Reading the Comics, December 15, 2018: Early Holiday Edition


So then this happened: Comic Strip Master Command didn’t have much they wanted me to write about this week. I made out three strips as being relevant enough to discuss at all. And even they don’t have topics that I felt I could really dig into. Coincidence, surely, although I like to think they were trying to help me get ahead of deadline on my A To Z essays for this last week of the run. It’s a noble thought, but doomed. I haven’t been more than one essay ahead of deadline the last three months. I know in past years I’ve gotten three or even four essays ahead of time and I don’t know why it hasn’t worked this time. I am going ahead and blaming that this these essays have been way longer than previous years’. So anyway, I thank Comic Strip Master Command for trying to make my Monday and my Thursday this week be less packed. It won’t help.

Darrin Bell and Theron Heir’s Rudy Park for the 10th uses mathematics as shorthand for a deep, thought-out theory of something. In this case, Randy’s theory of how to interest women. (He has rather a large number of romantic events around him.) It’s easy to suppose that people can be modeled mathematically. Even a crude model, one supposing that people have things they like and dislike, can give us good interesting results. This gets into psychology and sociology though. And probably requires computer modeling to get slightly useful results.

Rudy: 'You're wearing your lab coat. What's up?' Randy: 'Something big. Amending my unified theory of picking up chicks. Check it out.' (It's a blackboard filled with physics equations, as well as a sketch of a woman in a bikini.) Rudy: 'Explain, Doctor.' Randy: 'To start, you'll need a notepad and a gym membership.'
Darrin Bell and Theron Heir’s Rudy Park for the 10th of December, 2018. This strip is a rerun. It originally ran the 11th of January, 2010. Essays mentioning topics raised by Rudy Park are at this link.

Randy’s blackboard has a good number of legitimate equations on it. They’re maybe not so useful to his problem of modeling people, though. The lower left corner, for example, are three of Maxwell’s Equations, describing electromagnetism. I’m not sure about all of these, in part because I think some might be transcribed incorrectly. The second equation in the upper left, for example, looks like it’s getting at the curl of a conserved force field being zero, but it’s idiosyncratic to write that with a ‘d’ to start with. The symbols all over the right with both subscripts and superscripts look to me like tensor work. This turns up in electromagnetism, certainly. Tensors turn up anytime something, such as electrical conductivity, is different in different directions. But I’ve never worked deeply in those fields so all I can confidently say is that they look like they parse.

Nate's story: 'Barky the sheepdog stared in horror at the bloody foot on the barn floor. It was the fifth piece of Farmer Wobblewheel he'd found today. 'And don't forget about the three pieces we found yesterday!' said Winky the wonder monkey.' Franklin: 'What's a monkey doing on a farm?' Nate: 'Helping Barky discover who dismembered Farmer Wobblewheel *and* teaching us about numbers!' Story: ''Five pieces plus three pieces,' barked Barkey. 'That makes ... ' 'Eight,' chuckled Winky.' Francis: 'Ew.'
Lincoln Pierce’s Big Nate for the 14th of December, 2018. Other essays mentioning topics raised by Big Nate, both the current run — like this — and vintage 1990 are at this link.

Lincoln Pierce’s Big Nate for the 14th is part of a bit where Nate’s trying to write a gruesome detective mystery for kids. I’m not sure that’s a ridiculous idea, at least if the gore could be done at a level that wouldn’t be too visceral. Anyway, Nate has here got the idea of merging some educational value into the whole affair. It’s not presented as a story problem, just as characters explaining stuff to one another. There probably would be some room for an actual problem where Barky and Winky wanted to know something and had to work out how to find it from what they knew, though.

Playing in a cardboard box labelled SS Nora Dish. Jingles: 'Take the controls while I make the calculations for hyperspace.' Cecil: 'Wookie noise.' Jingles: 'Let's see. Bob has two bananas. He gives one to Joe who eats half and returns the remainder along with half a cantaloupe ... this ship needs a modern supercomputer.' Cecil: 'Wookie noise.'
Mel Henze’s Gentle Creatures for the 14th of December, 2018. All the essays where I’ve discussed Gentle Creatures are at this link although I suspect it’s mostly the same three comics discussed over and over.

Mel Henze’s Gentle Creatures for the 14th uses a story problem to stand in for science fictional calculations. The strip’s in reruns and I’ve included it here at least four times, I discover, so that’s probably enough for the comic until it gets out of reruns.


And since it was a low-volume week, let me mention strips I didn’t decide fit. Ray Kassinger asked about Tim Rickard’s Brewster Rockit for the 12th. Might it be a play on Schrödinger’s Cat, the famous thought-experiment about how to understand the mathematics of quantum mechanics? It’s possible, but I think it’s more likely just that cats like sitting in boxes. Thaves’s Frank and Ernest for the 13th looks like it should be an anthropomorphic numerals joke. But it’s playing on the idiom about three being a crowd, and the whole of the mathematical content is that three is a number. John Zakour and Scott Roberts’s Maria’s Day for the 15th mentions mathematics. Particularly, Maria wishing they weren’t studying it. It’s a cameo appearance; it could be any subject whose value a student doesn’t see. That’s all I can make of it.


This and my other Reading the Comics posts should all be available at this link. And please check back in Tuesday to see whether I make deadline for the letter ‘Y’ in my Fall 2018 Mathematics A To Z glossary.

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Reading the Comics, November 9, 2018: Standing For Things Edition


There was something in common in two of the last five comic strips worth attention from last week. That’s good enough to give the essay its name.

Greg Cravens’s The Buckets for the 8th showcases Toby discovering the point of letters in algebra. It’s easy to laugh at him being ignorant. But the use of letters this way is something it’s easy to miss. You need first to realize that we don’t need to have a single way to represent a number. Which is implicit in learning, say, that you can write ‘7’ as the Roman numeral ‘VII’ or so, but I’m not sure that’s always clear. And realizing that you could use any symbol to write out ‘7’ if you agree that’s what the symbol means? That’s an abstraction tossed onto people who often aren’t really up for that kind of abstraction. And that we can have a symbol for “a number whose identity we don’t yet know”? Or even “a number whose identity we don’t care about”? Don’t blame someone for rearing back in confusion at this.

Friend 1: 'That algebra test was awful.' Friend 2: 'Toby just gave up and handed his paper in!' Toby: 'No, I finished. My mom said as long as I studied I didn't have to do any chores.' Friend 1: 'That'd eat up all your gaming hours!' Toby: 'Yep. Hey, did you know algebra letters stand for things?'
Greg Cravens’s The Buckets for the 8th of November, 2018. I’m sorry I can’t figure out the names of Toby’s friends here. Character lists, cartoonists, please.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th talks about vectors and scalars. And about the little ways that instructors in one subject can sabotage one another. In grad school I was witness to the mathematics department feeling quite put-upon by the engineering departments, who thought we were giving their students inadequate calculus training. Meanwhile we couldn’t figure out what they were telling students about calculus except that it was screwing up their understanding.

Funtime Activity: Ruining students forever. Teacher: 'Physics students must learn the difference between vectors and scalars is that scalars don't exist.' Student: 'What about 'amount of apples'?' Teacher: 'Huh? Oh, you're referring to 'distance in apple-space'.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th of November, 2018. Also, shouldn’t that be “displacement in apple-space”?

To a physicist, a vector is a size and a direction together. (At least until they get seriously into mathematical physics when they need a more abstract idea.) A scalar is a number. Like, a real-valued number such as ‘4’. Maybe a complex-valued number such as ‘4 + 6i’. Vectors are great because a lot of physics problems become easier when thought of in terms of directions and amounts in that direction.

