Reading the Comics, July 7, 2018: Mutt and Jeff Relettering Scandal Edition


I apologize for not having a more robust introduction here. My week’s been chopped up by concern with the health of the older of our rabbits. Today’s proved to be less alarming than we had feared, but it’s still a lot to deal with. I appreciate your kind thoughts. Thank you.

Meanwhile the comics from last week have led me to discover something really weird going on with the Mutt and Jeff reruns.

Charles Schulz’s Peanuts Classics for the 6th has the not-quite-fully-formed Lucy trying to count the vast. She’d spend a while trying to count the stars and it never went well. It does inspire the question of how to count things when doing a simple tally is too complicated. There are many mathematical approaches. Most of them are some kind of sampling. Take a small enough part that you can tally it, and estimate the whole based on what your sample is. This can require ingenuity. For example, when estimating our goldfish population, it was impossible to get a good sample at one time. When tallying the number of visible stars in the sky, we have the problem that the Galaxy has a shape, and there are more stars in some directions than in others. This is why we need statisticians.

Lucy, going out in twilight with a pencil and sheet of paper: 'I'm going to count all the stars even if it kills me! People say I'm crazy, but I know I'm not , and that's what counts! I think I'll just sit here until it gets dark. This way I can take my time counting the stars. I'll mark 'em down as they come out. HA! There's the first one ... dum te ta te dum. There's another one. Two, three, four ... this is a cinch. Five, six, oh oh! SevenEightNineTen ... ElevenTwelveThirteen Oh, MY! They're coming out all over! SLOW DOWN! 21, 22, 23, 24, ... 35, 35, 40! Whew! (Gasp, gasp!) 41, 42 ... ' (Defeated Lucy sitting on the curb, exhausted, beneath the night sky.) 'Rats!'
Charles Schulz’s Peanuts Classics for the 6th of July, 2018. It originally ran the 4th of April, 1954. That is an adorable little adding machine and stool that Lucy has in the title panel there.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 6th looks initially like it’s meant for a philosophy blog’s Reading the Comics post. It’s often fruitful in the study of ethics to ponder doing something that is initially horrible, but would likely have good consequences. Or something initially good, but that has bad effects. These questions challenge our ideas about what it is to do good or bad things, and whether transient or permanent effects are more important, and whether it is better to be responsible for something (or to allow something) by action or inaction.

It comes to mathematics in the caption, though, and with an assist from the economics department. Utilitarianism seems to offer an answer to many ethical problems. It posits that we need to select a primary good of society, and then act so as to maximize that good. This does have an appeal, I suspect even to people who don’t thrill of the idea of finding the formula that describes society. After all, if we know the primary good of society, why should we settle for anything but the greatest value of that good? It might be difficult in practice, say, to discount the joy a musician would bring over her lifetime with her performances fairly against the misery created by making her practice the flute after school when she’d rather be playing. But we can imagine working with a rough approximation, at least. Then the skilled thinkers point out even worse problems and we see why utilitarianism didn’t settle all the big ethical questions, even in principle.

Professor: 'Suppose you want to kill a baker. But, if you kill him, a bunch of starving people will get access to his bread. Should you do it anyway?' Caption: 'All moral dilemmas can be rephrased as evil-maximization problems.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 6th of July, 2018. Confess I’m not sure the precise good-maximization reversal of this. I suppose it’s implying that the baker is refusing to give bread to starving people who can’t pay, and the hungry could alleviate the problem a while by eating the rich?

The mathematics, though. As Weinersmith’s caption puts it, we can phrase moral dilemmas as problems of maximizing evil. Typically we pose them as ones of maximizing good. Or at least of minimizing evil. But if we have the mechanism in place to find where evil is maximized, don’t we have the tools to find where good is? If we can find the set of social parameters x, y, and z which make E(x, y, z) as big as possible, can’t we find where -E(x, y, z) is as big, too? And isn’t that then where E(x, y, z) has to be smallest?

And, sure. As long as the maximum exists, or the minimum exists. Maybe we can tell whether or not there is one. But this is why when you look at the mathematics of finding maximums you realize you’re also doing minimums, or vice-versa. Pretty soon you either start referring to what you find as extremums. Or you stop worrying about the difference between a maximum and a minimum, at least unless you need to check just what you have found. Or unless someone who isn’t mathematically expert looks at you wondering if you know the difference between positive and negative numbers.

