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.

Advertisements

Reading the Comics, November 11, 2017: Pictured Comics Edition


And now the other half of last week’s comic strips. It was unusually rich in comics that come from Comics Kingdom or Creators.com, which have limited windows of access and therefore make me feel confident I should include the strips so my comments make any sense.

Rick Kirkman and Jerry Scott’s Baby Blues for the 9th mentions mathematics homework as a resolutely rage-inducing topic. It’s mathematics homework, obviously, or else it wouldn’t be mentioned around here. And even more specifically it’s Common Core mathematics homework. So it always is with attempts to teach subjects better. Especially mathematics, given how little confidence people have in their own mastery. I can’t blame parents for supposing any change to be just malice.

Boxing instructor: 'Now focus, Wanda! Think of something that makes you really angry, and take it out on the [punching] bag!' Wanda: 'HARD WATER SPOTS ON THE GLASSWARE!' She punches the bag hard enough to rip it apart. Instructor: 'Okay then ... ' Wanda: 'If I had pictured Common Core math homework, I could've put that sucker through the wall.'
Rick Kirkman and Jerry Scott’s Baby Blues for the 9th of November, 2017. Again I maybe am showing off my lack of domesticity here, but, really, hard water spots? But I admit I’d like to get the tannin stain out of my clear plastic teapot, so I guess we all have our things. I just don’t feel strongly enough to punch about it. I just want something that I can scrub with.

Bill Amend’s FoxTrot Classics for the 9th is about random numbers. As Jason says, it is hard to generate random numbers. Random numbers are a resource. Having a good source of them makes a lot of computation work. But they’re hard to make. It seems to be a contradiction to create random numbers by an algorithm. There’s reasons we accept pseudorandom numbers, or find quasirandom numbers. This strip originally ran the 16th of November, 2006.

A night scene. Lots of stars. Crazy Eddie: 'The number of stars is beyond my comprehension!' Hagar: 'Mine, too! What comes after five?'
Chris Browne’s Hagar the Horrible for the 10th of November, 2017. Before you go getting all smug about Hagar no grasping numbers beyond ‘five’, consider what a dog’s breakfast English has managed historically to make of ‘hundred’. Thank you.

Chris Browne’s Hagar the Horrible for the 10th is about the numerous. There’s different kinds of limits. There’s the greatest number of things we can count in an instant. There’s a limit to how long a string of digits or symbols we can remember. There’s the biggest number of things we can visualize. And “visualize” is a slippery concept. I think I have a pretty good idea what we mean when we say “a thousand” of something. I could calculate how long it took me to do something a thousand times, or to write a thousand of something. I know that it was at about a thousand words that, last A To Z sequence, I got to feeling I should wrap up any particular essay. But did I see any particular difference between word 999 and word 1,000? No; what I really knew was “about enough paragraphs” and maybe “fills just over two screens in my text editor”. So do I know what a thousand is? Anyway, we all have our limits, acknowledge them or not.

Archie: 'Moose, your math answers are all wrong!' Moose: 'I'll try again'. So ... Moose: 'Better?' Archie: 'Sorry, Moose! They're still wrong! And writing 'More or Less' after after each answer doesn't help!'
Henry Scarpelli and Craig Boldman’s Archie rerun for the 17th of November, 2017. It really reminds you how dumb Moose is given that he’s asking Archie for help with his mathematics. C’mon, you know Dilton Doiley. And this strip is surely a rerun from before Dilton would be too busy with his oyPhone or his drones or any other distraction; what’s he have to do except help Moose out?

Henry Scarpelli and Craig Boldman’s Archie rerun for the 17th is about Moose’s struggle with mathematics. Just writing “more or less” doesn’t fix an erroneous answer, true. But error margins, and estimates of where an answer should be, can be good mathematics. (Part of the Common Core that many parents struggle with is making the estimate of an answer the first step, and a refined answer later. Based on what I see crossing social media, this really offends former engineering majors who miss the value in having an expected approximate answer.) It’s part of how we define limits, and derivatives, and integrals, and all of calculus. But it’s in a more precise way than Moose tries to do.

