Reading the Comics, July 2, 2019: Back On Schedule Edition


I hoped I’d get a Reading the Comics post in for Tuesday, and even managed it. With this I’m all caught up to the syndicated comic strips which, last week, brought up some mathematics topic. I’m open for nominations about what to publish here Thursday. Write in quick.

Hilary Price’s Rhymes With Orange for the 30th is a struggling-student joke. And set in summer school, so the comic can be run the last day of June without standing out to its United States audience. It expresses a common anxiety, about that point when mathematics starts using letters. It superficially seems strange that this change worries students. Students surely had encountered problems where some term in an equation was replaced with a blank space and they were expected to find the missing term. This is the same work as using a letter. Still, there are important differences. First is that a blank line (box, circle, whatever) has connotations of “a thing to be filled in”. A letter seems to carry meaning in to the problem, even if it’s just “x marks the spot”. And a letter, as we use it in English, always stands for the same thing (or at least the same set of things). That ‘x’ may be 7 in one problem and 12 in another seems weird. I mean weird even by the standards of English orthography.

Summer School. Student, as the instructor writes a^2 + b^2 != c^2 on the board: 'Math isn't fair. It's numbers, numbers, numbers, then bam! It's letters.'
Hilary Price’s Rhymes With Orange for the 30th of June, 2019. Essays with some mention of Rhymes With Orange should be at this link.

A letter might represent a number whose value we wish to know; it might represent a number whose value we don’t care about. These are different ideas. We usually fall into a convention where numbers we wish to know are more likely x, y, and z, while those we don’t care about are more likely a, b, and c. But even that’s no reliable rule. And there may be several letters in a single equation. It’s one thing to have a single unknown number to deal with. To have two? Three? I don’t blame people fearing they can’t handle that.

Mark Leiknes’s Cow and Boy for the 30th has Billy and Cow pondering the Prisoner’s Dilemma. This is one of the first examples someone encounters in game theory. Game theory sounds like the most fun part of mathematics. It’s the study of situations in which there’s multiple parties following formal rules which allow for gains or losses. This is an abstract description. It means many things fit a mathematician’s idea of a game.

Billy: 'If we're ever arrested for the same crime we should never rat each other out. If we don't rat, then maybe we both go free. If we both rat, we both go to jail. If one rats, then the other goes to jail. But since we can't trust the interro --- ' Cow: 'BUT BOOGER GNOME STOLE THAT STEREO EQUIPMENT FOR HIS PIZZA BOX HOUSE!' Billy: 'YOU THINK THE COPS ARE GONNA BUY THAT?' Booger Gnome, with the stolen equipment: 'THERE'S NO @$#&* OUTLETS?!'
Mark Leiknes’s Cow and Boy rerun for the 30th of June, 2019. The comic strip is long since ended, but hasn’t quite rerun enough times for me to get tired of it. So essays featuring Cow and Boy appear this link. The gnome is a lawn gnome who came to life and … you know, this was a pretty weird comic and I understand why it didn’t make it in the newspapers. Just roll with it.

The Prisoner’s Dilemma is described well enough by Billy. It’s built on two parties, each — separately and without the ability to coordinate — having to make a choice. Both would be better off, under interrogation, to keep quiet and trust that the cops can’t get anything significant on them. But both have the temptation that if they rat out the other, they’ll get off free while their former partner gets screwed. And knowing that their partner has the same temptation. So what would be best for the two of them requires them both doing the thing that maximizes their individual risk. The implication is unsettling: everyone acting in their own best interest is supposed to produce the best possible result for society. And here, for the society of these two accused, it breaks down entirely.

Jason Poland’s Robbie and Bobby for the 1st is a rerun. I discussed it last time it appeared, in November 2016, which was before I would routinely include the strips under discussion. The strip’s built on wordplay, using the word ‘power’ in its connotations for might and for exponents.

Robbie: 'My opinion letter is really going to make a difference!' Bobby: 'More power to you, Robbie!' Robbie: 'You've been saying that a lot lately ... know what? I *do* feel more powerful! ... Ooh, an exponent!' (A '10' appears over Robbie's typewriter. Bobby grabs it.) Robbie: 'Hey! I earned that!' Bobby: 'You have no clue what I'll do with this power!' Next panel: Bobby's sleeping, with his sleep sound being 'zzzz^{10}'.
Jason Poland’s Robbie and Bobby rerun for the 1st of July, 2019. I think but am not sure that this comic strip has lapsed into eternal reruns. In any case the essays that mention some topic raised by Robbie and Bobby are at this link.