A mathematician would start out with vectors and scalars like that. But then she’d move into a more abstract idea. A vector, to a mathematician, is a thing you can add to another vector and get a vector out. A scalar is something that’s not a vector but that, multiplied by a vector, gets you a vector out. This sounds circular. But by defining ‘vector’ and ‘scalar’ in how they interact with each other we get a really sweet flexibility. We can use the same reasoning — and the same proofs — for lots of things. Directions, yes. But also matrices, and continuous functions, and probabilities of events, and more. That’s a bit much to give the engineering student who’s trying to work out some problem about … I don’t know. Whatever they do over in that department. Truss bridges or electrical circuits or something.

Billy: 'On the 80s station I think I just heard my favorite song ever! It's about carrying a laser down some road. I think it's called 'Carry a laser' and it's all about lasers!' Cow: 'Actually, it's 'Kyrie Eleison'. It means 'Lord, have Mercy'. It has nothing at all to do with lasers.' Billy: 'Right, and 'Hip to b^2' has nothing to do with algebra.' Cow: 'That I don't know.'s
Mark Leiknes’s Cow and Boy rerun for the 9th of November, 2018. It first ran the 19th of March, 2012.

Mark Leiknes’s Cow and Boy for the 9th is really about misheard song lyrics, a subject that will never die now that we don’t have the space to print lyrics in the album lining anymore, or album linings. But it has a joke resonant with that of The Buckets, in supposing that algebra is just some bunch of letters mixed up with numbers. And Cow and Boy was always a strip I loved, as baffling as it might be to a casual reader. It had a staggering number of running jokes, although not in this installment.

Brad: 'I think I've got this worked out. It takes 500 half-inch hairs to make a good moustache. If I grow one hair a week, and each new hair grows 1/8 inch per month, I can grow a perfect moustache in ... ' Luann: '225 years, not bad!'
Greg Evans’s Luann Againn for the 9th of November, 2018. It first ran the 9th of November, 1990.

Greg Evans’s Luann Againn for the 9th shows Brad happy to work out arithmetic when it’s for something he’d like to know. The figure Luan gives is ridiculously high, though. If he needs 500 hairs, and one new hair grows in each week, then that’s a little under ten years’ worth of growth. Nine years and a bit over seven months to be exact. If a moustache hair needs to be a half-inch long, and it grows at 1/8th of an inch per month, then it takes four months to be sufficiently long. So in the slowest possible state it’d be nine years, eleven months. I can chalk Luann’s answer up to being snidely pessimistic about his hair growth. But his calculator seems to agree and that suggests something went wrong along the way.

Test Question: 'Mr Gray drove 55 mph to a city 80 miles away. He made two stops: one for 20 minutes, and one for 5. How long did it take Mr Gray to reach the city?' Student's answer: 'This made my head hurt, so I'm just going to say 'the whole trip'. You can't argue that.'
John Zakour and Scott Roberts’s Maria’s Day for the 9th of November, 2018. Again, character lists. I don’t know which of the characters this is except that he’s either very small or has an enormous pencil.

John Zakour and Scott Roberts’s Maria’s Day for the 9th is a story problem joke. It looks to me like a reasonable story problem, too: the distance travelled and the speed are reasonable, and give sensible numbers. The two stops add a bit of complication that doesn’t seem out of line. And the kid’s confusion is fair enough. It takes some experience to realize that the problem splits into an easy part, a hard part, and an easy part. The first easy part is how long the stops take all together. That’s 25 minutes. The hard part is realizing that if you want to know the total travel time it doesn’t matter when the stops are. You can find the total travel time by adding together the time spent stopped with the time spent driving. And the other easy part is working out how long it takes to go 80 miles if you travel at 55 miles per hour. That’s just a division. So find that and add to it the 25 minutes spent at the two stops.


The various Reading the Comics posts should all be at this link. Essays which discuss The Buckets are at this link. The incredibly many essays mentioning Saturday Morning Breakfast Cereal are at this link. Essays which mention Cow and Boy are at this link. Essays inspired in part by Luann, both the current-day and the vintage 1990 run, are at this link. The credibly many essays mentioning Maria’s Day are at this link.

And through the end of December my Fall 2018 Mathematics A-To-Z should have two new posts a week. You might like some of them.

Reading the Comics, November 7, 2018: Shorthand and Reruns Edition


There’s two types of comics for the second of last week’s review. There’s some strips that are reruns. There’s some that just use mathematics as a shorthand for something else. There’s four strips in all.

John Deering’s Strange Brew for the 6th uses mathematics as shorthand for demonstrating intelligence. There’s no making particular sense out of the symbols, of course. And I’d think it dangerous that Lucky seems to be using both capital X and lowercase x in the same formula. There’s often times one does use the capital and lowercase versions of a letter in a formula. This is usually something like “x is one element of the set X, which is all the possible candidates for some thing”. In that case, you might get the case wrong, but context would make it clear what you meant. But, yes, sometimes there’s no sensible alternative and then you have to be careful.

Person upstairs: 'I don't understand how Lucky keeps getting out.' Lucky, the dog, is downstairs, writing out plans: 'V_1 Q_q = X'^4 y / B(4) x^2'
John Deering’s Strange Brew for the 6th of November, 2018. The mathematics is all fine but have they considered they never did close the patio door?

Randy Glasbergen’s Glasbergen Cartoons for the 6th uses mathematics as shorthand for a hard subject. It’s certainly an economical notation. Alas, you don’t just learn from your mistakes. You learn from comparing your mistakes to a correct answer. And thinking about why you made the mistakes you did, and how to minimize or avoid those mistakes again.

Student, to teacher: 'If we learn from our mistakes, shouldn't I make as many mistakes as possible?' On the blackboard is the problem 473 x 17.
Randy Glasbergen’s Glasbergen Cartoons for the 6th of November, 2018. The strip is a rerun, but I have no information to date when it’s from.

So how would I do this problem? Well, carrying out the process isn’t too hard. But what do I expect the answer to be, roughly? To me, I look at this and reason: 473 is about 500. So 473 x 17 is about 500 x 17. 500 x 17 is 1000 times eight-and-a-half. So start with “about 8500”. That’s too high, obviously. I can do better. 8500 minus some correction. What correction? Well, 473 is roughly 500 minus 25. So I’ll subtract 25 times 17. Which isn’t hard, because 25 times 4 is 100. So 25 times 17? That’s 25 times 16 plus 25 times 1. 25 times 16 is 100 times 4. So 25 times 17 is 425. 8500 minus 425 is 8075. I’m still a bit high, by 2 times 17. 2 times 17 is 34. So subtract 34 from 8075: it should be about 8041.

Student taking a test: 'Which of these is a right triangle?' (Figures a, b, and c.) Maria's answer: 'c is right. a is left. b is middle.'
John Zakour and Scott Roberts’s Maria’s Day for the 7th of November, 2018. Kind of curious whether this is meant to have one correct answer or an unspecified number of correct answers, since both ‘b’ and ‘c’ look plausibly like right triangles to me.

John Zakour and Scott Roberts’s Maria’s Day for the 7th is a joke built on jargon. Every field has its jargon. Some of it will be safely original terms: people’s names (“Bessel function”) or synthetic words (“isomorphism”) that can’t be easily confused with everyday language. But some of it will be common terms given special meaning. “Right” angles and “right” triangles. “Normal” numbers. “Group”. “Right” as a description for angles and triangles goes back a long way, at least to — well, Merriam-Webster.com says 15th century. But EtymologyOnline says late 14th century. Neither offers their manuscripts. I’ll chalk it up to differences in how they interpret the texts. And possibly differences in whether they would count, say, a reference to “a right angle” written in French or German rather than in English directly.

Literary Calendar. Several jokes, including: Saturday 7pm: an infinite number of chimpanzees discuss their multi-volume 'Treasury of Western Literature with no Typos' at the Museum of Natural History. Nit picking to follow.
Richard Thompson’s Richard’s Poor Almanac rerun for the 7th of November, 2016.

Richard Thompson’s Richard’s Poor Almanac for the 7th has been run before. It references the Infinite Monkey Theorem. The monkeys this time around write up a treasury of Western Literature, not merely the canon of Shakespeare. That’s at least as impressive a feat. Also, while this is a rerun — sad to say Richard Thompson died in 2016, and was forced to retire from drawing before that — his work was fantastic and deserves attention.