Teacher: 'Quincy, if you put your hand in your pocket and pulled out 65 cents ... and put your hand in the other pocket and pulled out 35 cents ... what would you have?' Quincy: 'Somebody else's pants!'
Ted Shearer’s Quincy for the 18th of September, 1978 and rerun the 11th of November, 2017. I feel like anytime I mention Quincy here I end up doing a caption about Ted Shearer’s art. But, I mean, look at the mathematics teacher in the second panel there. There’s voice in that face.

Ted Shearer’s Quincy for the 18th of September, 1978 is a story-problem joke. Some of these aren’t complicated strips.

Reading the Comics, August 5, 2017: Lazy Summer Week Edition


It wasn’t like the week wasn’t busy. Comic Strip Master Command sent out as many mathematically-themed comics as I might be able to use. But they were again ones that don’t leave me much to talk about. I’ll try anyway. It was looking like an anthropomorphic-symboles sort of week, too.

Tom Thaves’s Frank and Ernest for the 30th of July is an anthropomorphic-symbols joke. The tick marks used for counting make an appearance and isn’t that enough? Maybe.

Dan Thompson’s Brevity for the 31st is another entry in the anthropomorphic-symbols joke contest. This one sticks to mathematical symbols, so if the Frank and Ernest makes the cut this week so must this one.

Eric the Circle for the 31st, this installment by “T daug”, gives the slightly anthropomorphic geometric figure a joke that at least mentions a radius, and isn’t that enough? What catches my imagination about this panel particularly is that the “fractured radius” is not just a legitimate pun but also resembles a legitimate geometry drawing. Drawing a diameter line is sensible enough. Drawing some other point on the circle and connecting that to the ends of the diameter is also something we might do.

Scott Hilburn’s The Argyle Sweater for the 1st of August is one of the logical mathematics jokes you could make about snakes. The more canonical one runs like this: God in the Garden of Eden makes all the animals and bids them to be fruitful. And God inspects them all and finds rabbits and doves and oxen and fish and fowl all growing in number. All but a pair of snakes. God asks why they haven’t bred and they say they can’t, not without help. What help? They need some thick tree branches chopped down. The bemused God grants them this. God checks back in some time later and finds an abundance of baby snakes in the Garden. But why the delay? “We’re adders,” explain the snakes, “so we need logs to multiply”. This joke absolutely killed them in the mathematics library up to about 1978. I’m told.

John Deering’s Strange Brew for the 1st is a monkeys-at-typewriters joke. It faintly reminds me that I might have pledged to retire mentions of the monkeys-at-typewriters joke. But I don’t remember so I’ll just have to depend on saying I don’t think I retired the monkeys-at-typewriters jokes and trust that someone will tell me if I’m wrong.

Dana Simpson’s Ozy and Millie rerun for the 2nd name-drops multiplication tables as the sort of thing a nerd child wants to know. They may have fit the available word balloon space better than “know how to diagram sentences” would.

Mark Anderson’s Andertoons for the 3rd is the reassuringly normal appearance of Andertoons for this week. It is a geometry class joke about rays, line segments with one point where there’s an end and … a direction where it just doesn’t. And it riffs on the notion of the existence of mathematical things. At least I can see it that way.

Dad: 'How many library books have you read this summer, Hammie?' Hammie: 'About 47.' Zoe: 'HA!' Dad: 'Hammie ... ' Hammie: 'Okay ... two.' Dad: 'Then why did you say 47?' Hammie: 'I was rounding up.' Zoe: 'NOW he understands math!'
Rick Kirkman and Jerry Scott’s Baby Blues for the 5th of August, 2017. Hammie totally blew it by saying “about forty-seven”. Too specific a number to be a plausible lie. “About forty” or “About fifty”, something you can see as the result of rounding off, yes. He needs to know there are rules about how to cheat.

Rick Kirkman and Jerry Scott’s Baby Blues for the 5th is a rounding-up joke that isn’t about herds of 198 cattle.

Stephen Bentley’s Herb and Jamaal for the 5th tosses off a mention of the New Math as something well out of fashion. There are fashions in mathematics, as in all human endeavors. It startles many to learn this.

