Reading the Comics, March 30, 2019: Comics Kingdom is Screwed Up Edition

It doesn’t affect much this batch of comics, as they’re a bunch that all came from GoComics.com. But Comics Kingdom suffered a major redesign of the web site this week, and so it’s lost a lot of functionality. The ability to load your whole comics page at once, for example. Or the ability of archives to work. I’d had the URL for one strip copied down because it mentioned mathematics, albeit in so casual a manner I didn’t mean to write a paragraph about it. Good luck that I didn’t, as that URL now directs to a Spanish translation of a Katzenjammer Kids strip. Why? That’s a good question, and one that deserves an answer.

Anyway, I’m hoping that Comics Kingdom is able to get over their redesign soon. But I know they won’t. There’s never been a web site redesign that lowered functionality and made the page more infuriating to work with that was ever abandoned for the older, working version instead.

Enough about Comics Kingdom. Let me share a couple comic strips from a web site that works, although not as well as it did before its 2018 redesign.

Jim Meddick’s Monty for the 27th is part of a fun storyline. In it Monty and Moondog’s cell phones start texting on their own. It’s presented as the start of an Artificial Intelligence-based singularity, computers transcending human thought and going into business for themselves. This is shown by their working out mathematical truths, starting with arithmetic and going into Boolean algebra. Humans learn arithmetic first and Boolean algebra — logical statements and their combinations — later on, if ever.

Jim Meddick’s Monty for the 27th of March, 2019. Essays discussing anything from Monty should appear at this link.

Computers are certainly able to discover mathematics on their own. Or at least without close guidance; someone still has to write a program to do it. Automated proof finders are a well-established thing, though. They have not, so far as I’ve heard, discovered anything likely to threaten humanity.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 28th of March, 2019. Appearances of The Chuckle Brothers in this line of essays should be gathered here.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 28th is built on representing huge numbers. 81861³ is a big number: 548,568,842,280,381. Even bigger is 3757⁵: it’s 748,524,423,279,410,560. It’s silly to imagine needing an identification number that large. But it’s also a remarkable coincidence that both prisoners here have numbers that can be represented with no more than six digits. There aren’t so many 15-digit numbers that could be represented with as few as six digits. But then it would be an absurdly large prison if it “only” had 818,613 prisoners in it. That seems like the joke would have been harder to recognize, though.

Mark Parisi’s Off The Mark for the 28th of March, 2019. Essays inspired by something mentioned in Off The Mark should be gathered here.

Mark Parisi’s Off The Mark for the 28th is sort of the anthropomorphic numerals joke for the week. It’s also a joke for my friend with the meteorology degree, who I think doesn’t actually read these posts. Well, he probably got the comic forwarded to him anyway.

Daniel Beyer’s Long Story Short for the 29th is another prison joke. I’m not sure if someone at Comic Strip Master Command was worried about something. But a scrawl of mathematics is used as icon of skills learned in prison.

Daniel Beyer’s Long Story Short for the 29th of March, 2019. Essays discussing topics raised by Long Story Short should be here. There aren’t many, yet.

Mathematics has the reputation of being a subject someone can still do useful work in while in prison. Maybe even do more work, as it seems to offer the prospect of undistracted time to think. And there are examples of mathematicians doing noteworthy work while imprisoned. Bertrand Russell wrote the Introduction To Mathematical Philosophy while jailed for protesting the First World War. André Weil advanced his work in arithmetic geometry while in prison for resisting service in the Second World War. Évariste Galois spent six months in prison shortly before the end of his life, and used some of the time to work on the theory of equations for which we still remember him. I would not recommend prison as a way to advance one’s mathematical research. But it’s something which could happen.

Terry LaBan and Patty LaBan’s Edge City rerun for the 30th of March, 2019. It originally ran in 2004; I can’t say whether it ran the 30th of March then. And topics raised by Edge City should be discussed at this link.

Terry LaBan and Patty LaBan’s Edge City for the 30th showcases the motivation problem. Colin, like many people, is easily able to do complicated algorithms to do something he likes doing. Arithmetic drills, though, not so much. This is why we end up writing story problems with dubious amounts of story in them.

