It’s the start of another school year, and my seventh-grade son is learning algebra. As I sat beside him to coach him through some homework the other night, I shared my favorite bit of wisdom about how to make math problems—even complex ones—simple and error-free:
In my experience, the surest recipe for disaster is to short-circuit this rule. Collapse a few steps in your head in the name of efficiency, and you’ll forget a minus sign, or you’ll group incorrectly, or you’ll lose track of an exponent or an absolute value—and you’ll end up with a mess. You’ll have to debug your solution by slogging back through the problem from the beginning until you figure out where you went wrong.
It’s interesting—and maybe, profound—how nicely this piece of advice maps onto the design principle of progressive disclosure. The human mind is simply wired to perceive in broad outlines, and then to gradually clarify, a few details at a time.
Don’t believe me? Try a short experiment: draw this fractal.
I’ll bet that instead of laying down every pixel, like a printer, you immediately produce a simplification that captures the general shape as lines, with a lot of detail suppressed. You did this as a kid, when you drew stick figures and triangle+half-circle sailboats.
Artists sometimes squint to blur out what they don’t want to see, leaving only general patterns and colors. But coders never do, because we don’t expect code to work that way. Continue reading