Reading the Comics, August 16, 2019: The Comments Drive Me Crazy Edition


Last week was another light week of work from Comic Strip Master Command. One could fairly argue that nothing is worth my attention. Except … one comic strip got onto the calendar. And that, my friends, is demanding I pay attention. Because the comic strip got multiple things wrong. And then the comments on GoComics got it more wrong. Got things wrong to the point that I could not be sure people weren’t trolling each other. I know how nerds work. They do this. It’s not pretty. So since I have the responsibility to correct strangers online I’ll focus a bit on that.

Robb Armstrong’s JumpStart for the 13th starts off all right. The early Roman calendar had ten months, December the tenth of them. This was a calendar that didn’t try to cover the whole year. It just started in spring and ran into early winter and that was it. This may seem baffling to us moderns, but it is, I promise you, the least confusing aspect of the Roman calendar. This may seem less strange if you think of the Roman calendar as like a sports team’s calendar, or a playhouse’s schedule of shows, or a timeline for a particular complicated event. There are just some fallow months that don’t need mention.

Joe: 'Originally December was the tenth month of the calendar year. Guess what happens every 823 years? December is about to have five Saturdays, five Sundays, and five Mondays! It's a rare phenomenon!' Crunchy: 'Kinda like a cop who trusts the Internet.'
Robb Armstrong’s JumpStart for the 13th of August, 2019. Essays featuring JumpStart should appear at this link. I am startled to learn that this is a new tag, though. I hope the comic makes more appearances; it’s pleasantly weird in low-key ways. Well, I mean, those are cops driving an ice cream truck and that’s one of the more mundane things about the comic, you know?

Things go wrong with Rob’s claim that December will have five Saturdays, five Sundays, and five Mondays. December 2019 will have no such thing. It has four Saturdays. There are five Sundays, Mondays, and Tuesdays. From Crunchy’s response it sounds like Joe’s run across some Internet Dubious Science Folklore. You know, where you see a claim that (like) Saturn will be larger in the sky than anytime since the glaciers receded or something. And as you’d expect, it’s gotten a bit out of date. December 2018 had five Saturdays, Sundays, and Mondays. So did December 2012. And December 2007.

And as this shows, that’s not a rare thing. Any month with 31 days will have five of some three days in the week. August 2019, for example, has five Thursdays, Fridays, and Saturdays. October 2019 will have five Tuesdays, Wednesdays, and Thursdays. This we can show by the pigeonhole principle. And there are seven months each with 31 days in every year.

It’s not every year that has some month with five Saturdays, Sundays, and Mondays in it. 2024 will not, for example. But a lot of years do. I’m not sure why December gets singled out for attention here. From the setup about December having long ago been the tenth month, I guess it’s some attempt to link the fives of the weekend days to the ten of the month number. But we get this kind of December about every five or six years.

This 823 years stuff, now that’s just gibberish. The Gregorian calendar has its wonders and mysteries yes. None of them have anything to do with 823 years. Here, people in the comments got really bad at explaining what was going on.

So. There are fourteen different … let me call them year plans, available to the Gregorian calendar. January can start on a Sunday when it is a leap year. Or January can start on a Sunday when it is not a leap year. January can start on a Monday when it is a leap year. January can start on a Monday when it is not a leap year. And so on. So there are fourteen possible arrangements of the twelve months of the year, what days of the week the twentieth of January and the thirtieth of December can occur on. The incautious might think this means there’s a period of fourteen years in the calendar. This comes from misapplying the pigeonhole principle.

Here’s the trouble. January 2019 started on a Tuesday. This implies that January 2020 starts on a Wednesday. January 2025 also starts on a Wednesday. But January 2024 starts on a Monday. You start to see the pattern. If this is not a leap year, the next year starts one day of the week later than this one. If this is a leap year, the next year starts two days of the week later. This is all a slightly annoying pattern, but it means that, typically, it takes 28 years to get back where you started. January 2019 started on Tuesday; January 2020 on Wednesday, and January 2021 on Friday. the same will hold for January 2047 and 2048 and 2049. There are other successive years that will start on Tuesday and Wednesday and Friday before that.

Except.

The important difference between the Julian and the Gregorian calendars is century years. 1900. 2000. 2100. These are all leap years by the Julian calendar reckoning. Most of them are not, by the Gregorian. Only century years divisible by 400 are. 2000 was a leap year; 2400 will be. 1900 was not; 2100 will not be, by the Gregorian scheme.

These exceptions to the leap-year-every-four-years pattern mess things up. The 28-year-period does not work if it stretches across a non-leap-year century year. By the way, if you have a friend who’s a programmer who has to deal with calendars? That friend hates being a programmer who has to deal with calendars.

There is still a period. It’s just a longer period. Happily the Gregorian calendar has a period of 400 years. The whole sequence of year patterns from 2000 through 2019 will reappear, 2400 through 2419. 2800 through 2819. 3200 through 3219.

(Whether they were also the year patterns for 1600 through 1619 depends on where you are. Countries which adopted the Gregorian calendar promptly? Yes. Countries which held out against it, such as Turkey or the United Kingdom? No. Other places? Other, possibly quite complicated, stories. If you ask your computer for the 1619 calendar it may well look nothing like 2019’s, and that’s because it is showing the Julian rather than Gregorian calendar.)

Except.

This is all in reference to the days of the week. The date of Easter, and all of the movable holidays tied to Easter, is on a completely different cycle. Easter is set by … oh, dear. Well, it’s supposed to be a simple enough idea: the Sunday after the first spring full moon. It uses a notional moon that’s less difficult to predict than the real one. It’s still a bit of a mess. The date of Easter is periodic again, yes. But the period is crazy long. It would take 5,700,000 years to complete its cycle on the Gregorian calendar. It never will. Never try to predict Easter. It won’t go well. Don’t believe anything amazing you read about Easter online.

Norm, pondering: 'I have a new theory about life.' (Illustrated with a textbook, 'Quantum Silliness'.) 'It's not as simple as everything-is-easy, or everything-is-hard.' (Paper with 1 + 1 = 2; another with Phi = BA.) 'Instead, life is only hard when it should be easy and easy when it's expected to be hard. That way you're never prepared.' (The papers are torn up.) Friend: 'Seems to me you've stepped right into the middle of chaos theory.' Norm: 'Or just my 30s.'
Michael Jantze’s The Norm (Classics) for the 15th of August, 2019. I had just written how I wanted to share this strip more. Essays about The Norm, both the current (“4.0”) run and older reruns (“Classics”), are at this link.