This and every Reading the Comics post should be at this link. Essays discussing topics raised by Strange Brew are at this link. The essays discussing Glasbergen Cartoons are at this link. Essays which mention Maria’s Day, are at this link. And essays featuring Richard’s Poor Almanac are at this link.

My Fall 2018 Mathematics A-To-Z averages two new posts a week, through the end of December. Thanks again for reading.

Reading the Comics, November 3, 2018: Arithmetic Is Hard Edition


If there is a theme to the last comic strips from the previous week, it’s that kids find arithmetic hard. That’s a title for you.

Bill Watterson’s Calvin and Hobbes for the 2nd is one of the classics, of course. Calvin’s made the mistake of supposing that mathematics is only about getting true answers. We’ll accept the merely true, if that’s what we can get. But we want interesting. Which is stuff that’s not just true but is unexpected or unforeseeable in some way. We see this when we talk about finding a “proper” answer, or subset, or divisor, or whatever. Some things are true for every question, and so, who cares?

Also, is it really true that Calvin doesn’t know any of his homework problems? It’s possible, but did he check?

Calvin: 'I can't go outside until I finish my homework. What's five plus seven?' Hobbes: 'I don't know.' Calvin: 'I don't either.' Hobbes: 'Then write 'I don't know'.' Calvin: 'Hey that's a true answer, isn't it! I can write that for ALL of these! We're done!' As Calvin races outside one parent says, 'We'd better have a look at our prodigy's homework.'
Bill Watterson’s Calvin and Hobbes rerun for the 2nd of November, 2018. It first appeared the 4th of November, 1988.

Were I grading, I would accept an “I don’t know”, at least for partial credit, in certain conditions. Those involve the student writing out what they would like to do to try to solve the problem. If the student has a fair idea of something that ought to find a correct answer, then the student’s showing some mathematical understanding. But there are times that what’s being tested is proficiency at an operation, and a blank “I don’t know” would not help much with that.

7:30 am: Todd runs into the Beauty Rejuvenation Clinic. Later, in class. Teacher: 'So if we add these denominators ...' and Todd starts snoring, with eyes open. Teacher: 'Todd! What did I tell you about getting Botox injections in your eyelids on fractions day?!'
Patrick Roberts’s Todd the Dinosaur for the 2nd of November, 2018. I admit I’m not sure Botox works on eyelids like this. But that’s for whoever writes Reading the Comics for the Medical Stuff. Also I’m not sure what you would add the denominators for, but it’s late at night when I write this. I’m probably overlooking the obvious.

Patrick Roberts’s Todd the Dinosaur for the 2nd has an arithmetic cameo. Fractions, particularly. They’re mentioned as something too dull to stay awake through. So for the joke’s purpose this could have been any subject that has an exposition-heavy segment. Fractions do have more complicated rules than adding whole numbers do. And introducing those rules can be hard. But anything where you introduce rules instead of showing what you can do with them is hard. I’m thinking here of several times people have tried to teach me board games by listing all the rules, instead of setting things up and letting me ask “what am I allowed to do now?” the first couple turns. I’m not sure how that would translate to fractions, but there might be something.

Maria as superhero declares 'With my Mighty-Maria Heat Vision I'll divide this barricade!' She gets bounced off it. 'Drat! Division is my kryptonite!' She bounced off a sheet marked 450 / 9.
John Zakour and Scott Roberts’s Maria’s Day for the 2nd of November, 2018. I do like it when a comic strip finds reasons to stretch artistically. Superhero fantasy sequences are often good pretexts.

John Zakour and Scott Roberts’s Maria’s Day for the 2nd has another of Maria’s struggles with arithmetic. It’s presented as a challenge so fierce it can defeat even superheroes. Could be any subject, really. It’s hard to beat the visual economy of having it be a division problem, though.

Hammie to his parents: 'I'm building a giant killer robot out of legos! It's going to have rockets and lasers and all kinds of stuff!' Mom: 'I wish he'd get that excited about multiplication tables.' Dad: 'Maybe math needs to be more explodey.'
Rick Kirkman and Jerry Scott’s Baby Blues for the 3rd of November, 2018. Oh, like it’s possible to finish any even slightly complicated Lego project.

Rick Kirkman and Jerry Scott’s Baby Blues for the 3rd shows a bit of youthful enthusiasm. Hammie’s parents would rather that enthusiasm be put to memorizing multiplication facts. I’m not sure this would match the fun of building stuff. But I remember finding patterns inside the multiplication table fascinating. Like how you could start from a perfect square and get the same sequence of numbers as you moved out along a diagonal. Or tracing out where the same number appeared in different rows and columns, like how just everything could multiply into 24. Might be worth playing with some.


All of my Reading the Comics posts should be at this link. Essays where I take the chance to talk about Calvin and Hobbes are at this link. Essays that include Todd the Dinosaur are at this link. Essays with a mention of Maria’s Day should be at this link. And essays with a mention of Baby Blues are at this link. Finally, and through the rest of the year, my Fall 2018 Mathematics A-To-Z should be getting two new posts a week. Thanks again for reading.

Reading the Comics, October 14, 2018: Possessive Edition


The first two comics for this essay have titles of the form Name’s Thing, so, that’s why this edition title. That’s good enough, isn’t it? And besides this series there was a Perry Bible Fellowship which at least depicted mathematical symbols. It’s a rerun, though, even among those shown on GoComics.com. It was rerun recently enough that I featured it around here back in June. It’s a bit risque. But the strip was rerun the 12th. Maybe I also need to drop Perry Bible Fellowship from the roster of comics I read for this.

On to the comics I haven’t dropped.

Tony Buino and Gary Markstein’s Daddy’s Home for the 11th tries using specific examples to teach mathematics. There’s strangeness to arithmetic. It’s about these abstract things like “thirty” and “addition” and such. But these things match very well the behaviors of discrete objects, ones that don’t blend together or shatter by themselves. So we can use the intuition we have for specific things to get comfortable working with the abstract. This doesn’t stop, either. Mathematicians like to work on general, abstract questions; they let us answer big swaths of questions all at once. But working out a specific case is usually easier, both to prove and to understand. I don’t know what’s the most advanced mathematics that could be usefully practiced by thinking about cupcakes. Probably something in group theory, in studying the rotations of objects that are perfectly, or nearly, rotationally symmetric.

Dad: 'It's like this: if mom made 30 cupcakes, and you gave 12 friends two cupcakes each, how many would you have left?' Elliot: 'Cupcakes or friends?' Dad: 'Good question.'
Tony Buino and Gary Markstein’s Daddy’s Home for the 11th of October, 2018. The coloring makes the strip more visually interesting than just the sketchy line art would; I’m curious how it’s rendered in newspapers that print black-and-white comics.

John Zakour and Scott Roberts’s Maria’s Day for the 11th is a follow-up to a strip featured last week. Maria’s been getting help on her mathematics from one of her closet monsters. And includes the usual joke about Common Core being such a horrible thing that it must come from monsters. I don’t know whether in the comic strip’s universe the monster is supposed to be imaginary. (Usually, in a comic strip, the question of whether a character is imaginary-or-real is pointless. I think Richard Thompson’s Cul de Sac is the only one to have done something good with it.) But if the closet monster is in Maria’s imagination, it’s quite in line for her to think that teaching comes from some malevolent and inscrutable force.

Maria: 'OK, you helped me with my homework, and I brought you a whole package of hot dogs. You wouldn't gobble me up after all that, right?' Monster: 'Kid, those were tofu dogs. I promise nothing. 'Course, I do wanna hear how I did on the math. Y'know, monsters invented 'common core'.'
John Zakour and Scott Roberts’s Maria’s Day for the 11th of October, 2018. Yeah, snarking on Common Core is an easy joke, but then so is snarking on tofu dogs. I’ve been happy with Morningstar vegetarian hot dogs for years now, although I will admit we don’t usually have them as hot dogs but instead as ways to bulk up a macaroni and cheese or similar meal.

