Let’s see if I can’t close out the first week of June’s comics. I’d rather have published this either Tuesday or Thursday, but I didn’t have the time to write my statistics post for May, not yet. I’ll get there.
One of Gary Larson’s The Far Side reprints for the 4th is one I don’t remember seeing before. The thing to notice is the patient has a huge right brain and a tiny left one. The joke is about the supposed division between left-brained and right-brained people. There are areas of specialization in the brain, so that the damage or destruction of part can take away specific abilities. The popular imagination has latched onto the idea that people can be dominated by specialties of the either side of the brain. I’m not well-versed in neurology. I will hazard the guess that neurologists see “left-brain” and “right-brain” as amusing stuff not to be taken seriously. (My understanding is the division of people into “type A” and “type B” personalities is also entirely bunk unsupported by any psychological research.)
Bud Blake’s Tiger rerun for the 6th has Tiger complaining about his arithmetic homework. And does it in pretty nice form, really, doing some arithmetic along the way. It does imply that he’s starting his homework at 1 pm, though, so I guess it’s a weekend afternoon. It seems like rather a lot of homework for that age. Maybe he’s been slacking off on daily work and trying to make up for it.
John McPherson’s Close To Home for the 6th has a cheat sheet skywritten. It’s for a geometry exam. Any subject would do, but geometry lets cues be written out in very little space. The formulas are disappointingly off, though. We typically use ‘r’ to mean the radius of a circle or sphere, but then would use C for its circumference. That would be . The area of a circle, represented with A, would be . I’m not sure what ‘Vol.C’ would mean, although ‘Volume of a cylinder’ would make sense … if the next line didn’t start “Vol.Cyl”. The volume of a circular cylinder is , where r is the radius and h the height. For a non-circular cylinder, it’s the area of a cross-section times the height. So that last line may be right, if it extends out of frame.
Granted, though, a cheat sheet does not necessarily make literal sense. It needs to prompt one to remember what one needs. Notes that are incomplete, or even misleading, may be all that one needs.
I know; I’m more than a week behind the original publication of these strips. The Playful Math Education Blog Carnival took a lot of what attention I have these days. I’ll get caught up again soon enough. Comic Strip Master Command tried to help me, by having the close of a week ago being pretty small mathematics mentions, too. For example:
Craig Boldman and Henry Scarpelli’s Archie for the 27th has Moose struggling in mathematics this term. This is an interesting casual mention; the joke, of Moose using three words to describe a thing he said he could in two, would not fit sharply for anything but mathematics. Or, possibly, a measuring class, but there’s no high school even in fiction that has a class in measuring.
Bud Blake’s Vintage Tiger for the 27th has Tiger and Hugo struggling to find adjective forms for numbers. We can giggle at Hugo struggling for “quadruple” and going for something that makes more sense. We all top out somewhere, though, probably around quintuple or sextuple. I have never known anyone who claimed to know what the word would be for anything past decuple, and even staring at the dictionary page for “decuple” I don’t feel confident in it.
Hilary Price’s Rhymes With Orange for the 28th uses a blackboard full of calculations as shorthand for real insight into science. From context they’re likely working on some physics problem and it’s quite hard to do that without mathematics, must agree.
John Deering’s Strange Brew for the 28th name-drops slide rules, which, yeah, have mostly historical or symbolic importance these days. There might be some niche where they’re particularly useful (besides teaching logarithms), but I don’t know of it.
I can clear out all last week’s mathematically-themed comic strips in one move, it looks like. There were a fair number of strips; it’s just they mostly mention mathematics in passing.
Bill Amend’s FoxTrot for the 23rd — a new strip; it’s still in original production for Sundays — has Jason asking his older sister to double-check a mathematics problem. Double-checking work is reliably useful, as proof against mistakes both stupid and subtle. But that’s true of any field.
Jim Unger’s Herman for the 23rd has a parent complaining about the weird New Math. The strip is a rerun and I don’t know from when; it hardly matters. The New Math has been a whipping boy for mathematics education since about ten minutes after its creation. And the complaint attaches to every bit of mathematics education reform ever. I am sympathetic to parents, who don’t see why their children should be the test subjects for a new pedagogy. And who don’t want to re-learn mathematics in order to understand what their children are doing. But, still, let someone know you were a mathematics major and they will tell you how much they didn’t understand or like mathematics in school. It’s hard to see why not try teaching it differently.
(If you do go out pretending to be a mathematics major, don’t worry. If someone challenges you on a thing, cite “Euler’s Theorem”, and you’ll have said something on point. And I’ll cover for you.)
