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 And as you’d expect, it’s gotten a bit out of date.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, 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, March 30, 2019: Comics Kingdom is Screwed Up Edition


It doesn’t affect much this batch of comics, as they’re a bunch that all came from GoComics.com. But Comics Kingdom suffered a major redesign of the web site this week, and so it’s lost a lot of functionality. The ability to load your whole comics page at once, for example. Or the ability of archives to work. I’d had the URL for one strip copied down because it mentioned mathematics, albeit in so casual a manner I didn’t mean to write a paragraph about it. Good luck that I didn’t, as that URL now directs to a Spanish translation of a Katzenjammer Kids strip. Why? That’s a good question, and one that deserves an answer.

Anyway, I’m hoping that Comics Kingdom is able to get over their redesign soon. But I know they won’t. There’s never been a web site redesign that lowered functionality and made the page more infuriating to work with that was ever abandoned for the older, working version instead.

Enough about Comics Kingdom. Let me share a couple comic strips from a web site that works, although not as well as it did before its 2018 redesign.

Jim Meddick’s Monty for the 27th is part of a fun storyline. In it Monty and Moondog’s cell phones start texting on their own. It’s presented as the start of an Artificial Intelligence-based singularity, computers transcending human thought and going into business for themselves. This is shown by their working out mathematical truths, starting with arithmetic and going into Boolean algebra. Humans learn arithmetic first and Boolean algebra — logical statements and their combinations — later on, if ever.

Monty: 'Doc! Glad you're here! Our phones started texting without us!' Moondog: 'Now they're doing math!' (The phones text '2 x 2 = 4' and '4^4 = 256'.) Monty: 'They started with 2x2 = 4'. Professor Xemit: 'And now they're swapping advanced Boolean algebraic operations!' Monty: 'Doc ... what's going on?' Xemit: 'A dangerous nexus of AI has formed in your devices! And it must be stopped before it surpasses the combined intellect of all humanity!' Moondog: 'Not sure what that means, but it sounds like some serious data charges.'
Jim Meddick’s Monty for the 27th of March, 2019. Essays discussing anything from Monty should appear at this link.

Computers are certainly able to discover mathematics on their own. Or at least without close guidance; someone still has to write a program to do it. Automated proof finders are a well-established thing, though. They have not, so far as I’ve heard, discovered anything likely to threaten humanity.

Prisoner number 81861^3, talking to prisoner 3757^5: 'Man, this is one *big* prison!'
Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 28th of March, 2019. Appearances of The Chuckle Brothers in this line of essays should be gathered here.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 28th is built on representing huge numbers. 818613 is a big number: 548,568,842,280,381. Even bigger is 37575: it’s 748,524,423,279,410,560. It’s silly to imagine needing an identification number that large. But it’s also a remarkable coincidence that both prisoners here have numbers that can be represented with no more than six digits. There aren’t so many 15-digit numbers that could be represented with as few as six digits. But then it would be an absurdly large prison if it “only” had 818,613 prisoners in it. That seems like the joke would have been harder to recognize, though.

Anthropomorphic numeral 9, looking at temperatures on the Weather Channel. Caption: 'Nate wanted to work at the Weather Channel but didn't have a degree.'
Mark Parisi’s Off The Mark for the 28th of March, 2019. Essays inspired by something mentioned in Off The Mark should be gathered here.

Mark Parisi’s Off The Mark for the 28th is sort of the anthropomorphic numerals joke for the week. It’s also a joke for my friend with the meteorology degree, who I think doesn’t actually read these posts. Well, he probably got the comic forwarded to him anyway.

Daniel Beyer’s Long Story Short for the 29th is another prison joke. I’m not sure if someone at Comic Strip Master Command was worried about something. But a scrawl of mathematics is used as icon of skills learned in prison.