Michael Jantze’s The Norm (Classics) for the 15th is much less trouble. It uses some mathematics to represent things being easy and things being hard. Easy’s represented with arithmetic. Hard is represented with the calculations of quantum mechanics. Which, oddly, look very much like arithmetic. \phi = BA even has fewer symbols than 1 + 1 = 2 has. But the symbols mean different abstract things. In a quantum mechanics context, ‘A’ and ‘B’ represent — well, possibly matrices. More likely operators. Operators work a lot like functions and I’m going to skip discussing the ways they don’t. Multiplying operators together — B times A, here — works by using the range of one function as the domain of the other. Like, imagine ‘B’ means ‘take the square of’ and ‘A’ means ‘take the sine of’. Then ‘BA’ would mean ‘take the square of the sine of’ (something). The fun part is the ‘AB’ would mean ‘take the sine of the square of’ (something). Which is fun because most of the time, those won’t have the same value. We accept that, mathematically. It turns out to work well for some quantum mechanics properties, even though it doesn’t work like regular arithmetic. So \phi = BA holds complexity, or at least strangeness, in its few symbols.

Moose, bringing change and food back from the beach snack stand: 'Arch gave me five and a single so he gets ... $2.11 in change!' Archie: 'Right, Moose! Thanks!' (To Betty.) 'Notice how Moose can do math faster at the beach than he can anywhere else?' Betty: 'Why is that?' Moose, pointing to his feet: 'Easy! I don't have to take off my shoes to count my toes!'
Henry Scarpelli and Craig Boldman’s Archie rerun for the 16th of August, 2019. Essays exploring something mentioned by Archie ought to be at this link. The strip is in perpetual reruns but I don’t think I’ve exhausted the cycle of comics they reprint yet.

Henry Scarpelli and Craig Boldman’s Archie for the 16th is a joke about doing arithmetic on your fingers and toes. That’s enough for me.


There were some more comic strips which just mentioned mathematics in passing.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers rerun for the 11th has a blackboard of mathematics used to represent deep thinking. Also, it I think, the colorist didn’t realize that they were standing in front of a blackboard. You can see mathematicians doing work in several colors, either to convey information in shorthand or because they had several colors of chalk. Not this way, though.

Mark Leiknes’s Cow and Boy rerun for the 16th mentions “being good at math” as something to respect cows for. The comic’s just this past week started over from its beginning. If you’re interested in deeply weird and long-since cancelled comics this is as good a chance to jump on as you can get.

And Stephen ‘s Herb and Jamaal rerun for the 16th has a kid worried about a mathematics test.


That’s the mathematically-themed comic strips for last week. All my Reading the Comics essays should be at this link. I’ve traditionally run at least one essay a week on Sunday. But recently that’s moved to Tuesday for no truly compelling reason. That seems like it’s working for me, though. I may stick with it. If you do have an opinion about Sunday versus Tuesday please let me know.

Don’t let me know on Twitter. I continue to have this problem where Twitter won’t load on Safari. I don’t know why. I’m this close to trying it out on a different web browser.

And, again, I’m planning a fresh A To Z sequence. It’s never to early to think of mathematics topics that I might explain. I should probably have already started writing some. But you’ll know the official announcement when it comes. It’ll have art and everything.

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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.

Reading the Comics, May 11, 2019: I Concede I Am Late Edition


I concede I am late in wrapping up last week’s mathematically-themed comics. But please understand there were important reasons for my not having posted this earlier, like, I didn’t get it written in time. I hope you understand and agree with me about this.

Bill Griffith’s Zippy the Pinhead for the 9th brings up mathematics in a discussion about perfection. The debate of perfection versus “messiness” begs some important questions. What I’m marginally competent to discuss is the idea of mathematics as this perfect thing. Mathematics seems to have many traits that are easy to think of as perfect. That everything in it should follow from clearly stated axioms, precise definitions, and deductive logic, for example. This makes mathematics seem orderly and universal and fair in a way that the real world never is. If we allow that this is a kind of perfection then … does mathematics reach it?

Sluggo: 'You don't mess with perfection, Zippy.' Zippy: 'Sluggo, are you saying you're perfect?' Sluggo: 'Yes. I am perfect.' Zippy: 'And I am perfect too, Sluggo, huh?' Sluggo: 'No. You are not perfect. Your lines and your circles are irregular and messy.' Zippy: 'Which is better, Sluggo, perfect or messy?' Sluggo: 'Perfect is better. In a fight between messy and perfect, Sluggo always kills Zippy!' Zippy: 'In lieu of a human sacrifice, please accept this perfect parallelogram!'
Bill Griffith’s Zippy the Pinhead for the 9th of May, 2019. I am surprised to learn this is not a new tag. Essays discussing Zippy the Pinhead are at this link. Ernie, here, is Ernie Bushmiller, creator and longtime artist and writer for Nancy. He’s held in regard by some of the art community for his economic and streamlined drawing and writing style. You might or might not like his jokes, but you can’t deny that he made it easy to understand what was supposed to be funny and why it was supposed to be. It’s worth study if you like to know how comic strips can work.

Even the idea of a “precise definition” is perilous. If it weren’t there wouldn’t be so many pop mathematics articles about why 1 isn’t a prime number. It’s difficult to prove that any particular set of axioms that give us interesting results are also logically consistent. If they’re not consistent, then we can prove absolutely anything, including that the axioms are false. That seems imperfect. And few mathematicians even prepare fully complete, step-by-step proofs of anything. It takes ridiculously long to get anything done if you try. The proofs we present tend to show, instead, the reasoning in enough detail that we’re confident we could fill in the omitted parts if we really needed them for some reason. And that’s fine, nearly all the time, but it does leave the potential for mistakes present.

Zippy offers up a perfect parallelogram. Making it geometry is of good symbolic importance. Everyone knows geometric figures, and definitions of some basic ideas like a line or a circle or, maybe, a parallelogram. Nobody’s ever seen one, though. There’s never been a straight line, much less two parallel lines, and even less the pair of parallel lines we’d need for a parallellogram. There can be renderings good enough to fool the eye. But none of the lines are completely straight, not if we examine closely enough. None of the pairs of lines are truly parallel, not if we extend them far enough. The figure isn’t even two-dimensional, not if it’s rendered in three-dimensional things like atoms or waves of light or such. We know things about parallelograms, which don’t exist. They tell us some things about their shadows in the real world, at least.

Business Man on phone: 'A trillion is still a stop-and-think decision for me.'
Mark Litzler’s Joe Vanilla for the 9th of May, 2019. And this one is just barely not a new tag. This and other essays mentioning Joe Vanilla should be at this link.