Brian Gordon’s Fowl Language for the 25th has a father trying to explain the vastness of Big Numbers to their kid. Past a certain point none of us really know how big a thing is. We can talk about 300 sextillion stars, or anything else, and reason can tell us things about that number. But do we understand it? Like, can we visualize that many stars the way we can imagine twelve stars? This gets us into the philosophy of mathematics pretty soundly. 300 sextillion is no more imaginary than four is, but I know I feel more confident in my understanding of four. How does that make sense? And can you explain that to your kid?
Vic Lee’s Pardon my Planet for the 28th has an appearance by Albert Einstein. And a blackboard full of symbols. The symbols I can make out are more chemistry than mathematics, but they do exist just to serve as decoration.
As I referenced on Sunday while there were a good number of comic strips mentioning mathematics last week, there weren’t many touching deeply enough for me to make real essays about them. But you may enjoy seeing the strips anyway. So here’s the first half of this roster.
There were a healthy number of comic strips with at least a bit of mathematical content the past week. Enough that I would maybe be able to split them across three essays in all. This conflicts with my plans to post two A-To-Z essays, and two short pieces bringing archived things back to some attention, when you consider the other thing I need to post this week. Well, I’ll work out something, this week at least. But if Comic Strip Master Command ever sends me a really busy week I’m going to be in trouble.
Bud Blake’s Tiger rerun for the 7th has Punkinhead ask one of those questions so basic it ends up being good and deep. What is arithmetic, exactly? Other than that it’s the mathematics you learn in elementary school that isn’t geometry? — an answer that’s maybe not satisfying but at least has historical roots. The quadrivium, four of the seven liberal arts of old, were arithmetic, geometry, astronomy, and music. Each of these has a fair claim on being a mathematics study, though I’d agree that music is a small part of mathematics these days. (I first wrote a “minor” piece, and didn’t want people to think I was making a pun, but you’ll notice I’m sharing it anyway.) I can’t say what people who study music learn about mathematics these days. Still, I’m not sure I can give a punchy answer to the question.
Mathworld offers the not-quite-precise definition that arithmetic is the field of mathematics dealing with integers or, more generally, numerical computation. But then it also offers a mnemonic for the spelling of arithmetic, which I wouldn’t have put in the fourth sentence of an article on the subject. I’m also not confident in that limitation to integers. Arithmetic certainly is about things we do on the integers, like addition and subtraction, multiplication and division, powers, roots, and factoring. So, yes, adding five and two is certainly arithmetic. But would we say that adding one-fifth and two is not arithmetic? Most other definitions I find allow that it can be about the rational numbers, or the real numbers. Some even accept the complex-valued numbers. The core is addition and subtraction, multiplication and division.
Arithmetic blends almost seamlessly into more complicated fields. One is number theory, which is the posing of problems that anyone can understand and that nobody can solve. If you ever run across a mathematical conjecture that’s over 200 years old and that nobody’s made much progress on besides checking that it’s true for all the whole numbers below 21,000,000,000 – 1, it’s probably number theory. Another is group theory, in which we think about structures that look like arithmetic without necessarily having all its fancy features like, oh, multiplication or the ability to factor elements. And it weaves into computing. Most computers rely on some kind of floating-point arithmetic, which approximates a wide range of the rational numbers that we’d expect to actually need.
So arithmetic is one of those things so fundamental and universal that it’s hard to take a chunk and say that this is it.
John Zakour and Scott Roberts’s Maria’s Day for the 8th has Maria fretting over what division means for emotions. I was getting ready to worry about Maria having the idea division means getting less of something. Five divided by one-half is not less than either five or one-half. My understanding is this unsettles a great many people learning division. But she does explicitly say, divide two, which I’m reading as “divide by two”. (I mean to be charitable in my reading of comic strips. It’s only fair.)
Still, even division into two things does not necessarily make things less. One of the fascinating and baffling discoveries of the 20th century was the Banach-Tarski Paradox. It’s a paradox only in that it defies intuition. According to it, one ball can be divided into as few as five pieces, and the pieces reassembled to make two whole balls. I would not expect Maria’s Dad to understand this well enough to explain.
There were naturally comic strips with too marginal a mention of mathematics to rate paragraphs. Among them the past week were these.
Stephen Bentley’s Herb and Jamaal rerun for the 11th portrays the aftermath of realizing a mathematics problem is easier than it seemed. Realizing this after a lot of work should feel good, as discovering a clever way around tedious work is great. But the lost time can still hurt.
John Graziano’s Ripley’s Believe It or Not for the 26th mentions several fairly believable things. The relevant part is about naming the kind of surface that a Pringles chip represents. That is, the surface a Pringles chip would be if it weren’t all choppy and irregular, and if it continued indefinitely.
The shape is, as Graziano’s Ripley’s claims, a hypberbolic paraboloid. It’s a shape you get to know real well if you’re a mathematics major. They turn up in multivariable calculus and, if you do mathematical physics, in dynamical systems. It’s also a shape mathematics majors get to calling a “saddle shape”, because it looks enough like a saddle if you’re not really into horses.
