Re: [Fis] FIS / introductory text / 5 April 2004

Dear Loet,

In order to avoid confusion, I would put S as thermodynamic
entropy and H information theory entropy (both are entropy notations).
If H is called information it will be difficult.

When I tried to understand entropy and information, I tried to
relate them to other concepts or numeracally expressed in
other properties. They should be expressed or related to other concepts:

1. Entropy is related to disorder, information to order.
2. Entropy is related to symmetry. Information to nonsymmetry (opposite
of symmetry).
(Disorder related to symmetry and to entropy: see for example a website
http://www.bartleby.com/64/C004/024.html provided by
Michel today. Let us cite: "Here, disorder means the number of ways that
you can
rearrange a system so that it looks exactly the same".)
3. Entropy is related to the highest similarity (sameness),
information to distinguishability. I feel the last point (point 3) is
most helpful for me to grasp the entropy and information concepts:

"Higher distinction (distinguishability) - higher information" conforms
with standard information theory: when we do sampling, if we suddenly
find a new species (to say a new animal or plant species when we
are considering bioinformation or biological diversity assessment,
or a new molecule, to say suddenly a new molecule like C60 is discovered,
in chemoinformation, as Michel mentioned), then this
newly found individual has a lot of information, as a consequence that
this one is simply different from others (it is unusual). If this is 1
out of
1000000, the probability of this new species is 1 ppm. The information
is I (per species, for this species)=-log (0.000001)=log 100000. A lot
of information.

Similarly, if we find a piece of message is about something
happened somewhere very very unusual (very distinguishable from other things
happening everywhere, everyday), then this is "news" to be reported
in the TV and newspapers, because it is very different. Therefore,
difference
is related to information. Sameness is related to entropy.

Loet, what do you think?

Best regards,
Shu-Kun

I is based on the Shannon's definition of I

Information I per

Loet Leydesdorff wrote:

