As promised I have the Pi Day comic strips from my reading here. I read nearly all the comics run on Comics Kingdom and on GoComics, no matter how hard their web sites try to avoid showing comics. (They have some server optimization thing that makes the comics sometimes just not load.) (By server optimization I mean “tracking for advertising purposes”.)
Pi Day in the comics this year saw the event almost wholly given over to the phonetic coincidence that π sounds, in English, like pie. So this is not the deepest bench of mathematical topics to discuss. My love, who is not as fond of wordplay as I am, notes that the ancient Greeks likely pronounced the name of π about the same way we pronounce the letter “p”. This may be etymologically sound, but that’s not how we do it in English, and even if we switched over, that would not make things better.
Scott Hilburn’s The Argyle Sweater is one of the few strips not to be about food. It is set in the world of anthropomorphized numerals, the other common theme to the day.
Jules Rivera’s Mark Trail makes the most casual Pi Day reference. If the narrator hadn’t interrupted in the final panel no one would have reason to think this referenced anything.
Mark Parisi’s Off The Mark is the other anthropomorphic numerals joke for the day. It’s built on the familiar fact that the digits of π go on forever. This is true for any integer base. In base π, of course, the representation of π is just “10”. But who uses that? And in base π, the number six would be something with infinitely many digits. There’s no fitting that in a one-panel comic, though.
Doug Savage’s Savage Chickens is the one strip that wasn’t about food or anthropomorphized numerals. There is no practical reason to memorize digits of π, other than that you’re calculating something by hand and don’t want to waste time looking them up. In that case there’s not much call go to past 3.14. If you need more than about 3.14159, get a calculator to do it. But memorizing digits can be fun, and I will not underestimate the value of fun in getting someone interested in mathematics.
For my part, I memorized π out to 3.1415926535787932, so that’s sixteen digits past the decimal. Always felt I could do more and I don’t know why I didn’t. The next couple digits are 8462, which has a nice descending-fifths cadence to it. The 626 following is a neat coda. My describing it this way may give you some idea to how I visualize the digits of π. They might help you, if you figure for some reason you need to do this. You do not, but if you enjoy it, enjoy it.
This little essay should let me wrap up the rest of the comic strips from the past week. Most of them were casual mentions. At least I thought they were when I gathered them. But let’s see what happens when I actually write my paragraphs about them.
Thaves’s Frank and Ernest for the 2nd is a bit of wordplay, having Euclid and Galileo talking about parallel universes. I’m not sure that Galileo is the best fit for this, but I’m also not sure there’s another person connected who could be named. It’d have to be a name familiar to an average reader as having something to do with geometry. Pythagoras would seem obvious, but the joke is stronger if it’s two people who definitely did not live at the same time. Did Euclid and Pythagoras live at the same time? I am a mathematics Ph.D. and have been doing pop mathematics blogging for nearly a decade now, and I have not once considered the question until right now. Let me look it up.
It doesn’t make any difference. The comic strip has to read quickly. It might be better grounded to post Euclid meeting Gauss or Lobachevsky or Euler (although the similarity in names would be confusing) but being understood is better than being precise.
Stephan Pastis’s Pearls Before Swine for the 2nd is a strip about the foolhardiness of playing the lottery. And it is foolish to think that even a $100 purchase of lottery tickets will get one a win. But it is possible to buy enough lottery tickets as to assure a win, even if it is maybe shared with someone else. It’s neat that an action can be foolish if done in a small quantity, but sensible if done in enough bulk.
Mark Anderson’s Andertoons for the 3rd is the Mark Anderson’s Andertoons for the week. Wavehead has made a bunch of failed attempts at subtracting seven from ten, but claims it’s at least progress that some thing have been ruled out. I’ll go along with him that there is some good in ruling out wrong answers. The tricky part is in how you rule them out. For example, obvious to my eye is that the correct answer can’t be more than ten; the problem is 10 minus a positive number. And it can’t be less than zero; it’s ten minus a number less than ten. It’s got to be a whole number. If I’m feeling confident about five and five making ten, then I’d rule out any answer that isn’t between 1 and 4 right away. I’ve got the answer down to four guesses and all I’ve really needed to know is that 7 is greater than five but less than ten. That it’s an even number minus an odd means the result has to be odd; so, it’s either one or three. Knowing that the next whole number higher than 7 is an 8 says that we can rule out 1 as the answer. So there’s the answer, done wholly by thinking of what we can rule out. Of course, knowing what to rule out takes some experience.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th is the Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th for the week. It shows in joking but not wrong fashion a mathematical physicist’s encounters with orbital mechanics. Orbital mechanics are a great first physics problem. It’s obvious what they’re about, and why they might be interesting. And the mathematics of it is challenging in ways that masses on springs or balls shot from cannons aren’t.
