And Rosta wrote:

> (Also when I'm teaching & tired I have this perturbing
> problem of stating propositions that are the truth conditional
> opposite of what I intend to say. I worry about it, but probably
> the students are even tireder than I am & aren't listening anyway.)

Ah, the Absent-Minded Professor: writes A, says B, means C --- but it
should be D.  :-)

> The student ideally shouldn't have to, if in the first place they're
> taught a preliminary approximation of the Right Thing.

Yes, but.  You may know the difference between simplifying and
oversimplifying well enough, but the student does not.  In either
case, the second course holds him up to a jolt: the rules he learned
are no longer to be counted on, and so he must think (a dreadful fate).

One of the classic blunders, e.g., in learning relativity is to misapply
some formula, perfectly good in Newtonian physics, to the wider
Einsteinian context, in which it is nonsense.  (Example: relativistic kinetic
energy is *not* half the relativistic mass times the square of the velocity!)

There is / one art                   || John Cowan <[log in to unmask]>
no more / no less                    ||
to do / all things                   ||
with art- / lessness                 \\ -- Piet Hein