Jeff: 'You're such a fool, I'll bet you can't solve this simple problem!' Mutt: 'Which problem?' Jeff: 'If five men can eat a ham in five minutes, how long it will take ten men to eat that same ham?' Mutt: 'Well, some people eat slower.' Jeff: 'See? You just can't do it!' Mutt: 'Neither can you! It can't be solved!' Jeff: 'You say it can't be solved? Why?' Mutt: 'Because the first five men have ALREADY eaten the ham!'
Bud Fisher’s Mutt and Jeff for the 7th of July, 2018. So I found a previous iteration of this strip, from the 21st of February, 2015. They had relettered things, changing the wording slightly and making it overall somehow clunkier. The thing is, that 2015 strip looks to me like it might be a computer-lettered typeface too; look at the C’s, and the little loops on top of the letters. On the other hand, there’s some variation in the ? marks there. I understand relettering the more impenetrable old strips, especially if they don’t have the original material and have to go from archived newspaper prints. But the 2015 edition seems quite clear enough; why change that?

Bud Fisher’s Mutt and Jeff for the 7th has run here before. Except that was before they redid the lettering; it was a roast beef in earlier iterations. I was thinking to drop Mutt and Jeff from my Reading the Comics routine before all these mysteries in the lettering turned up. Anyway. The strip’s joke starts with a work-rate problems. Given how long some people take to do a thing, how long does it take a different number of people to do a thing? These are problems that demand paying attention to units, to the dimensions of a thing. That seems to be out of fashion these days, which is probably why these questions get to be baffling. But if eating a ham takes 25 person-minutes to do, and you have ten persons eating, you can see almost right away how long to expect it to take. If the ham’s the same size, anyway.

Teacher: 'Can you tell me how many triangles are in this diagram?' (It's an equilateral triangle, divided into thirds horizontally, and with the angle up top trisected, so that there are nine discrete figures inside.) Nancy, with a dozen scraps of used paper strewn around: 'Can you tell me how many pages we have to waste trying to solve this accursed puzzle?'
Olivia Jaimes’s Nancy for the 7th of July, 2018. There’s some real Old People Complaining in the comments, by the way, about how dare Nancy go sassing her elders like that. So, if you want to read those comments, judge wisely.

Olivia Jaimes’s Nancy for the 7th is built on a spot of recreational mathematics. Also on the frustration one can have when a problem looks like it’s harmless innocent fun and turns out to take just forever and you’re never sure you have the answers just right. The commenters on GoComics.com have settled on 18. I’m content with that answer.


Care for more of this? You can catch all my Reading the Comics posts at this link. Essays with Saturday Morning Breakfast Cereal content are at this link. Essays with Peanuts are at this link. Those with Mutt and Jeff are at this link. And those with Nancy are here. Thank you.

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Reading the Comics, May 29, 2018: Finding Reruns Edition


There were a bunch of mathematically-themed comic strips this past week. A lot of them are ones I’d seen before. One of them is a bit risque and I’ve put that behind a cut. This saves me the effort of thinking up a good nonsense name to give this edition, so there’s that going for me too.

Bill Amend’s FoxTrot Classics for the 24th of May ought to have run last Sunday, but I wasn’t able to make time to write about it. It’s part of a sequence of Jason tutoring Paige in geometry. She’s struggling with the areas of common shapes which is relatable. Many of these area formulas could be kept straight by thinking back to rectangles. The size of the area is equal to the length of the base times the length of the height. From that you could probably reason right away the area of a trapezoid. It would have the same area as a rectangle with a base of length the mean length of the trapezoid’s different-length sides. The parallelogram works like the rectangle, length of the base times the length of the height. That you can convince yourself of by imagining the parallelogram. Then imagine slicing a right triangle off one of its sides. Move that around to the other side. Put it together right and you have a rectangle. Already know the area of a rectangle. The triangle, then, you can get by imagining two triangles of the same size and shape. Rotate one of the triangles 180 degrees. Slide it over, so the two triangles touch. Do this right and you have a parallelogram and so you know the area. The triangle’s half the area of that parallelogram.

