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.

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Reading the Comics, October 19, 2018: More Short Things Edition


At least, I’d thought the last half of last week’s comics were mostly things I could discuss quickly. Then Frank and Ernest went and sprawled on me. Such will happen.

Before I get to that, I did want to mention that Gregory Taylor’s paneling for votes for the direction his mathematics-inspired serial takes:

You may enjoy; at least, give it a try.

Thaves’s Frank and Ernest for the 18th is a bit of wordplay. There’s something interesting culturally about phrasing “lots of math, but no chemistry”. Algorithms as mathematics makes sense. Much of mathematics is about finding processes to do interesting things. Algorithms, and the mathematics which justifies them, can at least in principle be justified with deductive logic. And we like to think that the universe must make deductive-logical sense. So it is easy to suppose that something mathematical simply must make logical sense.

Frank: 'It didn't go well? That date was selected for you by a sophisticated statistical algorithm.' Ernest: 'Lots of math, but no chemistry.'
Thaves’s Frank and Ernest for the 18th of October, 2018. One might argue this just represents the algorithm not having enough data. That there are aspects to both people which were poorly modelled. Could happen.

Chemistry, though. It’s a metaphor for whatever the difference is between a thing’s roster of components and the effect of the whole. The suggestion is that it is mysterious and unpredictable. It’s an attitude strange to actual chemists, who have a rather good understanding of why most things happen. My suspicion is that this sense of chemistry is old, dating to before we had a good understanding of why chemical bonds work. We have that understanding thanks to quantum mechanics, and its mathematical representations.

But we can still allow for things that happen but aren’t obvious. When we write about “emergent properties” we describe things which are inherent in whatever we talk about. But they only appear when the things are a large enough mass, or interact long enough. Some things become significant only when they have enough chance to be seen.

Zeno: 'Honey, I'd love to, but it's not as if I can traverse infinite regions in finite time!' Caption: 'Fun Fact: Zeno never took out the garbage.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th of October, 2018. I wrote all this text assuming Weinersmith meant Zeno of Elea. It’d be a heck of a thing if he meant Zeno, the Omni-King of the 12 Universes that I’m told is a thing in Dragon Ball. I guess they have different character designs.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th is about mathematicians’ favorite Ancient Greek philosopher they haven’t actually read. (In fairness, Zeno is hard to read, even for those who know the language.) Zeno’s famous for four paradoxes, the most familiar of which is alluded to here. To travel across a space requires travelling across half of it first. But this applies recursively. To travel any distance requires accomplishing infinitely many partial-crossings. How can you do infinitely many things, each of which take more than zero time, in less than an infinitely great time? But we know we do this; so, what aren’t we understanding? A callow young mathematics major would answer: well, pick any tiny interval of time you like. All but a handful of the partial-crossings take less than your tiny interval time. This seems like a sufficient answer and reason to chuckle at philosophers. Fine; an instant has zero time elapse during it. Nothing must move during that instant, then. So when does movement happen, if there is no movement during all the moments of time? Reconciling these two points slows the mathematician down.

Teacher: 'Todd, please come up to the chalkboard and do this fraction problem.' Todd: 'Uh-oh! It's late October, almost November! And hibernation is kicking in! I'll have the answer for ya next spring! Well, see ya!' Teacher: 'Todd! Get up here right now!' Student: 'Teacher, it's not safe to wake a hibernating T-Rex! Especially when I'm the first one he'll see!'
Patrick Roberts’s Todd the Dinosaur for the 19th of October, 2018. I’d imagine he would have a sufficient excuse in his arms not being able to reach the chalkboard, actually.

Patrick Roberts’s Todd the Dinosaur for the 19th mentions fractions. It’s only used to list a kind of mathematics problem a student might feign unconsciousness rather than do. And takes quite little space in the word balloon to describe. It’d be the same joke if Todd were asked to come up and give a ten-minute presentation on the Battle of Bunker Hill.

Penny: 'It says here the Rubik's Cube is still a top-selling gift for kids at Christmas.' Earl: 'Why for kids?? *I* can't even do it!' Burl: 'But it's great for kids. It keeps Timmy busy for hours, even though the poor kid doesn't realize yet that it's impossible to do.
Julie Larson’s The Dinette Set for the 19th of October, 2018. It ran originally the 12th of December, 2007. Among the stray, side, filler jokes, I like best that both Earl and Burl have mugs reading “And Dumber”.

Julie Larson’s The Dinette Set for the 19th mentions the Rubik’s Cube. Sometime I should do a proper essay about its mathematics. Any Rubik’s Cube can be solved in at most 20 moves. And it’s apparently known there are some cube configurations that take at least 20 moves, so, that’s nice to have worked out. But there are many approaches to solving a cube, none of which I am competent to do. Some algorithms are, apparently, easier for people to learn, at the cost of taking more steps. And that’s fine. You should understand something before you try to do it efficiently.

