## Reading the Comics, October 6, 2018: Square Root of 144 Edition

And I have three last strips from last week to talk about. For those curious, I have ten comics for this week that I flagged for mention, at least before reading the Saturday GoComics pages. So that will probably be two or three installments next week. It’ll depend how many Saturday GoComics strips raise a point I feel like discussing.

Jim Toomey’s Sherman’s Lagoon for the 5th uses arithmetic as the archetypical homework problem that’s short enough to fit in a panel but also too hard for an adult to do. And, neatly, easy for a computer to do. Were I either shark here I’d have reasoned out the square root of 144 something like this: they’re not getting homework where they’d be asked the square root of something that wasn’t a perfect square. So it’s got to be a whole number. 144 is between 100 and 400, so it’s got to be the square root of something between 10 and 20. 144 is pretty close to 100, so 144’s square root is probably close to 10. The square of 1 is 1, so 11 squared has to be one-hundred-something-and-one. The square of 2 is 4, so 12 squared has to be one-hundred-something-and-four. The square of 3 is 9, so 13 squared has to be one-hundred-something-and-nine. The square of 4 is 16, so 14 squared has to be at least one-hundred-something-and-six. And by then we’re getting pretty far from 10. So the only plausible candidate is 12. Test that out and, what do you know, there it is.

Greg Cravens’s The Buckets for the 6th is a riff on the monkeys-at-keyboards joke. Well, what keeps monkeys-at-typewriters from writing interesting things is that they don’t have any selection. They just produce text to no end, in principle. Picking out characters and words that carry narrative is what makes essayists and playwrights. … That said, I think every instructor has faced the essay that is, somehow, worse than gibberish. The process is to try to find anything that could be credited, even if it’s just including at least one of the words from the topic of the essay, and move briskly on.

Larry Wright’s Motley for the 6th is a riff on the idea tips are impossibly complicated to calculate. And that any mathematics might as well be algebra. My question: what the heck calculation is Debbie describing here? There are different ways to find a 15 percent tip. One two-step one is to divide the bill by ten, which is easy and gets you 10 percent. Then divide that by two, which is not-hard, and gets you 5 percent. Add together the 10 percent and 5 percent and you get 15 percent. A one-step method is to just divide by six. This gets you a bit under 17 percent, but that’s close enough. It just requires an ability to divide by six.

There’s other ways to go about it, surely. There are many ways to do any calculation you like. Some of them have the advantages of requiring fewer steps. Some require more steps, but hopefully easier steps. Debbie is, obviously, just describing a nonsensically complicated calculation, to fit the needs of the joke. I’m just trying to think of what a plausible process would lead into the first panel and still get the right answer.

My many Reading the Comics posts are at this link. Essays which mention Sherman’s Lagoon should be at this link. Other essays with The Buckets should appear at this link. And other essays discussing Motley Classics should be here.

## Reading the Comics, June 23, 2018: Big Duck Energy Edition

I didn’t have even some good nonsense for this edition’s title and it’s a day late already. And that for only having a couple of comics, most of them reruns. And then this came across my timeline:

Please let it not be a big milkshake duck. I can’t take it if it is.

Larry Wright’s Motley for the 21st uses mathematics as emblem of impossibly complicated stuff to know. I’m interested to see that biochemistry was also called in to represent something that needs incredible brainpower to know things that can be expressed in one panel. Another free little question: what might “2,368 to the sixth power times pi” be an answer to? The obvious answer to me is “what’s the area of a circle of radius 2,368 to the third power”. That seems like a bad quiz-show question to me, though. It tests a legitimate bit of trivia, but the radius is such an ugly number. There are some other obvious questions that might fit, like “what is the circumference of a circle of radius [ or diameter ] of (ugly number here)?” Or “what is the volume of a circle of radius (similarly ugly number here)?” But the radius (or diameter) of those surfaces would have to be really nasty numbers, ones with radicals of 2,368 — itself no charming number — in it.

And “2,368 to the sixth power times pi” is the answer to infinitely many questions. The challenge is finding one that’s plausible as a quiz-show question. That is it should test something that’s reasonable for a lay person to know, and to calculate while on stage, without pen or paper or much time to reflect. Tough set of constraints, especially to get that 2,368 in there. The sixth power isn’t so easy either.

Well, the biochemistry people don’t have an easy time thinking of a problem to match Debbie’s answer either. “Hydro- ” and “mono- ” are plausible enough prefixes, but as far as I know there’s no “nucleatic acid” to have some modified variant. Wright might have been thinking of nucleic acid, but as far as I know there’s no mononucleic acid, much less hydromononucleic acid. But, yes, that’s hardly a strike against the premise of the comic. It’s just nitpicking.