A few problems are very easy, like, one thing in circular orbit of another. A few problems are not bad, like, one thing in an elliptical or hyperbolic orbit of another. All our good luck runs out once we suppose the universe has three things in it. You’re left with problems that are doable if you suppose that one of the things moving is so tiny that it barely exists. This is near enough true for, for example, a satellite orbiting a planet. Or by supposing that we have a series of two-thing problems. Which is again near enough true for, for example, a satellite travelling from one planet to another. But these is all work that finds approximate solutions, often after considerable hard work. It feels like much more labor to smaller reward than we get for masses on springs or balls shot from cannons. Walking off to a presumably easier field is understandable. Unfortunately, none of the other fields is actually easier.
Pythagoras died somewhere around 495 BC. Euclid was born sometime around 325 BC. That’s 170 years apart. So Pythagoras was as far in Euclid’s past as, oh, Maria Gaetana Agnesi is to mine.
Pi Day was observed with fewer, and fewer on-point, comic strips than I had expected. It’s possible that the whimsy of the day has been exhausted. Or that Comic Strip Master Command advised people that the educational purposes of the day were going to be diffused because of the accident of the calendar. And a fair number of the strips that did run in the back half of last week weren’t substantial. So here’s what did run.
And now we get to the strips that actually ran on the 14th of March.
Hector D Cantú and Carlos Castellanos’s Baldo is a slightly weird one. It’s about Gracie reflecting on how much she’s struggled with mathematics problems. There are a couple pieces meant to be funny here. One is the use of oddball numbers like 1.39 or 6.23 instead of easy-to-work-with numbers like “a dollar” or “a nickel” or such. The other is that the joke is .. something in the vein of “I thought I was wrong once, but I was mistaken”. Gracie’s calculation indicates she thinks she’s struggled with a math problem a little under 0.045 times. It’s a peculiar number. Either she’s boasting that she struggles very little with mathematics, or she’s got her calculations completely wrong and hasn’t recognized it. She’s consistently portrayed as an excellent student, though. So the “barely struggles” or maybe “only struggles a tiny bit at the start of a problem” interpretation is more likely what’s meant.
π has infinitely many decimal digits, certainly. Of course, so does 2. It’s just that 2 has boring decimal digits. Rational numbers end up repeating some set of digits. It can be a long string of digits. But it’s finitely many, and compared to an infinitely long and unpredictable string, what’s that? π we know is a transcendental number. Its decimal digits go on in a sequence that never ends and never repeats itself fully, although finite sequences within it will repeat. It’s one of the handful of numbers we find interesting for reasons other than their being transcendental. This though nearly every real number is transcendental. I think any mathematician would bet that it is a normal number, but we don’t know that it is. I’m not aware of any numbers we know to be normal and that we care about for any reason other than their normality. And this, weirdly, also despite that we know nearly every real number is normal.
Dave Whamond’s Reality Check plays on the pun between π and pie, and uses the couple of decimal digits of π that most people know as part of the joke. It’s not an anthropomorphic numerals joke, but it is circling that territory.
Michael Cavna’s Warped celebrates Albert Einstein’s birthday. This is of marginal mathematics content, but Einstein did write compose one of the few equations that an average lay person could be expected to recognize. It happens that he was born the 14th of March and that’s, in recent years, gotten merged into Pi Day observances.
There were more mathematically-themed comic strips last week than I had time to deal with. This is in part because of something Saturday which took several more hours than I had expected. So let me start this week with some of the comics that, last week, mentioned mathematics in a marginal enough way there’s nothing to say about them besides yeah, that’s a comic strip which mentioned mathematics.
Jef Mallett’s Frazz for the 27th has a kid wondering why they need in-person instruction for arithmetic. (I’d agree that rehearsing arithmetic skills is very easy to automate. You can make practice problems pretty near without limit. How much this has to do with mathematics is a point of debate.)
The past week included another Friday the 13th. Several comic strips found that worth mention. So that gives me a theme by which to name this look over the comic strips.
Charles Schulz’s Peanuts rerun for the 12th presents a pretty wordy algebra problem. And Peppermint Patty, in the grips of a math anxiety, freezing up and shutting down. One feels for her. Great long strings of words frighten anyone. The problem seems a bit complicated for kids Peppermint Patty’s and Franklin’s age. But the problem isn’t helping. One might notice, say, that a parent’s age will be some nice multiple of a child’s in a year or two. That in ten years a man’s age will be 14 greater than the combined age of their ages then? What imagination does that inspire?
Grant Peppermint Patty her fears. The situation isn’t hopeless. It helps to write out just what know, and what we would like to know. At least what we would like to know if we’ve granted the problem worth solving. What we would like is to know the man’s age. That’s some number; let’s call it M. What we know are things about how M relates to his daughter’s and his son’s age, and how those relate to one another. Since we know several things about the daughter’s age and the son’s age it’s worth giving those names too. Let’s say D for the daughter’s age and S for the son’s.
So. We know the son is three years older than the daughter. This we can write as . We know that in one year, the man will be six times as old as the daughter is now. In one year the man will be M + 1 years old. The daughter’s age now is D; six times that is 6D. So we know that . In ten years the man’s age will be M + 10; the daughter’s age, D + 10; the son’s age, S + 10. In ten years, M + 10 will be 14 plus D + 10 plus S + 10. That is, . Or if you prefer, . Or even, .
