But the more important point: Suppose you've got an iron flywheel that's spinning very rapidly. That's definitely kinetic energy, so the average kinetic energy per molecule is high. Is it heat? That particular kinetic energy, of a spinning flywheel, doesn't look to you like heat, because you know how to extract most of it as useful work, and leave behind something colder (that is, with less mean kinetic energy per degree of freedom).

Systems in thermal contact (by radiation of nothing else) come to the same temperature. That makes it pretty objective if one of the systems is a thermometer, whether it's heat or not.

gyroscope

That was actually a joke. Though people would be hard-pressed to guess what happens if you try it.

Gyroscopes are very unintuitive, because people intuitively but incorrectly think that pushing on something changes its position, a mistake that gyroscopes bring out.

two systems in thermal contact trade energy to maximize the net entropy of the ensemble.

Actually the assumption is that two systems in thermal contact come to some equilibrium state.

Let this equilibrium state _maximize something_, call it S, and use calculus.

Energy is conserved.

Therefore the energy change in on system equals minus the energy change in the other, and the change in S wrt the energy change in each system has to be equal in both systems at the maximum of total S.

Call that change wrt energy the (inverse) temperature. Two systems in thermal contact come to the same temperature, is then what the assumption of some equilibrium of something comes to, after you rename the derivatives.

Only the assumption of an equilibrium has been introduced to get this.

That's where

I favor taking energy from earth rotation. Put a horizontal gyroscope across a circular track around the North Pole, and let the earth rotate under it. Take energy from the relative motion.

We have a thousand words for sorrow http://rhhardin.home.mindspring.com/sorrow.txt

I don't know if that affects the theory.

(computer clustering a short distance down paths of a thesaurus)

It's called entropy because somebody told Shannon that the same mathematical quantity already existed in thermodynamics, when the question what to call it came up.

I don't know that there's any other operational connection.

Like there's no entropy gradient giving the arrow of time, or system-wide increase.

Consider Cavell on baseball

People can agree about all the facts but argue about what the word means, which question is an empirical one. People don't know what their criteria are for something being a sound, and can only offer aspects that seem to count for it or against it. You have to try the argument and see if you can see it that way.

Perhaps in the end you can bring out what a sound is.

See Cavell on chairs, op cit. and derivatively Wittgenstein.

The people arguing are not making a mistake; the cognitive scientist is.

Are vibrations in the air that nobody hears, sound? That's the question.

It's not, curiously, a matter of definition.

See Stanley Cavell's discussion of what is a chair in _The Claim of Reason_ p.71

Wittgenstein goes a little deeper than is imagined.

It's easy to teach a dog what words mean, provided the dog has some interest you can quickly show in the thing meant.

I wrote out on a napkin, one day when she was two, all the words and phrases that my Doberman Susie definitely knew in context, and came up with 200.

All of them were for things that involved her somehow. The most direct naming of things was for toys ; but commands and so forth, and the ever-versitile ``fetch the ...'' where ... is something fetchable, provided a link to lots of items you could name. Her interest was then in fetching, and indirectly to the name of the thing.

People are no different. To teach what red is, you need some interest in red.