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.

Forget school-taught math, that’s how I best learned math…as a cashier…

LikeLike

I shouldn’t be surprised! Doing anything often will encourage people to find more accurate and faster ways to do it. So one speeds up either by just being better at recognizing common operations or by developing useful shortcuts. (The shortcuts can be disastrous if, for example, they accidentally cause some needed safety precaution not to be taken, but that doesn’t tend to apply in cashier work.)

LikeLiked by 1 person

Yeah, I used to drive my math teachers crazy with my shortcuts. But, I love when I see the light bulb go off in kids when I show them other ways to do math problems (even as a sub, I do sometimes get to teach :-) )

.

LikeLike

There is that. A weird shortcut or novel trick for a problem, even if it doesn’t lead to a generally useful technique, is good to have on the record. It inspires the imagination and lets folks know that there’s almost never just one way to do things.

LikeLiked by 1 person

Guestimation keeps the common sense in maths I, er … guess. As for Sudoku, is there any other way to do it than listing all possible #s in each box? I see people on buses and trains just staring at it – are they hoping for inspiration or else doing prodigious memory work?

LikeLike

I’m not an expert sudoku solver. I’d done some for a little while, especially after some students gave me a book of puzzles as a parting gift, but I never caught the bug.

But when I do them, it is … I wouldn’t say a

prodigiousamount of memory work. It would be picking out a cell and checking what the valid possible numbers are, then going across the row, column, and cell to see if there were any obvious contradictions, or whether that forced something suspicious in a nearby cell. I don’t suppose that works well for hard puzzles, but for the silly little easy and almost-medium puzzles I attacked it was fine. Something would turn up soon.LikeLiked by 1 person