So this is a system of three equation, all linear, in three variables. This is hopeful. We can hope there will be a solution. And there is. There are different ways to find an answer. Since I’m grading this, you can use the one that feels most comfortable to you. The problem still seems a bit advanced for Peppermint Patty and Franklin.
Julie Larson’s The Dinette Set rerun for the 13th has a bit of talk about a mathematical discovery. The comic is accurate enough for its publication. In 2008 a number known as M43112609 was proven to be prime. The number, 243,112,609 – 1, is some 12,978,189 digits long. It’s still the fifth-largest known prime number (as I write this).
Prime numbers of the form 2N – 1 for some whole number N are known as Mersenne primes. These are named for Marin Mersenne, a 16th century French friar and mathematician. They’re a neat set of numbers. Each Mersenne prime matches some perfect number. Nobody knows whether there are finite or infinitely many Mersenne primes. Every even perfect number has a form that matches to some Mersenne prime. It’s unknown whether there are any odd perfect numbers. As often happens with number theory, the questions are easy to ask but hard to answer. But all the largest known prime numbers are Mersenne primes; they’re of a structure we can test pretty well. At least that electronic computers can test well; the last time the largest known prime was found by mere mechanical computer was 1951. The last time a non-Mersenne was the largest known prime was from 1989 to 1992, and before that, 1951.
T Shepherd’s Snow Sez for the 13th finishes off the unlucky-13 jokes. It observes that whatever a symbol might connote generally, your individual circumstances are more important. There are people for whom 13 is a good omen, or for whom Mondays are magnificent days, or for whom black cats are lucky.
These are all the comics I can write paragraphs about. There were more comics mentioning mathematics last week. Here were some of them:
As teased with the Andertoons I featured Tuesday, there’s some mathematics comics slight enough I can’t write paragraphs about them. But people like seeing comics that at least say “mathematics”, so here’s your heads-up to them.
Mark Parisi’s Off The Mark for the 18th is an anthropomorphic numerals joke. The numerals in a paint-by-numbers kit are really serving the role of indices, rather than anything numerical. The instructions would be the same if, say, a letter ‘p’ or a small square represented purple.
Gene Mora’s Graffiti for the 23rd is also a spot of wordplay mentioning geometry. And it comes back to the joke about one shape being a kind of another that New Adventures of Queen Victoria was on about.
The first, important, thing is that I have not disappeared or done something worse. I just had one of those weeks where enough was happening that something had to give. I could either write up stuff for my mathematics blog, or I could feel guilty about not writing stuff up for my mathematics blog. Since I didn’t have time to do both, I went with feeling guilty about not writing, instead. I’m hoping this week will give me more writing time, but I am fooling only myself.
Second is that Comics Kingdom has, for all my complaining, gotten less bad in the redesign. Mostly in that the whole comics page loads at once, now, instead of needing me to click to “load more comics” every six strips. Good. The strips still appear in weird random orders, especially strips like Prince Valiant that only run on Sundays, but still. I can take seeing a vintage Boner’s Ark Sunday strip six unnecessary times. The strips are still smaller than they used to be, and they’re not using the decent, three-row format that they used to. And the archives don’t let you look at a week’s worth in one page. But it’s less bad, and isn’t that all we can ever hope for out of the Internet anymore?
And finally, Comic Strip Master Command wanted to make this an easy week for me by not having a lot to write about. It got so light I’ve maybe overcompensated. I’m not sure I have enough to write about here, but, I don’t want to completely vanish either.
Dave Whamond’s Reality Check for the 15th is … hm. Well, it’s not an anthropomorphic-numerals joke. It is some kind of wordplay, making concrete a common phrase about, and attitude toward, numbers. I could make the fussy difference between numbers and numerals here but I’m not sure anyone has the patience for that.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 17th touches around mathematics without, I admit, necessarily saying anything specific. The angel(?) welcoming the man to heaven mentions creating new systems of mathematics as some fit job for the heavenly host. The discussion of creating self-consistent physics systems seems mathematical in nature too. I’m not sure whether saying one could “attempt” to create self-consistent physics is meant to imply that our universe’s physics are not self-consistent. To create a “maximally complex reality using the simplest possible constructions” seems like a mathematical challenge as well. There are important fields of mathematics built on optimizing, trying to create the most extreme of one thing subject to some constraints or other.
I think the strip’s premise is the old, partially a joke, concept that God is a mathematician. This would explain why the angel(?) seems to rate doing mathematics or mathematics-related projects as so important. But even then … well, consider. There’s nothing about designing new systems of mathematics that ordinary mortals can’t do. Creating new physics or new realities is beyond us, certainly, but designing the rules for such seems possible. I think I understood this comic better then I had thought about it less. Maybe including it in this column has only made trouble for me.
