Donald's examples of the understanding of order by naive students is
entirely correct. That is exactly why relating entropy to disorder
is useless when it is done to enlighten naive students. The practice
of the overwhelming majority of teachers is to parrot that "meaning"
anyway. It is evident to me that it is not at all useful to define
disorder as being proportional to k log omega when telling naive
students about entropy. That was a frivolous suggestion at best.
Is there anyone out there who has actually approached the task of
introducing entropy in that way?
I disagree with Donald on this one. We should stay completely away
from any reference to disorder until we get to the statistical
mechanical application to something like the linear spin system,
the Ising model. At that point the idea of order is applicable, and
no sophisticated definition need be introduced. Until that is done
the students will have enough to do understanding entropy; they
don't need to assimilate another new concept, that of order, to
understand entropy. That would be completely backwards.