Chris Browne’s Raising Duncan rerun for the 23rd has a man admitting bad mathematics skills for why he can’t count the ways he loves his wife. The strip originally ran the 27th of September, 2003. (The strip was short-lived, and is in perpetual reruns. It may be worth reading at least one time through, though, since the pairs of main characters in it are eagerly in love, without being sappy about it, and it’s pleasant seeing people enthusiastic about each other. This is the strip that had the exchange “Marry me!” “I did!” “Marry me more!” “Okay!” that keeps bringing me cheer and relationship goals.)
One is that, as we’ve thought of counting numbers, there is always “one more”. This doesn’t have to be. We could work with perfectly good number systems that have a largest number. We do, in fact. Every computer programming language has some largest integer that it will deal with. If you need a larger number, you have to do something clever. Your clever idea will let you address some range of bigger numbers, but it too will have a maximum. We’ve set those limits large enough that, usually, they’re not an inconvenience. They’re still there.
But those limits are forced on us by the many failings of matter. What when we get just past Plato’s line’s division, into the reasoning of pure mathematics? There we can set up counting numbers. The standard way to do this is to suppose there is a number “1”. And to suppose that, for any counting number we have, there is a successor, a number one-plus-that. If Joey were to ask why there has to be, all Dennis could do is shrug. This makes an axiom out of there always being one more. If you don’t like it, make some other arithmetic. Anyway we only understand any of this using fallible matter, so good luck.
This progression can be heady, though. The counting numbers are probably the most understandable infinitely large set there is. Thinking about them seriously can induce the sort of dizzy awe that pondering Deep Time or the vastness of space can do. That seems a bit above Dennis’s age level, but some people are stricken with the infinite sooner than others are.
Charles Schulz’s Peanuts Begins rerun for the 2nd has Charlie Brown dismiss arithmetic as impractical. It fits the motif of mathematics as an unworldly subject. There’s the common joke that pure mathematics even dreams of being of no use to anyone. Arithmetic, though, has always been a practical subject. It introduces us to many abstract ideas, particularly group theory. This subject looks at what we can do with systems that work like arithmetic without necessarily having numbers, or anything that works with numbers.
And a couple of comic strips mentioned mathematics, although in too slight a way to discuss. Dana Simpson’s Phoebe and her Unicorn on the 30th of April started a sequence in which doodles on Phoebe’s homework came to life. That it’s mathematics homework was mostly incidental. I’m open to the argument that mathematics encourages doodling in a way that, say, spelling does not. I’d also be open to the argument you aren’t doing geometry if you don’t doodle. Anyway. Dan Thompson’s Brevity for the 2nd of May features Sesame Street’s Count von Count. It’s a bit of wordplay on the use of “numbers” for songs. And, of course, the folkloric tradition of vampires as compulsive counters.
There were a handful of comic strips from last week which I didn’t already discuss. Two of them inspire me to write about how we know how to do things. That makes a good theme.
Marcus Hamilton and Scott Ketcham’s Dennis the Menace for the 27th gets into deep territory. How does we could count to a million? Maybe some determined soul has actually done it. But it would take the better part of a month. Things improve some if we allow that anything a computing machine can do, a person could do. This seems reasonable enough. It’s heady to imagine that all the computing done to support, say, a game of Roller Coaster Tycoon could be done by one person working alone with a sheet of paper. Anyway, a computer could show counting up to a million, a billion, a trillion, although then we start asking whether anyone’s checked that it hasn’t skipped some numbers. (Don’t laugh. The New York Times print edition includes an issue number, today at 58,258, at the top of the front page. It’s meant to list the number of published daily editions since the paper started. They mis-counted once, in 1898, and nobody noticed until 1999.)
Anyway, allow that. Nobody doubts that, if we put enough time and effort into it, we could count up to any positive whole number, or as they say in the trade, “counting number”. But … there is some largest number that we could possibly count to, even if we put every possible resource and all the time left in the universe to that counting. So how do we know we “could” count to a number bigger than that? What does it mean to say we “could” if the circumstances of the universe are such that we literally could not?
Counting up to a number seems uncontroversial enough. If I wanted to prove it I’d say something like “if we can count to the whole number with value N, then we can count to the whole number with value N + 1 by … going one higher.” And “We can count to the whole number 1”, proving that by enunciating as clearly as I can. The induction follows. Fine enough. That’s a nice little induction proof.
But … what if we needed to do more work? What if we needed to do a lot of work? There is a corner of logic which considers infinitely long proofs, or infinitely long statements. They’re not part of the usual deductive logic that any mathematician knows and relies on. We’re used to, at least in principle, being able to go through and check every step of a proof. If that becomes impossible is that still a proof? It’s not my field, so I feel comfortable not saying what’s right and what’s wrong. But it is one of those lectures in your Mathematical Logic course that leaves you hanging your jaw open.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 27th is a joke about algorithms. These are the processes by which we know how to do a thing. Here, Hansel and Gretel are shown using what’s termed a “greedy algorithm” to follow pebbles back home. This kind of thing reflects trying to find an acceptable solution, in this case, finding a path somewhere. What makes it “greedy” is each step. You’re at a pebble. You can see other pebbles nearby. Which one do you go to? Go to some extreme one; in this case, the nearest. It could instead have been the biggest, or the shiniest, the one at the greatest altitude, the one nearest a water source. Doesn’t matter. You choose your summum bonum and, at each step, take the move that maximizes that.