>Dear Shu-Kun,
>
>I was just answering Michel's question for a suggestion about the
>relation with reference to Ebeling's book. The formula in the
>Szilard-Brillouin relation is:
>
>Delta S >= k(B) Delta H
>
>H is Shannon's H; k(B) the Boltzmann constant ( 1.381 * 10^-33 J/K), and
>S the thermodynamic entropy in J/K. I am not a physicists, but I just
>answered the question. The derivation is provided by Ebeling. I can
>reproduce it if you wish.
>
>Otherwise, I agreed largely with Michel's introductory paper. I don't
>understand your formula of Delta S > - Delta I. How is I defined? Can
>you give the formula? (Your second email was even more confusing.)
>
>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
> <mailto:loet@leydesdorff.net> loet@leydesdorff.net ;
><http://www.leydesdorff.net/> http://www.leydesdorff.net/
>
>
>
> <http://www.upublish.com/books/leydesdorff-sci.htm> The Challenge of
>Scientometrics ; <http://www.upublish.com/books/leydesdorff.htm> The
>Self-Organization of the Knowledge-Based Society
>
>
>
>
>>-----Original Message-----
>>From: fis-bounces@listas.unizar.es
>>[ <mailto:fis-bounces@listas.unizar.es>
>>
>>
>mailto:fis-bounces@listas.unizar.es] On Behalf Of Dr. Shu-Kun Lin
>
>
>>Sent: Monday, April 05, 2004 3:53 PM
>>To: fis@listas.unizar.es
>>Subject: Re: [Fis] FIS / introductory text / 5 April 2004
>>
>>
>>Dear Loet,
>>
>>You mean entropy S is equal to information (I), or almost
>>equal. Can you
>>still give
>>a little bit of sympathy to the relation that Delta S > - Delta
>>(information) and make some
>>comments on this different relation? If we can agree on the
>>relation that Delta S > - Delta (information), then we are
>>ready to ask "why information loss is related to entropy", a
>>question asked by
>>physicists at the
>> <http://www.lns.cornell.edu/spr/2000-12/msg0030047.html>
>>
>>
>http://www.lns.cornell.edu/spr/2000-12/msg0030047.html
>
>
>>website, and try to answer.
>>
>>Michel, thank you for your introduction.
>>
>>Shu-Kun
>>
>>
>>Loet Leydesdorff wrote:
>>
>>
>>
>>>Dear Michel,
>>>
>>>The relation between thermodynamic entropy and the information is
>>>provided by the Szilard-Brillouin relation as follows:
>>>
>>>Delta S >= k(B) Delta H
>>>
>>>(W. Ebeling. Chaos, Ordnung und Information. Frankfurt a.M.: Harri
>>>Deutsch Thun, 1991, at p. 60.)
>>>
>>>k(B) in this formula is the Boltzmann constant. Thus, a
>>>
>>>
>>physical change
>>
>>
>>>of the system can provide an information, but it does not have to.
>>>Unlike the thermodynamic entropy, probabilistic entropy has no
>>>dimensionality (because it is mathematically defined). The Boltmann
>>>constant takes care of the correction in the dimensionality in the
>>>equation.
>>>
>>>When applied as a statistics to other systems (e.g.,
>>>
>>>
>>biological ones)
>>
>>
>>>one obtains another (specific) theory of communication in
>>>
>>>
>>which one can
>>
>>
>>>perhaps find another relation between the (in this case biological)
>>>information and the probabilistic entropy. This can be
>>>
>>>
>>elaborated for
>>
>>
>>>each specific domain.
>>>
>>>With kind regards,
>>>
>>>
>>>Loet
>>>
>>>
>>>
>>> _____
>>>
>>>Loet Leydesdorff
>>>Science & Technology Dynamics, University of Amsterdam
>>>
>>>
>>Amsterdam School
>>
>>
>>>of Communications Research (ASCoR) Kloveniersburgwal 48, 1012 CX
>>>Amsterdam
>>>Tel.: +31-20-525 6598; fax: +31-20-525 3681
>>>< <mailto:loet@leydesdorff.net> mailto:loet@leydesdorff.net>
>>>
>>>
>loet@leydesdorff.net;
>
>
>>>< <http://www.leydesdorff.net/> http://www.leydesdorff.net/>
>>>
>>>
><http://www.leydesdorff.net> http://www.leydesdorff.net
>
>
>>>-----Original Message-----
>>>From: fis-bounces@listas.unizar.es
>>>[ <mailto:fis-bounces@listas.unizar.es>
>>>
>>>
>mailto:fis-bounces@listas.unizar.es]
>
>
>>>On Behalf Of Michel Petitjean
>>>Sent: Monday, April 05, 2004 9:15 AM
>>>To: fis@listas.unizar.es
>>>Subject: [Fis] FIS / introductory text / 5 April 2004
>>>
>>>
>>>2004 FIS session introductory text.
>>>
>>>Dear FISers,
>>>
>>>I would like to thank Pedro Marijuan for his kind invitation
>>>
>>>
>>to chair
>>
>>
>>>the 2004 FIS session. The session is focussed on "Entropy and
>>>Information". It is vast, that I am afraid to be able only to evoke
>>>some general aspects, discarding specific technical developments.
>>>
>>> Entropy and Information: two polymorphic concepts.
>>>
>>>Although these two concepts are undoubtly related, they have
>>>
>>>
>>different
>>
>>
>>>stories.
>>>
>>>Let us consider first the Information concept.
>>>There was many discussions in the FIS list about the meaning of
>>>Information. Clearly, there are several definitions. The information
>>>concept that most people have in mind is outside the scope of this
>>>text: is it born with Computer Sciences, or is it born with
>>>
>>>
>>Press, or
>>
>>
>>>does it exist since a so long time that nobody could date it?
>>>Neglecting the definitions from the dictionnaries (for each language
