Reading the Comics, June 1, 2019: More Than I Thought Edition


When I collected last week’s mathematically-themed comic strips I thought this set an uninspiring one. That changed sometime while I wrote. That’s the sort of week I like to have.

Richard Thompson’s Richard’s Poor Almanac for the 28th is a repeat; all these strips are. And I’ve featured it here before too. But never before in color, so I’ll take this chance to show it one last time. One of the depicted plants is the “Non-Euclidean Creeper”, which “ignores the geometry of the space-time continuum”. Non-Euclidean is one of those few geometry-related words that people recognize — maybe even only learn — in their adulthood. It has connotations of the bizarre and the weird and the wrong.

And it is a bit weird. While we live in a non-Euclidean space, we never really notice. Euclidean space is the geometry we’re used to from drawing shapes on paper and putting boxes in the corners of basements. And from this we’ve given “non-Euclidean” this sinister reputation. We credit it with defying common sense and even logic itself, although it’s geometry. It can’t defy logic. It can defy intuition. Non-Euclidean geometries have the idea that there are no such things as parallel lines. Or the idea that there are too many parallel lines. And it can get to weird results, particularly if we look at more than three dimensions of space. Those also tax the imagination. It will get a weed a bad reputation.

Your Spring Weeding Guide. Non-Euclidean Creeper. Hard to remove. Ignores the geometry of the spacetime continuum. Common to most yard. (Picture of a woman with garden knife trying to kill a plant that grows around the other side of hte panel.) False Tea Rose. Looks and smells exactly like the lovely tea rose, but it's a weed! Soon your yard will be covered in it! Root it out! Tear it up! Kill it! (Man with rake trying to kill a bush.) Bamzu. COmbines the robust unstoppability of kudzu with the hearty immortality of bamboo. It also attracts zebra mussels. Sell your house and get a condo. (Woman trying to kill a tidal wave of plant with a rake.) Dilatory Bulbvine. Also known as your leftover Christmas lights. Take them down already, it's Easter for crying out loud. (Man saying 'whoopsie' while taking off a strand of lights.)
Richard Thompson’s Richard’s Poor Almanac for the 28th of May, 2019. And, sadly, this probably wraps up the essays I can usefully write about this strip. Essays about Richard’s Poor Almanac should be at this link.

Chen Weng’s Messycow Comics for the 30th is about a child’s delight in learning how to count. I don’t remember ever being so fascinated by counting that it would distract me permanently. I do remember thinking it was amazing that once a pattern was established it kept on, with no reason to ever stop, or even change. My recollection is I thought this somehow unfair to the alphabet, which had a very sudden sharp end.

Girl: 'Mommy, I can count to 100!' Mom: 'Show me!' Girl counts up to 98 99, 100! Mom: 'Wow! Great job! I'm so proud!' (At bedtime.) Mom: 'OK, honey, time to sleep.' Girl: '1, 2, 3, 4.' (Getting the girl off a step.) Mom: 'We are late, let's GO!' Girl: '38, 39, 50? No, 40?' (Dragging the girl out of a room on fire.) Girl '66, 67, 68, 69 ... what's next?' Mom: 'What have I done?'
Chen Weng’s Messycow Comics for the 30th of May, 2019. This is a new strip around here. This and any future essays inspired by Messycow Comics should appear at this link.

The counting numbers — counting in general — seem to be things we’ve evolved to understand. Other animals know how to count. Here I recommend again Stanislas Dehaene’s The Number Sense: How the Mind Creates Mathematics, which describes some of the things we know about how animals do mathematics. It also describes how children come to understand it.

Samson’s Dark Side of the Horse for the 31st is a bit of play with arithmetic. Horace simplifies his problem by catching all the numerals with loops in them — the zeroes and the eights — and working with what’s left. Evidently he’s already cast out all the nines. (This is me making a joke. Casting out nines is a simple checksum that you can do which can guard against some common arithmetic mistakes. It doesn’t catch everything. But it is simple enough to do that it can be worth using.)

Horace working on the problem '100 x 80008005 ='. He strikes out many of the digits from where they appear over his head. What's left is '1 x 5 =', which he answers as 5.
Samson’s Dark Side of the Horse for the 31st of May, 2019. This comic appears a lot around here. Essays including Dark Side of the Horse appear at this link.

The part that disappoints me is that to load the problem up with digits with loops, we get a problem that’s not actually hard: 100 times anything is easy. If the problem were, say, 189 times 80008005 then you’d have a problem someone might sensibly refuse to do. But without those zeroes at the start it’d be harder to understand what Horace was doing. Maybe if it were 10089 times 800805 instead.

The Hookup. At a bar, an anthropomorphic B says to an anthropomorphic 4: 'If numbers don't lie, why did your profile say you were a ten?' (Title panel gag: the 4 says, 'Try me. Let's turn B4 into after.')
Hilary Price and Rina Piccolo’s Rhymes with Orange for the 1st of June, 2019. I don’t get enough chances to write about this comic, which I like, possibly because the title panel format amuses me more than it maybe objectively should. The chances I have had to write about Rhymes With Orange are at this link.

Hilary Price and Rina Piccolo’s Rhymes with Orange for the 1st is the anthropomorphic numerals joke for the week. Also the anthropomorphic letters joke. The capital B sees occasional use in mathematics. It can represent the ball, that is, the set of all points that represent the interior of a sphere of a set radius. Usually a radius of 1. It also sometimes appears in equations as a parameter, a number whose value is fixed for the length of the problem but whose value we don’t care about. I had thought there were a few other roles for B alone, such as a label to represent the Bessel functions. These are a family of complicated-looking polynomials with some nice properties it’s too great a diversion for me to discuss just now. But they seem to more often be labelled with a capital J for reasons that probably seemed compelling at the time. It’ll also get used in logic, where B might stand for the second statement of some argument. 4, meanwhile, is that old familiar thing.


And there were a couple of comics which I like, but which mentioned mathematics so slightly that I couldn’t put a paragraph into them. Henry Scarpelli and Craig Boldman’s Archie rerun for the 27th, for example, mentions mathematics class as one it’s easy to sleep through. And Tony Cochrane’s Agnes for the 28th also mentions mathematics class, this time as one it’s hard to pay attention to.


This clears out last week’s comic strips. This present week’s strips should be at this link on Sunday. I haven’t yet read Friday or Saturday’s comics, so perhaps there’s been a flood, but this has been a slow week so far.

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Reading the Comics, April 5, 2019: The Slow Week Edition


People reading my Reading the Comics post Sunday maybe noticed something. I mean besides my correct, reasonable complaining about the Comics Kingdom redesign. That is that all the comics were from before the 30th of March. That is, none were from the week before the 7th of April. The last full week of March had a lot of comic strips. The first week of April didn’t. So things got bumped a little. Here’s the results. It wasn’t a busy week, not when I filter out the strips that don’t offer much to write about. So now I’m stuck for what to post Thursday.

Jason Poland’s Robbie and Bobby for the 3rd is a Library of Babel comic strip. This is mathematical enough for me. Jorge Luis Borges’s Library is a magnificent representation of some ideas about infinity and probability. I’m surprised to realize I haven’t written an essay specifically about it. I have touched on it, in writing about normal numbers, and about the infinite monkey theorem.

At a tower. Bobby: 'The library of Babel!' Robbie: 'Inside is every book that will ever be written! It may take the rest of our lives to search, but it'll be worth it!' Bobby: 'What? No index?' Robbie: 'The search for meaning has no index.' Bobby (on the phone): 'I just downloaded one.' Robbie: 'It can't have everything. ... Mark Twain vs Frankenstein? Dante in Space? Harry Potter Infinity?' Bobby: 'Yep. All available as e-books too! Wow, Jeff Goldblum does the audio books.' Robbie: 'pfff. Well, forget this place!' (They leave a 'BORING' sign across the library's door.)
Jason Poland’s Robbie and Bobby for the 3rd of April, 2019. I would have sworn that I write more about this strip. But this seems to be the first time I’ve mentioned it since 2017. Well, that and other Robbie and Bobby-based essays are at this link.

