So one little secret of my Reading the Comics posts is I haven’t been writing them in a way that makes sense to me. To me, I should take each day’s sufficiently relevant comics, describe them in a paragraph or two, and then have a nice pile of text all ready for the posting Sunday and, if need be, later. I haven’t been doing that. I’ve let links pile up until Friday or Saturday, and then try to process them all, and if you’ve ever wondered why the first comic of the week gets 400 words about some subtlety while the last gets “this is a comic that exists”, there you go. This time around, let me try doing each day’s strips per day and see how that messes things up.
Jef Mallett’s Frazz for the 14th of January is another iteration of the “when will we ever use mathematics” complaint. The answer of “you’ll use it on the test” is unsatisfactory. But somehow, the answer of “you’ll use it to think deeply about something you had never considered before” also doesn’t satisfy. Anyway I’d like to see the idea that education is job-training abolished; I think it should be about making a person conversant with the history of human thought. That can’t be done perfectly, and we might ask whether factoring 32 is that important a piece, but it should certainly be striven for.
Ham’s Life on Earth for the 14th is a Gary Larsonesque riff on that great moment of calculus and physics history, Newton’s supposition that gravity has to follow a universally true law. I’m not sure this would have made my cut if I reviewed a week’s worth of strips at a time. Hm.
Mason Mastroianni’s B.C. for the 15th is a joke about story problem construction, and how the numbers in a story problem might be obvious nonsense. It’s also a cheap shot at animal hoarders, I suppose, but that falls outside my territory here.
Anthony Blades’s Bewley rerun for the 15th riffs on the natural number sense we all have. And we do have a number sense, remarkably. We might not be able to work out 9 times 6 instantly. But asked to pick from a list of possible values, we’re more likely to think that 58 is credible than that 78 or 38 are. It’s quite imprecise, but isn’t it amazing that it’s there at all?
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 16th is maybe marginal to include, too. It’s about the kinds of logic puzzles that mathematicians grow up reading and like to pass around. And the way you can fake out someone by presenting a problem with too obvious a solution. It’s not just professors who’ll be stymied by having the answer look too obvious, by the way. Everyone’s similarly vulnerable. To see anything, including an abstract thing like the answer to a puzzle, you need some idea of what you are looking at. If you don’t think the answer could be something that simple, you won’t see it there.
Elzie Segar’s Thimble Theatre for the 10th of August, 1931, was also reprinted the 17th. It’s an old gag, even back when it was first run. But I suppose there’s some numerical-conversion mathematics to wring out of it. Given the rate of exchange, a pezozee would seem to be 24 pazimees. I’m not sure we need so many units in-between the pazimee and the pezozee, but perhaps King Blozo’s land set its units in a time when fractions were less familiar to the public. The punch line depends on the pazimee being worth nothing and, taken literally, that has sad implications for the pezozee too. If you take the King as speaking roughly, though, sixteen times a small amount is … at least a less small amount. It wouldn’t take many doublings to go from an infinitesimally tiny sum to a respectable one.
And it turns out there were enough comic strips I need to split this into two segments. So I should schedule that to appear. It’s already written and everything.
It wasn’t just another busy week from Comic Strip Master Command. And a week busy enough for me to split the mathematics comics into two essays. It was one where I recognized one of the panels as one I’d featured before. Multiple times. Some of the comics I feature are in perpetual reruns and don’t have your classic, deep, Peanuts-style decades of archives to draw from. I don’t usually go checking my archives to see if I’ve mentioned a comic before, not unless something about it stands out. So for me to notice I’ve seen this strip repeatedly can mean only one thing: there was something a little bit annoying about it. Recognize it yet? You will.
Hy Eisman’s Popeye for the 7th of January, 2018 is an odd place for mathematics to come in. J Wellington Wimpy regales Popeye with all the intellectual topics he tried to impress his first love with, and “Euclidean postulates in the original Greek” made the cut. And, fair enough. Euclid’s books are that rare thing that’s of important mathematics (or scientific) merit and that a lay person can just pick up and read, even for pleasure. These days we’re more likely to see a division between mathematics writing that’s accessible but unimportant (you know, like, me) or that’s important but takes years of training to understand. Doing it in the original Greek is some arrogant showing-off, though. Can’t blame Carolyn for bailing on someone pulling that stunt.