The wicked mother knows something about this sort of algorithm, one that promises merely a solution and not the best solution. And that is that all these solutions can be broken. You can set up a problem that the algorithm can’t solve. Greedy algorithms are particularly vulnerable to this. They’re called “local maximums”. You find the best answer of the ones nearby, but not the best one you possibly could locate.
Why use an algorithm like this, that can be broken so? That’s because we often want to do problems like finding a path through the woods. There are so many possible paths that it’s hard to find one of the acceptable ones. But there are processes that will, typically, find an acceptable answer. Maybe processes that will let us take an acceptable answer and improve it to a good answer. And this is getting into my field.
Actual persons encountering one of these pebble rings would (probably) notice they were caught in a loop. And what they’d do, then, is suspend the greedy rule: instead of going to the nearest pebble they could find, they’d pick something else. Maybe simply the nearest pebble they hadn’t recently visited. Maybe the second-nearest pebble. Maybe they’d give up and strike out in a random direction, trusting they’ll find some more pebbles. This can lead them out of the local maximum they don’t want toward the “global maximum”, the path home, that they do. There’s no reason they can’t get trapped again — this is why the wicked mother made many loops — and no reason they might not get caught in a loop of loops again. Every algorithm like this can get broken by some problem, after all. But sometimes taking the not-the-best steps can lead you to a better solution. That’s the insight at the heart of “Metropolis-Hastings” algorithms, which was my field before I just read comic strips all the time.
Brian Fies’s The Last Mechanical Monster for the 24th is a repeat. I included it last October, when I first saw it on GoComics. Still, the equations in it are right, for ballistic flight. Ballistic means that something gets an initial velocity in a particular direction and then travels without any further impulse. Just gravity. It’s a pretty good description for any system where acceleration’s done for very brief times. So, things fired from guns. Rockets, which typically have thrust for a tiny slice of their whole journey and coast the rest of the time. Anything that gets dropped. Or, as in here, a mad scientist training his robot to smash his way through a bank, and getting flung so.
The symbols in the equations are not officially standardized. But they might as well be. ‘v’ here means the speed that something’s tossed into the air. It really wants to be ‘velocity’, but velocity, in the trades, carries with it directional information. And here that’s buried in ‘θ’, the angle with respect to vertical that the thing starts flight in. ‘g’ is the acceleration of gravity, near enough constant if you don’t travel any great distance over the surface of the Earth. ‘y0‘ is the height from which the thing started to fly. And so then ‘d’ becomes the distance travelled, while ‘t’ is the time it takes to travel. I’m impressed the mad scientist (the one from the original Superman cartoon, in 1941; Fies wrote a graphic novel about that man after his release from jail in the present day.)
Greg Cravens’s Hubris! for the 24th jokes about the dangers of tangled earbuds. For once, mathematics can help! There’s even a whole field of mathematics about this. Not earbuds specifically, but about knots. It’s called knot theory. I trust field was named by someone caught by surprise by the question. A knot, in this context, is made of a loop of thread that’s assumed to be infinitely elastic, so you can always stretch it out or twist it around some. And it’s frictionless, so you can slide the surface against itself without resistance. And you can push it along an end. These are properties that real-world materials rarely have.
But. They can be close enough. And knot theory tells us some great, useful stuff. Among them: your earbuds are never truly knotted. To be a knot at all, the string has to loop back and join itself. That is, it has to be like a rubber band, or maybe an infinity scarf. If it’s got loose ends, it’s no knot. It’s topologically just a straight thread with some twists made in the surface. They can come loose.
All that holds these earbuds together is the friction of the wires against each other. (That the earbud wire splits into a left and a right bud doesn’t matter, here.) They can be loosened. Let me share how.
My love owns, among other things, a marionette dragon. And once, despite it being stored properly, the threads for it got tangled, and those things are impossible to untangle on purpose. I, having had one (1) whole semester of knot theory in grad school, knew an answer. I held the marionette upside-down, by the dragon. The tangled wires and the crossed sticks that control it hung loose underneath. And then shook the puppet around. This made the wires, and the sticks, shake around. They untangled, quickly.
What held the marionette strings, and what holds earbuds, together, is just friction. It’s hard to make the wire slide loosely against itself. Shaking it around, though? That gives it some energy. That gives the wire some play. And here we have one of the handful of cases where entropy does something useful for us. There’s a limit to how tightly a wire can loop around itself. There’s no limit to how loosely it can go. Little, regular, random shakes will tend to loosen the wire. When it’s loose enough, it untangles naturally.
You can help this along. We all know how. Use a pen-point or a toothpick a needle to pry some of the wires apart. That makes the “knot” easier to remove. This works by the same principle. If you reduce how much the wire contacts itself, you reduce the friction on the wire. The wire can slide more easily into the un-knot that it truly is. The comic’s tech support guy gave up too easily.
