Reading the Comics, June 11, 2014: Unsound Edition


I can tell the school year is getting near the end: it took a full week to get enough mathematics-themed comic strips to put together a useful bundle of them this time. I don’t know what I’m going to do this summer when there’s maybe two comic strips I can talk about per week and I have to go finding my own initiative to write about things.

Jef Mallet’s Frazz (June 6) is a pun strip, yeah, although it’s one that’s more or less legitimate for a word problem. The reason I have to say “more or less” is that it’s not clear to me whether, per Caulfield’s specification, the amount of ore lost across each Great Lake is three percent of the original cargo or three percent of the remaining cargo. But writing a word problem so that there’s only the one correct solution is a skill that needs development no less than solving word problems is, and probably if we imagine Caulfield grading he’d realize there was an ambiguity when a substantial number of of the papers make the opposite assumption to what he’d had in his mind.

Ruben Bolling’s Tom the Dancing Bug (June 6, and I believe it’s a rerun) steps into some of the philosophically heady waters that one gets into when you look seriously at probability, and that get outright silly when you mix omniscience into the mix. The Supreme Planner has worked out what he concludes to be a plan certain of success, but: does that actually mean one will succeed? Even if we assume that the Supreme Planner is able to successfully know and account for every factor which might affect his success — well, for a less criminal plan, consider: one is certain to toss heads at least once, if one flips a fair coin infinitely many times. And yet it would not actually be impossible to flip a fair coin infinitely many times and have it turn up tails every time. That something can have a probability of 1 (or 100%) of happening and nevertheless not happen — or equivalently, that something can have a probability of 0 (0%) of happening and still happen — is exactly analogous to how a concept can be true almost everywhere, that is, it can be true with exceptions that in some sense don’t matter. Ruben Bolling tosses in the troublesome notion of the multiverse, the idea that everything which might conceivably happen does happen “somewhere”, to make these impossible events all the more imminent. I’m impressed Bolling is able to touch on so much, with a taste of how unsettling the implications are, in a dozen panels and stay funny about it.

Enos cheats, badly, on his test.
Bud Grace’s The Piranha Club for the 9th of June, 2014.

Bud Grace’s The Piranha Club (June 9) gives us Enos cheating with perfectly appropriate formulas for a mathematics exam. I’m kind of surprised the Pythagorean Theorem would rate cheat-sheet knowledge, actually, as I thought that had reached the popular culture at least as well as Einstein’s E = mc2 had, although perhaps it’s reached it much as Einstein’s has, as a charming set of sounds without any particular meaning behind them. I admit my tendency in giving exams, too, has been to allow students to bring their own sheet of notes, or even to have open-book exams, on the grounds that I don’t really care whether they’ve memorized formulas and am more interested in whether they can find and apply the relevant formulas. But that doesn’t make me right; I agree there’s value in being able to identify what the important parts of the course are and to remember them well, and even more value in being able to figure out the area of a triangle or a trapezoid from thinking hard about the subject on your own.

Jason Poland’s Robbie and Bobbie (June 10) is looking for philosophy and mathematics majors, so, here’s hoping it’s found a couple more. The joke here is about the classification of logical arguments. A valid argument is one in which the conclusion does indeed follow from the premises according to the rules of deductive logic. A sound argument is a valid argument in which the premises are also true. The reason these aren’t exactly the same thing is that whether a conclusion follows from the premise depends on the structure of the argument; the content is irrelevant. This means we can do a great deal of work, reasoning out things which follow if we suppose that proposition A being true implies B is false, or that we know B and C cannot both be false, or whatnot. But this means we may fill in, Mad-Libs-style, whatever we like to those propositions and come away with some funny-sounding arguments.

So this is how we can have an argument that’s valid yet not sound. It is valid to say that, if baseball is a form of band organ always found in amusement parks, and if amusement parks are always found in the cubby-hole under my bathroom sink, then, baseball is always found in the cubby-hole under my bathroom sink. But as none of the premises going into that argument are true, the argument’s not sound, which is how you can have anything be “valid but not sound”. Identifying arguments that are valid but not sound is good for a couple questions on your logic exam, so, be ready for that.

Edison Lee fails to catch a ball because he miscalculates where it should land.
John Hambrock’s The Brilliant Mind of Edison Lee, 11 June 2014.

John Hambrock’s The Brilliant Mind of Edison Lee (June 11) has the brilliant yet annoying Edison trying to prove his genius by calculating precisely where the baseball will drop. This is a legitimate mathematics/physics problem, of course: one could argue that the modern history of mathematical physics comes from the study of falling balls, albeit more of cannonballs than baseballs. If there’s no air resistance and if gravity is uniform, the problem is easy and you get to show off your knowledge of parabolas. If gravity isn’t uniform, you have to show off your knowledge of ellipses. Either way, you can get into some fine differential equations work, and that work gets all the more impressive if you do have to pay attention to the fact that a ball moving through the air loses some of its speed to the air molecules. That said, it’s amazing that people are able to, in effect, work out approximate solutions to “where is this ball going” in their heads, not to mention to act on it and get to the roughly correct spot, lat least when they’ve had some practice.

Reading the Comics, June 4, 2014: Intro Algebra Edition


I’m not sure that there is a theme to the most recent mathematically-themed comic strips that I’ve seen, all from GoComics in the past week, but they put me in mind of the stuff encountered in learning algebra, so let’s run with that. It’s either that or I start making these “edition” titles into something absolutely and utterly meaningless, which could be.

