Reading the Comics, October 19, 2019: Just The Casual Mentions Edition


Let me get out of the way last week’s comic strips that I thought didn’t need much discussion. There’s discussion creeping into them anyway. This is why there’s such a rush.

Greg Cravens’s The Buckets for the 14th has a kid longing for help with algebra.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 15th is a percentages joke. It’s really tempting to just add and subtract percentages like this, when talking about sales and interest and such. If the percentages are small, like, one or two percent, this is near enough to being right. A sale of 15 percent and interest of 22 percent? That’s not close enough to approximate like that. A 15 percent sale with 22 percent interest charge would come to about a 3.7 percent surcharge. But how long the charge stays on the credit card will affect the amount.

Bob Scott’s Bear With Me for the 17th has one of Molly’s friends trying to print a mathematics assignment.

Ryan North’s Dinosaur Comics for the 17th has one long message turn out to encode a completely unrelated thing. This is something you can deliberately build in to a signal. You might want to, in order to confound codebreakers working on your message. It’s possible in any message to encode a second by accident. As you’d think, the longer the unintentional message the less likely it is to just turn up.

Next Sunday should be the next time I do a Reading the Comics essay. Tomorrow and Thursday I hope to extend the A-to-Z sequence. I don’t know what’s going to happen here on Wednesday. I’m looking forward to finding out myself. See you then.

Reading the Comics, June 27, 2019: Closing A Slow Month Edition


Some months stretch my pop-mathematics writing skills, tasking me with finding new insights into the things I thought I understood and new ways to present them. Some months I’ve written about comic strips a lot. This was one of the latter. Here, let me nearly finish writing about the comic strips of June 2019 that had some mathematical content.

Jonathan Lemon’s Rabbits Against Magic for the 23rd is the Venn Diagram meta-joke for the week. Properly speaking, yes, Eight-Ball hasn’t drawn a Venn Diagram here. Representing two sets in a Venn Diagram, by the proper rules, requires two circles with one overlap. Indicating that both sets have the same elements means noting that there are no elements outside the intersection of these circles. One point of a Venn Diagram is showing all the possible logical relations between sets and maybe then marking off the ones that happen to be relevant to the problem. What Eight-Ball is drawing is an Euler Diagram, which has looser requirements. There’s no sense fighting this terminology battle, though. It makes cleaner pictures to draw a Venn Diagram modified to only show the relations that actually exist. If the goal is to communicate information, clarity counts. A joke counts as information.

Eight-Ball, drawing: 'I'm making my first Venn Diagram! See, in the first set I'm including people who like to think they're good at math. And see here, I'm using a second set to show which of those people like Venn diagrams. It's a perfect circle.' (He shows a circle with two small balloons, labelled A and B, stuck off it. Weenus looks to the audience unimpressed.) Weenus: 'Logic isn't really your thing.' Eight-Ball: 'I guess that changes the diagram!'
Jonathan Lemon’s Rabbits Against Magic for the 23rd of June, 2019. Oh, this strip again. You’ve seen Rabbits Against Magic in essays at this link.

Eight-Ball’s propositions are … well, a bit muddled. His first set is “people who like to think they are good at math”. His second set is “which of those people like Venn Diagrams”. This implies the second set can’t be anything but a subset of the first. So this we’d represent as one circle inside another, at least if we allow that there exists at least one person who likes to think they’re good at math, but still doesn’t like Venn Diagrams. It’s fine for the purposes of comic hyperbole to claim there is no such thing, of course, and I don’t quarrel with that.

Why not have the second group be “people who like Venn Diagrams”, without the restriction that they already think they’re good at math? Here I think there is a serious logical constraint. My suspicion is that Venn Diagrams are liked by people who don’t think they’re good at math. Also by people who aren’t good at math. Venn Diagrams are a wonderful tool because they present the relationships of sets in a way that uses our spatial intuitions. They wouldn’t make a good Internet joke format if they were liked only by people who think they’re good at math. Which is why Jonathan Lemon had to write the joke that way. It’s plausible comic hyperbole to say everyone who thinks they’re good at math likes Venn Diagrams. But there are too many people who react to explicit mathematics content with a shudder, but who like Venn Diagram jokes, to make “everyone who likes Venn Diagrams thinks they’re good at math” plausible.

