## Reading the Comics, February 9, 2019: Garfield Outwits Me Edition

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 &div; 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 $2\sqrt{82}$ then we get into tricky stuff. One response is to leave the answer like that: $2\sqrt{82}$ 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 &div; b equals b &div; 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.

And I grant there have been several comic strips here of marginal mathematics value. There was still one of such marginal value. Mark Parisi’s Off The Mark for the 7th has anthropomorphized numerals, in service of a temperature joke.

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.

## Reading the Comics, July 14, 2018: County Fair Edition

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 $E - mc^2$ 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?”).

I do many Reading the Comics posts. Others like this one are here. For other essays that mention Mustard and Boloney, look to this link. I admit I’m surprised there’s anything there; I didn’t remember having written about it before For other discussions of Emmy Lou, try this link. For this and other times I’ve written about Off The Mark try this link. For Nancy content, try this link. And for other Quincy essays you can read this link. Thank you.

## Reading the Comics, March 17, 2018: Pi Day 2018 Edition

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.)

Doug Savage’s Savage Chickens for the 14th is a collection of charts. Not all pie charts. And yes, it ran the 14th but avoids the pun it could make. I really like the tart charts, myself.

And now for the Pi Day strips proper.

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.)

## Reading the Comics, March 18, 2017: Pi Day Edition

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.