Paige: 'OK, let me see if I've got these area formulas memorized. For a triangle, it's 1/2 bh. For a trapezoid, it's 1/2 (a + b)h. And for a circle, it's pi r^2.' Jason: 'Yes! Yes! Yes! You got them all right! You're going to ace this test! I'm going to make $10!' Paige: 'I always get confused --- does h stand for my height or the triangle's? ... Just kidding.' Jason: 'WILL YOU QUIT TOYING WITH ME?!'
Bill Amend’s FoxTrot Classics for the 24th of May, 2018. It originally ran the 30th of May, 1996.

The circle, I don’t know. I think just remember that if someone says “pi” they’re almost certainly going to follow it with either “r squared” or “day”. One of those suggests an area; the other doesn’t. Best I can do.

Jeri: 'Arrrrhh'. Teena: 'Sup?' Jeri: 'I'm having issues with this math issue. It's the way they phrase these word things. They're like trick questions. I can never figure them out.' Teena: 'Here, let me see what you're having trouble with. ... 'Sarah sits next to Stephen, who is very good at algebra. This causes Sarah, who has issues with BOTH Steven AND algebra, to feel bad But if Sarah moves next to someone else, Steven will feel bad. How do you protect Sarah's and Steven's self-esteem?' Jeri: 'I'm not that comfortable with my answer.' Teena: 'Which is?' Jeri: 'Eleven.' Teena: 'It must be very interesting in your school.'
Allison Barrows’s PreTeena rerun for the 27th of May, 2018. It originally ran the 15th of February, 2004.

Allison Barrows’s PreTeena rerun for the 27th discusses self-esteem as though it were a good thing that children ought to have. This is part of the strip’s work to help build up the Old Person Complaining membership that every comics section community group relies on. But. There is mathematics in Jeri’s homework. Not mathematics in the sense of something particular to calculate. There’s just nothing to do there. But it is mathematics, and useful mathematics, to work out the logic of how to satisfy multiple requirements. Or, if it’s impossible to satisfy them all at once, then to come as near satisfying them as possible. These kinds of problems are considered optimization or logistics problems. Most interesting real-world examples are impossibly hard, or at least become impossibly hard before you realize it. You can make a career out of doing as best as possible in the circumstances.

Charles Schulz’s Peanuts rerun for the 27th features an extended discussion by Lucy about the nature of … well, she explicitly talks about “nothing”. Is she talking about zero? Probably; you have to get fairly into mathematics or philosophy to start worrying about the difference between the number zero and the idea of nothing. In Algebra, mathematicians learn to work with systems of things that work like numbers enough that you can add and subtract and multiply them together, without committing to the idea that they’re working with numbers. They will have something that works like zero, though, a “nothing” that can be added to or subtracted from anything without changing it. And for which multiplication turns something into that “nothing”.

Charlie Brown, at Lucy's Psychiatric Help 5 cents booth: 'I always wanted to go up to that little red-haired girl and talk to her, but I just couldn't. I couldn't start a conversation because I was such a nothing and she was something. If she had wanted to talk to me, it would have been easy because someone who is really something can just go right up to someone who is nothing, and just talk.' Lucy: 'I think your problem is mathematical, Charlie Brown.' Charlie Brown: 'Mathematical?' Lucy: 'If you add nothing and something, what do you get?' Charlie Brown: 'Something, I guess.' Lucy: 'Right ... now, if you subtract nothing from something, what do you get?' Charlie Brown: 'Something.' Lucy: 'Very good ... now, if you multiply something by nothing, what do you get?' Charlie Brown: 'Nothing.' Lucy: 'Five cents, please.' Charlie Brown: 'When you're a nothing, you have a hard time understanding anything!'
Charles Schulz’s Peanuts rerun for the 27th of May, 2018. It originally ran the 30th of May, 1971. This strip originally ran during a time when, in-continuity, the Little Red-Haired Girl had moved away and Charlie Brown was coping with having never spoken to her. At some point she moved back, possibly because Schulz felt he had done everything he could with that or possibly because he forgot she had moved away.

I’m with Charlie Brown in not understanding where Lucy was going with all this, though. Maybe she lost the thread herself.

