There won’t be, this week, any mathematically-themed comic strips featuring the long-running, Carl Anderson-created character Henry. You’ll come to see why I find this worth mentioning soon enough. Not today.
Hart, Mastroianni, and Parker’s Wizard of Id for the 2nd features the blackboard full of symbols to represent the difficult and unsolved problem. And sometimes it does seem like it takes magic to solve an equation. That magic usually takes the form of a transformation. That is, we find a way to rewrite the problem as something different, and find that this different problem is solvable. And then that the solution to this altered problem can be transformed into a solution of the original. This is normal magic, the kind any trained mathematician can do, if haltingly. But sometimes it’ll be just a stroke of imaginative genius, solving a problem that seems at first to have nothing to do with the original. This is genius work, and we all hope we can find a problem on which we can do that.
I can also take the strip to represent one of those things I’m curmudgeonly about. That is that I tend to look at big special-effects-laden attempts to make mathematics look beautiful as … well, they’re nice. But I don’t think they help anyone learn how to do anything. So that the Wizard’s work doesn’t actually solve the problem feels true to me.
Mort Walker and Dik Browne’s vintage Hi and Lois for the 3rd sees Chip struggling with mathematics. His father has a noble idea, that it’ll be easier if he tries to see the problems as fun puzzles. Maybe so, but I agree with Chip: there’s not a punch line to 246 ÷ 3. Also, points to Chip for doing that division right away. Clearly he isn’t bad at arithmetic; he just doesn’t like it. We’ve all got things like that.
Hector D Cantu and Carlos Castellanos’s Baldo for the 4th is a joke about being helpless with numbers. … Actually, from the phrasing, I’m not positive that Cruz doesn’t mean he got question number 9, or maybe 19, or maybe number 10 wrong. It’s a bit sloppy to not remember which question was, but I certainly know the pain of remembering having done a problem wrong.
There are times I feel like my writing here collapses entirely to Reading the Comics posts. It’s a temptation to just give up doing anything else. They’re easy to write, since the comics give me the subjects to discuss. And it offers a nice, accessible mix of same-old topics with the occasional oddball. It’s fun. But sometimes Comic Strip Master Command decides I’ve been doing enough of that. This is one of those weeks; I only found six comics in my normal reading that were on point enough to discuss. So here’s half of them.
Bill Rechin’s Crock for the 6th is … hm. Well, let’s call it a fractions joke. I’m curious exactly what the clerk’s joke is supposed to mean. Is it intended to suggest an impossibility, putting into something far more than it can hold? Or is it just meant to suggest gross overabundance? And deep down I suspect Rechin didn’t have any specific meaning; it’s just a good-sounding insult.
Hector D Cantu and Carlos Castellanos’s Baldo for the 7th is … hm. Well, let’s call it a wordplay joke. It works by “strength” having multiple meanings, and “numbers” having multiple meanings. And there being a convenient saying to link one to the other. If this were a busier week I wouldn’t even bring it up, but I hate going without anything around here.
They’ve been phasing Roman Numerals out for a long while. Arabic numerals got their grand introduction to the (Western) Roman Empire’s territories in 1202 by Leonardo of Pisa, known now as “Fibonacci”. His Liber Abaci (Book of Calculation) laid out the Arabic numerals scheme and place values, and how to use them. By 1228 he published an edition comparing Roman numerals to Arabic numerals.
This wasn’t the first anyone in western Europe had heard of them, mind. (It never is; anyone telling you anything was the first is simplifying.) Spanish monks in the 10th century studied Arabic texts, and wrote about what they found. But after Leonardo of Pisa, Arabic numerals started displacing Roman numerals at least in specialized trades. Florence, in what is now Italy, prohibited merchants from using Arabic numerals in 1299; they could use Roman numerals or write them out in words. This, presumably, to prevent cheating by use of strange, unfamiliar calculus. Arabic numerals escaped being tools of specialists in the 16th century, thanks in large part to the German mathematician Adam Ries, who explained the scheme in terms apprentices could understand.
Still, these days, a Roman numeral is mostly an affectation. Useful for bit of style; not for serious mathematics. Good for watches.
So Mark Anderson’s Andertoons has been missing from the list of mathematically-themed the last couple weeks. Don’t think I haven’t been worried about that. But it’s finally given another on-topic-enough strip and I’m not going to include it here. I’ve had a terrible week and I’m going to use the comics we got in last week slowly.