Olivia Jaimes’s Nancy for the 12th features one of the first interesting mathematics questions you do in physics. This is often done with calculus. Not much, but more than Nancy and Esther could realistically have. It could be worked out experimentally, and that’s likely what the teacher was hoping for. Calculus isn’t really necessary, although it does show skeptical students there’s some value in all this d-dx business they’ve been working through. You can find the same answers by dimensional analysis, which is less intimidating. But you’d still need to know some trigonometry functions. That’s beyond whatever Nancy’s grade level is too. In any case, Nancy is an expert at identifying unstated assumptions, and working out loopholes in them. I’m curious whether the teacher would respect Nancy’s skill here. (The way the writing’s been going, I think she would.)

Teacher: 'Your assignment is to figure out what release angle makes a thrown ball travel the farthest.' Nancy, at the top of a well: 'Straight down seems to work pretty well.'
Olivia Jaimes’s Nancy for the 12th of October, 2018. Nancy and Esther found similarly good results at Bottomless Chasm, on the edge of town.

Francesco Marciuliano and Jim Keefe’s Sally Forth for the 13th is about new-friend Jenny trying to work out her relationship with Hilary-Faye-and-Nona. It’s a good bit of character work, but that is outside my subject here. In the last panel Nona admits she’s been talking, or at least thinking about τ versus π. This references a minor nerd-squabble that’s been going on a couple years. π is an incredibly well-known, useful number. It’s the only transcendental number you can expect a normal person to have ever heard of. Humans noticed it, historically, because the length of the circumference of a circle is π times the length of its diameter. Going between “the distance across” and “the distance around” turns out to be useful.

Jenny: 'You know, actions speak louder than words. And you three talk a *lot*. But ... I'll see where this goes, and if you mean what you say ... so, what were you talking about?' Hilary: 'Oddly enough, it never seems to be about school.' Nona: 'I was thinking about tau versus pi. But that might have just been in my head.'
Francesco Marciuliano and Jim Keefe’s Sally Forth for the 13th of October, 2018. I like the composition in the first panel. It’s the rare cinematic angle that allows all four people who need to be in the panel to be shown without looking like a police lineup. (Which, yeah, the third panel kind of does. But I don’t know how to frame that so you can show all four characters and have the three talking, and have the dialogue balloons read in the logical order.)

The thing is, many mathematical and physics formulas find it more convenient to write things in terms of the radius of a circle or sphere. And this makes 2π show up in formulas. A lot. Even in things that don’t obviously have circles in them. For example, the Gaussian distribution, which describes how much a sample looks like the population it’s sampled from, has 2π in it. So, the τ argument does, why write out 2π all these places? Why not decide that that’s the useful number to think about, give it the catchy name τ, and use that instead? All the interesting questions about π have exact, obvious parallel questions about τ. Any answers about one give us answers about the other. So why not make this switch and then … pocket the savings in having shorter formulas?

You may sense in me a certain skepticism. I don’t see where changing over gets us anything worth the bother. But there are fashions in mathematics as with everything else. Perhaps τ has some ability to clarify things in ways we’ll come to better appreciate.


This and my other Reading the Comics posts are this link. Essays inspired by Daddy’s Home are at this link. Other essays that mention Maria’s Day discussions should be at this link. Essays with a mention of Nancy, old and new, are at this link. And essays in which Sally Forth gets discussed will be at this link. It’s a new tag today, which does surprise me.

Reading the Comics, October 6, 2018: Curve Edition


There’s three more comics from last week I want to talk about. To ease my workload I’m going to put those off until Saturday. This is not an attempt to inflate the number of posts I make so that I can do a post-a-day-for-a-month again, as has happened in previous A-to-Z series. I already missed yesterday anyway. I just didn’t have time to think of things to write about six comics yesterday.

Morrie Turner’s Wee Pals for the 3rd has an interesting description of a circle. Definitions are a big part of mathematical work. This is especially so as we tend to think of mathematical objects as things that relate to one another in different ways. You want a definition that includes the relationships that are important, and excludes the ones you don’t want.

Wellington: 'Can you describe a circle, Nipper?' Nipper: 'Sure! A circle is a curved line with no kinks in it ... its ends join up so as not to show where it began.'
Morrie Turner’s Wee Pals for the 3rd of October, 2018. It previously ran the 9th of October, 2013. I suspect the strip was a rerun even in 2013, as the lines are pretty tightly drawn; other strips around that era were much more erratic. Also in 2013 I don’t seem to have thought this strip worth mention, which shows how standards are mutating around these parts.

Nipper’s definition of a circle … well, eh. I wouldn’t say that captures a circle. A ‘closed smooth curve’, yes. It’s closed because the ends join up. It’s smooth because there aren’t any corners, any kinks in it. It’s a curve because … well, there you go. There are many interesting shapes that are closed smooth curves. You can find some by tossing a rubber band in the air and seeing what it looks like when it lands. But I think what most people find important about circles are ideas like all the points on a curve being the same distance from some single “center” point. Nipper would probably realize his definition didn’t work by experimenting. Try drawing shapes that meet the rule he set out, but that aren’t what he thinks a circle ought to be.

This can be fruitful. It can develop a sharper idea of what a definition ought to have. Or it might force you to accept, in order to get the cases you want included, that something which seems wrong has to count too. This mathematicians faced in the late 19th and early 20th centuries. We learned that the best definition we’ve had for an idea like “a continuous function” means we have to allow weird conclusions, like that it’s possible to have a function continuous at a single point and nowhere else. But any other definition rules out things we absolutely have to call continuous, so, what’s there to do?

(Flo and a friend watch Flo's teenage daughter and friend walk past.) Friend: 'Sometimes I look at those girls and wish I was that age again.' Flo: 'I can understand that. But then you remember how rich your life has been?' Friend: 'No. Then I remember the algebra.'
Jenny Campbell’s Flo and Friends for the 4th of October, 2018. I’m not sure which friend Flo is speaking with here; Wikipedia suggests either Ruthie or Winnie most likely. So if I may summarize: cast lists. Why do we not have them? Thank you.

Jenny Campbell’s Flo and Friends for the 4th presents algebra as one of the burdens of youth. And one that’s so harsh that it makes old age more pleasant. I get the unpleasantness of being stuck in a class one doesn’t understand or like. But my own slight experience with that thing where you wake up, and a thing hurts, and there’s no good reason but eventually it either goes away or you get so used to it you don’t realize it still actually hurts? I would take the boring class, most of the time.

Maria's Mother: 'Very good, Maria! You got every problem on your math homework right.' (Later.) Maria: 'Thanks for the help, Math Wiz!' Math-wiz monster in the closet: 'Yeah, yeah. Where's my raw chicken? A deal's a deal.'
John Zakour and Scott Roberts’s Maria’s Day for the 4th of October, 2018. All right, so she got the questions right, but we can see she didn’t write her name at the top of the page. Please, please, PLEASE make sure you put your name on the page. Every page, too. It’s so very stressful for your instructor to have to figure out which of the three anonymous papers are which.

John Zakour and Scott Roberts’s Maria’s Day for the 4th is a joke about how hard mathematics is. Maria’s finding the monsters in her room less frightening than arithmetic. Well, as long as she’s picking up a couple useful things about multiplication.


I do at least one Reading the Comics post per week, and often two.They’ll be at this link. Other appearances by Wee Pals should be at this link. Topics raised by Flo and Friends are discussed at this link. And essays mentioning Maria’s Day are at this link. Thanks as ever for reading. I’m trusting that you did, or you wouldn’t be seeing this.

Reading the Comics, July 23, 2018: Bad Mathematics Edition


I apologize for a post rougher than my norm. It has not been a gentle week. I am carrying on as best I can, but then, who isn’t? There is a common element to three of the strips featured this time around, so I have a meaningful name.

