I haven’t forgotten about the comic strips. It happens that last week’s were mostly quite casual mentions, strips that don’t open themselves up to deep discussions. I write this before I see what I actually have to write about the strips. But here’s the first half of the past week’s. I’ll catch up on things soon.
Bill Amend’s FoxTrot for the 22nd, a new strip, has Jason and Marcus using arithmetic problems to signal pitches. At heart, the signals between a pitcher and catcher are just an index. They’re numbers because that’s an easy thing to signal given that one only has fingers and that they should be visually concealed. I would worry, in a pattern as complicated as these two would work out, about error correction. If one signal is mis-read — as will happen — how do they recognize it, and how do they fix it? This may seem like a lot of work to put to a trivial problem, but to conceal a message is important, whatever the message is.
James Beutel’s Banana Triangle for the 23rd has a character trying to convince himself of his intelligence. And doing so by muttering mathematics terms, mostly geometry. It’s a common shorthand to represent deep thinking.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 25th is a joke about orders of magnitude. The order of magnitude is, roughly, how big the number is. Often the first step of a physics problem is to try to get a calculation that’s of the right order of magnitude. Or at least close to the order of magnitude. This may seem pretty lax. If we want to find out something with value, say, 231, it seems weird to claim victory that our model says “it will be a three-digit number”. But getting the size of the number right is a first step. For many problems, particularly in cosmology or astrophysics, we’re intersted in things whose functioning is obscure. And relies on quantities we can measure very poorly. This is why we can see getting the order magnitude about right as an accomplishment.
Pi Day was observed with fewer, and fewer on-point, comic strips than I had expected. It’s possible that the whimsy of the day has been exhausted. Or that Comic Strip Master Command advised people that the educational purposes of the day were going to be diffused because of the accident of the calendar. And a fair number of the strips that did run in the back half of last week weren’t substantial. So here’s what did run.
And now we get to the strips that actually ran on the 14th of March.
Hector D Cantú and Carlos Castellanos’s Baldo is a slightly weird one. It’s about Gracie reflecting on how much she’s struggled with mathematics problems. There are a couple pieces meant to be funny here. One is the use of oddball numbers like 1.39 or 6.23 instead of easy-to-work-with numbers like “a dollar” or “a nickel” or such. The other is that the joke is .. something in the vein of “I thought I was wrong once, but I was mistaken”. Gracie’s calculation indicates she thinks she’s struggled with a math problem a little under 0.045 times. It’s a peculiar number. Either she’s boasting that she struggles very little with mathematics, or she’s got her calculations completely wrong and hasn’t recognized it. She’s consistently portrayed as an excellent student, though. So the “barely struggles” or maybe “only struggles a tiny bit at the start of a problem” interpretation is more likely what’s meant.
π has infinitely many decimal digits, certainly. Of course, so does 2. It’s just that 2 has boring decimal digits. Rational numbers end up repeating some set of digits. It can be a long string of digits. But it’s finitely many, and compared to an infinitely long and unpredictable string, what’s that? π we know is a transcendental number. Its decimal digits go on in a sequence that never ends and never repeats itself fully, although finite sequences within it will repeat. It’s one of the handful of numbers we find interesting for reasons other than their being transcendental. This though nearly every real number is transcendental. I think any mathematician would bet that it is a normal number, but we don’t know that it is. I’m not aware of any numbers we know to be normal and that we care about for any reason other than their normality. And this, weirdly, also despite that we know nearly every real number is normal.
Dave Whamond’s Reality Check plays on the pun between π and pie, and uses the couple of decimal digits of π that most people know as part of the joke. It’s not an anthropomorphic numerals joke, but it is circling that territory.
Michael Cavna’s Warped celebrates Albert Einstein’s birthday. This is of marginal mathematics content, but Einstein did write compose one of the few equations that an average lay person could be expected to recognize. It happens that he was born the 14th of March and that’s, in recent years, gotten merged into Pi Day observances.
It was another pretty quiet week for mathematically-themed comic strips. Most of what did mention my subject just presented it as a subject giving them homework or quizzes or exams. But let’s look over what is here.
Ted Shearer’s Quincy for the 5th is the most interesting strip of the week, since it suggests an actual answerable mathematics problem. How much does a professional basketball player earn per dribble? The answer requires a fair bit of thought, like, what do you mean by “a professional basketball player”? There’s many basketball leagues around the world; even if we limit the question to United States-and-Canada leagues, there’s a fair number of minor leagues. If we limit it to the National Basketball Association there’s the question of whether the salary is the minimum union contract guarantee, or the mean salary, or the median salary. It’s exciting to look at the salary of the highest-paid players, too, of course.