Prisoner, to the other in his cell: 'You learn new skills after being here awhile.' On his wall are several lines of mathematical scrawls.
Daniel Beyer’s Long Story Short for the 29th of March, 2019. Essays discussing topics raised by Long Story Short should be here. There aren’t many, yet.

Mathematics has the reputation of being a subject someone can still do useful work in while in prison. Maybe even do more work, as it seems to offer the prospect of undistracted time to think. And there are examples of mathematicians doing noteworthy work while imprisoned. Bertrand Russell wrote the Introduction To Mathematical Philosophy while jailed for protesting the First World War. André Weil advanced his work in arithmetic geometry while in prison for resisting service in the Second World War. Évariste Galois spent six months in prison shortly before the end of his life, and used some of the time to work on the theory of equations for which we still remember him. I would not recommend prison as a way to advance one’s mathematical research. But it’s something which could happen.

Colin, showing a card: 'Check it out, Dad! This is one of the most powerful Spen-Yo-Do Cards, the Crystal Conquerer! It's worth 2500 power units, has a multiplier ratio of 10, and a destruction ratio of 2 over 15! It can only be defeated by a mage card of equal value or greater!' Dad: 'That's fine, Colin, but I came to check your homework. C'mon, what's 9 divided by 3?' Colin: 'How am I supposed to know?!'
Terry LaBan and Patty LaBan’s Edge City rerun for the 30th of March, 2019. It originally ran in 2004; I can’t say whether it ran the 30th of March then. And topics raised by Edge City should be discussed at this link.

Terry LaBan and Patty LaBan’s Edge City for the 30th showcases the motivation problem. Colin, like many people, is easily able to do complicated algorithms to do something he likes doing. Arithmetic drills, though, not so much. This is why we end up writing story problems with dubious amounts of story in them.


And I don’t want to devote too much space to this. But Brian Fies’s The Last Mechanical Monster for the 29th included the lead character, the Mad Scientist, working out the numbers of the Fibonacci sequence as a way to keep his mind going. The strip is a rerun and I discussed it when it first ran on GoComics.


There were quite a lot of mathematically-themed comic strips the week of the 24th of March. I’ll get to the actual strips of the past week soon, at this link. Also if anyone knows a way to get the old Comics Kingdom back please let me know.

Reading the Comics, August 2, 2018: Non-Euclidean Geometry Edition


There’s really only the one strip that I talk about today that gets into non-Euclidean geometries. I was hoping to have the time to get into negative temperatures. That came up in the comics too, and it’s a subject close to my heart. But I didn’t have time to write that and so must go with what I did have. I’ve surely used “Non-Euclidean Geometry Edition” as a name before too, but that name and the date of August 2, 2018? Just as surely not.

Mark Anderson’s Andertoons for the 29th is the Mark Anderson’s Andertoons for the week, at last. Wavehead gets to be disappointed by what a numerator and denominator are. Common problem; there are many mathematics things with great, evocative names that all turn out to be mathematics things.

Both “numerator” and “denominator”, as words, trace to the mid-16th century. They come from Medieval Latin, as you might have guessed. “Denominator” parses out roughly as “to completely name”. As in, break something up into some number of equal-sized pieces. You’d need the denominator number of those pieces to have the whole again. “Numerator” parses out roughly as “count”, as in the count of how many denominator-sized pieces you have. So for all that numerator and denominator look like one another, with with the meat of the words being the letters “n-m–ator”, their centers don’t have anything to do with one another. (I would believe a claim that the way the words always crop up together encouraged them to harmonize their appearances.)

On the board, the fraction 3/4 with the numerator and denominator labelled. Wavehead: 'You know, for something that sounds like two killer robots, this is really disappointing.'
Mark Anderson’s Andertoons for the 29th of July, 2018. Poor Wavehead is never going to get over his disappointment when he learns about the Fredholm Alternative. I still insist it’s an underrated mid-70s paranoia-thriller.