Man In Black: 'Ma'am! Ma'am! I'm from the government. I'm so glad we found you. You're the median citizen!' Woman: 'What?' MIB: 'In terms of retirment savings you're exactly in the middle! Half the country has more than you and half the country has less!' Woman: 'So?" MIB: 'There's an election coming. This is a briefcase containing one million dollars. I need you to deposit it in your bank account and pretend you never saw me.' Newspaper headline: 'MEDIAN AMERICAN IS NOW MILLIONAIRE'. Secondary headline: 'Math scores continue decline'.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 23rd of June, 2019. Oh, this strip again. You’ve seen Saturday Morning Breakfast Cereal in essays at this link.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 23rd is a lying-with-statistics joke. The median is an average of a data set. It’s “an” average because, in English, we mean several different things by “average”. Translated into mathematics these different things are, really, completely unrelated. The “median” is the midpoint of the ordered list of the data set. So, as the Man In Black says, half the data in the set is below that value, and half is above. This can be a better measure of “average” than the arithmetic mean is. It tells us a slight something about the distribution, about how the data is arranged. Not much, but then, it’s just one number. What do you want? It has an advantage over the arithmetic mean, which is the thing normal people intend when they say “average”. That advantage is that it’s relatively insensitive to outliers. One or two really large, or tiny, data points can throw the mean way off. The classic example we use these days is to look at the average wealth of twenty people in the room. If Bill Gates enters the room, the mean jumps way up. The median? Doesn’t alter much. (Bill Gates is the figure I see used these days, but it could be anyone impossibly wealthy. I imagine there are versions where it’s Jeff Bezos entering the room. I imagine a century ago, the proposition would be to imagine J P Morgan entering the room, except that a century ago he had been dead six years.)

Cook: 'Two cups water, one cup chicken stock.' Chicken the cook holds: 'Ding ding ding!' Cook: 'You know how to do math? What's 4 minus 2?' Chicken: 'Ding ding.' Cook: '3 plus 2?' Chicken dings five times. Cook: 'Something tells me you're worth more as a sideshow attraction than dinner.' [ Later ] Onlooker: 'A poker-playing chicken? He's probably worth a lot of money!' Chicken is wearing the dealer's cap and in front of a pile of chips. Cook, looking over his cards: 'I hope so! I'm down 50 bucks!'
Steve Skelton’s 2 Cows and a Chicken for the 26th of June, 2019. Oh, this strip ag — wait, no. Is this a new tag?. No, but the strip was on hiatus a while. 2 Cows And A Chicken has appeared before, in essays at this link. You know it wasn’t until transcribing this comic for the alt text that I realized the ‘dings’ were Chicken pecking at the pot and not a noise that he was making directly. I don’t know why I would have thought he’d have just been making ‘ding’ noises. Also it was the end of my transcribing when I realized what Chicken was doing.

Steve Skelton’s 2 Cows and a Chicken for the 26th shows off a counting chicken as a wonder. Animals do have some sense of mathematics. We know in some detail how well crows and ravens can count, and do simple arithmetic. This is partly because we know good ways to test crow and raven arithmetic skills. And we’ve come to appreciate their intelligence as deep and surprising. Chickens, to my knowledge, have gotten less study. But I would expect they’ve got skills. If nothing else, I would expect chickens to have a good understanding of the transitive property. This is the rule that if ‘a’ is greater than ‘b’, and ‘b’ is greater than ‘c’, then it follows that ‘a’ is greater than ‘c’. Chickens have a pecking order, and animals with that kind of hierarchy tend to know transitivity. I don’t know that the reasons for that link have been proven, but, c’mon. And animals doing arithmetic, like the cook says, have been good sideshow attractions or performances for a long while. They’ve also been good starts for scientific study, as people try to work out questions like how intelligence formed, and what other ways it might have formed.

Young kid: 'How do you spell 'fifteen'?' Mom: 'F-I-F-T ... ' (Young kid looks distressed.) Mom: 'What? Oh. 1-5.'
Greg Cravens’s The Buckets for the 27th of June, 2019. All right, this one appears kind of middlingly often. The Buckets turns up in essays at this link.

Greg Cravens’s The Buckets for the 27th is a joke about the representation of numbers. Cravens has a good observation here about learning the differences between representations, and of not being able to express just what representation you want. I love Eddie’s horrified face as his mother (Sarah) tries to spell out the word. There’s probably a good exercise to be done in thinking of as many ways to represent fifteen as possible.