Marc Anderson’s Andertoons (May 30) uses the classic setup of a board full of equation to indicate some serious, advanced thinking going on, and then puts in a cute animal twist on things. I don’t believe that the equation signifies anything, but I have to admit I’m not sure. It looks quite plausibly like something which might turn up in quantum mechanics (the “h” and “c” and lambda are awfully suggestive), so if Anderson made it up out of whole cloth he did an admirable job. If he didn’t make it up and someone recognizes it, please, let me know; I’m curious what it might be.

Marc Anderson reappears on the second of June has the classic reluctant student upset with the teacher who knew all along what x was. Knowledge of what x is is probably the source of most jokes about learning algebra, or maybe mathematics overall, and it’s amusing to me anyway that what we really care about is not what x is particularly — we don’t even do ourselves any harm if we call it some other letter, or for that matter an empty box — but learning how to figure out what values in the place of x would make the relationship true.

Jonathan Lemon’s Rabbits Against Magic (May 31) has the one-eyed rabbit Weenus doing miscellaneous arithmetic on the way to punning about things working out. I suppose to get to that punch line you have to either have mathematics or gym class as the topic, and I wouldn’t be surprised if Lemon’s done a version with those weight-lifting machines on screen. That’s not because I doubt his creativity, just that it’s the logical setup.

Eric Scott’s Back In The Day (June 2) has a pair of dinosaurs wondering about how many stars there are. Astronomy has always inspired mathematics. After one counts the number of stars one gets to wondering, how big the universe could be — Archimedes, classically, estimated the universe was about big enough to hold 1063 grains of sand — or how far away the sun might be — which the Ancient Greeks were able to estimate to the right order of magnitude on geometric grounds — and I imagine that looking deep into the sky can inspire the idea that the infinitely large and the infinitely small are at least things we can try to understand. Trying to count stars is a good start.

Steve Boreman’s Little Dog Lost (June 2) has a stick insect provide the excuse for some geometry puns.

Brian and Ron Boychuk’s The Chuckle Brothers (June 4) has a pie shop gag that I bet the Boychuks are kicking themselves for not having published back in mid-March.

Reading the Comics, May 18, 2014: Pop Math of the 80s Edition


And now there’ve suddenly been enough mathematics-themed comics for a fresh collection of the things. If there’s any theme this time around it’s to mathematics I remember filtering into popular culture in the 80s: the Drake Equation (which I, at least, first saw in Carl Sagan’s Cosmos and found haunting), and the Rubik’s Cube, which pop mathematics writers in the early 80s latched onto with an eagerness matched only by how they liked polyominoes in the mid-70s, and the Mandelbrot Set, which I think of as a mid-to-late 80s thing because that’s when it started covering science-oriented magazine covers and the screens of IBM PS/2’s being used by the kids in the math and science magnet programs.

Incidentally, this time around I’ve tried to include the Between Friends that I talk about, because I’m not convinced the link to its Comics Kingdom home site will last indefinitely. Gocomics.com seems to keep links from expiring, even for non-subscribers, but I’m curious whether it would be better-liked if I included images of the strips I talk about? I’m fairly confident that this is fair use, as I talk about mathematical subjects inspired by the strips, but I don’t know whether people care much about saving a click before reading my attempts to say something, anything, about a kid given a word problem about airplanes that he answers in a flippant manner.

Wulff and Morgenthaler’s WuMo (May 15) features Professor Rubik, “five minutes after” inventing what he’s famous for. Ernö Rubik really is a Professor (of architecture, at the Budapest College of Applied Arts when he invented his famous cube), and was interested in the relationships of things in space and of objects moving in space. The Rubik’s Cube is of interest mathematically because it offers a great excuse to introduce group theory to the average person. Group theory is, among other things, a way of studying structures that look like arithmetic but that aren’t necessarily on numbers. Rotations work very much like the addition of numbers, at least, the modular addition (where if a result is less than zero, or greater than some upper bound, you add or subtract that upper bound until the result is back in range), and the Rubik’s Cube offers several interacting sets of things to rotate, so that the groups represented by it are fascinatingly complex.

Though the cube was invented in 1974 it didn’t become an overwhelming phenomenon until 1979, and then much of the early 80s was spent in people making jokes about how frustrating they found it and occasionally buying books that were supposed to tell you how to solve it, but you couldn’t after all. Then there was a Saturday morning cartoon about the cube which I watched because I had horrible, horrible, horrible taste in cartoons as a kid. Anyway, it turns out that if you played it perfectly you could solve any Rubik’s Cube in no more than twenty steps, although this wasn’t proven until 2010. I confess I usually just give up around step 35 and take the cube apart. Don’t watch the cartoon.

Eric the Circle (May 17), this entry by “Designroo”, features Eric in the midst of the Mandelbrot Set. The Mandelbrot Set, basis for two-thirds of all the posters on the walls in the mathematics department from 1986 through 2002, was discovered by Benoît Mandelbrot in one of those triumphs of numerical computing. It’s not hard to describe how to make it — it’s only a little more advanced than the pastime of hitting a square root or a square button on a calculator and watching numbers dwindle to zero or grow infinitely large — but the number of calculations that need to be done to see it mean it’d never have been discovered before there were computers to do the hard work, of calculation and of visualization.

Among the neat things about the Mandelbrot set are that it does have inlets that look like circles, and it has an infinite number of them: if you zoom in closely at any point on the boundary of the Mandelbrot set you’ll find a not-quite-perfect replica of the original set, with the big carotid shape and the budding circles on the edges, over and over, inexhaustibly.