John Hambrock’s The Brilliant Mind of Edison Lee for the 8th is set in mathematics class. And Edison tries to use a pile of mathematically-tinged words to explain why it’s okay to read a Star Wars book instead of paying attention. Or at least to provide a response the teacher won’t answer. Maybe we can make something out of this by allowing the monetary value of something to be related to its relevance. But if we allow that then Edison’s messed up. I don’t know what quantity is measured by multiplying “every Star Wars book ever written” by “all the movies and merchandise”. But dividing that by the value of the franchise gets … some modest number in peculiar units divided by a large number of dollars. The number value is going to be small. And the dimensions are obviously crazy. Edison needs to pay better attention to the mathematics.
Johnny Hart’s B.C. for the 14th of July, 1960 shows off the famous equation of the 20th century. All part of the comic’s anachronism-comedy chic. The strip reran the 9th of January. “E = mc2” is, correctly, associated with Albert Einstein and some of his important publications of 1905. But the expression does have some curious precursors, people who had worked out the relationship (or something close to it) before Einstein and who didn’t quite know what they had. A short piece from Scientific American a couple years back describes pre-Einstein expressions of the equation from Oliver Heaviside, Henri Poincaré, and Fritz Hasenöhrl. I’m not surprised Poincaré had something close to this; it seems like he spent twenty years almost discovering Relativity. That’s all right; he did enough in dynamical systems that mathematicians aren’t going to forget him.
Jason Chatfield’s Ginger Meggs for the 9th draws my eye just because the blackboard lists “Prime Numbers”. Fair enough place setting, although what’s listed are 1, 3, 5, and 7. These days mathematicians don’t tend to list 1 as a prime number; it’s inconvenient. (A lot of proofs depend on their being exactly one way to factorize a number. But you can always multiply a number by ‘1’ a couple more times without changing its value. So ‘6’ is 3 times 2, but it’s also 3 times 2 times 1, or 3 times 2 times 1 times 1, or 3 times 2 times 1145,388,434,247. You can write around that, but it’s easier to define ‘1’ as not a prime.) But it could be defended. I can’t think any reason to leave ‘2’ off a list of prime numbers, though. I think Chatfield conflated odd and prime numbers. If he’d had a bit more blackboard space we could’ve seen whether the next item was 9 or 11 and that would prove the matter.
Paul Trap’s Thatababy for the 9th uses arithmetic — square roots — as the kind of thing to test whether a computer’s working. Everyone has their little tests like this. My love’s father likes to test whether the computer knows of the band Walk The Moon or of Christine Korsgaard (a prominent philosopher in my love’s specialty). I’ve got a couple words I like to check dictionaries for. Of course the test is only any good if you know what the answer should be, and what’s the actual square root of 3,278? Goodness knows. It’s got to be between 50 (50 squared is 25 hundred) and 60 (60 squared is 36 hundred). Since 3,278 is so much closer 3,600 than 2,500 its square root should be closer to 60 than to 50. So 57-point-something is plausible. Unfortunately square roots don’t lend themselves to the same sorts of tricks from reading the last digit that cube roots do. And 3,278 isn’t a perfect square anyway. Alexa is right on this one. Also about the specific gravity of cobalt, at least if Wikipedia is right and not conspiring with the artificial intelligences on this one. Catch you in 2021.
So I try to keep up with nearly all the comic strips run on Comics Kingdom and on GoComics. This includes some vintage strips: take some ancient comic like Peanuts or Luann and rerun it, day at a time, from the beginning. This is always enlightening. It’s always interesting to see a comic in that first flush of creative energy, before the characters have quite settled in and before the cartoonist has found stock jokes that work so well they don’t even have to be jokes anymore. One of the most startling cases for me has been Johnny Hart’s B.C. which, in its Back To B.C. incarnation, has been pretty well knocking it out of the park.