Mark Litzler’s Joe Vanilla for the 9th is a play on the old joke about “a billion dollars here, a billion dollars there, soon you’re talking about real money”. As we hear more about larger numbers they seem familiar and accessible to us, to the point that they stop seeming so big. A trillion is still a massive number, at least for most purposes. If you aren’t doing combinatorics, anyway; just yesterday I was doing a little toy problem and realized it implied 470,184,984,576 configurations. Which still falls short of a trillion, but had I made one arbitrary choice differently I could’ve blasted well past a trillion.

A Million Monkeys At A Million Typewriters. Scene of many monkeys on typewriters. One pauses, and thinks, and eventually pulls a bottle of liquor from the desk, thinking: 'But how can I credibly delay Hamlet's revenge until Act V?'
Ruben Bolling’s Super-Fun-Pak Comix for the 9th of May, 2019. This one I knew wouldn’t be a new tag, not with how nerdy-but-in-the-good-ways Ruben Bolling writes. Essays mentioning Super-Fun-Pak Comix are at this link.

Ruben Bolling’s Super-Fun-Pak Comix for the 9th is another monkeys-at-typewriters joke, that great thought experiment about probability and infinity. I should add it to my essay about the Infinite Monkey Theorem. Part of the joke is that the monkey is thinking about the content of the writing. This doesn’t destroy the prospect that a monkey given enough time would write any of the works of William Shakespeare. It makes the simple estimates of how unlikely that is, and how long it would take to do, invalid. But the event might yet happen. Suppose this monkey decided there was no credible way to delay Hamlet’s revenge to Act V, and tried to write accordingly. Mightn’t the monkey make a mistake? It’s easy to type a letter you don’t mean to. Or a word you don’t mean to. Why not a sentence you don’t mean to? Why not a whole act you don’t mean to? Impossible? No, just improbable. And the monkeys have enough time to let the improbable happen.

A big wobbly scribble. Caption; 'Eric the Circle in the 20th dimension, where shape has no meaning.'
Eric the Circle, this by Kingsnake, for the 10th of May, 2019. I keep figuring to retire Eric the Circle as it seems to be all in reruns. But then I keep finding strips that, as far as I can tell, I haven’t discussed before. Essays about stuff raised by Eric the Circle should be at this link.

Eric the Circle for the 10th, this one by Kingsnake, declares itself set in “the 20th dimension, where shape has no meaning”. This plays on a pop-cultural idea of dimensions as a kind of fairyland, subject to strange and alternate rules. A mathematician wouldn’t think of dimensions that way. 20-dimensional spaces — and even higher-dimensional spaces — follow rules just as two- and three-dimensional spaces do. They’re harder to draw, certainly, and mathematicians are not selected for — or trained in — drawing, at least not in United States schools. So attempts at rendering a high-dimensional space tend to be sort of weird blobby lumps, maybe with a label “N-dimensional”.

And a projection of a high-dimensional shape into lower dimensions will be weird. I used to have around here a web site with a rotatable tesseract, which would draw a flat-screen rendition of what its projection in three-dimensional space would be. But I can’t find it now and probably it ran as a Java applet that you just can’t get to work anymore. Anyway, non-interactive videos of this sort of thing are common enough; here’s one that goes through some of the dimensions of a tesseract, one at a time. It’ll give some idea how something that “should” just be a set of cubes will not look so much like that.

Hayden: 'I don't need to know long division because there's a calculator on my phone.' Dustin: 'What happens if someday you don't have a phone?' Hayden: 'Then I've got problems long division won't solve.'
Steve Kelly and Jeff Parker’s Dustin for the 11th of May, 2019. And, you know, this strip is just out there, doing its business. Essays about some topic raised by Dustin are at this link.

Steve Kelly and Jeff Parker’s Dustin for the 11th is a variation on the “why do I have to learn this” protest. This one is about long division and the question of why one needs to know it when there’s cheap, easily-available tools that do the job better. It’s a fair question and Hayden’s answer is a hard one to refute. I think arithmetic’s worth knowing how to do, but I’ll also admit, if I need to divide something by 23 I’m probably letting the computer do it.


And a couple of the comics that week seemed too slight to warrant discussion. You might like them anyway. Brian Boychuk and Ron Boychuk’s Chuckle Brothers for the 5th featured a poorly-written numeral. Charles Schulz’s Peanuts Begins rerun for the 6th has Violet struggling with counting. Glenn McCoy and Gary McCoy’s The Flying McCoys for the 8th has someone handing in mathematics homework. Henry Scarpelli and Craig Boldman’s Archie rerun for the 9th talks about Jughead sleeping through mathematics class. All routine enough stuff.


This and other Reading the Comics posts should appear at this link. I mean to have a post tomorrow, although it might make my work schedule a little easier to postpone that until Monday. We’ll see.

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, October 18, 2018: Quick Half-Week Edition


There were enough mathematically-themed comic strips last week to split across two essays. The first half of them don’t take too much time to explain. Let me show you.

Henry Scarpelli and Craig Boldman’s Archie for the 15th is the pie-chart wordplay joke for the week. I don’t remember there ever being pie at the high school cafeteria, but back when I was in high school I often skipped lunch to hang out in the computer room.

Jughead: 'Ummm! Nummm!' Archie: 'Quiet, Jug! We've got to get this group project finished!' Jughead: 'Mmm! I'm hungry! I'm off to the lunchroom for a snack!' Archie: 'I told you it was a mistake to include a pie chart in our report!'
Henry Scarpelli and Craig Boldman’s Archie rerun for the 15th of October, 2018. Oh gads. If Jughead makes this much noise just imagining food then when he really eats he’s got to be one of those people you can hear from the next state over. I have no information about when this strip first ran.

Will Henry’s Wallace the Brave for the 15th alludes to a report on trapezoids. I can’t imagine what about this would be so gold-star-worthy when I’ve surely already written plenty about trapezoids. … Really, that thing trying to classify how many different kinds of trapezoids there are would be my legacy to history if I hadn’t also written about how many grooves are on a record’s side.

Teacher: 'Wallace, Spud, fantastic report on trapezoids. Gold stars for each.' (Both are delighted; girl in the back says 'Lamesville.') Spud: 'I haven't gotten a gold star since I got my head stuck in that bannister.' Wallace: 'They buttered you up like an ear of corn.'
Will Henry’s Wallace the Brave for the 15th of October, 2018. All right, the strip is only marginally on topic. It and Breaking Cat News are the syndicated comic strips I’ve been most excited for since Richard Thompson wasn’t able to continue Cul de Sac.

Thaves’s Frank and Ernest for the 17th is, for me, extremely relatable content. I don’t say that my interest in mathematics is entirely because there was this Berenstain Bears book about jobs which made it look like a mathematician’s job was to do sums in an observatory on the Moon. But it didn’t hurt. When I joke about how seven-year-old me wanted to be the astronaut who drew Popeye, understand, that’s not much comic exaggeration.

