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

To: <fis@listas.unizar.es>
Subject: [Fis] definition(s) of disorder/chaos: an example

Dear FISers,

Here is the excellent suggestion of Karl:
> take a set of n objects. Investigate the collection of symbols on a most
> usual fragmentational state.
> Linearise the objects.
> Count, how many have a place with tension in the extent of: a) no, b) unit,
> c) multiples of unit.
> This measure has a distribution.
> Call the range where measure minimal (where the objects fit to their places
> nicely / most) as "ordered". Call other ranges "less ordered".

This is indeed suitable in many situations.
Now let us look to the case of N undistinguishable points on the
real line: e.g. having (x1,x2,x3) and (y1,y2,y3), how could we
produce a criteria to know which of (x1,x2,x3) and (y1,y2,y3) is
the more disordered ? It is one of the siplest situations (having
only 1 or 2 points would probably be too simple here). If it cannot
be solved, why ?

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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Received on Thu Jun 3 10:45:10 2004