Etymologically, “fifteen” has exactly the origin you would say if you were dragged out of a sound sleep by someone demanding the history of the word RIGHT NOW, THERE’S NO TIME TO EXPLAIN. In Old English it was “fiftyne”, with “fif” meaning “five” and “tyne” meaning “ten more than”. This construction, pretty much five-and-ten, has fallen out of favor in English. Once we get past nineteen we more commonly write out, like, “twenty-one” and “thirty-five” and such. The alternate construction, which would be, like, one-and-twenty, or nine-and-sixty, or such, seems to have fallen out of use except as a more poetic way to express the idea. I don’t know why, say, five-and-twenty would have shifted to twenty-five while the equivalent five-and-ten didn’t shift to … teenfive(?). I would make an uninformed guess that words used more commonly tend to be more stable, and we tend to need smaller numbers more than bigger ones.


I’ll have some more comic strips for you later in the week. Before then should be a statistics review, as I figure out whether anyone is reading this blog after a month when I wrote basically nothing. The next Reading the Comics post should be at this link probably on Thursday. Thank you for reading any of this.

Reading the Comics, March 19, 2019: Average Edition


This time around, averages seem important.

Mark Anderson’s Andertoons for the 18th is the Mark Anderson’s Andertoons for the week. This features the kids learning some of the commonest terms in descriptive statistics. And, as Wavehead says, the similarity of names doesn’t help sorting them out. Each is a kind of average. “Mean” usually is the arithmetic mean, or the thing everyone including statisticians calls “average”. “Median” is the middle-most value, the one that half the data is less than and half the data is greater than. “Mode” is the most common value. In “normally distributed” data, these three quantities are all the same. In data gathered from real-world measurements, these are typically pretty close to one another. It’s very easy for real-world quantities to be normally distributed. The exceptions are usually when there are some weird disparities, like a cluster of abnormally high-valued (or low-valued) results. Or if there are very few data points.

On the blackboard the teacher's written Median, Mode, and Mean, with a bunch of numbers from 3 through 15. Wavehead: 'I know they're all subtly different, but I have to say, the alliteration doesn't help.'
Mark Anderson’s Andertoons for the 18th of March, 2019. Essays which discuss topics raised by Andertoons can be found at this link. Also at this link, nearly enough.

The word “mean” derives from the Old French “meien”, that is, “middle, means”. And that itself traces to the Late Latin “medianus”, and the Latin “medius”. That traces back to the Proto-Indo-European “medhyo”, meaning “middle”. That’s probably what you might expect, especially considering that the mean of a set of data is, if the data is not doing anything weird, likely close to the middle of the set. The term appeared in English in the middle 15th century.

The word “median”, meanwhile, follows a completely different path. That one traces to the Middle French “médian”, which traces to the Late Latin “medianus” and Latin “medius” and Proto-Indo-European “medhyo”. This appeared as a mathematical term in the late 19th century; Etymology Online claims 1883, but doesn’t give a manuscript citation.

The word “mode”, meanwhile, follows a completely different path. This one traces to the Old French “mode”, itself from the Latin “modus”, meaning the measure or melody or style. We get from music to common values by way of the “style” meaning. Think of something being done “á la mode”, that is, “in the [ fashionable or popular ] style”. I haven’t dug up a citation about when this word entered the mathematical parlance.

So “mean” and “median” don’t have much chance to do anything but alliterate. “Mode” is coincidence here. I agree, it might be nice if we spread out the words a little more.

Edison, pointing to a checkerboard: 'So Grandpa if you put one cookie on the first square, two on the second, four on the next, then eight, and you keep doubling them until you fill all 64 squares do you know what you'll end up with?' Grandpa: 'A stomachache for a month?'
John Hambrock’s The Brilliant Mind of Edison Lee for the 18th of March, 2019. I’ve been talking about this strip a lot lately, it seems to me. Essays where I do discuss Edison Lee are at this link.

John Hambrock’s The Brilliant Mind of Edison Lee for the 18th has Edison introduce a sequence to his grandfather. Doubling the number of things for each square of a checkerboard is an ancient thought experiment. The notion, with grains of wheat rather than cookies, seems to be first recorded in 1256 in a book by the scholar Ibn Khallikan. One story has it that the inventor of chess requested from the ruler that many grains of wheat as reward for inventing the game.

If we followed Edison Lee’s doubling through all 64 squares we’d have, in total, need for 263-1 or 18,446,744,073,709,551,615 cookies. You can see why the inventor of chess didn’t get that reward, however popular the game was. It stands as a good display of how exponential growth eventually gets to be just that intimidatingly big.