Johnny Hart’s Back to BC for the 29th is a surprisingly sly joke about non-Euclidean geometries. You wouldn’t expect that given the reputation of the comic the last decade of Hart’s life. And I did misread it at first, thinking that after circumnavigating the globe Peter had come back to have what had been the right line touch the left. That the trouble was his stick wearing down I didn’t notice until I re-read.

But Peter’s problem would be there if his stick didn’t wear down. “Parallel” lines on a globe don’t exist. One can try to draw a straight line on the surface of a sphere. These are “great circles”, with famous map examples of those being the equator and the lines of longitude. They don’t keep a constant distance from one another, and they do meet. Peter’s experiment, as conducted, would be a piece of proof that they have to live on a curved surface.

Peter, holding up a Y-shaped stick: 'In proving to you rather dense individuals that parallel lines never meet I am about to embark on a heretofore unprecedented expedition which will encompass the globe. See you.' (He walks off, dragging both ends of the stick in the ground, creating parallel lines. He walks several panels; 'Fifty Thousand Miles Later' as the stick wears down and the parallel lines get less far apart ... he gets back where he started, with the stick worn down to a single ribbon, and the surviving line left.)
Johnny Hart’s Back to BC for the 29th of July, 2018. It originally ran it looks like, the 13th of August, 1961. Or I’m reading the second row, second panel wrong.

And this gets at one of those questions that bothers mathematicians, cosmologists, and philosophers. How do we know the geometry of the universe? If we could peek at it from outside we’d have some help, but that is a big if. So we have to rely on what we can learn from inside the universe. And we can do some experiments that tell us about the geometry we’re in. Peter’s line example would be one; he can use that to show the world’s curved in at least one direction. A couple more lines and he’d be confident the world was a sphere. If we could make precise enough measurements we could do better, with geometric experiments smaller than the circumference of the Earth. (Or universe.) Famously, the sum of the interior angles of a triangle tell us something about the space the triangle’s inscribed in. There are dangers in going from information about one point, or a small area, to information about the whole. But we can tell some things.

Dr Strange-y type doing mind stuff: 'Using my MENTALISTIC powers of the occult, I shall attempt to DOUBLE your brain power, Captain Victorious! Peruse the potency of ... PROFESSOR PECULIAR!' Captain Victorious: 'Mind ... reeling! So much ... information!! ... Two plus two equals ... four! Hey! It worked!' Professor Peculiar: 'I guess double was too relative a term.'
Phil Dunlap’s Ink Pen rerun for the 29th of July, 2018. This one originally ran the 21st of August, 2011.

Phil Dunlap’s Ink Pen for the 29th is another use of arithmetic as shorthand for intelligence. Might be fun to ponder how Captain Victorious would know that he was right about two plus two equalling four, if he didn’t know that already. But we all are in the same state, for mathematical truths. We know we’ve got it right because we believe we have a sound logical argument for the thing being true.

A 'Newton Enterprises' boat pulls up to a desert island. A skeleton's under the tree; beside it, a whiteboard that starts with 'Coconut' and proceeds through a few lines of text to, finally, 'F = GMm/R^2'. Caption: 'How Newton actually stumbled across his formula for the theory of gravity.'
Brian Boychuk and Ron Boychuk’s Chuckle Brothers for the 30th of July, 2018. All right, so the rubber boat is an obvious anachronism. But Newton’s pal Edmond Halley made some money building diving bells for people to excavate shipwrecks and if that doesn’t mess with your idea of what the 17th century was you’re a stronger one than I am.

Brian Boychuk and Ron Boychuk’s Chuckle Brothers for the 30th is a riff on the story of Isaac Newton and the apple. The story of Newton starting his serious thinking of gravity by pondering why apples should fall while the Moon did not is famous. And it seems to trace to Newton. We have a good account of it from William Stukeley, who in the mid-18th century wrote Memoirs of Sir Isaac Newton’s Life. Stukeley knew Newton, and claimed to get the story right from him. He also told it to his niece’s husband, John Conduitt. Whether this is what got Newton fired with the need to create such calculus and physics, or whether it was a story he composed to give his life narrative charm, is beyond my ability to say. It’s an important piece of mathematics history anyway.