Venn diagram of Content Warning. Bubble A: Violence. Bubble B: Mature Subject Matter. Bubble C: Coarse Language. Intersection of A and B: The Bible. Intersection of B and C: Thanksgiving Dinner. Intersection of C and A: Sports. Intersection of A, B, and C: Life.
John Atkinson’s Wrong Hands for the 19th of October, 2018. So … life is the intersection of Thanksgiving, the Bible, and Sports? … I could see the case for that.

John Atkinson’s Wrong Hands for the 19th is the Venn Diagram joke for the week. Good to have one around.


This and my other Reading the Comics posts are available at this link. The essays mentioning Frank and Ernest should be at this link. For just the Reading the Comics posts with Saturday Morning Breakfast Cereal content try this link. Essays which talk about things raised by Todd the Dinosaur are at this link. Posts that write about The Dinette Set are at this link. And the essays based on Wrong Hands should be at this link. And do please stick around for more of my Fall 2018 Mathematics A-To-Z, with another post due tomorrow that I need to write today.

Reading the Comics, June 29, 2018: Chuckle and Breakfast Cereal Edition


The last half of last week was not entirely the work of Chuckle Brothers and Saturday Morning Breakfast Cereal. It seemed like it, though. Let’s review.

Patrick Roberts’s Todd the Dinosaur for the 28th is a common sort of fear-of-mathematics joke. In this case the fear of doing arithmetic even when it is about something one would really like to know. I think the question got away from Todd, though. If they just wanted to know whether they had enough money, well, they need twelve dollars and have seven. Subtracting seven from twelve is only needed if they want to know how much more they need. Which they should want to know, but wasn’t part of the setup.

Kid: 'Do we have enough money to go to the movie?' Todd: 'Let's see! You ahve four dollars and I have three dollars. That's seven. The movie is twelve dollars for both of us. So twelve take away seven is ... *GASP* Oh no! I accidentally did math!' Kid: 'So?' Todd: 'This is SUMMER!' Kid: 'I don't even know you!'
Patrick Roberts’s Todd the Dinosaur for the 28th of June, 2018. I’m sorry, I don’t know the kid’s name.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 28th uses mathematics as the sine qua non of rocket science. As in, well, the stuff that’s hard and takes some real genius to understand. It’s not clear to me that the equations are actually rocket science. There seem to be a shortage of things in exponentials to look quite right to me. But I can’t zoom in on the art, so, who knows just what might be in there.

Professor-type in front of a class labelled Rocket Science 101: 'Doesn't ANYBODY understand this stuff?'
Brian Boychuk and Ron Boychuk’s The Chuckle Brothers rerun for the 28th of June, 2018. It originally ran the 16th of July, 2009. Relatable.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th is a set theory joke. Or a logic joke, anyway. It refers to some of the mathematics/logic work of Bertrand Russell. Among his work was treating seriously the problems of how to describe things defined in reference to themselves. These have long been a source of paradoxes, sometimes for fun, sometimes for fairy-tale logic, and sometimes to challenge our idea of what we mean by definitions of things. Russell made a strong attempt at describing what we mean when we describe a thing by reference to itself. The iconic example here was the “set of all sets not members of themselves”.

Caption: 'Nobody liked Bertrand Russell's scavenger hunts.' Items to find: 'The list of all lists that do not list themselves. (List here).'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th of June, 2018. Well, among other things, wouldn’t there be infinitely many such lists? Unless this description were enough to describe them all, by being a description of what to do to get you all of them?

Russell started out by trying to find some way to prove Georg Cantor’s theorems about different-sized infinities wrong. He worked out a theory of types, and what kinds of rules you can set about types of things. Most mathematicians these days prefer to solve the paradox with a particular organization of set theory. But Russell’s type theory still has value, particularly as part of the logic behind lambda calculus. This is an approach to organizing relationships between things that can do wonderful things, including in computer programming. It lets one write code that works extremely efficiently and can never be explained to another person, modified, or debugged ever. I may lack the proper training for the uses I’ve made of it.

News anchor: 'In a cruel, bizarre twist of fate, this week's $1 million winning lotto number 579281703 was shared by exactly one million people. In other news ... ' (The person watching the news has a lottery ticket number 579281703.)
Brian Boychuk and Ron Boychuk’s The Chuckle Brothers rerun for the 29th of June, 2018. It originally ran the 17th of July, 2009. You can tell it’s from so long ago because the TV set is pre-HD.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 29th is a lottery joke. It does happen that more than one person wins a drawing; sometimes three or even four people do, for the larger prizes. The chance that there’s a million winners? Frightfully unlikely unless something significant went wrong with the lottery mechanism.