The shape is one of the “quadratic surfaces”. These are shapes which can be described as the sets of Cartesian coordinates that make a quadratic equation true. Equations in Cartesian coordinates will have independent variables x, y, and z, unless there’s a really good reason. A quadratic equation will be the sum of some constant times x, and some constant times x2, and some constant times y, and some constant times y2, and some constant times z, and some constant times z2. Also some constant times xy, and some constant times yz, and some constant times xz. No xyz, though. And it might have some constant added to the mix at the end of all this.
There are seventeen different kinds of quadratic surfaces. Some of them are familiar, like ellipsoids or cones. Some hardly seem like they could be called “quadratic”, like intersecting planes. Or parallel planes. Some look like mid-century modern office lobby decor, like elliptic cylinders. And some have nice, faintly science-fictional shapes, like hyperboloids or, as in here, hyperbolic paraboloids. I’m not a judge of which ones would be good snack shapes.
Bud Blake’s Tiger for the 31st is a rerun, of course. Blake died in 2005 and no one else drew his comic strip. It’s a funny-answer-to-a-story-problem joke. And, more, it’s a repeat of a Tiger strip I’ve already run here. I admit a weird pride when I notice a comic strip doing a repeat. It gives me some hope that I might still be able to remember things. But this is also a special Tiger repeat. It’s the strip which made me notice Bud Blake redrawing comics he had already used. This one is not a third iteration of the strip which reran in April 2015 and June 2016. It’s a straight repeat of the June 2016 strip.
The mystery to me now is why King Features apparently has less than three years’ worth of reruns in the bank for Tiger. The comic ran from 1965 to 2003, and it’s not as though the strip made pop culture references or jokes ripped from the headlines. Even if the strip changed its dimensions over the decades, to accommodate shrinking newspapers, there should be a decade at least of usable strips to rerun.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 31st uses a chart to tease mathematicians, both in the comic and in the readership. The joke is in the format of the graph. The graph is supposed to argue that the Mathematician’s pedantry is increasing with time, and it does do that. But it is customary in this sort of graph for the independent variable to be the horizontal axis and the dependent variable the vertical. So, if the claim is that the pedantry level rises as time goes on, yes, this is a … well, I want to say wrong way to arrange the axes. This is because the chart, as drawn, breaks a convention. But convention is a tool to help people’s comprehension. We are right to ignore convention if doing so makes the chart better serve its purpose. Which, the punch line is, this does.
And now I’ll cover the handful of comic strips which ran last week and which didn’t fit in my Sunday report. And link to a couple of comics that ultimately weren’t worth discussion in their own right, mostly because they were repeats of ones I’ve already discussed. I have been trimming rerun comics out of my daily reading. But there are ones I like too much to give up, at least not right now.
Bud Blake’s Tiger for the 25th has Tiger quizzing Punkinhead on counting. The younger kid hasn’t reached the point where he can work out numbers without a specific physical representation. It would come, if he were in one of those comics where people age.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 24th is an optimization problem, and an expectation value problem. The wisdom-seeker searches for the most satisfying life. The mathematician-guru offers an answer based in probability and expectation values. List all the possible outcomes, and how probable each are, and how much of the relevant quantity you get (or lose) with each outcome. This is a quite utilitarian view of life-planning. Finding the best possible outcome, given certain constraints, is another big field of mathematics.
John Atkinson’s Wrong Hands for the 26th is a nonsense-equation panel. It’s built on a cute idea. If you do wan to know how many bears you can fit in the kitchen you would need something like this. Not this, though. You can tell by the dimensions. ‘x’, as the area of the kitchen, has units of, well, area. Square feet, or square meters, or square centimeters, or whatever is convenient to measure its area. The average volume of a bear, meanwhile, has units of … volume. Cubic feet, or cubic meters, or cubic centimeters, or the like. The one divided by the other has units of one-over-distance.
And I don’t know what the units of desire to have bears in your kitchen are, but I’m guessing it’s not “bear-feet”, although that would be worth a giggle. The equation would parse more closely if y were the number of bears that can fit in a square foot, or something similar. I say all this just to spoil Atkinson’s fine enough bit of nonsense.
Percy Crosby’s Skippy for the 26th is a joke built on inappropriate extrapolation. 3520 seconds is a touch under an hour. Skippy’s pace, if he could keep it up, would be running a mile every five minutes, 52 seconds. That pace isn’t impossible — I find it listed on charts for marathon runners. But that would be for people who’ve trained to be marathon or other long-distance runners. They probably have different fifty-yard run times.
And now for some of the recent comics that didn’t seem worth their own discussion, and why they didn’t.