Working out the number of dribbles per year is also a fun estimation challenge. Even if we pick a representative player there’s no getting an exact count of how many dribbles they’ve made over a year, even if we just consider “dribbling during games” to be what’s paid for. (And any reasonable person would have to count all the dribbling done during warm-up and practice as part of what’s being paid for.) But someone could come up with an estimate of, for example, about how long a typical player has the ball for a game, and how much of that time is spent moving the ball or preparing for a free throw or other move that calls for dribbling. How long a dribble typically takes. How many games a player typically plays over the year. The estimate you get from this will never, ever, be exactly right. But it should be close enough to give an idea how much money a player earns in the time it takes to dribble the ball once. So occasionally the comics put forth a good story problem after all.
Quincy on the 7th is again worrying about his mathematics and spelling tests. It’s a cute coincidence that these are the subjects worried about in Wee Pals too.
Paul Gilligan’s Pooch Cafe for the 7th is part of a string of jokes about famous dogs. This one’s a riff on Albert Einstein, mentioned here because Albert Einstein has such strong mathematical associations.
Greg Evans’s Luann Againn for the 12th features some poor tutoring on Gunther’s part. Usually a person isn’t stuck for what the answer to a problem is; they’re stuck on how to do it correctly. Maybe on how to do it efficiently. But tutoring is itself a skill, and it’s a hard one to learn. We don’t get enough instruction in how to do it.
The problem Luann’s doing is one of simplifying an expression. I remember doing a lot of this, in middle school algebra like that. Simplifying expressions does not change their value; we don’t create new ideas by writing them. So why simplify?
Any grammatically correct expression for a concept may be as good as any other grammatically correct expression. This is as true in writing as it is in mathematics. So what is good writing? There are a thousand right answers. One trait that I think most good writing has is that it makes concepts feel newly accessible. It frames something in a way which makes ideas easier to see. So it is with simplifying algebraic expressions. Finding a version of a formula that makes clearer what you would like to do makes the formula more useful.
Simplifying like this, putting an expression into the fewest number of terms, is common. It typically makes it easier to calculate with a formula. We calculate with formulas all the time. It often makes it easier to compare one formula to another. We compare formulas some of the time. So we practice simplifying like this a lot. Occasionally we’ll have a problem where this simplification is counter-productive and we’d do better to write out something as, to make up an example, instead. Someone who’s gotten good at simplifications, to the point it doesn’t take very much work, is likely to spot cases where one wants to keep part of the expression un-simplified.
Chen Weng’s Messycow Comics for the 13th starts off with some tut-tutting of lottery players. Objectively, yes, money put on a lottery ticket is wasted; even, for example, pick-three or pick-four daily games are so unlikely to pay any award as to be worth it. But I cannot make myself believe that this is necessarily a more foolish thing to do with a couple dollars than, say, buying a candy bar or downloading a song you won’t put on any playlists.
And as the Cow points out, the chance of financial success in art — in any creative field — is similarly ridiculously slight. Even skilled people need a stroke of luck to make it, and even then, making it is a marginal matter. (There is a reason I haven’t quit my job to support myself by blog-writing.) People are terrible at estimating probabilities, especially in situations that are even slightly complicated.
The past week started strong for mathematically-themed comics. Then it faded out into strips that just mentioned the existence of mathematics. I have no explanation for this phenomenon. It makes dividing up the week’s discussion material easy enough, though.
John Zakour and Scott Roberts’s Maria’s Day rerun for the 19th is a lottery joke. Maria’s come up with a scheme to certainly win the grand prize in a lottery. There’s no disputing that one could, on buying enough tickets, get an appreciable chance of winning. Even, in principle, get a certain win. There’s no guaranteeing a solo win, though. But sometimes lottery jackpots will grow large enough that even if you had to split the prize two or three ways it’d be worth it.
Tom Horacek’s Foolish Mortals for the 21st plays on the common wisdom that mathematicians’ best work is done when they’re in their 20s. Or at least their most significant work. I don’t like to think that’s so, as someone who went through his 20s finding nothing significant. But my suspicion is that really significant work is done when someone with fresh eyes looks at a new problem. Young mathematicians are in a good place to learn, and are looking at most everything with fresh eyes, and every problem is new. Still, experienced mathematicians, bringing the habits of thought that served well one kind of problem, looking at something new will recreate this effect. We just need to find ideas to think about that we haven’t worn down.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st has a petitioner asking god about whether P = NP. This is shorthand for a famous problem in the study of algorithms. It’s about finding solutions to problems, and how much time it takes to find the solution. This time usually depends on the size of whatever it is you’re studying. The question, interesting to mathematicians and computer scientists, is how fast this time grows. There are many classes of these problems. P stands for problems solvable in polynomial time. Here the number of steps it takes grows at, like, the square or the cube or the tenth power of the size of the thing. NP is non-polynomial problems, growing, like, with the exponential of the size of the thing. (Do not try to pass your computer science thesis defense with this description. I’m leaving out important points here.) We know a bunch of P problems, as well as NP problems.