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And I don’t want to devote too much space to this. But Brian Fies’s The Last Mechanical Monster for the 29th included the lead character, the Mad Scientist, working out the numbers of the Fibonacci sequence as a way to keep his mind going. The strip is a rerun and I discussed it when it first ran on GoComics.

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There were quite a lot of mathematically-themed comic strips the week of the 24th of March. I’ll get to the actual strips of the past week soon, at this link. Also if anyone knows a way to get the old Comics Kingdom back please let me know.

Reading the Comics, October 25, 2018: How To Save Your Tangled Earbuds Edition

The Playful Mathematics Education Blog Carnival has moved on! My successor, edition number 122, is at ArithmophobiaNoMore.com, with another mixture of the amusing, the informative, and the educational. Do please enjoy. Now on to filling out last week’s comic strips.

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.

Brian Fies’s The Last Mechanical Monster rerun for the 24th of October, 2018. It’s also appeared the 4th of October, 2017.

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.)

Dan Thompson’s Brevity for the 24th of October, 2018. I understand why sensibly the ‘2’ would be the character nearest the bouncer. But wouldn’t the joke read better if ‘2’ were on the left, so the panel read 2 + 1?

Dan Thompson’s Brevity for the 24th is the anthropomorphic numerals joke for this essay.

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.

Greg Cravens’s Hubris! for the 24th of October, 2018. So this is all happening in the midst of a sports festival, which is why there’s a Grey alien in Charlie Brown outfit. It’s a bit of a weird comic, but I like it.

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 of October, 2018. Better than working on Collatz conjectures in your head, anyway. 27 is a heck of a number to start from.

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.

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I can’t promise that every one of these Reading the Comics posts will be able to solve your minor problems. But if you want to try, you can read them here. The other essays mentioning The Last Mechanical Monster are at this link. Essays discussing ideas brought up by Brevity are at this link. Essays discussing Hubris will be at this link. It’s a new tag, though, so there’s only this post on it right now. Posts featuring Dark Side Of The Horse should be at link. And I do continue posting my Fall 2018 Mathematics A-To-Z, which is open for requests for more of the alphabet this week. Thanks for reading and thanks for making suggestions.

Reading the Comics, March 10, 2018: I Will Get To Pi Day Edition

There were fewer Pi Day comic strips than I had expected for this year. It’s gotten much more public mention than I had expected a pop-mathematics bit of whimsy might. But I’m still working off last week’s strips; I’ll get to this week’s next week. This makes sense to me, which is as good as making sense at all.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 7th is a percentages joke, as applied to hair. Lard doesn’t seem clear whether this would be 10% off the hair by individual strand length or by total volume. Either way, Lard’s right to wonder about the accuracy.

Mark Pett’s Mr Lowe rerun for the 7th is a standardized test joke. Part of the premise of Pett’s strip is that Mister Lowe is a brand-new teacher, which is why he makes mistakes like this problem. (This is touchy to me, as in grad school I hoped to make some spare money selling questions to a standardized testing company. I wasn’t good enough at it, and ultimately didn’t have the time to train up to their needs.) A multiple-choice question needs to clear and concise and to have one clearly best answer. As the given question’s worded, though, I could accept ‘2’ or ’12’ as a correct answer. With a bit of experience Lowe would probably clarify that Tommy and Suzie are getting the same number of apples and that together they should have 20 total.

Then on the 9th Mr Lowe has a joke about cultural bias in standardized tests. It uses an arithmetic problem as the type case. Mathematicians like to think of themselves as working in a universal, culturally independent subject. I suppose it is, but only in ways that aren’t interesting: if you suppose these rules of logic and these axioms and these definitions then these results follow, and it doesn’t matter who does the supposing. But start filtering that by stuff people care about, such as the time it takes for two travelling parties to meet, and you’ve got cultural influence. (Back when this strip was new the idea that a mathematics exam could be culturally biased was a fresh new topic of mockery among people who don’t pay much attention to the problems of teaching but who know what those who do are doing wrong.)

Ralph Hagen’s The Barn for the 8th — a new tag for my comics, by the way — lists a bunch of calculation tools and techniques as “obsolete” items. I’m assuming Rory means that longhand multiplication is obsolete. I’m not sure that it is, but I have an unusual perspective on this.

