But first, a bit of pseudo-Japanery:

Sky clears,
Moonlight on cherry blossoms;
I'm still doing trigonometry.

I was talking today with a good friend of mine in Starbucks (my home away from home) about my mind-numbing quest to learn and solve all the intricacies of trigonometric identities and formulas. It seems, I told her, that the more I do these things, the more complex and recondite they get. It's not enough now to just work with sines and cosines and tangents, I now have to work with addition and subtraction of angles, double angles, squares and square roots of of sines and cosines and their many equivalent re-statements, and now half-angles and their many equivalent re-statements. The problems are proliferating in an almost fractal-like pattern of complexity, where equivalents of equivalents of equivalents combine and recombine in hierarchical intricacies.

I have no idea of whether these are going to be important in my later studies or not, so I have set myself to learning all of them in the book. For all I know, someday a piece of math or physics will hinge on whether I know the deconstruction of cos⁴x into (cos²x)² and then into half-angle restatements. I'll probably have forgotten it anyway by then, and have to go looking it up in one of my old textbooks. Yet I have to go through it: it's in the book, so it must be important! I have to go through it, yet I am getting slower and slower and getting less out of it day by day.

My friend said, this sounds like you're playing the slots at Atlantic City! You're putting coin after coin in the machine, and pulling the handle, and spinning the wheel, but you're not winning anything. You keep playing, though, hoping that you'll hit the jackpot and a flood of mathematical understanding will pour out of the machine. But it won't happen. It's like an addiction.

I said, You know, it's true. It's like playing the slots. Every so often, I put in the coin and spin the wheels, and a handful of coins comes out in a little win. That's like when I actually solve one of these on my own. But then, since I'm feeling lucky, I try again, and again, and again, and I find more and more complex problems, and I don't solve them, and I've lost my money again.

So what do I do? What if I just skipped some of the stuff in the book about the more complex trigonometric identities, and went on to what I need more (at least in the context of my math studies) which is trigonometric graphing and equations? Eventually, I'll have to do just that. Because I can see that there's something about this ever-multiplying, ever-complexifying quality of trigonometric identities which can drag the unwary math-student in and never let them go. I have not had this type of experience recently, and it's kind of spooky to recognize it again.

Posted at 3:01 am | link