Doug Savage’s Savage Chickens for the 17th amuses me by making a strip out of a logic paradox. It’s not quite your “this statement is a lie” paradox, but it feels close to that, to me. To have the first chicken call it “Birthday Paradox” also teases a familiar probability problem. It’s not a true paradox. It merely surprises people who haven’t encountered the problem before. This would be the question of how many people you need to have in a group before there’s a 50 percent (75 percent, 99 percent, whatever you like) chance of at least one pair sharing a birthday.
And I notice on Wikipedia a neat variation of this birthday problem. This generalization considers splitting people into two distinct groups, and how many people you need in each group to have a set chance of a pair, one person from each group, sharing a birthday. Apparently both a 32-person group of 16 women and 16 men, or a 49-person group of 43 women and six men, have a 50% chance of some woman-man pair sharing a birthday. Neat.
Mark Parisi’s Off The Mark for the 18th sports a bit of wordplay. It’s built on how multiplication and division also have meanings in biology. … If I’m not mis-reading my dictionary, “multiply” meant any increase in number first, and the arithmetic operation we now call multiplication afterwards. Division, similarly, meant to separate into parts before it meant the mathematical operation as well. So it might be fairer to say that multiplication and division are words that picked up mathematical meaning.
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.
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 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.
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 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.
Some weeks there’s an obvious theme. Most weeks there’s not. But mid-March has formed a traditional theme for at least one day. I’m going to excerpt that from the rest of the week’s comics, because I’ve noticed what readership around here is like for stuff tagged “Pi Day” in mid-March. You all can do what you like with your pop-mathematics blogs.
Pi Day seems to have brought out fewer comics than in years past. The ones that were made, among the set I read, were also less on point. There was a lot of actual physical pie involved, too, suggesting the day might be escaping the realm of pop-mathematics silliness straight into pun nobody thinks about. Or maybe cartoonists just didn’t have a fresh angle this year.
John Hambrock’s The Brilliant Mind of Edison Lee shows off a nerd kind of mistake. At least one I think of as particularly nerdy. Wanting to calculate is a natural urge, especially for those who do it well. But to calculate the circumference of a pie from its diameter? What is exciting about that? More, does Grandpa recognize what a circumference is? It’s relatively easy to see the diameter of a pie. Area, also. But circumference? I’m not sure people are good at estimating the circumference of things, not by sight. You’d need a tape measure, or a similar flexible ruler, to start with and we don’t see that. Without the chance to measure it himself, Grandpa has to take the circumference (and, for that matter, diameter) at Edison Lee’s word. What would convince Grandpa of anything?
For example, even if Grandpa accepted that Edison Lee had multiplied one number by 3.14 and gotten another number he might ask: how do we know pi is the same for pies of all sizes? Could a small pie’s circumference be only three times the diameter’s length, while a large pie’s is four times that? Could Edison offer an answer for why 3.14, or some nearby number, is all that interesting?
Liz Climo’s Cartoons is an example of the second kind of strip I mentioned during my introductory paragraphs. While it’s nominally built on Pi Day, any mathematics is gone. It’s just about the pun. And, well, the fun of having a capybara around.
Mark Parisi’s Off The Mark is the most on-topic strip for the day. And the anthropomorphic numerals joke for the day, too. It’s built on there being infinitely many digits to π, which, true enough. There are also infinitely many digits to , mind; they’re just not so interesting a set. π being irrational gives us a never-ending variety of digits. It’s almost certainly normal, too. Any finite string of digits most likely appears infinitely often in this string.
We won’t ever know enough digits of π to depict all of them. But we can depict the digits we know, and many different ways. Here’s a 2015 Washington Post article with several pictures representing the digits, including some neat “random walk” ones. In those the digits are used to represent directions and distances for a thing to move, and it represents the number as this curious wispy structure. There’s amazing pictures to be made of this.
And last, a comic strip that I don’t think was trying to set up a Pi Day joke. But Bill Schorr’s The Grizzwells for the 13th is a routine story problem joke. But that the setup mentions pies? If this ran on the 14th I would feel confident Schorr was going for a Pi Day comic. But it didn’t, so I don’t know if Schorr was going for that or not.
It’s happened again: another slow week around here. My supposition is that Comic Strip Master Command was snowed in about a month ago, and I’m seeing the effects only now. There’s obviously no other reason that more comic strips didn’t address my particular narrow interest in one seven-day span.
Samson’s Dark Side of the Horse for the 18th is a numerals joke. The mathematics content is slight, I admit, but I’ve always had a fondness for Dark Side of the Horse. (I know it sounds like I have a fondness for every comic strip out there. I don’t quite, but I grant it’s close.) Conflating numerals and letters, and finding words represented by numerals, is an old tradition. It was more compelling in ancient days when letters were used as numerals so that it was impossible not to find neat coincidences. I suppose these days it’s largely confined to typefaces that make it easy to conflate a letter and a numeral. I mean moreso than the usual trouble telling apart 1 and l, 0 and O, or 5 and S. Or to special cases like hexadecimal numbers where, for ease of representation, we use the letters A through F as numerals.