The strip explains things well enough. The Library holds every book that will ever be written. In the original story there are some constraints. Particularly, all the books are 410 pages. If you wanted, say, a 600-page book, though, you could find one book with the first 410 pages and another book with the remaining 190 pages and then some filler. The catch, as explained in the story and in the comic strip, is finding them. And there is the problem of finding a ‘correct’ text. Every possible text of the correct length should be in there. So every possible book that might be titled Mark Twain vs Frankenstein, including ones that include neither Mark Twain nor Frankenstein, is there. Which is the one you want to read?

Over a pizza. Reggie: 'Don't let Jughead near the pizza! He always ends up eating half of it!' Jughead, with the cutter: 'Relax! I've divided it into four equal slices! Check it yourself!' Reggie: 'OK, I guess they do look equal.' Archie: 'Except for one thing! There are only three of us!' (Reggie and Archie each have one slice; Jughead has two.)
Henry Scarpelli and Craig Boldman’s Archie for the 4th of April, 2019. Now this strip I’ve written about as recently as October. That appearance, and other Archie strips, are discussed at this link.

Henry Scarpelli and Craig Boldman’s Archie for the 4th features an equal-divisions problem. In principle, it’s easy to divide a pizza (or anything else) equally; that’s what we have fractions for. Making them practical is a bit harder. I do like Jughead’s quick work, though. It’s got the slight-of-hand you expect from stage magic.

Caterpillars in an algebra classroom. On the back of one caterpillar student is a sign, 'Kick^{10} me'.
Scott Hilburn’s The Argyle Sweater for the 4th of April, 2019. And this strip I’ve written about … wait, can I really have gone since early March without mentioning? Huh. Well, so it appears. Essays discussing The Argyle Sweater appear at this link.

Scott Hilburn’s The Argyle Sweater for the 4th takes place in an algebra class. I’m not sure what algebraic principle 7^4 \times 13^6 demonstrates, but it probably came from somewhere. It’s 4,829,210. The exponentials on the blackboard do cue the reader to the real joke, of the sign reading “kick10 me”. I question whether this is really an exponential kicking situation. It seems more like a simple multiplication to me. But it would be harder to make that joke read clearly.

Tony Cochran’s Agnes for the 5th is part of a sequence investigating how magnets work. Agnes and Trout find just … magnet parts inside. This is fair. It’s even mathematics.

Looking over a pile of debris and a hammer on the table. Agnes: 'OK, we smashed a magnet. What do we see?' Trout: 'Uh. Magnet crumbs.' Agnes: 'Me too. I see magnet crumbs.' Trout: 'No gizmos, no gears, no wires. Just dirty black magnet crumbs.' Agnes: 'So what does this tell us about magnet function?' Trout: 'That it's one of God's many mysteries. Let's go eat.'
Tony Cochran’s Agnes for the 5th of April, 2019. And this strip I quite like, but don’t get to discuss enough. My essays featuring Agnes appears at this link.

Thermodynamics classes teach one of the great mathematical physics models. This is about what makes magnets. Magnets are made of … smaller magnets. This seems like question-begging. Ultimately you get down to individual molecules, each of which is very slightly magnetic. When small magnets are lined up in the right way, they can become a strong magnet. When they’re lined up in another way, they can be a weak magnet. Or no magnet at all.

How do they line up? It depends on things, including how the big magnet is made, and how it’s treated. A bit of energy can free molecules to line up, making a stronger magnet out of a weak one. Or it can break up the alignments, turning a strong magnet into a weak one. I’ve had physics instructors explain that you could, in principle, take an iron rod and magnetize it just by hitting it hard enough on the desk. And then demagnetize it by hitting it again. I have never seen one do this, though.

This is more than just a physics model. The mathematics of it is … well, it can be easy enough. A one-dimensional, nearest-neighbor model, lets us describe how materials might turn into magnets or break apart, depending on their temperature. Two- or three-dimensional models, or models that have each small magnet affected by distant neighbors, are harder.


And then there’s the comic strips that didn’t offer much to write about.
Brian Basset’s Red and Rover for the 3rd,
Liniers’s Macanudo for the 5th, Stephen Bentley’s Herb and Jamaal rerun for the 5th, and Gordon Bess’s Redeye rerun for the 5th all idly mention mathematics class, or things brought up in class.

Doug Savage’s Savage Chickens for the 2nd is another more-than-100-percent strip. Richard Thompson’s Richard’s Poor Almanac for the 3rd is a reprint of his Christmas Tree guide including a fir that “no longer inhabits Euclidean space”.

Mike Baldwin’s Cornered for the 31st depicts a common idiom about numbers. Eric the Circle for the 5th, by Rafoliveira, plays on the ∞ symbol.


And that covers the mathematically-themed comic strips from last week. There are more coming, though. I’ll show them on Sunday. Thanks for reading.

Reading the Comics, January 12, 2019: A Edition


As I said Sunday, last week was a slow one for mathematically-themed comic strips. Here’s the second half of them. They’re not tightly on point. But that’s all right. They all have titles starting with ‘A’. I mean if you ignore the article ‘the’, the way we usually do when alphabetizing titles.

Tony Cochran’s Agnes for the 11th is basically a name-drop of mathematics. The joke would be unchanged if the teacher asked Agnes to circle all the adjectives in a sentence, or something like that. But there are historically links between religious thinking and mathematics. The Pythagoreans, for example, always a great and incredible starting point for any mathematical topic or just some preposterous jokes that might have nothing to do with their reality, were at least as much a religious and philosophical cult. For a long while in the Western tradition, the people with the time and training to do advanced mathematics work were often working for the church. Even as people were more able to specialize, a mystic streak remained. It’s easy to understand why. Mathematics promises to speak about things that are universally true. It encourages thinking about the infinite. It encourages thinking about the infinitely tiny. It courts paradoxes as difficult as any religious Mystery. It’s easy to snark at someone who takes numerology seriously. But I’m not sure the impulse that sees magic in arithmetic is different to the one that sees something supernatural in a “transfinite” item.

Teacher: 'Agnes, what is 18 divided by 7?' Agnes: 'It matters not. I am being called to a religious life of heavy piety, general holiness, and things of that nature. I want none of math's Satanity to taint my walk.' Later, Agnes, to the principal: 'I'm toying with starting a compound in New Mexico, if you want to blow this cheap pop stand and find the light.'
Tony Cochran’s Agnes for the 11th of January, 2019. I’m always glad to have the chance to write about Agnes, and you can see things I’ve written about it at this link.

Scott Hilburn’s The Argyle Sweater for the 11th is another mistimed Pi Day joke. π is, famously, an irrational number. But so is every number, except for a handful of strange ones that we’ve happened to find interesting. That π should go on and on follows from what an irrational number means. It’s a bit surprising the 4 didn’t know all this before they married.

Cartoon Labelled 'Wife of Pi'. At a therapist's office. The therapist is a division sign. A pi with a face rolls its eyes. A 4 with a face complains, 'He's irrational and he goes on and on.'
Scott Hilburn’s The Argyle Sweater for the 11th of January, 2019. It’s not quite the most common strip mentioned here. But you can find other topics raised by The Argyle Sweater at this link.