Samson’s Dark Side of the Horse for the 25th is the Roman numerals joke for this essay. And a cute bit about coincidences between what you can spell out with Roman numerals and sounds people might make. Writing out calculations evokes peculiar, magical prowess. When they include, however obliquely, words? Or parts of words? Can’t blame people for seeing the supernatural in it.
I hate to disillusion anyone but I lack hard rules about what qualifies as a mathematically-themed comic strip. During a slow week, more marginal stuff makes it. This past week was going slow enough that I tagged Wednesday’s Quincy rerun, from March of 1979 for possible inclusion. And all it does is mention that Quincy’s got a mathematics test due. Fortunately for me the week picked up a little. It cheats me of an excuse to point out Ted Shearer’s art style to people, but that’s not really my blog’s business.
Also it may not surprise you but since I’ve decided I need to include GoComics images I’ve gotten more restrictive. Somehow the bit of work it takes to think of a caption and to describe the text and images of a comic strip feel like that much extra work.
Roy Schneider’s The Humble Stumble for the 13th of May is a logic/geometry puzzle. Is it relevant enough for here? Well, I spent some time working it out. And some time wondering about implicit instructions. Like, if the challenge is to have exactly four equally-sized boxes after two toothpicks are moved, can we have extra stuff? Can we put a toothpick where it’s just a stray edge, part of no particular shape? I can’t speak to how long you stay interested in this sort of puzzle. But you can have some good fun rules-lawyering it.
Jeff Harris’s Shortcuts for the 13th is a children’s informational feature about Aristotle. Aristotle is renowned for his mathematical accomplishments by many people who’ve got him mixed up with Archimedes. Aristotle it’s harder to say much about. He did write great texts that pop-science writers credit as giving us the great ideas about nature and physics and chemistry that the Enlightenment was able to correct in only about 175 years of trying. His mathematics is harder to summarize though. We can say certainly that he knew some mathematics. And that he encouraged thinking of subjects as built on logical deductions from axioms and definitions. So there is that influence.
Dan Thompson’s Brevity for the 15th is a pun, built on the bell curve. This is also known as the Gaussian distribution or the normal distribution. It turns up everywhere. If you plot how likely a particular value is to turn up, you get a shape that looks like a slightly melted bell. In principle the bell curve stretches out infinitely far. In practice, the curve turns into a horizontal line so close to zero you can’t see the difference once you’re not-too-far away from the peak.
Jason Chatfield’s Ginger Meggs for the 16th I assume takes place in a mathematics class. I’m assuming the question is adding together four two-digit numbers. But “what are 26, 24, 33, and 32” seems like it should be open to other interpretations. Perhaps Mr Canehard was asking for some class of numbers those all fit into. Integers, obviously. Counting numbers. Compound numbers rather than primes. I keep wanting to say there’s something deeper, like they’re all multiples of three (or something) but they aren’t. They haven’t got any factors other than 1 in common. I mention this because I’d love to figure out what interesting commonality those numbers have and which I’m overlooking.
Ed Stein’s Freshly Squeezed for the 17th is a story problem strip. Bit of a passive-aggressive one, in-universe. But I understand why it would be formed like that. The problem’s incomplete, as stated. There could be some fun in figuring out what extra bits of information one would need to give an answer. This is another new-tagged comic.
Henry Scarpelli and Craig Boldman’s Archie for the 19th name-drops calculus, credibly, as something high schoolers would be amazed to see one of their own do in their heads. There’s not anything on the blackboard that’s iconically calculus, it happens. Dilton’s writing out a polynomial, more or less, and that’s a fit subject for high school calculus. They’re good examples on which to learn differentiation and integration. They’re a little more complicated than straight lines, but not too weird or abstract. And they follow nice, easy-to-summarize rules. But they turn up in high school algebra too, and can fit into geometry easily. Or any subject, really, as remember, everything is polynomials.
Mark Anderson’s Andertoons for the 19th is Mark Anderson’s Andertoons for the week. Glad that it’s there. Let me explain why it is proper construction of a joke that a Fibonacci Division might be represented with a spiral. Fibonacci’s the name we give to Leonardo of Pisa, who lived in the first half of the 13th century. He’s most important for explaining to the western world why these Hindu-Arabic numerals were worth learning. But his pop-cultural presence owes to the Fibonacci Sequence, the sequence of numbers 1, 1, 2, 3, 5, 8, and so on. Each number’s the sum of the two before it. And this connects to the Golden Ratio, one of pop mathematics’ most popular humbugs. As the terms get bigger and bigger, the ratio between a term and the one before it gets really close to the Golden Ratio, a bit over 1.618.
So. Draw a quarter-circle that connects the opposite corners of a 1×1 square. Connect that to a quarter-circle that connects opposite corners of a 2×2 square. Connect that to a quarter-circle connecting opposite corners of a 3×3 square. And a 5×5 square, and an 8×8 square, and a 13×13 square, and a 21×21 square, and so on. Yes, there are ambiguities in the way I’ve described this. I’ve tried explaining how to do things just right. It makes a heap of boring words and I’m trying to reduce how many of those I write. But if you do it the way I want, guess what shape you have?