Thaves’s Frank and Ernest for the 8th is an anthropomorphic-numerals joke. I was annoyed when I first read this because I thought, wait, 97 isn’t a prime number. It is, of course. I have no explanation for my blunder.

Jon Rosenberg’s Scenes from a Multiverse has restarted its run on GoComics. The strip for the 8th is a riff on Venn Diagrams. And, it seems to me, about those logic-bomb problems about sets consisting of sets that don’t contain themselves and the like. You get weird and apparently self-destructive results pondering that stuff. The last time GoComics ran the Scenes from a Multiverse series I did not appreciate right away that there were many continuing stories. There might be follow-ups to this Former Venn Prime Universe story.

Brian Fies’s The Last Mechanical Monster for the 9th has the Mad Scientist, struggling his way into the climax of the story, testing his mind by calculating a Fibonacci Sequence. Whatever keeps you engaged and going. You can build a Fibonacci Sequence from any two starting terms. Each term after the first two is the sum of the previous two. If someone just says “the Fibonacci Sequence” they mean the sequence that starts with 0, 1, or perhaps with 1, 1. (There’s no interesting difference.) Fibonacci Sequences were introduced to the west by Leonardo of Pisa, who did so much to introduce Hindu-Arabic Numerals to a Europe that didn’t know it wanted this stuff. They touch on some fascinating stuff: the probability of not getting two tails in a row of a set number of coin tosses. Chebyshev polynomials. Diophantine equations. They also touch on the Golden Ratio, which isn’t at all important but that people like.

Nicholas Gurewitch’s Perry Bible Fellowship for the 9th just has a blackboard of arithmetic to stand in for schoolwork.

Reading the Comics, January 3, 2018: Explaining Things Edition

There were a good number of mathematically-themed comic strips in the syndicated comics last week. Those from the first part of the week gave me topics I could really sink my rhetorical teeth into, too. So I’m going to lop those off into the first essay for last week and circle around to the other comics later on.

Jef Mallett’s Frazz started a week of calendar talk on the 31st of December. I’ve usually counted that as mathematical enough to mention here. The 1st of January as we know it derives, as best I can figure, from the 1st of January as Julius Caesar established for 45 BCE. This was the first Roman calendar to run basically automatically. Its length was quite close to the solar year’s length. It had leap days added according to a rule that should have been easy enough to understand (one day every fourth year). Before then the Roman calendar year was far enough off the solar year that they had to be kept in synch by interventions. Mostly, by that time, adding a short extra month to put things more nearly right. This had gotten all confusingly messed up and Caesar took the chance to set things right, running 46 BCE to 445 days long.

But why 445 and not, say, 443 or 457? And I find on research that my recollection might not be right. That is, I recall that the plan was to set the 1st of January, Reformed, to the first new moon after the winter solstice. A choice that makes sense only for that one year, but, where to set the 1st is literally arbitrary. While that apparently passes astronomical muster (the new moon as seen from Rome then would be just after midnight the 2nd of January, but hitting the night of 1/2 January is good enough), there’s apparently dispute about whether that was the objective. It might have been to set the winter solstice to the 25th of December. Or it might have been that the extra days matched neatly the length of two intercalated months that by rights should have gone into earlier years. It’s a good reminder of the difficulty of reading motivation.

Brian Fies’s The Last Mechanical Monster for the 1st of January, 2018, continues his story about the mad scientist from the Fleischer studios’ first Superman cartoon, back in 1941. In this panel he’s describing how he realized, over the course of his long prison sentence, that his intelligence was fading with age. He uses the ability to do arithmetic in his head as proof of that. These types never try naming, like, rulers of the Byzantine Empire. Anyway, to calculate the cube root of 50,653 in his head? As he used to be able to do? … guh. It’s not the sort of mental arithmetic that I find fun.

But I could think of a couple ways to do it. The one I’d use is based on a technique called Newton-Raphson iteration that can often be used to find where a function’s value is zero. Raphson here is Joseph Raphson, a late 17th century English mathematician known for the Newton-Raphson method. Newton is that falling-apples fellow. It’s an iterative scheme because you start with a guess about what the answer would be, and do calculations to make the answer better. I don’t say this is the best method, but it’s the one that demands me remember the least stuff to re-generate the algorithm. And it’ll work for any positive number ‘A’ and any root, to the ‘n’-th power.

