[Fis] Distinguishability (was: Re[2]: definition(s) of disorder/chaos: an example)

To: <fis@listas.unizar.es>
Subject: [Fis] Distinguishability (was: Re[2]: definition(s) of disorder/chaos: an example)

Dear Rafael,

You wrote:
> Do you know the Jewish-German mathematician Felix Hausdorff? Vol. VII of his
> "Gesammelte Werke" has been published recently (Springer 2004, 902 pages)
> with his philosophical work. In a review of this volume that was published
> in the Frankfurter Allgemeine Zeitung (Dietmar Dath, June 7, 2004, Nr.130,
> p. 41) there is an interesting sentence on points. The "Hausdorffraum"
> (Hausdorff-space) is such that two points are then distinguishable if (and
> only if?) they are situated in two separate spaces ("in zwei nicht
> zusammenh=E4ngenden Umgewungen").

I know the famous mathematician Felix Hausdorff, which established
many fundamental theorems in topology. Thanks for this pointer.
This induces a interesting discussion about the concept of "distinguishability".
As for many other terms evoked during the FIS session, I am afraid
that, depending on the field, we get different definitions for this
concept: the Hausdorff definition (topology) is one of them.
An other one is shared by physicists and probabilists: "discernable"
or "not discenable" particles are involved in distributions modeling
physical phenomena: here, the particles may be complex objects rather
than points. An other one is involved in the "colored mixture model"
(see my email posted the 3 June): here, the points are in fact
distributions (a single point has to be viewed as the value taken by
an almost surely constant random vector).
Are there FISers aware of other definitions ?

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 Wed Jun 9 10:27:01 2004