Niklas Eriksson’s Carpe Diem for the 20th features reciting the digits of π as a pointless macho stunt. There are people who make a deal of memorizing digits of π. Everyone needs hobbies, and memorizing meaningless stuff is a traditional fanboy’s way of burying oneself in the thing appreciated. Me, I can give you π to … I want to say sixteen digits. I might have gone farther in my youth, but I was heartbroken when I learned one of the digits I had memorized I got wrong, and so after correcting that mess I gave up going farther.
It’s happened again: another slow week around here. My supposition is that Comic Strip Master Command was snowed in about a month ago, and I’m seeing the effects only now. There’s obviously no other reason that more comic strips didn’t address my particular narrow interest in one seven-day span.
Samson’s Dark Side of the Horse for the 18th is a numerals joke. The mathematics content is slight, I admit, but I’ve always had a fondness for Dark Side of the Horse. (I know it sounds like I have a fondness for every comic strip out there. I don’t quite, but I grant it’s close.) Conflating numerals and letters, and finding words represented by numerals, is an old tradition. It was more compelling in ancient days when letters were used as numerals so that it was impossible not to find neat coincidences. I suppose these days it’s largely confined to typefaces that make it easy to conflate a letter and a numeral. I mean moreso than the usual trouble telling apart 1 and l, 0 and O, or 5 and S. Or to special cases like hexadecimal numbers where, for ease of representation, we use the letters A through F as numerals.
Jef Mallett’s Frazz for the 18th is built on an ancient problem. I remember being frustrated with it. How is “questions 15 to 25” eleven questions when the difference between 15 and 25 is ten? The problem creeps into many fields. Most of the passion has gone out of the argument but around 1999 you could get a good fight going about whether the new millennium was to begin with January 2000 or 2001. The kind of problem is called a ‘fencepost error’. The name implies how often this has complicated someone’s work. Divide a line into ten segments. There are nine cuts on the interior of the line and the two original edges. I’m not sure I could explain to an elementary school student how the cuts and edges of a ten-unit-long strip match up to the questions in this assignment. I might ask how many birthdays someone’s had when they’re nine years old, though. And then flee the encounter.
Mark Parisi’s Off The Mark for the 19th is another numerals joke. This one’s also the major joke to make about an ice skater doing a figure eight: write the eight some other way. (I’d have sworn there was an M-G-M Droopy cartoon in which Spike demonstrates his ability to skate a figure 8, and then Droopy upstages him by skating ‘4 + 4’. I seem to be imagining it; the only cartoon where this seems to possibly fit is 1950’s The Chump Champ, and the joke isn’t in that one. If someone knows the cartoon I am thinking of, please let me know.) Here, the robot is supposed to be skating some binary numeral. It’s nothing close to an ‘8’, but perhaps the robot figures it needs to demonstrate some impressive number to stand out.
Bud Blake’s Tiger for the 21st has Tiger trying to teach his brother arithmetic. Working it out with fingers seems like a decent path to try, given Punkinhead’s age and background. And Punkinhead has a good point: why is the demonstration the easy problem and the homework the hard problem? I haven’t taught in a while, but do know I would do that sort of thing. My rationalization, I think, would be that a hard problem is usually hard because it involves several things. If I want to teach a thing, then I want to highlight just that thing. So I would focus on a problem in which that thing is the only tricky part, and everything else is something the students are so familiar with they don’t notice it. The result is usually an easy problem. There isn’t room for toughness. I’m not sure if that’s a thing I should change, though. Demonstrations of how to work harder problems are worth doing. But I usually think of those as teaching “how to use these several things we already know”. Using a tough problem to show one new thing, plus several already-existing tricky things, seems dangerous. It might be worth it, though.
There won’t be, this week, any mathematically-themed comic strips featuring the long-running, Carl Anderson-created character Henry. You’ll come to see why I find this worth mentioning soon enough. Not today.
Hart, Mastroianni, and Parker’s Wizard of Id for the 2nd features the blackboard full of symbols to represent the difficult and unsolved problem. And sometimes it does seem like it takes magic to solve an equation. That magic usually takes the form of a transformation. That is, we find a way to rewrite the problem as something different, and find that this different problem is solvable. And then that the solution to this altered problem can be transformed into a solution of the original. This is normal magic, the kind any trained mathematician can do, if haltingly. But sometimes it’ll be just a stroke of imaginative genius, solving a problem that seems at first to have nothing to do with the original. This is genius work, and we all hope we can find a problem on which we can do that.
I can also take the strip to represent one of those things I’m curmudgeonly about. That is that I tend to look at big special-effects-laden attempts to make mathematics look beautiful as … well, they’re nice. But I don’t think they help anyone learn how to do anything. So that the Wizard’s work doesn’t actually solve the problem feels true to me.