And that is why this is a correctly-formed joke about the Fibonacci Division.
And for another week running the pace of mathematically-themed comic strips has been near normal. There’s nowhere near enough to split the essay into two pieces, which is fine. There is some more work involved in including images for all the strips I discuss and this pace better fits the time I could make for writing this week. Will admit I’m scared of what’s going to happen when I have a busy week and Comic Strip Master Command orders more comics for me. I admit this isn’t an inspired name for the Edition. But the edition names are mostly there so people have a chance of telling whether they’ve read an installment before. The date alone doesn’t do it. A couple of words will. Maybe I should give up on meaningful names if there isn’t an obvious theme for the week. It’s got to be at least as good to name something “Coronet Blue Edition” as to name it “Lots Of Andertoons Edition”.
Frank Cho’s Liberty Meadows rerun for the 1st riffs on quantum computers. You’ve maybe seen much talk about them in pop science columns and blogs. They require a bunch of stuff that gets talked about as if it were magical. Quantum mechanics, obviously, the biggest bit of magic in popular science today. Complex-valued numbers, which make for much more convenient mathematical descriptions. Probability, which everyone thinks they understand and which it turns out nobody does. Vector spaces and linear algebra, which mathematics (and physics) majors get to know well. The mathematics of how a quantum computer computes is well-described as this sort of matrix and vector work. Quantum computing promises to be a really good way to do problems where the best available approach is grinding it out: testing every possibility and finding the best ones. No part of making a quantum computer is easy, though, so it’s hard to say when we’ll have the computing power to make a version of SimCity with naturally curving roads. (This is a new tag for my Reading the Comics essays, but I’ve surely featured the strip some before.)
Niklas Eriksson’s Carpe Diem for the 2nd is a mathematics-education-these-days joke. The extremely small child talking about counting-without-a-calculator as a subject worth studying. People are always complaining that people don’t do arithmetic well enough in their heads. I understand the frustration, considering last week I stymied a cashier at a Penn Station by giving $22.11 for my $11.61 order. I don’t know why he put in my payment as $20; why not let the machine designed to do this work, do the work? He did fine working out that I should get $10 in bills back but muddled up the change. As annoyances go it ranks up there with the fast food cashier asking my name for the order and entering it as “Joeseph”.
Lard’s World Peace Tips for the 4th mentions the Möbius Strip. It’s got to be the most famous exotic piece of geometry to have penetrated the popular culture. It’s also a good shape to introduce geometry students to a “non-orientable” surface. Non-orientable means about what you’d imagine. There’s not a way to put coordinates on it that don’t get weird. For example, try drawing an equator on the surface of the strip. Any curve along the surface that doesn’t run off the edges will do. The curve just has to meet itself. It looks like this divides the strip into two pieces. Fine, then; which of these two pieces is “north” and which is “south” of this equator? There’s not a way to do that. You get surprising results if you try.
Karen Montague-Reyes’s Clear Blue Water rerun for the 5th has Eve deploying a mathematical formula. She’s trying to describe the way that perception of time changes over the course of events. It’s not a bad goal. Many things turn out to be mathematically describable. I don’t see what the equation is supposed to even mean, but then, I haven’t seen the model she developed that implies this equation. (This is not a new tag and I’m surprised by that.)
Dan Thompson’s Brevity for the 6th is some mathematics wordplay, built on the abacus. I’m not sure there’s more to say about this, past that you can do much more on an abacus. You can, at least. I keep reading directions about how to multiply with it and then I look at mine and I feel helpless.
I learn, from reading not-yet-dead Usenet group rec.arts.comics.strips, that Rick Stromoski is apparently ending the comic Soup To Nutz. This is sad enough. But worse, GoComics.com has removed all but the current day’s strip from its archives. I had trusted that GoComics.com links were reliable in a way that Comics Kingdom and Creators.com weren’t. Now I learn that maybe I need to include images of the comics I review and discuss here lest my essays become unintelligible in the future? That’s not a good sign. I can do it, mind you. I just haven’t got started. You’ll know when I swing into action.
Norm Feuti, of Retail, still draws Sunday strips for Gil. They’re to start appearing on GoComics.com soon, and I can talk about them from my regular sources after that. But for now I follow the strip on Twitter. And last Sunday he posted this one.
It’s sort of a protesting-the-problem question. It’s also a reaction a lot of people have to “explain how you found the answer” questions. In a sense, yeah, the division shows how the answer was found. But what’s wanted — and what’s actually worth learning — is to explain why you did this calculation. Why, in this case, 216 divided by 8? Why not 216 times 8? Why not 8 divided by 216? Why not 216 minus 8? “How you found your answer” is probably a hard question to make interesting on arithmetic, unfortunately. If you’re doing a long sheet of problems practicing division, it’s not hard to guess that dividing is the answer. And that it’s the big number divided by the small. It can be good training to do blocks of problems that use the same approach, for the same reason it can be good training to focus on any exercise a while. But this does cheat someone of the chance to think about why one does this rather than that.
