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We humans are a curious lot. To satisfy curiosity we will endure pain, forego pleasure, and take risks. Curiosity, like our upright posture and our opposable thumbs, is one of our defining traits. If you’re a teacher, the innate curiosity of our species is your best friend and ally. If you can engage the students’ curiosity, they, and you, will succeed.
We are all more curious about some things than others. I will cheerfully tell people that I am curious about just about everything, but everything is relative, and I find some things of greater interest than others. So I shouldn’t be surprised that some people, at some times in their lives, find some topics of no interest at all.
I once was a math professor, and most of my teaching load consisted of freshman calculus. This was back in the 80s, and, in a class of, say, 25, at least 20 were premeds. They had no particular interest in calculus. Most had no interest at all in math, but they were required to take calculus. Some took only the first semester of calculus, and fulfilled their requirement of a year of math by taking a semester of finite math, figuring it would be easier.
It was in one such class that a student came to my office during office hours and asked to work through the first homework problem, then the second. When she asked me to work through the third, I realized that her intent was for me to do the entire assignment for her, so I told her that henceforth she should pick two problems for us to work through together. After that, she came to my office every week, with two problems to work through.
One week she picked a problem derived from thermodynamics. I don’t remember the exact details, but it was a problem that was, and may still be fairly common in calculus texts. The problem was to determine the equation of state of a gas, given a set of measurements of temperature and pressure at different volumes. An equation of state is a relation among the temperature, pressure and volume of the gas in question. The students were expected to assume that the gas in question was governed by the van der Waals equation of state, a particularly useful formula that is widely applied to gases. The van der Waals equation of state for a particular gas is specified by two parameters. Given experimental data, the students were asked to compute the parameters. We worked through the problem, and I asked her:
“You’re a premed, so you’re taking chemistry, aren’t you?”
“Yes.”
“So you’ve seen the van der Waals equation of state before?”
“Yes”
“So you know that the parameters are things like the size of the molecules?”
“That’s right.”
“So look what we have here. These measurements are just temperature, pressure and volume. With stuff you could buy for a couple of bucks at any hardware store, you can measure the size of individual molecules. Isn’t that cool?”
“No.”
“NO???? Why are you looking at me like that?”
“I’m amazed that you knew that.”
…Deep breath.
The great twentieth century physicist Richard Feynman said that if we could pass to future generations only one thing that we had learned about the physical universe, it would be that matter is made of atoms. He didn’t mean that to be a simple sentence to be memorized by rote. He meant it as a way of looking at the physical world. Air is made of little molecules, each made of two or three atoms at a time, so small that when the wind blows on your face you don’t feel like little grains are hitting you. A chemist or a physicist will tell you that there are about 6 times 10 to the power 23 molecules of air in the room you’re sitting in, about a trillion trillion. That’s Avogadro’s Number. It seems natural, then, at least to me, to ask how big a molecule is. The van der Waals equation of state gives a simple recipe for measuring the size of something so tiny that it cannot be seen, in the usual sense, in any microscope that anyone could ever build.
My great fundamental truth of the physical universe is but a small bump on a student’s road to medical school. I have to laugh. What else can I do?