Jef Mallett’s Frazz for the 18th is built on an ancient problem. I remember being frustrated with it. How is “questions 15 to 25” eleven questions when the difference between 15 and 25 is ten? The problem creeps into many fields. Most of the passion has gone out of the argument but around 1999 you could get a good fight going about whether the new millennium was to begin with January 2000 or 2001. The kind of problem is called a ‘fencepost error’. The name implies how often this has complicated someone’s work. Divide a line into ten segments. There are nine cuts on the interior of the line and the two original edges. I’m not sure I could explain to an elementary school student how the cuts and edges of a ten-unit-long strip match up to the questions in this assignment. I might ask how many birthdays someone’s had when they’re nine years old, though. And then flee the encounter.
Mark Parisi’s Off The Mark for the 19th is another numerals joke. This one’s also the major joke to make about an ice skater doing a figure eight: write the eight some other way. (I’d have sworn there was an M-G-M Droopy cartoon in which Spike demonstrates his ability to skate a figure 8, and then Droopy upstages him by skating ‘4 + 4’. I seem to be imagining it; the only cartoon where this seems to possibly fit is 1950’s The Chump Champ, and the joke isn’t in that one. If someone knows the cartoon I am thinking of, please let me know.) Here, the robot is supposed to be skating some binary numeral. It’s nothing close to an ‘8’, but perhaps the robot figures it needs to demonstrate some impressive number to stand out.
Bud Blake’s Tiger for the 21st has Tiger trying to teach his brother arithmetic. Working it out with fingers seems like a decent path to try, given Punkinhead’s age and background. And Punkinhead has a good point: why is the demonstration the easy problem and the homework the hard problem? I haven’t taught in a while, but do know I would do that sort of thing. My rationalization, I think, would be that a hard problem is usually hard because it involves several things. If I want to teach a thing, then I want to highlight just that thing. So I would focus on a problem in which that thing is the only tricky part, and everything else is something the students are so familiar with they don’t notice it. The result is usually an easy problem. There isn’t room for toughness. I’m not sure if that’s a thing I should change, though. Demonstrations of how to work harder problems are worth doing. But I usually think of those as teaching “how to use these several things we already know”. Using a tough problem to show one new thing, plus several already-existing tricky things, seems dangerous. It might be worth it, though.
Comic Strip Master Command decreed that this should be a slow week. The greatest bit of mathematical meat came at the start, with a Garfield that included a throwaway mathematical puzzle. It didn’t turn out the way I figured when I read the strip but didn’t actually try the puzzle.
Jim Davis’s Garfield for the 3rd is a mathematics cameo. Working out a problem is one more petty obstacle in Jon’s day. Working out a square root by hand is a pretty good tedious little problem to do. You can make an estimate of this that would be not too bad. 324 is between 100 and 400. This is worth observing because the square root of 100 is 10, and the square root of 400 is 20. The square of 16 is 256, which is easy for me to remember because this turns up in computer stuff a lot. But anyway, numbers from 300 to 400 have square roots that are pretty close to but a little less than 20. So expect a number between 17 and 20.
But after that? … Well, it depends whether 324 is a perfect square. If it is a perfect square, then it has to be the square of a two-digit number. The first digit has to be 1. And the last digit has to be an 8, because the square of the last digit is 4. But that’s if 324 is a perfect square, which it almost certainly is … wait, what? … Uh .. huh. Well, that foils where I was going with this, which was to look at a couple ways to do square roots.
One is to start looking at factors. If a number is equal to the product of two numbers, then its square root is the product of the square roots of those numbers. So dividing your suspect number 324 by, say, 4 is a great idea. The square root of 324 would be 2 times the square root of whatever 324 ÷ 4 is. Turns out that’s 81, and the square root of 81 is 9 and there we go, 18 by a completely different route.
So that works well too. If it had turned out the square root was something like then we get into tricky stuff. One response is to leave the answer like that: is exactly the square root of 328. But I can understand someone who feels like they could use a numerical approximation, so that they know whether this is bigger than 19 or not. There are a bunch of ways to numerically approximate square roots. Last year I worked out a way myself, one that needs only a table of trigonometric functions to work out. Tables of logarithms are also usable. And there are many methods, often using iterative techniques, in which you make ever-better approximations until you have one as good as your situation demands.
Anyway, I’m startled that the cheese doodles price turned out to be a perfect square (in cents). Of course, the comic strip can be written to have any price filled in there. The joke doesn’t depend on whether it’s easy or hard to take the square root of 324. But that does mean it was written so that the problem was surprisingly doable and I’m amused by that.
Ryan North’s Dinosaur Comics for the 4th goes in some odd directions. But it’s built on the wonder of big numbers. We don’t have much of a sense for how big truly large numbers. We can approach pieces of that, such as by noticing that a billion seconds is a bit more than thirty years. But there are a lot of truly staggeringly large numbers out there. Our basic units for things like distance and mass and quantity are designed for everyday, tabletop measurements. The numbers don’t get outrageously large. Had they threatened to, we’d have set the length of a meter to be something different. We need to look at the cosmos or at the quantum to see things that need numbers like a sextillion. Or we need to look at combinations and permutations of things, but that’s extremely hard to do.