Exponents have been written as numbers in superscript following a base for a long while now. The notation developed over the 17th century. I don’t know why mathematicians settled on superscripts, as opposed to the many other ways a base and an exponent might fit together. It’s a good mnemonic to remember, say, “z raised to the 10th” is z with a raised 10. But I don’t know the etymology of “raised” in a mathematical context well enough. It’s plausible that we say “raised” because that’s what the notation suggests.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 2nd argues for the beauty of mathematics as a use for it. It’s presented in a brutal manner, but saying brutal things to kids is a comic motif with history to it. Well, in an existentialist manner, but that gets pretty brutal quickly.

Kids: 'Will we ever use math?' Teacher: 'Of course! Life is an express train headed for oblivion city, and this proof of Pythagoras' theorem is one more pretty thing to contemplate before you pull into the station.' (The diagram is of a large square, with each leg divided into segments of length a and b; inside is a smaller square, connecting the segments within each of the outer square's edges, with the sides of this inner square length c.) Kid: 'I mean, like, will it get me a job?' Teacher: 'It got me this job conducting your express train!'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 2nd of July, 2019. This one doesn’t appear in every Reading the Comics essay, so you can find my discussions inspired by Saturday Morning Breakfast Cereal at this link.

The proof of the Pythagorean Theorem is one of the very many known to humanity. This one is among the family of proofs that are wordless. At least nearly wordless. You can get from here to a^2 + b^2 = c^2 with very little prompting. If you do need prompting, it’s this: there are two expressions for how much area of the square with sides a-plus-b. One of these expressions uses only terms of a and b. The other expression uses terms of a, b, and c. If this doesn’t get a bit of a grin out of you, don’t worry. There’s, like, 2,037 other proofs we already know about. We might ask whether we need quite so many proofs of the Pythagorean theorem. It doesn’t seem to be under serious question most of the time.


And then a couple comic strips last week just mentioned mathematics. Morrie Turner’s Wee Pals for the 1st of July has the kids trying to understand their mathematics homework. Could have been anything. Mike Thompson’s Grand Avenue for the 5th started a sequence with the kids at Math Camp. The comic is trying quite hard to get me riled up. So far it’s been the kids agreeing that mathematics is the worst, and has left things at that. Hrmph.


Whether or not I have something for Thursday, by Sunday I should have anotherReading the Comics post. It, as well as my back catalogue of these essays, should be at this link. Thanks for worrying about me.

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Reading the Comics, April 5, 2019: The Slow Week Edition


People reading my Reading the Comics post Sunday maybe noticed something. I mean besides my correct, reasonable complaining about the Comics Kingdom redesign. That is that all the comics were from before the 30th of March. That is, none were from the week before the 7th of April. The last full week of March had a lot of comic strips. The first week of April didn’t. So things got bumped a little. Here’s the results. It wasn’t a busy week, not when I filter out the strips that don’t offer much to write about. So now I’m stuck for what to post Thursday.

Jason Poland’s Robbie and Bobby for the 3rd is a Library of Babel comic strip. This is mathematical enough for me. Jorge Luis Borges’s Library is a magnificent representation of some ideas about infinity and probability. I’m surprised to realize I haven’t written an essay specifically about it. I have touched on it, in writing about normal numbers, and about the infinite monkey theorem.

At a tower. Bobby: 'The library of Babel!' Robbie: 'Inside is every book that will ever be written! It may take the rest of our lives to search, but it'll be worth it!' Bobby: 'What? No index?' Robbie: 'The search for meaning has no index.' Bobby (on the phone): 'I just downloaded one.' Robbie: 'It can't have everything. ... Mark Twain vs Frankenstein? Dante in Space? Harry Potter Infinity?' Bobby: 'Yep. All available as e-books too! Wow, Jeff Goldblum does the audio books.' Robbie: 'pfff. Well, forget this place!' (They leave a 'BORING' sign across the library's door.)
Jason Poland’s Robbie and Bobby for the 3rd of April, 2019. I would have sworn that I write more about this strip. But this seems to be the first time I’ve mentioned it since 2017. Well, that and other Robbie and Bobby-based essays are at this link.

The strip explains things well enough. The Library holds every book that will ever be written. In the original story there are some constraints. Particularly, all the books are 410 pages. If you wanted, say, a 600-page book, though, you could find one book with the first 410 pages and another book with the remaining 190 pages and then some filler. The catch, as explained in the story and in the comic strip, is finding them. And there is the problem of finding a ‘correct’ text. Every possible text of the correct length should be in there. So every possible book that might be titled Mark Twain vs Frankenstein, including ones that include neither Mark Twain nor Frankenstein, is there. Which is the one you want to read?