Edison, like many a young nerd, is trying to stagger his grandfather with the enormity of this. I don’t know that it would work. Grandpa ponders eating all that many cookies, since he’s a comical glutton. I’d estimate eating all that many cookies, at the rate of one a second, eight hours a day, to take something like eighteen billion centuries. If I’m wrong? It doesn’t matter. It’s a while. But is that any more staggering than imagining a task that takes a mere ten thousand centuries to finish?

Toby, looking at his homework, and a calculator, and a textbook: '... Wow. Crazy ... Huh. How about that? ... Am I stupid if math *always* has a surprise ending?'
Greg Cravens’s The Buckets for the 19th of March, 2019. It also seems like I discuss The Buckets more these days, as seen at this link.

Greg Cravens’s The Buckets for the 19th sees Toby surprised by his mathematics homework. He’s surprised by how it turned out. I know the feeling. Everyone who does mathematics enough finds that. Surprise is one of the delights of mathematics. I had a great surprise last month, with a triangle theorem. Thomas Hobbes, the philosopher/theologian, entered his frustrating sideline of mathematics when he found the Pythagorean Theorem surprising.

Mathematics is, to an extent, about finding interesting true statements. What makes something interesting? That depends on the person surprised, certainly. A good guideline is probably “something not obvious before you’ve heard it, thatlooks inevitable after you have”. That is, a surprise. Learning mathematics probably has to be steadily surprising, and that’s good, because this kind of surprise is fun.

If it’s always a surprise there might be trouble. If you’re doing similar kinds of problems you should start to see them as pretty similar, and have a fair idea what the answers should be. So, from what Toby has said so far … I wouldn’t call him stupid. At most, just inexperienced.

Caption: Eric had good feelings about his date. It turned out, contrary to what he first thought ... [ Venn Diagram picture of two circles with a good amount of overlap ] ... They actually had quite a lot in common.
Eric the Circle for the 19th of March, 2019, this one by Janka. This and other essays with Eric the Circle, by any artist, should be at this link.

Eric the Circle for the 19th, by Janka, is the Venn Diagram joke for the week. Properly any Venn Diagram with two properties has an overlap like this. We’re supposed to place items in both circles, and in the intersection, to reflect how much overlap there is. Using the sizes of each circle to reflect the sizes of both sets, and the size of the overlap to represent the size of the intersection, is probably inevitable. The shorthand calls on our geometric intuition to convey information, anyway.

She: 'What time is it?' He: 'The clock in the hall says 7:56, the oven clock says 8:02, the DVD clock says 8:07, and the bed table clock says 8:13.' She: 'Which one's right?' He: 'I dunno.' She: 'Let's ee. Four clocks ... carry the one ... divided by four ... ' He: 'Whenever we want to know what time it is we have to do algebra.' She: 'We better hurry, it's 8:05 and five-eighths!'
Tony Murphy’s It’s All About You for the 19th of March, 2019. And the occasional time I discuss something from It’s All About You are here.

Tony Murphy’s It’s All About You for the 19th has a bunch of things going on. The punch line calls “algebra” what’s really a statistics problem, calculating the arithmetic mean of four results. The work done is basic arithmetic. But making work seem like a more onerous task is a good bit of comic exaggeration, and algebra connotes something harder than arithmetic. But Murphy exaggerates with restraint: the characters don’t rate this as calculus.

Then there’s what they’re doing at all. Given four clocks, what’s the correct time? The couple tries averaging them. Why should anyone expect that to work?

There’s reason to suppose this might work. We can suppose all the clocks are close to the correct time. If they weren’t, they would get re-set, or not looked at anymore. A clock is probably more likely to be a little wrong than a lot wrong. You’d let a clock that was two minutes off go about its business, in a way you wouldn’t let a clock that was three hours and 42 minutes off. A clock is probably as likely to show a time two minutes too early as it is two minutes too late. This all suggests that the clock errors are normally distributed, or something like that. So the error of the arithmetic mean of a bunch of clock measurements we can expect to be zero. Or close to zero, anyway.