Mark Anderson’sAndertoons for the 28th is Mark Anderson’sAndertoons for the week. Wavehead’s worried about the verbs of both squaring and rounding numbers. Will say it’s a pair of words with contrary alternate meanings that I hadn’t noticed before. I have always taken the use of “square” to reflect, well, if you had a square with sides of size 4, then you’d have a square with area of size 16. The link seems obvious and logical. So on reflection that’s probably not at all where English gets it from. I mean, not to brag or anything but I’ve been speaking English all my life. If I’ve learned anything about it, it’s that the origin is probably something daft like “while Tisquantum [Squanto] was in England he impressed locals with his ability to do arithmetic and his trick of multiplying one number by itself got nicknamed squantuming, which got shortened to squaning to better fit the meter in a music-hall song about him, and a textbook writer in 1704 thought that was a mistake and `corrected’ it to squaring and everyone copied that”. I’m not even going to venture a guess about the etymology of “rounding”.

On the board: 2^2 = 4, 3^2 = 9, 4^2 = 16. Wavehead: 'Wait, we're squaring numbers now? We just figured out how to round them!'
Mark Anderson’sAndertoons for the 28th of May, 2018. But why would the examples be written out before the students were told what the were doing?

Marguerite Dabaie and Tom Hart’s Ali’s House for the 28th sets up a homework-help session over algebra. Can’t say where exactly Maisa is going wrong. Her saying “x equals 30 but the train equals” looks like trouble to me. It’s often good practice to start by writing out what are the things in the problem that seem important. And what symbol one wants each to mean. And what one knows about the relationship between these things. It helps clarify why someone would want to do that instead of something else. This is a new comic strip tag and I don’t think I’ve ever had cause to discuss it before.

Maisa: 'Can you help me with my homework?' Sahib: 'Dad promised me a hamburger.' Maisa: 'You see - x equals 30 but the train equals ... ' Sahib: 'Dad never makes hamburgers ... mutter mutter mutter.' Maisa: 'Look, I really need help with this.' Sahib: 'My brain isn't set on pay attention my brain is set on burger!'
Marguerite Dabaie and Tom Hart’s Ali’s House for the 28th of May, 2018. Relatable.

Hilary Price’s Rhymes With Orange for the 29th is a Rubik’s Cube joke. I’ve counted that as mathematical enough, usually. The different ways that you can rotate parts of the cube form a group. This is something like what I mentioned in the Peanuts discussion. The different rotations you can do can be added to or subtracted from each other, the way numbers can. (Multiplication I’m wary about.)

Rubik's Headquarters. It's a three-by-three wireframe with tiny offices inside. Person looking in: 'My corner office ... gone! I hate when they do a management shuffle.' [ Title panel, Other person: 'Rumor has it they're going to an open-concept model.' ]
Hilary Price’s Rhymes With Orange for the 29th of May, 2018. Pity whoever gets the center office, bottom layer.

And now here’s the strip that is unsuitable for reading at work, owing to the appearance of an undressed woman.

Continue reading “Reading the Comics, May 29, 2018: Finding Reruns Edition”

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.

Reading the Comics, February 7, 2018: Not Taking Algebra Too Seriously Edition


There were nearly a dozen mathematically-themed comic strips among what I’d read, and they almost but not quite split mid-week. Better, they include one of my favorite ever mathematics strips from Charles Schulz’s Peanuts.

Jimmy Halto’s Little Iodine for the 4th of December, 1956 was rerun the 2nd of February. Little Iodine seeks out help with what seems to be story problems. The rate problem — “if it takes one man two hours to plow seven acros, how long will it take five men and a horse to … ” — is a kind I remember being particularly baffling. I think it’s the presence of three numbers at once. It seems easy to go from, say, “if you go two miles in ten minutes, how long will it take to go six miles?” to an answer. To go from “if one person working two hours plows seven acres then how long will five men take to clear fourteen acres” to an answer seems like a different kind of problem altogether. It’s a kind of problem for which it’s even wiser than usual to carefully list everything you need.

