I'm such a geek.
I was still pretty awake when I went to bed last night, and Matt was in the computer room chatting with Braz and KT. So, as I often do, I let my mind wander, and pretty soon I was having imaginary conversations with imaginary people. (Or rather, real people who were only there in my imagination.)
Wait, that's not the thing that makes me a geek! Everyone does that, right?
Right?
Um, guys? You can stop laughing, now.
Anyway, I was having these imaginary conversations, in my head. (No, I'm not stupid enough to have them out loud.) And the subject turned - gods only know how - to mathematics.
I mean, it makes a certain amount of sense. I have a master's degree in theoretical mathematics, after all. In this imaginary conversation, I was explaining to whoever it was that sometimes I felt kindof dumb because I've forgotten practically all the math I learned in graduate school. But then it occurs to me that I still know more math than most people ever know. I could still teach calculus, if I had to - how many people could say that?
And then it occured to me to wonder if I could still teach calculus. I've been a computer programmer for five years, and while it's frequently a challenging job, I hardly ever use any math more advanced than algebra. And basic algebra, at that.
I mean, derivatives, I said to myself, my imaginary conversational partner slowly fading away, I can do derivatives in my sleep, except maybe the trig stuff. (I'd been in an accelerated math program in high school that skipped trigonometry altogether, except for a one-week "refresher" on it in my pre-calculus class. As a result, I never was very good with trig.) But could I still do integrals? I was never all that great with integrals to begin with.
I gave myself an integral to do. int( x^2 dx ). (Well, the web isn't really the best place for mathematical notation. In my mind the exponent was properly poised as a superscript, and the squiggly integral sign was out in front.)
I barely hesitated before remembering that if you want nice neat answers, you have to have a coefficient. int( 3x^2 dx ). Wait, wait, don't make it that obvious. int( 6 x^2 dx ). Obvious? I demanded of myself indignantly. I'm not making a test here or anything! I stopped futzing with the question and solved the integral. 2x^3 + C, where C is some constant. (I was proud that I remembered to add the constant. Countless quizzes received only partial credit for forgetting that damned constant.)
Pshaw, myself answered. That's a baby problem.
Well, I said, somewhat defensively. If you've got several things added together, then you can just integrate each piece separately and then add them back together at the end.
What about-
No trig! I reminded myself, interrupting.
- multiplied items? How do you break apart an integral when things have been multiplied together?
Now here, I was stumped. I knew you couldn't break apart multiples and just multiply them back together again when you finished integrating. To prove it to myself, I broke my 6x^2 into 6x and x. Wait! I recalled triumphantly. You can move constant multipliers out of the integral!
Oh, very good, myself said dryly. What about that x^2?
Oops. I'm boring you, aren't I? The upshot of that was that I spent about twenty minutes drawing with my finger on Matt's pillow, and still couldn't remember how to break the formula apart. Finally, Matt came to bed.
"Sweetie? You still love me, right? Even if I'm a complete and utter geek?"
"Of course," he said. "Why?"
I told him that I couldn't sleep because I was stuck on a calculus problem. He looked at me with sympathy - or perhaps it was the sort of pity that people offer to the mentally deranged - and kissed me goodnight.
About ten minutes later, he remembered something he had to do downstairs, and got up. I gave up, turned on the light, and fetched my calculus book from my bookshelf. (Yes, I kept all my math books. Yes, I keep them in my bedroom.) Ah-ha! You can't break apart an integral around multiplications unless you're breaking apart different variables.
With a sense of relief, I put the book back on its shelf, turned out the light, and slept like a baby until the cat woke me up at 3:30.
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