How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

This is a cubic equation, which is to say it involves x raised to the third power. Fortunately, there is a cubic formula that allows you to figure out, by a direct computation, what values of x could have gone in the box to make 12 fall out when you turn the crank. But you didn’t learn the cubic formula in school, and the reason you didn’t learn it in school is that it’s kind of a mess, and wasn’t worked out until the late Renaissance, when itinerant algebraists roamed across Italy, engaging one another in fierce public equation-solving battles with money and status on the line. The few people who knew the cubic formula kept it to themselves or wrote it down in cryptic rhymed verse. Long story. The point is, reverse engineering is hard. The problem of inference, which is what the Bible coders were wrestling with, is hard because it’s exactly this kind of problem. When we are scientists, or Torah scholars, or toddlers gaping at the clouds, we are presented with observations and asked to build theories—what went into the box to produce the world that we see? Inference is a hard thing, maybe the hardest thing. From the shape of the clouds and the way they move we struggle to go backward, to solve for x, the system that made them.