There’s reasons this might not work. For example, a clock might systematically run late. My mantle clock, for example, usually drifts about a minute slow over the course of the week it takes to wind. Or the clock might be deliberately set wrong: it’s not unusual to set an alarm clock to five or ten or fifteen minutes ahead of the true time, to encourage people to think it’s later than it really is and they should hurry up. Similarly with watches, if their times aren’t set by Internet-connected device. I don’t know whether it’s possible to set a smart watch to be deliberately five minutes fast, or something like that. I’d imagine it should be possible, but also that the people programming watches don’t see why someone might want to set their clock to the wrong time. From January to March 2018, famously, an electrical grid conflict caused certain European clocks to lose around six minutes. The reasons for this are complicated and technical, and anyway The Doctor sorted it out. But that sort of systematic problem, causing all the clocks to be wrong in the same way, will foil this take-the-average scheme.

Murphy’s not thinking of that, not least because this comic’s a rerun from 2009. He was making a joke, going for the funnier-sounding “it’s 8:03 and five-eights” instead of the time implied by the average, 8:04 and a half. That’s all right. It’s a comic strip. Being amusing is what counts.


There were just enough mathematically-themed comic strips this past week for one more post. When that is ready, it should be at this link. I’ll likely post it Tuesday.

Reading the Comics, November 9, 2018: Standing For Things Edition


There was something in common in two of the last five comic strips worth attention from last week. That’s good enough to give the essay its name.

Greg Cravens’s The Buckets for the 8th showcases Toby discovering the point of letters in algebra. It’s easy to laugh at him being ignorant. But the use of letters this way is something it’s easy to miss. You need first to realize that we don’t need to have a single way to represent a number. Which is implicit in learning, say, that you can write ‘7’ as the Roman numeral ‘VII’ or so, but I’m not sure that’s always clear. And realizing that you could use any symbol to write out ‘7’ if you agree that’s what the symbol means? That’s an abstraction tossed onto people who often aren’t really up for that kind of abstraction. And that we can have a symbol for “a number whose identity we don’t yet know”? Or even “a number whose identity we don’t care about”? Don’t blame someone for rearing back in confusion at this.

Friend 1: 'That algebra test was awful.' Friend 2: 'Toby just gave up and handed his paper in!' Toby: 'No, I finished. My mom said as long as I studied I didn't have to do any chores.' Friend 1: 'That'd eat up all your gaming hours!' Toby: 'Yep. Hey, did you know algebra letters stand for things?'
Greg Cravens’s The Buckets for the 8th of November, 2018. I’m sorry I can’t figure out the names of Toby’s friends here. Character lists, cartoonists, please.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th talks about vectors and scalars. And about the little ways that instructors in one subject can sabotage one another. In grad school I was witness to the mathematics department feeling quite put-upon by the engineering departments, who thought we were giving their students inadequate calculus training. Meanwhile we couldn’t figure out what they were telling students about calculus except that it was screwing up their understanding.

Funtime Activity: Ruining students forever. Teacher: 'Physics students must learn the difference between vectors and scalars is that scalars don't exist.' Student: 'What about 'amount of apples'?' Teacher: 'Huh? Oh, you're referring to 'distance in apple-space'.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th of November, 2018. Also, shouldn’t that be “displacement in apple-space”?

To a physicist, a vector is a size and a direction together. (At least until they get seriously into mathematical physics when they need a more abstract idea.) A scalar is a number. Like, a real-valued number such as ‘4’. Maybe a complex-valued number such as ‘4 + 6i’. Vectors are great because a lot of physics problems become easier when thought of in terms of directions and amounts in that direction.

A mathematician would start out with vectors and scalars like that. But then she’d move into a more abstract idea. A vector, to a mathematician, is a thing you can add to another vector and get a vector out. A scalar is something that’s not a vector but that, multiplied by a vector, gets you a vector out. This sounds circular. But by defining ‘vector’ and ‘scalar’ in how they interact with each other we get a really sweet flexibility. We can use the same reasoning — and the same proofs — for lots of things. Directions, yes. But also matrices, and continuous functions, and probabilities of events, and more. That’s a bit much to give the engineering student who’s trying to work out some problem about … I don’t know. Whatever they do over in that department. Truss bridges or electrical circuits or something.

Billy: 'On the 80s station I think I just heard my favorite song ever! It's about carrying a laser down some road. I think it's called 'Carry a laser' and it's all about lasers!' Cow: 'Actually, it's 'Kyrie Eleison'. It means 'Lord, have Mercy'. It has nothing at all to do with lasers.' Billy: 'Right, and 'Hip to b^2' has nothing to do with algebra.' Cow: 'That I don't know.'s
Mark Leiknes’s Cow and Boy rerun for the 9th of November, 2018. It first ran the 19th of March, 2012.

