I’ve never had any motivation for higher mathematics. I stopped at trigonometry in high school, and I took a course called business calculus in college that was tailor-made for liberal arts majors who didn’t plan to enter “the sequence” (Calculus I-IV). I escaped with a B, and I worked my ass off for it. The hardest college courses I took were advanced communications theory, world history II, and that business calculus course.
And make no mistake, it is a question of motivation. I’m thoroughly confident that I have the mental horsepower; I just don’t want to do it. I applaud and am thankful for those who do. They do something in which I have no interest which nevertheless is a necessary component for the fluid function of the world.
However, for many years now, I have enjoyed the philosophical side of mathematics. I can daydream for quite a long time thinking about the fact that just as numbers are infinite to the left of the decimal point, so are they to the right. An extremely accurate gauge showing the average temperature of the earth would have numbers spinning wildly on it, if you only ventured far enough to the right. So would a gauge showing your weight. So would one showing the potential energy of the gasoline in your car’s tank. So would one showing just about anything you can name.
There is no such thing as a straight line in the universe. When you get far enough to the right of the decimal point, it’s not straight. There is no such thing a circle. Ditto; sub “circular” for “straight.” These are constructs we pretend exist because said pretending is useful, and the precision to which we extend said constructs is enough. Really, though, they are as phantasmic as parallel lines in Euclidean geometry. Those numbers go, and go, and go, and go to the right, which means that if those so-called “parallel” lines are in the same plane, they intersect somewhere. Period.
How long is the coastline of Florida? There’s no good number, really. Think of Florida as your coffee table. Measure the total length around it. Got it? OK, good. Oh, but you know what? There’s a little dent where you hit it with your Segway on that one side. (What the hell are you doing running a Segway in your living room? For that matter, what are you doing with one of those things at all? Don’t worry; you so totally don’t look like a lazy geek on it.) Did you measure the distance in and out of that dent? No? Well, better measure again. Got it? OK, good. But really, how far in did you measure? Did you consider the imperfections inherent in the material? Wood is anything but uniform, you know. No, but you’ve got it now? OK, good. How about…
You can go to molecules. From molecules, you can go to atoms. From atoms, you can go to protons, neutrons, and electrons. From protons, neutrons, and electrons, you can go to quarks and leptons. From quarks and leptons, you can go to…nobody’s quite sure yet, but you can bet we’ll have it discovered and named soon enough.
The bottom line is that the coastline of Florida, or the run around your coffee table, or any other distance you care to name, is infinite. We stop at a certain precision merely because it is convenient to do so.
I love this stuff in the abstract. I don’t love the seemingly endless plugging and chugging that comes with trying to advance our knowledge of it. As I said earlier, I admire those who do. If God exists—and I’ve made clear in earlier posts that I think He does—He may be numerical. May He bless those pursuing Him in such venues.
What if the answer really is 42?