Wherefor and Why

[stoutfellow]

My student's assignment for today involved some rather tedious calculations. She handed me the write-up, and I scanned it - one of those situations where it's easier to verify that an answer is correct than to actually get the answer. No problems.

Then we went on to the topic of the day, The Care and Feeding of Involutions. I showed her a bunch of tricks for dealing with involutions (transformations whose square is the identity transformation): projecting to eigenspaces, computing the dimensions of eigenspaces without computing the spaces themselves, tricks with commuting involutions, stuff like that. In passing, I pointed out how they could be used to simplify those tedious calculations. Her response was pleased - "Yeah, that's much better" - but there was a hint of asperity in it. (Unspoken: "Why didn't you show me this before assigning me that problem?" "So you'd appreciate it!")

There is a psychological element to the business....

Comments

[ndrosen]

This takes me back more than thirty-five years: I ran into the lass who had been my high school semi-girlfriend, and she wanted me to help her with calculus, so we headed to a used book store, and found a place to sit down, I helped her a bit with dy, dx, and such, and she said she had seen it before, but hadn’t understood dy and wherefore of it.