Mark Leiknes’s Cow and Boy for the 9th is really about misheard song lyrics, a subject that will never die now that we don’t have the space to print lyrics in the album lining anymore, or album linings. But it has a joke resonant with that of The Buckets, in supposing that algebra is just some bunch of letters mixed up with numbers. And Cow and Boy was always a strip I loved, as baffling as it might be to a casual reader. It had a staggering number of running jokes, although not in this installment.

Brad: 'I think I've got this worked out. It takes 500 half-inch hairs to make a good moustache. If I grow one hair a week, and each new hair grows 1/8 inch per month, I can grow a perfect moustache in ... ' Luann: '225 years, not bad!'
Greg Evans’s Luann Againn for the 9th of November, 2018. It first ran the 9th of November, 1990.

Greg Evans’s Luann Againn for the 9th shows Brad happy to work out arithmetic when it’s for something he’d like to know. The figure Luan gives is ridiculously high, though. If he needs 500 hairs, and one new hair grows in each week, then that’s a little under ten years’ worth of growth. Nine years and a bit over seven months to be exact. If a moustache hair needs to be a half-inch long, and it grows at 1/8th of an inch per month, then it takes four months to be sufficiently long. So in the slowest possible state it’d be nine years, eleven months. I can chalk Luann’s answer up to being snidely pessimistic about his hair growth. But his calculator seems to agree and that suggests something went wrong along the way.

Test Question: 'Mr Gray drove 55 mph to a city 80 miles away. He made two stops: one for 20 minutes, and one for 5. How long did it take Mr Gray to reach the city?' Student's answer: 'This made my head hurt, so I'm just going to say 'the whole trip'. You can't argue that.'
John Zakour and Scott Roberts’s Maria’s Day for the 9th of November, 2018. Again, character lists. I don’t know which of the characters this is except that he’s either very small or has an enormous pencil.

John Zakour and Scott Roberts’s Maria’s Day for the 9th is a story problem joke. It looks to me like a reasonable story problem, too: the distance travelled and the speed are reasonable, and give sensible numbers. The two stops add a bit of complication that doesn’t seem out of line. And the kid’s confusion is fair enough. It takes some experience to realize that the problem splits into an easy part, a hard part, and an easy part. The first easy part is how long the stops take all together. That’s 25 minutes. The hard part is realizing that if you want to know the total travel time it doesn’t matter when the stops are. You can find the total travel time by adding together the time spent stopped with the time spent driving. And the other easy part is working out how long it takes to go 80 miles if you travel at 55 miles per hour. That’s just a division. So find that and add to it the 25 minutes spent at the two stops.


The various Reading the Comics posts should all be at this link. Essays which discuss The Buckets are at this link. The incredibly many essays mentioning Saturday Morning Breakfast Cereal are at this link. Essays which mention Cow and Boy are at this link. Essays inspired in part by Luann, both the current-day and the vintage 1990 run, are at this link. The credibly many essays mentioning Maria’s Day are at this link.

And through the end of December my Fall 2018 Mathematics A-To-Z should have two new posts a week. You might like some of them.

Reading the Comics, October 6, 2018: Square Root of 144 Edition


And I have three last strips from last week to talk about. For those curious, I have ten comics for this week that I flagged for mention, at least before reading the Saturday GoComics pages. So that will probably be two or three installments next week. It’ll depend how many Saturday GoComics strips raise a point I feel like discussing.

Jim Toomey’s Sherman’s Lagoon for the 5th uses arithmetic as the archetypical homework problem that’s short enough to fit in a panel but also too hard for an adult to do. And, neatly, easy for a computer to do. Were I either shark here I’d have reasoned out the square root of 144 something like this: they’re not getting homework where they’d be asked the square root of something that wasn’t a perfect square. So it’s got to be a whole number. 144 is between 100 and 400, so it’s got to be the square root of something between 10 and 20. 144 is pretty close to 100, so 144’s square root is probably close to 10. The square of 1 is 1, so 11 squared has to be one-hundred-something-and-one. The square of 2 is 4, so 12 squared has to be one-hundred-something-and-four. The square of 3 is 9, so 13 squared has to be one-hundred-something-and-nine. The square of 4 is 16, so 14 squared has to be at least one-hundred-something-and-six. And by then we’re getting pretty far from 10. So the only plausible candidate is 12. Test that out and, what do you know, there it is.

