Why I Love Math, Part 1: Because I Love Clever Movies

It’s no secret, I’m a mathy person. In fact, I just spent several hours of my free time this weekend trying to learn some new math, even though I didn’t need it for work.

Understandably, this seems ridiculous to a lot of folks. I probably get asked, “how can you enjoy this stuff?” more often than I get asked any other question about math or physics.

Well, one of the reasons I love math is that I love surprises, and math is full of them. Two mathematical concepts that initially look very different might turn out to be exactly the same. A problem that looks literally impossible might turn out to have a really easy solution, if you’re clever about it. Or a very simple idea might turn out to have much more important consequences than you’d ever have thought.

Whenever I find a situation like this in mathematics, I get a real thrill. But it’s not some esoteric, high-level pleasure reserved for academics. On the contrary, it’s the same sense of “Oh wow! Oh awesome!” that anyone can get from watching a good, clever movie.
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The High Probability of Coincidence

Coincidences are quite likely.

The odds of any particular coincidence will be quite small. But there are so many possible coincidences that the odds of any coincidence are very high.

Take any deck of cards. Shuffle it, ideally 7 times*. What are the odds that you find a pair of queens on the top of the deck? About half a percent, it turns out. Very small.

CardShuffleBut what are the odds of finding a pair of any kind, anywhere in the deck? I don’t know actually. That’s hard to calculate. But it’s much, much larger.  Go ahead, check for yourself. I just tried it five different times myself, and never failed to find at least one pair. Often more than one.

This is probably fairly obvious. But you’d be surprised how easy it is to lose sight of it.

Before a presidential election, for example, news magazines tend to fill up with stories about weird things that can predict the results. They’re played for laughs, of course. But when you see these articles discussed in comments, you’ll find lots of readers determined to explain “why” these coincidences work.

Some of them may have explanations, it’s true.** But the point is, these coincidences don’t need explaining because their existence is not unlikely.

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Happy Pi-Day!

It’s now March fourtteenth at 1:59 PM, meaning it’s 3.14 1:59. Happy Pi Day, everyone! (PS, if you are a european, please do not misconstrue this to mean that pi is 14.3 1359.) Here’s a little something to celebrate the day by.

Actually, I debated for a while about whether I should post this particular clip, because in some ways it’s completely arbitrary. People get obsessed with the digits of special numbers, but they’re meaningless. Its the same fallicy that people succumb to when they think there must be something special about being the 1 millionth customer. In base 6, they’re actually the 33233344th customer. Which suddenly doesn’t seem so special, now does it? Similarly, I could rewrite pi in another base and this song would no longer have any particular relevance to the number pi. His choice of what scale, what key, and what numbering scheme are also all just up to him. The whole thing is actually just an project in constrained composition, where he’s chosen an arbitrary set of rules he has to stick to and managed to make an attractive piece of music out of it.

So I was hesitant to spread this around, lest people who like to attach too much mystical meaning to science and math start calling it “the harmonies of mother nature” or something like that. But then again, it really is an impressively well-constructed song, given the restrictions he had to work with. And that really is a great hat/vest combo he’s wearing….

∫ The World’s Coolest Paperweight

This is a Gömböc:

What is a Gömböc, you ask? It is the answer to a surprisingly tricky math problem, it is the secret to how many tortoises survive, and it would be one cool toy to have on your desk.

But perhaps put most plainly, the Gömböc (that last “c” is pronounced like a “tch,” by the way) is the only convex three-dimensional shape* which will balance in only one position by virtue of it’s shape alone. I’m struggling here to describe it’s properties both accurately and non-technically, but if you’ll bear with me, I’ll show you what I mean.

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My Favorite Paradox

Sometimes people make fun of my for my tendency not to wave to them when I’m walking about campus. And while it’s true that most of the time I’m daydreaming about just what I would do if at that moment I suddenly had a jetpack, occasionally it’s something interesting. Here’s a puzzle which used to rattle around my brain whenever I was walking to/from school as a little kid, which I still think of occasionally and in fact, have only just in the last year or two come fully understand.

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Things I Learned From Teaching Undergraduates: “Did Obama’s Trip Really Cost $200m Per Day?” Edition

Okay, so this isn’t one of my usual “Things I Learned From Teaching Undergraduates.” But the title technically fit, so I wanted to use it.

The other day I was crusing various conservatives blogs–I like to do this; it helps me put myself in their shoes, remind myself that they’re real people, and occasionally, provide me with something to laugh at (just like when I read the crazier left-wing bloggers, let’s be fair). Anyway, I came across this doozy of a post from Michelle Malkin, in which she (okay, her underblogger Doug Powers) claims that Obama’s current trip to India is costing taxpayers $200 million dollars a day. Powers supports this by  quoting an anonymous Indian official:

“The huge amount of around $200 million would be spent on security, stay and other aspects of the Presidential visit,” a top official of the Maharashtra Government privy to the arrangements for the high-profile visit said.

Could this possibly be true?

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If I May Brag on Behalf of My School for a Moment

One of the tangentially fun things about being at Stony Brook is the sort of “David and Goliath” fun of knowing that, in spite of being a smaller, state-funded school, we sport an excellent physics department with enough clout to attract visitors and speakers from all of the “big name” universities around the world. That’s something most schools can’t do, even some of the other public universities that are known for their physics programs. Even Colorado, while home to a lot of excellent physicists, didn’t manage to attract the big-name guys elsewhere as speakers very often.

That’s why I’m excited about what’s happening tomorrow, as our (literally) shiny new building, the Simons Center for Geometry and Physics, opens for the first time and holds its inaugural conference on mathematical physics. Read more of this post