I appreciate the secondary joke that the marriage counselor is a “Hugh Jripov”, and the counselor’s being a ripoff is signaled by being a ÷ sign. It suggests that maybe successful reconciliation isn’t an option. I’m curious why the letters ‘POV’ are doubled, in the diploma there. In a strip with tighter drafting I’d think it was suggesting the way a glass frame will distort an image. But Hilburn draws much more loosely than that. I don’t know if it means anything.

Wavehead working on the problem 17 + 7 at the blackboard. He's circled the 17, put a ? under the equals sign, added an ! before the +, and a * after it. Teacher: 'This is math; you don't need to annotate.'
Mark Anderson’s Andertoons for the 12th of January, 2019. There’s more essays with Andertoons at this link.

Mark Anderson’s Andertoons for the 12th is the Mark Anderson’s Andertoons for the essay. I’m so relieved to have a regular stream of these again. The teacher thinks Wavehead doesn’t need to annotate his work. And maybe so. But writing down thoughts about a problem is often good practice. If you don’t know what to do, or you aren’t sure how to do what you want? Absolutely write down notes. List the things you’d want to do. Or things you’d want to know. Ways you could check your answer. Ways that you might work similar problems. Easier problems that resemble the one you want to do. You find answers by thinking about what you know, and the implications of what you know. Writing these thoughts out encourages you to find interesting true things.

And this was too marginal a mention of mathematics even for me, even on a slow week. But Georgia Dunn’s Breaking Cat News for the 12th has a cat having a nightmare about mathematics class. And it’s a fun comic strip that I’d like people to notice more.


And that’s as many comics as I have to talk about from last week. Sunday, I should have another Reading the Comics post and it’ll be at this link.

Reading the Comics, January 1, 2019: New Year’s Day Edition


It’s a new year. That doesn’t mean I’m not going to keep up some of my old habits. One of them is reading the comics for the mathematics bits. For example …

Johnny Hart’s Back To BC for the 30th presents some curious use of mathematics. At least the grammar of mathematics. It’s a bunch of statements that are supposed to, taken together, overload … I’m going to say BC’s … brain. (I’m shaky on which of the characters is Peter and which is BC. Their difference in hair isn’t much of a visual hook.) Certainly mathematics inspires that feeling that one’s overloaded one’s brain. The long strings of reasoning and (ideally) precise definitions are hard to consider. And the proofs mathematicians find the most fun are, often, built cleverly. That is, going about their business demonstrating things that don’t seem relevant, and at the end tying them together. It’s hard to think.

Peter: 'The sum of the four sides of an isosceles triangle is equal to the ... ' BC, thinking: 'Four?' Peter: 'Hypotenuse of a rectangular circle ... ' BC, thinking: 'A rectangular circle?' Peter: 'Having a mean radius of x divided by alpha centura ... ' BC, thinking: 'Having.' SNAP! (He rubs his head.) BC: 'I think that must have been my mind.'
Johnny Hart’s Back To BC for the 30th of December, 2018. The strip says it’s from the 18th of February, 1962. Essays inspired by B.C., both 1962 vintage and 2019 current, should be at this link.

But then … Peter … isn’t giving a real mathematical argument. He’s giving nonsense. And obvious nonsense, rather than nonsense because the writer wanted something that sounded complicated without caring what was said. Talking about a “four-sided triangle” or a “rectangular circle” has to be Peter trying to mess with BC’s head. Confidently-spoken nonsense can sound as if it’s deeper wisdom than the listener has. Which, fair enough: how can you tell whether an argument is nonsense or just cleverer than you are? Consider the kind of mathematics proof I mentioned above, where the structure might almost be a shaggy dog joke. If you can’t follow the logic, is it because the argument is wrong or because you haven’t worked out why it is right?

I believe that … Peter … is just giving nonsense and trusting that … BC … won’t know the difference, but will wear himself out trying to understand. Pranks.

Doctor: 'I'm not an accountant. I'm your doctor. However, by trying to do your taxes by yourself, I've calculated your brain has depreciated by nearly 68%.'
Tim Lachowski’s Get A Life for the 31st of December, 2018. Essays discussing things raised by Get A Life should be at this link.

Tim Lachowski’s Get A Life for the 31st just has some talk about percentages and depreciation and such. It’s meant to be funny that we might think of a brain depreciating, as if anatomy could use the same language as finance. Still, one of the virtues of statistics is the ability to understand a complicated reality with some manageable set of numbers. If we accept the convention that some number can represent the value of a business, why not the convention that some number could represent the health of a brain? So, it’s silly, but I can imagine a non-silly framing for it.

Trout: 'Two thousand and nineteen years, that's a long time.' Agnes: 'Yep! Earth has been around a while!' Trout: 'Were people even alive back then?' Agnes: 'Someone had to start counting, so I guess so, yeah.' Trout: 'Who taught them to count?' Agnes: 'Probably the people selling calendars.'
Tony Cochran’s Agnes for the 1st of January, 2019. This and other essays discussing Agnes should be at this link.

Tony Cochran’s Agnes for the 1st is about calendars. The history of calendars is tied up with mathematics in deep and sometimes peculiar ways. One might imagine that a simple ever-increasing index from some convenient reference starting time would do. And somehow that doesn’t. Also, the deeper you go into calendars the more you wonder if anyone involved in the project knew how to count. If you ever need to feel your head snapping, try following closely just how the ancient Roman calendar worked. Especially from the era when they would occasionally just drop an extra month in to the late-middle of February.

The Julian and Gregorian calendars have a year number that got assigned proleptically, that is, with the year 1 given to a set of dates that nobody present at the time called the year 1. Which seems fair enough; not many people in the year 1 had any idea that something noteworthy was under way. Calendar epochs dated to more clear events, like the reign of a new emperor or the revolution that took care of that whole emperor problem, will more reliably start with people aware of the new numbers. Proleptic dating has some neat side effects, though. If you ever need to not impress someone, you can point out that the dates from the 1st of March, 200 to the 28th of February, 300 both the Julian and the Gregorian calendar dates exactly matched.

Dad: 'OK, Suzie, you hate math. And actually, 1/37 of me understands exactly how you feel.' Suzie: 'Lay off, Dad.'
Niklas Eriksson’s Carpe Diem for the 2nd of January, 2019. And appearances by Carpe Diem in my essays should be at this link.

Niklas Eriksson’s Carpe Diem for the 2nd is a dad joke about mathematics. And uses fractions as emblematic of mathematics, fairly enough. Introducing them and working with them are the sorts of thing that frustrate and confuse. I notice also the appearance of “37” here. Christopher Miller’s fascinating American Cornball: A Laffopedic Guide to the Formerly Funny identifies 37 as the current “funniest number”, displacing the early 20th century’s preferred 23 (as in skidoo). Among other things, odd numbers have a connotation of seeming more random than even numbers; ask someone to pick a whole number from 1 to 50 and you’ll see 37’s and 33’s more than you’ll see, oh, 48’s. Why? Good question. It’s among the mysteries of psychology. There’s likely no really deep reason. Maybe a sense that odd numbers are, well, odd as in peculiar, and that a bunch of peculiarities will be funny. Now let’s watch the next decade make a food of me and decide the funniest number is 64.


I’m glad to be back on schedule publishing Reading the Comics posts. I should have another one this week. It’ll be at this link when it’s ready. Thanks for reading.

Reading the Comics, September 22, 2018: Last Chance Edition


I plan tomorrow to have another of my Mathematics A To Z posts. This weekend I’ll publish this month’s Playful Mathematics Blog Carnival. So if you’ve seen any web site, blog, video, podcast, or other reference that had something that delighted and taught you something, this is your last chance to let me know, and let my audience know about it. Please leave a comment if you know about anything I ought to see. Thank you.

Mark Tatulli’s Lio for the 20th is a numerals and a wordplay joke. It is not hard to make numerals tattooed on a person an alarming thing. But when done with (I trust) the person’s consent, and done whimsically like this, it’s more a slightly odd bit of play.

