Blog post: swansont: … But You Can Derive Everything Else

I was thinking about the bit in the Grace Hopper video I linked to the other day, in which she complains about the mental challenge when she did her initial navy training: she had forgotten how to memorize, and there was a lot of memorization involved. As she put it, you can't derive the organization of the navy.

In physics, however, you can derive a lot of things. I don't recall exactly when I realized it, but somewhere along the way I realized that I didn't have to waste time memorizing page after page of equations, because from a few basic ones, many others can be derived. This is clear right off the bat in physics, because the first topic taught is usually kinematics, and all of the equations derive from the mathematical definitions of acceleration and velocity being derivatives. Doing the proper integral recreates a whole bunch of equations. Applying them properly (i.e. adding in some trig and algebra) yield a whole host more that many students memorize (like several related to projectile motion).

I had trouble convincing most students of this when I was teaching. Invariably, they would blanch in horror at the suggestion that they derive equations, but these were typically not the physics majors who were resisting me, so perhaps that's one of the kinds of thought processes that separate us from other other kinds of students, even within STEM topics. (though even physics majors are not totally immune to the "you're not going to actually make me apply the math I learned in math class" attitude.) So it was nice to hear RDML Hopper say that. Read and comment on the full post