Reading the Comics, July 30, 2017: Not Really Mathematics edition


It’s been a busy enough week at Comic Strip Master Command that I’ll need to split the results across two essays. Any other week I’d be glad for this, since, hey, free content. But this week it hits a busy time and shouldn’t I have expected that? The odd thing is that the mathematics mentions have been numerous but not exactly deep. So let’s watch as I make something big out of that.

Mark Tatulli’s Heart of the City closed out its “Math Camp” storyline this week. It didn’t end up having much to do with mathematics and was instead about trust and personal responsibility issues. You know, like stories about kids who aren’t learning to believe in themselves and follow their dreams usually are. Since we never saw any real Math Camp activities we don’t get any idea what they were trying to do to interest kids in mathematics, which is a bit of a shame. My guess would be they’d play a lot of the logic-driven puzzles that are fun but that they never get to do in class. The story established that what I thought was an amusement park was instead a fair, so, that might be anywhere Pennsylvania or a couple of other nearby states.

Rick Kirkman and Jerry Scott’s Baby Blues for the 25th sees Hammie have “another” mathematics worksheet accident. Could be any subject, really, but I suppose it would naturally be the one that hey wait a minute, why is he doing mathematics worksheets in late July? How early does their school district come back from summer vacation, anyway?

Hammie 'accidentally' taps a glass of water on his mathematics paper. Then tears it up. Then chews it. Mom: 'Another math worksheet accident?' Hammie: 'Honest, Mom, I think they're cursed!'
Rick Kirkman and Jerry Scott’s Baby Blues for the 25th of July, 2017 Almost as alarming: Hammie is clearly way behind on his “faking plausible excuses” homework. If he doesn’t develop the skills to make a credible reason why he didn’t do something how is he ever going to dodge texts from people too important not to reply to?

Olivia Walch’s Imogen Quest for the 26th uses a spot of mathematics as the emblem for teaching. In this case it’s a bit of physics. And an important bit of physics, too: it’s the time-dependent Schrödinger Equation. This is the one that describes how, if you know the total energy of the system, and the rules that set its potential and kinetic energies, you can work out the function Ψ that describes it. Ψ is a function, and it’s a powerful one. It contains probability distributions: how likely whatever it is you’re modeling is to have a particle in this region, or in that region. How likely it is to have a particle with this much momentum, versus that much momentum. And so on. Each of these we find by applying a function to the function Ψ. It’s heady stuff, and amazing stuff to me. Ψ somehow contains everything we’d like to know. And different functions work like filters that make clear one aspect of that.

Dan Thompson’s Brevity for the 26th is a joke about Sesame Street‘s Count von Count. Also about how we can take people’s natural aptitudes and delights and turn them into sad, droning unpleasantness in the service of corporate overlords. It’s fun.

Steve Sicula’s Home and Away rerun for the 26th is a misplaced Pi Day joke. It originally ran the 22nd of April, but in 2010, before Pi Day was nearly so much a thing.

Doug Savage’s Savage Chickens for the 26th proves something “scientific” by putting numbers into it. Particularly, by putting statistics into it. Understandable impulse. One of the great trends of the past century has been taking the idea that we only understand things when they are measured. And this implies statistics. Everything is unique. Only statistical measurement lets us understand what groups of similar things are like. Does something work better than the alternative? We have to run tests, and see how the something and the alternative work. Are they so similar that the differences between them could plausibly be chance alone? Are they so different that it strains belief that they’re equally effective? It’s one of science’s tools. It’s not everything which makes for science. But it is stuff easy to communicate in one panel.

Neil Kohney’s The Other End for the 26th is really a finance joke. It’s about the ways the finance industry can turn one thing into a dazzling series of trades and derivative trades. But this is a field that mathematics colonized, or that colonized mathematics, over the past generation. Mathematical finance has done a lot to shape ideas of how we might study risk, and probability, and how we might form strategies to use that risk. It’s also done a lot to shape finance. Pretty much any major financial crisis you’ve encountered since about 1990 has been driven by a brilliant new mathematical concept meant to govern risk crashing up against the fact that humans don’t behave the way some model said they should. Nor could they; models are simplified, abstracted concepts that let hard problems be approximated. Every model has its points of failure. Hopefully we’ll learn enough about them that major financial crises can become as rare as, for example, major bridge collapses or major airplane disasters.