(Lio walks past a man who's got many different renderings of the numeral '2' on his arms. He comes up to a storefront: 'Tattwos'.)
Mark Tatulli’s Lio for the 20th of September, 2018. It … seems a little out of the usual run of Lio‘s sense of humor, but then I don’t know where else Tatulli could have used the joke.

Tony Cochrane’s Agnes for the 21st is ultimately a strip about motivating someone to learn arithmetic. Agnes’s reasoning is sound, though. If the only reason to learn this unpleasant chore is because your job may need it, why not look at another job? We wouldn’t try to convince someone who didn’t want to learn French that they’ll need it for their job as … a tour guide in Quebec? There’s plenty of work that doesn’t need that. I suspect kids don’t buy “this is good for your future job” as a reason. Even if it were, general education should not be job training either.

Teacher: 'Agnes, please finish the third division problem.' Agnes: 'I don't think so. I'm going to be a diesel mechanic.' Teacher: 'Do you even know what that is?' Agnes: 'No, but I found a brochure in Grandma's sock drawer, and the people in it looked rapturous about work.' Teacher: 'Diesel mechanics need to know division.' Agnes: 'Fine, I'll go with one of the others. How about a mortician?'
Tony Cochrane’s Agnes for the 21st of September, 2018. Agnes doesn’t pursue being a mortician, at least this time, and instead tries out keeping a journal.

Juba’s Viivi and Wagner for the 21st gives Wagner a short-lived ambition to be a wandering mathematician. The abacus serves as badge of office. There are times and places that his ambition wouldn’t be completely absurd. Before the advent of electric and electronic computing, people who could calculate were worth hiring for their arithmetic. In 18th Century London there was a culture of “penny universities”, people with academic training making a living by giving lectures and courses to whatever members of the public cared to come to their talk, often in coffee-houses or barns.

Wagner: 'I decided to be a wandering mathematician. I already bought an abacus. I'll earn my living by performing simple additions and subtractions.' Viivi : 'You'll probably starve to death.' Wagner: 'I don't do probability calculus.'
Juba’s Viivi and Wagner for the 21st of September, 2018. This puts me in mind of a Peanuts where Sally Brown wondered about what if their father lost their job. What could she do to help the family earn its living? She suggested: she could make her bed.

Mathematicians learn that there used to be public spectacles, mathematicians challenging one another to do problems, with real cash or jobs on the line. They learn this because one such challenge figures in to the story of Gerolamo Cardano and Niccolò Fontana, known as Tartaglia. It’s about how we learned formulas to solve some kinds of polynomials. You may sense uncertainty in my claim there. It’s because it turns out it’s hard to find clear records of this sort of challenge outside the Cardano-Tartaglia match. That isn’t to say these things weren’t common. It’s just that I’ve been slowly learning to be careful about my claims.

(I’m aided here by a startling pair of episodes of The History of Philosophy Without Any Gaps podcast. This pair — “Trivial Pursuits: Fourteenth Century Logic” and “Sara Uckleman on Obligations” — describe a fascinating logic game that sounds like it would still be a great party game, for which there’s numerous commentaries and rule sets and descriptions of how to play. But no records of people actually ever playing it, or talking about games they had played, or complaining about being cheated out of a win or stuff like that. It’s a strong reminder to look closely at what your evidence does support.)

Father: 'Son, I know you pretended to be sick today so you could skip school.' Kid: 'But I didn't!' Father: 'Shhh. It's OK. Don't tell Mom, but I got tickets to a luchador show this afternoon.' Kid: 'Oh boy!' [ LATER ... ] Luchador: 'Raaa! I'm the masked Karl Weierstrass and I'm WRESTLING with how to rigorously define the limit of a function!' Kid: 'Nooooooooooooo!'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 22nd of September, 2018. So do you think the father is really into the luchador show in the last panel or is he just going along with this while his kid comes to hate promises of fun?

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 22nd is the comforting return of Zach Weinersmith to these essays. And yes, it’s horrible parenting to promise something fun and have it turn out to be a mathematics lecture, but that’s part of the joke.

Karl Weierstrass was a real person, and a great mathematician best known for giving us a good, rigorous idea of what a limit is. We need limits because, besides their being nice things to have, calculus depends on them. At least, calculus depends on thinking about calculations on infinitely many things. Or on things infinitesimally small. Trying to do this works pretty well, much of the time. But you can also start calculating like this and get nonsense. How to tell whether your particular calculation works out or is nonsense?

Weierstrass worked out a good, rigorous idea for what we mean by a limit. It mostly tracks with what we’d intuitively expect. And it avoids all the dangerous spots we’ve noticed so far. Particularly, it doesn’t require us to ever look at anything that’s infinitely vast, or infinitesimally small. Anything we calculate on is done with regular arithmetic, that we’re quite confident in. But it lets us draw conclusions about the infinitely numerous or tiny. It’s brilliant work. When it’s presented to someone in the start of calculus, it leaves them completely baffled but they can maybe follow along with the rules. When it’s presented to mathematics majors in real analysis, it leaves them largely baffled but they can maybe follow along with the reasons. Somewhere around grad school I got comfortable with it, even excited. Weierstrass’s sort of definition turns up all over the place in real and in functional analysis. So at the least you get very comfortable with it.

So it is part of Weinersmith’s joke that this is way above that kid’s class level. As a joke, that fails for me. The luchador might as well be talking complete nonsense and the kid would realize that right away. There’s not the threat that this is something he ought to be able to understand. But it will probably always be funny to imagine mathematician wrestlers. Can count on that. I didn’t mean that as a joke, but you’ll notice I’m letting it stand.


And with that, you know what I figure to post on Sunday. It and my other Reading the Comics posts should be at this tag. Other appearances of Lio should be at this link. The mentions of Agnes should be at this link. Essays with some mention of Viivi and Wagner will be at this link, although it’s a new tag, so who knows how long it’ll take for the next to appear? And other essays with Saturday Morning Breakfast Cereal will be at this link when there’s any to mention.

Reading the Comics, March 31, 2018: A Normal Week Edition


I have a couple loose rules about these Reading the Comics posts. At least one a week, whether there’s much to talk about or not. Not too many comics in one post, because that’s tiring to read and tiring to write. Trying to write up each day’s comics on the day mitigates that some, but not completely. So I tend to break up a week’s material if I can do, say, two posts of about seven strips each. This year, that’s been necessary; I’ve had a flood of comics on-topic or close enough for me to write about. This past week was a bizarre case. There really weren’t enough strips to break up the workload. It was, in short, a normal week, as strange as that is to see. I don’t know what I’m going to do Thursday. I might have to work.

Aaron McGruder’s Boondocks for the 25th of March is formally just a cameo mention of mathematics. There is some serious content to it. Whether someone likes to do a thing depends, to an extent, on whether they expect to like doing a thing. It seems likely to me that if a community encourages people to do mathematics, then it’ll have more people who do mathematics well. Mathematics does at least have the advantage that a lot of its fields can be turned into games. Or into things like games. Is one knot the same as another knot? You can test the laborious but inevitably correct way, trying to turn one into the other. Or you can find a polynomial that describes both knots and see if those two are the same polynomials. There’s fun to be had in this. I swear. And, of course, making arguments and finding flaws in other people’s arguments is a lot of mathematics. And good fun for anybody who likes that sort of thing. (This is a new tag for me.)

