Aug 052007

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?

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 Posted by at 9:34 pm

  9 Responses to “To the right of the decimal point”

  1. Ah yes, this takes me back to my angsty nights spent laying in bed pondering similar questions/theories/”things”.

    And yes, the answer CLEARLY is 42.

  2. My husband is one of those whose job (and love) it is to figure this sort of stuff out. As an engineer, he finds fascination and enjoyment in numbers.

    The darling man blew my mind a while back when he explained that one can start a distance from a wall and move in HALF that distance every time but never, ever hit the wall. I’m STILL thinking that one over.

    Give me comma rules and gerunds any day…

  3. Sorry, I gotta contradict you on this one. The distance around your coffee table is finite. You can take it out to an infinite number of decimal places but there is an upper limit where you can safely say the table is not bigger than some distance. That makes it finite. Kind of like the value Pi. It may go on for ever but it is no bigger than 3.15 so it is a finite, although irrational, number.

    Numbers are cool. There are an infinite number of integers (1, 2, 3, ..) but you can count them in both directions (known as countably infinite). However, between any two integers there also exists an infinite number of values (all those decimal places) that you cannot count (known as uncountably infinite).

    On the wall example, I had a math professor explain it a different way: A man can start 10 feet from a woman. If he moves closer by have the distance between them each step, he will never get to the woman. He will, however, eventually get close enough for all practical purposes 😉

  4. You know – I love the visual image of irrational numbers. It’s like they’re shady or something and continually coming to logically incorrect conclusions.

  5. BB, thanks for the correction.

  6. I think the answer to life, the universe, and everything is definitely (huge booming voice with tons of Echo)
    Foooooorrtyyyyyy Twwwwwoooooooo!

  7. Okay. That means that our whole solar system could be, like one tiny atom in the fingernail of some other giant being. This is too much! That means one tiny atom in my fingernail could be —

    Could be one little tiny universe…

  8. I like the imaginary numbers the best.

  9. Oh – did you know that pi and e went on a blind date?

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