Reading the Comics, May 13, 2014: Good Class Problems Edition
Someone in Comic Strip Master Command must be readying for the end of term, as there’s been enough comic strips mentioning mathematics themes to justify another of these entries, and that’s before I even start reading Wednesday’s comics. I can’t say that there seem to be any overarching themes in the past week’s grab-bag of strips, but, there are a bunch of pretty good problems that would fit well in a mathematics class here.
Darrin Bell’s Candorville (May 6) comes back around to the default application of probability, questions in coin-flipping. You could build a good swath of a probability course just from the questions the strip implies: how many coins have to come up heads before it becomes reasonable to suspect that something funny is going on? Two is obviously too few; two thousand is likely too many. But improbable things do happen, without it signifying anything. So what’s the risk of supposing something’s up when it isn’t? What’s the risk of dismissing the hints that something is happening?
Mark Anderson’s Andertoons (May 8) is another entry in the wiseacre schoolchild genre (I wonder if I’ve actually been consistent in describing this kind of comic, but, you know what I mean) and suggesting that arithmetic just be done on the computer. I’m sympathetic, however much fun it is doing arithmetic by hand.
Justin Boyd’s Invisible Bread (May 9) is honestly a marginal inclusion here, but it does show a mathematics problem that’s correctly formed and would reasonably be included on a precalculus or calculus class’s worksheets. It is a problem that’s a no-brainer, really, but that fits the comic’s theme of poorly functioning.
Steve Moore’s In The Bleachers (May 12) uses baseball scores and the start of a series. A series, at least once you’re into calculus, is the sum of a sequence of numbers, and if there’s only finitely many of them, here, there’s not much that’s interesting to say. Each sequence of numbers has some sum and that’s it. But if you have an infinite series — well, there, all sorts of amazing things become possible (or at least logically justified), including integral calculus and numerical computing. The series from the panel, if carried out, would come to a pair of infinitely large sums — this is called divergence, and is why your mathematician friends on Facebook or Twitter are passing around that movie poster with a math formula for a divergent series on it — and you can probably get a fair argument going about whether the sum of all the even numbers would be equal to the sum of all the odd numbers. (My advice: if pressed to give an answer, point to the other side of the room, yell, “Look, a big, distracting thing!” and run off.)
Samson’s Dark Side Of The Horse (May 13) is something akin to a pun, playing as it does on the difference between a number and a numeral and shifting between the ways we might talk about “three”. Also, I notice for the first time that apparently the little bird sometimes seen in the comic is named “Sine”, which is probably why it flies in such a wavy pattern. I don’t know how I’d missed that before.
Rick Detorie’s One Big Happy (May 13, rerun) is also a strip that plays on the difference between a number and its representation as a numeral, really. Come to think of it, it’s a bit surprising that in Arabic numerals there aren’t any relationships between the representations for numbers; one could easily imagine a system in which, say, the symbol for “four” were a pair of whatever represents “two”. In A History Of Mathematical Notations Florian Cajori notes that there really isn’t any system behind why a particular numeral has any particular shape, and he takes a section (Section 96 in Book 1) to get engagingly catty about people who do. I’d like to quote it because it’s appealing, in that way:
A problem as fascinating as the puzzle of the origin of language relates to the evolution of the forms of our numerals. Proceeding on the tacit assumption that each of our numerals contains within itself, as a skeleton so to speak, as many dots, strokes, or angles as it represents units, imaginative writers of different countries and ages have advanced hypotheses as to their origin. Nor did these writers feel that they were indulging simply in pleasing pastimes or merely contributing to mathematical recreations. With perhaps only one exception, they were as convinced of the correctness of their explanations as are circle-squarers of the soundness of their quadratures.
Cajori goes on to describe attempts to rationalize the Arabic numerals as “merely … entertaining illustrations of the operation of a pseudo-scientific imagination, uncontrolled by all the known facts”, which gives some idea why Cajori’s engaging reading for seven hundred pages about stuff like where the plus sign comes from.