Herman: 'Dad, can you help me with my math homework?' Sherman: 'Highly doubtful. But I'm sure Alexa can. Ask her anything.' Herman: 'Alexa, what's the square root of 144?' Alexa: 'The square root of 144 is 12.' Herman: 'Wow. She's good. has Mom finally decided to replace you?' Sherman: 'Should I be worried?'
Jim Toomey’s Sherman’s Lagoon for the 5th of October, 2018. And if you’re wondering how an Alexa eavesdropping device is working underwater, go away. The strip’s not for you, and that’s your loss, because it’s nicely low-key weird and teaches me more about ocean biology than I ever imagined I’d know.

Greg Cravens’s The Buckets for the 6th is a riff on the monkeys-at-keyboards joke. Well, what keeps monkeys-at-typewriters from writing interesting things is that they don’t have any selection. They just produce text to no end, in principle. Picking out characters and words that carry narrative is what makes essayists and playwrights. … That said, I think every instructor has faced the essay that is, somehow, worse than gibberish. The process is to try to find anything that could be credited, even if it’s just including at least one of the words from the topic of the essay, and move briskly on.

Eddie: 'You know the old saying about putting an infinite number of monkeys at an infinite number of typewriters, and eventually they'll accidentally write Shakespeare's plays?' Toby: 'I guess.' Eddie: 'My English teacher says that nothing about our class should worry those monkeys ONE BIT!'
Greg Cravens’s The Buckets for the 6th of October, 2018. I’m mostly sure the guy with all the hair is Eddie but, again, character lists. Please.

Larry Wright’s Motley for the 6th is a riff on the idea tips are impossibly complicated to calculate. And that any mathematics might as well be algebra. My question: what the heck calculation is Debbie describing here? There are different ways to find a 15 percent tip. One two-step one is to divide the bill by ten, which is easy and gets you 10 percent. Then divide that by two, which is not-hard, and gets you 5 percent. Add together the 10 percent and 5 percent and you get 15 percent. A one-step method is to just divide by six. This gets you a bit under 17 percent, but that’s close enough. It just requires an ability to divide by six.

Debbie, on the phone: '... multiply by two and move the decimal over one digit ... then divide by four and subtract that answer from the first answer.' Toady: 'Were you helping someone with their algebra?' Debbie: 'No, Dad's at the restaurant and wanted to leave a 15 percent tip.'
Larry Wright’s Motley for the 6th of October, 2018. This strip originally ran in 1987, although I can’t make out when. Also see earlier comments about cast lists; I had to look through about a month’s worth of comics to find both characters’ names here.

There’s other ways to go about it, surely. There are many ways to do any calculation you like. Some of them have the advantages of requiring fewer steps. Some require more steps, but hopefully easier steps. Debbie is, obviously, just describing a nonsensically complicated calculation, to fit the needs of the joke. I’m just trying to think of what a plausible process would lead into the first panel and still get the right answer.

My many Reading the Comics posts are at this link. Essays which mention Sherman’s Lagoon should be at this link. Other essays with The Buckets should appear at this link. And other essays discussing Motley Classics should be here.

Reading the Comics, April 28, 2018: Friday Is Pretty Late Edition


I should have got to this yesterday; I don’t know. Something happened. Should be back to normal Sunday.

Bill Rechin’s Crock rerun for the 26th of April does a joke about picking-the-number-in-my-head. There’s more clearly psychological than mathematical content in the strip. It shows off something about what people understand numbers to be, though. It’s easy to imagine someone asked to pick a number choosing “9”. It’s hard to imagine them picking “4,796,034,621,322”, even though that’s just as legitimate a number. It’s possible someone might pick π, or e, but only if that person’s a particular streak of nerd. They’re not going to pick the square root of eleven, or negative eight, or so. There’s thing that are numbers that a person just, offhand, doesn’t think of as numbers.

Crock to the two prisoners in lockboxes: 'Guess the number I'm thinking and I'll set you free.' First prisoner: '4,796,034,621,322.' Crock: 'Sorry, it's nine.' Second prisoner: 'What made you guess THAT number?' First prisoner: 'It was the first one to pop into my head.'
Bill Rechin’s Crock rerun for the 26th of April, 2018. Going ahead and guessing there’s another Crock with the same setup, except the prisoner guesses nine, and Crock says it was 4,796,034,621,322, and then in the final panel we see that Crock really had thought nine and lied.