Not this week, I’m sad to admit. This week it’s been doing a bunch of mathematics jokes, which is what gives me my permission to talk about it here. The jokes have been, eh, the usual, given the setup. A bit fresher, I suppose, for the characters in the strip having had fewer of their edges worn down by time. Probably there’ll be at least one that gets a bit of a grin.
Mark Tatulli’s Heart of the City has a number appear on the 12th. That’s been about as much mathematical content as Heart’s experience at Math Camp has taken. The story’s been more about Dana, her camp friend, who’s presented as good enough at mathematics to be bored with it, and the attempt to sneak out to the nearby amusement park. What has me distracted is wondering what amusement park this could be, given that Heart’s from Philadelphia and the camp’s within bus-trip range and in the forest. I can’t rule out that it might be Knoebels Amusement Park, in Elysburg, Pennsylvania, in which case Heart and Dana are absolutely right to sneak out of camp because it is this amazing place.
Mort Walker’s Beetle Bailey Vintage for the 21st of December, 1960 was rerun the 14th. I can rope this into mathematics. It’s about Cookie trying to scale up a recipe to fit Camp Swampy’s needs. Increasing the ingredient count is easy, or at least it is if your units scale nicely. I wouldn’t want to multiple a third of a teaspoon by 200 without a good stretching beforehand and maybe a rubdown afterwards. But the time needed to cook a multiplied recipe, that gets mysterious. As I understand it — the chemistry of cooking is largely a mystery to me — the center of the trouble is that to cook a thing, heat has to reach throughout the interior. But heat can only really be applied from the surfaces of the cooked thing. (Yes, theoretically, a microwave oven could bake through the entire volume of something. But this would require someone inventing a way to bake using a microwave.) So we must balance the heat that can be applied over what surface to the interior volume and any reasonable time to cook the thing. Won’t deny that at some point it seems easier to just make a smaller meal.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 14th goes to the old “inference testing” well again. This comes up from testing whether something strange is going on. Measure something in a sample. Is the result appreciably different from what would be a plausible result if nothing interesting is going on? The null hypothesis is the supposition that there isn’t anything interesting going on: the measurement’s in the range of what you’d expect given that the world is big and complicated. I’m not sure what the physicist’s exact experiment would have been. I suppose it would be something like “you lose about as much heat through your head as you do any region of skin of about the same surface area”. So, yeah, freezing would be expected, considering.
Percy Crosby’s Skippy for the 17th of May, 1930, and rerun the 15th, maybe doesn’t belong here. It’s just about counting. Never mind. I smiled at it, and I’m a fan of the strip. Give it a try; it’s that rare pre-Peanuts comic that still feels modern.
So this past week saw a lot of comic strips with some mathematical connection put forth. There were enough just for the 26th that I probably could have done an essay with exclusively those comics. So it’s another split-week edition, which suits me fine as I need to balance some of my writing loads the next couple weeks for convenience (mine).
Tony Cochrane’s Agnes for the 25th of June is fun as the comic strip almost always is. And it’s even about estimation, one of the things mathematicians do way more than non-mathematicians expect. Mathematics has a reputation for precision, when in my experience it’s much more about understanding and controlling error methods. Even in analysis, the study of why calculus works, the typical proof amounts to showing that the difference between what you want to prove and what you can prove is smaller than your tolerance for an error. So: how do we go about estimating something difficult, like, the number of stars? If it’s true that nobody really knows, how do we know there are some wrong answers? And the underlying answer is that we always know some things, and those let us rule out answers that are obviously low or obviously high. We can make progress.
