Knowledge and its uses
Knowing how to do something, and doing it, are not the same thing.
Our astronomer has just completed a series of calculations inspired by the Great Conjunction of last year, dealing with what happens when one planet passes in front of another. Once he puts them in order and writes them up, we may summarize them here. But for now, he has a surprising observation: in all this work, he used nothing more advanced than High School mathematics.
Of course to calculate when planet-planet phenomena actually happen requires mathematics of a significantly higher order, together with a reasonably powerful computer. He asked a different question: if one planet passed in front of another, what would a naked-eye observer see? Since he was interested in a generic answer, not the details of any one event, he could simplify the situation a lot. He set his planets on circular orbits at average speeds, and worked out average brightnesses and times. Any of his more capable students could have done the same, in principle. But none of them has done so, or is likely to. Indeed, even if he’d challenged his most capable students with the problem, few if any would have succeeded, though they had all the tools. Even, he thought, if he’d broken the problem down into its component parts.
He realized that there is a certain fearlessness in attacking a problem that comes with having done that sort of thing before. It wasn’t until he was in grad school that he realized how structured his learning environment had been up to that time, and only then got some experience in using the mathematical and physical tools he’d had for years.
We think something similar goes on with students learning foreign languages. One can ace the quizzes and tests, the grammar and syntax lessons, the reading and listening; and still be tongue-tied when faced with using the language to say something. Part of it is bashfulness, and not wanting to make mistakes, but we think there’s something more. There’s a matter of realizing you have a tool and having the courage to use it.
It’s not for lack of suggestion. Our tutor is impressed by how much the math textbooks he deals with try to find real-world examples for the lesson at hand, and the physics and chemistry books are not far behind. He finds them sometimes idealized and contrived, but the idea is sound. Unfortunately, they’re still part of a very structured environment.
All of this makes us wonder. In school, we pick up many intellectual tools, and use them mostly just to pass the test; then we drop them. What could we do if we had the courage to use them?