Bill Amend’s FoxTrot (May 17, rerun) asks why there aren’t geometry books on tape. It’s not quite an absurd question: in principle, geometry is a matter of deductive logic, and is about the relationship between ideas we call “points” and “lines” and “angles” and the like. Pictures are nice to have, as appeals to intuition, but our intuition can be wrong, and pictures can lead us astray, as any optical illusion will prove. And yet it’s so very hard to do away with that intuition. We may not know a compelling reason why the things we draw on sheets of paper should correspond to the results of logical, deductive reasoning that ought to be true whether drawn or not and whether, for that matter, a universe existed or not, but seeing representations of the relationships of geometric objects seems to help nearly everyone understand them better than simply knowing the reasons they should have those relationships.

The notion of learning geometry without drawings takes one fairly close to the Bourbaki project, the famous/infamous early 20th century French mathematical collective that tried to work out the logical structure of all mathematics on a purely formal, reasoned basis without any appeals to diagrams or physical intuition at all. It was an ambitious, controversial, and fruitful program that got permanently tainted because following from it was the “New Math”, an attempt at mathematics educational reform of the 60s and 70s which crashed hard against the problem that parents will only support educational reform that doesn’t involve teaching a thing in ways different from how they learned it.

Sondra Bell-Lundy's _Between Friends_, 18 May 2014: mothers draw a Venn Diagram.
Sondra Bell-Lundy’s _Between Friends_, 18 May 2014: mothers draw a Venn Diagram.

Sandra Bell-Lundy’s Between Friends (May 18) brings up my old nemesis of Venn Diagrams, although it gets them correct.

T Lewis and Michael Fry’s Over The Hedge (May 18) showcases the Drake Equation, a wonderful bit of reasoning that tries to answer the question of “how many species capable of interstellar communication are there”, considering that we only have evidence for at most one. It’s a wonderful bit of word-problem-type reasoning: given what we do know, which amounts mostly to how many stars there are, how can we work out what we would like to know? Frank Drake, astronomer, and co-designer of the plaque on Pioneers 10 and 11, made some estimates of what factors are relevant in going from what we do know to what we would like to know, and how they might relate. When Drake first published the equation only the number of stars could be reasonably estimated; today we can also add a good estimate of how likely a star is to have planets, and a fair estimate of how likely a planet is to be livable. The other steps are harder to estimate. But the process Drake used, of evaluating what he would need to know in order to give an answer, is still strong: there may be things about the equation which are wrong — factors that interact in ways not previously considered, for example — but it divides a huge problem into a series of smaller ones that can, hopefully, be studied and understood in pieces and through this process be turned into knowledge.

And finally, Jeff Harris’s Shortcuts (May 18), a kid’s activity/information panel, spends a half-a-comics-page talking about numbers and numerals. It’s a pretty respectable short guide to numbers and their representations, including some of the more famous number-representation schemes.

Reading the Comics, May 13, 2014: Good Class Problems Edition


Someone in Comic Strip Master Command must be readying for the end of term, as there’s been enough comic strips mentioning mathematics themes to justify another of these entries, and that’s before I even start reading Wednesday’s comics. I can’t say that there seem to be any overarching themes in the past week’s grab-bag of strips, but, there are a bunch of pretty good problems that would fit well in a mathematics class here.

Darrin Bell’s Candorville (May 6) comes back around to the default application of probability, questions in coin-flipping. You could build a good swath of a probability course just from the questions the strip implies: how many coins have to come up heads before it becomes reasonable to suspect that something funny is going on? Two is obviously too few; two thousand is likely too many. But improbable things do happen, without it signifying anything. So what’s the risk of supposing something’s up when it isn’t? What’s the risk of dismissing the hints that something is happening?

Mark Anderson’s Andertoons (May 8) is another entry in the wiseacre schoolchild genre (I wonder if I’ve actually been consistent in describing this kind of comic, but, you know what I mean) and suggesting that arithmetic just be done on the computer. I’m sympathetic, however much fun it is doing arithmetic by hand.

Justin Boyd’s Invisible Bread (May 9) is honestly a marginal inclusion here, but it does show a mathematics problem that’s correctly formed and would reasonably be included on a precalculus or calculus class’s worksheets. It is a problem that’s a no-brainer, really, but that fits the comic’s theme of poorly functioning.

Steve Moore’s In The Bleachers (May 12) uses baseball scores and the start of a series. A series, at least once you’re into calculus, is the sum of a sequence of numbers, and if there’s only finitely many of them, here, there’s not much that’s interesting to say. Each sequence of numbers has some sum and that’s it. But if you have an infinite series — well, there, all sorts of amazing things become possible (or at least logically justified), including integral calculus and numerical computing. The series from the panel, if carried out, would come to a pair of infinitely large sums — this is called divergence, and is why your mathematician friends on Facebook or Twitter are passing around that movie poster with a math formula for a divergent series on it — and you can probably get a fair argument going about whether the sum of all the even numbers would be equal to the sum of all the odd numbers. (My advice: if pressed to give an answer, point to the other side of the room, yell, “Look, a big, distracting thing!” and run off.)

Samson’s Dark Side Of The Horse (May 13) is something akin to a pun, playing as it does on the difference between a number and a numeral and shifting between the ways we might talk about “three”. Also, I notice for the first time that apparently the little bird sometimes seen in the comic is named “Sine”, which is probably why it flies in such a wavy pattern. I don’t know how I’d missed that before.

