I knew my readership would drop off after I fell back from daily posting. Apparently it was worse than I imagined and nobody read my little blog here over the weekend. That’s fair enough; I had to tend other things myself. Still, for the purpose of maximizing the number of page views around here, taking two whole days off in a row was a mistake. There’s some more discussed in this Reading The Comics installment.
Word problems are dull. At least at the primary-school level. There’s all these questions about trains going in different directions or ropes sweeping out areas or water filling troughs. So Aaron McGruder’s Boondocks rerun from the 5th of May (originally run the 22nd of February, 2001) is a cute change. It’s at least the start of a legitimate word problem, based on the ways the recording industry took advantage of artists in the dismal days of fifteen years ago. I’m sure that’s all been fixed by now. Fill in some numbers and the question might interest people.
Glenn McCoy and Gary McCoy’s The Duplex for the 5th of May is a misunderstanding-fractions joke. I’m amused by the idea of messing up quarter-pound burgers. But it also brings to mind a summer when I worked for the Great Adventure amusement park and got assigned one day as cashier at the Great American Hamburger Stand. Thing is, I didn’t know anything about the stand besides the data point that they probably sold hamburgers. So customers would order stuff I didn’t know, and I couldn’t find how to enter it on the register, and all told it was a horrible mess. If you were stuck in that impossibly slow-moving line, I am sorry, but it was management’s fault; I told them I didn’t know what I was even selling. Also I didn’t know the drink cup sizes so I just charged you for whatever you said and if I gave you the wrong size I hope it was more soda than you needed.
On a less personal note, I have heard the claim about why one-third-pound burgers failed in United States fast-food places. Several chains tried them out in the past decade and they didn’t last, allegedly because too many customers thought a third of a pound was less than a quarter pound and weren’t going to pay more for less beef. It’s … plausible enough, I suppose, because people have never been good with fractions. But I suspect the problem is more linguistic. A quarter-pounder has a nice rhythm to it. A half-pound burger is a nice strong order to say. A third-pound burger? The words don’t even sound right. You have to say “third-of-a-pound burger” to make it seem like English, and it’s a terribly weak phrase. The fast food places should’ve put their money into naming it something that suggested big-ness but not too-big-to-eat.
Mark Tatulli’s Heart of the City for the 5th is about Heart’s dread of mathematics. Her expressed fear, that making one little mistake means the entire answer is wrong, is true enough. But how how much is that “enough”? If you add together someting that should be (say) 18, and you make it out to be 20 instead, that is an error. But that’s a different sort of error from adding them together and getting 56 instead.
And errors propagate. At least they do in real problems, in which you are calculating something because you want to use it for something else. An arithmetic error on one step might grow, possibly quite large, with further steps. That’s trouble. This is known as an “unstable” numerical calculation, in much the way a tin of picric acid dropped from a great height onto a fire is an “unstable” chemical. The error might stay about as large as it started out being, though. And that’s less troublesome. A mistake might stay predictable. The calculation is “stable” In a few blessed cases an error might be minimized by further calculations. You have to arrange the calculations cleverly to make that possible, though. That’s an extremely stable calculation.
And this is important because we always make errors. At least in any real calculation we do. When we want to turn, say, a formula like πr2 into a number we have to make a mistake. π is not 3.14, nor is it 3.141592, nor is it 3.14159265358979311599796346854418516. Does the error we make by turning π into some numerical approximation matter? It depends what we’re calculating, and how. There’s no escaping error and it might be a comfort to Heart, or any student, to know that much of mathematics is about understanding and managing error.
Joe Martin’s Boffo for the 6th of May is in its way about the wonder of very large numbers. On some reasonable assumptions — that our experience is typical, that nothing is causing traits to be concentrated one way or another — we can realize that we probably will not see any extreme condition. In this case, it’s about the most handsome men in the universe probably not even being in our galaxy. If the universe is large enough and people common enough in it, that’s probably right. But we likely haven’t got the least handsome either. Lacking reason to suppose otherwise we can guess that we’re in the vast middle.
David L Hoyt and Jeff Knurek’s Jumble for the 6th of May mentions mathematicians and that’s enough, isn’t it? Without spoiling the puzzle for anyone, I will say that “inocci” certainly ought to be a word meaning something. So get on that, word-makers.
Dave Blazek’s Loose Parts for the 6th brings some good Venn Diagram humor back to my pages. Good. It’s been too long.