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I had a professor who I never forgot. We learn, for instance, that the gravitational attraction between two objects is the product of the masses divided by the square of the distance between them... F=(M*m)/r^2, in the parlance (There's more to it actually, but that's the basics.) This is just a fact to be memorized, a basic truth in physics. Now he gave open-book tests, take-homes, etc... he was very generous, as long as you could get correct answers onto the page, he was good with it. But that's because while you learned that F=(M*m)/r^2, on the test you were more likely to see a question like this:
"Space around planet Zog IV has been flattened into a 2-dimensional continuum by a collision with a space-bourne dinosaur. What is the formula for gravitational attraction in this now 2-dimensional space?" And suddenly, if you didn't understand *why* F=(M*m)/r^2 in 3-dimensional space, how that equation was derived, and be able to apply that understanding to a situation where a fundamental underlying physical constant was different, you weren't going to get the point. Just memorizing the facts you were taught wasn't good enough to get an A in that class.
But not being the kind of crazy super-genius who can immediately reckon new physical equations in his head to account for interstellar sauropods wouldn't kill your grade, either. As I recall, although he was famous for these sorts of very tough questions, he didn't grade *that* tough. I still managed to pass that class OK. And although I didn't get the question right on that test — I didn't even know how to begin to figure it out — he inspired me to be curious about it. And 25 years after finally finding out, I still remember that the force of gravitational attraction in 2-D space, something there's really no reason to ever know, is (M*m)/r, and with minimal brushing up I could probably still tell you exactly why that is, which is probably the entire point.
I appreciated his teaching style.
"Space around planet Zog IV has been flattened into a 2-dimensional continuum by a collision with a space-bourne dinosaur. What is the formula for gravitational attraction in this now 2-dimensional space?" And suddenly, if you didn't understand *why* F=(M*m)/r^2 in 3-dimensional space, how that equation was derived, and be able to apply that understanding to a situation where a fundamental underlying physical constant was different, you weren't going to get the point. Just memorizing the facts you were taught wasn't good enough to get an A in that class.
But not being the kind of crazy super-genius who can immediately reckon new physical equations in his head to account for interstellar sauropods wouldn't kill your grade, either. As I recall, although he was famous for these sorts of very tough questions, he didn't grade *that* tough. I still managed to pass that class OK. And although I didn't get the question right on that test — I didn't even know how to begin to figure it out — he inspired me to be curious about it. And 25 years after finally finding out, I still remember that the force of gravitational attraction in 2-D space, something there's really no reason to ever know, is (M*m)/r, and with minimal brushing up I could probably still tell you exactly why that is, which is probably the entire point.
I appreciated his teaching style.
