Dear Loet,
On Apr 22, 2004, at 11:33 AM, Loet Leydesdorff wrote:
> I can follow Michel, but I don't understand your intervention.
> Probabilistic entropy is a measure of dividedness, not of symmetry.
> Symmetry is a geomterical property, while probabilistic entropy
> provides
> an information calculus. Perhaps, a numerical example would be helpful.
> Can you provide one?
I wish that i could, but I would not be sure how to go about it in this
case. Perhaps my comments on your scenario below will help.
> For example, if we take a symmetrical distribution of relative
> frequencies like 3,2,1,1,2,3, the entropy in this distribution would be
> similar to any other order of it.
I disagree that this is generally true. You seem to be assuming that
there is no meaning or physical reality (constraint) in the order of
the sequence.
> For example: 1,1,2,2,3,3.
But what if this is not the order in which these values actually appear?
> One can use
> probabilistic entropy for optimization of the dividedness, for example,
> in grouping and clustering. But I cannot easily think of an entropy
> measure that would enable us to distinguish between these two series.
Neither can I, but this is not inconsistent with the point I was trying
to make. My point was that the concept of entropy has grown and
changed since its inception as a purely statistical measure to which
deeper meaning later became attached. As a result of this history, the
traditional measures of entropy have become more narrowly focused
relative to the breadth of the concept. At this point, the traditional
measures all seem to represent toy models of the concept of entropy.
You might argue that the measures were derived in a more rigorous
(mathematical) framework, and that the drift and spreading of the
concept has distorted a well-founded notion of entropy. I would argue
that the evolution of this concept has been sufficiently rigorous that
it has become more useful and probably closer to truth (in the Akeike
Information Content sense). I appreciate that I am on thin ice here,
because I cannot prove that the concept has developed to better
represent natural thermodynamics. On the other hand, I think that my
argument is sufficiently plausible that it should also give pause to
those who argue that the concept should not be allowed to drift away
from the meaning of the measure.
> Can you -- or perhaps Shu-Kun -- explain why you nevertheless argue in
> this way? It is not sufficient to tell us that one concept is "more
> powerful" than another without a demonstration.
You have a good point. I'm not sure that I can do this justice without
more thought, and I see that Shu-Kun has responded, so I will read what
he had to say before I give it a shot.
Sincerely,
Guy Hoelzer
Department of Biology
University of Nevada Reno
Reno, NV 89557
Phone: 775-784-4860
Fax: 775-784-1302
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Received on Sat Apr 24 20:11:23 2004
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