Huey: 'Ugh ... this video is terrible. Turn it.' Riley: 'You say everything is terrible. You're a hater.' Huey: 'Y'know ... the brutally honest critiques that you call 'hating' are why black people have always been at the forefront of music and culture. Artists knew that if they didn't excel, black people would yell and boo and heckle them off the stage Tough audiences have always made our artists better ... ' Riley: 'Uh-huh ... ' Huey: 'Now if we could only get black people to start booing each other in math class ... ' Riley: 'Whatever, hater.'
Aaron McGruder’s Boondocks for the 25th of March of March, 2018. Yeah, all right, but I would not want to be the teacher keeping a class of people heckling the student working a story problem on the board from turning abusive.

Ted Shearer’s Quincy for the 30th of January, 1979 and rerun the 26th names arithmetic as the homework Quincy’s most worried about. Or would like to put off the most. Harmless enough.

Quincy: 'I just heard one whole neighborhood is without electric power! I hope it's where my teacher lives.' Grandmother: 'Why?' Quincy: 'She won't be able to mark arithmetic papers.'
Ted Shearer’s Quincy for the 30th of January, 1979 and rerun the 26th of March, 2018. Because if there’s one thing that improves a teacher’s mood while grading, it’s having to do it while hurried after a night of rotten sleep in an apartment that possibly hasn’t got any heat!

Mike Thompson’s Grand Avenue for the 26th is a student-resisting-the-problem joke. A variable like ‘x’ serves a couple of roles. One of them is the name for a number whose value we don’t explicitly know, but which we hope to work out. And that’s the ‘x’ seen here. The other role of ‘x’ is the name for a number whose value we don’t know and don’t particularly care about. Since those are different reasons to use ‘x’ maybe we ought to have different names for the concepts. But we don’t and there’s probably no separating them now.

On the board: '17 + x = 21; solve for x'. Michael: 'x is unknown, so I'd hate to disrespect x's desire for privacy by disclosing its identity!'
Mike Thompson’s Grand Avenue for the 26th of March, 2018. And it took me more work than I wanted to figure out the kid’s name, so here: it’s Michael. Source: the Andrews-McMeel Syndication page about the comic. Cast page, since they use Javascript that keeps me from linking to that.

Tony Cochran’s Agnes for the 27th grumbles that mathematics and clairvoyance are poorly taught. Well, everyone who loves mathematics grumbles that the subject is poorly taught. I don’t know what the clairvoyants think but I’ll bet the same.

Agnes, thinking: 'In my mind, I'm seeing snow. Piles of it ... crippling traffic. Paralyzing the city. Scaring the fearless. Closing school.' Grandmom, clapping: 'Sun's out! School starts in an hour! Let's go! Hup! Hup! Hup' Agnes, thinking: 'Seems public schools excel at teaching clairvoyance as much as they do math.'
Tony Cochran’s Agnes for the 27th of March, 2018. In fairness, once students have got a little clairvoyant it becomes crazy hard to do assessment testing.

Mark Pett’s Lucky Cow rerun for the 28th is about sudoku. As with any puzzle the challenge is having rules that are restrictive enough to be interesting. This is also true of any mathematical field, though. You want ideas that imply a lot of things are true, but that also imply enough interesting plausible things are not true.

Leticia: 'You're doing a sudoku puzzle, Neil?' Neil: 'Yep! And I'm timing myself!' Leticia: 'How are you doing?' Neil: 'Really well, Leticia! See? I can complete it faster than the average!' Leticia: 'Wow! It's a challenge to fit the numbers in while following all the rules.' Neil, thinking: 'There are rules?'
Mark Pett’s Lucky Cow rerun for the 28th of March, 2018. It’s not that I’m not amused by the strip. But the mechanism of setting up the premise, developing it, and delivering the punch line really stands out sorely here. It’s hard to believe in someone saying Leticia’s line the third panel.

Rick DeTorie’s One Big Happy rerun for the 30th has Ruthie working on a story problem. One with loose change, which seems to turn up a lot in story problems. I never think of antes for some reason.

Dad: 'If Karen puts three quarters on the table ... and Kyle adds two nickels and one penny ... what would you have?' Ruthie: 'A very lopsided ante!'
Rick DeTorie’s One Big Happy rerun for the 30th of March, 2018. Grandpa plays a lot of card games with Ruthie maybe people should know.

Stephen Beals’s Adult Children for the 31st depicts mathematics as the stuff of nightmares. (Although it’s not clear to me this is meant to recount a nightmare. Reads like it, anyway.) Calculus, too, which is an interesting choice. Calculus seems to be a breaking point for many people. A lot of people even who were good at algebra or trigonometry find all this talk about differentials and integrals and limits won’t cohere into understanding. Isaac Asimov wrote about this several times, and the sad realization that for as much as he loved mathematics there were big important parts of it that he could not comprehend.

Berle: 'It was just a happy stroll through the gloomy graveyard when suddenly ... ' Spivak's Calculus, 3rd Edition appears. Berle: 'Math jumped out of nowhere!' Harvey: 'Drink it off.'
Stephen Beals’s Adult Children for the 31st of March, 2018. Spivak’s Calculus is one of the standard textbooks for intro students, by the way, although my own education was on James (not that James) Stewart. Spivak’s also noted for a well-regarded guide to TeX, which incidentally used a set of gender-neutral third-person singular pronouns (e[y]/em/eir) that some online communities embraced.

I’m curious why calculus should be such a discontinuity, but the reasons are probably straightforward. It’s a field where you’re less interested in doing things to numbers and more interested in doing things to functions. Or to curves that a function might represent. It’s a field where information about a whole region is important, rather than information about a single point. It’s a field where you can test your intuitive feeling for, say, a limit by calculating a couple of values, but for which those calculations don’t give the right answer. Or at least can’t be guaranteed to be right. I don’t know if the choice of what to represent mathematics was arbitrary. But it was a good choice certainly. (This is another newly-tagged strip.)

Reading the Comics, February 17, 2018: Continuing Deluge Month


February’s been a flooding month. Literally (we’re about two blocks away from the Voluntary Evacuation Zone after the rains earlier this week) and figuratively, in Comic Strip Master Command’s suggestions about what I might write. I have started thinking about making a little list of the comics that just say mathematics in some capacity but don’t give me much to talk about. (For example, Bob the Squirrel having a sequence, as it does this week, with a geometry tutor.) But I also know, this is unusually busy this month. The problem will recede without my having to fix anything. One of life’s secrets is learning how to tell when a problem’s that kind.

Patrick Roberts’s Todd the Dinosaur for the 12th just shows off an arithmetic problem — fractions — as the thing that can be put on the board and left for students to do.

Todd: *Sniff sniff* 'Hey! What's that on the floor?' (He follows a trail of beef jerky, eating, until he's at the chalkboard.) Teacher: 'Well, hello, Todd! Say, while you're up there, why don't you do that fractions problem on the board?' Todd: 'Darn you, tasty Slim jims!'
Patrick Roberts’s Todd the Dinosaur for the 12th of February, 2018. I’ll risk infecting you with one of my problems: I look at this particular comic and wonder what happened right before the first panel to lead to this happening.

Ham’s Life on Earth for the 12th has a science-y type giving a formula as “something you should know”. The formula’s gibberish, so don’t worry about it. I got a vibe of it intending to be some formula from statistics, but there’s no good reason for that. I’ve had some statistical distribution problems on my mind lately.

Eric Teitelbaum and Bill Teitelbaum’s Bottomliners for the 12th maybe influenced my thinking. It has a person claiming to be a former statistician, and his estimate of how changing his job’s affected his happiness. Could really be any job that encourages people to measure and quantify things. But “statistician” is a job with strong connotations of being able to quantify happiness. To have that quantity feature a decimal point, too, makes him sound more mathematical and thus, more surely correct. I’d be surprised if “two and a half times” weren’t a more justifiable estimate, given the margin for error on happiness-measurement I have to imagine would be there. (This seems to be the first time I’ve featured Bottomliners at least since I started tagging the comic strips named. Neat.)