If you’d like more Reading the Comics essays you can find them at this link. Some of the many essays to mention Andertoons are at this link. Other essays mentioning B.C. (vintage and current) are at this link. The comic strip Ink Pen gets its mentions at this link, although I’m surprised to learn it’s a new tag today. And the Chuckle Brothers I discuss at this link. Thank you.

Reading the Comics, June 29, 2018: Chuckle and Breakfast Cereal Edition


The last half of last week was not entirely the work of Chuckle Brothers and Saturday Morning Breakfast Cereal. It seemed like it, though. Let’s review.

Patrick Roberts’s Todd the Dinosaur for the 28th is a common sort of fear-of-mathematics joke. In this case the fear of doing arithmetic even when it is about something one would really like to know. I think the question got away from Todd, though. If they just wanted to know whether they had enough money, well, they need twelve dollars and have seven. Subtracting seven from twelve is only needed if they want to know how much more they need. Which they should want to know, but wasn’t part of the setup.

Kid: 'Do we have enough money to go to the movie?' Todd: 'Let's see! You ahve four dollars and I have three dollars. That's seven. The movie is twelve dollars for both of us. So twelve take away seven is ... *GASP* Oh no! I accidentally did math!' Kid: 'So?' Todd: 'This is SUMMER!' Kid: 'I don't even know you!'
Patrick Roberts’s Todd the Dinosaur for the 28th of June, 2018. I’m sorry, I don’t know the kid’s name.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 28th uses mathematics as the sine qua non of rocket science. As in, well, the stuff that’s hard and takes some real genius to understand. It’s not clear to me that the equations are actually rocket science. There seem to be a shortage of things in exponentials to look quite right to me. But I can’t zoom in on the art, so, who knows just what might be in there.

Professor-type in front of a class labelled Rocket Science 101: 'Doesn't ANYBODY understand this stuff?'
Brian Boychuk and Ron Boychuk’s The Chuckle Brothers rerun for the 28th of June, 2018. It originally ran the 16th of July, 2009. Relatable.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th is a set theory joke. Or a logic joke, anyway. It refers to some of the mathematics/logic work of Bertrand Russell. Among his work was treating seriously the problems of how to describe things defined in reference to themselves. These have long been a source of paradoxes, sometimes for fun, sometimes for fairy-tale logic, and sometimes to challenge our idea of what we mean by definitions of things. Russell made a strong attempt at describing what we mean when we describe a thing by reference to itself. The iconic example here was the “set of all sets not members of themselves”.

Caption: 'Nobody liked Bertrand Russell's scavenger hunts.' Items to find: 'The list of all lists that do not list themselves. (List here).'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th of June, 2018. Well, among other things, wouldn’t there be infinitely many such lists? Unless this description were enough to describe them all, by being a description of what to do to get you all of them?

Russell started out by trying to find some way to prove Georg Cantor’s theorems about different-sized infinities wrong. He worked out a theory of types, and what kinds of rules you can set about types of things. Most mathematicians these days prefer to solve the paradox with a particular organization of set theory. But Russell’s type theory still has value, particularly as part of the logic behind lambda calculus. This is an approach to organizing relationships between things that can do wonderful things, including in computer programming. It lets one write code that works extremely efficiently and can never be explained to another person, modified, or debugged ever. I may lack the proper training for the uses I’ve made of it.

News anchor: 'In a cruel, bizarre twist of fate, this week's $1 million winning lotto number 579281703 was shared by exactly one million people. In other news ... ' (The person watching the news has a lottery ticket number 579281703.)
Brian Boychuk and Ron Boychuk’s The Chuckle Brothers rerun for the 29th of June, 2018. It originally ran the 17th of July, 2009. You can tell it’s from so long ago because the TV set is pre-HD.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 29th is a lottery joke. It does happen that more than one person wins a drawing; sometimes three or even four people do, for the larger prizes. The chance that there’s a million winners? Frightfully unlikely unless something significant went wrong with the lottery mechanism.