Steve McGarry’s KidTown for the 22nd of July is a kids-information panel. It’s a delivery system for some neat trivia about numbers. I’d never encountered the bit about the factorial of 10 (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) being as many seconds as there are in six weeks. I’m curious how I missed that. But it’s definitely one of those slightly useful bits of calendar mathematics to keep around. Some other useful ones are that three years is about 1100 days, and that a century is about three billion seconds. That line about 12 + 3 – 4 + 5 + 67 + 8 + 9 is probably a useful answer to some mathematics riddle such as might beset Nancy.

Informational panel noting, among other things, that 10! seconds are exactly six weeks; that 111111111 x 111111111 is 12345678987654321, things like that.
Steve McGarry’s KidTown for the 22nd of July, 2018. These are all cute enough facts. The “Use The News” activity suggestion is a pretty bad reach, though.

John Zakour and Scott Roberts’s Maria’s Day for the 23rd depicts Maria misunderstanding what it is to be bad at mathematics. The Star Wars movie episode numbers show a quirky indexing scheme, yes. But the numbers in this case are mostly nominal variables. If we spoke of the movies only by their titles … well, it would be harder to guess whether The Empire Strikes Back or Return of the Jedi came first. All the names suggest is that they ought to follow on something else happening beforehand. And people would likely use numbers for shorthand anyway. Star Trek fans talk still about the odd- and even-numbered movies, even though no Star Trek movie’s had a number attached to it since 1991.

Maria: 'So Star Wars 4 came first, and first one was made fourth?' Dad: 'Yep.' Maria: 'And the guy who made 'em is all rich now?' Dad: 'Yeah.' Maria: 'So you can be bad at math and still be a big success.' Dad: 'Wrong lesson.'
John Zakour and Scott Roberts’s Maria’s Day for the 23rd of July, 2018. Also you can be a professional writer and fumble, as happened when the first panel was written or lettered. (I hate when I do that myself and shouldn’t tease Zakour and Roberts so.)

A nominal variable is as the … er … name suggests. It’s a way to reference something, but the value doesn’t mean very much. We see these, often with numbers attached, often enough to not notice it. We start to realize it when we have those moments of thinking, isn’t it odd that the office building starts numbering rooms from 101, rather than, say, 1? Or that there’s no numbers between (say) 129 and 201? Using a number carries some information, in that it suggests we think there is a preferred order for things. But your neighborhood would be no different if all the building addresses were 1000 higher, and the Star Wars movies would be no different if the one from 1977 came to be dubbed Episode 14 instead.

(I am open to an argument that the Star Wars episode numbers are ordinal variables. This is why I hedged by calling them “mostly” nominal. An ordinal variable describes some preferred order for the things. The difference between numbers isn’t particularly meaningful, just the relationship between them. And, yeah, it would be peculiar if The Empire Strikes Back had a higher episode number than did Return of the Jedi. Viewing the movies in that order would create several apparent continuity errors. But there are differences between internal chronology and production order and other ways one might watch the movies. But it seems to me the ordinary use for the numbers, if someone uses them at all, is as a label.)

Francis: 'Momma, can you write me a check for my rent?' Momma: 'Not right now, dear. 60 Minutes just started . It's about grown men who can't do simple arithmetic. Can you wait till it's over?' Francis: 'How long will it take?'
Mell Lazarus’s Momma rerun for the 23rd of July, 2018. As you maybe guessed, it first appeared the 23rd of July, 2007. I make no claims about appearances since then and before July 2018. The strip ran a lot of reruns in the months before Lazarus’s death.

Mell Lazarus’s Momma for the 23rd is another strip built on people being bad at mathematics. Arithmetic, anyway. I’m not sure this quite counts as an arithmetic joke. Granting the (correct) assumption that an episode of 60 Minutes is ordinarily 60 minutes long, is not recognizing how long the show will take really a use of mathematics? Isn’t it more reading comprehension? … And to be fair to the ever-beleaguered Francis, it’s rather more likely 60 Minutes just had one segment about grown men incapable of doing arithmetic. Asking how long that is likely to take is a fair question.

Arrogant deer: 'OK, Dennis. What's five plus five?' Dennis: 'Ooh. Ah, that would be ten?' Arrogant :'Now, subtract five from ten.' Dennis: 'Ummm ... eight. No, two. No, six! Nine?' Arrogant: 'That's it. You're the weakest member of the herd.' Dennis: 'C'mon, guys! Just because I'm stupid doesn't mean I'm weak!'
Adrian Raeside’s The Other Coast for the 23rd of July, 2018. So would it have improved the joke if Dennis had fumbled adding five and five too? Or does it make Dennis look dumber to not know that if five plus five equals ten, then ten minus five has to equal five? Genuinely don’t know which would be the better setup.

Adrian Raeside’s The Other Coast for the 23rd is another strip conflating arithmetic skill with intelligence. And intelligence with fitness. It’s flattering stuff, at least for people who are good at arithmetic and who feel flattered to be called intelligent. But there’s a lot of presumption here. And a common despicable attitude: merry little eugenicists (they’re always cheery about it, aren’t they?) always conclude they are fit ones.


Other essays that discuss topics raised in KidTown are on this link. When I’ve had cause to discuss Maria’s Day those essays are here. Other times I’ve talked about Momma should be on this link. And other essays that mention The Other Coast should be on this link. It’s a new tag, so it might take some time to get other entries.

As ever, the whole set of Reading the Comics posts should be at this link.

Reading the Comics, April 25, 2018: Coronet Blue Edition


You know what? Sometimes there just isn’t any kind of theme for the week’s strips. I can use an arbitrary name.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st of April, 2018 would have gone in last week if I weren’t preoccupied on Saturday. The joke is aimed at freshman calculus students and then intro Real Analysis students. The talk about things being “arbitrarily small” turns up a lot in these courses. Why? Well, in them we usually want to show that one thing equals another. But it’s hard to do that. What we can show is some estimate of how different the first thing can be from the second. And if you can show that that difference can be made small enough by calculating it correctly, great. You’ve shown the two things are equal.

Delta and epsilon turn up in these a lot. In the generic proof of this you say you want to show the difference between the thing you can calculate and the thing you want is smaller than epsilon. So you have the thing you can calculate parameterized by delta. Then your problem becomes showing that if delta is small enough, the difference between what you can do and what you want is smaller than epsilon. This is why it’s an appropriately-formed joke to show someone squeezed by a delta and an epsilon. These are the lower-case delta and epsilon, which is why it’s not a triangle on the left there.

Mad scientist cackling at a man being crushed between giant delta and epsilon figure: 'And now, good doctor, we will see how you fit between this delta and this epsilon!' Caption: Soon, soon the calculus teacher would become arbitrarily small.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st of April, 2018. I feel vaguely personally called out by the calculus teacher wearing cargo shorts, tall white socks, and sandals.

For example, suppose you want to know how long the perimeter of an ellipse is. But all you can calculate is the perimeter of a polygon. I would expect to make a proof of it look like this. Give me an epsilon that’s how much error you’ll tolerate between the polygon’s perimeter and the ellipse’s perimeter. I would then try to find, for epsilon, a corresponding delta. And that if the edges of a polygon are never farther than delta from a point on the ellipse, then the perimeter of the polygon and that of the ellipse are less than epsilon away from each other. And that’s Calculus and Real Analysis.

John Zakour and Scott Roberts’s Maria’s Day for the 22nd is the anthropomorphic numerals joke for this week. I’m curious whether the 1 had a serif that could be wrestled or whether the whole number had to be flopped over, as though it were a ruler or a fat noodle.