>>>and culture), I would say that anybody has his own concept.
>>>Philosophers and historians have to look. The content of the FIS
>>>archives suggests that the field is vast.
>>>
>>>Now let us look to scientific definitions. Those arising from
>>>mathematics are rigorous, but have different meanings. An example is
>>>the information concept emerging from information theory (Hartley,
>>>Wiener, Shannon, Renyi,...). This concept, which arises from
>>>probability theory, has little connections with the Fisher
>>>
>>>
>>information,
>>
>>
>>>which arises also from probability theory. The same word is
>>>
>>>
>>used, but
>>
>>
>>>two rigorous concepts are defined. One is mostly related to coding
>>>theory, and the other is related to estimation theory. One
>>>
>>>
>>deals mainly
>>
>>
>>>with non numerical finite discrete distributions, and the other is
>>>based on statistics from samples of parametrized family of
>>>distributions. Even within the framework of information
>>>
>>>
>>theory, there
>>
>>
>>>are several definitions of information (e.g. see the last chapter of
>>>Renyi's book on Probability Theory). This situation arises often in
>>>mathematics: e.g., there are several concepts of "distance", and,
>>>despite the basic axioms they all satisfy, nobody would say
>>>
>>>
>>that they
>>
>>
>>>have the same meaning, even when they are defined on a common space.
>>>
>>>Then, mathematical tools are potential (and sometimes demonstrated)
>>>simplified models for physical phenomenons. On the other hand,
>>>scientists may publish various definitions of information
>>>
>>>
>>for physical
>>
>>
>>>situations. It does not mean that any of these definitions should be
>>>confused between themselves and confused with the
>>>
>>>
>>mathematical ones. In
>>
>>
>>>many papers, the authors insist on the analogies between their own
>>>concepts and those previously published by other authors:
>>>
>>>
>>this attitude
>>
>>
>>>may convince the reviewers of the manuscript that the work has
>>>interest, but contribute to the general confusion, particularly when
>>>the confusing terms are recorded in the bibliographic databases.
>>>Searching in databases with the keyword "information" would
>>>
>>>
>>lead to a
>>
>>
>>>considerable number of hits: nobody would try it without
>>>
>>>
>>constraining
>>
>>
>>>the search with other terms (did some of you tried?).
>>>
>>>We consider now the Entropy concepts. The two main ones are the
>>>informational entropy and the thermodynamical entropy. The first one
>>>has non ambiguous relations with information (in the sense of
>>>information theory), since both are defined within the
>>>
>>>
>>framework of a
>>
>>
>>>common theory. Let us look now to the thermodynamical entropy, which
>>>was defined by Rudolf Clausius in 1865. It is a physical concept,
>>>usually introduced from the Carnot Cycle. The existence of
>>>
>>>
>>entropy is
>>
>>
>>>postulated, and it is a state function of the system. Usual
>>>
>>>
>>variables
>>
>>
>>>are temperature and pressure. Entropy calculations are
>>>
>>>
>>sometimes made
>>
>>
>>>discarding the implicit assumptions done for an idealized
>>>
>>>
>>Carnot Cycle.
>>
>>
>>>Here come difficulties. E.g., the whole universe is sometimes
>>>considered as a system for which the the entropy is assumed to have
>>>sense. Does the equilibrium of such a system has sense? Does
>>>thermodynamical state functions make sense here? And what
>>>
>>>
>>about "the"
>>
>>
>>>temperature? These latter variable, even when viewed as a
>>>
>>>
>>function of
>>
>>
>>>coordinates and/or time, has sense only for a restricted number of
>>>situations. These difficulties appear for many other
>>>
>>>
>>systems. At other
>>
>>
>>>scales, they may appear for microscopic systems, and for macroscopic
>>>systems unrelated to thermochemistry. In fact, what is often
>>>
>>>
>>implicitly
>>
>>
>>>postulated is that the thermodynamical entropy theory could work
>>>outside thermodynamics.
>>>
>>>Statistical mechanics creates a bridge between microscopic and
>>>macroscopic models, as evidenced from the work of Boltzmann.
>>>
>>>
>>These two
>>
>>
>>>models are different. One is a mathematical model for an idealized
>>>physical situation (punctual balls, elastic collisions,
>>>
>>>
>>distribution of
>>
>>
>>>states, etc..), and the other is a simplified physical
>>>
>>>
>>model, working
>>
>>
>>>upon a restricted number of conditions. The expression of
>>>
>>>
>>the entropy,
>>
>>
>>>calculated via statistical mechanics methods, is formally similar to
>>>the informational entropy. This latter has appeared many
>>>
>>>
>>decades after
>>
>>
>>>the former. Thus, the pioneers of information theory (Shannon, von
>>>Neumann) who retain the term "entropy", are undoubtly responsible of
>>>the historical link between <<Entropy>> and <<Information>>
>>>
>>>
>>(e.g. see
>>
>>
>>><http://www.bartleby.com/64/C004/024.html>
>>>
>>>
>http://www.bartleby.com/64/C004/024.html).