Iodone, going into a department store. 'Boy, we got tough homework for tomorrow.' At Information: 'If it takes one man two hours to plow seven acres, how long will it take five men and a horse to --- etc' Clerk: 'Wha? Uh ... let me get a pencil. Will you repeat that, please? ... Cipher ... two o carry ... mmm ... times x ... minus ... mmm ... now let me think ... ' NEXT DAY; Teacher: 'Sharkey Shannon, 92, very good, Sharkey. Shalimar Shultz, 94, excellent, Shalimar. Iodine Tremblechin ... zero ... every problem wrong! Iodine ... I just can't understand it ... not one single answer correct!' Iodine, at the Complaint Department: 'Somebody in this store has to write a hundred times 'I will henceforth study harder'!
Jimmy Halto’s Little Iodine for the 2nd of December, 1956 and rerun the 4th of February, 2018. It’s the rare Little Iodine where she doesn’t get her father fired!

Kieran Meehan’s Pros and Cons for the 5th uses a bit of arithmetic. It looks as if it’s meant to be a reminder about following the conclusions of one’s deductive logic. It’s more common to use 1 + 1 equalling 2, or 2 + 2 equalling 4. Maybe 2 times 2 being 4. But then it takes a little turn into numerology, trying to read more meaning into numbers than is wise. (I understand why people should use numerological reasoning, especially given how much mathematicians like to talk up mathematics as descriptions of reality and how older numeral systems used letters to represent words. And that before you consider how many numbers have connotations.)

Judge: 'Members of the jury, before retiring to consider your verdict, I shall give you my summing-up. 3 + 3 = 6. There are six letters in the word 'guilty'. Coincidence? I don't believe in coincidences.'
Kieran Meehan’s Pros and Cons for the 5th of February, 2018. I grant the art is a bit less sophisticated than in Little Iodine. But the choice of two features to run outside the panels and into the white gutters is an interesting one and I’m not sure what Meehan is going for in choosing one word balloon and the judge’s hand to run into the space like that.

Charles Schulz’s Peanuts for the 5th of February reruns the strip from the 8th of February, 1971. And it is some of the best advice about finding the values of x and y, and about approaching algebra, that I have ever encountered.

Trixie: 'Look at all the birds!! I wonder how many there are! Sic, nine, five, 'leven, eight, fwee, two! Only two! It sure looked like there were more!'
Mort Walker and Dik Browne’s Hi and Lois for the 10th of August, 1960 was rerun the 6th of February, 2018. And I do like Trixie’s look of bafflement in the last panel there; it’s more expressive than seems usual for the comic even in its 1960s design.

Mort Walker and Dik Browne’s Hi and Lois for the 10th of August, 1960 was rerun the 6th of February. It’s a counting joke. Babies do have some number sense. At least babies as old as Trixie do, I believe, in that they’re able to detect that something weird is going on when they’re shown, eg, two balls put into a box and four balls coming out. (Also it turns out that stage magicians get called in to help psychologists study just how infants and toddlers understand the world, which is neat.)

John Zakour and Scott Roberts’s Maria’s Day for the 7th is Ms Payne’s disappointed attempt at motivating mathematics. I imagine she’d try going on if it weren’t a comic strip limited to two panels.

Reading the Comics, January 9, 2018: Be Squared Edition


It wasn’t just another busy week from Comic Strip Master Command. And a week busy enough for me to split the mathematics comics into two essays. It was one where I recognized one of the panels as one I’d featured before. Multiple times. Some of the comics I feature are in perpetual reruns and don’t have your classic, deep, Peanuts-style decades of archives to draw from. I don’t usually go checking my archives to see if I’ve mentioned a comic before, not unless something about it stands out. So for me to notice I’ve seen this strip repeatedly can mean only one thing: there was something a little bit annoying about it. Recognize it yet? You will.

Hy Eisman’s Popeye for the 7th of January, 2018 is an odd place for mathematics to come in. J Wellington Wimpy regales Popeye with all the intellectual topics he tried to impress his first love with, and “Euclidean postulates in the original Greek” made the cut. And, fair enough. Euclid’s books are that rare thing that’s of important mathematics (or scientific) merit and that a lay person can just pick up and read, even for pleasure. These days we’re more likely to see a division between mathematics writing that’s accessible but unimportant (you know, like, me) or that’s important but takes years of training to understand. Doing it in the original Greek is some arrogant showing-off, though. Can’t blame Carolyn for bailing on someone pulling that stunt.