Mark Anderson’s Andertoons for the 26th sees Wavehead ask about “borrowing” in subtraction. It’s a riff on some of the terminology. Wavehead’s reading too much into the term, naturally. But there are things someone can reasonably be confused about. To say that we are “borrowing” ten does suggest we plan to return it, for example, and we never do that. I’m not sure there is a better term for this turning a digit in one column to adding ten to the column next to it, though. But I admit I’m far out of touch with current thinking in teaching subtraction.

On the board: 51 - 26, with the 51 rewritten as 4 with a borrowed 11. Wavehead: 'So we're just borrowing 10 no questions asked? What about a credit check? What's the interest rate?'
Mark Anderson’s Andertoons for the 26th of April, 2018. This is Mark Anderson’s Andertoons for the week.

Greg Cravens’s The Buckets for the 26th is kind of a practical probability question. And psychology also, since most of the time we don’t put shirts on wrong. Granted there might be four ways to put a shirt on. You can put it on forwards or backwards, you can put it on right-side-out or inside-out. But there are shirts that are harder to mistake. Collars or a cut around the neck that aren’t symmetric front-to-back make it harder to mistake. Care tags make the inside-out mistake harder to make. We still manage it, but the chance of putting a shirt on wrong is a lot lower than the 75% chance we might naively expect. (New comic tag, by the way.)

Larry: 'Your shirt is on all wrong.' Toby: 'It was bound to happen.' Larry: 'What? Why?' Toby: 'There's FOUR different ways a shirt can go on! That gives me only, like, a 20% chance any time I put it on.'
Greg Cravens’s The Buckets for the 26th of April, 2018. I’m not sure Larry (the father)’s disbelief at his kid figuring putting the shirt on all wrong was bound to happen. It’s a mistake we all make; accepting the inevitability of that doesn’t seem that wrong.

Charles Schulz’s Peanuts rerun for the 27th is surely set in mathematics class. The publication date interests me. I’m curious if this is the first time a Peanuts kid has flailed around and guessed “the answer is twelve!” Guessing the answer is twelve would be a Peppermint Patty specialty. But it has to start somewhere.

Sally, at her schooldesk: 'The answer is twelve! It isn't? How about six? Four? Nine? Two? Ten? ... Do you have the feeling that I'm guessing?'
Charles Schulz’s Peanuts rerun for the 27th of April, 2018. This strip first ran the 30th of April, 1971. It also was rerun the 25th of April, 2003, with a different colorization scheme for some reason.

Knowing nothing about the problem, if I did get the information that my first guess of 12 was wrong, yeah, I’d go looking for 6 or 4 as next guesses, and 12 or 48 after that. When I make an arithmetic mistake, it’s often multiplying or dividing by the wrong number. And 12 has so many factors that they’re good places to look. Subtracting a number instead of adding, or vice-versa, is also common. But there’s nothing in 12 by itself to suggest another place to look, if the addition or subtraction went wrong. It would be in the question which, of course, doesn’t exist.

Venn Diagram. One circle's labelled 'Venn Diagrams'; the second 'Jokes'. The intersection is 'Lazy Cartoonists'.
Maria Scrivan’s Half-Full for the 28th of April, 2018. Hey, cartoonists deserve easy days at work too. And there’s not always a convenient holiday they can have the cast just gather around and wish everyone a happy instance of.

Maria Scrivan’s Half-Full for the 28th is the Venn Diagram joke for this week. It could include an extra circle for bloggers looking for content they don’t need to feel inspired to write. This one isn’t a new comics tag, which surprises me.

Guy: 'Relax. Half the time, job interviewers don't even read your resume. They just see how long it is.' Mathematician: 'Really?' Guy: 'Yeah. Where are you going?' Mathematician: 'To make a Mobius strip.' Interviewer: 'Wow! I've never met someone with *infinite* skills and work experience.' Mathematician: 'I don't like to brag.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th of April, 2018. If I had seen this strip in 2007 maybe I would’ve got that tenure-track posting instead of going into the world of technically being an extant mathematics blog.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th uses the M&oum;bius Strip. It’s an example of a surface that you could just go along forever. There’s nothing topologically special about the M&oum;bius Strip in this regard, though. The mathematician would have as infinitely “long” a résumé if she tied it into a simple cylindrical loop. But the M&oum;bius Strip sounds more exotic, not to mention funnier. Can’t blame anyone going for that instead.