Charlie Pondrebarac’s CowTown for the 22nd is on at least its third appearance since I started reading the comics for the mathematics stuff regularly. I covered it in June 2016 and also in August 2015. This suggests a weird rerun cycle for the comic. Popping out of Jim Smith’s mouth is the null symbol, which represents a set that hasn’t got any elements. That set is known as the null set. Every set, including the null set, contains a null set. This fact makes set theory a good bit easier than it otherwise would be. That’s peculiar, considering that it is literally nothing. But everything one might want to say about “nothing” is peculiar. That doesn’t make it dispensable.

Julie Larson’s Dinette Set for the 22nd sees the Penny family’s adults bemoaning the calculator their kid needs for middle school. I admit feeling terror at being expected to buy a hundred-dollar calculator for school. But I also had one (less expensive) when I was in high school. It saves a lot of boring routine work. And it allows for playful discoveries about arithmetic. Some of them are cute trivialities, such as finding the Golden Ratio and similar quirks. And a calculator does do essentially the work that a slide rule might, albeit more quickly and with more digits of precision. It can’t help telling you what to calculate or why, but it can take the burden out of getting the calculation done. Still, a hundred bucks. Wow.

Tony Carrillo’s F Minus for the 23rd puts out the breaking of a rule of arithmetic as a whimsical, inexplicable event. A moment of two plus two equalling five, whatever it might do for the structure of the universe, would be awfully interesting for the philosophy of mathematics. Given what we ordinarily think we mean by ‘two’ and ‘plus’ and ‘equals’ and ‘five’ that just can’t happen. And what would it mean for two plus to to equal five for a few moments? Mathematicians often think about the weird fact that mathematical structures — crafted from definitions and logic — describe the real world stunningly well. Would this two plus two equalling five be something that was observed in the real world, and checked against definitions that suddenly allowed this? Would this be finding a chain of reasoning that supported saying two plus two equalled five, only to find a few minutes later that a proof everyone was satisfied with was now clearly wrong?

That’s a particularly chilling prospect, if you’re in the right mood. We like to think mathematical proofs are absolute and irrefutable, things which are known to be true regardless of who knows them, or what state they’re in, or anything. And perhaps they are. They seem to come as near as mortals can to seeing Platonic forms. (My understanding is that mathematical constructs are not Platonic forms, at least in Plato’s view of things. But they are closer to being forms than, say, apples put on a table for the counting would be.) But what we actually know is whether we, fallible beings comprised of meat that thinks, are satisfied that we’ve seen a proof. We can be fooled. We can think something is satisfactory because we haven’t noticed an implication that’s obviously wrong or contradictory. Or because we’re tired and are feeling compliant. Or because we ate something that’s distracting us before we fully understand an argument. We may have a good idea of what a satisfactory logical proof would be. But stare at the idea hard enough and we realize we might never actually know one.

If you’d like to see more Reading the Comics posts, you can find them at this link. If you’re interested in the individual comics, here you go. My essays tagged with CowTown are here. Essays tagged Dinette Set are at this link. The essays that mention F Minus since I started adding strip tags are here. And this link holds the Motley comics.

Although the hyperbolic cosine is interesting and I could go on about it.

Eric the Circle for the 18th of June is a bit of geometric wordplay for the week. A secant is — well, many things. One of the important things is it’s a line that cuts across a circle. It intersects the circle in two points. This is as opposed to a tangent, which touch it in one. Or missing it altogether, which I think hasn’t got any special name. “Secant” also appears as one of the six common trig functions out there.

In value the secant of an angle is just the reciprocal of the cosine of that angle. Where the cosine is never smaller than -1 nor larger than 1, the secant is always either greater than 1 or smaller than -1. It’s a useful function to have by name. We can write “the secant of angle θ” as $sec(\theta)$. The otherwise sensible-looking $\cos^{-1}(\theta)$ is unavailable, because we use that to mean “the angle whose cosine is θ”. We need to express that idea, the “arc-cosine” or “inverse cosine”, quite a bit too. And $\cos(\theta)^{-1}$ would look like we wanted the cosine of one divided by θ. Ultimately, we have a lot of ideas we’d like to write down, and only so many convenient quick shorthand ways to write them. And by using secant as its own function we can let the arc-cosine have a convenient shorthand symbol. These symbols are a point where you see the messy, human, evolutionary nature of mathematical symbols at work.