Greg Evans’s Luann Againn for the 10th reprints the strip of the 10th of December, 1989. And as often happens, mathematics is put up as the stuff that’s too hard to really do. The expressions put up don’t quite parse; there’s nothing to solve. But that’s fair enough for a panicked brain. To not recognize what the problem even is makes it rather hard to solve.
Ruben Bolling’s Super-Fun-Pak Comix for the 10th is an installation of Quantum Mechanic, playing on the most fun example of non-commutative processes I know. That’s the uncertainty principle, which expresses itself as pairs of quantities that can’t be precisely measured simultaneously. There are less esoteric kinds of non-commutative processes. Like, rotating something 90 degrees along a horizontal and then along a vertical axis will turn stuff different from 90 degrees vertical and then horizontal. But that’s too easy to understand to capture the imagination, at least until you’re as smart as an adult and as thoughtful as a child.
Jeff Stahler’s Moderately Confused for the 11th features the classic blackboard full of equations, this time to explain why Christmas lights wouldn’t work. There is proper mathematics in lights not working. It’s that electrical-engineering work about the flow of electricity. The problem is, typically, a broken or loose bulb. Maybe a burnt-out fuse, although I have never fixed a Christmas lights problem by replacing the fuse. It’s just something to do so you can feel like you’ve taken action before screaming in rage and throwing the lights out onto the front porch. More interesting to me is the mathematics of strands getting tangled. The idea — a foldable thread, marked at regular intervals by points that can hook together — seems trivially simple. But it can give insight into how long molecules, particularly proteins, will fold together. It may help someone frustrated to ponder that their light strands are knotted for the same reasons life can exist. But I’m not sure it ever does.
Comic Strip Master Command had a slow week for everyone. This is odd since I’d expect six to eight weeks ago, when the comics were (probably) on deadline, most (United States) school districts were just getting back to work. So education-related mathematics topics should’ve seemed fresh. I think I can make that fit. No way can I split this pile of comics over two days.
Hector D Cantu and Carlos Castellanos’s Baldo for the 17th has Gracie quizzed about percentages of small prices, apparently as a test of her arithmetic. Her aunt has other ideas in mind. It’s hard to dispute that this is mathematics people use in real life. The commenters on GoComics got into an argument about whether Gracie gave the right answers, though. That is, not that 20 percent of $5.95 is anything about $1.19. But did Tia Carmen want to know what 20 percent of $5.95, or did she want to know what $5.95 minus 20 percent of that price was? Should Gracie have answered $4.76 instead? It took me a bit to understand what the ambiguity was, but now that I see it, I’m glad I didn’t write a multiple-choice test with both $1.19 and $4.76 as answers. I’m not sure how to word the questions to avoid ambiguity yet still sound like something one of the hew-mons might say.
Dan Thompson’s Brevity for the 19th uses the blackboard and symbols on it as how a mathematician would prove something. In this case, love. Arithmetic’s a good visual way of communicating the mathematician at work here. I don’t think a mathematician would try arguing this in arithmetic, though. I mean if we take the premise at face value. I’d expect an argument in statistics, so, a mathematician showing various measures of … feelings or something. And tests to see whether it’s plausible this cluster of readings could come out by some reason other than love. If that weren’t used, I’d expect an argument in propositional logic. And that would have long strings of symbols at work, but they wouldn’t look like arithmetic. They look more like Ancient High Martian. Just saying.
Dave Coverly’s Speed Bump for the 20th is designed with crossover appeal in mind and I wonder if whoever does Reading the Comics for English Teacher Jokes is running this same strip in their collection for the week.
Darrin Bell’s Candorville for the 21st sees Lemont worry that he’s forgotten how to do long division. And, fair enough: any skill you don’t use in long enough becomes stale, whether it’s division or not. You have to keep in practice and, in time, have to decide what you want to keep in practice about. (That said, I have a minor phobia about forgetting how to prove the Contraction Mapping Theorem, as several professors in grad school stressed how it must always be possible to give a coherent proof of that, even if you’re startled awake in the middle of the night by your professor.) Me, I would begin by estimating what 4,858.8 divided by 297.492 should be. 297.492 is very near 300. And 4,858.8 is a little over 4800. And that’s suggestive because it’s obvious that 48 divided by 3 is 16. Well, it’s obvious to me. So I would expect the answer to be “a little more than 16” and, indeed, it’s about 16.3.
