And now, I think, I’ve got caught up on the mathematics-themed comics that appeared at Comics Kingdom and at Gocomics.com over the past week and a half. I’m sorry to say today’s entries don’t get to be about as rich a set of topics as the previous bunch’s, but on the other hand, there’s a couple Comics Kingdom strips that I feel comfortable using as images, so there’s that. And come to think of it, none of them involve the setup of a teacher asking a student in class a word problem, so that’s different.
Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. (February 21) tells the old joke about how much of fractions someone understands. To me the canonical version of the joke was a Sydney Harris panel in which one teacher complains that five-thirds of the class doesn’t understand a word she says about fractions, but it’s all the same gag. I’m a touch amused that three and five turn up in this version of the joke too. That probably reflects writing necessity — especially for this B.C. the numbers have to be a pair that obviously doesn’t give you one-half — and that, somehow, odd numbers seem to read as funnier than even ones.
Bud Fisher’s Mutt and Jeff (February 21) decimates one of the old work-rate problems, this one about how long it takes a group of people to eat a pot roast. It was surely an old joke even when this comic first appeared (and I can’t tell you when it was; Gocomics.com’s reruns have been a mixed bunch of 1940s and 1950s ones, but they don’t say when the original run date was), but the spread across five panels treats the joke well as it’s able to be presented as a fuller stage-ready sketch. Modern comic strips value an efficiently told, minimalist joke, but pacing and minor punch lines (“some men don’t eat as fast as others”) add their charm to a comic.
Dave Whamond’s Reality Check (February 21) mixes up pirate and mathematics jokes because, well, why not? It’s a little odd to have both functions R(x) and Rrrr(x) in an expression, but it’s not implausible. Function names tend to be chosen either to draw no attention to themselves — thus f(x) and g(x), which everybody uses — or to serve some mnemonic purpose. Multi-letter function names stand out a little, but, if you have several functions describing the same kind of thing, it can be hard to resist using the same main letter, and add extra letters to distinguish between the similar-kind-of-thing being described. It’s a matter of what’s convenient.
Mikael Wulff and Anders Morgenthaler’s Truth Facts (February 22) uses sudoku and calculus as markers on the line of intellectually challenging problems. Amusingly to folks who got through Calculus I in good shape is that the calculus equation shown isn’t actually a hard one. It asserts , which is a use of the (correct) fact that the integral of the sum of two things equals the integral of the first thing plus the integral of the second thing. That’s usually a good step in completing an integral, since it turns a bigger problem into a set of smaller problems that can typically be done independently of one another, but it’s not the hard part of calculus.
Bud Blake’s Tiger (February 23, rerun) gets at a fair question, actually: why does the teacher do the easy ones and save the tough ones for the student? I suppose it’s that it’s normal to try teaching as few new things at a time as possible, in the hopes that all the things being taught are kept distinct and clear, while a tough problem typically requires noticing and remembering and making use of many things over the course of the problem. But it’s working out tough problems that are the most satisfying, when you do them, and which really test the breadth of one’s knowledge, and whether you’ve learned the important task of selecting the right intellectual tools for the task at hand. Still, I do wonder if it wouldn’t help next time I teach to do a couple easy demonstrations and then at least one full-on hard problem with many twists and turns before turning it all over to homework.
Bill Rechin’s Crock (February 24, rerun, I’m pretty sure) just uses “math freaks” as a comic/insulting term for the first person to pull out multiplication in an argument. It’s cute enough. I’m not offended.
Zach Weinersmith’s Saturday Morning Breakfast Cereal (February 24) is built on explaining Stokes’s Theorem in a funny way, but it is fair enough. Stokes’s Theorem is one of a group of theorems that you encounter in multivariable calculus, all of which are built around this somewhat startling idea: you can exchange a (particular) calculation of something on the surface of an object for a (specific) calculation of something within its entire volume, and vice-versa. This is great: we often want to understand what is going on inside a volume but be able only to study what is going on in the surface, and you can see right away why being able to switch between “an integral over the whole volume” and “an integral over its boundary” might be useful. And even if we can as easily study the interior or the boundary of a volume, there’s an excellent chance one integral or the other is the easier to evaluate, and so we do whichever is the easier.
Stokes’s theorem, in three-dimensional spaces, is about the “curl” of a function and that is fairly described as how swirly it is. The curl of a function at a point describes how much that function looks like it’s rotating around that point. The easiest-to-visualize (to me) interpretation is to look at a flowing stream; the function is the velocity of water at a point. Imagine fixing a little paddlewheel to a point; how quickly it turns is the curl of the water’s velocity at that point.
The theorem is named, almost fairly, for Sir George Stokes, who particularly advanced the mathematical study of fluids, particularly fluids with viscosity. The Navier-Stokes equations, a simple-to-state, difficult-to-solve set of differential equations, describe the flow of viscous fluids and you could have a fruitful career studying just them. He didn’t; he also studied optics, fluorescence, and spectroscopic analysis, and became an expert in studying the many railway and bridge disasters to strike Britain in the 19th century. If that wasn’t enough, he also served as Member of Parliament for Cambridge University from 1887 to 1892, so, he was doing all right for himself.
Jim Benton’s Cartoons (February 24) shows off a particular case of discipline self-importance which starts off with mathematics, fairly enough. It brings to mind a night at pinball league a couple weeks back where one of our friends was saying he was thinking of going on to get a doctorate in chemical engineering since, after all, if you had one in that field there would always be jobs because employers know chemical engineers can master any field. “Yeah,” I said, “that’s what they tell us in mathematics, too.” And my love, the philosopher, added that they tell philosophy majors that employers love philosophy PhD-holders for their ability to master any subject. We didn’t really want to spoil his confidence about his future career but, after all, learning has to be done.
Of this collection I think the funniest is probably the Mutt and Jeff, minimal as its mathematical content really is. It’s just the best-structured and paced joke of the set, I think. Anyway, now I hope to get back to the surprisingly complicated world of goldfish-counting.