Maria at her desk challenges a giant number 4 to arm wrestling; she slams its 'arm' down easily. Other numerals flee as she yells out: 'Okay, anyone else wanna take me on? Huh? --- Yeah, didn't think so!' Reality: she's at her desk with a book and some paper and says, "Whew! This math homework was tough --- but I think I got it down.'
John Zakour and Scott Roberts’s Maria’s Day for the 22nd of April, 2018. I’m curious whether Zakour and Roberts deliberately put 2 and 3 to the left, with pain stars indicating they’ve been beaten already, while the bigger numbers are off to the side. Or was it just an arbitrary choice? The numbers are almost in order, left to right, except that the 7’s out of place. So maybe the ordering is just coincidence?

Anthony Blades’s Bewley for the 23rd offers advice for what to do if you’ve not got your homework. This strip’s already been run, and mentioned here. I might drop this from my reading if it turns out the strip is done and I’ve exhausted all the topics it inspires.

Bea: 'Aaaah! I forgot to do my maths homework!' Tonus: 'I did mine.' Bea: 'Can I copy yours?' Tonus: 'Of course you can. I didn't know the answers so I drew a picture of a scary dinosaur.' [ Silent penultimate panel. ] Bea: 'Better than nothing.' Tonus: 'Remember the big teeth. Big teeth make it scary.'
Anthony Blades’s Bewley for the 23rd of April, 2018. Whenever a comic strip with this setup begins I think of the time in geometry class when I realized I hadn’t done any homework and wondered if I could get something done in the time it took papers to be passed up. This in a class of twelve students. No, there was not, even though the teacher started from the other side of the classroom.

Dave Whamond’s Reality Check for the 23rd is designed for the doors of mathematics teachers everywhere. It does incidentally express one of those truths you barely notice: that statisticians and mathematicians don’t seem to be quite in the same field. They’ve got a lot of common interest, certainly. But they’re often separate departments in a college or university. When they do share a department it’s named the Department of Mathematics and Statistics, itself an acknowledgement that they’re not quite the same thing. (Also it seems to me it’s always Mathematics-and-Statistics. If there’s a Department of Statistics-and-Mathematics somewhere I don’t know of it and would be curious.) This has to reflect historical influence. Statistics, for all that it uses the language of mathematics and that logical rigor and ideas about proofs and all, comes from a very practical, applied, even bureaucratic source. It grew out of asking questions about the populations of nations and the reliable manufacture of products. Mathematics, even the mathematics that is about real-world problems, is different. A mathematician might specialize in the equations that describe fluid flows, for example. But it could plausibly be because they have interesting and strange analytical properties. It’d be only incidental that they might also say something enlightening about why the plumbing is stopped up.

[ Clown Statistician vs Clown mathematician. ] The Clown Statistician holds up a pie chart, ready to throw it. The mathematician holds up a pi symbol, ready to throw it. Corner squirrel's comment: 'There's always room for more pi.'
Dave Whamond’s Reality Check for the 23rd of April, 2018. I’m not sure I’ve laughed more at a dumb joke than I have at this in a long while.

Neal Rubin and Rod Whigham’s Gil Thorp for the 24th seems to be setting out the premise for the summer storyline. It’s sabermetrics. Or at least the idea that sports performance can be quantized, measured, and improved. The principle behind that is sound enough. The trick is figuring out what are the right things to measure, and what can be done to improve them. Also another trick is don’t be a high school student trying to lecture classmates about geometry. Seriously. They are not going to thank you. Even if you turn out to be right. I’m not sure how you would have much control of the angle your ball comes off the bat, but that’s probably my inexperience. I’ve learned a lot about how to control a pinball hitting the flipper. I’m not sure I could quantize any of it, but I admit I haven’t made a serious attempt to try either. Also, when you start doing baseball statistics you run a roughly 45% chance of falling into a deep well of calculation and acronyms of up to twelve letters from which you never emerge. Be careful. (This is a new comic strip tag.)

[ With rain delaying (baseball) practice, Kevin Pelwecki expounds on his new favorite subject --- ] Kevin: 'Launch angle! You want the ball coming off the bat at 25 degrees.' Teammate: 'Anyone else notice we're taking math lessons --- from a guy who barely passed geometry?'
Neal Rubin and Rod Whigham’s Gil Thorp for the 24th of April, 2018. Are … both word balloons coming from the same guy? In the last panel there. I understand one guy starting and another closing a thought but that’s usually something you do with an established in-joke that anyone can feed and anyone else can finish. A spontaneous insult like this seems like it only needs the one person, but the word balloon tails are weird if they’re both from the same guy.

Randy Glasbergen’s Glasbergen Cartoons rerun for the 25th feels a little like a slight against me. Well, no matter. Use the things that get you in the mood you need to do well. (Not a new comic strip tag because I’m filing it under ‘Randy Glasbergen’ which I guess I used before?)

Kid with guitar: 'I start every song by counting 1-2-3-4 because it reminds me of math. Math depresses me and that helps me sing the blues.'
Randy Glasbergen’s Glasbergen Cartoons rerun for the 25th of April, 2018. OK, but what’s his guitar plugged in to?

Reading the Comics, February 10, 2018: I Meant To Post This Thursday Edition


Ah, yes, so, in the midst of feeling all proud that I’d gotten my Reading the Comics workflow improved, I went out to do my afternoon chores without posting the essay. I’m embarrassed. But it really only affects me looking at the WordPress Insights page. It publishes this neat little calendar-style grid that highlights the days when someone’s posted and this breaks up the columns. This can only unnerve me. I deserve it.

Tom Thaves’s Frank and Ernest for the 8th of February is about the struggle to understand zero. As often happens, the joke has a lot of truth to it. Zero bundles together several ideas, overlapping but not precisely equal. And part of that is the idea of “nothing”. Which is a subtly elusive concept: to talk about the properties of a thing that does not exist is hard. As adults it’s easy to not notice this anymore. Part’s likely because mastering a concept makes one forget what it took to understand. Part is likely because if you don’t have to ponder whether the “zero” that’s “one less than one” is the same as the “zero” that denotes “what separates the count of thousands from the count of tens in the numeral 2,038” you might not, and just assume you could explain the difference or similarity to someone who has no idea.

John Zakour and Scott Roberts’s Maria’s Day for the 8th has maria and another girl bonding over their hatred of mathematics. Well, at least they’re getting something out of it. The date in the strip leads me to realize this is probably a rerun. I’m not sure just when it’s from.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th proposes a prank based on mathematical use of the word “arbitrarily”. This is a word that appears a lot in analysis, and the strip makes me realize I’m not sure I can give a precise definition. An “arbitrarily large number”, for example, would be any number that’s large enough. But this also makes me realize I’m not sure precisely what joke Weinersmith is going for. I suppose that if someone were to select an arbitrarily large number they might pick 53, or a hundred, or million billion trillion. I suppose Weinersmith’s point is that in ordinary speech an arbitrarily made choice is one selection from all the possible alternatives. In mathematical speech an arbitrarily made choice reflects every possible choice. To speak of an arbitrarily large number is to say that whatever selection is made, we can go on to show this interesting stuff is true. We’d typically like to prove the most generically true thing possible. But picking a single example can be easier to prove. It can certainly be easier to visualize. 53 is probably easier to imagine than “every number 52 or larger”, for example.

Quincy: 'Someday I'm gonna write a book, Gran.' Grandmom: 'Wonderful. Will you dedicate it to me?' Quincy: 'Sure. In fact, if you want, I'll dedicate this math homework to you.'
Ted Shearer’s Quincy for the 16th of December, 1978 and reprinted the 9th of February, 2018. I’m not sure just what mathematics homework Quincy could be doing to inspire him to write a book, but then, it’s not like my mind doesn’t drift while doing mathematics either. And book-writing’s a common enough daydream that most people are too sensible to act on.

Ted Shearer’s Quincy for the 16th of December, 1978 was rerun the 9th of February. It just shows Quincy at work on his mathematics homework, and considering dedicating it to his grandmother. Mathematics books have dedications, just as any other book does. I’m not aware of dedications of proofs or other shorter mathematics works, but there’s likely some. There’s often a note of thanks, usually given to people who’ve made the paper’s writers think harder about the subjects. But I don’t think there’s any reason a paper wouldn’t thank someone who provided “mere” emotional support. I just don’t have examples offhand.

