Real Analysis Gothic
- For every epsilon there is a delta. Where is it? Epsilon does not know where delta is. Zero does not know where delta is, it is too far away. Nobody knows where delta is; every number is so far from the other numbers. They are getting further apart. Epsilon is so very small.
- You are walking up a staircase. You try to take a step, but another step emerges in the middle. A hooded figure appears at the top. You scream and try to run downstairs, but this staircase has so many steps. It is getting closer, closer.
- You compute a Fourier series at a point; it is different than the value of the function. That’s normal, you say, unconvinced, as you are overwhelmed by a sense of dread. You start to apply the inversion formula, but think better of it. You still have scars from the last time.
- You cut yourself into three pieces and eat the middle one. It hurts, yes, but you are so tender. You do it again and again and again and again… Your mouth eats your mouth. You are perfect.
- A year ago today you were teaching calculus. “So you see, it’s easier to take derivatives than integrals” you said. You coughed, the blood splattered out of your mouth, it formed Thomae’s function on the floor. Now you are at the same point in your lesson plan. The stain is still there. It looks up at you, expectantly.
- You are talking to a complex analyst. Differentiable functions are smooth, he says. Bounded differentiable functions are constant, he says. What are you doing, he says. I’ll call the police, he says. He doesn’t say anything now.