Patrick Roberts’s Todd the Dinosaur for the 11th has mathematics as the thing Todd’s trying to get out of doing. (I suppose someone could try to argue the Y2K bug was an offshoot of mathematics, on the grounds that computer science has so much to do with mathematics. I wouldn’t want to try defending that, though.) I grant that most fraction-to-decimal conversion problems hit that sweet spot of being dull, tedious, and seemingly pointless. There’s some fun decimal expansions of fractions. The sevenths and the elevenths and 1/243 have charm to them. There’s some kid who’ll become a mathematician because at the right age she was told about . 3/16th? Eh.
Mark Anderson’s Andertoons for the 11th is the Mark Anderson’s Andertoons for the week. I don’t remember seeing a spinny wheel like this used to introduce probability. It’s a good prop, though. I would believe in a class having it.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 11th is built on the Travelling Salesman Problem. It’s one of the famous unsolved and hard problems of mathematics. Weinersmith’s joke is a nice gag about one way to “solve” the problem, that of making it irrelevant. But even if we didn’t need to get to a collection of places efficiently mathematicians would still like to know good ways to do it. It turns out that finding the shortest (quickest, cheapest, easiest, whatever) route connecting a bunch of places is great problem. You can phrase enormously many problems about doing something as well as possible as a Travelling Salesman Problem. It’s easy conceptually to find the answer: try out all the possibilities and pick the best one. But if there’s more than a handful of cities, there are so many possible routes there’s no checking them all, not before you die of old age. We can do very well finding approximate answers, including by my specialization of Monte Carlo methods. In those you take a guess at an answer. Then make, randomly, a change. You’ll either have made things better or worse. If you’ve made it better, keep the change. If you’ve made it worse, usually you reject the change but sometimes you keep it. And repeat. In surprisingly little time you’ll get a really good answer. Maybe not the best possible, but a great answer for how straightforward setting it up was.
Computer science prof tells students one of the major problems in theoretical computer science is to prove P = NP; less than stellar student announces that P = 0 is a solution. https://t.co/xH9l8xkzzn
Dan Thompson’s Brevity for the 12th is a Rubik’s Cube joke. There’s not a lot of mathematics to that. But I do admire how Thompson was careful enough to draw a Rubik’s Cube that actually looks like the real article; it’s not just an isometric cube with thick lines partitioning it. Look at the corners of each colored sub-cube. I may be the only reader to notice this but I’m glad Thompson did the work.
Mason Mastroianni’s The Wizard of Id for the 12th gets Sir Rodney in trouble with the King for doing arithmetic. I haven’t read the comments on GoComics.com. I’d like to enter “three” as my guess for how many comments one would have to read before finding the “weapons of math instruction” joke in there.
Steve Moore’s In The Bleachers for the 13th features a story problem as a test of mental acuity. When the boxer can’t work out what the heck the trains-leaving-Penn-Station problem even means he’s ruled unfit to keep boxing. The question is baffling, though. As put, the second train won’t ever overtake the first. The question: did Moore just slip up? If the first train were going 30 miles per hour and the second 40 there would be a perfectly good, solvable question in this. Or was Moore slipping in an extra joke, making the referee’s question one that sounds like it was given wrong? Don’t know, so I’ll suppose the second.
There were enough comics last week to justify splitting them across two posts. But several of them were on a single theme. So they’re bundled together and you see what the theme is already if you pay attention to the edition titles.
Jeff Mallet’s Frazz on the 26th of February had a joke about a story problem going awry. Properly this should’ve been included in the Sunday update, but the theme was riffed on the next several days, and so I thought moving this made for a better split. In this case the kids resist the problem on the grounds that the cost ($1.50 for a pair of socks) is implausibly low. And now I’m reminded that a couple months ago I wondered if a comic strip (possibly Frazz again) gave a plausible price for apples. And I go to a great farmer’s market nearly every week and look at the apple prices and never think to write them down so I can check.
But the topic, and the attempt to use the price of socks as a joke, continued on the 27th. Here the resistance was on the grounds there might be a sale on. Fair enough, although the students should feel free to ask about sales. And the teacher ought to be able to offer that. Also, it seems to me that “twice $5” is a different problem to “twice $1.50”, at least at this level. An easier one, I’d say, too. If the pair of socks were $4.50 it would preserve what I imagine is the point being tested. I think that’s how to multiply a compound fraction or a number with a decimal. But Frazz’s characters know the objectives better than I do.
The topic gets clarified on the 28th, which doesn’t end the students’ resistance on the grounds of plausibility. This seems to portray the kids as more conscious of clothing prices than I think I was as a kid, but it’s Mallet’s comic strip. He knows what his kids care about. The sequence closes out the 1st of March with a coda that’s the sort of joke every academic department tells about the others.
Julie Larson’s Dinette Set rerun for the 27th is an extended bit of people not understanding two-for-one sales. I’m tickled by it, but I won’t think ill of you if you decide you don’t want to read all those word balloons. There’s some further jokes in the signs and the t-shirts people are wearing, but they’re not part of the main joke. (Larson would often include stray extra jokes like that. It always confuses people who didn’t get the strip’s humor style.)