Student in mathematics class: 'I'd like a career where I solve simple subtraction problems like this. I'd be making a difference.'
Thaves’s Frank and Ernest for the 17th of October, 2018. “I’d be getting taped to the doors of mathematics teacher’s classrooms — saaaaaay!”

Justin Thompson’s Mythtickle rerun for the 17th is a timely choice about lotteries and probabilities. Vlad raises a fair point about your chance of being struck by lightning. It seems like that’s got to depend on things like where you are. But it does seem like we know what we mean when we say “the chance you’ll be hit by lightning”. At least I think it means “the probability that a person will be hit by lightning at some point in their life, if we have no information about any environmental facts that might influence this”. So it would be something like the number of people struck by lightning over the course of a year divided by the number of people in the world that year. You might have a different idea of what “the chance you’ll be hit by lightning” means, and it’s worth trying to think what precisely that does mean to you.

Dziva: 'Lottery tickets? Are you bats? Vlad, your chances of getting hit by lightning are better than winning a lottery jackpot.' Vlad: 'Lightning where? The location of the lightning is a variable that should be included in your determination. So do you mean like, lightning in the Atacama Desert where it never rains, or like lightning in, say, Transylvania? Cause back home, let me tell ya ... ' Dziva: 'Oh, I got it, I got it, I ... um.' [ Transylvanian convenience store with a werewolf cashier; lightning outside. ] Dziva: 'Two computer lotto-picks on the BIG one and make it SNAPPY, wolfie!!!'
Justin Thompson’s Mythtickle rerun for the 17th of October, 2018. Not to step on a joke Thompson left nicely underplayed, but I find funny the premise that of course the clerk in the Transylvanian convenience store is a werewolf. I have no information about when this strip first ran.

Lotteries are one of those subjects that a particular kind of nerd likes to feel all smug about. Pretty sure every lottery comic ever has drawn a comment about a tax on people who can’t do mathematics. This one did too. But then try doing the mathematics. The Mega Millions lottery, in the US, has a jackpot for the first drawing this week estimated at more than a billion dollars. The chance of winning is about one in 300 million. A ticket costs two dollars. So what is the expectation value of playing? You lose two dollars right up front, in the cost of the ticket. What do you get back? A one-in-300-million chance of winning a billion dollars. That is, you can expect to get back a bit more than three dollars. The implication is: you make a profit of dollar on each ticket you buy. There’s something a bit awry here, as you can tell from my decision not to put my entire savings into lottery tickets this week. But I won’t say someone is foolish or wrong if they buy a couple.

Student, to the teacher in front of a blackboard full of symbols: 'Can't you just round it off?'
Mike Baldwin’s Cornered for the 18th of October, 2018. What is that grit on the teacher’s desk, to the reader’s right of the pen?

Mike Baldwin’s Cornered for the 18th is a bit of mathematics-circling wordplay, featuring the blackboard full of equations. The blackboard doesn’t have any real content on it, but it is a good visual shorthand. And it does make me notice that rounding a quantity off is, in a way, making it simpler. If we are only a little interested in the count of the thing, “two thousand forty” or even “two thousand” may be more useful than the exact 2,038. The loss of precision may be worth it for the ease with which the rounded-off version is remembered and communicated.


If you’d like to see more Reading the Comics posts then try this link. Other essays which mention Archie should be at this link. Topics raised by Wallace the Brave should be at this link. Frank and Ernest is the subject of essays at this link. Topics brought up by Mythtickle are at this link. It’s a new tag, though, and I’m not sure there’ll ever be another use of it. And this and other essays mentioning Cornered are at this link. And do please stick around for more of my Fall 2018 Mathematics A-To-Z, coming twice a week through the rest of the year, I hope.

Reading the Comics, May 18, 2018: Quincy Doesn’t Make The Cut Edition


I hate to disillusion anyone but I lack hard rules about what qualifies as a mathematically-themed comic strip. During a slow week, more marginal stuff makes it. This past week was going slow enough that I tagged Wednesday’s Quincy rerun, from March of 1979 for possible inclusion. And all it does is mention that Quincy’s got a mathematics test due. Fortunately for me the week picked up a little. It cheats me of an excuse to point out Ted Shearer’s art style to people, but that’s not really my blog’s business.

Also it may not surprise you but since I’ve decided I need to include GoComics images I’ve gotten more restrictive. Somehow the bit of work it takes to think of a caption and to describe the text and images of a comic strip feel like that much extra work.

Roy Schneider’s The Humble Stumble for the 13th of May is a logic/geometry puzzle. Is it relevant enough for here? Well, I spent some time working it out. And some time wondering about implicit instructions. Like, if the challenge is to have exactly four equally-sized boxes after two toothpicks are moved, can we have extra stuff? Can we put a toothpick where it’s just a stray edge, part of no particular shape? I can’t speak to how long you stay interested in this sort of puzzle. But you can have some good fun rules-lawyering it.

Dad: A guy showed me a brain teaser down at the coffee shop. Watch.' Molly: Ooh, coolie! I'm good at these!' Dad: 'OK, you've got 5 equal-sized boxes here ... moving only 2 toothpicks, make it into FOUR equal-size boxes.' (It's three matchstick boxes in the top row, and two underneath, with the rightmost of the top row above the leftmost of the bottom row.) Dad: 'Heh-heh! THAT ought to keep you busy for a while!' Molly: 'I'll have it in a minute.' Silent final panel, Molly there, bloodshot eyes, late at night.
Roy Schneider’s The Humble Stumble rerun for the 13th of May, 2018. This originally ran the 18th of August, 2006, but I wasn’t doing mathematics blogs back then. Also, Molly there is me with any mathematics puzzle, which is why I panic whenever someone brings one to me. This is a new tag for the comic strip.

Jeff Harris’s Shortcuts for the 13th is a children’s informational feature about Aristotle. Aristotle is renowned for his mathematical accomplishments by many people who’ve got him mixed up with Archimedes. Aristotle it’s harder to say much about. He did write great texts that pop-science writers credit as giving us the great ideas about nature and physics and chemistry that the Enlightenment was able to correct in only about 175 years of trying. His mathematics is harder to summarize though. We can say certainly that he knew some mathematics. And that he encouraged thinking of subjects as built on logical deductions from axioms and definitions. So there is that influence.

A panel full of jokes, activities, and trivia relating to Aristotle. There's no way for me to summarize it all (which includes a word search and a maze as activities) in the space available.
Jeff Harris’s Shortcuts for the 13th of May, 2018. That demonstration of Aristotle’s syllogisms is the same one I see when I search DuckDuckGo for ‘aristotle mathematics’ so it must come right from his texts that I’ve never read! That’s how citations work, right?