Tom Horacek’s Foolish Mortals for the 4th is a marginal inclusion for this week’s strips, but it’s a low-volume week. The intended joke is just showing off a “tube sock” and an “inner tube sock”. But it happens to depict these as a cylinder and a torus and those are some fun shapes to play with. Particularly, consider this: it’s easy to go from a flat surface to a cylinder. You know this because you can roll a piece of paper up and get a good tube. And it’s not hard to imagine going from a cylinder to a torus. You need the cylinder to have a good bit of give, but it’s easy to imagine stretching it around and taping one end to the other. But now you’ve got a shape that is very different from a sheet of paper. The four-color map theorem, for example, no longer holds. You can divide the surface of the torus so it needs at least seven colors.
Mastroianni and Hart’s B.C. for the 5th is a bit of wordplay. As I said, this was a low-volume week around here. The word “logarithm” derives, I’m told, from the modern-Latin ‘logarithmus’. John Napier, who advanced most of the idea of logarithms, coined the term. It derives from ‘logos’, here meaning ‘ratio’, and ‘re-arithmos’, meaning ‘counting number’. The connection between ratios and logarithms might not seem obvious. But suppose you have a couple of numbers, and we’ll reach deep into the set of possible names and call them a, b, and c. Suppose a ÷ b equals b ÷ c. Then the difference between the logarithm of a and the logarithm of b is the same as the difference between the logarithm of b and the logarithm of c. This lets us change calculations on numbers to calculations on the ratios between numbers and this turns out to often be easier work. Once you’ve found the logarithms. That can be tricky, but there are always ways to do it.
Bill Rechin’s Crock for the 8th is not quite a bit of wordplay. But it mentions fractions, which seem to reliably confuse people. Otis’s father is helpless to present a concrete, specific example of what fractions mean. I’d probably go with change, or with slices of pizza or cake. Something common enough in a child’s life.
These are all the mathematically-themed comic strips for the past week. Next Sunday, I hope, I’ll have more. Meanwhile please come around here this week to see what, if anything, I think to write about.
The title doesn’t mean anything. My laptop’s random-draw of pictures pulled up one from the county fair last year is all. I’m just working too close to deadline to have a good one. Pet rabbit has surgery scheduled and we are hoping that turns out well for everyone involved.
Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 12th has the blackboard of mathematical symbols. Familiar old shorthand of conflating mathematics ability with genius, or at least intelligence. The blackboard isn’t particularly full of expressions, possibly because Caulfield and Rouillard’s art might not be able to render too much detail clearly. It’s also got a sort-of appearance of Einstein’s most famous equation. Although with perhaps an extra joke to it. Suppose we’re to take ‘E’ and ‘M’ and ‘C’ to mean what they do in Einstein’s use. Then has to equal zero. And there are many things you can safely do with zero. Dividing by it, though, isn’t one. I shan’t guess whether Caulfield and Rouillard were being that sly, though.
Marty Links’s Emmy Lou rerun for the 13th tries to be a paradox. How can one like mathematics without liking figures? But arithmetic is just one part of mathematics. Surely the most-used part, if we go by real-world utility. But not everything. Arithmetic is often useful, yes. But you can do good work in (say) logic or knot theory or geometry with only a slight ability to add or subtract or multiply. There’s not enough emphasis put on that in early education. I suppose it reflects the reasonable feeling that people do need to be competent at arithmetic, which is useful. But it gives one a distorted view of what mathematics can be.
Mark Parisi’s Off The Markfor the 13th is the anthropomorphic numerals joke for the week. And it presents being multiplied by zero as a terrifying fate for other numbers. This seems to reflect the idea that being multiplied by zero is equivalent to being made into nothing. That it’s being killed. Zero enjoys this dual meaning, culturally, representing both a number and the concept of a thing that doesn’t exist and the concept of non-existence. If being turned from one number to another is a numeral murder, then a 2 sneaking in with a + sign would be at least as horrifying. But that joke wouldn’t work, and I know that too.
Olivia Jaimes’s Nancy for the 14th is another recreational-mathematics puzzle. I know nothing of Jaimes’s background but apparently it involves a keen interest in that kind of play that either makes someone love or hate mathematics. (Myself, I’m only slightly interested in these kinds of puzzles, most of the time.) This one — add one line to ‘fix’ the equation 5 + 5 + 5 + 5 = 555 — I hadn’t encountered before. Took some fuming to work it out. The obvious answer, of course, is to add a slash across the = sign so that it means “does not equal”.
But that answer’s dull. What mathematicians like are statements that are true and interesting. There are many things that 5 + 5 + 5 + 5 does not equal. Why single out 555 from that set? So negating the equals sign meets the specifications of the problem, slightly better than Nancy does herself. It doesn’t have the surprise of the answer Nancy’s teacher wants.
