(Host) You might not expect a shopping cart to inspire deep thoughts about calculus, but that’s what happened to commentator Dan Rockmore the other day.
(Rockmore) While walking through the Hanover Food COOP yesterday my thoughts turned to Sir Isaac Newton. Some of you know that it is Newton, the seventeenth century English scientist who is responsible for figuring out most of the laws of Nature, most famously, the law of Gravity, that universal truth that explains both why our feet stay firmly planted on the ground, as well as why the moon spins reliably around the earth, and even helps put rockets reliably into space. Legend has it that Nature itself shook loose the law of gravity from Newton’s noggin’, bringing it to his mind when he was plunked on the head by a shiny red apple while resting under a tree in the English countryside.
But no, it wasn’t a stroll through the produce section that turned my thoughts to Newton. Instead, it was a constellation of shopping carts on the edge of the COOP parking lot.
So, why Newton? Was I thinking of a version of his law of Gravitation that might have predicted an inevitable collision of those carts? No, not that. Instead, it was thoughts of the mathematical tools that Newton developed to find the laws of nature. This was the mathematics of calculus. Calculus is the math of the physical world, because it is the math of change, and if there is one thing that characterizes life, it’s change.
In particular, Newton figured out how to measure a big change as the accumulation or of a bunch of very tiny, even infinitesimal changes. This is called integration and it is one of the most basic mathematical tools in all of science.
When I saw those lonely shopping carts on the side of the parking lot, it seemed just another of a bunch of little changes in the Upper Valley that I’ve noticed since returning here after spending most of the last year in New York City. When I first arrived in Hanover I was charmed by the way in which everyone returned their shopping cart to the entry of the COOP. It was an unwritten social contract of consideration and neighborliness delighted me.
So, when I saw those lonely shopping carts on the side of the parking lot, in violation of what had been an unwritten local law of Nature, and looked beyond them to see a river of cars backed up to the next light, coming from the office parks up the road, I thought about the changes that have come to the Upper Valley, and realized that you didn’t need to be a rocket scientist to understand that the loss of a few little things can add up to a lot.
From Hanover, New Hampshire, this is Dan Rockmore.
Dan Rockmore is a professor of mathematics and computer science at Dartmouth College. He spoke to us from our studio in Norwich.