Dan Thompson’s Brevity for the 15th is a pun, built on the bell curve. This is also known as the Gaussian distribution or the normal distribution. It turns up everywhere. If you plot how likely a particular value is to turn up, you get a shape that looks like a slightly melted bell. In principle the bell curve stretches out infinitely far. In practice, the curve turns into a horizontal line so close to zero you can’t see the difference once you’re not-too-far away from the peak.

Baseball manager warning the player, 'Watch out, he's got a wicked curve'. The pitcher is a classic hand-style bell with clapper, and also arms and a glove and ball.
Dan Thompson’s Brevity for the 15th of May, 2018. I am curious whether there’s any significance to Thompson’s uniforms, particularly the player having a ‘B’ camp and a ‘U’ shoulder patch. I don’t think there’s an obvious relevance to the statistics jokes being made.

Jason Chatfield’s Ginger Meggs for the 16th I assume takes place in a mathematics class. I’m assuming the question is adding together four two-digit numbers. But “what are 26, 24, 33, and 32” seems like it should be open to other interpretations. Perhaps Mr Canehard was asking for some class of numbers those all fit into. Integers, obviously. Counting numbers. Compound numbers rather than primes. I keep wanting to say there’s something deeper, like they’re all multiples of three (or something) but they aren’t. They haven’t got any factors other than 1 in common. I mention this because I’d love to figure out what interesting commonality those numbers have and which I’m overlooking.

Teacher: 'Meggs! Pop quiz: what are 26, 24, 33, and 32?' Ginger Meggs, after a panel of silent thought: 'Your last four payslips?'
Jason Chatfield’s Ginger Meggs for the 16th of May, 2018. Little surprised Ginger didn’t name cricketeers with those uniform numbers, trusting that cricket players have uniform numbers.

Ed Stein’s Freshly Squeezed for the 17th is a story problem strip. Bit of a passive-aggressive one, in-universe. But I understand why it would be formed like that. The problem’s incomplete, as stated. There could be some fun in figuring out what extra bits of information one would need to give an answer. This is another new-tagged comic.

Nate, the son: 'We're supposed to do today's homework with our parents.' Mom: 'Okay.' Nate: '1. If there are 28 kids in a class, and the education budget is cut by $465 million, how many will be in the class next year?' Dad: 'Taking parental involvement to the next level.' Nate: '2. If the teacher's insurance doesn't cover nervous breakdowns ... '
Ed Stein’s Freshly Squeezed rerun for the 17th of May, 2018. This originally ran the 5th of May, 2011 and maybe I even featured it then. … No, it doesn’t look like I did. Well, I can only imagine how very well this appeal to the parents of the school district under guise of homework went over!

Henry Scarpelli and Craig Boldman’s Archie for the 19th name-drops calculus, credibly, as something high schoolers would be amazed to see one of their own do in their heads. There’s not anything on the blackboard that’s iconically calculus, it happens. Dilton’s writing out a polynomial, more or less, and that’s a fit subject for high school calculus. They’re good examples on which to learn differentiation and integration. They’re a little more complicated than straight lines, but not too weird or abstract. And they follow nice, easy-to-summarize rules. But they turn up in high school algebra too, and can fit into geometry easily. Or any subject, really, as remember, everything is polynomials.

Archie: 'It's amazing how Dilton can do calculus in his head!' Reggie: 'Yeah, I suppose! I guess I'll settle for being the school's most admired athlete and greatest sex symbol!' Jughead: 'It's amazing how Reggie does all that in *his* head, too!'
Henry Scarpelli and Craig Boldman’s Archie rerun for the 19th of May, 2018. And yeah, C^2 + x + 1) isn’t really a coherent expression. It’s either missing a ( mark or, if the C is the open-parentheses, then it’s got nothing-in-particular squared. Also I am so bothered to have close-parentheses and open-parentheses out of order that last sentence. You have no idea.

Mark Anderson’s Andertoons for the 19th is Mark Anderson’s Andertoons for the week. Glad that it’s there. Let me explain why it is proper construction of a joke that a Fibonacci Division might be represented with a spiral. Fibonacci’s the name we give to Leonardo of Pisa, who lived in the first half of the 13th century. He’s most important for explaining to the western world why these Hindu-Arabic numerals were worth learning. But his pop-cultural presence owes to the Fibonacci Sequence, the sequence of numbers 1, 1, 2, 3, 5, 8, and so on. Each number’s the sum of the two before it. And this connects to the Golden Ratio, one of pop mathematics’ most popular humbugs. As the terms get bigger and bigger, the ratio between a term and the one before it gets really close to the Golden Ratio, a bit over 1.618.

Business group looking at a slide showing the golden spiral. Speaker: 'And, as you can see, the Fibonacci division is right on track.'
Mark Anderson’s Andertoons for the 19th of May, 2018. I wonder which direction it’s moving in.

So. Draw a quarter-circle that connects the opposite corners of a 1×1 square. Connect that to a quarter-circle that connects opposite corners of a 2×2 square. Connect that to a quarter-circle connecting opposite corners of a 3×3 square. And a 5×5 square, and an 8×8 square, and a 13×13 square, and a 21×21 square, and so on. Yes, there are ambiguities in the way I’ve described this. I’ve tried explaining how to do things just right. It makes a heap of boring words and I’m trying to reduce how many of those I write. But if you do it the way I want, guess what shape you have?

And that is why this is a correctly-formed joke about the Fibonacci Division.

Reading the Comics, April 11, 2018: Obscure Mathematical Terms Edition


I’d like to open today’s installment with a trifle from Thomas K Dye. He’s a friend, and the cartoonist behind the long-running web comic Newshounds, its new spinoff Infinity Refugees, and some other projects.

Dye also has a Patreon, most recently featuring a subscribers-only web comic. And he’s good enough to do the occasional bit of spot art to spruce up my work here.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 9th of April, 2018 is, for me, relatable. I think I’ve read off this anecdote before. The first time I took Real Analysis I was completely lost. Getting me slightly less lost was borrowing a library book on Real Analysis from the mathematics library. The book was in French, a language I can only dimly read. But the different presentation and, probably, the time I had to spend parsing each sentence helped me get a basic understanding of the topic. So maybe trying algebra upside-down isn’t a ridiculous idea.

Archie: 'I can't make any sense out of this algebra!' Jughead: 'Er, Arch! Your book is upside-down!' Archie: 'Yeah, I know! I already tried it the other way, and it didn't make sense then either!'
Henry Scarpelli and Craig Boldman’s Archie rerun for the 9th of April, 2018. Finally, an artistic explanation for putting the name of the book being read on house left!