We can understand the cosine of an angle θ by imagining a right triangle with hypotenuse of length 1. Set that so the hypotenuse makes angle θ with respect to the x-axis. Then the opposite leg of that right triangle will be the cosine of θ away from the origin. The secant, now, that works differently. Again here imagine a right triangle, but this time one of the legs has length 1. And that leg is at an angle θ with respect to the x-axis. Then the far leg of that right triangle is going to cross the x-axis. And it’ll do that at a point that’s the secant of θ away from the origin.

Larry Wright’s Motley Classics for the 19th speaks of algebra as the way to explain any sufficiently complicated thing. Algebra’s probably not the right tool to analyze a soap opera, or any drama really. The interactions of characters are probably more a matter for graph theory. That’s the field that studies groups of things and the links between them. Occasionally you’ll see analyses of, say, which characters on some complicated science fiction show spend time with each other and which ones don’t. I’m not aware of any that were done on soap operas proper. I suspect most mathematics-oriented nerds view the soaps as beneath their study. But most soap operas do produce a lot of show to watch, and to summarize; I can’t blame them for taking a smaller, easier-to-summarize data set to study. (Also I’m not sure any of these graphs reveal anything more enlightening than, “Huh, really thought The Doctor met Winston Churchill more often than that”.)

Olivia Jaimes’s Nancy for the 19th is a joke on getting students motivated to do mathematics. Set a problem whose interest people see and they can do wonderful things.

Dave Whamond’s Reality Check for the 19th is our Venn Diagram strip for the week. I say the real punch line is the squirrel’s, though. Properly, yes, the Venn Diagram with the two having nothing in common should still have them overlap in space. There should be a signifier inside that there’s nothing in common, such as the null symbol or an x’d out intersection. But not overlapping at all is so commonly used that it might as well be standard.

Teresa Bullitt’s Frog Applause for the 21st uses a thought balloon full of mathematical symbols as icon for far too much deep thinking to understand. I would like to give my opinion about the meaningfulness of the expressions. But they’re too small for me to make out, and GoComics doesn’t allow for zooming in on their comics anymore. I looks like it’s drawn from some real problem, based on the orderliness of it all. But I have no good reason to believe that.

If you’d like more of these Reading the Comics posts, you can find them in reverse chronological order at this link. If you’re interested in the comics mentioned particularly here, Eric the Circle strips are here. Frog Applause comics are on that link. Motley strips are on that link. Nancy comics are on that page. And And Reality Check strips are here.

## Reading the Comics, December 30, 2017: Looking To 2018 Edition

The last full week of 2017 was also a slow one for mathematically-themed comic strips. You can tell by how many bits of marginally relevant stuff I include. In this case, it also includes a couple that just mention the current or the upcoming year. So you’ve been warned.

Mac King and Bill King’s Magic in a Minute activity for the 24th is a logic puzzle. I’m not sure there’s deep mathematics to it, but it’s some fun to reason out.

John Graziano’s Ripley’s Believe It Or Not for the 24th mentions the bit of recreational group theory that normal people know, the Rubik’s Cube. The group theory comes in from rotations: you can take rows or columns on the cube and turn them, a quarter or a half or a three-quarters turn. Which rows you turn, and which ways you turn them, form a group. So it’s a toy that inspires deep questions. Who wouldn’t like to know in how few moves a cube could be solved? We know there are at least some puzzles that take 18 moves to solve. (You can calculate the number of different cube arrangements there are, and how many arrangements you could make by shuffling a cube around with 17 moves. There’s more possible arrangements than there are ones you can get to in 17 moves; therefore, there must be at least one arrangement that takes 18 moves to solve.) A 2010 computer-assisted proof by Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge showed that at most 20 face turns are needed for every possible cube to be solved. I don’t know if there’s been any success figuring out whether 19 or even 18 is necessarily enough.

Bill Griffith’s Zippy the Pinhead for the 26th just mentions algebra as a thing that Griffith can’t really remember, even in one of his frequent nostalgic fugues. I don’t know that Zippy’s line about the fifth dimension is meant to refer to geometry. It might refer to the band, but that would be a bit odd. Yes, I know, Zippy the Pinhead always speaks oddly, but in these nostalgic fugue strips he usually provides some narrative counterpoint.

Larry Wright’s Motley Classics for the 26th originally ran in 1986. I mention this because it makes the odd dialogue of getting “a new math program” a touch less odd. I confess I’m not sure what the kid even got. An educational game? Something for numerical computing? The coal-fired, gear-driven version of Mathematica that existed in the 1980s? It’s a mystery, it is.

