Re: [Fis] definition(s) of disorder/chaos

A small suggestion for discussion:
When order and other concepts are defined in a quantitative way (how
much is it?)
and relative way (which one has more chaos?), very simple examples
should be given.
Shu-Kun

Michel Petitjean wrote:

>To: <fis@listas.unizar.es>
>Subject: [Fis] definition(s) of disorder/chaos
>
>Dear FISers,
>
>I would like to outline the excellent remarks of Jerry LR Chandler:
>
>
>>the terms "order" and "disorder" are not opposites in the
>>mathematical sense
>>
>>
>and:
>
>
>>Set theory is one foundation of mathematics. An abstract concept of order
>>enters set theory via the "well - ordered axiom." One expression of this
>>axiom ( Stoll, Set Theory and Logic, 1961) states:
>>
>>"a well ordered set is a partially ordered set such that each non-empty
>>subset has a least or first element."
>>...
>>
>>
>
>Partial ordering and total ordering are well known
>concepts in set theory. In fact the transitive (but non symmetric)
>relation of order between elements is a basic concept.
>So, in this sense, there is no ambiguity about what is order.
>Now, except negating order, disorder is not defined.
>But it seems to me that many authors working with concepts of disorder
>or chaos, are not working with the well known definition issued
>from set theory.
>In the context of the FIS session about Information/Entropy,
>my question would have been rather:
>which definitions for disorder/chaos ?
>Pertinent replies were posted by Devin, Gyorgy, Robert, Loet,
>and Stan.
>An other way to discuss about order/disorder/chaos is to look
>to what could be their maximum/minimum, if any. Coming back to
>set theory, we could see that "well ordered" and "totally ordered"
>are different criteria: the experimentalist has to clarify in his
>mind what are his needs. If the actual concepts of order in set
>theory suffice, it is OK. If not, we have to elaborate definitions
>from properties, these latter depending on the local area in which
>we are working.
>I notice that the order concept in set theory falls in what I called
>the "static" case (no time) in a previous post, although it
>appeared from other postings that the time has to play a role
>in order/disorder/chaos. We move forward.
>Some minor questions:
>- are the measure(s) of order/disorder/chaos changed when the space unit is changed ?
>- are the measure(s) of order/disorder/chaos changed when the time unit is changed ?
>Other questions:
>- Processes: what relations between periodicity, aperiodicity, and
>order/disorder/chaos ? And what about ergodicity ? Equilibrium ? Randomness ?
>
>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.org
>http://petitjeanmichel.free.fr/itoweb.petitjean.html
>http://petitjeanmichel.free.fr/itoweb.petitjean.freeware.html
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>
>

-- 
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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