I have been reading Eugenia Cheng’s How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics. I’ve really been enjoying works of nonfiction this summer. (I also read another good book, Jill Lepore’s The Secret History of Wonder Woman, while on vacation.)
These books are a welcome relief from last few novels that I’ve read, in which characters seem to die with alarming regularity.
Cheng’s book is really fun; it’s got recipes as well as lots of witty comments about mathematical concepts and how mathematicians think. For instance, she begins one section with a Jane Austen riff, “It is a truth universally acknowledged that mathematics is difficult,” and then goes on to question this very assumption, telling us “why math is easy and life is hard.”
Math helps us break things down into basic abstract principles, and proceeds logically. Life most definitely doesn’t work this way. (I sometimes think there might be something of that nature to skating, too, especially when I’ve had one of those “toxic people” encounters. Edges? I can handle edges–or at least trying to do edges.)
I recommend this book if you like math games and mind games, or want to know what “category theory” is. Or read it if you want to hear what making custard, online dating, or Battenberg (checkerboard) cakes have to do with math. Or if you need a new idea for how to eat Brussels sprouts (by dipping them in homemade chocolate)!
Cheng does a wonderful job of illustrating how mathematicians think and work by referring to how we do other everyday things, like cooking or making friends. One idea has really resonated with me as I’ve been thinking about the new skating season. She details the difference between external and internal motivation, which she asks us to think about as two different ways of traveling around a new city. One either makes a beeline for the famous sights, or wanders around the streets. Of course, a lot of travel involves both: one might stumble upon some great little cafe while heading for the Eiffel Tower. Cheng returns to mathematical examples, like talking about how, in his efforts to prove Fermat’s Last Theorem, Andrew Wiles made lots of other discoveries.
I think many of us adult skaters also blend external and internal motivation. While I was still doing freestyle, it was not hard to identify external motivations: all those jumps, particularly that axel, were enough to get me going. Spins were fun, too. For both, I found it easy to tell if I was improving or not.
Ice dancing has been quite a different story. At first I wanted to learn as many compulsory dances as possible; that was when doing them at social sessions was a regular incentive. I used to also be really motivated by tests, but in recent years I have not tested very much. External motivators for me remain my lessons (that little bit of praise from coaches goes a long way), but otherwise I’ve had to restructure my thinking, since the opportunities for the hard-core external motivators (tests, competitions) are now few and far between.
The past year, I have relied a lot more on internal motivation. My former yoga teacher used to tell us at the beginning of each session: “Find out what is available to you today.” I have found that saying to be useful on days when my hip and foot feel particularly painful. I’ve also (as is evident in this blog) been learning about how my body is put together and exploring different ways of moving on ice. Working on basic edges and turns has felt a bit like wandering around unexplored terrain; I’m not at all sure where I’ll wind up.
For the new season, I think I need some of both. Cheng suggests that
When math is done purely by external motivation, it might be like taking such a determined route to the Notre Dame that you walk up a horrible main road for ages. You could say this is math that is overly utilitarian or pragmatic. When it’s done purely by internal motivation, you might go on a very pretty journey but never arrive at anything notable. You could say this is math that is overly idealistic or aesthetic. When the two coincide you get a journey that is interesting in its own right, with a destination that is also interesting in its own right–the best of both worlds and the most beautiful of mathematics.
As things heal and get stronger, I’ve been thinking of more possible skating destinations, less vague than “improving my edge quality” or “standing up straight” or “feeling no pain.” Cheng describes watching a documentary on the construction of St. Paul’s Cathedral in London, and realizing that the famous dome there–actually made of three domes, with an inner and an outer and a third hidden dome that’s actually supporting the structure–resembled her doctoral thesis, which combined internal motivation (the internal logic of the mathematical situation), external motivation (its applications), and a “hidden” structure that mediated between the two.
So I have no idea how I will use these insights, but I do believe that somehow both the wandering and those destinations (someday the golds!) will take me where I need to go. And I hope to figure out my third dome along the way.
Another fun idea comes when Cheng describes how category theory works in mathematics. She considers social relationships: how we are connected through mutual friends, teachers, and family members. For instance, she describes the “Erdős number” that imagines the degrees of separation among the well-known mathematician Paul Erdős, his different collaborators, and, in turn, their collaborators. (It’s sort of like the “six degrees of Kevin Bacon” idea.)
When I posted about my “Ben Agosto” moment, other skating bloggers wrote about meeting Mr. Agosto or having their pros take a workshop from him. So we are all connected! Skating is full of these sorts of relationships; we can even make up nice diagrams full of arrows that link us all to different skaters, or pros, or competitions like Adult Nationals. Big rink (at least when I’m doing power pulls), small world!
Cheng doesn’t mention skating (or Ben Agosto!) in her book. But she is a Senior Lecturer of Pure Mathematics at Sheffield University in Sheffield, England (“the largest city in England with no professional orchestra”–this book is full of fun facts.) My dance blades were made with Sheffield steel, so there’s another way in which I am categorically connected to this author (other than the fact that I’ve read her book).
Describing this Sheffield-based relationship mathematically? Totally beyond me. I’ll stick to skating!