As an associate dean, I find myself in many meetings of various types. In these settings one thing I hear often is “There’s no need to re-invent the wheel.” It’s hard to look at the wheels on any vehicle today and think that they haven’t been fundamentally re-invented multiple times. Some people look at a wheel and say, “Yup, that’s as good as it gets.” Others look at that same wheel and say, “We’re starting from a pretty good place here but I bet we could make that thing better.” One might be inclined to claim that these responses mean that there are two kinds of people in the world, something else one hears often as well. More likely there are as many types of people in the world as there are people. All those people produce a spectrum of responses to any situation. The “wheel is just fine as “ position and the “let’s make the wheel better” position would represent the two tails of such a distribution. In my introductory electricity and magnetism class we encounter the LC (inductor-capacitor) circuit. We work hard to understand how we know the amount of charge is on the capacitor at any time. The differential equation that emerges looks a lot like the one students saw describing the position of a mass on a spring. Taking what you have learned in some other area and applying that idea to the wheel is a fantastic way to re-invent that wheel.
“Fine,” you say (well, that’s what I am pretending you say) but what does any of this have to do with John Cougar Mellencamp or the Beatles. Well it’s not really going to be the Beatles but Sir Paul McCartney. I grew up about twenty miles from where John Cougar Mellencamp grew up and he hit it big when I was transitioning from middle school to high school. I was particularly impressed with his hit “Small Town” and the line “No, I cannot forget from where it is I come from.” Now, here was a truly re-invented wheel – starting and ending a phrase with the same preposition. I was proud of my fellow Hoosier for this re-invention. Only years later did I pay attention to McCartney’s “Live and Let Die” lyrics and to my ear the line in there sounds like “in this ever-changing world in which we live in,” pretty much the same structure as the phrase from Small Town. I should have known that such a seemingly new structure could be traced to a Beatle. I poked around on the web before writing this and realized that there is an ongoing debate over whether this phrase is actually, “in this ever-changing world in which we’re living.” See a relatively recent Washington Post story, for example.
The wheel I was pondering had been under development for a while. Of course. For our purposes here it doesn’t matter what the line in “Live and Let Die” is. The fact that my Southern Indiana-trained ear heard it the way it did, means that we can hardly consider the structure Mellencamp used as particularly new. But that’s OK. Even when “Live and Let Die” was written I’m sure we could trace a foundation of doing interesting things to hold meter or rhyme. Perhaps we would find that same structure popping up multiple times in the past. Building on a foundation to drive an idea little further is progress, just as is using an idea in different setting from the original. It’s why I push my students to fully understand what has been done previously so that when the time is right to re-invent some wheel they will be ready.