Happy Pi Day!

This year’s Pi Day is a little more significant than the rest because we can also capture the year in accordance with the digits of pi if you write out the date American-style: 3/14/15. This isn’t as good as back in 1592, a hundred years after Colombus sailed the ocean blue. It rhymes better than 1593, which should be more significant if you take into account significant figures. So next year should be more significant than this year. Hah! I can’t believe how much I packed into this first paragraph. I’m on muscle relaxants because of a bad back so it might be making me a little loopier than usual. (You might have noticed that I’ve blogged a little less the past couple of weeks. This was to avoid sitting in front of my computer because of my back problems, however I’m getting better!)

Given that it’s Pi Day, it seems appropriate for me to excerpt Jordan Ellenberg’s How Not to Be Wrong. I finished this book a couple of weeks ago, and wrote about the first chapter in an earlier post.

Chapter 5 is titled “More Pie than Plate”. Ellenberg provides several examples to illustrate a slogan to live by: “Don’t talk about percentages of numbers when the numbers might be negative.” If you do so, you might find that you could draw some ridiculous conclusions. Here’s an excerpt of one of his examples. You should read his book on some of the more relevant (and longer) examples that made actual news, and have a much more serious impact.

“For example, say I run a coffee shop. People, sad to say, are not buying my coffee; last month I lost $500 on that part of my business. Fortunately, I had the prescience to install a pastry case and a CD rack, and those two operations made a $750 profit each. In all, I made $1000 this month, and 75% of that amount came from my pastry case. Which sounds like the pastry case is what’s really moving my business right now; almost all my profit is croissant-driven. Except that it’s just as correct to say that 75% of my profits came from the CD rack. And imagine, if I’d lost $1000 more on coffee – then my total profits would be zero, infinity percent of which would be coming from pastry! Seventy-five percent sounds like it means ‘almost all’, but when you’re dealing with numbers that could be either positive or negative, like profits, it might mean something different.”

One of my favorite parts of Ellenberg’s book is his introduction titled “When am I going to use this?” This is a perennial favorite question of students in math and science classes. Ellenberg first quotes what might be a standard response: “I know this seems dull to you, but remember, you don’t know what career you’ll choose – you may not see the relevance now, but you might go into a field where it’ll be really important that you know how to ...”

Hmm… this makes me think of the catchphrases we use to promote a liberal arts education. “We prepare you for the careers of the future. No one knows what they’ll be at the speed at which things are progressing. Today’s jobs that you might train narrowly for will be gone tomorrow. So you must be prepared for the future, and the training you get from a liberal arts curriculum will get you there!” I’m a strong proponent of a liberal arts education but sometimes this rings hollow to students (and possibly parents who might be footing the bill).

Ellenberg suggests a different response. I’m going to excerpt his response below but replace “mathematics” with “science” or “chemistry”.

“[Science] is not just a sequence of [steps] to be carried out by rote until your patience or stamina runs out – although it might seem that way from what you’ve been taught in [such courses]. Those [chemistry problems I’ve assigned] are to [science] as weight training or calisthenics are to soccer. If you want to play soccer – I mean, really play, […] you’ve got to do a lot of boring, repetitive, apparently pointless drills. Do professional players ever use those drills? Well, you won’t see anybody on the field curling a weight or zigzagging between traffic cones. But you do see players using the strength, speed, insight, and flexibility they built up by doing those drills, week after tedious weeks. Learning those drills is part of soccer.”

“[Chemistry] is pretty much the same. You may not be aiming for a career [in chemistry]. That’s fine – most people aren’t. But you can still [learn how to think scientifically]. You probably already are [thinking scientifically], even if you don’t call it that. [Science] is woven into the way we reason [about the natural world] And [chemistry] makes you better at things. Knowing [chemistry] is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world. With the tools of [chemistry] in hand, you can understand the world in a deeper, sounder and more meaningful way.”

That’s what I would like to say in my introductory chemistry classes, particularly the non-majors class. (I get to teach one this coming Fall and I’m excited about it!) Now it turns out that there are quite a number of real-world examples where I can illustrate the usefulness of knowing some chemistry. So my job is probably easier than Ellenberg’s at least at the introductory level of chemistry. However, where things start to be more similar is when I teach the dreaded Physical Chemistry sequence. (The students dread “P-Chem”. I don’t dread teaching it, although it is more time-consuming than any other class I’ve taught because office hours are always full of students.) Quantum Chemistry has a lot of math and computing integrals (Ellenberg’s original example) is something the students have to do. So I do find myself having to “defend” mathematics and its importance.

Ellenberg concludes his story: “Even if I did give my student the full inspirational speech, she might – if she is really sharp – remain unconvinced. ‘That sounds good, Professor,’ she’ll say. ‘But it’s pretty abstract. You say that with mathematics at your disposal you can get things right you’d otherwise get wrong. But what kind of things? Give me an actual example.’ And at that point I would tell her the story of Abraham Wald and the missing bullet holes.”

Get a copy of Ellenberg’s book if you want to know the story!