Rick Detorie’s One Big Happy (May 13, rerun) is also a strip that plays on the difference between a number and its representation as a numeral, really. Come to think of it, it’s a bit surprising that in Arabic numerals there aren’t any relationships between the representations for numbers; one could easily imagine a system in which, say, the symbol for “four” were a pair of whatever represents “two”. In A History Of Mathematical Notations Florian Cajori notes that there really isn’t any system behind why a particular numeral has any particular shape, and he takes a section (Section 96 in Book 1) to get engagingly catty about people who do. I’d like to quote it because it’s appealing, in that way:

A problem as fascinating as the puzzle of the origin of language relates to the evolution of the forms of our numerals. Proceeding on the tacit assumption that each of our numerals contains within itself, as a skeleton so to speak, as many dots, strokes, or angles as it represents units, imaginative writers of different countries and ages have advanced hypotheses as to their origin. Nor did these writers feel that they were indulging simply in pleasing pastimes or merely contributing to mathematical recreations. With perhaps only one exception, they were as convinced of the correctness of their explanations as are circle-squarers of the soundness of their quadratures.

Cajori goes on to describe attempts to rationalize the Arabic numerals as “merely … entertaining illustrations of the operation of a pseudo-scientific imagination, uncontrolled by all the known facts”, which gives some idea why Cajori’s engaging reading for seven hundred pages about stuff like where the plus sign comes from.

Reading the Comics, April 21, 2014: Bill Amend In Name Only Edition


Recently the National Council of Teachers of Mathematics met in New Orleans. Among the panelists was Bill Amend, the cartoonist for FoxTrot, who gave a talk about the writing of mathematics comic strips. Among the items he pointed out as challenges for mathematics comics — and partly applicable to any kind of teaching of mathematics — were:

  • Accessibility
  • Stereotypes
  • What is “easy” and “hard”?
  • I’m not exactly getting smarter as I age
  • Newspaper editors might not like them

Besides the talk (and I haven’t found a copy of the PowerPoint slides of his whole talk) he also offered a collection of FoxTrot comics with mathematical themes, good for download and use (with credit given) for people who need to stock up on them. The link might be expire at any point, note, so if you want them, go now.

While that makes a fine lead-in to a collection of mathematics-themed comic strips around here I have to admit the ones I’ve seen the last couple weeks haven’t been particularly inspiring, and none of them are by Bill Amend. They’ve covered a fair slate of the things you can write mathematics comics about — physics, astronomy, word problems, insult humor — but there’s still interesting things to talk about. For example:

Continue reading “Reading the Comics, April 21, 2014: Bill Amend In Name Only Edition”

Reading the Comics, March 26, 2014: Kitchen Science Department


It turns out that three of the comic strips to be included in this roundup of mathematics-themed strips mentioned things that could reasonably be found in kitchens, so that’s why I’ve added that as a subtitle. I can’t figure a way to contort the other entries to being things that might be in kitchens, but, given that I don’t get to decide what cartoonists write about I think I’m doing well to find any running themes.

Ralph Hagen’s The Barn (March 19) is built around a possibly accurate bit of trivia which tries to stagger the mind by considering the numinous: how many stars are there? This evokes, to me at least, one of the famous bits of ancient Greek calculations (for which they get much less attention than the geometers and logicians did), as Archimedes made an effort to estimate how many grains of sand could fit inside the universe. Archimedes had apparently little fear of enormous numbers, and had to strain the Greek system for representing numbers to get at such enormous quantities. But he was an ingenious reasoner: he was able to estimate, for example, the sizes and distances to the Moon and the Sun based on observing, with the naked eye, the half-moon; and his work on problems like finding the value of pi get surprisingly close to integral calculus and would probably be a better introduction to the subject than pre-calculus courses are. It’s quite easy in considering how big (and how old) the universe is to get to numbers that are really difficult to envision, so, trying to reduce that by imagining stars as grains of salt might help, if you can imagine a ball of salt eight miles across.

Continue reading “Reading the Comics, March 26, 2014: Kitchen Science Department”

Reading the Comics, February 21, 2014: Circumferences and Monkeys Edition


And now to finish off the bundle of mathematic comics that I had run out of time for last time around. Once again the infinite monkeys situation comes into play; there’s also more talk about circumferences than average.

Brian and Ron Boychuk’s The Chuckle Brothers (February 13) does a little wordplay on how “circumference” sounds like it could kind of be a knightly name, which I remember seeing in a minor Bugs Bunny cartoon back in the day. “Circumference” the word derives from the Latin, “circum” meaning around and “fero” meaning “to carry”; and to my mind, the really interesting question is why do we have the words “perimeter” and “circumference” when it seems like either one would do? “Circumference” does have the connotation of referring to just the boundary of a circular or roughly circular form, but why should the perimeter of circular things be so exceptional as to usefully have its own distinct term? But English is just like that, I suppose.

Paul Trapp’s Thatababy (February 13) brings back the infinite-monkey metaphor. The infinite monkeys also appear in John Deering’s Strange Brew (February 20), which is probably just a coincidence based on how successfully tossing in lots of monkeys can produce giggling. Or maybe the last time Comic Strip Master Command issued its orders it sent out a directive, “more infinite monkey comics!”

Ruben Bolling’s Tom The Dancing Bug (February 14) delivers some satirical jabs about Biblical textual inerrancy by pointing out where the Bible makes mathematical errors. I tend to think nitpicking the Bible mostly a waste of good time on everyone’s part, although the handful of arithmetic errors are a fair wedge against the idea that the text can’t have any errors and requires no interpretation or even forgiveness, with the Ezra case the stronger one. The 1 Kings one is about the circumference and the diameter for a vessel being given, and those being incompatible, but it isn’t hard to come up with a rationalization that brings them plausibly in line (you have to suppose that the diameter goes from outer wall to outer wall, while the circumference is that of an inner wall, which may be a bit odd but isn’t actually ruled out by the text), which is why I think it’s the weaker.

