Reading the Comics, August 14, 2022: Not Being Wrong Edition

The handful of comic strips I’ve chosen to write about this week include a couple with characters who want to not be wrong. That’s a common impulse among people learning mathematics, that drive to have the right answer.

Will Henry’s Wallace the Brave for the 8th opens the theme, with Rose excited to go to mathematics camp as a way of learning more ways to be right. I imagine everyone feels this appeal of mathematics, arithmetic particularly. If you follow these knowable rules, and avoid calculation errors, you get results that are correct. Not just coincidentally right, but right for all time. It’s a wonderful sense of security, even when you get past that childhood age where so little is in your control.

Will Henry’s Wallace the Brave for the 8th of August, 2022. This and other essays mentioning Wallace the Brave are at this link.

A thing that creates a problem, if you love this too closely, is that much of mathematics builds on approximations. Things we know not to be right, but which we know are not too far wrong. You expect this from numerical mathematics, yes. But it happens in analytic mathematics too. I remember struggling in high school physics, in the modeling a pendulum’s swing. To do this you have to approximate the sine of the angle the pendulum bob with the angle itself. This approximation is quite good, if the angle is small, as you can see from comparing the sine of 0.01 radians to the number 0.01. But I wanted to know when that difference was accounted for, and it never was.

(An alternative interpretation is to treat the path swung by the end of the pendulum as though it were part of a parabola, instead of the section of circle that it really is. A small arc of parabola looks much like a small arc of circle. But there is a difference, not accounted for.)

Nor would it be. A regular trick in analytic mathematics is to show that the thing you want is approximated well enough by a thing you can calculate. And then show that if one takes a limit of the thing you can calculate you make the error infinitesimally small. This is all rigorous and you can in time come to accept it. I hope Rose someday handles the discovery that we get to right answers through wrong-but-useful ones well.

Charles Schulz’s Peanuts Begins for the 8th of August, 2022. It originally ran the 11th of August, 1954. Essays with some mention of Peanuts (or Peanuts Begins) are at this link.

Charles Schulz’s Peanuts Begins for the 8th is one that I have featured here before. It’s built on Lucy not accepting that the answer to a multiplication can be zero, even if it is zero times zero. It’s also built on the mixture of meanings between “zero” and “nothing” and “not existent”. Lucy’s right that zero times zero has to be something, as in a thing with some value. But we also so often use zero to mean “nothing that exists” makes zero a struggle to learn and to work with.

Dan Thompson’s Brevity for the 12th of August, 2022. My various essays with some mention of Brevity should be at this link.

Dan Thompson’s Brevity for the 12th is an anthropomorphic numerals joke, built on the ancient playground pun about why six is afraid of seven. And a bit of wordplay about odd and even numbers on top of that. For this I again offer the followup joke that I first heard a couple of years ago. Why was it that 7 ate 9? Because 7 knows to eat 3-squared meals a day!

Lincoln Pierce’s Big Nate for the 14th of August, 2022. Essays including some topic mentioned in Big Nate should be at this link.

Lincoln Pierce’s Big Nate for the 14th is a baseball statistics joke. Really a sabermetrics joke. Sabermetrics and other fine-grained sports analysis study at the enormous number of games played, and situations within those games. The goal is to find enough similar situations to make estimates about outcomes. This is through what’s called the “frequentist” interpretation of statistics. That is, if this situation has come up a hundred times before, and it’s led to one particular outcome 85 of those times, then there’s an 85 percent chance of that outcome in this situation.

Baseball is well-posed to set up this sort of analysis. The organized game has always demanded the keeping of box scores, close records of what happened in what order. Other sports can have the same techniques applied, though. It’s not likely that Randy has thrown enough pitches to estimate his chance of giving up a walk-off grand slam. But combine all the little league teams there are, and all the seasons they’ve played? That starts to sound plausible. Doesn’t help the feeling that one was scheduled for a win and then it didn’t happen.

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And that’s enough comics for now. All of my Reading the Comics posts should be at this link, and I hope to have another next week. Thanks for reading.

Reading the Comics, August 5, 2017: Lazy Summer Week Edition

It wasn’t like the week wasn’t busy. Comic Strip Master Command sent out as many mathematically-themed comics as I might be able to use. But they were again ones that don’t leave me much to talk about. I’ll try anyway. It was looking like an anthropomorphic-symboles sort of week, too.