Ryan Pagelow’s Buni for the 27th is really a calendar joke. It seems to qualify as an anthropomorphic numerals joke, though. It’s not a rare sentiment either.

Jef Mallett’s Frazz for the 29th is similarly a calendar joke. It does play on 2017 being a prime number, a fact that doesn’t really mean much besides reassuring us that it’s not a leap year. I’m not sure just what’s meant by saying it won’t repeat for another 2017 years, at least that wouldn’t be just as true for (say) 2015 or 2019. But as Frazz points out, we do cling to anything that floats in times like these.

## Reading the Comics, May 31, 2017: Feast Week Edition

You know we’re getting near the end of the (United States) school year when Comic Strip Master Command orders everyone to clear out their mathematics jokes. I’m assuming that’s what happened here. Or else a lot of cartoonists had word problems on their minds eight weeks ago. Also eight weeks ago plus whenever they originally drew the comics, for those that are deep in reruns. It was busy enough to split this week’s load into two pieces and might have been worth splitting into three, if I thought I had publishing dates free for all that.

Larry Wright’s Motley Classics for the 28th of May, a rerun from 1989, is a joke about using algebra. Occasionally mathematicians try to use the the ability of people to catch things in midair as evidence of the sorts of differential equations solution that we all can do, if imperfectly, in our heads. But I’m not aware of evidence that anyone does anything that sophisticated. I would be stunned if we didn’t really work by a process of making a guess of where the thing should be and refining it as time allows, with experience helping us make better guesses. There’s good stuff to learn in modeling how to catch stuff, though.

Also I want to say some very good words about Jantze’s graphical design. The mock textbook cover for the title panel on the left is so spot-on for a particular era in mathematics textbooks it’s uncanny. The all-caps Helvetica, the use of two slightly different tans, the minimalist cover art … I know shelves stuffed full in the university mathematics library where every book looks like that. Plus, “[Mathematics Thing] And Their Applications” is one of the roughly four standard approved mathematics book titles. He paid good attention to his references.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 28th deploys a big old whiteboard full of equations for the “secret” of the universe. This makes a neat change from finding the “meaning” of the universe, or of life. The equations themselves look mostly like gibberish to me, but Wise and Aldrich make good uses of their symbols. The symbol $\vec{B}$, a vector-valued quantity named B, turns up a lot. This symbol we often use to represent magnetic flux. The B without a little arrow above it would represent the intensity of the magnetic field. Similarly an $\vec{H}$ turns up. This we often use for magnetic field strength. While I didn’t spot a $\vec{E}$ — electric field — which would be the natural partner to all this, there are plenty of bare E symbols. Those would represent electric potential. And many of the other symbols are what would naturally turn up if you were trying to model how something is tossed around by a magnetic field. Q, for example, is often the electric charge. ω is a common symbol for how fast an electromagnetic wave oscillates. (It’s not the frequency, but it’s related to the frequency.) The uses of symbols is consistent enough, in fact, I wonder if Wise and Aldrich did use a legitimate sprawl of equations and I’m missing the referenced problem.

John Graziano’s Ripley’s Believe It Or Not for the 28th mentions how many symbols are needed to write out the numbers from 1 to 100. Is this properly mathematics? … Oh, who knows. It’s just neat to know.

Mark O’Hare’s Citizen Dog rerun for the 29th has the dog Fergus struggle against a word problem. Ordinary setup and everything, but I love the way O’Hare draws Fergus in that outfit and thinking hard.

The Eric the Circle rerun for the 29th by ACE10203040 is a mistimed Pi Day joke.

Bill Amend’s FoxTrot Classicfor the 31st, a rerun from the 7th of June, 2006, shows the conflation of “genius” and “good at mathematics” in everyday use. Amend has picked a quixotic but in-character thing for Jason Fox to try doing. Euclid’s Fifth Postulate is one of the classic obsessions of mathematicians throughout history. Euclid admitted the thing — a confusing-reading mess of propositions — as a postulate because … well, there’s interesting geometry you can’t do without it, and there doesn’t seem any way to prove it from the rest of his geometric postulates. So it must be assumed to be true.

There isn’t a way to prove it from the rest of the geometric postulates, but it took mathematicians over two thousand years of work at that to be convinced of the fact. But I know I went through a time of wanting to try finding a proof myself. It was a mercifully short-lived time that ended in my humbly understanding that as smart as I figured I was, I wasn’t that smart. We can suppose Euclid’s Fifth Postulate to be false and get interesting geometries out of that, particularly the geometries of the surface of the sphere, and the geometry of general relativity. Jason will surely sometime learn.