Mort Walker and Dik Browne’s vintage Hi and Lois for the 3rd sees Chip struggling with mathematics. His father has a noble idea, that it’ll be easier if he tries to see the problems as fun puzzles. Maybe so, but I agree with Chip: there’s not a punch line to 246 ÷ 3. Also, points to Chip for doing that division right away. Clearly he isn’t bad at arithmetic; he just doesn’t like it. We’ve all got things like that.
Hector D Cantu and Carlos Castellanos’s Baldo for the 4th is a joke about being helpless with numbers. … Actually, from the phrasing, I’m not positive that Cruz doesn’t mean he got question number 9, or maybe 19, or maybe number 10 wrong. It’s a bit sloppy to not remember which question was, but I certainly know the pain of remembering having done a problem wrong.
Once again the name of this Reading the Comics edition has nothing to do with any of the strips. I’m just aware that Weezer’s cover of Africa is quite popular right now and who am I to deny people things they want? (I like the cover, but it’s not different enough for me to feel satisfied by it. I tend to like covers that highlight something minor in the original, or that go in a strange direction. Shifting a peppy song into a minor key doesn’t count anymore. But bear in mind, I’m barely competent at listening to music. Please now enjoy my eight hours of early electronica in which various beeps and whistles are passed off as music.)
Samson’s Dark Side of the Horse for the 3rd is the Roman numerals joke for the week. And a welcome return for Dark Side of the Horse. It feels like it’s been gone a while. I wouldn’t try counting by Roman numerals to lull myself to sleep; it seems like too much fussy detail work. But I suppose if you’ve gotten good at it, it’s easy.
Jef Mallett’s Frazz for the 3rd builds on removing statistics from their context. It’s a common problem. It’s possible to measure so very many things. Without a clear idea of what we should expect as normal the measurement doesn’t tell us much. And it can be hard to know what the right context for something even is. Let me deconstruct Caulfield’s example. We’re supposed to reflect on and consider that 40% of all weekdays are Monday and Friday too. But it’s not only weekdays that people work. Even someone working a Sunday might take a sick day. Monday and Friday are a bit over 28% of the whole week. But more people do work Monday-to-Friday than do Saturdays and Sundays, so the Sunday sick day is surely rarer than the Monday. So even if we grant Caulfield’s premise, what does it tell us?
Jason Chatfield’s Ginger Meggs for the 3rd is a bit of why-learn-mathematics propaganda. Megg’s father has a good answer. But it does shift the question back one step. Also I see in the top row that Meggs has one of those comic-strip special editions where the name of the book is printed on the back cover instead. (I’m also skeptical of the photo and text layout on the newspaper Megg’s father is reading. But I don’t know the graphic design style of Australian, as opposed to United States, newspapers.)
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 3rd may belong on some philosopher’s Reading the Comics blog instead. No matter. There’s some mathematical-enough talk going on here. There’s often many ways to approach the same problem. For example, approaching a system as a handful of items. Or as a huge number of them. Or as infinitely many things. Or as a continuum of things. There are advantages each way. A handful of things, for example, we can often model as interactions between pairs of things. We can model a continuum as a fluid. A vast number of things can let one’s computer numerically approximate a fluid. Or infinitely many particles if that’s more convenient.
To describe all these different models as sharing an “ontology-space” is good mathematical jargon too. In this context the “-space” would mean the collection of all these things that are built by the same plan but with different values of whichever parameter matters.
Bud Blake’s Tiger for the 6th of August, 1965 features Einstein’s famous equation. I suppose it’s showing how well-informed Julian is, that he knows and can present such a big result. There is beauty in mathematics (and physics). Mathematicians (and physicists) find the subject beautiful to start with, and try to find attractive results. I’m curious what the lay reader makes of mathematical symbols, though, just as pieces of art. I remember as a child finding this beauty in a table of integrals in the front of one of my mother’s old college textbooks. All those parallel rows of integral symbols drew me in though nothing I’d seen in mathematics had prepared me to even read it. I still find that beautiful, but I can’t swear that I would even if I hadn’t formed that impression early in life. Are lay and professional readers’ views of mathematical-expression beauty similar? How are they different?
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st mentions mathematics — geometry, primarily — as something a substitute teacher has tried teaching with the use of a cucumber and condom. These aren’t terrible examples to use to make concrete the difference between volumes and surface areas. There are limitations, though. It’s possible to construct a shape that has a finite volume but an infinitely large surface area, albeit not using cucumbers.
There’s also a mention of the spring constant, and physics. This isn’t explicitly mathematical. But the description of movement on a spring are about the first interesting differential equation of mathematical physics. The solution is that of simple harmonic motion. I don’t think anyone taking the subject for the first time would guess at the answer. But it’s easy enough to verify it’s right. And this motion — sine waves — just turns up everywhere in mathematical physics.