Tom Thaves’s Frank and Ernest for the 30th of July is an anthropomorphic-symbols joke. The tick marks used for counting make an appearance and isn’t that enough? Maybe.

Dan Thompson’s Brevity for the 31st is another entry in the anthropomorphic-symbols joke contest. This one sticks to mathematical symbols, so if the Frank and Ernest makes the cut this week so must this one.

Eric the Circle for the 31st, this installment by “T daug”, gives the slightly anthropomorphic geometric figure a joke that at least mentions a radius, and isn’t that enough? What catches my imagination about this panel particularly is that the “fractured radius” is not just a legitimate pun but also resembles a legitimate geometry drawing. Drawing a diameter line is sensible enough. Drawing some other point on the circle and connecting that to the ends of the diameter is also something we might do.

Scott Hilburn’s The Argyle Sweater for the 1st of August is one of the logical mathematics jokes you could make about snakes. The more canonical one runs like this: God in the Garden of Eden makes all the animals and bids them to be fruitful. And God inspects them all and finds rabbits and doves and oxen and fish and fowl all growing in number. All but a pair of snakes. God asks why they haven’t bred and they say they can’t, not without help. What help? They need some thick tree branches chopped down. The bemused God grants them this. God checks back in some time later and finds an abundance of baby snakes in the Garden. But why the delay? “We’re adders,” explain the snakes, “so we need logs to multiply”. This joke absolutely killed them in the mathematics library up to about 1978. I’m told.

John Deering’s Strange Brew for the 1st is a monkeys-at-typewriters joke. It faintly reminds me that I might have pledged to retire mentions of the monkeys-at-typewriters joke. But I don’t remember so I’ll just have to depend on saying I don’t think I retired the monkeys-at-typewriters jokes and trust that someone will tell me if I’m wrong.

Dana Simpson’s Ozy and Millie rerun for the 2nd name-drops multiplication tables as the sort of thing a nerd child wants to know. They may have fit the available word balloon space better than “know how to diagram sentences” would.

Mark Anderson’s Andertoons for the 3rd is the reassuringly normal appearance of Andertoons for this week. It is a geometry class joke about rays, line segments with one point where there’s an end and … a direction where it just doesn’t. And it riffs on the notion of the existence of mathematical things. At least I can see it that way.

Rick Kirkman and Jerry Scott’s Baby Blues for the 5th of August, 2017. Hammie totally blew it by saying “about forty-seven”. Too specific a number to be a plausible lie. “About forty” or “About fifty”, something you can see as the result of rounding off, yes. He needs to know there are rules about how to cheat.

Rick Kirkman and Jerry Scott’s Baby Blues for the 5th is a rounding-up joke that isn’t about herds of 198 cattle.

Stephen Bentley’s Herb and Jamaal for the 5th tosses off a mention of the New Math as something well out of fashion. There are fashions in mathematics, as in all human endeavors. It startles many to learn this.

Reading the Comics, November 26, 2016: What is Pre-Algebra Edition

Here I’m just closing out last week’s mathematically-themed comics. The new week seems to be bringing some more in at a good pace, too. Should have stuff to talk about come Sunday.

Darrin Bell and Theron Heir’s Rudy Park for the 24th brings out the ancient question, why do people need to do mathematics when we have calculators? As befitting a comic strip (and Sadie’s character) the question goes unanswered. But it shows off the understandable confusion people have between mathematics and calculation. Calculation is a fine and necessary thing. And it’s fun to do, within limits. And someone who doesn’t like to calculate probably won’t be a good mathematician. (Or will become one of those master mathematicians who sees ways to avoid calculations in getting to an answer!) But put aside the obviou that we need mathematics to know what calculations to do, or to tell whether a calculation done makes sense. Much of what’s interesting about mathematics isn’t a calculation. Geometry, for an example that people in primary education will know, doesn’t need more than slight bits of calculation. Group theory swipes a few nice ideas from arithmetic and builds its own structure. Knot theory uses polynomials — everything does — but more as a way of naming structures. There aren’t things to do that a calculator would recognize.

Richard Thompson’s Poor Richard’s Almanac for the 25th I include because I’m a fan, and on the grounds that the Summer Reading includes the names of shapes. And I’ve started to notice how often “rhomboid” is used as a funny word. Those who search for the evolution and development of jokes, take heed.

