(This is the second writing assignment for Justin Lanier’s smooc)
Preamble: So one of the great (but difficult!) parts of being part of Justin’s smooc is that, while there are assignments and structures, it’s pretty self-directed, with lots of options. This post wanders a bit, since it’s mostly intended to help me process some of the ideas we’ve encountered and discussed so far. Here goes.
Yesterday, a sad analogy popped into my head:
Why exactly is Episode IV (the original Star Wars) so awesome?
- It just drops you into this awesome universe!
- It’s part of a fully-fledged universe, but doesn’t explain everything to you. You have to glean some information from the context of the story (like any well-written story).
- It fills you with a sense of wonder. You know it does.
- It’s kind of charmingly imperfect and messy.
- Yeah, there’s a story, and the plot is awesome, but the thing that makes the original Star Wars so excellent is the feeling of myth. (It’s such a strong example of the hero cycle that the reprint of The Hero with a Thousand Faces actually has Luke Skywalker on the cover.)
Why exactly is Episode I so lame?
- It’s not a very good story in itself. So much of the plot is just to set up what is going to happen in the original movies.
- In my opinion, the extra movies make the Star Wars universe seem smaller, not bigger. They force the whole, overgrown universe into an annoyingly tidy, linearized package.
- You’re told pretty much everything. How the Force works. Everyone’s motives for all their actions. BORRRRING. Every character is basically a wind-up toy. It’s too polished and everything fits together too well.
Now imagine you had NEVER seen Star Wars and were taken to see Episode I. Is it any surprise then that so many people are turned off by their image of math? UGH. You are told to sit through all this exposition so you’ll understand the really good stuff better, and this exposition has a bunch of totally useless fluff padded in. No matter how great the old Star Wars movies are, you’re probably not going to get excited about them.
This is why it’s so important to see at least some of the “amazing stuff” first. As part of the smooc, we’ve been thinking back on our own mathematical experiences, and while in my short mathematical life there’s been plenty of sometimes boring and sometimes necessary work to get through, many of the big motivating moments in my mathematical life have been “drops,” where a teacher, a friend, or a lecturer gave to me an idea that was weird, “over my head,” and amazing.
Here’s an example.
My first big experience doing math with other people outside of school came when I got into a residential math camp in 7th grade. This was life-changing for a number of reasons, but the first was a lunch over spring break that students and their parents were invited to, where we would work on problems, get to know the staff and other prospective students, and see a guest lecturer.
This lecturer was a middle-aged man, a professor at a university, but he wasn’t talking about math it seemed. He was talking about balls, and donuts, and coffee cups, and squishing coffee cups until they looked like donuts. He used a big word that sounded like he was talking about maps.
And then he tied his ankles together and flipped his pants inside out.
About half the parents stared in silence while the other half laughed and clapped (I’m proud to count my dad among the latter). And that was it!
(I found out much later that this guy was Michael Starbird, a math professor at the University of Texas known for writing a book called The Heart of Mathematics, which the American Mathematical Monthly called the best book for non-mathematicians it had ever reviewed. See this link for a video of a kid flipping his pants!)
These are silly analogies and examples perhaps, but they speak to an incredibly important part of my mathematical experience. I don’t believe that mathematics is a narrow and linear path you can just follow. That will cheapen “the beginning” and put “the end” so far away most people will never reach it. Of course there are some facts you have to know before you can fully understand other facts, and there are skills you need to have before you can learn other skills, but to me, this needs to happen along with the understanding of just how wide the mathematical world it is.
Another short story:
Last summer I got the chance to work with an amazing teacher as a TA for a summer program a lot like the one I went to. He said one time that it’s best to hand little “gifts” to students every now and then, amazing simple mathematical ideas like how to compute the 46th digit of 1/47 without dividing 1 by 47 to 46 decimal paces. I countered that students should be made to figure things out for themselves (fancying myself a hardcore constructivist), and he said something along the following lines: “Yes, just like you should earn most of what you have. But that doesn’t take away from the pleasure of a gift.” And of course, an unwrapped gift is not nearly as fun; a gift is that much better when it’s wrapped and you have to figure out how to unwrap it.
This pants trick was just such a gift. It was another eight years before I “learned topology.” Maybe this is self-centered, but I think this is the way that math should feel; that surprise, without explanation, helped to make me feel like I was right at the edge of some larger story (and I was).
(Note to self: Terence Tao in this reading for our smooc seems to settle on a quality of good mathematics as a piece of “mathematics that is “on to something”, that it is a piece of a larger puzzle waiting to be explored further.” In other words, good mathematics strikes a balance between answers and questions. Is this related? He’s talking about the mathematical research carried out in universities, but criterion seems similar.)
I have been lucky that much of my mathematical experience has been old Star Wars and not new Star Wars. There are all sorts of other benefits of a good math education, but already specific facts (even at my young age) are leaking out of my brain at a faster rate than they used to. I always valued my problem solving skills and content knowledge (perhaps overvalued that), but only recently do I find myself valuing more and more that feeling of getting to witness and to be a very small part of something very big and nonlinear; I find myself valuing the aspect of wonder, the aspect of myth.