So what are the chances of a million lottery winners? If I’m not mistaken the only way to do this is to work out a binomial distribution. The binomial distribution is good for cases where you have many attempts at doing a thing, where each thing can either succeed or fail, and the likelihood of success or failure is independent of all the other attempts. In this case each lottery ticket is an attempt; it winning is success and it losing is failure. Each ticket has the same chance of winning or losing, and that chance doesn’t depend on how many wins or losses there are. What is that chance? … Well, if each ticket has one chance in a million of winning, and there are a million tickets out there, the chance of every one of them winning is about one-millionth raised to the millionth power. Which is so close to zero it might as well be nothing. … And yet, for all that it’s impossible, there’s not any particular reason it couldn’t happen. It just won’t.

What I Learned This Year. Kid: 'Um ... you can divide a number by 3 if the sum of its digits can be divided by 3.' [ Later ] Frazz: 'So, what'd you learn this year?' Kid: 'Don't go last on what-I-learned-this-year day.'
Jef Mallet’s Frazz for the 29th of June, 2018. Sorry, again, not sure of this kid’s name. The comic is often so good about casually dropping in character names.

Jef Mallet’s Frazz for the 29th is a less dire take on what-you-learned-this-year. In this case it’s trivia, but it’s a neat sort of trivia. Once you understand how it works you can understand how to make all sorts of silly little divisibility rules. The threes rule — and the nines rule — work by the same principle. Suppose you have a three-digit number. Let me call ‘a’ the digit in the hundreds column, ‘b’ the digit in the tens column, and ‘c’ the digit in the ones column. Then the number is equal to 100\cdot a + 10\cdot b + 1\cdot c . And, well, that’s equal to 99\cdot a + 1\cdot a + 9 \cdot b + 1 \cdot b + 1 \cdot c . Which is 99\cdot a + 9 \cdot b + a + b + c . 99 times any whole number is a multiple of 9, and also of 3. 9 times any whole number is a multiple of 9, and also of 3. So whether the original number is divisible by 9, or by 3, depends on whether a + b + c is. And that’s why adding the digits up tells you whether a number is a whole multiple of three.

This has only proven anything for three-digit numbers. But with that proof in mind, you probably can imagine what the proof looks like for two- or four-digit numbers, and would believe there’s one for five- and for 500-digit numbers. Or, for that matter, the proof for an arbitrarily long number. So I’ll skip actually doing that. You can fiddle with it if you want a bit of fun yourself.

Also maybe it’s me, or the kind of person who gets into mathematics. But I find silly little rules like this endearing. It’s a process easy to understand that anyone can do and it tells you something not obvious from when you start. It feels like getting let in on a magic trick. That seems like the sort of thing that endears people to mathematics.

Michael: 'Grandma broke out the math workbooks!' Gabby: 'She does this every summer!' (They hide behind a tree.) Gabby: 'Says she doesn't want us to forget what we learned during the school year.' Michael: 'She has a point. We do need to keep our homework-avoidance skills sharp.'
Mike Thompson’s Grand Avenue for the 29th of June, 2018. At the risk of taking the art too literally: isn’t that tree kind of short to be that fat? Shouldn’t the leaves start higher up?

Mike Thompson’s Grand Avenue for the 29th is trying to pick its fight with me again. I can appreciate someone wanting to avoid kids losing their mathematical skills over summer. It’s just striking how Thompson has consistently portrayed their grandmother as doing this in a horrible, joy-crushing manner.

Greek: 'Why are you the wisest man, Socrates?' Socrates: 'Because I know one thing: that I know nothing.' Greek: 'That's all you know?' Socrates: 'I mean strictly speaking ... ' Greek: 'What about the infinite universe of analytic statements, like if A = A then A = A?' Socrates: 'Okay yeah That stuff. Just that.' Greek: 'Just ALL of math.' (Pause.) Greek: 'Sorry, did I make you sad?' Socrates: 'I can't be certain, but probably.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 29th of June, 2018. I am curious if anyone in the philosophy department would offer an idea which Ancient Greek might be chatting with Socrates here. If Weinersmith had anyone in mind I would guess whichever one has Socrates getting a slave to do a geometry proof. But there’s also … I want to say Parmenides, where the elder scholar whips the young Socrates in straight syllogisms. Again, if anyone specific was in mind and it wasn’t just “another Ancient Greek type”.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 29th gets into a philosophy-of-mathematics problem. Also a pure philosophy problem. It’s a problem of what things you can know independently of experience. There are things it seems as though are true, and that seem independent of the person who is aware of them, and what culture that person comes from. All right. Then how can these things be relevant to the specifics of the universe that we happen to be in just now? If ‘2’ is an abstraction that means something independent of our universe, how can there be two books on the table? There’s something we don’t quite understand yet, and it’s taking our philosophers and mathematicians a long while to work out what that is.