Bill Whitehead’s Free Range (February 16) uses a blackboard full of mathematics as a generic “this is something really complicated” signifier. The symbols as written don’t make a lot of sense, although I admit it’s common enough while working out a difficult problem to work out weird bundles of partly-written expressions or abuses of notation (like on the middle left of the board, where a bracket around several equations is shown as being less than a bracket around fewer equations), just because ideas are exploding faster than they can be written out sensibly. Hopefully once the point is proven you’re able to go back and rebuild it all in a form which makes sense, either by going into standard notation or by discovering that you have soem new kind of notation that has to be used. It’s very exciting to come up with some new bit of notation, even if it’s only you and a couple people you work with who ever use it. Developing a good way of writing a concept might be the biggest thrill in mathematics, even better than proving something obscure or surprising.

Jonathan Lemon’s Rabbits Against Magic (February 18) uses a blackboard full of mathematics symbols again to give the impression of someone working on something really hard. The first two lines of equations on 8-Ball’s board are the time-dependent Schrödinger Equations, describing how the probability distribution for something evolves in time. The last line is Euler’s formula, the curious and fascinating relationship between pi, the base of the natural logarithm e, imaginary numbers, one, and zero.

Todd Clark’s Lola (February 20) uses the person-on-an-airplane setup for a word problem, in this case, about armrest squabbling. Interesting to me about this is that the commenters get into a squabble about how airplane speeds aren’t measured in miles per hour but rather in nautical miles, although nobody not involved in air traffic control really sees that. What amuses me about this is that what units you use to measure the speed of the plane don’t matter; the kind of work you’d do for a plane-travelling-at-speed problem is exactly the same whatever the units are. For that matter, none of the unique properties of the airplane, such as that it’s travelling through the air rather than on a highway or a train track, matter at all to the problem. The plane could be swapped out and replaced with any other method of travel without affecting the work — except that airplanes are more likely than trains (let’s say) to have an armrest shortage and so the mock question about armrest fights is one in which it matters that it’s on an airplane.

Bill Watterson’s Calvin and Hobbes (February 21) is one of the all-time classics, with Calvin wondering about just how fast his sledding is going, and being interested right up to the point that Hobbes identifies mathematics as the way to know. There’s a lot of mathematics to be seen in finding how fast they’re going downhill. Measuring the size of the hill and how long it takes to go downhill provides the average speed, certainly. Working out how far one drops, as opposed to how far one travels, is a trigonometry problem. Trying the run multiple times, and seeing how the speed varies, introduces statistics. Trying to answer questions like when are they travelling fastest — at a single instant, rather than over the whole run — introduce differential calculus. Integral calculus could be found from trying to tell what the exact distance travelled is. Working out what the shortest or the fastest possible trips introduce the calculus of variations, which leads in remarkably quick steps to optics, statistical mechanics, and even quantum mechanics. It’s pretty heady stuff, but I admit, yeah, it’s math.

Reading the Comics, October 8, 2013


As promised, I’ve got a fresh round of mathematics-themed comic strips to discuss, something that’s rather fun to do because it offers such an easy answer to the question of what to write about today. Once you have the subject and a deadline the rest of the writing isn’t so very hard. So here’s some comics with all the humor safely buried in exposition:

Allison Barrows’s PreTeena (September 24, Rerun) brings the characters to “Performance Camp” and a pun on one of the basic tools of trigonometry. The pun’s routine enough, but I’m delighted to see that Barrows threw in a (correct) polynomial expression for the sine of an angle, since that’s the sort of detail that doesn’t really have to be included for the joke to read cleanly but which shows that Barrows made the effort to get it right.

Polynomial expansions — here, a Taylor series — are great tools to have, because, generally, polynomials are nice and well-behaved things. They’re easy to compute, they’re easy to analyze, they’re pretty much easy to do whatever you might want to do. Being able to shift a complicated or realistic function into a polynomial, even a polynomial with infinitely many terms, is often a big step towards making a complicated problem easy.

Continue reading “Reading the Comics, October 8, 2013”

Reading the Comics, September 11, 2013


I may need to revise my seven-or-so-comic standard for hosting one of these roundups of mathematics-themed comic strips, at least during the summer vacation. We’ll see how they go as the school year picks up and cartoonists return to the traditional jokes of students not caring about algebra and kids giving wiseacre responses to word problems.

Jan Eliot’s Stone Soup began a sequence on the 26th of August in which Holly, the teenager, has to do flash cards to improve her memorization of the multiplication tables. It’s a baffling sequence to me, at least, since I can’t figure why a high schooler needs to study the times tables (on the 27th, Grandmom says it’s because it will make mathematics easier the more arithmetic she can do in her head). It’s also a bit infuriating because I can’t see a way to make sure Holly sees mathematics as tedious drudge work more than getting drilled by flash cards through summer vacation, particularly as she’s at an age where she ought to be doing algebra or trigonometry or geometry.

Steve Moore’s In The Bleachers (September 1) uses a bit of mathematics as a throwaway “something complicated to be thinking about” bit. I do like that the mathematics shown at least parses. I’m not sure offhand what problem the pitcher is trying to solve, that is, but the steps in it are done correctly, and even show off a nice bit of implicit differentiation. That’s a bit of differential calculus where you’ll find the rate of change of one variable with respect to another depends on the value of the variable, which isn’t actually hard to do if you follow the rules correctly but which, as I remember it, produces a vague sense of unease at its introduction. Probably it feels vaguely illicit to have a function defined in, in parts, in terms of itself.

