Reading the Comics, April 28, 2013

The flow of mathematics-themed comic strips almost dried up in April. I’m going to assume this reflects the kids of the cartoonists being on Spring Break, and teachers not placing exams immediately after the exam, in early to mid-March, and that we were just seeing the lag from that. I’m joking a little bit, but surely there’s some explanation for the rash of did-you-get-your-taxes-done comics appearing two weeks after April 15, and I’m fairly sure it isn’t the high regard United States newspaper syndicates have for their Canadian readership.

Dave Whamond’s Reality Check (April 8) uses the “infinity” symbol and tossed pizza dough together. The ∞ symbol, I understand, is credited to the English mathematician John Wallis, who introduced it in the Treatise on the Conic Sections, a text that made clearer how conic sections could be described algebraically. Wikipedia claims that Wallis had the idea that negative numbers were, rather than less than zero, actually greater than infinity, which we’d regard as a quirky interpretation, but (if I can verify it) it makes for an interesting point in figuring out how long people took to understand negative numbers like we believe we do today.

Jonathan Lemon’s Rabbits Against Magic (April 9) does a playing-the-odds joke, in this case in the efficiency of alligator repellent. The joke in this sort of thing comes to the assumption of independence of events — whether the chance that a thing works this time is the same as the chance of it working last time — and a bit of the idea that you find the probability of something working by trying it many times and counting the successes. Trusting in the Law of Large Numbers (and the independence of the events), this empirically-generated probability can be expected to match the actual probability, once you spend enough time thinking about what you mean by a term like “the actual probability”.

Samson’s Dark Side of the Horse (April 11) merges a counting-sheep joke into a digits-of-pi joke, with the irrational nature of π given as a cure for insominia. Pi gets all the attention in jokes like this; the other irrational numbers people might know — e, the square root of 2, the natural logarithm of ten, the golden ratio — just can’t compete with its celebrity. The rhythm of the joke pretty much requires an irrational number not much larger than three be used, and I can’t think of an irrational number not much larger than three that anybody cares about besides π either, much less one that would be recognized.

Dan Thompson’s Brevity (April 17) brings back William Thomson, Lord Kelvin, for a joke. I could have sworn I’d mentioned Thompson’s apparent delight in 19th century thermodynamicists in his comic strips before, but I don’t apprear to have it. (In any event, Hobbs here is apparently unaware that Kelvin had a rather comfortable bankroll, as he was a skilled inventor as well as a master of mathematics and physics; to use the example I have on hand, Kelvin was partner in the firm which sold compasses and binnacles to the Royal Navy for decades.)

Charles Schulz’s Peanuts (April 18; originally run April 21, 1966) continues Schulz’s thread of Linus attempting to teach a strongly resistant Sally basic mathematics, in this case, fractions. I suspect Sally’s a little young for fractions, but the ages of the Peanuts cast are fluid, and it isn’t like age-inappropriate homework assignments were at all rare in the strip’s run, as the numerous times someone had to read Tess of the d’Urbervilles indicates. It wasn’t until about two years ago that I finally read Tess of the d’Urbervilles and realized how riotously inappropriate that is for elementary school kids, and also how much I hate Alec D’Urberville.

Tony Cochrane’s Agnes (April 26) uses the traditional personal-answer-to-the-arithmetic-problem format, something Cochrane would come back to for the May 1st strip, incidentally. Don’t read the comments. What’s sadly lost in arithmetic teaching of this kind is that a lot of mathematics can be meaningfully debated, and that at least on the bleeding edge of a subject a lot of time is spent working out what we do want the things studied, and the operations, and their results to mean. It’s harder to get to that in arithmetic like this. I suppose an instructor who felt free about how to use class time might try showing ways that you could make “20 times 75” turn out to be two — the most obvious way to me would be to work in arithmetic modulo 1498, which says something important about my standards of “obvious” — and why we do or don’t use that, and what for. But it seems as though a question like that demands fluency with regular multiplication, I think, and I’d fear that the students would be hopelessly confused.

Rick Stromoski’s Soup to Nutz (April 26) has the kids talk about “geometry pizza” on the basis of there being enough different kinds of shapes involved in taking home and slicing a pizza. The controversial part may be calling the slices triangles, since after all, they’re not. The outer edge is an arc instead. However, if we were to slice the pizza finely enough, we could imagine the difference between the arc which comes from the pizza’s rim and that of a straight line becoming so small that we just don’t care. So we could imagine taking the circular pizza and slicing it up, and then taking the slices and laying them out in a long row, with the broad side down and then the point (which was the center of the circular pie) down, broad side, point side, and so on, until we get something that’s pretty near a rectangle. (You can do this with two or three slices of pizza, too, but it’ll be a bumpy rectangle.) And once you do this, you have the most important conceptual stuff you need to understand integral calculus.

Eric the Circle (April 27) (in this case by “krisis”) has a joke about Eric, a circle, not being able to fit in his pants because of not understanding the circumference formula. The joke — and I believe this is what commenter Jules934 is getting at with the “Neither did krisis” comment — does assume that Eric is actually a sphere, though, since the relevant dimension as the picture is actually drawn, flat, would be the length of a secant or, at most, the diameter of Eric. But that’s getting a bit complicated.

Gene Weingerten, Dan Weingarten, and David Clark’s Barney and Clyde (April 28) retells one of the legends about Carl Friedrich Gauss, the story that as a child he had a flash of insight which let him work out the sum of the numbers 1 through 100 in a flash. I don’t know if the legend is true. Gauss is legendary enough he doesn’t need the help of further tales of childhood greatness. But the insight — about ways to add up a string of uniformly-spaced numbers (known as “arithmetic series”) — is a great one, and the formula for these series is probably best explained using exactly the approach Cynthia did.

And for a final bit, I don’t have the time to discuss, or even mention, the many web comics out there, but Busybee Comics, drawn by a friend of mine, illustrated on April 29th what’s often called Hilbert’s Paradox of the Grand Hotel, one of those things that’s amazing about infinitely large sets. This particular paradox, I think, is best encountered when you’re a young teenager and have started getting seriously bored with the algebra and trigonometry you’re facing because this is mathematics that is supremely accessible and yet surprising.

I have a dim memory of this paradox being illustrated in a science fiction short story, but I’m not positive who wrote it. The story I recall as having an early 60s vibe and I have the dread suspicion the author wrote it in an attempt to point at mathematicians and laugh at them for suggesting a crazy thing like “you can put together two infinitely large sets of the same size and get a set of the same size back again”. Unfortunately, it’s very easy to take one’s instinctive ideas and proclaim that anything contradicting them is wrong, and infinitely large sets offer a lot of accessible ideas that contradict one’s instincts and that take time to understand.