Dear Bob,
I read your paper (Information, 2011) with much interest. I agree that
meaning is not directly observable in terms of probability distributions,
but remains as you so nicely express apophatic. In the social sciences, we
not only have different meanings, but also different horizons of meaning
(Husserl).
Formulas 2a (Shannon) and 2b (Kullback-Leibler) are traditional. Could you,
please, provide me with a reference for the derivation of Eq. 2c at p. 627?
Many thanks in advance.
Best,
Loet
Loet Leydesdorff
University of Amsterdam
Amsterdam School of Communications Research (ASCoR)
l...@leydesdorff.net ; http://www.leydesdorff.net/
Honorary Professor, SPRU, University of Sussex;
Guest Professor Zhejiang Univ., Hangzhou; Visiting Professor, ISTIC,
Beijing;
Visiting Professor, Birkbeck, University of London;
http://scholar.google.com/citations?user=ych9gNYJhl=en
-Original Message-
From: Fis [mailto:fis-boun...@listas.unizar.es] On Behalf Of Robert E.
Ulanowicz
Sent: Saturday, September 27, 2014 6:25 PM
To: John Collier
Cc: fis@listas.unizar.es
Subject: Re: [Fis] MAXENT applied to ecology
Dear John,
I came across the article and wrote to John Harte. My email to him and his
kind response are appended below.
I brief, I believe John is on the correct pathway, and it is one that I have
been treading for some 35 years now. I think, however, that one cannot
simply apply statistical entropy in an unconditional way. Like physical
entropy, statistical entropy has meaning only in a relative sense. That is,
it can only be measured with respect to some reference situation (cf., the
third law of thermodynamics). (We've been over this together in connection
with the Brooks and Wiley hypothesis.)
By invoking a reference state (even if that state should be reflexive, as is
done with weighted networks), one discovers that statistical entropy alone
does not parse out order from disorder. Once such parsing has been made, one
may then follow the course of order and disorder, in the context of the
chosen reference state.
http://people.biology.ufl.edu/ulan/pubs/FISPAP.pdf
http://people.biology.ufl.edu/ulan/pubs/FISPAP.pdf
John did not suggest a solution to my ignorance about the almost constant
proportion between constraint and indeterminism in ecosystem trophic
networks. Maybe someone on FIS can suggest one?
Peace,
Bob
Subject: Re: Ecological thermodynamics
From: John HARTE mailto:jha...@berkeley.edu jha...@berkeley.edu
Date: Fri, September 26, 2014 9:03 am
To: Robert Ulanowicz mailto:u...@umces.edu u...@umces.edu
Dear Bob,
I am in South Africa, Cape Town region, on sabbatical and enjoying immensely
the wildlife and botanical preserves, and especially traipsing through the
fynbos. Off to Chile next week for a month.
I have thought about trophic networks and maxent only to the extent that I
realized that the linkage distribution across nodes in most real networks
does indeed follow (with some scatter of course)) a Boltzmann distribution.
But I have shied away from looking at what theory has to say about flow
rates between nodes because the data are so spotty.
Recently I have been working with a graduate student on a state-counting
approach, a la Boltzmann,to understanding competitive coexistence. It turns
out the method actually predicts the dependence of demographic rates on
population sizes. The outcome differs somewhat from the variety of
dependences found in the usual Lotka-Volterra type models.What's
interesting to me is that, as in your work, a quantitative and testable
tradeoff arises for populations, in this case between the capacity to adapt
under evolution and capacity to survive under competition.
I enjoy reading your papers!
Cheers,
John
John Harte
Professor of Ecosystem Sciences
ERG/ESPM
310 Barrows Hall
University of California
Berkeley, CA 94720 USA
On Thu, Sep 25, 2014 at 7:06 AM, Robert E. Ulanowicz
mailto:u...@umces.edu u...@umces.edu wrote:
Dear John,
I notice that you have made considerable headway with applying MAXENT
to ecological theory. I was thinking you might find interesting some
results we have observed that might be of help in your search for global
metrics.
In particular, we have discovered that weighted networks of trophic
exchanges fall within a very narrow range as regards the ratio of
mutual information and conditional entropy. (See Figure 7 on p1089 of
http://people.biology.ufl.edu/ulan/pubs/Dual.pdf
http://people.biology.ufl.edu/ulan/pubs/Dual.pdf.) Admittedly, this
observation is based on sketchy data, but if it does hold up, then
Equations (5) below the figure might suggest a method superior to
MAXENT (for ecosystems only, of course) for estimating missing data?
On the other hand, notice that the variable F as defined in Equation
(4) bears strong resemblance to the entropy formalism, except
