I have a new resolution: I will use color in equations from now on. My inspiration was a post on the Fourier transform [thanks to Kalid for referring me to it]. The author, Stuart Riffle, begins with a familiar experience… a mathematical formula that looks like a complicated hodgepodge of symbols.
What I found was the Discrete Fourier Transform (DFT), which looks like this:
This formula, as anyone can see, makes no sense at all. I decided that Fourier must have been speaking to aliens, because if you gave me all the time and paper in the world, I would not have been able to come up with that.
What follows in the article is Stuart’s aha moment, and a careful picking apart of what each piece of the formula means:
Don’t worry if this doesn’t make sense: there’s a lot of context and background math here. The point is that each piece of the formula means something very specific. For example, one thing that’s happening is we’re taking an average of a bunch of points. Without the color, it would be really hard to parse that particular meaning inside the equation. (Notice that the symbols that indicate to us that we’re taking an average are spread out over the whole equation. Nothing is harder or slower to read than math.)
So from now on, when I write the Pythagorean Theorem, on a chalkboard or in a post, I’ll try to write
Clearer than the “a squared plus b square equals c squared” so many of us committed to memory? I think so.