Lincoln Pierce’s Big Nate rerun for the 9th presents an arithmetic sequence, which is always exciting to work with, if you’re into sequences. I had thought Nate was talking about mathematics quizzes but I see that’s not specified. Could be anything. … And yes, there is something cool in finding a pattern. Much of mathematics is driven by noticing, or looking for, patterns in things and then describing the rules by which new patterns can be made. There’s many easy side questions to be built from this. When would quizzes reach a particular value? When would the total number of points gathered reach some threshold? When would the average quiz score reach some number? What kinds of patterns would match the 70-68-66-64 progression but then do something besides reach 62 next? Or 60 after that? There’s some fun to be had. I promise.

Nate: 'Four quizzes ago, I got a 70. Three quizzes ago, I got a 68. Two quizzes ago, I got a 66, and last quiz I got a 64! See the pattern?' Francis: 'The pattern of academic incompetence?' Nate: 'No, the way it keeps decreasing by twos! Isn't that COOL?'
Lincoln Pierce’s Big Nate rerun for the 9th of April, 2018. Trick question: there’s infinitely many sequences that would start 70, 68, 66, 64. But when we extrapolate this sort of thing we tend to assume that it’ll be some simple sequence. These are often arithmetic — each term increasing or decreasing by the same amount — or geometric — each term the same multiple of the one before. They don’t have to be. These are just easy ones to look for and often turn out well, or at least useful.

Mike Thompson’s Grand Avenue for the 10th is one of the resisting-the-teacher’s-problem style. The problem’s arithmetic, surely for reasons of space. The joke doesn’t depend on the problem at all.

Teacher: 'Gabby, can you solve the problem?' [ '33 x 22' on the blackboard. ] Gabby: 'No, thank you. You're the adult, so I'll let you solve the problem. Why do you need a kid? Adults are able to solve problems on their own.' [ Gabby sits outside the Principal's office, thinking ] 'Looks like he solved his problem after all.'
Mike Thompson’s Grand Avenue for the 10th of April, 2018. My grudge against Grand Avenue is well-established and I fear it will make people think I am being needlessly picky at this. But Gabby’s protest would start from a logical stance if the teacher asked “Would you solve the problem?” Then she’d have reason to argue that adults should be able to solve the problem. “Can” you doesn’t reflect on who ought to solve arithmetic problems.

Dave Whamond’s Reality Check for the 10th similarly doesn’t depend on what the question is. It happens to be arithmetic, but it could as easily be identifying George Washington or picking out the noun in a sentence.

Dog reading an exam: 'Do you know the square root of 81? Do you? Do you? Yes, you do!'
Dave Whamond’s Reality Check for the 10th of April, 2018. I keep wanting to think the exam is playing on the pun between K-9 and canine but it’s not quite there.

Leigh Rubin’s Rubes for the 10th riffs on randomness. In this case it’s riffing on the unpredictability and arbitrariness of random things. Random variables are very interesting in certain fields of mathematics. What makes them interesting is that any specific value — the next number you generate — is unpredictable. But aggregate information about the values is predictable, often with great precision. For example, consider normal distributions. (A lot of stuff turns out to be normal.) In that case we can be confident that the values that come up most often are going to be close to the arithmetic mean of a bunch of values. And that there’ll be about as many values greater than the mean as there are less than the mean. And this will be only loosely true if you’ve looked at a handful of values, at ten or twenty or even two hundred of them. But if you looked at, oh, a hundred thousand values, these truths would be dead-on. It’s wonderful and it seems to defy intuition. It just works.

Door to the Randomness Research Institute. Sign hanging on the doorknob: 'Be Back In: (Your Guess Is As Good As Ours.)'
Leigh Rubin’s Rubes for the 10th of April, 2018. My guess, in the absence of other information, would be “back in about as long as the last time we were out”. In surprisingly many cases your best plausible guess about what the next result should be is whatever the last result was.

John Atkinson’s Wrong Hands for the 10th is the anthropomorphic numerals joke for the week. It’s easy to think of division as just making numbers smaller: 4 divided by 6 is less than either 4 or 6. 1 divided by 4 is less than either 1 or 4. But this is a bad intuition, drawn from looking at the counting numbers that don’t look boring. But 4 divided by 1 isn’t less than either 1 or 4. Same with 6 divided by 1. And then when we look past counting numbers we realize that’s not always so. 6 divided by ½ gives 12, greater than either of those numbers, and I don’t envy the teachers trying to explain this to an understandably confused student. And whether 6 divided by -1 gives you something smaller than 6 or smaller than -1 is probably good for an argument in an arithmetic class.

'The Great Divide'. Numeral 6, looking at an obelus, and speaking to a 4 and a 1; 'It's the guy from division. Looks like we're downsizing'.
John Atkinson’s Wrong Hands for the 10th of April, 2018. Oh yeah, remember a couple months ago when the Internet went wild about how ÷ was a clever way of representing fractions, with the dots representing the numerator and denominator? … Yeah, that wasn’t true, but it’s a great mnemonic.

Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 11th has an argument about predicting humans mathematically. It’s so very tempting to think people can be. Some aspects of people can. In the founding lore of statistics is the astonishment at how one could predict how many people would die, and from what causes, over a time. No person’s death could be forecast, but their aggregations could be. This unsettles people. It should: it seems to defy reason. It seems to me even people who embrace a deterministic universe suppose that while, yes, a sufficiently knowledgeable creature might forecast their actions accurately, mere humans shouldn’t be sufficiently knowledgeable.

Priti: 'Did you know that all human culture can be represented with GRAPHS?!' Sloan: 'Doubtful. Here. Read Machiavelli, Durkheim, and Montesquieu.' Priti: 'I see a lot of French and a lack of graphs.' Sloan: 'Not everything can be represented graphical [sic]. Plus it's full of CITATIONS! Wonderful, wonderful citations!' Priti: 'So, you don't think your behavior can be predicted mathematically?' Sloan: 'Correct.' Priti: 'Predictable'.
Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 11th of April, 2018. So when James Webb, later of NASA fame, was named Under-Secretary of State in 1949 one of his projects was to bring more statistical measure to foreign affairs. He had done much to quantify economic measures, as head of the Bureau of the Budget. But he wasn’t able to overcome institutional skepticism (joking about obvious nonsense like “Bulgaria is down a point!”), and spent his political capital instead on a rather necessary reorganization of the department. That said, I would not trust the wildly enthusiastic promises of any pop mathematics book proclaiming human cultures can be represented by any simple numerical structure.

No strips are tagged for the first time this essay. Just noticing.