Continue reading “Reading the Comics, September 11, 2013”

Reading the Comics, July 5, 2013


I’m surprised to discover it’s been over a month since I had a roster of mathematics-themed comic strips to share, but that’s how things happen to happen. It’s also been a month with repeated references to “finding square roots”, I suppose because that sounds like a really math-y thing to do. It’s certainly computationally challenging; the task of finding such is even a (very minor) moment in Isaac Asimov’s magnificent short story about arithmetic, “The Feeling Of Power”. I remember reading the procedure for finding them when I was a kid, and finding that with considerable effort, I was able to, though I’d probably refuse to do more than give a rough estimate of such a root nowadays.

Bill Watterson’s Calvin and Hobbes (June 4, rerun) is another entry in the long string of jokes about “why bother studying mathematics”, but Watterson’s craft lifts it above average. Admire that fourth panel: that’s every resistant student in one pose.

Continue reading “Reading the Comics, July 5, 2013”

Reading the Comics, April 28, 2013


The flow of mathematics-themed comic strips almost dried up in April. I’m going to assume this reflects the kids of the cartoonists being on Spring Break, and teachers not placing exams immediately after the exam, in early to mid-March, and that we were just seeing the lag from that. I’m joking a little bit, but surely there’s some explanation for the rash of did-you-get-your-taxes-done comics appearing two weeks after April 15, and I’m fairly sure it isn’t the high regard United States newspaper syndicates have for their Canadian readership.

Dave Whamond’s Reality Check (April 8) uses the “infinity” symbol and tossed pizza dough together. The ∞ symbol, I understand, is credited to the English mathematician John Wallis, who introduced it in the Treatise on the Conic Sections, a text that made clearer how conic sections could be described algebraically. Wikipedia claims that Wallis had the idea that negative numbers were, rather than less than zero, actually greater than infinity, which we’d regard as a quirky interpretation, but (if I can verify it) it makes for an interesting point in figuring out how long people took to understand negative numbers like we believe we do today.

Jonathan Lemon’s Rabbits Against Magic (April 9) does a playing-the-odds joke, in this case in the efficiency of alligator repellent. The joke in this sort of thing comes to the assumption of independence of events — whether the chance that a thing works this time is the same as the chance of it working last time — and a bit of the idea that you find the probability of something working by trying it many times and counting the successes. Trusting in the Law of Large Numbers (and the independence of the events), this empirically-generated probability can be expected to match the actual probability, once you spend enough time thinking about what you mean by a term like “the actual probability”.

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Reading the Comics, April 5, 2013


Before getting to the next round of comic strips that mention mathematics stuff, I’d like to do a bit of self-promotion. Freshly published is the book Oh, Sandy: An Anthology Of Humor For A Serious Purpose, edited by Lynn Beighley, Peter Barlow, Andrea Donio, and A J Fader. This is a collection of humorous bits, written out of a sense of needing to do something useful after the Superstorm. I have an essay in there, based on the strange feelings I had of being remote (and quite safe) while seeing my home state — and particularly the piers at Seaside Heights, New Jersey — being battered by a storm. The book is available also through CreateSpace.

Jenny Campbell’s Flo and Friends (March 23) mentions π, and what’s really a fairly indistinct question for a tutor to ask the student. “Explain pi” is more open-ended than I think could be useful to answer: you could write books trying to describe what it’s used for, never mind the history of studying it. After all, it’s the only transcendental number with enough pop cultural cachet to appear routinely in newspaper comic strips; what constitutes an explanation of it? Alas, the strip just goes for the easiest pi pun to be made.

Scott Hilburn’s The Argyle Sweater (March 25) returns to the gimmick of anthropomorphized numerals. It’s a cute enough joke; it’s also apparently a different pair of 1 and 2 from earlier in the month. I do wonder what, in this panel’s continuity, subtraction might mean. Still, Hilburn is obviously never far from thinking of anthropomorphized numbers, as he came back to the setting on April 3, with another 2 putting in an appearance.

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Reading the Comics, March 12, 2013


I’ve got my seven further comic strips with mentions of mathematical topics, so I can preface that a bit with my surprise that at least some of the Gocomics.com comics didn’t bother to mention Pi Day, March 14. It might still be a slightly too much of a This Is Something People Do On The Web observance to be quite sensible for the newspaper comic strips. But there are quite a few strips on Gocomics.com that only appear online, and I thought one of them might.

(I admit I’m a bit of a Pi Day grouch, on the flimsy grounds that 3/14 is roughly 0.214, which is a rotten approximation to π. But American-style date-writing never gets very good at approximating π. The day-month format used in most of the world offers 22/7 as a less strained Pi Day candidate, except that there’s few schools in session then, wiping out whatever use the day has as a playfully educational event.)

Gene Weingarten, Dan Weingarten and David Clark’s Barney and Clyde (March 4) introduces a character which I believe is new to the strip, “Norman the math fanatic”. (He hasn’t returned since, as of this writing.) The setup is about the hypothetical and honestly somewhat silly argument about learning math being more important than learning English. I’m not sure I could rate either mathematics or English (or, at least, the understanding of one’s own language) as more important. The panel ends with the traditional scrawl of symbols as shorthand for “this is complicated mathematics stuff”, although it’s not so many symbols and it doesn’t look like much of a problem to me. Perhaps Norman is fanatic about math but doesn’t actually do it very well, which is not something he should be embarrassed about.

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Reading the Comics, February 13, 2013


I will return to the plausibility of Rex Morgan, MD, considered as a statistics problem, though I need time to do that pesky thinking thing and I’ve had all sorts of unreasonable demands on my time, such as work expecting me to work, and scheduling it all is such a problem. But I’ve got a fresh batch of eight comic strips that in some way mention mathematics, and I wrote paragraphs on most of those as they turned up in the day’s pages, so I can share those with you. Also I’m pleased to see that posting a Rex Morgan strip for the purpose of talking about it hasn’t brought about the end of the world, so I may be able to resume covering King Features or North American Syndicate strips when they say things worth mentioning (which they seem to do less than the Gocomics.com comics do, but I haven’t done the statistics to make that claim seriously).