>
>
>>>Although "entropy" is a well known term in information
>>>
>>>
>>theory, and used
>>
>>
>>>coherently with the term "information" in this area, the
>>>
>>>
>>situation is
>>
>>
>>>different in science. I do not know what is "information" in
>>>theermodynamics (does anybody know?). However, "chemical
>>>
>>>
>>information"
>>
>>
>>>is a well known area of chemistry, which covers many topics,
>>>
>>>
>>including
>>
>>
>>>data mining in chemical data bases. In fact, chemical
>>>
>>>
>>information was
>>
>>
>>>reognized as a major field when the ACS decided in 1975 to
>>>
>>>
>>rename one
>>
>>
>>>of its journals "Journal of Chemical Information and Computer
>>>Sciences": it was previously named the "Journal of Chemical
>>>Documentation". There are little papers in this journal which are
>>>connected with entropy (thermodunamical of informational).
>>>
>>>
>>An example
>>
>>
>>>is the 1996 paper of Shu-Kun Lin, relating entropy with
>>>
>>>
>>similarity and
>>
>>
>>>symmetry. Similarity is itself a major area in chemical information,
>>>but I consider that the main area of chemical information is
>>>
>>>
>>related to
>>
>>
>>>chemical databases, such that the chemical information is
>>>
>>>
>>represented
>>
>>
>>>by the nodes and edges graph associated to a structural formula.
>>>Actually, mathematical tools able to work on this kind of chemical
>>>information are lacking, particulary for statistics (did anyone
>>>performed statistics on graphs?).
>>>
>>>In 1999, the links between information sciences and entropy
>>>
>>>
>>were again
>>
>>
>>>recognized, when Shu-Kun lin created the open access journal
>>>
>>>
>>"Entropy":
>>
>>
>>><<An International and Interdisciplinary Journal of Entropy and
>>>Information Studies>>. Although most pluridisciplinary
>>>
>>>
>>journals are at
>>
>>
>>>the intersection of two areas, Shu-Kun Lin is a pionneer in
>>>
>>>
>>the field
>>
>>
>>>of transdisciplinarity, permitting the publication in a
>>>
>>>
>>single journal
>>
>>
>>>of works related to entropy and/or information theory,
>>>
>>>
>>originating from
>>
>>
>>>mathematics, physics, chemistry, biology, economy, and philosophy.
>>>
>>>The concept of information exists in other sciences for
>>>
>>>
>>which the term
>>
>>
>>>entropy is used. Bioinformation is a major concept in
>>>
>>>
>>bioinformatics,
>>
>>
>>>for which I am not specialist. Thus I hope that Pedro Marijuan would
>>>like to help us to understand what are the links between
>>>
>>>
>>bioinformation
>>
>>
>>>and entropy. Entropy and information are known from economists and
>>>philosophers. I also hope they add their voice to those of
>>>
>>>
>>scientists
>>
>>
>>>and mathematicians, to enlight our discussions during the session.
>>>
>>>Now I would like to draw some provocative conclusions. Analogies
>>>between concepts or between formal expressions of quantities
>>>
>>>
>>are useful
>>
>>
>>>for the spirit, for the quality of the papers, and sometimes
>>>
>>>
>>they are
>>
>>
>>>used by modellers to demonstrate why their work merit funds (does
>>>anybody never do that?). The number of new concepts in sciences
>>>(includes mathematics, economy, humanities, and so on) is
>>>
>>>
>>increasing,
>>
>>
>>>and new terms are picked in our natural language: the task of the
>>>teachers becomes harder and harder. Entropy and Information are like
>>>the "fourth dimension", one century ago: they offer in common the
>>>ability to provide exciting topics to discuss.
>>>
>>>
>>Unfortunately, Entropy
>>
>>
>>>and Information are much more difficult to handle.
>>>
>>>Michel Petitjean Email:
>>>
>>>
>>petitjean@itodys.jussieu.fr
>>
>>
>>>Editor-in-Chief of Entropy entropy@mdpi.org
>>>ITODYS (CNRS, UMR 7086) ptitjean@ccr.jussieu.fr
>>>1 rue Guy de la Brosse Phone: +33 (0)1 44 27 48 57
>>>75005 Paris, France. FAX : +33 (0)1 44 27 68 14
>>><http://www.mdpi.net> http://www.mdpi.net
>>>
>>>
><http://www.mdpi.org> http://www.mdpi.org
>
>
>>><http://petitjeanmichel.free.fr/itoweb.petitjean.html>
>>>
>>>
>http://petitjeanmichel.free.fr/itoweb.petitjean.html
>
>
>>><http://petitjeanmichel.free.fr/itoweb.petitjean.freeware.html>
>>>
>>>
>http://petitjeanmichel.free.fr/itoweb.petitjean.freeware.html
>
>
>>>_______________________________________________
>>>fis mailing list
>>>[email protected] <http://webmail.unizar.es/mailman/listinfo/fis>
>>>
>>>
>http://webmail.unizar.es/mailman/listinfo/fis
>
>
>>>
>>>
>>>
>>>
>>>
>>--
>>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) Fax +41 61 302 8918
>>E-mail: lin@mdpi.org
>> <http://www.mdpi.org/lin/> http://www.mdpi.org/lin/
>>
>>
>>
>>_______________________________________________
>>fis mailing list
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>>
>>
>http://webmail.unizar.es/mailman/listinfo/fis
>
>
>
>
>
>

-- 
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)
Fax +41 61 302 8918
E-mail: lin@mdpi.org
http://www.mdpi.org/lin/
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