Ruben Bolling’s Super-Fun-Pak Comix for the 12th reprinted a panel called The Uncertainty Principal that baffled commenters there. It’s a pun on “Uncertainty Principle”, the surprising quantum mechanics result that there are some kinds of measurements that can’t be taken together with perfect precision. To know precisely where something is destroys one’s ability to measure its momentum. To know the angular momentum along one axis destroys one’s ability to measure it along another. This is a physics result (note that the panel’s signed “Heisenberg”, for the name famously attached to the Uncertainty Principle). But the effect has a mathematical side. The operations that describe finding these incompatible pairs of things are noncommutative; it depends what order you do them in.

We’re familiar enough with noncommutative operations in the real world: to cut a piece of paper and then fold it usually gives something different to folding a piece of paper and then cutting it. To pour batter in a bowl and then put it in the oven has a different outcome than putting batter in the oven and then trying to pour it into the bowl. Nice ordinary familiar mathematics that people learn, like addition and multiplication, do commute. These come with partners that don’t commute, subtraction and division. But I get the sense we don’t think of subtraction and division like that. It’s plain enough that ‘a’ divided by ‘b’ and ‘b’ divided by ‘a’ are such different things that we don’t consider what’s neat about that.

In the ordinary world the Uncertainty Principle’s almost impossible to detect; I’m not sure there’s any macroscopic phenomena that show it off. I mean, that atoms don’t collapse into electrically neutral points within nanoseconds, sure, but that isn’t as compelling as, like, something with a sodium lamp and a diffraction grating and an interference pattern on the wall. The limits of describing certain pairs of properties is about how precisely both quantities can be known, together. For everyday purposes there’s enough uncertainty about, say, the principal’s weight (and thus momentum) that uncertainty in his position won’t be noticeable. There’s reasons it took so long for anyone to suspect this thing existed.

Samson’s Dark Side of the Horse for the 13th uses a spot of arithmetic as the sort of problem coffee helps Horace solve. The answer’s 1.

Mike Baldwin’s Cornered for the 14th is a blackboard-full-of-symbols panel. Well, a whiteboard. It’s another in the line of mathematical proofs of love.

Dana Simpson’s Ozy and Millie rerun for the 14th has the title characters playing “logical fallacy tag”. Ozy is, as Millie says, making an induction argument. In a proper induction argument, you characterize something with some measure of size. Often this is literally a number. You then show that if it’s true that the thing is true for smaller problems than you’re interested in, then it has to also be true for the problem you are interested in. Add to that a proof that it’s true for some small enough problem and you’re done. In this case, Ozy’s specific fallacy is an appeal to probability: all but one of the people playing tag are not it, and therefore, any particular person playing the game isn’t it. That it’s fallacious really stands out when there’s only two people playing.

Ed: 'Only recently, scientists discovered pigeons understand space and time.' Pigeon: 'They never questioned us before. We're waiting for them to ask us about the Grand Unified Theory of Physics next.'
Alex Hallatt’s Arctic Circle for the 16th of February, 2018. As ever, I learn things from doing this! Specifically the names of the penguins which I’d somehow not thought about before. Ed’s the one with a pair of antenna-like feathers on his head. Oscar has the smooth head. Gordo has the set of bumps.

Alex Hallatt’s Arctic Circle for the 16th riffs on the mathematics abilities of birds. Pigeons, in this case. The strip starts from their abilities understanding space and time (which are amazing) and proposes pigeons have some insight into the Grand Unified Theory. Animals have got astounding mathematical abilities, should point out. Don’t underestimate them. (This also seems to be the first time I’ve tagged Arctic Circle which doesn’t seem like it could be right. But I didn’t remember naming the penguins before so maybe I haven’t? Huh. Mind, I only started tagging the comic strip titles a couple months ago.)

Tony Cochrane’s Agnes for the 17th has the title character try bluffing her way out of mathematics homework. Could there be a fundamental flaw in mathematics as we know it? Possibly. It’s hard to prove that any field complicated enough to be interesting is also self-consistent. And there’s a lot of mathematics out there. And mathematics subjects often develop with an explosion of new ideas and then a later generation that cleans them up and fills in logical gaps. Symplectic geometry is, if I’m following the news right, going into one of those cleaning-up phases now. Is it likely to be uncovered by a girl in elementary school? I’m skeptical, and also skeptical that she’d have a replacement system that would be any better. I admire Agnes’s ambition, though.

Mike Baldwin’s Cornered for the 17th plays on the reputation for quantum mechanics as a bunch of mathematically weird, counter-intuitive results. In fairness to the TV program, I’ve had series run longer than I originally planned too.

Reading the Comics, January 31, 2018: Workload Edition


I thought my new workflow of writing my paragraph or two about each comic was going to help me keep up and keep fresher with the daily comics. And then Comic Strip Master Command decided that everybody had to do comics that at least touched on some mathematical subject. I don’t know. I’m trying to keep up but will admit, I didn’t get to writing anything about Friday’s or Saturday’s strips yet. They’ll keep a couple days.

Bill Amend’s FoxTrot Classicsfor the 29th of January reprints the strip from the 5th of February, 1996. (The Classics reprints finally reached the point where Amend retired from daily strips, and jumped back a dozen years to continue printing.) It just mentions mathematics exams, and high performances on both is all.

Josh Shalek’s Kid Shay Comics reprint for the 29th tosses off a mention of Uncle Brian attempting a great mathematical feat. In this case it’s the Grand Unification Theory, some logically coherent set of equations that describe the fundamental forces of the universe. I think anyone with a love for mathematics makes a couple quixotic attempts on enormously vast problems like this. Or the Riemann Hypothesis, or Goldbach’s Conjecture, or Fermat’s Last Theorem. Yes, Fermat’s Last Theorem has been proven, but there’s no reason there couldn’t be an easier proof. Similarly there’s no reason there couldn’t be a better proof of the Four Color Map theorem. Most of these attempts end up the way Brian’s did. But there’s value in attempting this anyway. Even when you fail, you can have fun and learn fascinating things in the attempt.

Carol Lay’s Lay Lines for the 29th is a vignette about a statistician. And one of those statisticians with the job of finding surprising correlations between things. I think it’s also a riff on the hypothesis that free markets are necessarily perfect: if there’s any advantage to doing something one way, it’ll quickly be found and copied until that is the normal performance of the market. Anyone doing better than average is either taking advantage of concealed information, or else is lucky.

Matt Lubchansky’s Please Listen To Me for the 29th depicts a person doing statistical work for his own purposes. In this case he’s trying to find what factors might be screwing up the world. The expressions in the second panel don’t have an obvious meaning to me. The start of the expression \int exp\left(\frac{1}{N_0}\right) at the top line suggests statistical mechanics to me, for what that’s worth, and the H and Ψ underneath suggest thermodynamics or quantum mechanics. So if Lubchansky was just making up stuff, he was doing it with a good eye for mathematics that might underly everything.

Rick Stromoski’s Soup to Nutz for the 29th circles around the anthropomorphic numerals idea. It’s not there exactly, but Andrew is spending some time giving personality to numerals. I can’t say I give numbers this much character. But there are numbers that seem nicer than others. Usually this relates to what I can do with the numbers. 10, for example, is so easy to multiply or divide by. If I need to multiply a number by, say, something near thirty, it’s a delight to triple it and then multiply by ten. Twelve and 24 and 60 are fun because they’re so relatively easy to find parts of. Even numbers often do seem easier to work with, just because splitting an even number in half saves us from dealing with decimals or fractions. Royboy sees all this as silliness, which seems out of character for him, really. I’d expect him to be up for assigning traits to numbers like that.

