So, it has been hot around here. Extremely hot. Like, hot to the point that there’s nothing to do but form hyperbolic statements about the heat. This does not help anyone feel cooler, but it does help us feel like we’re doing something relevant to the weather. The result is that I haven’t had time to think about my comic strip reading. I’ve been very busy trying to pop my head off and leave it in the freezer. This has not worked. Our refrigerator’s dying and we have a replacement scheduled to arrive this week.
The consequence is that I haven’t had time to write my paragraphs about the comic strips that mention mathematical issues of substance. To not be a complete void, though, let me give you the marginalia. These are the comics that mentioned mathematics in some way so slight that I don’t think them worth further discussion. I’ll get to substantial stuff Tuesday. Thank you.
The last burst of mathematically-themed comic strips last week nearly all came the 1st of the month. But the count fell just short. I can only imagine what machinations at Comic Strip Master Command went wrong, that we couldn’t get a full four comics for the same day. Well, life is messy and things will happen.
Stephen Bentley’s Herb and Jamaal for the 1st is a rerun. I discussed it last time I noticed it too. I’d previously taken Herb to be gloating about not using the calculus he’d studied. I may be reading too much into what seems like a smirk in the final panel, though. Could be he’s thinking of the strangeness that something which, at the time, is challenging and difficult and all-consuming turns out to not be such a big deal. Which could be much of high school.
But my first instinct is still to read this as thinking of the “uselessness” of calculus. It betrays the terrible attitude that education is about job training. It should be about letting people be literate in the world’s great thoughts. Mathematics seems to get this attitude a lot, but I’m aware I may feel a confirmation bias. If I had become a French major perhaps I’d pay attention to all the comic strips where someone giggles about how they never use the foreign languages they learned in high school either.
Jon Rosenberg’s Scenes from a Multiverse for the 1st is set in a “Mathpinion City”, showing people arguing about mathematical truths. It seems to me a political commentary, about the absurdity of rejecting true things over perceived insults. The 1+1=3 partisans aren’t even insisting they’re right, just that the other side is obnoxious. Arithmetic here serves as good source for things that can’t be matters of opinion, at least provided we’ve agreed on what’s meant by ideas like ‘1’ and ‘3’.
Mathematics is a human creation, though. What we decide to study, and what concepts we think worth interesting, are matters of opinion. It’s difficult to imagine people who think 1+1=2 a statement so unimportant they don’t care whether it’s true or false. At least not ones who reason anything like we do. But that is our difficulty, not a constraint on what life could think.
Neil Kohney’s The Other End for the 1st has a mathematics cameo. It’s the subject of a quiz so difficult that the kid begs for God’s help sorting it out. The problems all seem to be simplifying expressions. It’s a skill worth having. There are infinitely many ways to write the same quantity. Some of them are more convenient than others. Brief expressions, for example, are often easier to understand. But a longer expression might let us tease out relationships that are good to know. Many analysis proofs end up becoming simpler when you multiply by one — that is, multiplying by and dividing by the same quantity, but using the numerator to reduce one part of the expression and the denominator to reduce some other. Or by adding zero, in which you add and subtract a quantity and use either side to simplify other parts of the expression. So, y’know, just do the work. It’s better that way.
Mark Anderson’s Andertoons for the 2nd is the Mark Anderson’s Andertoons for the week. Wavehead’s learning about invertible operations: that a particular division can undo a multiplication. Or, presumably, that a particular multiplication can undo a division. Fair to wonder why you’d want to do that, though. Most of the operations we use in arithmetic have inverses, or come near it. (There’s one thing you can multiply by which you can’t divide out.) The term used in group theory for this is to say the real numbers are a “field”. This is a ring in which not just does addition have an inverse, but so does multiplication. And the operations commute; dividing by four and multiplying by four is as good as multiplying by for and dividing by four. You can build interesting mathematical structures that don’t have some of these properties. Elementary-school division, where you might describe (say) 26 divided by 4 as “6 with a remainder of 2” is one of them.
There were fewer Pi Day comic strips than I had expected for this year. It’s gotten much more public mention than I had expected a pop-mathematics bit of whimsy might. But I’m still working off last week’s strips; I’ll get to this week’s next week. This makes sense to me, which is as good as making sense at all.
Mark Pett’s Mr Lowe rerun for the 7th is a standardized test joke. Part of the premise of Pett’s strip is that Mister Lowe is a brand-new teacher, which is why he makes mistakes like this problem. (This is touchy to me, as in grad school I hoped to make some spare money selling questions to a standardized testing company. I wasn’t good enough at it, and ultimately didn’t have the time to train up to their needs.) A multiple-choice question needs to clear and concise and to have one clearly best answer. As the given question’s worded, though, I could accept ‘2’ or ’12’ as a correct answer. With a bit of experience Lowe would probably clarify that Tommy and Suzie are getting the same number of apples and that together they should have 20 total.