Popeye: 'Did ya ever think of gittin' hitched?' Wimpy: 'Many times! I didn't plan to be a bachelor. In fact, my first love was Carolyn. While we dined on burgers at Roughhouse's she listened to my discourse on Schopenhauer, followed by my chat that included both Kafka and Camus. Then, as I walked her home, I recited Euclidean postulates in the original Greek!' Popeye: 'Y'wuz really on a roll!' Wimpy: 'When we got to her door she said, 'Wimpy, it's been a perfect evening. Please don't spoil it by EVER asking me out again!''.
Hy Eisman’s Popeye for the 7th of January, 2018. Why does Wimpy’s shirt have a belly button?

Mark O’Hare’s Citizen Dog rerun for the 7th continues last essay’s storyline about Fergus taking Maggie’s place at school. He’s having trouble understanding the story within a story problem. I sympathize.

John Hambrock’s The Brilliant Mind of Edison Lee for the 8th is set in mathematics class. And Edison tries to use a pile of mathematically-tinged words to explain why it’s okay to read a Star Wars book instead of paying attention. Or at least to provide a response the teacher won’t answer. Maybe we can make something out of this by allowing the monetary value of something to be related to its relevance. But if we allow that then Edison’s messed up. I don’t know what quantity is measured by multiplying “every Star Wars book ever written” by “all the movies and merchandise”. But dividing that by the value of the franchise gets … some modest number in peculiar units divided by a large number of dollars. The number value is going to be small. And the dimensions are obviously crazy. Edison needs to pay better attention to the mathematics.

Teacher: 'Mister Lee, what are you reading?' Edison Lee: 'The Legends of Luke Skywalker.' Teacher: 'Ah, and how would that be relevant to this math class?' Edison: 'If you take every Star Wars book ever written, multiply them by all the movies and merchandise, and divide that by the net worth of the franchise, you have a small fortune of relevance.' (Teacher looks away.) Edison thinks: 'My mouth needs a seven-second broadcast delay.'
John Hambrock’s The Brilliant Mind of Edison Lee for the 8th of January, 2018. No, I haven’t got any idea how the third panel leads to the fourth. I mean, I know what should lead from there to there — a moment of Edison realizing he’s said something so impolitic he can’t carry on — but that moment isn’t there. The teacher seems to just shrug the whole nonsense off. Something went wrong in the composing of the joke.

Johnny Hart’s B.C. for the 14th of July, 1960 shows off the famous equation of the 20th century. All part of the comic’s anachronism-comedy chic. The strip reran the 9th of January. “E = mc2” is, correctly, associated with Albert Einstein and some of his important publications of 1905. But the expression does have some curious precursors, people who had worked out the relationship (or something close to it) before Einstein and who didn’t quite know what they had. A short piece from Scientific American a couple years back describes pre-Einstein expressions of the equation from Oliver Heaviside, Henri Poincaré, and Fritz Hasenöhrl. I’m not surprised Poincaré had something close to this; it seems like he spent twenty years almost discovering Relativity. That’s all right; he did enough in dynamical systems that mathematicians aren’t going to forget him.

Tim Lachowski’s Get A Life for the 9th is at least the fourth time I’ve seen this panel since I started doing Reading the Comics posts regularly. (Previous times: the 5th of November, 2012 and the 10th of March, 2015 and the 14th of July, 2016.) I’m like this close to concluding the strip’s in perpetual rerun and I can drop it from my daily reading.

Jason Chatfield’s Ginger Meggs for the 9th draws my eye just because the blackboard lists “Prime Numbers”. Fair enough place setting, although what’s listed are 1, 3, 5, and 7. These days mathematicians don’t tend to list 1 as a prime number; it’s inconvenient. (A lot of proofs depend on their being exactly one way to factorize a number. But you can always multiply a number by ‘1’ a couple more times without changing its value. So ‘6’ is 3 times 2, but it’s also 3 times 2 times 1, or 3 times 2 times 1 times 1, or 3 times 2 times 1145,388,434,247. You can write around that, but it’s easier to define ‘1’ as not a prime.) But it could be defended. I can’t think any reason to leave ‘2’ off a list of prime numbers, though. I think Chatfield conflated odd and prime numbers. If he’d had a bit more blackboard space we could’ve seen whether the next item was 9 or 11 and that would prove the matter.

