Analogies are _useful_ but when we forget that mathematics is
*but* an analogy to physical systems, we can end up with our
heads in the clouds very quickly.
This was written by a professor _for_ other professors who teach
physics.
It's very important because a student who leaves school with
excessive dependence upon analogous forms to understand
concepts, will then teach and practice physics with those
analogous forms embedded in their conceptual framework and can
lead them to some very bad science.