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Reblog: I don’t get it


If I could do any of these moves it would considerably improve my dancing.

EDUtainment BLOG @ DEVRICK.com

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I Try Telling Jokes, Too


I’d like to take a moment — after my most popular month ever, according to the WordPress statistics, one in which my little math blog managed to reach not just the 7,777th viewer but also the 8,000th, with the nice round 8,192nd looking like it’s coming soon — to announce the inauguration of another blog of my hopefully creative writing.

This one, Nebushumor.wordpress.com, is for the writing that I at least intend to be funny, and while I concede the number of people who actually share my sense of humor is perhaps not overwhelming, there’s probably some out there who do, and I’d appreciate your looking and following if you like what you see. Right now I’m still in the stage of starting a new project where I feel hideously embarrassed that I put myself forward like that, all set for public humiliation and whatnot, but that feeling will pass. I hope.

Also, I found a setting that lets me turn on little numeric ratings for all my various articles. I’m hoping that people enjoy this because if there’s one thing I’ve learned about the Internet, it’s that people like getting to click stuff. Plus turning it on satisfied my urge to fiddle with the look of this blog a while, since I can’t find another WordPress theme that I like for it.

Reading the Comics, January 29, 2013


I’ve got enough mathematics-themed comic strips for a fresh installment of my comic tracking. I also want to mention the January 29th Jumble has a math teacher joke in it, but I don’t know a reasonably archivable way to point to that. Jumble.com, which I think is the official web site, is suffering some kind of database glitch so there could be anything there. Also, from working it out, “rimpet” may not be a word but it does look like it ought to be.

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Reading the Comics, January 21, 2013


Feast or famine, as I said. It’s not a week since the last comics roundup and I have eight comic strips that have enough mathematical content for me to discuss. Well, they’re fun essays to write, and people seem to quite like them, so why not another so soon?

Well, because I’m overlooking all the King Features Syndicate comics. I’m not actually overlooking them — I’m keeping track of just which ones have something I could write about — but they haven’t had a nice, archive-friendly way to point people to the strips being discussed. (Most newspaper web sites that have King Features comics have links to those pages expire in a measly 28 days.) Based on the surprising number of people who come to my site by searching for Norm Feuti’s Retail comic strip, they certainly deserve to be talked about. I’ll have something worked out about that soon, I promise.

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Cutting Commentary


It might be that one functional definition of a friend is “someone who can say stuff that would be insulting, but you mostly don’t mind”. I had been chatting with a friend who wasn’t aware of my little blogging effort here, and gave the front page URL. My friend claimed to get a headache “from just a casual perusal!”

I know what’s intended: an acknowledgement that the writing I’ve been doing has been at least math-flavored, and that’s got almost universal acclaim as something really hard that stresses the mind to think about, and delivered in the form of a joke. It’s an overused joke, to my tastes, but an overused joke can serve several positive purposes. It can be one of the landmarks that one is in an emotionally comfortable place, or mark that the people sharing it share this in common, or that whatever is being joked about has connections to other times the joke’s been used.

Still, the joke is a bit of a complicated insult too: it insults both the writer, for not being understandable, and the reader, for not understanding. But I know that it’s not meant to insult, and I’m hardly in a position to turn away compliments when I can find them.

All this muttering I mean, largely, to warn that I am working out whether I’m good enough to write a couple pieces towards a question that really is somewhat head-spinning in a way that someone who isn’t a math or physics major would have a hope of following. I might not be; as I do research I realize I’m hitting questions I can’t fully satisfy myself about. If I can, I may go forward and you’ll see what perusal headaches really look like.

Reading the Comics, January 16, 2013


I was beginning to wonder whether my declaration last time that I’d post a comics review every time I had seven to ten strips to talk about was going to see the extinguishing of math-themed comic strips. It only felt like it. The boom-and-bust cycle continues, though; it took better than two weeks to get six such strips, and then three more came in two days. But that’s the fun of working on relatively rare phenomena. Let me get to the most recent installment of math-themed comics, mostly from Gocomics.com:

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Reading The Comics, December 28, 2012


As per my declaration I’d do these reviews when I had about seven to ten comics to show off, I’m entering another in the string of mathematics-touching comic strip summaries. Unless the last two days of the year are a bumper crop this finishes out 2012 in the comics and I hope to see everyone in the new year.

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Reading The Comics, December 15, 2012


I’ve been trying to balance how often I do the comics reviews with how often I do other essays; I admit the comics feel like particular fun to write, but the other essays are less reactive. This leaves me feeling like after I’ve done a comics roundup I should do a couple in which I come up with the topic, the exposition, and all the supplementary matter for a while, but that encourages pileups in the comics. I’m thinking of shifting over to some kind of rule less dependent on my feeling, such as writing a comics article whenever I have (say) seven to ten features to show off. We’ve got that more than that now, it turns out, so let me start out with some that came across my desktop since the last comics review.

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Reading the Comics, November 21, 2012


It’s been long enough since my last roundup of mathematics-themed comics to host a new one. I’m also getting stirred to try tracking how many of these turn up per day, because they certainly feel like they run in a feast-or-famine pattern. There’d be no point to it, besides satisfying my vague feelings that everything can be tracked, but there’s data laying there all ready to be measured, isn’t there?

