Math and Motion: When Our Limbs Become the Roots of Our Tree of Thought

I was told that Oswald Veblen did his best thinking while chopping wood. Similarly, a daughter of Joe Kohn, the great mathematician who died recently, told me that her father very much disliked reaching the point in aging when he could no longer walk, because walking was so important to his act of thinking. Though I'm not a mathematician, I've had insights and ideas come to me while washing dishes, chopping wood, or more generally when my hands and mind are working together. There is something in the connection between body and mind, as if our arms and legs were the roots of the tree of thought. Of course, the scientist side of my brain is immediately looking for evidence to support or contradict this thesis. Do those who have lost the use of their limbs also have eureka moments?

Recently I felt the urge to ask a mathematician if he did his best thinking while bicycling. The prompt for the question is something of a story. I was walking down the hallway of a medical building, fresh from my annual dermatology exam. There was an older couple walking just ahead of me, and they were disagreeing as to who would drive the car home. He wanted to drive, but she was insisting that she drive, given that he had just received some medication. He said he was just fine, however, and their back and forth seemed headed for an argument. In retrospect, it was as if I were a kid listening to his parents. Something came to mind, and I decided to go with it. Wishing to defuse the situation with some humor, I blurted out from a few feet behind them, "Okay, how about I drive you home?" 

They turned around, still in stride towards the door to the stairwell, and the man responded "Do you drive a stick shift?" This was music to my ears, as I love driving a stick shift. I told him about the '94 Ford Ranger I use for my work at Herrontown Woods, and as we headed down the stairs, we talked stick shifts we'd known, like the "3 on a tree" in my '63 Chevy station wagon--a car that was emphatically beige because my mother was big on beige. We continued to talk as we left the building. I said that when driving a stick shift, the driver must listen closely to the engine. That delicate interplay between clutch and accelerator--it's like a dance with the machine. (Though I didn't mention this, maybe that relationship is why my ear is also attuned to the sound of other machines, like when the furnace kicks on, and the implications for my personal contribution to climate change.)

As we reached my bicycle (I clearly had not thought through the logistics of driving them home), he recounted having taken a bad spill on his bike. He had been biking on Canal Road and gotten so caught up in mathematical thoughts that he didn't notice a pothole. 

My ears perked up when he mentioned math, given of course that I am working to restore Oswald Veblen's house. "Are you a mathematician?," I asked. He responded affirmatively and told me his name. His story fit well with a video a botanist friend of mine had posted a week before on facebook, in which my friend is riding his bike along a broad trail, one hand on the handlebar, the other holding the camera, pointing at different plants and calling out their latin names as he passed by. The video ends abruptly when he falls off of his bike, breaking a couple bones in the process. He's on the mend, but high-speed botany, like high speed math, has its risks.

Biking home, I wished I had asked the mathematician whether he does his best thinking while riding a bike. I looked him up, found his home page, and sent him an email. His response? "I haven't done much good Math thinking while biking. The accident was more than 20 years ago and it taught me to concentrate on biking when on the bike."

Not the answer I was looking for, but all for the best, and a lot more fun than an argument over who is going to drive.