And as ever, if you’d like to see more Reading the Comics posts, please look to this page. For essays with Todd the Dinosaur in them, look here. For essays with the Chuckle Brothers, here you go. For some of the many, many essays with Saturday Morning Breakfast Cereal, follow this link. For more talk about Frazz, look here. And for the Grand Avenue comics, try this link please.

Reading the Comics, March 13, 2018: One Of My Assumptions Is Shaken Edition


I learn, from reading not-yet-dead Usenet group rec.arts.comics.strips, that Rick Stromoski is apparently ending the comic Soup To Nutz. This is sad enough. But worse, GoComics.com has removed all but the current day’s strip from its archives. I had trusted that GoComics.com links were reliable in a way that Comics Kingdom and Creators.com weren’t. Now I learn that maybe I need to include images of the comics I review and discuss here lest my essays become unintelligible in the future? That’s not a good sign. I can do it, mind you. I just haven’t got started. You’ll know when I swing into action.

Norm Feuti, of Retail, still draws Sunday strips for Gil. They’re to start appearing on GoComics.com soon, and I can talk about them from my regular sources after that. But for now I follow the strip on Twitter. And last Sunday he posted this one.

It’s sort of a protesting-the-problem question. It’s also a reaction a lot of people have to “explain how you found the answer” questions. In a sense, yeah, the division shows how the answer was found. But what’s wanted — and what’s actually worth learning — is to explain why you did this calculation. Why, in this case, 216 divided by 8? Why not 216 times 8? Why not 8 divided by 216? Why not 216 minus 8? “How you found your answer” is probably a hard question to make interesting on arithmetic, unfortunately. If you’re doing a long sheet of problems practicing division, it’s not hard to guess that dividing is the answer. And that it’s the big number divided by the small. It can be good training to do blocks of problems that use the same approach, for the same reason it can be good training to focus on any exercise a while. But this does cheat someone of the chance to think about why one does this rather than that.

Patrick Roberts’s Todd the Dinosaur for the 11th has mathematics as the thing Todd’s trying to get out of doing. (I suppose someone could try to argue the Y2K bug was an offshoot of mathematics, on the grounds that computer science has so much to do with mathematics. I wouldn’t want to try defending that, though.) I grant that most fraction-to-decimal conversion problems hit that sweet spot of being dull, tedious, and seemingly pointless. There’s some fun decimal expansions of fractions. The sevenths and the elevenths and 1/243 have charm to them. There’s some kid who’ll become a mathematician because at the right age she was told about \frac{1}{8991} . 3/16th? Eh.

Teacher: 'Who would like to come up here and work this converting-fractions-to-decimals problem on the board? Let's see ... how about you, Todd?' Todd: 'Look out! Y2K! AAAGH! This is terrible! Just terrible! It finally caught up with us! Goodbye, electricity! Goodbye, civilized society!' Todd: 'Nice try, Todd. Y2K never happened!' Todd: 'Uh, yeah, I knew that. I was just saying' that Y2K is the answer to that problem on the board!' Teacher: 'Also a nice try. Now get up here!'
Patrick Roberts’s Todd the Dinosaur for the 11th of March, 2018. I’m not sure that the loss of electricity would actually keep someone from doing chalkboard work, especially if there’s as many windows as we see here to let light in. I mean, yes, there’d be problems after school, but just during school? The end of civilization is not the cure-all people present it as being.

Mark Anderson’s Andertoons for the 11th is the Mark Anderson’s Andertoons for the week. I don’t remember seeing a spinny wheel like this used to introduce probability. It’s a good prop, though. I would believe in a class having it.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 11th is built on the Travelling Salesman Problem. It’s one of the famous unsolved and hard problems of mathematics. Weinersmith’s joke is a nice gag about one way to “solve” the problem, that of making it irrelevant. But even if we didn’t need to get to a collection of places efficiently mathematicians would still like to know good ways to do it. It turns out that finding the shortest (quickest, cheapest, easiest, whatever) route connecting a bunch of places is great problem. You can phrase enormously many problems about doing something as well as possible as a Travelling Salesman Problem. It’s easy conceptually to find the answer: try out all the possibilities and pick the best one. But if there’s more than a handful of cities, there are so many possible routes there’s no checking them all, not before you die of old age. We can do very well finding approximate answers, including by my specialization of Monte Carlo methods. In those you take a guess at an answer. Then make, randomly, a change. You’ll either have made things better or worse. If you’ve made it better, keep the change. If you’ve made it worse, usually you reject the change but sometimes you keep it. And repeat. In surprisingly little time you’ll get a really good answer. Maybe not the best possible, but a great answer for how straightforward setting it up was.