Reading the Comics, November 11, 2017: Pictured Comics Edition


And now the other half of last week’s comic strips. It was unusually rich in comics that come from Comics Kingdom or Creators.com, which have limited windows of access and therefore make me feel confident I should include the strips so my comments make any sense.

Rick Kirkman and Jerry Scott’s Baby Blues for the 9th mentions mathematics homework as a resolutely rage-inducing topic. It’s mathematics homework, obviously, or else it wouldn’t be mentioned around here. And even more specifically it’s Common Core mathematics homework. So it always is with attempts to teach subjects better. Especially mathematics, given how little confidence people have in their own mastery. I can’t blame parents for supposing any change to be just malice.

Boxing instructor: 'Now focus, Wanda! Think of something that makes you really angry, and take it out on the [punching] bag!' Wanda: 'HARD WATER SPOTS ON THE GLASSWARE!' She punches the bag hard enough to rip it apart. Instructor: 'Okay then ... ' Wanda: 'If I had pictured Common Core math homework, I could've put that sucker through the wall.'
Rick Kirkman and Jerry Scott’s Baby Blues for the 9th of November, 2017. Again I maybe am showing off my lack of domesticity here, but, really, hard water spots? But I admit I’d like to get the tannin stain out of my clear plastic teapot, so I guess we all have our things. I just don’t feel strongly enough to punch about it. I just want something that I can scrub with.

Bill Amend’s FoxTrot Classics for the 9th is about random numbers. As Jason says, it is hard to generate random numbers. Random numbers are a resource. Having a good source of them makes a lot of computation work. But they’re hard to make. It seems to be a contradiction to create random numbers by an algorithm. There’s reasons we accept pseudorandom numbers, or find quasirandom numbers. This strip originally ran the 16th of November, 2006.

A night scene. Lots of stars. Crazy Eddie: 'The number of stars is beyond my comprehension!' Hagar: 'Mine, too! What comes after five?'
Chris Browne’s Hagar the Horrible for the 10th of November, 2017. Before you go getting all smug about Hagar no grasping numbers beyond ‘five’, consider what a dog’s breakfast English has managed historically to make of ‘hundred’. Thank you.

Chris Browne’s Hagar the Horrible for the 10th is about the numerous. There’s different kinds of limits. There’s the greatest number of things we can count in an instant. There’s a limit to how long a string of digits or symbols we can remember. There’s the biggest number of things we can visualize. And “visualize” is a slippery concept. I think I have a pretty good idea what we mean when we say “a thousand” of something. I could calculate how long it took me to do something a thousand times, or to write a thousand of something. I know that it was at about a thousand words that, last A To Z sequence, I got to feeling I should wrap up any particular essay. But did I see any particular difference between word 999 and word 1,000? No; what I really knew was “about enough paragraphs” and maybe “fills just over two screens in my text editor”. So do I know what a thousand is? Anyway, we all have our limits, acknowledge them or not.

Archie: 'Moose, your math answers are all wrong!' Moose: 'I'll try again'. So ... Moose: 'Better?' Archie: 'Sorry, Moose! They're still wrong! And writing 'More or Less' after after each answer doesn't help!'
Henry Scarpelli and Craig Boldman’s Archie rerun for the 17th of November, 2017. It really reminds you how dumb Moose is given that he’s asking Archie for help with his mathematics. C’mon, you know Dilton Doiley. And this strip is surely a rerun from before Dilton would be too busy with his oyPhone or his drones or any other distraction; what’s he have to do except help Moose out?

Henry Scarpelli and Craig Boldman’s Archie rerun for the 17th is about Moose’s struggle with mathematics. Just writing “more or less” doesn’t fix an erroneous answer, true. But error margins, and estimates of where an answer should be, can be good mathematics. (Part of the Common Core that many parents struggle with is making the estimate of an answer the first step, and a refined answer later. Based on what I see crossing social media, this really offends former engineering majors who miss the value in having an expected approximate answer.) It’s part of how we define limits, and derivatives, and integrals, and all of calculus. But it’s in a more precise way than Moose tries to do.

Teacher: 'Quincy, if you put your hand in your pocket and pulled out 65 cents ... and put your hand in the other pocket and pulled out 35 cents ... what would you have?' Quincy: 'Somebody else's pants!'
Ted Shearer’s Quincy for the 18th of September, 1978 and rerun the 11th of November, 2017. I feel like anytime I mention Quincy here I end up doing a caption about Ted Shearer’s art. But, I mean, look at the mathematics teacher in the second panel there. There’s voice in that face.

Ted Shearer’s Quincy for the 18th of September, 1978 is a story-problem joke. Some of these aren’t complicated strips.

Reading the Comics, April 15, 2017: Extended Week Edition


It turns out last Saturday only had the one comic strip that was even remotely on point for me. And it wasn’t very on point either, but since it’s one of the Creators.com strips I’ve got the strip to show. That’s enough for me.

Henry Scarpelli and Craig Boldman’s Archie for the 8th is just about how algebra hurts. Some days I agree.

'Ugh! Achey head! All blocked up! Throbbing! Completely stuffed!' 'Sounds like sinuses!' 'No. Too much algebra!'
Henry Scarpelli and Craig Boldman’s Archie for the 8th of April, 2017. Do you suppose Archie knew that Dilton was listening there, or was he just emoting his fatigue to himself?

Ruben Bolling’s Super-Fun-Pak Comix for the 8th is an installation of They Came From The Third Dimension. “Dimension” is one of those oft-used words that’s come loose of any technical definition. We use it in mathematics all the time, at least once we get into Introduction to Linear Algebra. That’s the course that talks about how blocks of space can be stretched and squashed and twisted into each other. You’d expect this to be a warmup act to geometry, and I guess it’s relevant. But where it really pays off is in studying differential equations and how systems of stuff changes over time. When you get introduced to dimensions in linear algebra they describe degrees of freedom, or how much information you need about a problem to pin down exactly one solution.

It does give mathematicians cause to talk about “dimensions of space”, though, and these are intuitively at least like the two- and three-dimensional spaces that, you know, stuff moves in. That there could be more dimensions of space, ordinarily inaccessible, is an old enough idea we don’t really notice it. Perhaps it’s hidden somewhere too.

Amanda El-Dweek’s Amanda the Great of the 9th started a story with the adult Becky needing to take a mathematics qualification exam. It seems to be prerequisite to enrolling in some new classes. It’s a typical set of mathematics anxiety jokes in the service of a story comic. One might tsk Becky for going through university without ever having a proper mathematics class, but then, I got through university without ever taking a philosophy class that really challenged me. Not that I didn’t take the classes seriously, but that I took stuff like Intro to Logic that I was already conversant in. We all cut corners. It’s a shame not to use chances like that, but there’s always so much to do.