So what are the chances of a million lottery winners? If I’m not mistaken the only way to do this is to work out a binomial distribution. The binomial distribution is good for cases where you have many attempts at doing a thing, where each thing can either succeed or fail, and the likelihood of success or failure is independent of all the other attempts. In this case each lottery ticket is an attempt; it winning is success and it losing is failure. Each ticket has the same chance of winning or losing, and that chance doesn’t depend on how many wins or losses there are. What is that chance? … Well, if each ticket has one chance in a million of winning, and there are a million tickets out there, the chance of every one of them winning is about one-millionth raised to the millionth power. Which is so close to zero it might as well be nothing. … And yet, for all that it’s impossible, there’s not any particular reason it couldn’t happen. It just won’t.

What I Learned This Year. Kid: 'Um ... you can divide a number by 3 if the sum of its digits can be divided by 3.' [ Later ] Frazz: 'So, what'd you learn this year?' Kid: 'Don't go last on what-I-learned-this-year day.'
Jef Mallet’s Frazz for the 29th of June, 2018. Sorry, again, not sure of this kid’s name. The comic is often so good about casually dropping in character names.

Jef Mallet’s Frazz for the 29th is a less dire take on what-you-learned-this-year. In this case it’s trivia, but it’s a neat sort of trivia. Once you understand how it works you can understand how to make all sorts of silly little divisibility rules. The threes rule — and the nines rule — work by the same principle. Suppose you have a three-digit number. Let me call ‘a’ the digit in the hundreds column, ‘b’ the digit in the tens column, and ‘c’ the digit in the ones column. Then the number is equal to 100\cdot a + 10\cdot b + 1\cdot c . And, well, that’s equal to 99\cdot a + 1\cdot a + 9 \cdot b + 1 \cdot b + 1 \cdot c . Which is 99\cdot a + 9 \cdot b + a + b + c . 99 times any whole number is a multiple of 9, and also of 3. 9 times any whole number is a multiple of 9, and also of 3. So whether the original number is divisible by 9, or by 3, depends on whether a + b + c is. And that’s why adding the digits up tells you whether a number is a whole multiple of three.

This has only proven anything for three-digit numbers. But with that proof in mind, you probably can imagine what the proof looks like for two- or four-digit numbers, and would believe there’s one for five- and for 500-digit numbers. Or, for that matter, the proof for an arbitrarily long number. So I’ll skip actually doing that. You can fiddle with it if you want a bit of fun yourself.

Also maybe it’s me, or the kind of person who gets into mathematics. But I find silly little rules like this endearing. It’s a process easy to understand that anyone can do and it tells you something not obvious from when you start. It feels like getting let in on a magic trick. That seems like the sort of thing that endears people to mathematics.

Michael: 'Grandma broke out the math workbooks!' Gabby: 'She does this every summer!' (They hide behind a tree.) Gabby: 'Says she doesn't want us to forget what we learned during the school year.' Michael: 'She has a point. We do need to keep our homework-avoidance skills sharp.'
Mike Thompson’s Grand Avenue for the 29th of June, 2018. At the risk of taking the art too literally: isn’t that tree kind of short to be that fat? Shouldn’t the leaves start higher up?

Mike Thompson’s Grand Avenue for the 29th is trying to pick its fight with me again. I can appreciate someone wanting to avoid kids losing their mathematical skills over summer. It’s just striking how Thompson has consistently portrayed their grandmother as doing this in a horrible, joy-crushing manner.

