordering definable in finite

>> terms/statements/databases/configurations/etc., there is no reason to

>> assume that there exists a single finite universe for all

>> observers/LSs/agents/etc. to "exist in."

>

> It depends on the signal, I think. Simple signals are easily

> communicated and understood by all. Those that are complex,

> become more interpretive and relative. We assume though that

> there is a correct interpretation, but really what we have

> is many interpretations with a wide variance. So we can overlap

> some of them. See the maximum entropy link on my web page.

Agreed! The more correlations/overlaps that systems have the more they can be said to have correlated (logically consistent) interpretations. Do we say that they have minimal or maximal mutual entropy?

> The maximal overlap of all these interpretations is what

> we usually look for. I think this is what IIRs and MIMs do.

> At some level, each interpretation must be constrained to

> have a minimal amount of truthfulness in the case of physics.

> But when someone says "I don't like that painting", it is

> hard to relate this to another person's "I like that painting.".

> There appears to be no possible overlap of these variances and

> we can think of them as being conjugate frames of reference or

> topologically discrete ?

>

>> >CONCLUSIONS ?

>> >

>> > Acquiring information about an unknown system reduces the entropy of that

>> system ->with respect to the model of that system-. This has nothing to do

>> with reducing the >thermodynamic entropy of the system itself. That is, it

>> has nothing to do with the system >itself giving up degrees of freedom to

>> the observer. As you note from Pierce:

>> >

>> >> "It seems irrelevant to relate such entropies to the

>> >> entropy of physics, except perhaps through the energy required to

>> >> transmit a bit of information under highly idealized conditions."

>>

>> Again, there is NO absolute unique definition of energy or entropy or

>> space-time ordering of events.

>

> Only relative entropies, which what I meant in terms of the model

> having entropy as distinct from the thermo entropy of the system that

> it is trying to model. But that thermo energy is not perceivable

> by that system as a whole. I'm getting the picture of local systems

> now.

Excellent! :)

>> All such are defined contextually. The

>> relationship between optimization and contextual definiteness is very

>> evident in the problem of computing extremal geodesics in an n-body

>> configuration space. Typical perturbation schemes impose an absolutist

>> infinitesimal time granulation that disallows for relativistic contractions

>> and dilations. This issue has attracted the attention of many

>> mathematicians, most notably Ilya Prigogine, whose work we have discussed

>> before…

>>

>> >In Pierce's example, the information about a systems state is assumed to

>> require a >certain amount of energy from the system. That information

>> reduces the entropy of the >observer's model by an amount equal to the

>> energy needed to acquire the information >from the system.

>> >

>> >But this energy need not come from the observed system.

>>

>> It does not have to. It does not need to come "from anywhere;" "free"

>> energy (potential) here is dissipated (thermodynamic entropy) by the

>> mechanism of communication/interaction. We need to look at this more closely!

>>

>> >A non-interactive measurement would not alter the system's state. Pierce's

>> assumption >that the system must give up energy to expose it's Fourier

>> state information is >apparently not valid.

>>

>> I disagree completely or do not understand what you mean by

>> "non-interactive measurement." This statement seems to imply that a system

>> can have a sharp (definite) state independent of observations of its

>> conjugate states. As Bohr tried to explain, Bohm expounded and Hitoshi

>> axiomatizes, a quantum system is a whole that can not be

>> measured/observed/known about/etc. in terms of "parts" at all!

>

> I'll re-think this now that I know more.

:)

>> >For instance, in order to determine the positional state of a particle we

>> >can observe it with light and thus alter its momentum. But quantum

>> >mechanically, we nowadays know that Heisenberg principle has nothing to do

>> >with perturbative measurements which Pierce's remark seems to imply:

>> >

>> >> "There is one very odd implication of what we have just covered.

>> >> Clearly, the energy needed to transmit information about the state of a

>> >>physical system keeps us from ever knowing the past in complete

>> >>detail. If we can never know the past fully, can we declare that the

>> >>past is indeed unique?"

>>

>> This speaks to my point that there is NO unique past for all!

>

> I'll have to re-address this later.

OK. :)

>> >When we observe a single particle's position state, it need not perturb

>> >the particle's state. What the Heisenberg/Fourier uncertainty implies is

>> >that the time of the position measurement is uncertain in the range of L/c

>> >of the light used to observe the particle, where L is the wavelength.

>>

>> What is the metric ("rulestick") used to determine the wavelength? If we

>> are thinking in general relativistic terms we are without a unique one!

>> Hitoshi covers this on his page…

What is important is that we do NOT need a unique (Absolute) metric!

>> >If the particle, is given the deBroglie wavelength L'=h/mv

>> >the position is further uncertain in that region of length ?

>> >Then the total uncertainty in position is in the sum of these

>> >uncertainties ?:

>> >

>> > delta_x = 1/k + h/p'

>> >

>> >(where k is the wavenumber uncertainty) the time is uncertain in the

>> >region:

>> >

>> > delta_t = 1/f + h/E'

>> >

>> >'E is the particle energy, each of the terms is valid on their own but I

>> don't know if you >just add them simply like this?

>>

>> Could you explain this further?

>

> When I return. I was considering variances in general. A mixture of

> Fourier uncertainties with a sliding window or something like that...

:)

>> >One thing about entropy and systems is that you never see the potential

>> between two >charges dissipate.

>>

>> That is a very good question! Maybe Wheeler's idea that charge is a

>> topological property deserves a closer inspection. I need to get his new

>> biography… But, thinking further, what do we mean exactly by "that you

>> never see the potential between two charges dissipate;" all we can detect

>> potential-wise is dependent on how far the charges are from each other. We

>> never see objects travel at v > c either, that does not forbid it.

>> Remember, we are talking about restrictions on possible observations not

>> actual acts! This gets to your question of black bodies; I call it an event

>> horizon problem. Since we agree that Local Systems are by necessity finite,

>> we must come to terms with finite bounds and other restrictions.

>

> Yes indeedy! Back soon...

>

>>

>> >[1]Cambel's book "Applied Chaos Theory" Chapter 8 points out abit about

>> >the many kinds of "entropy".

>> >

>> >[2]"Text Compression" Bell, Cleary, Witten

>> >

Later,

Stephen