1. “Necessary but not sufficient condition.” Geometry, 1992. Math is generally taught as if it is a tango, not a time to get down. Tango is too rigid for me. I never got to get down in math class the way I could when I was writing a paper. “Necessary but not sufficient” was one lively spot in my slow, stiff study of mathematics. I suffered a great deal in geometry. Proofs I found agonizing and ridiculous. Why should I spend time proving something we already knew was true? I could see the logic, so why should I memorize all those theorems? I wrote a diatribe to this effect at the bottom of one of my tests, and my teacher promptly referred me to the counselor’s office.
I remember being charmed, in elementary school, by the notion that a square was a rectangle, but a rectangle was not a square. I was really amazed. I had been given a sorting mechanism. I get frustrated now when my students don’t have this sorter. Just because you studied and answered all the questions does not mean you will pass the test. Necessary, but not sufficient. Being in love is a necessary but not sufficient condition for a happy relationship. Coffee is a necessary but not sufficient condition for a happy morning. You get the idea.
2. “Correlation is not causation.” Comparative Politics, 1998. This was the one year I attended a huge public university, and the walk across the green lawn, and the professor’s repetition of that phrase, are all I remember of his class. Rarely, rarely in life are effects clearly linked with effects. Statisticians will try to tell you they have a way of reasonably defining statistical significance so that it’s meaningful, but in my humble opinion, they scoot and slide as they see fit.
Better to keep an open mind about what is correlated and what it might mean than jump into a decision based on what is. In high school, we studied Hume, and I fell in love with skepticism. Just because the sun rose yesterday, doesn’t mean it will rise today. Just because you crashed your car yesterday doesn’t mean you won’t also crash it today. I was primed for the “correlation/causation” business, and when I heard it, I was immediately committed. It’s not an excuse for indecision. Skepticism leaves room for creativity. Because you just never know.
3. “The only true wisdom is knowing you know nothing.” European History, 1993. Ever since my first run through the Greek philosophers, I’ve returned to this idea. I have a tendency to go into any given meeting certain that I know the answers. Reminding myself that I have only one point of view, and I am missing many skill sets and facts and experiences that could be helpful encourages me to not close myself off from good suggestions.
As a spiritual idea, keeping an open mind, and leaving room for what you don’t know, encourages you to respect other people, and possibly even to let there be, as they say, a “higher power.” Even higher than The Amazing Me.