John Atkinson’s Wrong Hands for the 25th is the awaited anthropomorphic-numerals and symbols joke for this past week. I enjoy the first commenter’s suggestion tha they should have stayed in unknown territory.

Rick Kirkman and Jerry Scott’s Baby Blues for the 26th of November, 2016. I suppose Kirkman and Scott know their characters better than I do but isn’t Zoe like nine or ten? Isn’t pre-algebra more a 7th or 8th grade thing? I can’t argue Grandma being post-algebra but I feel like the punch line was written and then retrofitted onto the characters.

Rick Kirkman and Jerry Scott’s Baby Blues for the 26th does a little wordplay built on pre-algebra. I’m not sure that Zoe is quite old enough to take pre-algebra. But I also admit not being quite sure what pre-algebra is. The central idea of (primary school) algebra — that you can do calculations with a number without knowing what the number is — certainly can use some preparatory work. It’s a dazzling idea and needs plenty of introduction. But my dim recollection of taking it was that it was a bit of a subject heap, with some arithmetic, some number theory, some variables, some geometry. It’s all stuff you’ll need once algebra starts. But it is hard to say quickly what belongs in pre-algebra and what doesn’t.

Art Sansom and Chip Sansom’s The Born Loser for the 26th uses two ancient staples of jokes, probabilities and weather forecasting. It’s a hard joke not to make. The prediction for something is that it’s very unlikely, and it happens anyway? We all laugh at people being wrong, which might be our whistling past the graveyard of knowing we will be wrong ourselves. It’s hard to prove that a probability is wrong, though. A fairly tossed die may have only one chance in six of turning up a ‘4’. But there’s no reason to think it won’t, and nothing inherently suspicious in it turning up ‘4’ four times in a row.

We could do it, though. If the die turned up ‘4’ four hundred times in a row we would no longer call it fair. (This even if examination proved the die really was fair after all!) Or if it just turned up a ‘4’ significantly more often than it should; if it turned up two hundred times out of four hundred rolls, say. But one or two events won’t tell us much of anything. Even the unlikely happens sometimes.

Even the impossibly unlikely happens if given enough attempts. If we do not understand that instinctively, we realize it when we ponder that someone wins the lottery most weeks. Presumably the comic’s weather forecaster supposed the chance of snow was so small it could be safely rounded down to zero. But even something with literally zero percent chance of happening might.

Imagine tossing a fair coin. Imagine tossing it infinitely many times. Imagine it coming up tails every single one of those infinitely many times. Impossible: the chance that at least one toss of a fair coin will turn up heads, eventually, is 1. 100 percent. The chance heads never comes up is zero. But why could it not happen? What law of physics or logic would it defy? It challenges our understanding of ideas like “zero” and “probability” and “infinity”. But we’re well-served to test those ideas. They hold surprises for us.

Reading the Comics, June 21, 2015: Blatantly Padded Edition, Part 2

I said yesterday I was padding one mathematics-comics post into two for silly reasons. And I was. But there were enough Sunday comics on point that splitting one entry into two has turned out to be legitimate. Nice how that works out sometimes.

Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. (June 19) uses mathematics as something to heap upon a person until they yield to your argument. It’s a fallacious way to argue, but it does work. Even at a mathematical conference the terror produced by a screen full of symbols can chase follow-up questions away. On the 21st, they present mathematics as a more obviously useful thing. Well, mathematics with a bit of physics.

Nate Frakes’s Break Of Day (June 19) is this week’s anthropomorphic algebra joke.

Niklas Eriksson’s Carpe Diem for the 20th of June, 2015.

Niklas Eriksson’s Carpe Diem (June 20) is captioned “Life at the Quantum Level”. And it’s built on the idea that quantum particles could be in multiple places at once. Whether something can be in two places at once depends on coming up with a clear idea about what you mean by “thing” and “places” and for that matter “at once”; when you try to pin the ideas down they prove to be slippery. But the mathematics of quantum mechanics is fascinating. It cries out for treating things we would like to know about, such as positions and momentums and energies of particles, as distributions instead of fixed values. That is, we know how likely it is a particle is in some region of space compared to how likely it is somewhere else. In statistical mechanics we resort to this because we want to study so many particles, or so many interactions, that it’s impractical to keep track of them all. In quantum mechanics we need to resort to this because it appears this is just how the world works.

