Reading the Comics, August 31, 2019: Martin V Edition


And so the Reading the Comics posts have returned to Sunday after a month in exile to Tuesdays. I’m curious whether Sunday is actually the best day to post my signature series of essays, since everybody is usually doing stuff on the weekends. Tuesdays more people are at work and looking for other things to think about. But at least for the duration of the A to Z series there’s not a good time to schedule them besides Sundays. So Sundays it is and I’ll possibly think things over again in December, if all goes well.

Ralph Hagen’s The Barn for the 27th poses a question that’s ridiculous when you look at it. Why should being twenty times as old as your newborn (sic) when you’re twenty years old imply you’d be twenty times as old as the newborn when you’re sixty? Age increases linearly. The ratios between ages, though, those decrease, in a ratio asymptotically approaching 1. So as far as that goes, this strip isn’t much of anything.

Rory, sheep: 'How come if you're 20 when our child is born, you're 20 times older when your child is born, but by the time you're 60, you're only 1.5 times older?' (Rory leaves.) Stan, cow: 'Did you order a math puzzle?' Karl, frog: 'Nope. Cheese pizza, extra flies.'
Ralph Hagen’s The Barn for the 27th of August, 2019. I was wondering if this might be a new tag. It’s not. Other essays featuring The Barn are at this link.

But I do like how it captures the way a mathematics puzzle can come from nowhere. Often interesting ones seem to generate themselves. You notice a pattern and wonder whether it reaches some interesting point. If you convince yourself it does, you wonder when it does. If it does not, you wonder why it can’t. This is the fun sort of mathematics, and you create it by looking at the two separate tile patterns in the kitchen or, as here, thinking about the ages of parent and child. Anything that catches the imagination of a bored mind. It’s fun being there.

Rory (the sheep) makes a common enough slip. Saying a twenty-year-old with a newborn is twenty times as old as the newborn is, implicitly, saying the newborn is one year old. This kind of error is so common it’s got a folksy name, the “fencepost error”. It has a more respectable name, for its LinkedIn profile, the “off-by-one error”. But you see the problem. Say that your birthday is the 1st of September. How many times were you alive on the 1st of September by the time you’re ten years old? Eleven times, the first one being the one you were born on, with one more counted up each year you’d lived. This was probably more clear before I explained it.

Teacher: 'You deserve an 'A' for your creative writing, Jughaid. But this is 'rithmetic!!' On the blackboard Jughead's written out 2 + 4 = 10, 6 + 5 = 7, 8 + 3 = 15, 7 + 1 = 5, 9 + 4 = 23.
John Rose’s Barney Google and Snuffy Smith for the 27th of August, 2019. This one I kept finding when I was looking for The Barn. Essays based on something raised by Barney Google should be at this link.

John Rose’s Barney Google and Snuffy Smith for the 27th has Mis Prunelly complimenting Jughaid’s creativity, but not wanting it in arithmetic. There is creativity in mathematics. And there is great value in calculating something in an original way. There’s value in calculating things wrong, too, if it’s an approximate calculation. Knowing whether your answer is nearer 10 or 20 is of some value, and it might be all that you in fact want. That’s being wrong in a productive way, though.

Harry Bliss and Steve Martin’s Bliss for the 27th uses a string of mathematical symbols as emblem of genius. Most of the symbols look just near enough meaningful that I wonder if Bliss and Martin got a mathematician friend of theirs to give them some scraps. Why I say mathematician rather than, say, physicist is because some of the lines look more mathematician than physicist.

Illustrated book cover: 'They Called Me Dumbo: A Memoir of Redemption'. Dumbo's shown in front of Princeton, and writing a column of arithmetic using a pencil held by his trunk.
Harry Bliss and Steve Martin’s Bliss for the 27th of August, 2019. Essays that do feature Bliss should be gathered at this link.

