I've used a few of my recent posts to talk about the ways in which I see math in the everyday - from the bakeries and art galleries of Santa Fe, to news about space travel. Today's reflection is another of those, inspired by what is probably for many of us the most number-filled stretch of the day: exercise time. Outside of a hospital, bank, or trading floor, there are few places that are more "en-numbered" than today's gym. Whether you are counting the number of reps you do, watching the timer count down (or up) on the treadmill or exercise bike, or using one of the bazillion different personal health monitors that count your steps, keep track of heart rate, estimate your calorie loss, numbers guide many a personal health regimen.
Just the fact of there being numbers involved doesn't make it math - although some of us might make math out of them. (For example, I like varying my counts, sometimes going by twos, threes, fours or fives.) But a place where many of us are "doing math", whether we know it or not, is with these now ubiquitous personal health monitors. You may have noticed certain relationships between the various numbers that they record - simple ones like faster heart rate means more calories expended or an increase in some kind of strange new trademarked metric. These observations are the first step to modeling - no, not being a model (although maybe, if you work out a lot!), but rather mathematical modeling. That is, thinking about how one number that is the output of some process might be related to a collection of other observed numbers.
Spin class is a place where I think about this a lot. The bikes are fitted with little meters that allow you to set the amount of "torque" on the wheel (higher number means more difficult to pedal), while also allowing you to monitor the rate at which you are pedaling (in revolutions per minute - "rpm"). Generally, the instructor tells you where to set the torque as well as what kind of rpm to shoot for, while encouraging or goading you to "crush it", all with the help of a dance music playlist, specially designed to keep you engaged, moving, and maybe even smiling.
Some mysterious combination of your torque and rpms produces a measure of the "power" that you are generating that accumulates in the ever growing "total". What is the formula that gives these numbers? Could I make a model of my class performance? I might start with a simple model - say look at my average over the last few classes. Probably that's too simple ("previous performance is not an indicator of future spinnings!"). I could build on this and incorporate the beat of the music or how much sleep I had the previous night. Maybe I should toss in time of day and the fraction of bikes in the class that are occupied. Is there an instructor rating or mood level I could include? The "form" of the model is important ("linear", "exponential", etc.?) as are the "weights" I attach to each of these factors. Those would need to be estimated from previous rides. And this isn't just about spinning - analogous ideas are used in finance, marketing, medicine, or any data-intensive activity. These are some of the things that go through my head as I pump my legs to the beat.
There's other math in the spin class. The steady beat of the music brings to mind the mathematics of Fourier analysis, designed to disentangle the combinations of air disturbances that make up sounds into basic fundamental regularly beating tones. These are generally measured in "cycles per second," echoing the rpms that we focus on while riding. If you close your eyes, the hum of the spinning wheels in the humid darkened room, synchronized to the target rpm, can make it feel like being surrounded by cicadas on a hot summer night whose own group oscillatory behavior is a kind of "sync" that has much in common mathematically with the network of muscles that give rise to the rhythmic workings of the heart, that in turn (no pun intended!) is the engine for each of the class's participants.
This post was spun out of free-floating thoughts generated by an exercise class and it occurs to me that the general subject of "where do ideas come from" is a part of this story. Everyone is different, but for me it seems to be related at least somewhat to motion, along with being already primed to be thinking about the subject. For example, lately I've been thinking quite a bit about math and the world and when I enter the class my thoughts are already hovering around the idea and here we have this essay. I can remember several specific moments where while in motion, knotty problems suddenly became unraveled for me: finishing a twenty-four hour algebra take-home exam in while in the weight room in college, making a key conceptual breakthrough to unlock the last chapter of my doctoral dissertation while in Mike's Gym of Somerville, and most memorable, while jogging in Hanover, a sudden and surprising epiphany that unlocked a problem and finished off a paper. The sensation is always the same: a sudden clarity that makes the confusion seem suddenly so ridiculous (a "doh!" moment, as the great philosopher Homer Simpson would say) that there is not even a rush to write down the answer, the clouds once cleared remain so and when I finally can sit down the answer just spills out. Those moments are rare, but precious.
Maybe it's the endorphins, maybe it's the refocusing of attention on some other activity that enables a new idea. Perhaps it is the momentary feeling of being untethered that movement can create, that we then recapitulate in our minds to have a good idea. It is a feeling of being free, forgetting for a moment that we are bound by gravity or logic or convention and with that, every once in a while magic happens. Sometimes, you might just need to spin your wheels for a bit to find the new and the beautiful.