If you don’t get how to do it, highlight over the paragraph below for a hint.
There are actually three ways to add the stroke to make this equation true. The three ways are equivalent, though. Notice that the symbols on the board comprise strokes and curves and consider that the meaning of the symbol can be changed by altering the composition of those strokes and curves.
Ted Shearer’s Quincy for the 21st of May, 1979, and rerun the 14th is a joke about making mathematics problems relevant. And, yeah, I’ll give Mrs Glover credit for making problems that reflect stuff students know they’re going to have to deal with. Also that they may have already dealt with and so have some feeling for what plausible answers will be. It’s tough to find many problems like that which don’t repeat themselves too much. (“If your pants need a new patch every two months how many would you have in three years?”).
So today I am trying out including images for all the mathematically-themed comic strips here. This is because of my discovery that some links even on GoComics.com vanish without warning. I’m curious how long I can keep doing this. Not for legal reasons. Including comics for the purpose of an educational essay about topics raised by the strips is almost the most fair use imaginable. Just because it’s a hassle copying the images and putting them up on WordPress.com and that’s even before I think about how much image space I have there. We’ll see. I might try to figure out a better scheme.
Also in this batch of comics are the various Pi Day strips. There was a healthy number of mathematically-themed comics on the 14th of March. Many of those were just coincidence, though, with no Pi content. I’ll group the Pi Day strips together.
Tom Batiuk’s Funky Winkerbean for the 2nd of April, 1972 is, I think, the first appearance of Funky Winkerbean around here. Comics Kingdom just started running the strip, as well as Bud Blake’s Tiger and Bill Hoest’s Lockhorns, from the beginning as part of its Vintage Comics roster. And this strip really belonged in Sunday’s essay, but I noticed the vintage comics only after that installment went to press. Anyway, this strip — possibly the first Sunday Funky Winkerbean — plays off a then-contemporary fear of people being reduced to numbers in the face of a computerized society. If you can imagine people ever worrying about something like that. The early 1970s were a time in American society when people first paid attention to the existence of, like, credit reporting agencies. Just what they did and how they did it drew a lot of critical examination. Josh Lauer’s recently published Creditworthy: a History of Consumer Surveillance and Financial Identity in America gets into this.
Bob Scott’s Bear With Me for the 14th sees Molly struggling with failure on a mathematics test. Could be any subject and the story would go as well, but I suppose mathematics gets a connotation of the subject everybody has to study for, even the geniuses. (The strip used to be called Molly and the Bear. In either name this seems to be the first time I’ve tagged it, although I only started tagging strips by name recently.)
Bud Fisher’s Mutt and Jeff rerun for the 14th is a rerun from sometime in 1952. I’m tickled by the problem of figuring out how many times Fisher and his uncredited assistants drew Mutt and Jeff. Mutt saying that the boss “drew us 14,436 times” is the number of days in 45 years, so that makes sense if he’s counting the number of strips drawn. The number of times that Mutt and Jeff were drawn is … probably impossible to calculate. There’s so many panels each strip, especially going back to earlier and earlier times. And how many panels don’t have Mutt or don’t have Jeff or don’t have either in them? Jeff didn’t appear in the strip until March of 1908, for example, four months after the comic began. (With a different title, so the comic wasn’t just dangling loose all that while.)
Scott Hilburn’s The Argyle Sweater for the 14th starts the Pi Day off, of course, with a pun and some extension of what makes 3/14 get its attention. And until Hilburn brought it up I’d never thought about the zodiac sign for someone born the 14th of March, so that’s something.
Mark Parisi’s Off The Mark for the 14th riffs on one of the interesting features of π, that it’s an irrational number. Well, that its decimal representation goes on forever. Rational numbers do that too, yes, but they all end in the infinite repetition of finitely many digits. And for a lot of them, that digit is ‘0’. Irrational numbers keep going on with more complicated patterns. π sure seems like it’s a normal number. So we could expect that any finite string of digits appears somewhere in its decimal expansion. This would include a string of digits that encodes any story you like, The Neverending Story included. This does not mean we might ever find where that string is.
Michael Cavna’s Warped for the 14th combines the two major joke threads for Pi Day. Specifically naming Archimedes is a good choice. One of the many things Archimedes is famous for is finding an approximation for π. He’d worked out that π has to be larger than 310/71 but smaller than 3 1/7. Archimedes used an ingenious approach: we might not know the precise area of a circle given only its radius. But we can know the area of a triangle if we know the lengths of its legs. And we can draw a series of triangles that are enclosed by a circle. The area of the circle has to be larger than the sum of the areas of those triangles. We can draw a series of triangles that enclose a circle. The area of the circle has to be less than the sum of the areas of those triangles. If we use a few triangles these bounds are going to be very loose. If we use a lot of triangles these bounds can be tight. In principle, we could make the bounds as close together as we could possibly need. We can see this, now, as a forerunner to calculus. They didn’t see it as such at the time, though. And it’s a demonstration of what amazing results can be found, even without calculus, but with clever specific reasoning. Here’s a run-through of the process.