(It’s even less on point, but Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 21st of June has a bit of riffing on Schrödinger’s Cat.)

Brian and Ron Boychuk’s Chuckle Brothers (June 20) name-drops algebra as the kind of mathematics kids still living with their parents have trouble with. That’s probably required by the desire to make a joking definition of “aftermath”, so that some specific subject has to be named. And it needs parents to still be watching closely over their kids, something that doesn’t quite fit for college-level classes like Intro to Differential Equations. So algebra, geometry, or trigonometry it must be. I am curious whether algebra reads as the funniest of that set of words, or if it just fits better in the space available. ‘Geometry’ is as long a word as ‘algebra’, but it may not have the same connotation of being an impossibly hard class.

Jimmy Hatlo’s Little Iodine for the 18th of April, 1954, and rerun the 18th of June, 2015.

And from the world of vintage comic strips, Jimmy Hatlo’s Little Iodine (June 21, originally run the 18th of April, 1954) reminds us that anybody can do any amount of arithmetic if it’s something they really want to calculate.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney (June 21) is another strip using the idea of mathematics — and particularly word problems — to signify great intelligence. I suppose it’s easier to recognize the form of a word problem than it is to recognize a good paper on the humanities if you only have two dozen words to show it in.

Juba’s Viivi and Wagner (June 21) is a timely reminder that while sudokus may be fun logic puzzles, they are ultimately the puzzle you decide to make of them.

Reading the Comics, June 11, 2015: Bonus Education Edition

The coming US summer vacation suggests Comic Strip Master Command will slow down production of mathematics-themed comic strips. But they haven’t quite yet. And this week I also found a couple comics that, while not about mathematics, amused me enough that I want to include them anyway. So those bonus strips I’ll run at the end of my regular business here.

Bill Hinds’s Tank McNamara (June 6) does a pi pun. The pithon mathematical-snake idea is fun enough and I’d be interested in a character design. I think the strip’s unjustifiably snotty about tattoos. But comic strips have a strange tendency to get snotty about other forms of art.

A friend happened to mention one problem with tattoos that require straight lines or regular shapes is that human skin has a non-flat Gaussian curvature. Yes, that’s how the friend talks. Gaussian curvature is, well, a measure of how curved a surface is. That sounds obvious enough, but there are surprises: a circular cylinder, such as the label of a can, has the same curvature as a flat sheet of paper. You can see that by how easy it is to wrap a sheet of paper around a can. But a ball hasn’t, and you see that by how you can’t neatly wrap a sheet of paper around a ball without crumpling or tearing the paper. Human skin is kind of cylindrical in many places, but not perfectly so, and it changes as the body moves. So any design that looks good on paper requires some artistic imagination to adapt to the skin.

Bill Amend’s FoxTrot (June 7) sets Jason and Marcus working on their summer tans. It’s a good strip for adding to the cover of a trigonometry test as part of the cheat-sheet.

Dana Simpson’s Phoebe and her Unicorn (June 8) makes what I think is its first appearance in my Reading the Comics series. The strip, as a web comic, had been named Heavenly Nostrils. Then it got the vanishingly rare chance to run as a syndicated newspaper comic strip. And newspaper comics page editors don’t find the word “nostril” too inherently funny to pass up. Thus the more marketable name. After that interesting background I’m sad to say Simpson delivers a bog-standard “kids not understanding fractions” joke. I can’t say much about that.

Ruben Bolling’s Super Fun-Pak Comix (June 10, rerun) is an installment of everyone’s favorite literary device model of infinite probabilities. A Million Monkeys At A Million Typewriters subverts the model. A monkey thinking about the text destroys the randomness that it depends upon. This one’s my favorite of the mathematics strips this time around.

And Dan Thompson’s traditional Brevity appearance is the June 11th strip, an Anthropomorphic Numerals joke combining a traditional schoolyard gag with a pun I didn’t notice the first time I read the panel.

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And now here’s a couple strips that aren’t mathematical but that I just liked too much to ignore. Also this lets Mark Anderson’s Andertoons get back on my page. The June 10th strip is a funny bit of grammar play.

Percy Crosby’s Skippy (June 6, rerun from sometime in 1928) tickles me for its point about what you get at the top and the bottom of the class. Although tutorials and office hours and extracurricular help, and automated teaching tools, do customize things a bit, teaching is ultimately a performance given to an audience. Some will be perfectly in tune with the performance, and some won’t. Audiences are like that.