November closed out with another of those weeks not quite busy enough to justify splitting into two. I blame Friday and Saturday. Nothing mathematically-themed was happening them. Suppose some days are just like that.
Johnny Hart’s Back To BC for the 26th is an example of using mathematical truths as profound statements. I’m not sure that I’d agree with just stating the Pythagorean Theorem as profound, though. It seems like a profound statement has to have some additional surprising, revelatory elements to it. Like, knowing the Pythagorean theorem is true means we can prove there’s exactly one line parallel to a given line and passing through some point. Who’d see that coming? I don’t blame Hart for not trying to fit all that into one panel, though. Too slow a joke. The strip originally ran the 4th of September, 1960.
Zach Weinersmith’s Saturday Morning Breakfast Cereal makes its first appearance for the week on the 26th. It’s an anthropomorphic-numerals joke and some wordplay. Interesting trivia about the whole numbers that never actually impresses people: a whole number is either a perfect square, like 1 or 4 or 9 or 16 are, or else its square root is irrational. There’s no whole number with a square root that’s, like, 7.745 or something. Maybe I just discuss it with people who’re too old. It seems like the sort of thing to reveal to a budding mathematician when she’s eight.
Saturday Morning Breakfast Cereal makes another appearance the 29th. The joke’s about using the Greek ε, which has a long heritage of use for “a small, positive number”. We use this all the time in analysis. A lot of proofs in analysis are done by using ε in a sort of trick. We want to show something is this value, but it’s too hard to do. Fine. Pick any ε, a positive number of unknown size. So then we’ll find something we can calculate, and show that the difference between the thing we want and the thing we can do is smaller than ε. And that the value of the thing we can calculate is that. Therefore, the difference between what we want and what we can do is smaller than any positive number. And so the difference between them must be zero, and voila! We’ve proved what we wanted to prove. I have always assumed that we use ε for this for the association with “error”, ideally “a tiny error”. If we need another tiny quantity we usually go to δ, probably because it’s close to ε and ‘d’ is still a letter close to ‘e’. (The next letter after ε is ζ, which carries other connotations with it and is harder to write than δ is.) Anyway, Weinersmith is just doing a ha-ha, your penis is small joke.
There seems to be no Mark Anderson’s Andertoons for this week. There’ve been some great ones (like on the 26th or the 28th and the 29th) but they’re not at all mathematical. I apologize for the inconvenience and am launching an investigation into this problem.
Comic Strip Master Command had a slow week for everyone. This is odd since I’d expect six to eight weeks ago, when the comics were (probably) on deadline, most (United States) school districts were just getting back to work. So education-related mathematics topics should’ve seemed fresh. I think I can make that fit. No way can I split this pile of comics over two days.
Hector D Cantu and Carlos Castellanos’s Baldo for the 17th has Gracie quizzed about percentages of small prices, apparently as a test of her arithmetic. Her aunt has other ideas in mind. It’s hard to dispute that this is mathematics people use in real life. The commenters on GoComics got into an argument about whether Gracie gave the right answers, though. That is, not that 20 percent of $5.95 is anything about $1.19. But did Tia Carmen want to know what 20 percent of $5.95, or did she want to know what $5.95 minus 20 percent of that price was? Should Gracie have answered $4.76 instead? It took me a bit to understand what the ambiguity was, but now that I see it, I’m glad I didn’t write a multiple-choice test with both $1.19 and $4.76 as answers. I’m not sure how to word the questions to avoid ambiguity yet still sound like something one of the hew-mons might say.
Dan Thompson’s Brevity for the 19th uses the blackboard and symbols on it as how a mathematician would prove something. In this case, love. Arithmetic’s a good visual way of communicating the mathematician at work here. I don’t think a mathematician would try arguing this in arithmetic, though. I mean if we take the premise at face value. I’d expect an argument in statistics, so, a mathematician showing various measures of … feelings or something. And tests to see whether it’s plausible this cluster of readings could come out by some reason other than love. If that weren’t used, I’d expect an argument in propositional logic. And that would have long strings of symbols at work, but they wouldn’t look like arithmetic. They look more like Ancient High Martian. Just saying.
Dave Coverly’s Speed Bump for the 20th is designed with crossover appeal in mind and I wonder if whoever does Reading the Comics for English Teacher Jokes is running this same strip in their collection for the week.
Darrin Bell’s Candorville for the 21st sees Lemont worry that he’s forgotten how to do long division. And, fair enough: any skill you don’t use in long enough becomes stale, whether it’s division or not. You have to keep in practice and, in time, have to decide what you want to keep in practice about. (That said, I have a minor phobia about forgetting how to prove the Contraction Mapping Theorem, as several professors in grad school stressed how it must always be possible to give a coherent proof of that, even if you’re startled awake in the middle of the night by your professor.) Me, I would begin by estimating what 4,858.8 divided by 297.492 should be. 297.492 is very near 300. And 4,858.8 is a little over 4800. And that’s suggestive because it’s obvious that 48 divided by 3 is 16. Well, it’s obvious to me. So I would expect the answer to be “a little more than 16” and, indeed, it’s about 16.3.