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Reading the Comics, October 25, 2012


As before, this is going to be the comics other than those run through King Features Syndicate, since I haven’t found a solution I like for presenting their mathematics-themed comic strips for discussion. But there haven’t been many this month that I’ve seen either, so I can stick with gocomics.com strips for today at least. (I’m also a little irked that Comics Kingdom’s archives are being shut down — it’s their right, of course, but I don’t like having so many dead links in my old articles.) But on with the strips I have got.

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Reading the Comics, October 13, 2012


I suppose it’s been long enough to resume the review of math-themed comic strips. I admit there are weeks I don’t have much chance to write regular articles and then I feel embarrassed that I post only comic strips links, but I do enjoy the comics and the comic strip reviews. This one gets slightly truncated because King Features Syndicate has indeed locked down their Comics Kingdom archives of its strips, making it blasted inconvenient to read and nearly impossible to link to them in any practical, archivable way. They do offer a service, DailyInk.com, with their comic strips, but I can hardly expect every reader of mine to pay up over there just for the odd day when Mandrake the Magician mentions something I can build a math problem from. Until I work out an acceptable-to-me resolution, then, I’ll be dropping to gocomics.com and a few oddball strips that the Houston Chronicle carries.

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Reading the Comics, September 26, 2012


I haven’t time to write a short piece today so let me go through a fresh batch of math-themed comic strips instead. There might be a change coming to these features soon, both in the strips I read and in how I present them, since Comics Kingdom, which provides the King Features Syndicate comic strips, has shown signs that they’re tightening up web access to their strips.

I can’t blame them for wanting to make sure people go through paths they control — and, pay for, at least in advertising clicks — but I can fault them for doing a rotten job of it. They’re just not very good web masters, and end up serving strips — you may have seen them if you’ve gone to the comics page of your local newspaper — that are tiny, which kills plot-heavy features like The Phantom or fine-print heavy features like Slylock Fox Sunday pages, and loaded with referrer-based and cookie-based nonsense that makes it too easy to fail to show a comic altogether or to screw up hopelessly loading up several web browser tabs with different comics in them.

For now that hasn’t happened, at least, but I’m warning that if it does, I might not necessarily read all the King Features strips — their advertising claims they have the best strips in the world, but then, they also run The Katzenjammer Kids which, believe it or not, still exists — and might not be able to comment on them. We’ll see. On to the strips for the middle of September, though:

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Reading the Comics, September 11, 2012


Since the last installment of these mathematics-themed comic strips there’s been a steady drizzle of syndicated comics touching on something mathematical. This probably reflects the back-to-school interests that are naturally going to interest the people drawing either Precocious Children strips or Three Generations And A Dog strips.

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Reading the Comics, August 27, 2012


I’m also surprised to find it’s been about a month since my last roundup of mathematics-themed comic strips, but that’s about how it worked out. There was a long stretch of not many syndicated comics touching on any subjects at all and then a rush as cartoonists noticed that summer vacation is on the verge of ending. (I understand in some United States school districts it already has ended, but I grew up in a state where school simply never started before Labor Day, so the idea of school in August feels fundamentally implausible.)

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Reading the Comics, July 28, 2012


I intend to be back to regular mathematics-based posts soon. I had a fine idea for a couple posts based on Sunday’s closing of the Diaster Transport roller coaster ride at Cedar Point, actually, although I have to technically write them first. (My bride and I made a trip to the park to get a last ride in before its closing, and that lead to inspiration.) But reviews of math-touching comic strips are always good for my readership, if I’m readin the statistics page here right, so let’s see what’s come up since the last recap, going up to the 14th of July.

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Reading the Comics, July 14, 2012


I hope everyone’s been well. I was on honeymoon the last several weeks and I’ve finally got back to my home continent and new home so I’ll try to catch up on the mathematics-themed comics first and then plunge into new mathematics content. I’m splitting that up into at least two pieces since the comics assembled into a pretty big pile while I was out. And first, I want to offer the link to the July 2 Willy and Ethel, by Joe Martin, since even though I offered it last time I didn’t have a reasonably permanent URL for it.

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Reading the Comics, June 13, 2012


Because there weren’t many math-themed comic strips, that’s why I went so long without an update in my roster of comic strips that mention math subjects. After Mike Peters’s Mother Goose and Grimm put in the start of a binomial expression the comics pages — through King Features Syndicate and gocomics.com — decided to drop the whole subject pretty completely for the rest of May. It picked up a little in June.

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When To Run For The Train


I mean to return to the subject brought up Monday, about the properties of things that don’t exist, since as BunnyHugger noted I cheated in talking briefly about what properties they have or don’t have. But I wanted to bring up a nice syllogism whose analysis I’d alluded to a couple weeks back, and which it turns out I’d remembered wrong, in details but not in substance.

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Where Rap Music and Discrete Mathematics meet.


It’s the weekend; why not spread a bit of mathematics humor, using the basic element of mathematics humor, the Venn diagram?

Interestingly, Venn diagrams are also an overlap between Mathematics Humor and Philosophy Humor.

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Mid-April 2012 Comics Review


I’ve gotten enough comics, I think, to justify a fresh roundup of mathematics appearances in the comic strips. Unfortunately the first mathematics-linked appearance since my most recent entry is also the most badly dated. Pab Sugenis’s The New Adventures of Queen Victoria took (the appropriate) day to celebrate the birthday of Tom Lehrer, but fails to mention his actual greatest contribution to American culture, the “Silent E” song for The Electric Company. He’s also author of the humorous song “Lobachevsky”, which is pretty much the only place to go if you need a mathematics-based song and can’t use They Might Be Giants for some reason. (I regard Lehrer’s “New Math” song as not having a strong enough melody to count.)

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