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

Dear Michel,

thanks for the reply. Very shortly:

> There are two replies.
> (a) short reply: (x1,x2,x3)=(1,2,3) and (x1,x2,x3)=(1,3,2) constitutes
either the same data ("indistiguishable points") or different data
("distiguishable points").

in this case you are making points distinguishable through numbers, aren't
you? Aristotle would probably say that points as such are only
distinguishable by the very fact that they are posited or not.

> (b) long reply: points are allowed to have the same coordinates, and in
fact, they may be weighted, and in fact we have to work with distributions
rather with sets. But this does not suffice. The full model involves a
mixture (in the probabilistic sense) of distributions, each distribution
being flagged with a color, and having
 its own weight. A rigorous presentation is too long, but may be found in
my papers: J.Math.Chem. 2004,35[3],147-158, and also in J.Math.Phys.
2002,43,4147-4157. The model involves a measurable "space of colors". A
single point with a color is just a marginal distribution in the euclidean
space (the marginal r.v. is almost surely constant). Two points with a
color and a third one with an other color are, after projecting in the
euclidean space, a finite discrete distribution of two equally probable
points and a discrete distribution of one point with prob.=1, both
distributions having each their own weight, respectively 2/3 and 1/3 here.
There are more complex examples.>

again in this case you are adding something to points, for instance colours
and weights (mathematical and/or physical...), that is to say you are
'in-forming' (!) points with some kind of quality and thus producing order.

Rafael

_______________________________________________
fis mailing list
fis@listas.unizar.es
http://webmail.unizar.es/mailman/listinfo/fis
Received on Sun Jun 6 17:03:44 2004