So you want the n-th root of ‘A’. Start with your current guess about what this root is. (If you have no idea, try ‘1’ or ‘A’.) Call that guess ‘x’. Then work out this number:

Ta-da! You have, probably, now a better guess of the n-th root of ‘A’. If you want a better guess yet, take the result you just got and call that ‘x’, and go back calculating that again. Stop when you feel like your answer is good enough. This is going to be tedious but, hey, if you’re serving a prison term of the length of US copyright you’ve got time. (It’s possible with this sort of iterator to get a worse approximation, although I don’t think that happens with n-th root process. Most of the time, a couple more iterations will get you back on track.)

But that’s work. Can we think instead? Now, most n-th roots of whole numbers aren’t going to be whole numbers. Most integers aren’t perfect powers of some other integer. If you think 50,653 is a perfect cube of something, though, you can say some things about it. For one, it’s going to have to be a two-digit number. 10³ is 1,000; 100³ is 1,000,000. The second digit has to be a 7. 7³ is 343. The cube of any number ending in 7 has to end in 3. There’s not another number from 1 to 9 with a cube that ends in 3. That’s one of those things you learn from playing with arithmetic. (A number ending in 1 cubes to something ending in 1. A number ending in 2 cubes to something ending in 8. And so on.)

So the cube root has to be one of 17, 27, 37, 47, 57, 67, 77, 87, or 97. Again, if 50,653 is a perfect cube. And we can do better than saying it’s merely one of those nine possibilities. 40 times 40 times 40 is 64,000. This means, first, that 47 and up are definitely too large. But it also means that 40 is just a little more than the cube root of 50,653. So, if 50,653 is a perfect cube, then it’s most likely going to be the cube of 37.

Bill Watterson’s Calvin and Hobbes rerun for the 2nd is a great sequence of Hobbes explaining arithmetic to Calvin. There is nothing which could be added to Hobbes’s explanation of 3 + 8 which would make it better. I will modify Hobbes’s explanation of what the numerator. It’s ridiculous to think it’s Latin for “number eighter”. The reality is possibly more ridiculous, as it means “a numberer”. Apparently it derives from “numeratus”, meaning, “to number”. The “denominator” comes from “de nomen”, as in “name”. So, you know, “the thing that’s named”. Which does show the terms mean something. A poet could turn “numerator over denominator” into “the number of parts of the thing we name”, or something near enough that.

Hobbes continues the next day, introducing Calvin to imaginary numbers. The term “imaginary numbers” tells us their history: they looked, when first noticed in formulas for finding roots of third- and fourth-degree polynomials, like obvious nonsense. But if you carry on, following the rules as best you can, that nonsense would often shake out and you’d get back to normal numbers again. And as generations of mathematicians grew up realizing these acted like numbers we started to ask: well, how is an imaginary number any less real than, oh, the square root of six?

Hobbes’s particular examples of imaginary numbers — “eleventeen” and “thirty-twelve” — are great-sounding compositions. They put me in mind, as many of Watterson’s best words do, of a 1960s Peanuts in which Charlie Brown is trying to help Sally practice arithmetic. (I can’t find it online, as that meme with edited text about Sally Brown and the sixty grapefruits confounds my web searches.) She offers suggestions like “eleventy-Q” and asks if she’s close, which Charlie Brown admits is hard to say.

James Allen’s Mark Trail for the 3rd of January, 2018. James Allen has changed many things about the comic strip since Jack Elrod’s retirement, as I have observed over on the other blog. There are less ruthlessly linear stories. There’s no more odd word balloon placement implying that giant squirrels are talking about the poachers. Mark Trail sometimes has internal thoughts. I’m glad that he does still choose to over-emphasize declarations like “[Your Dad]’s out on the porch reading the paper!” There are some traditions.

And finally, James Allen’s Mark Trail for the 3rd just mentions mathematics as the subject that Rusty Trail is going to have to do some work on instead of allowing the experience of a family trip to Mexico to count. This is of extremely marginal relevance, but it lets me include a picture of a comic strip, and I always like getting to do that.