Greek: 'Why are you the wisest man, Socrates?' Socrates: 'Because I know one thing: that I know nothing.' Greek: 'That's all you know?' Socrates: 'I mean strictly speaking ... ' Greek: 'What about the infinite universe of analytic statements, like if A = A then A = A?' Socrates: 'Okay yeah That stuff. Just that.' Greek: 'Just ALL of math.' (Pause.) Greek: 'Sorry, did I make you sad?' Socrates: 'I can't be certain, but probably.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 29th of June, 2018. I am curious if anyone in the philosophy department would offer an idea which Ancient Greek might be chatting with Socrates here. If Weinersmith had anyone in mind I would guess whichever one has Socrates getting a slave to do a geometry proof. But there’s also … I want to say Parmenides, where the elder scholar whips the young Socrates in straight syllogisms. Again, if anyone specific was in mind and it wasn’t just “another Ancient Greek type”.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 29th gets into a philosophy-of-mathematics problem. Also a pure philosophy problem. It’s a problem of what things you can know independently of experience. There are things it seems as though are true, and that seem independent of the person who is aware of them, and what culture that person comes from. All right. Then how can these things be relevant to the specifics of the universe that we happen to be in just now? If ‘2’ is an abstraction that means something independent of our universe, how can there be two books on the table? There’s something we don’t quite understand yet, and it’s taking our philosophers and mathematicians a long while to work out what that is.


And as ever, if you’d like to see more Reading the Comics posts, please look to this page. For essays with Todd the Dinosaur in them, look here. For essays with the Chuckle Brothers, here you go. For some of the many, many essays with Saturday Morning Breakfast Cereal, follow this link. For more talk about Frazz, look here. And for the Grand Avenue comics, try this link please.

Reading the Comics, May 27, 2017: Panels Edition


Can’t say this was too fast or too slow a week for mathematically-themed comic strips. A bunch of the strips were panel comics, so that’ll do for my theme.

Norm Feuti’s Retail for the 21st mentions every (not that) algebra teacher’s favorite vague introduction to group theory, the Rubik’s Cube. Well, the ways you can rotate the various sides of the cube do form a group, which is something that acts like arithmetic without necessarily being numbers. And it gets into value judgements. There exist algorithms to solve Rubik’s cubes. Is it a show of intelligence that someone can learn an algorithm and solve any cube? — But then, how is solving a Rubik’s cube, with or without the help of an algorithm, a show of intelligence? At least of any intelligence more than the bit of spatial recognition that’s good for rotating cubes around?

'Rubik's cube, huh? I never could solve one of those.' 'I'm just fidgeting with it. I never bothered learning the algorithm either.' 'What algorithm?' 'The pattern you use to solve it.' 'Wait. All you have to do to solve it is memorize a pattern?' 'Of course. How did you think people solved it?' 'I always thought you had to be super smart to figure it out.' 'Well, memorizing the pattern does take a degree of intelligence.' 'Yeah, but that's not the same thing as solving it on your own.' 'I'm sure some people figured out the algorithm without help.' 'I KNEW Chad Gustafson was a liar! He was no eighth-grade prodigy, he just memorized the pattern!' 'Sounds like you and the CUBE have some unresolved issues.'
Norm Feuti’s Retail for the 21st of May, 2017. A few weeks ago I ran across a book about the world of competitive Rubik’s Cube solving. I haven’t had the chance to read it, but am interested by the ways people form rules for what would seem like a naturally shapeless feature such as solving Rubik’s Cubes. Not featured: the early 80s Saturday morning cartoon that totally existed because somehow that made sense back then.

I don’t see that learning an algorithm for a problem is a lack of intelligence. No more than using a photo reference shows a lack of drawing skill. It’s still something you need to learn, and to apply, and to adapt to the cube as you have it to deal with. Anyway, I never learned any techniques for solving it either. Would just play for the joy of it. Here’s a page with one approach to solving the cube, if you’d like to give it a try yourself. Good luck.

Bob Weber Jr and Jay Stephens’s Oh, Brother! for the 22nd is a word-problem avoidance joke. It’s a slight thing to include, but the artwork is nice.