The most distinctive one, to me, is right above Dumbo’s pencil and trunk there: g^{-1}\cdot g = e . This is the kind of equation you’ll see all the time in group theory. It’s an important field of mathematics, the one studying sets that work like arithmetic does. This starts with groups, which have a set of things and a binary operation between those things. Think of it as either addition or multiplication. You notice that g^{-1} \cdot g = e already looks like multiplication. ‘g’ and ‘h’ serve, for group theory, the roles that ‘x’ and ‘y’ do in (high school) algebra. ‘x’ and ‘y’ mean some number, whose value we might or might not care about. Similarly, ‘g’ and ‘h’ are some elements, things in the set for our group. We might or might not care which ones they are. e means the identity element, the thing which won’t change the value of the other partner in an operation. The thing that works like zero for addition, or like one for multiplication. And g^{-1} means the inverse of g : the thing which, added (or multiplied) to g gives us the identity element. So if we were talking addition and g were 5, then g^{-1} would be -5. This might not sound like very much, but we can make it complicated.

Also distinctive to me: that first line. I’m not perfectly sure I’m transcribing this right. But it looks a good deal to me like the binomial distribution. This is the probability of seeing something happen k times, if you give it n chances to happen, and every chance has the same probability p of it happening. The formula isn’t quite right. It’s missing a power on the (1 – p) term at the end. But it’s wrong in ways that make sense for the need to draw something legible.

Just under Dumbo’s pencil, too, is a line that I had to look up how to render in WordPress’s LaTeX. It’s the one about \left| X \cup  Y \right| = \left| X \right| + \left| Y \right| . The union symbol, the U there, speaks of set theory. It means to form a new set, one that has all the elements in the set called X or the set called Y or both. The straight vertical lines flanking these set names or descriptions are how we describe taking the norm, finding the size, of a set. This is ordinarily how many things are inside the set. If the sets X and Y have no elements in common, then the size of the union of X and Y will be the size of the set X plus the size of the set Y.

There’s other lines that come near making sense. The line about f : x \rightarrow xnW has the form of the “mapping” way to define a function. I just don’t understand what the rule here means. The final line, = e \frac{-t^2}{2} ! , first … well, this sort of e-raised-to-the-minus-something-squared form turns up all the time. But second, to end a bit of work with an exclamation point really captures the surprise and joy of having reached a goal. Mathematicians take delight in their work, like you’d expect.

A 'solved' Rubik's cube sits on the left. On the right a scrambled cube, with one row of the top face a quarter-turn out of place, says, 'Some days are better than others.'
Maria Scrivan’s Half Full for the 29th of August, 2019. Other appearances by Half Full should be behind this link.

Maria Scrivan’s Half Full for the 29th is a Rubik’s Cube joke. A variation of it ran back in June 2018. I hate that this time I noticed that on the right, the cubelet — with white on top, red on the lower left, and green on the lower right — is inconsistent with the ordered cube. The corresponding cubelet there has blue on top, red on the lower left, and green on the lower right. Well, maybe the cube on the right had its color stickers applied differently. This is a little thing. But it’s close to a problem that turns up all the time in representing geometry. It’s easy to say you have, say, axes going in the x, y, and z directions. But which direction is x? Which is y? Which is z? You can lay all three out so every pair makes a right angle. Whatever way you lay them out will turn out to be, up to a rotation, one of two patterns. Let’s say the x axis points east, and the y axis points north. Then the z axis can point up. Or it can point down. You can pick which one makes sense for your problem. The two choices are mirror images of the other. You get primed to notice this when you do mathematical physics. The Rubik’s Cube on the left is just this kind of representation, with (let’s say) the red face pointing in the x direction, the green face pointing in the y direction, and the blue pointing in the z direction. Which is a lot of thought to put into what was an arbitrary choice, as I’m sure the cartoonist (or whoever did the coloring) just wanted a cube that looked attractive.


There were a surprising number of comics that mentioned mathematics, but not enough for a paragraph. I’ll feature them in another essay run here sometime this week. Also starting this week: the Fall 2019 Mathematics A To Z. It’s still not too late to suggest topics for the letters C through H!

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Reading the Comics, August 9, 2019: Venn Diagrams Edition


Thanks for sticking around as I finally got to the past week’s comic strips. There were just enough for me to divide them into two chunks and not feel like I’m cheating anyone of my sparkling prose.

Sandra Bell-Lundy’s Between Friends for the 4th is another entry in this strip’s string of not-quite-Venn-Diagram jokes. As will happen, the point of the diagram seems clear enough even if it doesn’t quite parse. And it isn’t a proper Venn diagram, of course; a Venn diagram for five propositions has to have 31 regions, representing all the possible ways five things can combine or be excluded. They can be beautiful to look at, but start losing their value as ways to organize thought. This is again a Euclid diagram, which doesn’t need to show every possible overlap.