Dan Thompson’s Brevity for the 12th is a Rubik’s Cube joke. There’s not a lot of mathematics to that. But I do admire how Thompson was careful enough to draw a Rubik’s Cube that actually looks like the real article; it’s not just an isometric cube with thick lines partitioning it. Look at the corners of each colored sub-cube. I may be the only reader to notice this but I’m glad Thompson did the work.

Mason Mastroianni’s The Wizard of Id for the 12th gets Sir Rodney in trouble with the King for doing arithmetic. I haven’t read the comments on GoComics.com. I’d like to enter “three” as my guess for how many comments one would have to read before finding the “weapons of math instruction” joke in there.

Jef Mallett’s Frazz for the 13th has mathematics homework given as the thing lost by the time change. It’s just a cameo mention.

Steve Moore’s In The Bleachers for the 13th features a story problem as a test of mental acuity. When the boxer can’t work out what the heck the trains-leaving-Penn-Station problem even means he’s ruled unfit to keep boxing. The question is baffling, though. As put, the second train won’t ever overtake the first. The question: did Moore just slip up? If the first train were going 30 miles per hour and the second 40 there would be a perfectly good, solvable question in this. Or was Moore slipping in an extra joke, making the referee’s question one that sounds like it was given wrong? Don’t know, so I’ll suppose the second.

Reading the Comics, February 17, 2018: Continuing Deluge Month


February’s been a flooding month. Literally (we’re about two blocks away from the Voluntary Evacuation Zone after the rains earlier this week) and figuratively, in Comic Strip Master Command’s suggestions about what I might write. I have started thinking about making a little list of the comics that just say mathematics in some capacity but don’t give me much to talk about. (For example, Bob the Squirrel having a sequence, as it does this week, with a geometry tutor.) But I also know, this is unusually busy this month. The problem will recede without my having to fix anything. One of life’s secrets is learning how to tell when a problem’s that kind.

Patrick Roberts’s Todd the Dinosaur for the 12th just shows off an arithmetic problem — fractions — as the thing that can be put on the board and left for students to do.

Todd: *Sniff sniff* 'Hey! What's that on the floor?' (He follows a trail of beef jerky, eating, until he's at the chalkboard.) Teacher: 'Well, hello, Todd! Say, while you're up there, why don't you do that fractions problem on the board?' Todd: 'Darn you, tasty Slim jims!'
Patrick Roberts’s Todd the Dinosaur for the 12th of February, 2018. I’ll risk infecting you with one of my problems: I look at this particular comic and wonder what happened right before the first panel to lead to this happening.

Ham’s Life on Earth for the 12th has a science-y type giving a formula as “something you should know”. The formula’s gibberish, so don’t worry about it. I got a vibe of it intending to be some formula from statistics, but there’s no good reason for that. I’ve had some statistical distribution problems on my mind lately.

Eric Teitelbaum and Bill Teitelbaum’s Bottomliners for the 12th maybe influenced my thinking. It has a person claiming to be a former statistician, and his estimate of how changing his job’s affected his happiness. Could really be any job that encourages people to measure and quantify things. But “statistician” is a job with strong connotations of being able to quantify happiness. To have that quantity feature a decimal point, too, makes him sound more mathematical and thus, more surely correct. I’d be surprised if “two and a half times” weren’t a more justifiable estimate, given the margin for error on happiness-measurement I have to imagine would be there. (This seems to be the first time I’ve featured Bottomliners at least since I started tagging the comic strips named. Neat.)

Ruben Bolling’s Super-Fun-Pak Comix for the 12th reprinted a panel called The Uncertainty Principal that baffled commenters there. It’s a pun on “Uncertainty Principle”, the surprising quantum mechanics result that there are some kinds of measurements that can’t be taken together with perfect precision. To know precisely where something is destroys one’s ability to measure its momentum. To know the angular momentum along one axis destroys one’s ability to measure it along another. This is a physics result (note that the panel’s signed “Heisenberg”, for the name famously attached to the Uncertainty Principle). But the effect has a mathematical side. The operations that describe finding these incompatible pairs of things are noncommutative; it depends what order you do them in.

We’re familiar enough with noncommutative operations in the real world: to cut a piece of paper and then fold it usually gives something different to folding a piece of paper and then cutting it. To pour batter in a bowl and then put it in the oven has a different outcome than putting batter in the oven and then trying to pour it into the bowl. Nice ordinary familiar mathematics that people learn, like addition and multiplication, do commute. These come with partners that don’t commute, subtraction and division. But I get the sense we don’t think of subtraction and division like that. It’s plain enough that ‘a’ divided by ‘b’ and ‘b’ divided by ‘a’ are such different things that we don’t consider what’s neat about that.