Paul Trap’s Thatababy for the 9th uses arithmetic — square roots — as the kind of thing to test whether a computer’s working. Everyone has their little tests like this. My love’s father likes to test whether the computer knows of the band Walk The Moon or of Christine Korsgaard (a prominent philosopher in my love’s specialty). I’ve got a couple words I like to check dictionaries for. Of course the test is only any good if you know what the answer should be, and what’s the actual square root of 3,278? Goodness knows. It’s got to be between 50 (50 squared is 25 hundred) and 60 (60 squared is 36 hundred). Since 3,278 is so much closer 3,600 than 2,500 its square root should be closer to 60 than to 50. So 57-point-something is plausible. Unfortunately square roots don’t lend themselves to the same sorts of tricks from reading the last digit that cube roots do. And 3,278 isn’t a perfect square anyway. Alexa is right on this one. Also about the specific gravity of cobalt, at least if Wikipedia is right and not conspiring with the artificial intelligences on this one. Catch you in 2021.

Charles Schulz’s Peanuts for the 8th of October, 1953, is about practical uses of mathematics. It got rerun on the 9th of January.

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


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

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

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

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

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

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

\frac{1}{n}\left( (n - 1) \cdot x + \frac{A}{x^{n - 1}} \right)

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

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

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

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

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

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

Cherry Trail: 'Good morning, honey! Where's Dad?' Mark Trail: 'He's out on the porch reading the paper!' Cherry: 'Rusty sure is excited about our upcoming trip to Mexico!' Mark: 'Did you get everything worked out with the school?' Cherry: 'Rusty will need to do some math assignments, but he'll get credit for his other subjects since it's an educational trip!'
James Allen’s Mark Trail for the 3rd of January, 2018. James Allen has changed many things about the comic strip since Jack Elrod’s retirement, as I have observed over on the other blog. There are less ruthlessly linear stories. There’s no more odd word balloon placement implying that giant squirrels are talking about the poachers. Mark Trail sometimes has internal thoughts. I’m glad that he does still choose to over-emphasize declarations like “[Your Dad]’s out on the porch reading the paper!” There are some traditions.

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

Reading the Comics, October 2017: Mathematics Anxiety Edition


Comic Strip Master Command hasn’t had many comics exactly on mathematical points the past week. I’ll make do. There are some that are close enough for me, since I like the comics already. And enough of them circle around people being nervous about doing mathematics that I have a title for this edition.

Tony Cochrane’s Agnes for the 24th talks about math anxiety. It’s not a comic strip that will do anything to resolve anyone’s mathematics anxiety. But it’s funny about its business. Agnes usually is; it’s one of the less-appreciated deeply-bizarre comics out there.

John Atkinson’s Wrong Hands for the 24th might be the anthropomorphic numerals joke for this week. Or it might be the anthropomorphic letters joke. Or something else entirely.

Charles Schulz’s Peanuts for the 24th reruns the comic from the 2nd of November, 1970. It has Sally discovering that multiplication is much easier than she imagined. As it is, she’s not in good shape. But if you accept ‘tooty-two’ as another name for ‘four’ and ‘threety-three’ as another name for ‘nine’, why not? And she might do all right in group theory. In that you can select a bunch of things, called ‘elements’, and describe their multiplication to fit anything you like, provided there’s consistency. There could be a four-forty-four if that seems to answer some question.

Patron of the Halloween Costume Advice booth: 'I want to be a zombie!' Regular character whose name I can't remember and can't find: 'That's a tough one ... we have to find a way to get you into character. Here [ handing a textbook over ] --- sit through one of Miss Barnes's math classes.'
Steve Kelley and Jeff Parker’s Dustin for the 25th of October, 2017. The kid’s premise this week is about advice for maximizing trick-or-treating hauls. So it circles around sabermetrics and the measurement of every possible metric relevant to a situation. It’s a bit baffling to me, since I just do not remember the quality of a costume relating to how much candy I’d gotten. Nor to what I give out, at least once you get past “high school kid not even bothering to dress up”. And even they’ll get a couple pieces although, yeah, if they did anything they’d get the full-size peanut butter cups. (We’re trying to build a reputation here.) What I’m saying is, I don’t see how the amount of candy depends on more than “have a costume” and “spend more time out there”. I mean, are people really withholding the fruit-flavored Tootsie Rolls because some eight-year-old doesn’t have an exciting enough costume? Really?