(Don’t read the comments on GoComics. There’s some slide-rule-snobbishness, and some snark about the uselessness of the skill or the dumbness of Facebook readers, and one comment about too many people knowing how to multiply by someone who’s reading bad population-bomb science fiction of the 70s.)
It wasn’t like the week wasn’t busy. Comic Strip Master Command sent out as many mathematically-themed comics as I might be able to use. But they were again ones that don’t leave me much to talk about. I’ll try anyway. It was looking like an anthropomorphic-symboles sort of week, too.
Dan Thompson’s Brevity for the 31st is another entry in the anthropomorphic-symbols joke contest. This one sticks to mathematical symbols, so if the Frank and Ernest makes the cut this week so must this one.
Eric the Circle for the 31st, this installment by “T daug”, gives the slightly anthropomorphic geometric figure a joke that at least mentions a radius, and isn’t that enough? What catches my imagination about this panel particularly is that the “fractured radius” is not just a legitimate pun but also resembles a legitimate geometry drawing. Drawing a diameter line is sensible enough. Drawing some other point on the circle and connecting that to the ends of the diameter is also something we might do.
Scott Hilburn’s The Argyle Sweater for the 1st of August is one of the logical mathematics jokes you could make about snakes. The more canonical one runs like this: God in the Garden of Eden makes all the animals and bids them to be fruitful. And God inspects them all and finds rabbits and doves and oxen and fish and fowl all growing in number. All but a pair of snakes. God asks why they haven’t bred and they say they can’t, not without help. What help? They need some thick tree branches chopped down. The bemused God grants them this. God checks back in some time later and finds an abundance of baby snakes in the Garden. But why the delay? “We’re adders,” explain the snakes, “so we need logs to multiply”. This joke absolutely killed them in the mathematics library up to about 1978. I’m told.
John Deering’s Strange Brew for the 1st is a monkeys-at-typewriters joke. It faintly reminds me that I might have pledged to retire mentions of the monkeys-at-typewriters joke. But I don’t remember so I’ll just have to depend on saying I don’t think I retired the monkeys-at-typewriters jokes and trust that someone will tell me if I’m wrong.
Mark Anderson’s Andertoons for the 3rd is the reassuringly normal appearance of Andertoons for this week. It is a geometry class joke about rays, line segments with one point where there’s an end and … a direction where it just doesn’t. And it riffs on the notion of the existence of mathematical things. At least I can see it that way.
It’s been a busy enough week at Comic Strip Master Command that I’ll need to split the results across two essays. Any other week I’d be glad for this, since, hey, free content. But this week it hits a busy time and shouldn’t I have expected that? The odd thing is that the mathematics mentions have been numerous but not exactly deep. So let’s watch as I make something big out of that.
Mark Tatulli’s Heart of the City closed out its “Math Camp” storyline this week. It didn’t end up having much to do with mathematics and was instead about trust and personal responsibility issues. You know, like stories about kids who aren’t learning to believe in themselves and follow their dreams usually are. Since we never saw any real Math Camp activities we don’t get any idea what they were trying to do to interest kids in mathematics, which is a bit of a shame. My guess would be they’d play a lot of the logic-driven puzzles that are fun but that they never get to do in class. The story established that what I thought was an amusement park was instead a fair, so, that might be anywhere Pennsylvania or a couple of other nearby states.
Rick Kirkman and Jerry Scott’s Baby Blues for the 25th sees Hammie have “another” mathematics worksheet accident. Could be any subject, really, but I suppose it would naturally be the one that hey wait a minute, why is he doing mathematics worksheets in late July? How early does their school district come back from summer vacation, anyway?
Olivia Walch’s Imogen Quest for the 26th uses a spot of mathematics as the emblem for teaching. In this case it’s a bit of physics. And an important bit of physics, too: it’s the time-dependent Schrödinger Equation. This is the one that describes how, if you know the total energy of the system, and the rules that set its potential and kinetic energies, you can work out the function Ψ that describes it. Ψ is a function, and it’s a powerful one. It contains probability distributions: how likely whatever it is you’re modeling is to have a particle in this region, or in that region. How likely it is to have a particle with this much momentum, versus that much momentum. And so on. Each of these we find by applying a function to the function Ψ. It’s heady stuff, and amazing stuff to me. Ψ somehow contains everything we’d like to know. And different functions work like filters that make clear one aspect of that.
Dan Thompson’s Brevity for the 26th is a joke about Sesame Street‘s Count von Count. Also about how we can take people’s natural aptitudes and delights and turn them into sad, droning unpleasantness in the service of corporate overlords. It’s fun.
Doug Savage’s Savage Chickens for the 26th proves something “scientific” by putting numbers into it. Particularly, by putting statistics into it. Understandable impulse. One of the great trends of the past century has been taking the idea that we only understand things when they are measured. And this implies statistics. Everything is unique. Only statistical measurement lets us understand what groups of similar things are like. Does something work better than the alternative? We have to run tests, and see how the something and the alternative work. Are they so similar that the differences between them could plausibly be chance alone? Are they so different that it strains belief that they’re equally effective? It’s one of science’s tools. It’s not everything which makes for science. But it is stuff easy to communicate in one panel.