Like, in this comic, God talks about the problem of planning a long delivery route. Finding the shortest path that gets to a bunch of points is an NP problem. What we don’t know about NP problems is whether the problem is we haven’t found a good solution yet. Maybe next year some bright young 68-year-old mathematician will toss of a joke on a Reddit subthread and then realize, oh, this actually works. Which would be really worth knowing. One thing we know about NP problems is there’s a big class of them that are all, secretly, versions of each other. If we had a good solution for one we’d have a solution for all of them. So that’s why a mathematician or computer scientist would like to hear God’s judgement on how the world is made.
Hector D. Cantú and Carlos Castellanos’s Baldo for the 22nd has Baldo asking his sister to do some arithmetic. I fancy he’s teasing her. I like doing some mental arithmetic. If nothing else it’s worth having an expectation of the answer to judge whether you’ve asked the computer to do the calculation you actually wanted.
Mike Thompson’s Grand Avenue for the 22nd has Gabby demanding to know the point of learning Roman numerals. As numerals, not much that I can see; they serve just historical and decorative purposes these days, mostly as a way to make an index look more fancy. As a way to learn that how we represent numbers is arbitrary, though? And that we can use different schemes if that’s more convenient? That’s worth learning, although it doesn’t have to be Roman numerals. They do have the advantage of using familiar symbols, though, which (say) the Babylonian sexagesimal system would not.
Today, I’m just listing the comics from last week that mentioned mathematics, but which didn’t raise a deep enough topic to be worth discussing. You know what a story problem looks like. I can’t keep adding to that.
Hector D. Cantú and Carlos Castellanos’s Baldo for the 10th quotes René Descartes, billing him as a “French mathematician”. Which is true, but the quote is one about living properly. That’s more fairly a philosophical matter. Descartes has some reputation for his philosophical work, I understand.
John Graziano’s Ripley’s Believe It or Not for the 26th mentions several fairly believable things. The relevant part is about naming the kind of surface that a Pringles chip represents. That is, the surface a Pringles chip would be if it weren’t all choppy and irregular, and if it continued indefinitely.
The shape is, as Graziano’s Ripley’s claims, a hypberbolic paraboloid. It’s a shape you get to know real well if you’re a mathematics major. They turn up in multivariable calculus and, if you do mathematical physics, in dynamical systems. It’s also a shape mathematics majors get to calling a “saddle shape”, because it looks enough like a saddle if you’re not really into horses.
The shape is one of the “quadratic surfaces”. These are shapes which can be described as the sets of Cartesian coordinates that make a quadratic equation true. Equations in Cartesian coordinates will have independent variables x, y, and z, unless there’s a really good reason. A quadratic equation will be the sum of some constant times x, and some constant times x2, and some constant times y, and some constant times y2, and some constant times z, and some constant times z2. Also some constant times xy, and some constant times yz, and some constant times xz. No xyz, though. And it might have some constant added to the mix at the end of all this.
There are seventeen different kinds of quadratic surfaces. Some of them are familiar, like ellipsoids or cones. Some hardly seem like they could be called “quadratic”, like intersecting planes. Or parallel planes. Some look like mid-century modern office lobby decor, like elliptic cylinders. And some have nice, faintly science-fictional shapes, like hyperboloids or, as in here, hyperbolic paraboloids. I’m not a judge of which ones would be good snack shapes.
Bud Blake’s Tiger for the 31st is a rerun, of course. Blake died in 2005 and no one else drew his comic strip. It’s a funny-answer-to-a-story-problem joke. And, more, it’s a repeat of a Tiger strip I’ve already run here. I admit a weird pride when I notice a comic strip doing a repeat. It gives me some hope that I might still be able to remember things. But this is also a special Tiger repeat. It’s the strip which made me notice Bud Blake redrawing comics he had already used. This one is not a third iteration of the strip which reran in April 2015 and June 2016. It’s a straight repeat of the June 2016 strip.
The mystery to me now is why King Features apparently has less than three years’ worth of reruns in the bank for Tiger. The comic ran from 1965 to 2003, and it’s not as though the strip made pop culture references or jokes ripped from the headlines. Even if the strip changed its dimensions over the decades, to accommodate shrinking newspapers, there should be a decade at least of usable strips to rerun.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 31st uses a chart to tease mathematicians, both in the comic and in the readership. The joke is in the format of the graph. The graph is supposed to argue that the Mathematician’s pedantry is increasing with time, and it does do that. But it is customary in this sort of graph for the independent variable to be the horizontal axis and the dependent variable the vertical. So, if the claim is that the pedantry level rises as time goes on, yes, this is a … well, I want to say wrong way to arrange the axes. This is because the chart, as drawn, breaks a convention. But convention is a tool to help people’s comprehension. We are right to ignore convention if doing so makes the chart better serve its purpose. Which, the punch line is, this does.
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.