Reading the Comics, October 4, 2017: Time-Honored Traditions Edition

It was another busy week in mathematically-themed comic strips last week. Busy enough I’m comfortable rating some as too minor to include. So it’s another week where I post two of these Reading the Comics roundups, which is fine, as I’m still recuperating from the Summer 2017 A To Z project. This first half of the week includes a lot of rerun comics, and you’ll see why my choice of title makes sense.

Lincoln Pierce’s Big Nate: First Class for the 1st of October reprints the strip from the 2nd of October, 1993. It’s got a well-formed story problem that, in the time-honored tradition of this setup, is subverted. I admit I kind of miss the days when exams would have problems typed out in monospace like this.

Ashleigh Brilliant’s Pot-Shots for the 1st is a rerun from sometime in 1975. And it’s an example of the time-honored tradition of specifying how many statistics are made up. Here it comes in at 43 percent of statistics being “totally worthless” and I’m curious how the number attached to this form of joke changes over time.

The Joey Alison Sayers Comic for the 2nd uses a blackboard with mathematics — a bit of algebra and a drawing of a sphere — as the designation for genius. That’s all I have to say about this. I remember being set straight about the difference between ponies and horses and it wasn’t by my sister, who’s got a professional interest in the subject.

Mark Pett’s Lucky Cow rerun for the 2nd is a joke about cashiers trying to work out change. As one of the GoComics.com commenters mentions, the probably best way to do this is to count up from the purchase to the amount you have to give change for. That is, work out $12.43 to $12.50 is seven cents, then from $12.50 to $13.00 is fifty more cents (57 cents total), then from $13.00 to $20.00 is seven dollars ($7.57 total) and then from $20 to $50 is thirty dollars ($37.57 total).

It does make me wonder, though: what did Neil enter as the amount tendered, if it wasn’t $50? Maybe he hit “exact change” or whatever the equivalent was. It’s been a long, long time since I worked a cash register job and while I would occasionally type in the wrong amount of money, the kinds of errors I would make would be easy to correct for. (Entering $30 instead of $20 for the tendered amount, that sort of thing.) But the cash register works however Mark Pett decides it works, so who am I to argue?

Keith Robinson’s Making It rerun for the 2nd includes a fair bit of talk about ratios and percentages, and how to inflate percentages. Also about the underpaying of employees by employers.

Mark Anderson’s Andertoons for the 3rd continues the streak of being Mark Anderson Andertoons for this sort of thing. It has the traditional form of the student explaining why the teacher’s wrong to say the answer was wrong.

Brian Fies’s The Last Mechanical Monster for the 4th includes a bit of legitimate physics in the mad scientist’s captioning. Ballistic arcs are about a thing given an initial speed in a particular direction, moving under constant gravity, without any of the complicating problems of the world involved. No air resistance, no curvature of the Earth, level surfaces to land on, and so on. So, if you start from a given height (‘y₀‘) and a given speed (‘v’) at a given angle (‘θ’) when the gravity is a given strength (‘g’), how far will you travel? That’s ‘d’. How long will you travel? That’s ‘t’, as worked out here.

(I should maybe explain the story. The mad scientist here is the one from the first, Fleischer Studios, Superman cartoon. In it the mad scientist sends mechanical monsters out to loot the city’s treasures and whatnot. As the cartoon has passed into the public domain, Brian Fies is telling a story of that mad scientist, finally out of jail, salvaging the one remaining usable robot. Here, training the robot to push aside bank tellers has gone awry. Also, the ground in his lair is not level.)

Tom Toles’s Randolph Itch, 2 am rerun for the 4th uses the time-honored tradition of Albert Einstein needing a bit of help for his work.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th uses the time-honored tradition of little bits of physics equations as designation of many deep thoughts. And then it gets into a bit more pure mathematics along the way. It also reflects the time-honored tradition of people who like mathematics and physics supposing that those are the deepest and most important kinds of thoughts to have. But I suppose we all figure the things we do best are the things it’s important to do best. It’s traditional.

And by the way, if you’d like more of these Reading the Comics posts, I put them all in the category ‘Comic Strips’ and I just now learned the theme I use doesn’t show categories for some reason? This is unsettling and unpleasant. Hm.