Over a pizza. Reggie: 'Don't let Jughead near the pizza! He always ends up eating half of it!' Jughead, with the cutter: 'Relax! I've divided it into four equal slices! Check it yourself!' Reggie: 'OK, I guess they do look equal.' Archie: 'Except for one thing! There are only three of us!' (Reggie and Archie each have one slice; Jughead has two.)
Henry Scarpelli and Craig Boldman’s Archie for the 4th of April, 2019. Now this strip I’ve written about as recently as October. That appearance, and other Archie strips, are discussed at this link.

Henry Scarpelli and Craig Boldman’s Archie for the 4th features an equal-divisions problem. In principle, it’s easy to divide a pizza (or anything else) equally; that’s what we have fractions for. Making them practical is a bit harder. I do like Jughead’s quick work, though. It’s got the slight-of-hand you expect from stage magic.

Caterpillars in an algebra classroom. On the back of one caterpillar student is a sign, 'Kick^{10} me'.
Scott Hilburn’s The Argyle Sweater for the 4th of April, 2019. And this strip I’ve written about … wait, can I really have gone since early March without mentioning? Huh. Well, so it appears. Essays discussing The Argyle Sweater appear at this link.

Scott Hilburn’s The Argyle Sweater for the 4th takes place in an algebra class. I’m not sure what algebraic principle 7^4 \times 13^6 demonstrates, but it probably came from somewhere. It’s 4,829,210. The exponentials on the blackboard do cue the reader to the real joke, of the sign reading “kick10 me”. I question whether this is really an exponential kicking situation. It seems more like a simple multiplication to me. But it would be harder to make that joke read clearly.

Tony Cochran’s Agnes for the 5th is part of a sequence investigating how magnets work. Agnes and Trout find just … magnet parts inside. This is fair. It’s even mathematics.

Looking over a pile of debris and a hammer on the table. Agnes: 'OK, we smashed a magnet. What do we see?' Trout: 'Uh. Magnet crumbs.' Agnes: 'Me too. I see magnet crumbs.' Trout: 'No gizmos, no gears, no wires. Just dirty black magnet crumbs.' Agnes: 'So what does this tell us about magnet function?' Trout: 'That it's one of God's many mysteries. Let's go eat.'
Tony Cochran’s Agnes for the 5th of April, 2019. And this strip I quite like, but don’t get to discuss enough. My essays featuring Agnes appears at this link.

Thermodynamics classes teach one of the great mathematical physics models. This is about what makes magnets. Magnets are made of … smaller magnets. This seems like question-begging. Ultimately you get down to individual molecules, each of which is very slightly magnetic. When small magnets are lined up in the right way, they can become a strong magnet. When they’re lined up in another way, they can be a weak magnet. Or no magnet at all.

How do they line up? It depends on things, including how the big magnet is made, and how it’s treated. A bit of energy can free molecules to line up, making a stronger magnet out of a weak one. Or it can break up the alignments, turning a strong magnet into a weak one. I’ve had physics instructors explain that you could, in principle, take an iron rod and magnetize it just by hitting it hard enough on the desk. And then demagnetize it by hitting it again. I have never seen one do this, though.

This is more than just a physics model. The mathematics of it is … well, it can be easy enough. A one-dimensional, nearest-neighbor model, lets us describe how materials might turn into magnets or break apart, depending on their temperature. Two- or three-dimensional models, or models that have each small magnet affected by distant neighbors, are harder.


And then there’s the comic strips that didn’t offer much to write about.
Brian Basset’s Red and Rover for the 3rd,
Liniers’s Macanudo for the 5th, Stephen Bentley’s Herb and Jamaal rerun for the 5th, and Gordon Bess’s Redeye rerun for the 5th all idly mention mathematics class, or things brought up in class.

Doug Savage’s Savage Chickens for the 2nd is another more-than-100-percent strip. Richard Thompson’s Richard’s Poor Almanac for the 3rd is a reprint of his Christmas Tree guide including a fir that “no longer inhabits Euclidean space”.

Mike Baldwin’s Cornered for the 31st depicts a common idiom about numbers. Eric the Circle for the 5th, by Rafoliveira, plays on the ∞ symbol.


And that covers the mathematically-themed comic strips from last week. There are more coming, though. I’ll show them on Sunday. Thanks for reading.

Reading the Comics, October 2017: Mathematics Anxiety Edition


Comic Strip Master Command hasn’t had many comics exactly on mathematical points the past week. I’ll make do. There are some that are close enough for me, since I like the comics already. And enough of them circle around people being nervous about doing mathematics that I have a title for this edition.