Five pairwise intersecting circles labelled 'Job Requirements', 'Parent Assistance', 'Supportive Mother', 'Husband Attention', and 'Household Upkeep'. Susan is flopped in her chair, thinking, 'Finally! NOW I can put myself first.'
Sandra Bell-Lundy’s Between Friends for the 4th of August, 2019. Essays in which I discuss something brought up by Between Friends should be at this link.

Michael Jantze’s The Norm 4.0 for the 5th is the other Venn Diagram joke for the week. Again properly the first one, showing the complete lack of overlap between two positions, is an Euler rather than a Venn diagram. The second, the “Amity Venn diagram on planet X”, is a Venn diagram and showing the intersection of blue and yellow regions as green is a nice way to show that. (I’m not fond of the gender stereotyping here, nor of the conflation of gender and chromosomes. But the comic strip does have to rely on shorthands or there’s just not going to be the space to compose a joke.)

Label: Venn Diagrams of Amity. The Amity Diagram of Planet Y. Two separate bubbles, Bro 1 and Bro 2, each arguing the designated hitter rule; Norm points out, no overlap. The Amity Diagram of Planet X. Two bubbles nearly completely overlapped, their colors blending together; one says 'This is a wonderful pinot grigio' and the other 'This is an amazing pinot grigio', and Norm thinks he needs a bigger marker to color this in.
Michael Jantze’s The Norm 4.0 for the 5th of August, 2019. Essays mentioning The Norm, either the current (“4.0”) run or older strips being rerun, should be at this link. There aren’t many, which is a shame. I like the comic.

Harry Bliss’s Bliss for the 6th name-checks tetrahedrons. These are the shapes the rest of us would probably call pyramids or perhaps d4. It’s a bit silly to suppose a hairball should be a tetrahedron. But natural processes will form particular shapes. The obvious example is the hexagonal prisms of honeycombs, which come about for reasons … I’m not sure biologists are completely agreed on. Hexagons do seem to be efficient ways to encompass a lot of volume with a minimum of material, at least. But even the classic hairball looks like that for reasons, related to how it’s created and how it’s expelled from the cat. They just don’t usually have corners.

Man, looking over a cat that's coughing up small pyramids: 'Ross, get in here! Mittens is coughing up hair-tetrahedrons again!'
Harry Bliss’s Bliss for the 6th of August, 2019. No credit to Steve Martin this time. Essays with a mention of Bliss should be gathered here.

Niklas Eriksson’s Carpe Diem for the 9th has you common blackboard full of symbols to represent mathematical work. It also evokes a well-worn joke that defines a mathematician as a mechanism for turning coffee into theorems. The explosion of creativity though is true to mathematicians, though. When inspiration is flowing the notes will get abundant and start going in many different wild directions. The symbols in the comic strip don’t mean anything. But that’s not inauthentic. The notes written during an inspired burst will be nonsensical. The great idea needs to be preserved. It can be cleaned up and, one hopes, made presentable later.

Man pointing to a line of equations on the blackboard, and where it goes from a single line to several lines of weaving expressions, with many arrows from one to another, and a lot of exclamation points: 'And here's the historic moment with Smith brought me a large cup of coffee.'
Niklas Eriksson’s Carpe Diem for the 9th of August, 2019. The essays discussing something raised by Carpe Diem should be at this link.

This and other Reading the Comics posts are at this link. I should have a fresh one on Thursday, wrapping up the past week.

Reading the Comics, May 8, 2019: Strips With Art I Like Edition


Of course I like all the comics. … Well, that’s not literally true; but I have at least some affection for nearly all of the syndicated comics. This essay I bring up some strips, partly, because I just like them. This is my content hole. If you want a blog not filled with comic strips, go start your own and don’t put these things on it.

Mark Anderson’s Andertoons for the 5th is the Mark Anderson’s Andertoons for the week. Also a bit of a comment on the ability of collective action to change things. Wavehead is … well, he’s just wrong about making the number four plus the number four equal to the number seven. Not based on the numbers we mean by the words “four” and “seven”, and based on the operation we mean by “plus” and the relationship we mean by “equals”. The meaning of those things is set by, ultimately, axioms and deductive reasoning and the laws of deductive reasoning and there’s no changing the results.