John Zakour and Scott Roberts’s Working Daze for the 15th is a response to Dr Stephen Hawking’s death. The coincidence that he did die on the 14th of March made for an irresistibly interesting bit of trivia. Zakour and Roberts could get there first, thanks to working on a web comic and being quick on the draw. (I’m curious whether they replaced a strip that was ready to go for the 15th, or whether they normally work one day ahead of publication. It’s an exciting but dangerous way to go.)
No surprise what the recurring theme for this set of mathematics-mentioning comic strips is. Look at the date range. But here goes.
Henry Scarpelli and Craig Boldman’s Archie rerun for the 13th uses algebra as the thing that will stun a class into silence. I know the silence. As a grad student you get whole minutes of instructions on how to teach a course before being sent out as recitation section leader for some professor. And what you do get told is the importance of asking students their thoughts and their ideas. This maybe works in courses that are obviously friendly to opinions or partially formed ideas. But in Freshman Calculus? It’s just deadly. Even if you can draw someone into offering an idea how we might start calculating a limit (say), they’re either going to be exactly right or they’re going to need a lot of help coaxing the idea into something usable. I’d like to have more chatty classes, but some subjects are just hard to chat about.
Steve Skelton’s 2 Cows And A Chicken for the 13th includes some casual talk about probability. As normally happens, they figure the chances are about 50-50. I think that’s a default estimate of the probability of something. If you have no evidence to suppose one outcome is more likely than the other, then that is a reason to suppose the chance of something is 50 percent. This is the Bayesian approach to probability, in which we rate things as more or less likely based on what information we have about how often they turn out. It’s a practical way of saying what we mean by the probability of something. It’s terrible if we don’t have much reliable information, though. We need to fall back on reasoning about what is likely and what is not to save us in that case.
Scott Hilburn’s The Argyle Sweater lead off the Pi Day jokes with an anthropomorphic numerals panel. This is because I read most of the daily comics in alphabetical order by title. It is also because The Argyle Sweater is The Argyle Sweater. Among π’s famous traits is that it goes on forever, in decimal representations, yes. That’s not by itself extraordinary; dull numbers like one-third do that too. (Arguably, even a number like ‘2’ does, if you write all the zeroes in past the decimal point.) π gets to be interesting because it goes on forever without repeating, and without having a pattern easily describable. Also because it’s probably a normal number but we don’t actually know that for sure yet.
Mark Parisi’s Off The Mark panel for the 14th is another anthropomorphic numerals joke and nearly the same joke as above. The answer, dear numeral, is “chained tweets”. I do not know that there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. But there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. If there isn’t, there is now.
John Zakour and Scott Roberts’s Working Daze for the 14th is your basic Pi Day Wordplay panel. I think there were a few more along these lines but I didn’t record all of them. This strip will serve for them all, since it’s drawn from an appealing camera angle to give the joke life.
Dave Blazek’s Loose Parts for the 14th is a mathematics wordplay panel but it hasn’t got anything to do with π. I suspect he lost track of what days he was working on, back six or so weeks when his deadline arrived.
Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 15th is some sort of joke about the probability of the world being like what it seems to be. I’m not sure precisely what anyone is hoping to express here or how it ties in to world peace. But the world does seem to be extremely well described by techniques that suppose it to be random and unpredictable in detail. It is extremely well predictable in the main, which shows something weird about the workings of the world. It seems to be doing all right for itself.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th is built on the staggering idea that the Earth might be the only place with life in the universe. The cosmos is a good stand-in for infinitely large things. It might be better as a way to understand the infinitely large than actual infinity would be. Somehow thinking of the number of stars (or whatnot) in the universe and writing out a representable number inspires an understanding for bigness that the word “infinity” or the symbols we have for it somehow don’t seem to, at least to me.
Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 17th gives us valuable information about how long ahead of time the comic strips are working. Arithmetic is probably the easiest thing to use if one needs an example of a fact. But even “2 + 2 = 4” is a fact only if we accept certain ideas about what we mean by “2” and “+” and “=” and “4”. That we use those definitions instead of others is a reflection of what we find interesting or useful or attractive. There is cultural artifice behind the labelling of this equation as a fact.
Jimmy Johnson’s Arlo and Janis for the 18th capped off a week of trying to explain some point about the compression and dilution of time in comic strips. Comic strips use space and time to suggest more complete stories than they actually tell. They’re much like every other medium in this way. So, to symbolize deep thinking on a subject we get once again a panel full of mathematics. Yes, I noticed the misquoting of “E = mc2” there. I am not sure what Arlo means by “Remember the boat?” although thinking on it I think he did have a running daydream about living on a boat. Arlo and Janis isn’t a strongly story-driven comic strip, but Johnson is comfortable letting the setting evolve. Perhaps all this is forewarning that we’re going to jump ahead to a time in Arlo’s life when he has, or has had, a boat. I don’t know.