This is What I Do

When I was younger I used to like Encyclopedia Brown books. If you never read those, they were little volumes of short stories in which a Encyclopedia Brown (who is a boy) is confronted with mysteries. Not big, criminal-investigation-type mysteries, but little domestic ones, like whether someone legitimately won a race, or whether a bully cheated kids out of their money. As I recall, the reader gets to hear the case, and then Encyclopedia gives his answer, and then there's a break in the narrative where you can try to figure out what it was that Encyclopedia saw before he explains.

I wasn't very good at solving the mysteries myself, but I liked reading the books. One of the only solutions I can remember was a girl caught in a lie because she had folded a paper eight times to fit it inside a small box. "Ah ha!" says Encyclopedia. "It's impossible to fold a piece of paper more than 7 times with your bare hands. She must be lying." She was - she had used pliers (or something of that sort) to make the last fold.

I don't remember what was on the paper, or why she lied about it in the first place. But I do remember being curious about the paper folding. It seemed strange to me that one couldn't fold a piece of paper more than seven times. And so I tried. And Encyclopedia was right. I was hard-pressed even to get to seven. If you've never heard about this, you should try it. With a really long length of toilet paper that you think you should be able to fold in half lengthwise many, many, many times. You'll be surprised how few times you can actually fold it before it becomes impossible to continue.

There's this mathy blog on the NY Times online that I've been reading. The author is systematically working his way through mathematical concepts, from the very simple to more complex, in the attempt to show how math is both comprehensible and useful. His audience is the average slightly-math-phobic adult, but I'd venture to say his most enthusiastic followers are probably people like myself who already kind of like the subject.

[Warning: The next paragraph contains some math. I think it's reasonably understandable and interesting, but if math scares you, just skim the paragraph. I don't spend very long on the math.]

The most recent one talked about logarithms, and had a little note about paper folding, and why it's more impossible to fold paper than you think it would be. It has to do with the fact that the length of the paper is decreasing by powers of two at the same time that the width is increasing by powers of two, and exponential functions grow really fast. Faster than you'd expect. By the time you get to, say, n = 10, a linear function like 2n is going to be at 20, and a quadratic function like n² will be at 100. But an exponential function like 2ⁿ (which is what we're working with in the paper folding) is going to be at 1024. Those are dramatic differences.

[Okay, done with the math now.]

Apparently some middle school student derived a formula to predict how many times you'll be able to fold a piece of paper of a certain length and width, and then went about using the formula to set the world record for paper folding (of the non-origami type). A question from Brady (who introduced me to the blog in the first place) about why the equation would have pi in it intrigued me, and I have spent bits and pieces of my spare time over the last few days not only figuring out what pi has to do with anything¹ but trying to derive the formula myself. If a middle school student can do it, I should be able to.

I haven't figured out her formula yet and it's kind of frustrating me. But it's also kind of reminding me about why I like math. And what I like about math. Which is that math fundamentally makes sense, but also requires a lot of creativity.

A lot of people don't realize this - about the making sense or the creativity. This past Saturday, we had a ward activity in which several of us were "nominated" to do short presentations on what we do, and what I do is teach math to teachers. I talked about that, and about making sense of the multiplication algorithm, and I actually got a lot of positive feedback about my presentation. So many people have experiences that turn them off to mathematics, and most of these experiences involve having to memorize lots of rules without understanding where the rules came from or why we should care. People who manage to make it all the way to higher mathematics tend not to care that much anymore about where the rules came from and so they don't always help things. And many people teaching lower level mathematics never really learned where it all came from themselves, so it's hard for them to pass it along. The field of mathematics education is the middle ground where we try to change all that.

My job is to show people why the mathematics they have always hated (or at least been more or less indifferent to) is actually really, really cool. And it is! I feel like what I put into the mathematics I do is less far removed than you might think from the more "right-brained" things I do like creating a photo montage, or discussing an episode of Lost, or writing a book review, or watching a movie that makes me really think, or playing Boggle. Real math is not plugging things into formulas, it's piecing together bits of information and making sense of them and using them to create something new.

I didn't really like math until college. So it's funny to me sometimes to see where I've come to. But it also makes the challenge of helping other people come to this realization about math that much more rewarding.


¹ You create semicircles at the folds, in case you were wondering.