Mark Anderson’s Andertoons for the 10th relieves the worry that Mark Anderson’s Andertoons might not have got in an appearance this week. It’s your common kid at the chalkboard sort of problem, this one a kid with no idea where to put the decimal. As always happens I’m sympathetic. The rules about where to move decimals in this kind of multiplication come out really weird if the last digit, or worse, digits in the product are zeroes.

Mel Henze’s Gentle Creatures is in reruns. The strip from the 10th is part of a story I’m so sure I’ve featured here before that I’m not even going to look up when it aired. But it uses your standard story problem to stand in for science-fiction gadget mathematics calculation.

Dave Blazek’s Loose Parts for the 12th is the natural extension of sleep numbers. Yes, I’m relieved to see Dave Blazek’s Loose Parts around here again too. Feels weird when it’s not.

Bill Watterson’s Calvin and Hobbes rerun for the 13th is a resisting-the-story-problem joke. But Calvin resists so very well.

John Deering’s Strange Brew for the 13th is a “math club” joke featuring horses. Oh, it’s a big silly one, but who doesn’t like those too?

Dan Thompson’s Brevity for the 14th is one of the small set of punning jokes you can make using mathematician names. Good for the wall of a mathematics teacher’s classroom.

Shaenon K Garrity and Jefferey C Wells’s Skin Horse for the 14th is set inside a virtual reality game. (This is why there’s talk about duplicating objects.) Within the game, the characters are playing that game where you start with a set number (in this case 20) tokens and take turn removing a couple of them. The “rigged” part of it is that the house can, by perfect play, force a win every time. It’s a bit of game theory that creeps into recreational mathematics books and that I imagine is imprinted in the minds of people who grow up to design games.

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


No surprise what the recurring theme for this set of mathematics-mentioning comic strips is. Look at the date range. But here goes.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 13th uses algebra as the thing that will stun a class into silence. I know the silence. As a grad student you get whole minutes of instructions on how to teach a course before being sent out as recitation section leader for some professor. And what you do get told is the importance of asking students their thoughts and their ideas. This maybe works in courses that are obviously friendly to opinions or partially formed ideas. But in Freshman Calculus? It’s just deadly. Even if you can draw someone into offering an idea how we might start calculating a limit (say), they’re either going to be exactly right or they’re going to need a lot of help coaxing the idea into something usable. I’d like to have more chatty classes, but some subjects are just hard to chat about.

Mr Weatherby walks past a silent class. 'What a well-behaved class! ... Flutesnoot, how do you get them to be so quiet and still?' 'I just asked for a volunteer to solve an algebra problem!'
Henry Scarpelli and Craig Boldman’s Archie rerun for the 13th of March, 2017. I didn’t know the mathematics teacher’s name and suppose that “Flutesnoot” is as plausible as anything. Anyway, I admire his ability to stand in front of a dead-silent class. The stage fright the scenario produces is powerful. At least when I was taught how to teach we got nothing about stage presence or how to remain confident during awkward pauses. What I know I learned from a half-year Drama course in high school.

Steve Skelton’s 2 Cows And A Chicken for the 13th includes some casual talk about probability. As normally happens, they figure the chances are about 50-50. I think that’s a default estimate of the probability of something. If you have no evidence to suppose one outcome is more likely than the other, then that is a reason to suppose the chance of something is 50 percent. This is the Bayesian approach to probability, in which we rate things as more or less likely based on what information we have about how often they turn out. It’s a practical way of saying what we mean by the probability of something. It’s terrible if we don’t have much reliable information, though. We need to fall back on reasoning about what is likely and what is not to save us in that case.

Scott Hilburn’s The Argyle Sweater lead off the Pi Day jokes with an anthropomorphic numerals panel. This is because I read most of the daily comics in alphabetical order by title. It is also because The Argyle Sweater is The Argyle Sweater. Among π’s famous traits is that it goes on forever, in decimal representations, yes. That’s not by itself extraordinary; dull numbers like one-third do that too. (Arguably, even a number like ‘2’ does, if you write all the zeroes in past the decimal point.) π gets to be interesting because it goes on forever without repeating, and without having a pattern easily describable. Also because it’s probably a normal number but we don’t actually know that for sure yet.

Mark Parisi’s Off The Mark panel for the 14th is another anthropomorphic numerals joke and nearly the same joke as above. The answer, dear numeral, is “chained tweets”. I do not know that there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. But there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. If there isn’t, there is now.

John Zakour and Scott Roberts’s Working Daze for the 14th is your basic Pi Day Wordplay panel. I think there were a few more along these lines but I didn’t record all of them. This strip will serve for them all, since it’s drawn from an appealing camera angle to give the joke life.

Dave Blazek’s Loose Parts for the 14th is a mathematics wordplay panel but it hasn’t got anything to do with π. I suspect he lost track of what days he was working on, back six or so weeks when his deadline arrived.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 15th is some sort of joke about the probability of the world being like what it seems to be. I’m not sure precisely what anyone is hoping to express here or how it ties in to world peace. But the world does seem to be extremely well described by techniques that suppose it to be random and unpredictable in detail. It is extremely well predictable in the main, which shows something weird about the workings of the world. It seems to be doing all right for itself.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th is built on the staggering idea that the Earth might be the only place with life in the universe. The cosmos is a good stand-in for infinitely large things. It might be better as a way to understand the infinitely large than actual infinity would be. Somehow thinking of the number of stars (or whatnot) in the universe and writing out a representable number inspires an understanding for bigness that the word “infinity” or the symbols we have for it somehow don’t seem to, at least to me.

Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 17th gives us valuable information about how long ahead of time the comic strips are working. Arithmetic is probably the easiest thing to use if one needs an example of a fact. But even “2 + 2 = 4” is a fact only if we accept certain ideas about what we mean by “2” and “+” and “=” and “4”. That we use those definitions instead of others is a reflection of what we find interesting or useful or attractive. There is cultural artifice behind the labelling of this equation as a fact.

Jimmy Johnson’s Arlo and Janis for the 18th capped off a week of trying to explain some point about the compression and dilution of time in comic strips. Comic strips use space and time to suggest more complete stories than they actually tell. They’re much like every other medium in this way. So, to symbolize deep thinking on a subject we get once again a panel full of mathematics. Yes, I noticed the misquoting of “E = mc2” there. I am not sure what Arlo means by “Remember the boat?” although thinking on it I think he did have a running daydream about living on a boat. Arlo and Janis isn’t a strongly story-driven comic strip, but Johnson is comfortable letting the setting evolve. Perhaps all this is forewarning that we’re going to jump ahead to a time in Arlo’s life when he has, or has had, a boat. I don’t know.