(Don’t read the comments on GoComics. There’s some slide-rule-snobbishness, and some snark about the uselessness of the skill or the dumbness of Facebook readers, and one comment about too many people knowing how to multiply by someone who’s reading bad population-bomb science fiction of the 70s.)
My guide for how many comics to include in one of these essays is “at least five, if possible”. Occasionally there’s a day when Comic Strip Master Command sends that many strips at once. Last Sunday was almost but not quite such a day. But the business of that day did mean I had enough strips to again divide the past week’s entries. Look for more comics in a few days, if all goes well here. Thank you.
Mark Anderson’s Andertoons for the 26th reminds me of something I had wholly forgot about: decimals inside fractions. And now that this little horror’s brought back I remember my experience with it. Decimals in fractions aren’t, in meaning, any different from division of decimal numbers. And the decimals are easily enough removed. But I get the kid’s horror. Fractions and decimals are both interesting in the way they represent portions of wholes. They spend so much time standing independently of one another it feels disturbing to have them interact. Well, Andertoons kid, maybe this will comfort you: somewhere along the lines decimals in fractions just stop happening. I’m not sure when. I don’t remember when the last one passed my experience.
Hector Cantu and Carlos Castellanos’s Baldo for the 26th is built on a riddle. It’s one that depends on working in shifting addition from “what everybody means by addition” to “what addition means on a clock”. You can argue — I’m sure Gracie would — that “11 plus 3” does not mean “eleven o’clock plus three hours”. But on what grounds? If it’s eleven o’clock and you know something will happen in three hours, “two o’clock” is exactly what you want. Underlying all of mathematics are definitions about what we mean by stuff like “eleven” and “plus” and “equals”. And underlying the definitions is the idea that “here is a thing we should like to know”.
Addition of hours on a clock face — I never see it done with minutes or seconds — is often used as an introduction to modulo arithmetic. This is arithmetic on a subset of the whole numbers. For example, we might use 0, 1, 2, and 3. Addition starts out working the way it does in normal numbers. But then 1 + 3 we define to be 0. 2 + 3 is 1. 3 + 3 is 2. 2 + 2 is 0. 2 + 3 is 1 again. And so on. We get subtraction the same way. This sort of modulo arithmetic has practical uses. Many cryptography schemes rely on it, for example. And it has pedagogical uses; modulo arithmetic turns up all over a mathematics major’s Introduction to Not That Kind Of Algebra Course. You can use it to learn a lot of group theory with something a little less exotic than rotations and symmetries of polygonal shapes or permutations of lists of items. A clock face doesn’t quite do it, though. We have to pretend the ’12’ at the top is a ‘0’. I’ve grown more skeptical about whether appealing to clocks is useful in introducing modulo arithmetic. But it’s been a while since I’ve needed to discuss the matter at all.
Rob Harrell’s Big Top rerun for the 26th mentions sudoku. Remember when sudoku was threatening to take over the world, or at least the comics page? Also, remember comics pages? Good times. It’s not one of my hobbies, but I get the appeal.
Bob Shannon’s Tough Town I’m not sure if I’ve featured here before. It’s one of those high concept comics. The patrons at a bar are just what you see on the label, and there’s a lot of punning involved. Now that I’ve over-explained the joke please enjoy the joke. There are a couple of strips prior to this one featuring the same characters; they just somehow didn’t mention enough mathematics words for me to bring up here.
Norm Feuti’s Retail for the 27th is about the great concern-troll of mathematics education: can our cashiers make change? I’m being snottily dismissive. Shops, banks, accountants, and tax registries are surely the most common users of mathematics — at least arithmetic — out there. And if people are going to do a thing, ordinarily, they ought to be able to do it well. But, of course, the computer does arithmetic extremely well. Far better, or at least more indefatigably, than any cashier is going to be able to do. The computer will also keep track of the prices of everything, and any applicable sales or discounts, more reliably than the mere human will. The whole point of the Industrial Revolution was to divide tasks up and assign them to parties that could do the separate parts better. Why get worked up about whether you imagine the cashier knows what $22.14 minus $16.89 is?
I will say the time the bookstore where I worked lost power all afternoon and we had to do all the transactions manually we ended up with only a one-cent discrepancy in the till, thank you.