Bud Blake’s Tiger rerun for the 23rd just mentions mathematics as a topic Hugo finds challenging, and what’s challenging about it. So a personal story: when I took Intro to Linear Algebra my freshman year one day I spaced on the fact we had an exam. So, I put the textbook on the shelf under my desk, and then forgot to take it when I left. The book disappeared, of course, and the professor never heard of it being turned in to lost-and-found or anything. Fortunately the homework was handwritten questions passed out on photocopies (ask your parents), so I could still do the assignments, but for all those, you know, definitions and examples I had to rely on my own notes. I don’t know why I couldn’t ask a classmate. Shyness, probably. Came through all right, though.
Cathy Law’s Claw for the 23rd technically qualifies as an anthropomorphic-numerals joke, in this panel about the smothering of education by the infection of guns into American culture.
Jim Meddick’s Monty for the 23rd has wealthy child Wedgwick unsatisfied with a mere ball of snow. He instead has a snow Truncated Icosahedron (the hyphens in Jarvis’s word balloon may baffle the innocent reader). This is a real shape, one that’s been known for a very long time. It’s one of the Archimedean Solids, a set of 13 solids that have convex shapes (no holes or indents or anything) and have all vertices the same, the identical number of edges coming in to each point in the same relative directions. The truncated icosahedron you maybe also know as the soccer ball shape, at least for those old-style soccer balls made of patches that were hexagons and pentagons. An actual truncated icosahedron needs twelve pentagons, so the figure drawn in the third panel isn’t quite right. At least one pentagonal face would be visible. But that’s also tricky to draw. The aerodynamics of a truncated icosahedron are surely different from those of a sphere. But in snowball-fight conditions, probably not different enough to even notice.
Mark Litzler’s Joe Vanilla for the 24th uses a blackboard full of formulas to represent an overcomplicated answer. The formulas look, offhand, like gibberish to me. But I’ll admit uncertainty since the odd capitalization of “iG(p)” at the start makes me think of some deeper group theory or knot theory symbols. And to see an “m + p” and an “m – p” makes me think of quantum mechanics of atomic orbitals. (But then an “m – p2” is weird.) So if this were anything I’d say it was some quantum chemistry formula. But my gut says if Litzler did take the blackboard symbols from anything, it was without going back to references. (Which he has no need to do, I should point out; the joke wouldn’t be any stronger — or weaker — if the blackboard meant anything.)
And now, finally, we get what we’ve been waiting so long for: my having enough energy and time to finish up last week’s comics. And I make excuses to go all fanboy over Elzie Segar’s great Thimble Theatre. Also more attention to Zach Weinersmith. You’ve been warned.
Mark Anderson’s Andertoons for the 13th is finally a breath of Mark Anderson’s Andertoons around here. Been far too long. Anyway it’s an algebra joke about x’s search for identity. And as often happens I’m sympathetic here. It’s not all that weird to think of ‘x’ as a label for some number. Knowing whether it means “a number whose value we haven’t found yet” or “a number whose value we don’t care about” is one trick, though. It’s not something you get used to from learning about, like, ‘6’. And knowing whether we can expect ‘x’ to have held whatever value it represented before, or whether we can expect it to be something different, is another trick.
Bud Blake’s Tiger for the 15th is a bit of kid logic about how to make a long column of numbers easier to add. I endorse the plan of making the column shorter, although I’d do that by trying to pair up numbers that, say, add to 10 or 20 or something else easy to work with. Partial sums can make the overall work so much easier. And probably avoid mistakes.
Elzie Segar’s Thimble Theatre for the 8th of July, 1931, is my most marginal inclusion yet. It was either that strip or the previous day’s worth including. I’m throwing it in here because Segar’s Thimble Theatre keeps being surprisingly good. And, heck, slowing a count by going into fractions is viable way to do it. As the clobbered General Bunzo points out, you can drag this out longer by going into hundredths. Or smaller units. There is no largest real number less than ten; if it weren’t incredibly against the rules, boxers could make use of that.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th is about those mathematics problems with clear and easy-to-understand statements whose answers defy intuition. Weinersmith is completely correct about all of this. I’m surprised he doesn’t mention the one about how you could divide an orange into five pieces, reassemble the pieces, and get back two spheres each the size of a sun.
The back half of last week’s mathematically themed comic strips aren’t all that deep. They make up for it by being numerous. This is how calculus works, so, good job, Comic Strip Master Command. Here’s what I have for you.
Mark Anderson’s Andertoons for the 20th marks its long-awaited return to these Reading The Comics posts. It’s of the traditional form of the student misunderstanding the teacher’s explanations. Arithmetic edition.
Marty Links’s Emmy Lou for the 20th was a rerun from the 22nd of September, 1976. It’s just a name-drop. It’s not like it matters for the joke which textbook was lost. I just include it because, what the heck, might as well.
