Re: entropy

[palmer@sfu.ca (Leigh Palmer)]

> Is a nice homogeneous glass of water more "disordered" than a glass
> containing the same amount of crushed ice?  If I drop some food coloring
> into a glass of water, and watch the pretty swirly patterns as I stir
> the cup, is there more "disorder" in the intermediate swirls, or in
> the final, uniformly colored result?  Depends, I would maintain, on
> what we mean by "disorder".  If you'd like to *define* disorder to
> be the logarithm of the number of states accessible to the system,
> then yeah, entropy is disorder.  But most students, I think, have a
> rather imprecise conception of "disorder", so using this word without
> a precise definition doesn't help them much, I'm afraid.

The baby's gone out with the bathwater! The idea of instilling a concept
involves getting the student to relate something he doesn't know about
to something he does. You have utterly abandoned this goal when you take
the concept with which he is familiar, disorder, and relate it to yet
another definition. You presented him with a tautology, not an analogy!

I have a very clear idea of what disorder is. Related to a pack of cards
I can tell you that a new pack is rarely as disordered straight out of
the box as it is after it has been shuffled. I shall demonstrate* that
the entropy of the pack of cards has nothing whatever to do with its
entropy, and that should thorougly discredit the analogy.

You need not define disorder for me or your students. They and most
reasonable men - and women too - would agree with my example of disorder
as I have stated it despite your helpful improvement on its precision.
Don't do that; it doesn't help.

Leigh

* on the weekend...