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.

Tipping The Toy


My brother phoned to remind me how much more generally nervous I should be about things, as well as to ask my opinion in an utterly pointless dispute he was having with his significant other. The dispute was over no stakes whatsoever and had no consequences of any practical value so I can see why it’d call for an outside expert. It’s more one of physics, but I did major in physics long ago, and it’s easier to treat mathematically anyway, and it was interesting enough that I spent the rest of the night working it out and I’m still not positive I’m unambiguously right. I could probably find out for certain with some simple experiments, but that would be precariously near trying, and so is right out. Let me set up the problem, though, since it’s interesting and should offer room for people to argue I’m completely wrong.

Continue reading “Tipping The Toy”