Tony Cochrane’s Agnes for the 24th talks about math anxiety. It’s not a comic strip that will do anything to resolve anyone’s mathematics anxiety. But it’s funny about its business. Agnes usually is; it’s one of the less-appreciated deeply-bizarre comics out there.

John Atkinson’s Wrong Hands for the 24th might be the anthropomorphic numerals joke for this week. Or it might be the anthropomorphic letters joke. Or something else entirely.

Charles Schulz’s Peanuts for the 24th reruns the comic from the 2nd of November, 1970. It has Sally discovering that multiplication is much easier than she imagined. As it is, she’s not in good shape. But if you accept ‘tooty-two’ as another name for ‘four’ and ‘threety-three’ as another name for ‘nine’, why not? And she might do all right in group theory. In that you can select a bunch of things, called ‘elements’, and describe their multiplication to fit anything you like, provided there’s consistency. There could be a four-forty-four if that seems to answer some question.

Patron of the Halloween Costume Advice booth: 'I want to be a zombie!' Regular character whose name I can't remember and can't find: 'That's a tough one ... we have to find a way to get you into character. Here [ handing a textbook over ] --- sit through one of Miss Barnes's math classes.'
Steve Kelley and Jeff Parker’s Dustin for the 25th of October, 2017. The kid’s premise this week is about advice for maximizing trick-or-treating hauls. So it circles around sabermetrics and the measurement of every possible metric relevant to a situation. It’s a bit baffling to me, since I just do not remember the quality of a costume relating to how much candy I’d gotten. Nor to what I give out, at least once you get past “high school kid not even bothering to dress up”. And even they’ll get a couple pieces although, yeah, if they did anything they’d get the full-size peanut butter cups. (We’re trying to build a reputation here.) What I’m saying is, I don’t see how the amount of candy depends on more than “have a costume” and “spend more time out there”. I mean, are people really withholding the fruit-flavored Tootsie Rolls because some eight-year-old doesn’t have an exciting enough costume? Really?

Steve Kelley and Jeff Parker’s Dustin for the 25th might be tied in to mathematics anxiety. At least it expresses how the thought of mathematics will cause some people to shut down entirely. Shame for them, but I can’t deny it’s so.

Young magician touching the wand to the whiteboard to show 15 divided by 3 is 5. His instructor: 'No relying on the wand --- I want to see how you arrived at the right answer.' (The title panel calls the strip The Tutor, with the tutor saying 'Someday when you're wizened you'll thank me.')
Hilary Price’s Rhymes with Orange for the 26th of October, 2017. The signature also credits Rina Piccolo, late of Six Chix and Tina’s Groove. The latter strip ended in July 2017, and she left the former last year. Maybe she’s picking up some hours part-timing on Rhymes With Orange; her signature’s been on many strips recently. Wikipedia doesn’t have anything relevant to say, and the credit on the web site doesn’t reflect Piccolo’s work, if she is a regular coauthor now.

Hilary Price’s Rhymes with Orange for the 26th is a calculator joke, made explicitly magical. I’m amused but also wonder if those are small wizards or large mushrooms. And it brings up again the question: why do mathematics teachers care about seeing how you got the answer? Who cares, as long as the answer is right? And my answer there is that yeah, sometimes all we care about is the answer. But more often we care about why someone knows the answer is this instead of that. The argument about what makes this answer right — or other answers wrong — should make it possible to tell why. And it often will help inform other problems. Being able to use the work done for one problem to solve others, or better, a whole family of problems, is fantastic. It’s the sort of thing mathematicians naturally try to do.

Jason Poland’s Robbie and Bobby for the 26th is an anthropomorphic geometry joke. And it’s a shape joke I don’t remember seeing, at least not under my Reading the Comics line of jokes. (Maybe I’ve just forgotten). Also, trapezoids: my most popular post of all time ever, even though it’s only got a couple months’ lead on the other perennial favorite, about how many grooves are on a record’s side.

Jeremy pours symbols from his mathematics notebook into a funnel in his head. They pour out his ears. He says 'My study habits are ineffective' to Pierce, who asks, 'Have you tried earplugs?'
Jerry Scott and Jim Borgman’s Zits for the 27th of October, 2017. I understand people who don’t find Zits a particularly strong comic. (My experience is it’s more loved by my parent’s cohort than by mine.) But I will say when Scott and Borgman go for visual metaphor the strip is easily ten times better. I think the cartoonists have some editorial-cartoon experience and they’ll sometimes put it to good use.

Jerry Scott and Jim Borgman’s Zits for the 27th uses mathematics as the emblem of complicated stuff in need of study. It’s a good visual. I have to say Jeremy’s material seems unorganized to start with, though.