Jef Mallett’s Frazz for the 21st uses the form of a story problem. It’s a trick question anyway; there’s really no way the Doppler effect is going to make an ice cream truck’s song unrecognizable, not even at highway speeds. Too distant to hear, that’s a possibility. Also I don’t know how strictly regional this is but the ice cream trucks around here have gone in for interrupting the music every couple seconds with some comical sound effect, like a “boing” or something. I don’t know what this hopes to achieve besides altering the timeline of when the ice cream seller goes mad.
Mark Litzler’s Joe Vanilla for the 21st I already snuck in here last week, in talking about ‘x’. The variable does seem like a good starting point. And, yeah, hypothesis block is kind of a thing. There’s nothing quite like staring at a problem that should be interesting and having no idea where to start. This happens even beyond grade school and the story problems you do then. What to do about it? There’s never one thing. Study it a good while, read about related problems a while. Maybe work on something that seems less obscure a while. It’s very much like writer’s block.
Ryan North’s Dinosaur Comics rerun for the 22nd straddles the borders between mathematics, economics, and psychology. It’s a problem about making forecasts about other people’s behavior. It’s a mystery of game theory. I don’t know a proper analysis for this game. I expect it depends on how many rounds you get to play: if you have a sense of what people typically do, you can make a good guess of what they will do. If everyone gets a single shot to play, all kinds of crazy things might happen.
Jef Mallet’s Frazz gets in again on the 22nd with some mathematics gibberish-talk, including some tossing around of the commutative property. Among other mistakes Caulfield was making here, going from “less is more to therefore more is less” isn’t commutation. Commutation is about binary operations, where you match a pair of things to a single thing. The operation commutes if it never matters what the order of the pair of things is. It doesn’t commute if it ever matters, even a single time, what the order is. Commutativity gets introduced in arithmetic where there are some good examples of the thing. Addition and multiplication commute. Subtraction and division don’t. From there it gets forgotten until maybe eventually it turns up in matrix multiplication, which doesn’t commute. And then it gets forgotten once more until maybe group theory. There, whether operations commute or not is as important a divide as the one between vertebrates and invertebrates. But I understand kids not getting why they should care about commuting. Early on it seems like a longwinded way to say what’s obvious about addition.
Bud Blake’s Tiger rerun for the 23rd starts with a real-world example of your classic story problem. I like the joke in it, and I also like Hugo’s look of betrayal and anger in the second panel. A spot of expressive art will do so good for a joke.
And now finally I can close out last week’s many mathematically-themed comic strips. I had hoped to post this Thursday, but the Why Stuff Can Orbit supplemental took up my writing energies and eventually timeslot. This also ends up being the first time I’ve had one of Joe Martin’s comic strips since the Houston Chronicle ended its comics pages and I admit I’m not sure how I’m going to work this. I’m also not perfectly sure what the comic strip means.
So Joe Martin’s Mister Boffo for the 1st of June seems to be about a disastrous mathematics exam with a kid bad enough he hasn’t even got numbers exactly to express the score. Also I’m not sure there is a way to link to the strip I mean exactly; the archives for Martin’s strips are not … organized the way I would have done. Well, they’re his business.
Greg Evans’s Luann Againn for the 1st reruns the strip from the 1st of June, 1989. It’s your standard resisting-the-word-problem joke. On first reading the strip I didn’t get what the problem was asking for, and supposed that the text had garbled the problem, if there were an original problem. That was my sloppiness is all; it’s a perfectly solvable question once you actually read it.
Doug Bratton’s Pop Culture Shock Therapy for the 1st is a wordplay joke that uses word problems as emblematic of mathematics. I’m okay with that; much of the mathematics that people actually want to do amounts to extracting from a situation the things that are relevant and forming an equation based on that. This is what a word problem is supposed to teach us to do.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 1st — maybe I should have done a Reading the Comics for that day alone — riffs on the idle speculation that God would be a mathematician. It does this by showing a God uninterested in two logical problems. The first is the question of whether there’s an odd perfect number. Perfect numbers are these things that haunt number theory. (Everything haunts number theory.) It starts with idly noticing what happens if you pick a number, find the numbers that divide into it, and add those up. For example, 4 can be divided by 1 and 2; those add to 3. 5 can only be divided by 1; that adds to 1. 6 can be divided by 1, 2, and 3; those add to 6. For a perfect number the divisors add up to the original number. Perfect numbers look rare; for a thousand years or so only four of them (6, 28, 496, and 8128) were known to exist.
All the perfect numbers we know of are even. More, they’re all numbers that can be written as the product for certain prime numbers ‘p’. (They’re the ones for which is itself a prime number.) What we don’t know, and haven’t got a hint about proving, is whether there are any odd prime numbers. We know some things about odd perfect numbers, if they exist, the most notable of them being that they’ve got to be incredibly huge numbers, much larger than a googol, the standard idea of an incredibly huge number. Presumably an omniscient God would be able to tell whether there were an odd perfect number, or at least would be able to care whether there were. (It’s also not known if there are infinitely many perfect numbers, by the way. This reminds us that number theory is pretty much nothing but a bunch of easy-to-state problems that we can’t solve.)
