If you call it behavioral rather than predictable it doesn't require a predictor. It's just an arrangement in time.
-- Russ On Sat, Aug 7, 2010 at 12:14 PM, Nicholas Thompson < [email protected]> wrote: > Grant – > > > > Glad you are on board, here. I will read this carefully. > > > > Does this have anything to do with the Realism Idealism thing. > Predictibility requires a person to be predicting; organization is there > even if there is no one there to predict one part from another. > > > > N > > > > *From:* [email protected] [mailto:[email protected]] *On > Behalf Of *Grant Holland > *Sent:* Saturday, August 07, 2010 2:06 PM > *To:* [email protected]; The Friday Morning Applied Complexity Coffee > Group > > *Subject:* Re: [FRIAM] entropy and uncertainty, REDUX > > > > Russ - Yes. > > > I use the terms "organizational" and "predictable", rather than > "structural" and "behavioral", because of my particular interests. They > amount to the same ideas. Basically they are two orthogonal dimensions of > certain state spaces as they change. > > I lament the fact that the same term "entropy" is used to apply to both > meanings, however. Especially since few realize that these two meanings are > being conflated with the same word. Von Foerster actually defined the word > "entropy" in two different places within the same book of essays to mean > each of these two meanings! Often the word "disorder" is used. And people > don't know whether "disorder" refers to "disorganization" or whether it > refers to "unpredictability". This word has fostered the further unfortunate > confusion. > > It seems few people make the distinction that you have. This conflation > causes no end of confusion. I really wish there were 2 distinct terms. In my > work, I have come up with the acronym "DOUPBT" for the "unpredictable" > meaning of entropy. (Or, "behavioral", as you call it.) This stands for > Degree Of UnPredictaBiliTy.) I actually use Shannon's formula for this > meaning. > > This all came about because 1) Clausius invented the term entropy to mean > "dissipation" (a kind of dis-organization, in my terms). 2) But then Gibbs > came along and started measuring the degree of unpredictability involved in > knowing the "arrangements" (positions and momenta) of molecules in an ideal > gas. The linguistic problem was that Gibbs (and Boltzmann) use the same term > - entropy - as had Clausius, even though Clausius emphasized a structural > (dissipation) idea, whereas Gibbs emphasized an unpredictability idea > (admittedly, unpredictability of "structural" change). > > To confuse things even more, Shannon came along and defined entropy in > purely probabilistic terms - as a direct measure of unpredictability. So, > historically, the term went from a purely structural meaning, to a mixture > of structure and unpredictability to a pure unpredictability meaning. No > wonder everyone is confused. > > Another matter is that Clausius, Boltzmann and Gibbs were all doing > Physics. But Shannon was doing Mathematics. > > My theory is Mathematics. I'm not doing Physics. So I strictly need > Shannon's meaning. My "social problem" is that every time I say "entropy", > too many people assume I'm talking about "dissipation" when I am not. I'm > always talking about "disorganization" when I use the term in my work. So, I > have gone to using the phrase "Shannon's entropy", and never the word in its > naked form. (Admittedly, I eventually also combine in a way similar to > Gibbs:-[ . > But I do not refer to the combined result as "entropy".) > > :-P > Grant > > > Russ Abbott wrote: > > Is it fair to say that Grant is talking about what one might call > structural vs. behavioral entropy? > > Let's say I have a number of bits in a row. That has very low structural > entropy. It takes very few bits to describe that row of bits. But let's say > each is hooked up to a random signal. So behaviorally the whole thing has > high entropy. But the behavioral uncertainty of the bits is based on the > assumed randomness of the signal generator. So it isn't really the bits > themselves that have high behavioral entropy. They are just a "window" > through which we are observing the high entropy randomness behind them. > > This is a very contrived example. Is it at all useful for a discussion of > structural entropy vs. behavioral entropy? I'm asking that in all > seriousness; I don't have a good sense of how to think about this. > > This suggests another thought. A system may have high entropy in one > dimension and low entropy in another. Then what? Most of us are very close > to the ground most of the time. But we don't stay in one place in that > relatively 2-dimensional world. This sounds a bit like Nick's example. If > you know that an animal is female, you can predict more about how she will > act than if you don't know that. > > One other thought Nick talked about gradients and the tendency for them to > dissipate. Is that really so? If you put two mutually insoluble liquids in > a bottle , one heavier than another, the result will be a layer cake of > liquids with a very sharp gradient between them. Will that ever dissipate? > > What I think is more to the point is that potential energy gradients will > dissipate. Nature abhors a potential energy gradient -- but not all > gradients. > > > -- Russ > > > > On Thu, Aug 5, 2010 at 11:09 AM, Grant Holland <[email protected]> > wrote: > > Glen is very close to interpreting what I mean to say. Thanks, Glen! > > (But of course, I have to try one more time, since I've thought of another > - hopefully more compact - way to approach it...) > > Logically speaking, "degree of unpredictability" and "degree of > disorganization" are orthogonal concepts and ought to be able to vary > independently - at least in certain domains. If one were to develop a theory > about them (and I am), then that theory should provide for them to be able > to vary