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.