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: [hidden email] [mailto:[hidden email]] On Behalf Of Grant Holland
Sent: Saturday, August 07, 2010 2:06 PM
To: [hidden email]; 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 <[hidden email]> 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, thevery language which GRANT seems to argue is impossible.OK. But that doesn't change the sense much. Grant seemed to be arguingthat it's because we use a common language to talk about the twoconcepts, the concepts are erroneously conflated. I.e. Grant not onlyadmits the possibility of a common language, he _laments_ the commonlanguage because it facilitates the conflation of the two differentconcepts ... unless I've misinterpreted what he's said, of course.I would like to apologize to everybody for these errors. I am beginningto think I am too old to be trusted with a distribution list. It’s notthat I don’t go over the posts before I send them … and in fact, what Isent represented weeks of thinking and a couple of evenings of drafting… believe it or not! It seems that there are SOME sorts of errors Icannot see until they are pointed out to me, and these seem to be, oflate, the fatal ones.We're all guilty of this. It's why things like peer review andcriticism are benevolent gifts from those who donate their time andeffort to criticize others. It's also why e-mail and forums are morepowerful and useful than the discredit they usually receive. While it'strue that face-to-face conversation has higher bandwidth, e-mail,forums, and papers force us to think deeply and seriously about what wesay ... and, therefore think. So, as embarrassing as "errors" like thisfeel, they provide the fulcrum for clear and critical thinking. I saylet's keep making them!Err with Gusto! ;-)
--Grant HollandVP, Product Development and Software EngineeringNuTech Solutions404.427.4759
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FRIAM Applied Complexity Group listserv
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============================================================FRIAM Applied Complexity Group listservMeets Fridays 9a-11:30 at cafe at St. John's Collegelectures, archives, unsubscribe, maps at http://www.friam.org
--Grant HollandVP, Product Development and Software EngineeringNuTech Solutions404.427.4759
============================================================
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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