Briefly, on Plateaus
I live in fear of the horizontal asymptote. I'd like to end this post here and now, leaving my readers with the image of a man who spends his days checking over his shoulder for a dotted line, but I suppose I must explain. No, I'm not afraid of calculus. Well, I am , but only superficially. What I want to talk about is much more serious than calculus (that is, if such a thing is possible; my AP calc teacher certainly wouldn't admit as much). I'm terrified of what the asymptote represents when considered in the context of my ambitions. For the uninitiated, an asymptote is a line that is constantly approached but never crossed by a curve. Here's a picture for reference: Now imagine that my goal is to be ever-improving, which it is. What if there was a point I could never cross? Oh God, what if I've reached the point already and don't even know it? This is the horizontal asymptote, my great fear. Of course, this concept could also be depicted as a plateau, ...