Russell Myers’s Broom Hilda for the 25th is about one explanation given for why time keeps seeming to pass faster as one age. This is a mathematical explanation, built on the idea that the same linear unit of time is a greater proportion of a young person’s lifestyle so of course it seems to take longer. This is probably partly true. Most of our senses work by a sense of proportion: it’s easy to tell a one-kilogram from a two-kilogram weight by holding them, and easy to tell a five-kilogram from a ten-kilogram weight, but harder to tell a five from a six-kilogram weight.
As ever, though, I’m skeptical that anything really is that simple. My biggest doubt is that it seems to me time flies when we haven’t got stories to tell about our days, when they’re all more or less the same. When we’re doing new or exciting or unusual things we remember more of the days and more about the days. A kid has an easy time finding new things, and exciting or unusual things. Broom Hilda, at something like 1500-plus years old and really a dour, unsociable person, doesn’t do so much that isn’t just like she’s done before. Wouldn’t that be an influence? And I doubt that’s a complete explanation either. Real things are more complicated than that yet.
Norm Feuti’s Retail for the 26th is about how you get good at arithmetic. I suspect there’s two natural paths; you either find it really interesting in your own right, or you do it often enough you want to find ways to do it quicker. Marla shows the signs of learning to do arithmetic quickly because she does it a lot: turning “30 percent off” into “subtract ten percent three times over” is definitely the easy way to go. The alternative is multiplying by seven and dividing by ten and you don’t want to multiply by seven unless the problem gives a good reason why you should. And I certainly don’t fault the customer not knowing offhand what 30 percent off $25 would be. Why would she be in practice doing this sort of problem?
Johnny Hart’s Back To B.C. for the 26th reruns the comic from the 30th of December, 1959. In it … uh … one of the cavemen guys has found his calendar for the next year has too many days. (Think about what 1960 was.) It’s a common problem. Every calendar people have developed has too few or too many days, as the Earth’s daily rotations on its axis and annual revolution around the sun aren’t perfectly synchronized. We handle this in many different ways. Some calendars worry little about tracking solar time and just follow the moon. Some calendars would run deliberately short and leave a little stretch of un-named time before the new year started; the ancient Roman calendar, before the addition of February and January, is famous in calendar-enthusiast circles for this. We’ve now settled on a calendar which will let the nominal seasons and the actual seasons drift out of synch slowly enough that periodic changes in the Earth’s orbit will dominate the problem before the error between actual-year and calendar-year length will matter. That’s a pretty good sort of error control.
8,978,432 is not anywhere near the number of days that would be taken between 4,000 BC and the present day. It’s not a joke about Bishop Ussher’s famous research into the time it would take to fit all the Biblically recorded events into history. The time is something like 24,600 years ago, a choice which intrigues me. It would make fair sense to declare, what the heck, they lived 25,000 years ago and use that as the nominal date for the comic strip. 24,600 is a weird number of years. Since it doesn’t seem to be meaningful I suppose Hart went, simply enough, with a number that was funny just for being riotously large.
Mark Tatulli’s Heart of the City for the 26th places itself on my Grand Avenue warning board. There’s plenty of time for things to go a different way but right now it’s set up for a toxic little presentation of mathematics. Heart, after being grounded, was caught sneaking out to a slumber party and now her mother is sending her to two weeks of Math Camp. I’m supposing, from Tatulli’s general attitude about how stuff happens in Heart and in Lio that Math Camp will not be a horrible, penal experience. But it’s still ominous talk and I’m watching.
Brian Fies’s Mom’s Cancer story for the 26th is part of the strip’s rerun on GoComics. (Many comic strips that have ended their run go into eternal loops on GoComics.) This is one of the strips with mathematical content. The spatial dimension of a thing implies relationships between the volume (area, hypervolume, whatever) of a thing and its characteristic linear measure, its diameter or radius or side length. It can be disappointing.
Nicholas Gurewitch’s Perry Bible Fellowship for the 26th is a repeat of one I get on my mathematics Twitter friends now and then. Should warn, it’s kind of racy content, at least as far as my usual recommendations here go. It’s also a little baffling because while the reveal of the unclad woman is funny … what, exactly, does it mean? The symbols don’t mean anything; they’re just what fits graphically. I think the strip is getting at Dr Loring not being able to see even a woman presenting herself for sex as anything but mathematics. I guess that’s funny, but it seems like the idea isn’t quite fully developed.