In the ordinary world the Uncertainty Principle’s almost impossible to detect; I’m not sure there’s any macroscopic phenomena that show it off. I mean, that atoms don’t collapse into electrically neutral points within nanoseconds, sure, but that isn’t as compelling as, like, something with a sodium lamp and a diffraction grating and an interference pattern on the wall. The limits of describing certain pairs of properties is about how precisely both quantities can be known, together. For everyday purposes there’s enough uncertainty about, say, the principal’s weight (and thus momentum) that uncertainty in his position won’t be noticeable. There’s reasons it took so long for anyone to suspect this thing existed.

Samson’s Dark Side of the Horse for the 13th uses a spot of arithmetic as the sort of problem coffee helps Horace solve. The answer’s 1.

Mike Baldwin’s Cornered for the 14th is a blackboard-full-of-symbols panel. Well, a whiteboard. It’s another in the line of mathematical proofs of love.

Dana Simpson’s Ozy and Millie rerun for the 14th has the title characters playing “logical fallacy tag”. Ozy is, as Millie says, making an induction argument. In a proper induction argument, you characterize something with some measure of size. Often this is literally a number. You then show that if it’s true that the thing is true for smaller problems than you’re interested in, then it has to also be true for the problem you are interested in. Add to that a proof that it’s true for some small enough problem and you’re done. In this case, Ozy’s specific fallacy is an appeal to probability: all but one of the people playing tag are not it, and therefore, any particular person playing the game isn’t it. That it’s fallacious really stands out when there’s only two people playing.

Ed: 'Only recently, scientists discovered pigeons understand space and time.' Pigeon: 'They never questioned us before. We're waiting for them to ask us about the Grand Unified Theory of Physics next.'
Alex Hallatt’s Arctic Circle for the 16th of February, 2018. As ever, I learn things from doing this! Specifically the names of the penguins which I’d somehow not thought about before. Ed’s the one with a pair of antenna-like feathers on his head. Oscar has the smooth head. Gordo has the set of bumps.

Alex Hallatt’s Arctic Circle for the 16th riffs on the mathematics abilities of birds. Pigeons, in this case. The strip starts from their abilities understanding space and time (which are amazing) and proposes pigeons have some insight into the Grand Unified Theory. Animals have got astounding mathematical abilities, should point out. Don’t underestimate them. (This also seems to be the first time I’ve tagged Arctic Circle which doesn’t seem like it could be right. But I didn’t remember naming the penguins before so maybe I haven’t? Huh. Mind, I only started tagging the comic strip titles a couple months ago.)

Tony Cochrane’s Agnes for the 17th has the title character try bluffing her way out of mathematics homework. Could there be a fundamental flaw in mathematics as we know it? Possibly. It’s hard to prove that any field complicated enough to be interesting is also self-consistent. And there’s a lot of mathematics out there. And mathematics subjects often develop with an explosion of new ideas and then a later generation that cleans them up and fills in logical gaps. Symplectic geometry is, if I’m following the news right, going into one of those cleaning-up phases now. Is it likely to be uncovered by a girl in elementary school? I’m skeptical, and also skeptical that she’d have a replacement system that would be any better. I admire Agnes’s ambition, though.

Mike Baldwin’s Cornered for the 17th plays on the reputation for quantum mechanics as a bunch of mathematically weird, counter-intuitive results. In fairness to the TV program, I’ve had series run longer than I originally planned too.

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, September 1, 2017: Getting Ready For School Edition


In the United States at least it’s the start of the school year. With that, Comic Strip Master Command sent orders to do back-to-school jokes. They may be shallow ones, but they’re enough to fill my need for content. For example:

Bill Amend’s FoxTrot for the 27th of August, a new strip, has Jason fitting his writing tools to the class’s theme. So mathematics gets to write “2” in a complicated way. The mention of a clay tablet and cuneiform is oddly timely, given the current (excessive) hype about that Babylonian tablet of trigonometric values, which just shows how even a nearly-retired cartoonist will get lucky sometimes.

Dan Collins’s Looks Good On Paper for the 27th does a collage of school stuff, with mathematics the leading representative of the teacher-giving-a-lecture sort of class.

Olivia Walch’s Imogen Quest for the 28th uses calculus as the emblem of stuff that would be put on the blackboard and be essential for knowing. It’s legitimate formulas, so far as we get to see, the stuff that would in fact be in class. It’s also got an amusing, to me at least, idea for getting students’ attention onto the blackboard.

