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] <mailto:[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
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------------------------------------------------------------------------
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FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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--
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