Zach Weinersmith’s Saturday Morning Breakfast Cereal Again for the 26th has a mathematician snort about plotting a giraffe logarithmically. This is all about representations of figures. When we plot something we usually start with a linear graph: a couple of axes perpendicular to one another. A unit of movement in the direction of any of those axes represents a constant difference in whatever that axis measures. Something growing ten units larger, say. That’s fine for many purposes. But we may want to measure something that changes by a power law, or that grows (or shrinks) exponentially. Or something that has some region where it’s small and some region where it’s huge. Then we might switch to a logarithmic plot. Here the same difference in space along the axis represents a change that’s constant in proportion: something growing ten times as large, say. The effective result is to squash a shape down, making the higher points more nearly flat.
And to completely smother Weinersmith’s fine enough joke: I would call that plot semilogarithmically. I’d use a linear scale for the horizontal axis, the gazelle or giraffe head-to-tail. But I’d use a logarithmic scale for the vertical axis, ears-to-hooves. So, linear in one direction, logarithmic in the other. I’d be more inclined to use “logarithmic” plots to mean logarithms in both the horizontal and the vertical axes. Those are useful plots for turning up power laws, like the relationship between a planet’s orbital radius and the length of its year. Relationships like that turn into straight lines when both axes are logarithmically spaced. But I might also describe that as a “log-log plot” in the hopes of avoiding confusion.
And now to wrap up last week’s mathematically-themed comic strips. It’s not a set that let me get into any really deep topics however hard I tried overthinking it. Maybe something will turn up for Sunday.
Mason Mastroianni, Mick Mastroianni, and Perri Hart’s B.C. for the 7th tries setting arithmetic versus celebrity trivia. It’s for the old joke about what everyone should know versus what everyone does know. One might question whether Kardashian pet eating habits are actually things everyone knows. But the joke needs some hyperbole in it to have any vitality and that’s the only available spot for it. It’s easy also to rate stuff like arithmetic as trivia since, you know, calculators. But it is worth knowing that seven squared is pretty close to 50. It comes up when you do a lot of estimates of calculations in your head. The square root of 10 is pretty near 3. The square root of 50 is near 7. The cube root of 10 is a little more than 2. The cube root of 50 a little more than three and a half. The cube root of 100 is a little more than four and a half. When you see ways to rewrite a calculation in estimates like this, suddenly, a lot of amazing tricks become possible.
Leigh Rubin’s Rubes for the 7th is a “mathematics in the real world” joke. It could be done with any mythological animals, although I suppose unicorns have the advantage of being relatively easy to draw recognizably. Mermaids would do well too. Dragons would also read well, but they’re more complicated to draw.
Mark Pett’s Mr Lowe rerun for the 8th has the kid resisting the mathematics book. Quentin’s grounds are that how can he know a dated book is still relevant. There’s truth to Quentin’s excuse. A mathematical truth may be universal. Whether we find it interesting is a matter of culture and even fashion. There are many ways to present any fact, and the question of why we want to know this fact has as many potential answers as it has people pondering the question.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th is a paean to one of the joys of numbers. There is something wonderful in counting, in measuring, in tracking. I suspect it’s nearly universal. We see it reflected in people passing around, say, the number of rivets used in the Chrysler Building or how long a person’s nervous system would reach if stretched out into a line or ever-more-fanciful measures of stuff. Is it properly mathematics? It’s delightful, isn’t that enough?
Bill Rechin’s Crock rerun for the 11th is a name-drop of mathematics. Really anybody’s homework would be sufficiently boring for the joke. But I suppose mathematics adds the connotation that whatever you’re working on hasn’t got a human story behind it, the way English or History might, and that it hasn’t got the potential to eat, explode, or knock a steel ball into you the way Biology, Chemistry, or Physics have. Fair enough.