Tony Carrillo’s F Minus for the 29th is here to amuse me. I could go on to some excuse about how the sextant would be used for the calculations that tell someone where he is. But really I’m including it because I was amused and I like how detailed a sketch of a sextant Carrillo included here.

Jim Meddick’s Monty for the 29th features the rich obscenity Sedgwick Nuttingham III, also getting ready for school. In this case the summer mathematics tutoring includes some not-really-obvious game dubbed Integer Ball. I confess a lot of attempts to make games out of arithmetic look to me like this: fun to do but useful in practicing skills? But I don’t know what the rules are or what kind of game might be made of the integers here. I should at least hear it out.

Michael Cavna’s Warped for the 30th lists a top ten greatest numbers, spoofing on mindless clickbait. Cavna also, I imagine unintentionally, duplicates an ancient David Letterman Top Ten List. But it’s not like you can expect people to resist the idea of making numbered lists of numbers. Some of us have a hard time stopping.

Todd: 'If I'm gonna get a good job someday, I've decided I'm gonna have to buckle down and get serious with my studies!' 'Good for you, Todd!' 'When I get to Junior High and High School, I'm gonna take stuff like trickanometree, calculatorius and alge-brah! Hee hee! Snicker! Snicker!' 'What?' 'I said Bra! Hee! Hee!' 'Better keep buckling down, bub.'
Patrick Roberts’s Todd the Dinosaur for the 1st of September, 2017. So Paul Dirac introduced to quantum mechanics a mathematical construct known as the ‘braket’. It’s written as a pair of terms, like, < A | B > . These can be separated into pieces, with < A | called the ‘bra’ and | B > the ‘ket’. We’re told in the quantum mechanics class that this was a moment of possibly “innocent” overlap between what’s a convenient mathematical name and, as a piece of women’s clothing, unending amusement to male physics students. I do not know whether that’s so. I don’t see the thrill myself except in the suggestion that great physicists might be aware of women’s clothing.

Patrick Roberts’s Todd the Dinosaur for the 1st of September mentions a bunch of mathematics as serious studies. Also, to an extent, non-serious studies. I don’t remember my childhood well enough to say whether we found that vaguely-defined thrill in the word “algebra”. It seems plausible enough.

Reading the Comics, August 15, 2017: Cake Edition


It was again a week just busy enough that I’m comfortable splitting the Reading The Comments thread into two pieces. It’s also a week that made me think about cake. So, I’m happy with the way last week shaped up, as far as comic strips go. Other stuff could have used a lot of work Let’s read.

Stephen Bentley’s Herb and Jamaal rerun for the 13th depicts “teaching the kids math” by having them divide up a cake fairly. I accept this as a viable way to make kids interested in the problem. Cake-slicing problems are a corner of game theory as it addresses questions we always find interesting. How can a resource be fairly divided? How can it be divided if there is not a trusted authority? How can it be divided if the parties do not trust one another? Why do we not have more cake? The kids seem to be trying to divide the cake by volume, which could be fair. If the cake slice is a small enough wedge they can likely get near enough a perfect split by ordinary measures. If it’s a bigger wedge they’d need calculus to get the answer perfect. It’ll be well-approximated by solids of revolution. But they likely don’t need perfection.

This is assuming the value of the icing side is not held in greater esteem than the bare-cake sides. This is not how I would value the parts of the cake. They’ll need to work something out about that, too.

Mac King and Bill King’s Magic in a Minute for the 13th features a bit of numerical wizardry. That the dates in a three-by-three block in a calendar will add up to nine times the centered date. Why this works is good for a bit of practice in simplifying algebraic expressions. The stunt will be more impressive if you can multiply by nine in your head. I’d do that by taking ten times the given date and then subtracting the original date. I won’t say I’m fond of the idea of subtracting 23 from 230, or 17 from 170. But a skilled performer could do something interesting while trying to do this subtraction. (And if you practice the trick you can get the hang of the … fifteen? … different possible answers.)

Bill Amend’s FoxTrot rerun for the 14th mentions mathematics. Young nerd Jason’s trying to get back into hand-raising form. Arithmetic has considerable advantages as a thing to practice answering teachers. The questions have clear, definitely right answers, that can be worked out or memorized ahead of time, and can be asked in under half a panel’s word balloon space. I deduce the strip first ran the 21st of August, 2006, although that image seems to be broken.