independently. > > Of course, for some "applications" of that theory, these > "predictability/unpredictability" and "organization/disorganization" > variables may be dependent on each other. For example, in Thermodynamics, it > may be that the degree unpredictability and the degree of disorganization > are correlated. (This is how many people seem to interpret the second law.) > But this is specific to a Physics application. > > However, in other applications, it could be that the degree uncertainty and > the degree of disorganization vary independently. For example, I'm > developing a mathematic theory of living and lifelike systems. Sometimes in > that domain there is a high degree of predictability that an organo-chemical > entity is organized, and sometimes there is unpredictability around that. > The same statement goes for predictability or unpredictability around > disorganization. Thus, in the world of living systems, unpredictability > and disorganization can vary independently. > > To make matters more interesting, these two variables can be joined in a > joint space. For example, in the "living systems example" we could ask about > the probability of advancing from a certain disorganized state in one moment > to a certain organized state in the next moment. In fact, we could look at > the entire probability distribution of advancing from this certain > disorganized state at this moment to all possible states at the next moment > - some of which are more disorganized than others. But if we ask this > question, then we are asking about a probability distribution of states that > have varying degrees of organization associated with them. But, we also have > a probability distribution involved now, so we can ask "what is it's Shannon > entropy?" That is, what is its degree of unpredictability? So we have > created a joint space that asks about both disorganization and > unpredictability at the same time. This is what I do in my theory ("Organic > Complex Systems"). > > Statistical Thermodynamics (statistical mechanics) also mixes these two > orthogonal variables in a similar way. This is another way of looking at > what Gibbs (and Boltzmann) contributed. Especially Gibbs talks about the > probability distributions of various "arrangements" (organizations) of > molecules in an ideal gas (these arrangements, states, are defined by > position and momentum). So he is interested in probabilities of various > "organizations" of molecules. And, the Gibbs formula for entropy is a > measurement of this combination of interests. I suspect that it is this > combination that is confusing to so many. (Does "disorder" mean > "disorganization", or does it mean "unpredictability". In fact, I believe > reasonable to say that Gibbs formula measures "the unpredictability of being > able to talk about which "arrangements" will obtain." > > In fact, Gibbs formula for thermodynamic entropy looks exactly like > Shannon's - except for the presence of a constant in Gibbs formula. They are > isomorphic! However, they are speaking to different domains. Gibbs is > modeling a physics phenomena, and Shannon is modeling a mathematical > statistics phenomena. The second law applies to Gibbs conversation - but not > to Shannon's. > > In my theory, I use Shannon's - but not Gibbs'. > > (Oops, I guess that wasn't any shorter than Glen's explanation. :-[ ) > > Grant > > > > glen e. p. ropella wrote: > > Nicholas Thompson wrote circa 08/05/2010 08:30 AM: > > > > All of this, it seems to me, can be accommodated by – indeed requires – > > a common language between information entropy and physics entropy, the > > very language which GRANT seems to argue is impossible. > > > > OK. But that doesn't change the sense much. Grant seemed to be arguing > > that it's because we use a common language to talk about the two > > concepts, the concepts are erroneously conflated. I.e. Grant not only > > admits the possibility of a common language, he _laments_ the common > > language because it facilitates the conflation of the two different > > concepts ... unless I've misinterpreted what he's said, of course. > > > > > > I would like to apologize to everybody for these errors. I am beginning > > to think I am too old to be trusted with a distribution list. It’s not > > that I don’t go over the posts before I send them … and in fact, what I > > sent represented weeks of thinking and a couple of evenings of drafting > > … believe it or not! It seems that there are SOME sorts of errors I > > cannot see until they are pointed out to me, and these seem to be, of > > late, the fatal ones. > > > > > We're all guilty of this. It's why things like peer review and > > criticism are benevolent gifts from those who donate their time and > > effort to criticize others. It's also why e-mail and forums are more > > powerful and useful than the discredit they usually receive. While it's > > true that face-to-face conversation has higher bandwidth, e-mail, > > forums, and papers force us to think deeply and seriously about what we > > say ... and, therefore think. So, as embarrassing as "errors" like this > > feel, they provide the fulcrum for clear and critical thinking. I say > > let's keep making them! > > > > Err with Gusto! ;-) > > > > > > > > -- > > Grant Holland > > VP, Product Development and Software Engineering > > NuTech Solutions > > > 404.427.4759 > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > > > ------------------------------ > > > > ============================================================ > > FRIAM Applied Complexity Group listserv > > Meets Fridays 9a-11:30 at cafe at St. John's College > > lectures, archives, unsubscribe, maps at http://www.friam.org > > > > -- > > Grant Holland > > VP, Product Development and Software Engineering > > NuTech Solutions > > 404.427.4759 > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org >
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