Wavehead, to another student: 'If I say 4 + 4 = 7 it's wrong. If you say 4 + 4 = 7 it's wrong. But if the entire first grade says 4 + 4 = 7, well, now she has to take us seriously.
Mark Anderson’s Andertoons for the 5th of May, 2019. Essays mentioning Andertoons are at this link and also at nearly every Reading the Comics post, it feels like.

But. The thing we’re referring to when we say “seven”? Or when we write the symbol “7”? That is convention. That is a thing we’ve agreed on as a reference for this concept. And that we can change, if we decide we want to. We’ve done this. Look at a thousand-year-old manuscript and the symbol that looks like ‘4’ may represent the number we call five. And the names of numbers are just common words. They’re subject to change the way every other common word is. Which is, admittedly, not very subject. It would be almost as much bother to change the word ‘four’ as it would be to change the word ‘mom’. But that’s not impossible. Just difficult.

Viivi: 'Oh, sorry! Oh, pain!' Wagner: 'Stop worrying. 85% of fears never come through.' Viivi: 'That means 15% do! It's worse than I thought.'
Juba’s Viivi and Wagner for the 5th of May, 2019. I don’t often have chances to talk about Viivi and Wagner but when I do, it’s here.

Juba’s Viivi and Wagner for the 5th is a bit of a percentage joke. The characters also come to conclude that a thing either happens or it does not; there’s no indefinite states. This principle, the “excluded middle”, is often relied upon for deductive logic, and fairly so. It gets less clear that this can be depended on for predictions of the future, or fears for the future. And real-world things come in degrees that a mathematical concept might not. Like, your fear of the home catching fire comes true if the building burns down. But it’s also come true if a quickly-extinguished frying pan fire leaves the wall scorched, embarrassing but harmless. Anyway, relaxing someone else’s anxiety takes more than a quick declaration of statistics. Show sympathy.

Dogs in school. The dog teacher is pointing to '1 + 1' on the blackboard. A dog student whispers to the other, 'Sometimes I feel so stupid.'
Harry Bliss and Steve Martin’s Bliss for the 6th of May, 2019. Yes, by the way, it’s the Steve Martin you know and love from Looney Tunes: Back In Action and from the 1996 Sergeant Bilko movie. Anyway I haven’t had chance to write about this strip before but this and future appearances of Bliss should be here.

Harry Bliss and Steve Martin’s Bliss for the 6th is a cute little classroom strip, with arithmetic appearing as the sort of topic that students feel overwhelmed and baffled by. It could be anything, but mathematics uses the illustration space efficiently. The strip may properly be too marginal to include, but I like Bliss’s art style and want more people to see it.

Spud: 'It's official, Wallace. My socks are *too* tight. And I know it'll take at least three minutes to run home and change. Yet I can see the bus is only two stops away.' Wallace: 'I can stall for a good thirty seconds.' Spud: 'My life is a sadistic math problem.'
Will Henry’s Wallace the Brave for the 7th of May, 2019. This is one of the comic strips I’m most excited about, the last several years. Wallace the Brave appears in essays at this link.

Will Henry’s Wallace the Brave for the 7th puts up what Spud calls a sadistic math problem. And, well, it is a story problem happening in their real life. You could probably turn this into an actual exam problem without great difficulty.

Ruthie, holding up a triangle: 'What's this shape?' James: 'A square!' Ruthie: 'I already *told* you what it is, James! You're just acting dumb to hurt my feelings! Stop it! N-n-now (sob) what does this look like to you? (Sniff)?' James: 'A cryangle!'
Rick Detorie’s One Big Happy for the 8th of May, 2019. There are two strings of One Big Happy available for daily reading. Appearances by the current or the several-years-old GoComics prints of One Big Happy should be at this link.

Rick Detorie’s One Big Happy for the 8th is a bit of wordplay built around geometry, as Ruthie plays teacher. She’s a bit dramatic, but she always has been.


I’ll read some more comics for later in this week. That essay, and all similar comic strip talk, should appear at this link. Thank you.