Ed Allison’s Unstrange Phenomena for the 14th suggests changes in the definition of the mile and the gallon to effortlessly improve the fuel economy of cars. As befits Allison’s Dadaist inclinations the numbers don’t work out. As it is, if you defined a New Mile of 7,290 feet (and didn’t change what a foot was) and a New Gallon of 192 fluid ounces (and didn’t change what an old fluid ounce was) then a 20 old-miles-per-old-gallon car would come out to about 21.7 new-miles-per-new-gallon. Commenter Del_Grande points out that if the New Mile were 3,960 feet then the calculation would work out. This inspires in me curiosity. Did Allison figure out the numbers that would work and then make a mistake in the final art? Or did he pick funny-looking numbers and not worry about whether they made sense? No way to tell from here, I suppose. (Allison doesn’t mention ways to get in touch on the comic’s About page and I’ve only got the weakest links into the professional cartoon community.)

Todd the Dinosaur in the playground. 'Kickball, here we come!' Teacher's voice: 'Hold it right there! What is 128 divided by 4?' Todd: 'Long division?' He screams until he wakes. Trent: 'What's wrong?' Todd: 'I dreamed it was the first day of school! And my teacher made me do math ... DURING RECESS!' Trent: 'Stop! That's too scary!'
Patrick Roberts’s Todd the Dinosaur for the 15th of August, 2017. Before you snipe that there’s no room on the teacher’s worksheet for Todd to actually give an answer, remember that it’s an important part of dream-logic that it’s impossible to actually do the commanded task.

Patrick Roberts’s Todd the Dinosaur for the 15th mentions long division as the stuff of nightmares. So it is. I guess MathWorld and Wikipedia endorse calling 128 divided by 4 long division, although I’m not sure I’m comfortable with that. This may be idiosyncratic; I’d thought of long division as where the divisor is two or more digits. A three-digit number divided by a one-digit one doesn’t seem long to me. I’d just think that was division. I’m curious what readers’ experiences have been.

Reading the Comics, March 25, 2017: Slow Week Edition


Slow week around here for mathematically-themed comic strips. These happen. I suspect Comic Strip Master Command is warning me to stop doing two-a-week essays on reacting to comic strips and get back to more original content. Message received. If I can get ahead of some projects Monday and Tuesday we’ll get more going.

Patrick Roberts’s Todd the Dinosaur for the 20th is a typical example of mathematics being something one gets in over one’s head about. Of course it’s fractions. Is there anything in elementary school that’s a clearer example of something with strange-looking rules and processes for some purpose students don’t even know what they are? In middle school and high school we get algebra. In high school there’s trigonometry. In high school and college there’s calculus. In grad school there’s grad school. There’s always something.

Teacher: 'Todd, are you wearing water wings? Why, pray tell?' 'So I can make it to the third grade! We're startin' fractions today and YOU said you had a feeling I was gonna get in over my head.' 'Dang!'
Patrick Roberts’s Todd the Dinosaur for the 20th of March, 2017. I’ll allow the kids-say-the-darndest-things setup for the strip. I’m stuck on wondering just how much good water wings that size could do. Yes, he’s limited by his anatomy but aren’t we all?

Jeff Stahler’s Moderately Confused for the 21st is the usual bad-mathematics-of-politicians joke. It may be a little more on point considering the Future Disgraced Former President it names, but the joke is surely as old as politicians and hits all politicians with the same flimsiness.

John Graziano’s Ripley’s Believe It Or Not for the 22nd names Greek mathematician Pythagoras. That’s close enough to on-point to include here, especially considering what a slow week it’s been. It may not be fair to call Pythagoras a mathematician. My understanding is we don’t know that actually did anything in mathematics, significant or otherwise. His cult attributed any of its individuals’ discoveries to him, and may have busied themselves finding other, unrelated work to credit to their founder. But there’s so much rumor and gossip about Pythagoras that it’s probably not fair to automatically dismiss any claim about him. The beans thing I don’t know about. I would be skeptical of anyone who said they were completely sure.

Vic Lee’s Pardon My Planet for the 23rd is the usual sort of not-understanding-mathematics joke. In this case it’s about percentages, which are good for baffling people who otherwise have a fair grasp on fractions. I wonder if people would be better at percentages if they learned to say “percent” as “out of a hundred” instead. I’m sure everyone who teaches percentages teaches that meaning, but that doesn’t mean the warning communicates.

'OK, then let's compromise. I'll be right most of the time - at least 46 percent of the time. And you can be right whenever there is math involved.'
Vic Lee’s Pardon My Planet for the 23rd of March, 2017. Don’t mind me, I’m busy trying to convince myself the back left leg of that park bench is hidden behind the guy’s leg and not missing altogether and it’s still pretty touch-and-go on that.

Stephan Pastis’s Pearls Before Swine for the 24th jams a bunch of angle puns into its six panels. I think it gets most of the basic set in there.

Samson’s Dark Side Of The Horse for the 25th mentions sudokus, and that’s enough for a slow week like this. I thought Horace was reaching for a calculator in the last panel myself, and was going to say that wouldn’t help any. But then I checked the numbers in the boxes and that made it all better.