Neil Kohney’s The Other End for the 26th is really a finance joke. It’s about the ways the finance industry can turn one thing into a dazzling series of trades and derivative trades. But this is a field that mathematics colonized, or that colonized mathematics, over the past generation. Mathematical finance has done a lot to shape ideas of how we might study risk, and probability, and how we might form strategies to use that risk. It’s also done a lot to shape finance. Pretty much any major financial crisis you’ve encountered since about 1990 has been driven by a brilliant new mathematical concept meant to govern risk crashing up against the fact that humans don’t behave the way some model said they should. Nor could they; models are simplified, abstracted concepts that let hard problems be approximated. Every model has its points of failure. Hopefully we’ll learn enough about them that major financial crises can become as rare as, for example, major bridge collapses or major airplane disasters.
It turns out last Saturday only had the one comic strip that was even remotely on point for me. And it wasn’t very on point either, but since it’s one of the Creators.com strips I’ve got the strip to show. That’s enough for me.
Ruben Bolling’s Super-Fun-Pak Comix for the 8th is an installation of They Came From The Third Dimension. “Dimension” is one of those oft-used words that’s come loose of any technical definition. We use it in mathematics all the time, at least once we get into Introduction to Linear Algebra. That’s the course that talks about how blocks of space can be stretched and squashed and twisted into each other. You’d expect this to be a warmup act to geometry, and I guess it’s relevant. But where it really pays off is in studying differential equations and how systems of stuff changes over time. When you get introduced to dimensions in linear algebra they describe degrees of freedom, or how much information you need about a problem to pin down exactly one solution.
It does give mathematicians cause to talk about “dimensions of space”, though, and these are intuitively at least like the two- and three-dimensional spaces that, you know, stuff moves in. That there could be more dimensions of space, ordinarily inaccessible, is an old enough idea we don’t really notice it. Perhaps it’s hidden somewhere too.
Amanda El-Dweek’s Amanda the Great of the 9th started a story with the adult Becky needing to take a mathematics qualification exam. It seems to be prerequisite to enrolling in some new classes. It’s a typical set of mathematics anxiety jokes in the service of a story comic. One might tsk Becky for going through university without ever having a proper mathematics class, but then, I got through university without ever taking a philosophy class that really challenged me. Not that I didn’t take the classes seriously, but that I took stuff like Intro to Logic that I was already conversant in. We all cut corners. It’s a shame not to use chances like that, but there’s always so much to do.
Mark Anderson’s Andertoons for the 10th relieves the worry that Mark Anderson’s Andertoons might not have got in an appearance this week. It’s your common kid at the chalkboard sort of problem, this one a kid with no idea where to put the decimal. As always happens I’m sympathetic. The rules about where to move decimals in this kind of multiplication come out really weird if the last digit, or worse, digits in the product are zeroes.
Mel Henze’s Gentle Creatures is in reruns. The strip from the 10th is part of a story I’m so sure I’ve featured here before that I’m not even going to look up when it aired. But it uses your standard story problem to stand in for science-fiction gadget mathematics calculation.
Dave Blazek’s Loose Parts for the 12th is the natural extension of sleep numbers. Yes, I’m relieved to see Dave Blazek’s Loose Parts around here again too. Feels weird when it’s not.
John Deering’s Strange Brew for the 13th is a “math club” joke featuring horses. Oh, it’s a big silly one, but who doesn’t like those too?
Dan Thompson’s Brevity for the 14th is one of the small set of punning jokes you can make using mathematician names. Good for the wall of a mathematics teacher’s classroom.
Shaenon K Garrity and Jefferey C Wells’s Skin Horse for the 14th is set inside a virtual reality game. (This is why there’s talk about duplicating objects.) Within the game, the characters are playing that game where you start with a set number (in this case 20) tokens and take turn removing a couple of them. The “rigged” part of it is that the house can, by perfect play, force a win every time. It’s a bit of game theory that creeps into recreational mathematics books and that I imagine is imprinted in the minds of people who grow up to design games.
Since I suspect that the comics roundup posts are the most popular ones I post, I’m very glad to see there was a bumper crop of strips among the ones I read regularly (from King Features Syndicate and from gocomics.com) this past week. Some of those were from cancelled strips in perpetual reruns, but that’s fine, I think: there aren’t any particular limits on how big an electronic comics page one can have, after all, and while it’s possible to read a short-lived strip long enough that you see all its entries, it takes a couple go-rounds to actually have them all memorized.
I’ve got enough new mathematics-themed comic strips to assemble them into a fresh post. It’s a challenge to time these rightly; I don’t want to waste everyone’s time with a set weekly post, particularly since the syndicated comics might just not have anything. On the other hand, waiting until a set number of strips have passed before my eyes seems likely to just encourage me to wonder how marginally a strip can touch mathematics before I include it. Dave Coverly’s Speed Bump, from the 6th of May, is a fine marginal case: there’s a mathematics problem in it, but it’s not at all a mathematics strip. It’s just very easy to put a math problem on the chalkboard and have it be understood the scenario is “student with no idea how to answer”.