Jef Mallet’s Frazz for the 9th looks like one of those creative-teaching exercises I sometimes see in Mathematics Education Twitter: the teacher gives answers and the students come up with story problems to match. That’s not a bad project. I’m not sure how to grade it, but I haven’t done anything that creative when I’ve taught. I’m sorry I haven’t got more to say about it since the idea seems fun.

Redeye: 'C'mon, Pokey. Time for your lessons. Okay, what do you get when you divide 5,967,342 by 973 ... ?' Pokey: 'A headache!'
Gordon Bess’s Redeye for the 30th of September, 1971 and reprinted the 10th of February, 2018. I realized I didn’t know the father’s name and looked it up, and Wikipedia revealed to me that he’s named Redeye. You know, like the comic strip implies right there in the title. Look, I just read the comics, I can’t be expected to think about the comics too.

Gordon Bess’s Redeye for the 30th of September, 1971 was rerun the 10th. It’s a bit of extremely long division and I don’t blame Pokey for giving up on that problem. Starting from 5,967,342 divided by 973 I’d say, well, that’s about six million divided by a thousand, so the answer should be near six thousand. I don’t think the last digits of 2 and 3 suggest anything about what the final digit should be, if this divides evenly. So the only guidance I have is that my answer ought to be around six thousand and then we have to go into actually working. It turns out that 973 doesn’t go into 5,967,342 a whole number of times, so I sympathize more with Pokey. The answer is a little more than 6,132.9311.

Reading the Comics, February 7, 2018: Not Taking Algebra Too Seriously Edition


There were nearly a dozen mathematically-themed comic strips among what I’d read, and they almost but not quite split mid-week. Better, they include one of my favorite ever mathematics strips from Charles Schulz’s Peanuts.

Jimmy Halto’s Little Iodine for the 4th of December, 1956 was rerun the 2nd of February. Little Iodine seeks out help with what seems to be story problems. The rate problem — “if it takes one man two hours to plow seven acros, how long will it take five men and a horse to … ” — is a kind I remember being particularly baffling. I think it’s the presence of three numbers at once. It seems easy to go from, say, “if you go two miles in ten minutes, how long will it take to go six miles?” to an answer. To go from “if one person working two hours plows seven acres then how long will five men take to clear fourteen acres” to an answer seems like a different kind of problem altogether. It’s a kind of problem for which it’s even wiser than usual to carefully list everything you need.

Iodone, going into a department store. 'Boy, we got tough homework for tomorrow.' At Information: 'If it takes one man two hours to plow seven acres, how long will it take five men and a horse to --- etc' Clerk: 'Wha? Uh ... let me get a pencil. Will you repeat that, please? ... Cipher ... two o carry ... mmm ... times x ... minus ... mmm ... now let me think ... ' NEXT DAY; Teacher: 'Sharkey Shannon, 92, very good, Sharkey. Shalimar Shultz, 94, excellent, Shalimar. Iodine Tremblechin ... zero ... every problem wrong! Iodine ... I just can't understand it ... not one single answer correct!' Iodine, at the Complaint Department: 'Somebody in this store has to write a hundred times 'I will henceforth study harder'!
Jimmy Halto’s Little Iodine for the 2nd of December, 1956 and rerun the 4th of February, 2018. It’s the rare Little Iodine where she doesn’t get her father fired!

Kieran Meehan’s Pros and Cons for the 5th uses a bit of arithmetic. It looks as if it’s meant to be a reminder about following the conclusions of one’s deductive logic. It’s more common to use 1 + 1 equalling 2, or 2 + 2 equalling 4. Maybe 2 times 2 being 4. But then it takes a little turn into numerology, trying to read more meaning into numbers than is wise. (I understand why people should use numerological reasoning, especially given how much mathematicians like to talk up mathematics as descriptions of reality and how older numeral systems used letters to represent words. And that before you consider how many numbers have connotations.)

Judge: 'Members of the jury, before retiring to consider your verdict, I shall give you my summing-up. 3 + 3 = 6. There are six letters in the word 'guilty'. Coincidence? I don't believe in coincidences.'
Kieran Meehan’s Pros and Cons for the 5th of February, 2018. I grant the art is a bit less sophisticated than in Little Iodine. But the choice of two features to run outside the panels and into the white gutters is an interesting one and I’m not sure what Meehan is going for in choosing one word balloon and the judge’s hand to run into the space like that.

Charles Schulz’s Peanuts for the 5th of February reruns the strip from the 8th of February, 1971. And it is some of the best advice about finding the values of x and y, and about approaching algebra, that I have ever encountered.

Trixie: 'Look at all the birds!! I wonder how many there are! Sic, nine, five, 'leven, eight, fwee, two! Only two! It sure looked like there were more!'
Mort Walker and Dik Browne’s Hi and Lois for the 10th of August, 1960 was rerun the 6th of February, 2018. And I do like Trixie’s look of bafflement in the last panel there; it’s more expressive than seems usual for the comic even in its 1960s design.

Mort Walker and Dik Browne’s Hi and Lois for the 10th of August, 1960 was rerun the 6th of February. It’s a counting joke. Babies do have some number sense. At least babies as old as Trixie do, I believe, in that they’re able to detect that something weird is going on when they’re shown, eg, two balls put into a box and four balls coming out. (Also it turns out that stage magicians get called in to help psychologists study just how infants and toddlers understand the world, which is neat.)

John Zakour and Scott Roberts’s Maria’s Day for the 7th is Ms Payne’s disappointed attempt at motivating mathematics. I imagine she’d try going on if it weren’t a comic strip limited to two panels.

Reading the Comics, November 4, 2017: Slow, Small Week Edition


It was a slow week for mathematically-themed comic strips. What I have are meager examples. Small topics to discuss. The end of the week didn’t have anything even under loose standards of being on-topic. Which is fine, since I lost an afternoon of prep time to thunderstorms that rolled through town and knocked out power for hours. Who saw that coming? … If I had, I’d have written more the day before.

Mac King and Bill King’s Magic in a Minute for the 29th of October looks like a word problem. Well, it is a word problem. It looks like a problem about extrapolating a thing (price) from another thing (quantity). Well, it is an extrapolation problem. The fun is in figuring out what quantities are relevant. Now I’ve spoiled the puzzle by explaining it all so.

Olivia Walch’s Imogen Quest for the 30th doesn’t say it’s about a mathematics textbook. But it’s got to be. What other kind of textbook will have at least 28 questions in a section and only give answers to the odd-numbered problems in back? You never see that in your social studies text.

Eric the Circle for the 30th, this one by Dennill, tests how slow a week this was. I guess there’s a geometry joke in Jane Austen? I’ll trust my literate readers to tell me. My doing the world’s most casual search suggests there’s no mention of triangles in Pride and Prejudice. The previous might be the most ridiculously mathematics-nerdy thing I have written in a long while.

Tony Murphy’s It’s All About You for the 31st does some advanced-mathematics name-dropping. In so doing, it’s earned a spot taped to the door of two people in any mathematics department with more than 24 professors across the country. Or will, when they hear there was a gap unification theory joke in the comics. I’m not sure whether Murphy was thinking of anything particular in naming the subject “gap unification theory”. It sounds like a field of mathematical study. But as far as I can tell there’s just one (1) paper written that even says “gap unification theory”. It’s in partition theory. Partition theory is a rich and developed field, which seems surprising considering it’s about breaking up sets of the counting numbers into smaller sets. It seems like a time-waster game. But the game sneaks into everything, so the field turns out to be important. Gap unification, in the paper I can find, is about studying the gaps between these smaller sets.

There’s also a “band-gap unification” problem. I could accept this name being shortened to “gap unification” by people who have to say its name a lot. It’s about the physics of semiconductors, or the chemistry of semiconductors, as you like. The physics or chemistry of them is governed by the energies that electrons can have. Some of these energies are precise levels. Some of these energies are bands, continuums of possible values. When will bands converge? When will they not? Ask a materials science person. Going to say that’s not mathematics? Don’t go looking at the papers.