Zippy, in front of the Wein-O-Rama Restaurant: 'Different parts of Einstein's theory of relativity are being proven true all th'time ... hmm ... what about th'idea that an exact DUPLICATE of everything exists at th'same time on th'other side of th'universe? Or, in this case, on 'th'other side of th'the Wein-O-Rama restaurant!' Other Zippy, at the other end of the the Wein-O-Rama restaurant: 'What happens in Rhode Island stays in Rhode Island! Yow!'
Bill Griffith’s Zippy the Pinhead for the 30th of January, 2018. The the Wein-O-Rama is in Cranston, Rhode Island, and I do hope that this strip is now part of the “In Pop Culture” segment of Cranson’s Wikipedia page. DuckDuckGo’s search for Wein-O-Rama pops up, for me, this sentence from a TripAdvisor.com review: “When we go to Weinorama its [sic] always for the wieners [sic], that `RI-only’ treat. I’ll always order them all the way, but my wife always says ‘no onions’.” Thus does reality merge imperceptibly into Zippy the Pinhead comics, evoking the surrealist character’s ancient dictum, “Life is a blur of Republicans and meat”.

Bill Griffith’s Zippy the Pinhead for the 30th mentions Albert Einstein and relativity. And Zippy ruminates on the idea that there’s duplicates of everything, in the vastness of the universe. It’s an unsettling idea that isn’t obviously ruled out by mathematics alone. There’s, presumably, some chance that a bunch of carbon and hydrogen and oxygen and other atoms happened to come together in such a way as to make our world as we know it today. If there’s a vast enough universe, isn’t there a chance that a bunch of carbon and hydrogen and oxygen and other atoms happened to come together that same way twice? Three times? If the universe is infinitely large, might it not happen infinitely many times? In any number of variations? It’s hard to see why not, but even if it is possible, that’s no reason to think it must happen either. And whether those duplicates are us is a question for philosophers studying the problem of identity and what it means to be one person rather than some other person. (It turns out to be a very difficult problem and I’m glad I’m not expected to offer answers.)

Tony Cochrane’s Agnes attempts to use mathematics to reason her way to a better bedtime the 31st. She’s not doing well. Also this seems like it’s more of an optimization problem than a simple arithmetic one. What’s the latest bedtime she can get that still allows for everything that has to be done, likely including getting up in time and getting enough sleep? Also, just my experience but I didn’t think Agnes was old enough to stay up until 10 in the first place.

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, June 26, 2017: Deluge Edition, Part 1


So this past week saw a lot of comic strips with some mathematical connection put forth. There were enough just for the 26th that I probably could have done an essay with exclusively those comics. So it’s another split-week edition, which suits me fine as I need to balance some of my writing loads the next couple weeks for convenience (mine).

Tony Cochrane’s Agnes for the 25th of June is fun as the comic strip almost always is. And it’s even about estimation, one of the things mathematicians do way more than non-mathematicians expect. Mathematics has a reputation for precision, when in my experience it’s much more about understanding and controlling error methods. Even in analysis, the study of why calculus works, the typical proof amounts to showing that the difference between what you want to prove and what you can prove is smaller than your tolerance for an error. So: how do we go about estimating something difficult, like, the number of stars? If it’s true that nobody really knows, how do we know there are some wrong answers? And the underlying answer is that we always know some things, and those let us rule out answers that are obviously low or obviously high. We can make progress.

Russell Myers’s Broom Hilda for the 25th is about one explanation given for why time keeps seeming to pass faster as one age. This is a mathematical explanation, built on the idea that the same linear unit of time is a greater proportion of a young person’s lifestyle so of course it seems to take longer. This is probably partly true. Most of our senses work by a sense of proportion: it’s easy to tell a one-kilogram from a two-kilogram weight by holding them, and easy to tell a five-kilogram from a ten-kilogram weight, but harder to tell a five from a six-kilogram weight.

As ever, though, I’m skeptical that anything really is that simple. My biggest doubt is that it seems to me time flies when we haven’t got stories to tell about our days, when they’re all more or less the same. When we’re doing new or exciting or unusual things we remember more of the days and more about the days. A kid has an easy time finding new things, and exciting or unusual things. Broom Hilda, at something like 1500-plus years old and really a dour, unsociable person, doesn’t do so much that isn’t just like she’s done before. Wouldn’t that be an influence? And I doubt that’s a complete explanation either. Real things are more complicated than that yet.

Mac and Bill King’s Magic In A Minute for the 25th features a form-a-square puzzle using some triangles. Mathematics? Well, logic anyway. Also a good reminder about open-mindedness when you’re attempting to construct something.

'Can you tell me how much this would be with the discount?' 'It would be ... $17.50.' 'How did you do that so fast?' 'Ten percent of 25 is $2.50 ... times three is $7.50 ... round that to $8.00 ... $25 minus $8 is $17 ... add back the 50 cents and you get $17.50.' 'So you're like a math genius?' (Thinking) 'I never thought so before I started working here.'
Norm Feuti’s Retail for the 26th of June, 2017. So, one of my retail stories that I might well have already told because I only ever really had one retail job and there’s only so many stories you get working a year and a half in a dying mall’s book store. I was a clerk at Walden Books. The customer wanted to know for this book whether the sticker’s 10 percent discount was taken before or after the state’s 6 percent sales tax was applied. I said I thought the discount taken first and then tax applied, but it didn’t matter if I were wrong as the total would be the same amount. I calculated what it would be. The customer was none too sure about this, but allowed me to ring it up. The price encoded in the UPC was wrong, something like a dollar more than the cover price, and the subtotal came out way higher. The customer declared, “See?” And wouldn’t have any of my explaining that he was hit by a freak event. I don’t remember other disagreements between the UPC price and the cover price, but that might be because we just corrected the price and didn’t get a story out of it.

Norm Feuti’s Retail for the 26th is about how you get good at arithmetic. I suspect there’s two natural paths; you either find it really interesting in your own right, or you do it often enough you want to find ways to do it quicker. Marla shows the signs of learning to do arithmetic quickly because she does it a lot: turning “30 percent off” into “subtract ten percent three times over” is definitely the easy way to go. The alternative is multiplying by seven and dividing by ten and you don’t want to multiply by seven unless the problem gives a good reason why you should. And I certainly don’t fault the customer not knowing offhand what 30 percent off $25 would be. Why would she be in practice doing this sort of problem?

Johnny Hart’s Back To B.C. for the 26th reruns the comic from the 30th of December, 1959. In it … uh … one of the cavemen guys has found his calendar for the next year has too many days. (Think about what 1960 was.) It’s a common problem. Every calendar people have developed has too few or too many days, as the Earth’s daily rotations on its axis and annual revolution around the sun aren’t perfectly synchronized. We handle this in many different ways. Some calendars worry little about tracking solar time and just follow the moon. Some calendars would run deliberately short and leave a little stretch of un-named time before the new year started; the ancient Roman calendar, before the addition of February and January, is famous in calendar-enthusiast circles for this. We’ve now settled on a calendar which will let the nominal seasons and the actual seasons drift out of synch slowly enough that periodic changes in the Earth’s orbit will dominate the problem before the error between actual-year and calendar-year length will matter. That’s a pretty good sort of error control.

8,978,432 is not anywhere near the number of days that would be taken between 4,000 BC and the present day. It’s not a joke about Bishop Ussher’s famous research into the time it would take to fit all the Biblically recorded events into history. The time is something like 24,600 years ago, a choice which intrigues me. It would make fair sense to declare, what the heck, they lived 25,000 years ago and use that as the nominal date for the comic strip. 24,600 is a weird number of years. Since it doesn’t seem to be meaningful I suppose Hart went, simply enough, with a number that was funny just for being riotously large.

