Re: [Fis] Re: miscellanea / temperature / symmetry

Test: Where is my reply I sent two days ago/

Loet Leydesdorff wrote:

> Dear Shu-Kun,
>
> Thank you for the explanation. I now understand the confusion.
>
> Probablistic entropy can be considered as a measure of the uncertainty
> in a distribution. Which label we attach to this uncertainty depends
> on the theoretical perspective that we use. For example, from an
> evolutionary perspective we can call it variation as opposed to
> selection. From a dynamic perspective change versus stability.
> Selection is taking place at each moment in time; stabilization can
> only be evaluated over a time axis.
>
> Shannon's H --I am almost sorry for using it-- was defined for the
> measurement of the entropy at a specific moment in time. One can
> further derive from it a measure which is sometimes indicated as I
> (e.g., Theil 1972) which measures the "dissipation":
>
> I = Sigma q(i) 2log q(i)/p(i)
>
> In this formula Sigma q(i) represents the a posteriori probability
> distribution and Sigma p(i) the a priori one. I then measures the
> change in terms of bits of information. It can be shown that I >= 0.
> This accords also with the second law in thermodynamic entropy, but it
> can be considered as a probabilistic (formal) equivalent.
>
> The measure I can easily be extended to the multidimensional case and
> then be used as a measure for the stability. It remains to be proven
> that symmetrical configurations are more stable than non-symmetrical
> ones because this depends on the systems properties. For example, in
> almost all evolutionary selection processes highly skewed
> distributions are produced which can be extremely well buffered
> against change.
>
> A convenient extension of this reasoning about measuring change in
> distributions is provided by the Markov property. The Markov property:
> the best prediction of the next state of a system is its current
> state. If a distribution (e.g., a system) is stable one expect it to
> exhibit the Markov property (because variations in one part of the
> system can be compensated in another part). For example, one can test
> the amount of change on the assumption of systemness in a distribution
> versus the amount of change in the sum of the composing elements and
> then make an evaluation of the stability of the system. (This can also
> be extended to higher-dimensional arrays!)
>
> I have elaborated this into a test on systemness. For example, in:
>
> Loet Leydesdorff & Nienke Oomes, Is the European Monetary System
> Converging to Integration? Social Science Information 38 (1999) 57-86;
> preprint version at http://users.fmg.uva.nl/lleydesdorff/avril/ems.pdf
>
> Are EU Networks Anticipatory Systems? An empirical and analytical
> approach, in: Daniel M. Dubois (Ed.), Computing Anticipatory Systems
> -- CASYS'99 (Woodbury, NY: American Physics Institute, 2000), pp. 171-181;
> Preprint version at http://users.fmg.uva.nl/lleydesdorff/casys99/index.htm
>
> I don't exclude that symmetrical systems may have other entropical
> properties than non-symmetrical ones, but I think that this needs to
> be proven. I don't expect this to be the case for living and
> meaning-processing systems except perhaps for lower-order ones like
> amoebae. These systems tend to produce highly skewed distributions
> because of ongoing selection and hyperselection processes.
>
> With kind regards,
>
>
> Loet
>
> ------------------------------------------------------------------------
>
> Loet Leydesdorff
> Amsterdam School of Communications Research (ASCoR)
> Kloveniersburgwal 48, 1012 CX Amsterdam
> Tel.: +31-20- 525 6598; fax: +31-20- 525 3681
> loet@leydesdorff.net <mailto:loet@leydesdorff.net>;
> http://www.leydesdorff.net/
>
> The Challenge of Scientometrics
> <http://www.upublish.com/books/leydesdorff-sci.htm> ; The
> Self-Organization of the Knowledge-Based Society
> <http://www.upublish.com/books/leydesdorff.htm>
>

-- 
Dr. Shu-Kun Lin
Molecular Diversity Preservation International (MDPI)
Matthaeusstrasse 11, CH-4057 Basel, Switzerland
Tel. +41 61 683 7734 (office)
Tel. +41 79 322 3379 (mobile)
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E-mail: lin@mdpi.org
http://www.mdpi.org/lin/