Then on the 9th Mr Lowe has a joke about cultural bias in standardized tests. It uses an arithmetic problem as the type case. Mathematicians like to think of themselves as working in a universal, culturally independent subject. I suppose it is, but only in ways that aren’t interesting: if you suppose these rules of logic and these axioms and these definitions then these results follow, and it doesn’t matter who does the supposing. But start filtering that by stuff people care about, such as the time it takes for two travelling parties to meet, and you’ve got cultural influence. (Back when this strip was new the idea that a mathematics exam could be culturally biased was a fresh new topic of mockery among people who don’t pay much attention to the problems of teaching but who know what those who do are doing wrong.)
Ralph Hagen’s The Barn for the 8th — a new tag for my comics, by the way — lists a bunch of calculation tools and techniques as “obsolete” items. I’m assuming Rory means that longhand multiplication is obsolete. I’m not sure that it is, but I have an unusual perspective on this.
Thaves’s Frank and Ernest for the 8th is an anthropomorphic-numerals joke. I was annoyed when I first read this because I thought, wait, 97 isn’t a prime number. It is, of course. I have no explanation for my blunder.
Jon Rosenberg’s Scenes from a Multiverse has restarted its run on GoComics. The strip for the 8th is a riff on Venn Diagrams. And, it seems to me, about those logic-bomb problems about sets consisting of sets that don’t contain themselves and the like. You get weird and apparently self-destructive results pondering that stuff. The last time GoComics ran the Scenes from a Multiverse series I did not appreciate right away that there were many continuing stories. There might be follow-ups to this Former Venn Prime Universe story.
Brian Fies’s The Last Mechanical Monster for the 9th has the Mad Scientist, struggling his way into the climax of the story, testing his mind by calculating a Fibonacci Sequence. Whatever keeps you engaged and going. You can build a Fibonacci Sequence from any two starting terms. Each term after the first two is the sum of the previous two. If someone just says “the Fibonacci Sequence” they mean the sequence that starts with 0, 1, or perhaps with 1, 1. (There’s no interesting difference.) Fibonacci Sequences were introduced to the west by Leonardo of Pisa, who did so much to introduce Hindu-Arabic Numerals to a Europe that didn’t know it wanted this stuff. They touch on some fascinating stuff: the probability of not getting two tails in a row of a set number of coin tosses. Chebyshev polynomials. Diophantine equations. They also touch on the Golden Ratio, which isn’t at all important but that people like.
I do not know what’s possessed John Rose, cartoonist for Barney Google and Snuffy Smith — possibly the oldest syndicated comic strip not in perpetual reruns — to decide he needs to mess with my head. So far as I’m aware we haven’t ever even had any interactions. While I’ll own up to snarking about the comic strip here and there, I mean, the guy draws Barney Google and Snuffy Smith. He won’t attract the snark community of, say, Marmaduke, but he knew the job was dangerous when he took it. There’s lots of people who’ve said worse things about the comic than I ever have. He can’t be messing with them all.
Zach Weinersmith’s Saturday Morning Breakfast Cereal gets my attention again for the 10th. There is this famous quotation from Leopold Kronecker, one of the many 19th century German mathematicians who challenged, and set, our ideas of what mathematics is. In debates about what should count as a proof Kronecker said something translated in English to, “God created the integers, all else is the work of man”. He favored proofs that only used finite numbers, and only finitely many operations, and was skeptical of existence proofs. Those are ones that show something with desired properties must exist, without necessarily showing how to find it. Most mathematicians accept existence proofs. If you can show how to find that thing, that’s a constructive proof. Usually mathematicians like those better.
Jon Rosenberg’s Scenes From A Multiverse for the 11th is a fun, simple joke with some complex stuff behind it. It’s riffing on the kind of atheist who wants moral values to come from something in the STEM fields. So here’s a mathematical basis for some moral principles. There are, yes, ethical theories that have, or at least imply having, mathematics behind them. Utilitarianism at least supposes that ethical behavior can be described as measurable and computable quantities. Nobody actually does that except maybe to make video games more exciting. But it’s left with the idea that one could, and hope that this would lead to guidance that doesn’t go horribly wrong.
Greg Evans and Karen Evans’s Luann for the 13th uses mathematics to try building up the villainy of one of the strip’s designated villains. Ann Eiffel, there, uses a heap of arithmetic to make her lingerie sale sound better. This isn’t simply a riff on people not wanting to do arithmetic, although I understand people not wanding to work out what five percent of a purchase of over $200 is. There’s a good deal of weird psychology in getting people to buy things. Merely naming a number, for example, gets people to “anchor” their expectations to it. To speak of a free gift worth $75 makes any purchase below $75 seem more economical. To speak of a chance to win $1,000 prepares people to think they’ve got a thousand dollars coming in, and that they can safely spend under that. It’s amazing stuff to learn about, and it isn’t all built on people being too lazy to figure out what five percent off of $220 would be.
T Lewis and Michael Fry’s Over the Hedge for the 13th uses &infty; along the way to making nonsense out of ice-skating judging. It’s a good way to make a hash of a rating system. Most anything done with infinitely large numbers or infinitely large sets challenges one’s intuition at least. This is part of what Leopold Kronecker was talking about.