Some miscellaneous other things we know about an odd perfect number, other than whether any exist: if there are odd perfect numbers, they’re not divisible by 105. They’re equal to one more than a whole multiple of 12. They’re also 117 more than a whole multiple of 468, and they’re 81 more than a whole multiple of 324. They’ve got to have at least 101 prime factors, and there have to be at least ten distinct prime factors. There have to be at least twelve distinct prime factors if 3 isn’t a factor of the odd perfect number. If this seems like a screwy list of things to know about a thing we don’t even know exists, then welcome to number theory.
The beard question I believe is a reference to the logician’s paradox. This is the one postulating a village in which the village barber shaves all, but only, the people who do not shave themselves. Given that, who shaves the barber? It’s an old joke, but if you take it seriously you learn something about the limits of what a system of logic can tell you about itself.
George Herriman’s Krazy Kat for the 10th of July, 1939 was rerun the 2nd of June. I’m not sure that it properly fits here, but the talk about Officer Pupp running at 60 miles per hour and Ignatz Mouse running forty and whether Pupp will catch Mouse sure reads like a word problem. Later strips in the sequence, including the ways that a tossed brick could hit someone who’d be running faster than it, did not change my mind about this. Plus I like Krazy Kat so I’ll take a flimsy excuse to feature it.
For the first time in ages there aren’t enough mathematically-themed comic strips to justify my cutting the week’s roundup in two. No, I have no idea what I’m going to write about for Thursday. Let’s find out together.
Jenny Campbell’s Flo and Friends for the 19th faintly irritates me. Flo wants to make sure her granddaughter understands that just because it takes people on average 14 minutes to fall asleep doesn’t mean that anyone actually does, by listing all sorts of reasons that a person might need more than fourteen minutes to sleep. It makes me think of a behavior John Allen Paulos notes in Innumeracy, wherein the statistically wise points out that someone has, say, a one-in-a-hundred-million chance of being killed by a terrorist (or whatever) and is answered, “ah, but what if you’re that one?” That is, it’s a response that has the form of wisdom without the substance. I notice Flo doesn’t mention the many reasons someone might fall asleep in less than fourteen minutes.
But there is something wise in there nevertheless. For most stuff, the average is the most common value. By “the average” I mean the arithmetic mean, because that is what anyone means by “the average” unless they’re being difficult. (Mathematicians acknowledge the existence of an average called the mode, which is the most common value (or values), and that’s most common by definition.) But just because something is the most common result does not mean that it must be common. Toss a coin fairly a hundred times and it’s most likely to come up tails 50 times. But you shouldn’t be surprised if it actually turns up tails 51 or 49 or 45 times. This doesn’t make 50 a poor estimate for the average number of times something will happen. It just means that it’s not a guarantee.
Gary Wise and Lance Aldrich’s Real Life Adventures for the 19th shows off an unusually dynamic camera angle. It’s in service for a class of problem you get in freshman calculus: find the longest pole that can fit around a corner. Oh, a box-spring mattress up a stairwell is a little different, what with box-spring mattresses being three-dimensional objects. It’s the same kind of problem. I want to say the most astounding furniture-moving event I’ve ever seen was when I moved a fold-out couch down one and a half flights of stairs single-handed. But that overlooks the caged mouse we had one winter, who moved a Chinese finger-trap full of crinkle paper up the tight curved plastic to his nest by sheer determination. The trap was far longer than could possibly be curved around the tube. We have no idea how he managed it.
J R Faulkner’s Promises, Promises for the 20th jokes that one could use Roman numerals to obscure calculations. So you could. Roman numerals are terrible things for doing arithmetic, at least past addition and subtraction. This is why accountants and mathematicians abandoned them pretty soon after learning there were alternatives.
Mark Anderson’s Andertoons for the 21st is the Mark Anderson’s Andertoons for the week. Probably anything would do for the blackboard problem, but something geometry reads very well.
Jef Mallett’s Frazz for the 21st makes some comedy out of the sort of arithmetic error we all make. It’s so easy to pair up, like, 7 and 3 make 10 and 8 and 2 make 10. It takes a moment, or experience, to realize 78 and 32 will not make 100. Forgive casual mistakes.
Bud Fisher’s Mutt and Jeff rerun for the 22nd is a similar-in-tone joke built on arithmetic errors. It’s got the form of vaudeville-style sketch compressed way down, which is probably why the third panel could be made into a satisfying final panel too.
Bud Blake’s Tiger rerun for the 23rd just name-drops mathematics; it could be any subject. But I need some kind of picture around here, don’t I?