Steve Kelley and Jeff Parker’s Dustin for the 25th might be tied in to mathematics anxiety. At least it expresses how the thought of mathematics will cause some people to shut down entirely. Shame for them, but I can’t deny it’s so.

Young magician touching the wand to the whiteboard to show 15 divided by 3 is 5. His instructor: 'No relying on the wand --- I want to see how you arrived at the right answer.' (The title panel calls the strip The Tutor, with the tutor saying 'Someday when you're wizened you'll thank me.')
Hilary Price’s Rhymes with Orange for the 26th of October, 2017. The signature also credits Rina Piccolo, late of Six Chix and Tina’s Groove. The latter strip ended in July 2017, and she left the former last year. Maybe she’s picking up some hours part-timing on Rhymes With Orange; her signature’s been on many strips recently. Wikipedia doesn’t have anything relevant to say, and the credit on the web site doesn’t reflect Piccolo’s work, if she is a regular coauthor now.

Hilary Price’s Rhymes with Orange for the 26th is a calculator joke, made explicitly magical. I’m amused but also wonder if those are small wizards or large mushrooms. And it brings up again the question: why do mathematics teachers care about seeing how you got the answer? Who cares, as long as the answer is right? And my answer there is that yeah, sometimes all we care about is the answer. But more often we care about why someone knows the answer is this instead of that. The argument about what makes this answer right — or other answers wrong — should make it possible to tell why. And it often will help inform other problems. Being able to use the work done for one problem to solve others, or better, a whole family of problems, is fantastic. It’s the sort of thing mathematicians naturally try to do.

Jason Poland’s Robbie and Bobby for the 26th is an anthropomorphic geometry joke. And it’s a shape joke I don’t remember seeing, at least not under my Reading the Comics line of jokes. (Maybe I’ve just forgotten). Also, trapezoids: my most popular post of all time ever, even though it’s only got a couple months’ lead on the other perennial favorite, about how many grooves are on a record’s side.

Jeremy pours symbols from his mathematics notebook into a funnel in his head. They pour out his ears. He says 'My study habits are ineffective' to Pierce, who asks, 'Have you tried earplugs?'
Jerry Scott and Jim Borgman’s Zits for the 27th of October, 2017. I understand people who don’t find Zits a particularly strong comic. (My experience is it’s more loved by my parent’s cohort than by mine.) But I will say when Scott and Borgman go for visual metaphor the strip is easily ten times better. I think the cartoonists have some editorial-cartoon experience and they’ll sometimes put it to good use.

Jerry Scott and Jim Borgman’s Zits for the 27th uses mathematics as the emblem of complicated stuff in need of study. It’s a good visual. I have to say Jeremy’s material seems unorganized to start with, though.

Reading the Comics, May 9, 2015: Trapezoid Edition


And now I get caught up again, if briefly, to the mathematically-themed comic strips I can find. I’ve dubbed this one the trapezoid edition because one happens to mention the post that will outlive me.

Todd Clark’s Lola (May 4) is a straightforward joke. Monty’s given his chance of passing mathematics and doesn’t understand the prospect is grim.

'What number am I thinking of?' '9,618,210.' 'Right!' 'He always thinks of the same number.'
Joe Martin’s Willy and Ethel for the 4th of May, 2015. The link will likely expire in early June.

Joe Martin’s Willy and Ethel (May 4) shows an astounding feat of mind-reading, or of luck. How amazing it is to draw a number at random from a range depends on many things. It’s less impressive to pick the right number if there are only three possible answers than it is to pick the right number out of ten million possibilities. When we ask someone to pick a number we usually mean a range of the counting numbers. My experience suggests it’s “one to ten” unless some other range is specified. But the other thing affecting how amazing it is is the distribution. There might be ten million possible responses, but if only a few of them are likely then the feat is much less impressive.

The distribution of a random number is the interesting thing about it. The number has some value, yes, and we may not know what it is, but we know how likely it is to be any of the possible values. And good mathematics can be done knowing the distribution of a value of something. The whole field of statistical mechanics is an example of that. James Clerk Maxwell, famous for the equations which describe electromagnetism, used such random variables to explain how the rings of Saturn could exist. It isn’t easy to start solving problems with distributions instead of particular values — I’m not sure I’ve seen a good introduction, and I’d be glad to pass one on if someone can suggest it — but the power it offers is amazing.

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