Whether partition theory or materials since it seems like a weird topic. Maybe Murphy just put together words that sounded mathematical. Maybe he has a friend in the field.

Bill Amend’s FoxTrot Classics for the 1st of November is aiming to be taped up to the high school teacher’s door. It’s easy to show how the square root of two is irrational. Takes a bit longer to show the square root of three is. Turns out all the counting numbers are either perfect squares — 1, 4, 9, 16, and so on — or else have irrational square roots. There’s no whole number with a square root of, like, something-and-three-quarters or something-and-85-117ths. You can show that, easily if tediously, for any particular whole number. What’s it look like to show for all the whole numbers that aren’t perfect squares already? (This strip originally ran the 8th of November, 2006.)

Guy Gilchrist’s Nancy for the 1st does an alphabet soup joke, so like I said, it’s been a slow week around here.

John Zakour and Scott Roberts’s Maria’s Day for the 2nd is really just mathematics being declared hated, so like I said, it’s been a slow week around here.

Reading the Comics, October 12, 2017: Busy Saturday Soon Edition


The week was looking ready to be one where I have my five paragraphs about how something shows off a word problem and that’s it. And then Comic Strip Master Command turned up the flow of comics for Saturday. So, here’s my five paragraphs about something being word problems and we’ll pick up the other half of them soon.

Bill Whitehead’s Free Range for the 10th is an Albert Einstein joke. That’s usually been enough. That it mentions curved space, the exotic geometries that make general relativity so interesting, gives it a little more grounding as a mathematical comic. It’s a bit curious, surely, that curved space strikes people as so absurd. Nobody serious argues whether we live on a curved space, though, not when we see globes and think about shapes that cover a big part of the surface of the Earth. But there is something different about thinking of three-dimensional space as curved; it’s hard to imagine curved around what.

Brian Basset’s Red and Rover started some word problems on the 11th, this time with trains travelling in separate directions. The word problem seemed peculiar, since the trains wouldn’t be 246 miles apart at any whole number of hours. But they will be at a reasonable fraction more than a whole number of hours, so I guess Red has gotten to division with fractions.

Red and Rover are back at it the 12th with basically the same problem. This time it’s with airplanes. Also this time it’s a much worse problem. While you can do the problem still, the numbers are uglier. It’ll be just enough over two hours and ten minutes that I wonder if the numbers got rewritten away from some nicer set. For example, if the planes had been flying at 360 and 540 miles per hour, and the question was when they would be 2,100 miles apart, then you’d have a nice two-and-a-third hours.

'Todd, don't be anxious about your fractions homework! I can make it easy to understand! Let's say you have a whole pie!' 'Oooh! Pie!' 'In order to have three-quarters of the pie, how much of the pie will you give to me?' 'NONE! YOU CAN'T HAVE ANY! THE PIE IS MINE! MINE! ALL MINE!' 'The answer is 'don't use pie in your word problems'.'
Patrick Roberts’s Todd the Dinosaur for the 12th of October, 2017. And I for one am totally convinced the first and second panels were independently drawn and weren’t just a copy-pasted panel with some editing on Todd’s mouth and the woman’s arm. Also the last panel isn’t the first two panels copied and slightly edited again.

Patrick Roberts’s Todd the Dinosaur for the 12th is another in the line of jokes about fraction-teaching going wrong by picking a bad example.

John Zakour and Scott Roberts’s Maria’s Day for the 12th uses mathematics as the iconic worst-possible-case for a pop quiz. I suppose spelling might have done too.

Reading the Comics, August 26, 2017: Dragon Edition


It’s another week where everything I have to talk about comes from GoComics.com. So, no pictures. The Comics Kingdom and the Creators.com strips are harder for non-subscribers to read so I feel better including those pictures. There’s not an overarching theme that I can fit to this week’s strips either, so I’m going to name it for the one that was most visually interesting to me.

Charlie Pondrebarac’s CowTown for the 22nd I just knew was a rerun. It turned up the 26th of August, 2015. Back then I described it as also “every graduate students’ thesis defense anxiety dream”. Now I wonder if I have the possessive apostrophe in the right place there. On reflection, if I have “every” there, then “graduate student” has to be singular. If I dropped the “every” then I could talk about “graduate students” in the plural and be sensible. I guess that’s all for a different blog to answer.

Mike Thompson’s Grand Avenue for the 22nd threatened to get me all cranky again, as Grandmom decided the kids needed to do arithmetic worksheets over the summer. The strip earned bad attention from me a few years ago when a week, maybe more, of the strip was focused on making sure the kids drudged their way through times tables. I grant it’s a true attitude that some people figure what kids need is to do a lot of arithmetic problems so they get better at arithmetic problems. But it’s hard enough to convince someone that arithmetic problems are worth doing, and to make them chores isn’t helping.

John Zakour and Scott Roberts’s Maria’s Day for the 22nd name-drops fractions as a worse challenge than dragon-slaying. I’m including it here for the cool partial picture of the fire-breathing dragon. Also I take a skeptical view of the value of slaying the dragons anyway. Have they given enough time for sanctions to work?

Maria’s Day pops back in the 24th. Needs more dragon-slaying.

Eric the Circle for the 24th, this one by Dennill, gets in here by throwing some casual talk about arcs around. That and π. The given formula looks like nonsense to me. \frac{pi}{180}\cdot 94 - sin 94\deg has parts that make sense. The first part will tell you what radian measure corresponds to 94 degrees, and that’s fine. Mathematicians will tend to look for radian measures rather than degrees for serious work. The sine of 94 degrees they might want to know. Subtracting the two? I don’t see the point. I dare to say this might be a bunch of silliness.

Cathy Law’s Claw for the 25th writes off another Powerball lottery loss as being bad at math and how it’s like algebra. Seeing algebra in lottery tickets is a kind of badness at mathematics, yes. It’s probability, after all. Merely playing can be defended mathematically, though, at least for the extremely large jackpots such as the Powerball had last week. If the payout is around 750 million dollars (as it was) and the chance of winning is about one in 250 million (close enough to true), then the expectation value of playing a ticket is about three dollars. If the ticket costs less than three dollars (and it does; I forget if it’s one or two dollars, but it’s certainly not three), then, on average you could expect to come out slightly ahead. Therefore it makes sense to play.

Except that, of course, it doesn’t make sense to play. On average you’ll lose the cost of the ticket. The on-average long-run you need to expect to come out ahead is millions of tickets deep. The chance of any ticket winning is about one in 250 million. You need to play a couple hundred million times to get a good enough chance of the jackpot for it to really be worth it. Therefore it makes no sense to play.

Mathematical logic therefore fails us: we can justify both playing and not playing. We must study lottery tickets as a different thing. They are (for the purposes of this) entertainment, something for a bit of disposable income. Are they worth the dollar or two per ticket? Did you have other plans for the money that would be more enjoyable? That’s not my ruling to make.

Samson’s Dark Side Of The Horse for the 25th just hurts my feelings. Why the harsh word, Samson? Anyway, it’s playing on the typographic similarity between 0 and O, and how we bunch digits together.

Grouping together three decimal digits as a block is as old, in the Western tradition, as decimal digits are. Leonardo of Pisa, in Liber Abbaci, groups the thousands and millions and thousands of millions and such together. By 1228 he had the idea to note this grouping with an arc above the set of digits, like a tie between notes on a sheet of music. This got cut down, part of the struggle in notation to write as little as possible. Johannes de Sacrobosco in 1256 proposed just putting a dot every third digit. In 1636 Thomas Blundeville put a | mark after every third digit. (I take all this, as ever, from Florian Cajori’s A History Of Mathematical Notations, because it’s got like everything in it.) We eventually settled on separating these stanzas of digits with a , or . mark. But that it should be three digits goes as far back as it could.