Mark Tatulli’s Heart of the City for the 26th places itself on my Grand Avenue warning board. There’s plenty of time for things to go a different way but right now it’s set up for a toxic little presentation of mathematics. Heart, after being grounded, was caught sneaking out to a slumber party and now her mother is sending her to two weeks of Math Camp. I’m supposing, from Tatulli’s general attitude about how stuff happens in Heart and in Lio that Math Camp will not be a horrible, penal experience. But it’s still ominous talk and I’m watching.

Brian Fies’s Mom’s Cancer story for the 26th is part of the strip’s rerun on GoComics. (Many comic strips that have ended their run go into eternal loops on GoComics.) This is one of the strips with mathematical content. The spatial dimension of a thing implies relationships between the volume (area, hypervolume, whatever) of a thing and its characteristic linear measure, its diameter or radius or side length. It can be disappointing.

Nicholas Gurewitch’s Perry Bible Fellowship for the 26th is a repeat of one I get on my mathematics Twitter friends now and then. Should warn, it’s kind of racy content, at least as far as my usual recommendations here go. It’s also a little baffling because while the reveal of the unclad woman is funny … what, exactly, does it mean? The symbols don’t mean anything; they’re just what fits graphically. I think the strip is getting at Dr Loring not being able to see even a woman presenting herself for sex as anything but mathematics. I guess that’s funny, but it seems like the idea isn’t quite fully developed.

Zach Weinersmith’s Saturday Morning Breakfast Cereal Again for the 26th has a mathematician snort about plotting a giraffe logarithmically. This is all about representations of figures. When we plot something we usually start with a linear graph: a couple of axes perpendicular to one another. A unit of movement in the direction of any of those axes represents a constant difference in whatever that axis measures. Something growing ten units larger, say. That’s fine for many purposes. But we may want to measure something that changes by a power law, or that grows (or shrinks) exponentially. Or something that has some region where it’s small and some region where it’s huge. Then we might switch to a logarithmic plot. Here the same difference in space along the axis represents a change that’s constant in proportion: something growing ten times as large, say. The effective result is to squash a shape down, making the higher points more nearly flat.

And to completely smother Weinersmith’s fine enough joke: I would call that plot semilogarithmically. I’d use a linear scale for the horizontal axis, the gazelle or giraffe head-to-tail. But I’d use a logarithmic scale for the vertical axis, ears-to-hooves. So, linear in one direction, logarithmic in the other. I’d be more inclined to use “logarithmic” plots to mean logarithms in both the horizontal and the vertical axes. Those are useful plots for turning up power laws, like the relationship between a planet’s orbital radius and the length of its year. Relationships like that turn into straight lines when both axes are logarithmically spaced. But I might also describe that as a “log-log plot” in the hopes of avoiding confusion.

Reading the Comics, May 13, 2017: Quiet Tuesday Through Saturday Edition


From the Sunday and Monday comics pages I was expecting another banner week. And then there was just nothing from Tuesday on, at least not among the comic strips I read. Maybe Comic Strip Master Command has ordered jokes saved up for the last weeks before summer vacation.

Tony Cochrane’s Agnes for the 7th is a mathematics anxiety strip. It’s well-expressed, since Cochrane writes this sort of hyperbole well. It also shows a common attitude that words and stories are these warm, friendly things, while mathematics and numbers are cold and austere. Perhaps Agnes is right to say some of the problem is familiarity. It’s surely impossible to go a day without words, if you interact with people or their legacies; to go without numbers … well, properly impossible. There’s too many things that have to be counted. Or places where arithmetic sneaks in, such as getting enough money to buy a thing. But those don’t seem to be the kinds of mathematics people get anxious about. Figuring out how much change, that’s different.

I suppose some of it is familiarity. It’s easier to dislike stuff you don’t do often. The unfamiliar is frightening, or at least annoying. And humans are story-oriented. Even nonfiction forms stories well. Mathematics … has stories, as do all human projects. But the mathematics itself? I don’t know. There’s just beautiful ingenuity and imagination in a lot of it. I’d just been thinking of the just beautiful scheme for calculating logarithms from a short table. But it takes time to get to that beauty.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 7th is a fractions joke. It might also be a joke about women concealing their ages. Or perhaps it’s about mathematicians expressing things in needlessly complicated ways. I think that’s less a mathematician’s trait than a common human trait. If you’re expert in a thing it’s hard to resist the puckish fun of showing that expertise off. Or just sowing confusion where one may.

Daniel Shelton’s Ben for the 8th is a kid-doing-arithmetic problem. Even I can’t squeeze some deeper subject meaning out of it, but it’s a slow week so I’ll include the strip anyway. Sorry.

Brian Boychuk and Ron Boychuk’s Chuckle Brothers for the 8th is the return of anthropomorphic-geometry joke after what feels like months without. I haven’t checked how long it’s been without but I’m assuming you’ll let me claim that. Thank you.

Reading the Comics, February 6, 2017: Another Pictureless Half-Week Edition


Got another little flood of mathematically-themed comic strips last week and so once again I’ll split them along something that looks kind of middle-ish. Also this is another bunch of GoComics.com-only posts. Since those seem to be accessible to anyone whether or not they’re subscribers indefinitely far into the future I don’t feel like I can put the comics directly up and will trust you all to click on the links that you find interesting. Which is fine; the new GoComics.com design makes it annoyingly hard to download a comic strip. I don’t think that was their intention. But that’s one of the two nagging problems I have with their new design. So you know.

Tony Cochran’s Agnes for the 5th sees a brand-new mathematics. Always dangerous stuff. But mathematicians do invent, or discover, new things in mathematics all the time. Part of the task is naming the things in it. That’s something which takes talent. Some people, such as Leonhard Euler, had the knack a great novelist has for putting names to things. The rest of us muddle along. Often if there’s any real-world inspiration, or resemblance to anything, we’ll rely on that. And we look for terminology that evokes similar ideas in other fields. … And, Agnes would like to know, there is mathematics that’s about approximate answers, being “right around” the desired answer. Unfortunately, that’s hard. (It’s all hard, if you’re going to take it seriously, much like everything else people do.)

Scott Hilburn’s The Argyle Sweater for the 5th is the anthropomorphic numerals joke for this essay.

Carol Lay’s Lay Lines for the 6th depicts the hazards of thinking deeply and hard about the infinitely large and the infinitesimally small. They’re hard. Our intuition seems well-suited to handing a modest bunch of household-sized things. Logic guides us when thinking about the infinitely large or small, but it takes a long time to get truly conversant and comfortable with it all.

Paul Gilligan’s Pooch Cafe for the 6th sees Poncho try to argue there’s thermodynamical reasons for not being kind. Reasoning about why one should be kind (or not) is the business of philosophers and I won’t overstep my expertise. Poncho’s mathematics, that’s something I can write about. He argues “if you give something of yourself, you inherently have less”. That seems to be arguing for a global conservation of self-ness, that the thing can’t be created or lost, merely transferred around. That’s fair enough as a description of what the first law of thermodynamics tells us about energy. The equation he reads off reads, “the change in the internal energy (Δ U) equals the heat added to the system (U) minus the work done by the system (W)”. Conservation laws aren’t unique to thermodynamics. But Poncho may be aware of just how universal and powerful thermodynamics is. I’m open to an argument that it’s the most important field of physics.

Jonathan Lemon’s Rabbits Against Magic for the 6th is another strip Intro to Calculus instructors can use for their presentation on instantaneous versus average velocities. There’s been a bunch of them recently. I wonder if someone at Comic Strip Master Command got a speeding ticket.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 6th is about numeric bases. They’re fun to learn about. There’s an arbitrariness in the way we represent concepts. I think we can understand better what kinds of problems seem easy and what kinds seem harder if we write them out different ways. But base eleven is only good for jokes.