Hitchhiker’s Guide

August 18, 2010

I made it part way through the newest of the Hitchhiker’s Guide to the Galaxy movies last night. I stopped right after the pivotal moment where the supercomputer gives the answer to life, the universe, and everything: 42. When they ask what the story is, the supercomputer points out that they never really gave it the question. Forty-two is the right answer, no doubt, but finding the question will take some real work. An absolutely classic moment.

Today I started thinking about how perfectly that scene fits the state of mathematics in mainstream education. We’re all answers, no questions.

I’ll give you my favorite example. What’s the area of a circle? If you remember your high school geometry, you’ll recall that there’s a formula for this, namely:

“The area of the circle is pi times the radius squared.”

Pause here. Does this answer mean any more to you than 42? Probably it means less. What’s pi, after all, and how does it all work? We need to slow down, and remember our question.

What is the area of a circle?

No tricks. No formulas. You’re just a human being, looking at one of the simplest and most fundamental shapes there is, just like you’re ancestors once did before anyone had any idea about formulas. What do you do?

In fact, let’s say you knew everything else you wanted to know about the circle: the diameter (i.e., the distance across is, or d in the picture above); the circumference (or distance around, c in the picture above); the radius isn’t pictured, but it’s just half the diameter. Anything you want, let’s say you know it. How can you figure it out.

Maybe not everyone can solve this problem. But it’s worth starting with the question. When you get to the answer, it has a chance of actually meaning something. Forty-two, after all, was never much help.

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