Reading the Comics, May 9, 2015: Trapezoid Edition

And now I get caught up again, if briefly, to the mathematically-themed comic strips I can find. I’ve dubbed this one the trapezoid edition because one happens to mention the post that will outlive me.

Todd Clark’s Lola (May 4) is a straightforward joke. Monty’s given his chance of passing mathematics and doesn’t understand the prospect is grim.

Joe Martin’s Willy and Ethel for the 4th of May, 2015. The link will likely expire in early June.

Joe Martin’s Willy and Ethel (May 4) shows an astounding feat of mind-reading, or of luck. How amazing it is to draw a number at random from a range depends on many things. It’s less impressive to pick the right number if there are only three possible answers than it is to pick the right number out of ten million possibilities. When we ask someone to pick a number we usually mean a range of the counting numbers. My experience suggests it’s “one to ten” unless some other range is specified. But the other thing affecting how amazing it is is the distribution. There might be ten million possible responses, but if only a few of them are likely then the feat is much less impressive.

The distribution of a random number is the interesting thing about it. The number has some value, yes, and we may not know what it is, but we know how likely it is to be any of the possible values. And good mathematics can be done knowing the distribution of a value of something. The whole field of statistical mechanics is an example of that. James Clerk Maxwell, famous for the equations which describe electromagnetism, used such random variables to explain how the rings of Saturn could exist. It isn’t easy to start solving problems with distributions instead of particular values — I’m not sure I’ve seen a good introduction, and I’d be glad to pass one on if someone can suggest it — but the power it offers is amazing.

Reading the Comics, April 10, 2015: Getting Into The Story Problem Edition

I know it’s been like forever, or four days, since the last time I had a half-dozen or so mathematically themed comic strips to write about, but if Comic Strip Master Command is going to order cartoonists to give me stuff to write about I’m not going to turn them away. Several seemed to me about the struggle to get someone to buy into a story — the thing being asked after in a word problem, perhaps, or about the ways mathematics is worth knowing, or just how the mathematics in a joke’s setup are presented — and how skepticism about these things can turn up. So I’ll declare that the theme of this collection.

Steve Sicula’s Home And Away started a sequence on April 7th about “is math really important?”, with the father trying to argue that it’s so very useful. I’m not sure anyone’s ever really been convinced by the argument that “this is useful, therefore it’s important, therefore it’s interesting”. Lots of things are useful or important while staying fantastically dull to all but a select few souls. I would like to think a better argument for learning mathematics is that it’s beautiful, and astounding, and it allows you to discover new ways of studying the world; it can offer all the joy of any art, even as it has a practical side. Anyway, the sequence goes on for several days, and while I can’t say the arguments get very convincing on any side, they do allow for a little play with the fourth wall that I usually find amusing in comics which don’t do that much.

Reading the Comics, January 17, 2015: Finding Your Place Edition

This week’s collection of mathematics-themed comic strips includes one of the best examples of using mathematics in real life, because it describes how to find your position if you’re lost in, in this case, an uncharted island. I’m only saddened that I couldn’t find a natural way to work in how to use an analog watch as a makeshift compass, so I’m shoehorning it in up here, as well as pointing out that if you don’t have an analog clock to use, you can still approximate it by drawing the hands of the clock on a sheet of paper and using that as a pretend watch, and there is something awesome about using a sheet of paper with the time drawn on it as a way to finding north.

Dave Whamond’s Reality Check (January 12) is a guru-on-the-mountain joke, explaining that the answers to life are in the back of the math book. It’s certainly convention for a mathematics book, at least up through about Intro Differential Equations, to include answers to the problems, or at least a selection of problems, in the back, and on reflection it’s a bit of an odd convention. You don’t see that in, say, a history book even where the questions can be reduced to picking out trivia from the main text. I suppose the math-answers convention reflects an idea that there’s a correct way to go about solving a problem, and therefore, you can check whether you picked the correct way and followed it correctly with no more answer than a printed “15/2” as guide. In this way, I suppose, a mathematics textbook can be self-teaching — at least, the eager student can do some of her own pass/fail grading — which was probably invaluable back in the days when finding a skilled mathematics teacher was so much harder than it is today.