Brian and Ron Boychuk’s Chuckle Brothers for the 23rd is a very slight thing to include, but it’s looking like a slow week. I need something here. If you don’t see it then things picked up. They similarly tried sprucing things up the 27th, with another joke for taping onto the door.

Nate Fakes’s Break of Day for the 24th features the traditional whiteboard full of mathematics scrawls as a sign of intelligence. The scrawl on the whiteboard looks almost meaningful. The integral, particularly, looks like it might have been copied from a legitimate problem in polar or cylindrical coordinates. I say “almost” because while I think that some of the r symbols there are r’ I’m not positive those aren’t just stray marks. If they are r’ symbols, it’s the sort of integral that comes up when you look at surfaces of spheres. It would be the electric field of a conductive metal ball given some charge, or the gravitational field of a shell. These are tedious integrals to solve, but fortunately after you do them in a couple of introductory physics-for-majors classes you can just look up the answers instead.

Samson’s Dark Side of the Horse for the 26th is the Roman numerals joke for this installment. I feel like it ought to be a pie chart joke too, but I can’t find a way to make it one.

Izzy Ehnes’s The Best Medicine Cartoon for the 27th is the anthropomorphic numerals joke for this paragraph.

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, January 28, 2017: Chuckle Brothers Edition


The week started out quite busy and I was expecting I’d have to split my essay again. It didn’t turn out that way; Comic Strip Master Command called a big break on mathematically-themed comics from Tuesday on. And then nobody from Comics Kingdom or from Creators.com needed inclusion either. I just have a bunch of GoComics links and a heap of text here. I bet that changes by next week. Still no new Jumble strips.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 22nd was their first anthropomorphic numerals joke of the week.

Kevin Fagan’s Drabble for the 22nd uses arithmetic as the sort of problem it’s easy to get clearly right or clearly wrong. It’s a more economical use of space than (say) knowing how many moons Saturn’s known to have. (More than we thought there were as long ago as Thursday.) I do like that there’s a decent moral to this on the way to the punch line.

Bill Amend’s FoxTrot for the 22nd has Jason stand up for “torus” as a better name for doughnuts. You know how nerdy people will like putting a complicated word onto an ordinary thing. But there are always complications. A torus ordinarily describes the shape made by rotating a circle around an axis that’s in the plane of the circle. The result is a surface, though, the shell of a doughnut and none of the interior. If we’re being fussy. I don’t know of a particular name for the torus with its interior and suspect that, if pressed, a mathematician would just say “torus” or maybe “doughnut”.

We can talk about toruses in two dimensions; those look just like circles. The doughnut-shell shape is a torus in three dimensions. There’s torus shapes made by rotating spheres, or hyperspheres, in four or more dimensions. I’m not going to draw them. And we can also talk about toruses by the number of holes that go through them. If a normal torus is the shape of a ring-shaped pool toy, a double torus is the shape of a two-seater pool toy, a triple torus something I don’t imagine exists in the real world. A quadruple torus could look, I imagine, like some pool toys Roller Coaster Tycoon allows in its water parks. I’m saying nothing about whether they’re edible.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers for the 23rd was their second anthropomorphic numerals joke of the week. I suppose sometimes you just get an idea going.

Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 23rd jokes about mathematics skills versus life. The growth is fine enough; after all, most of us are at, or get to, our best at something while we’re training in it or making regular use of it. So the joke peters out into the usual “I never use mathematics in real life” crack, which, eh. I agree it’s what I feel like my mathematics skills have done ever since I got my degree, at any rate.

Teresa Burritt’s Frog Applause for the 24th describes an extreme condition which hasn’t been a problem for me. I’m not an overindulgey type.

Randy Glasbergen’s Glasbergen Cartoons rerun for the 26th is the pie chart joke for this week.

Michael Fry’s Committed rerun for the 28th just riffs on the escalation of hyperbole, and what sure looks like an exponential growth of hyperbolic numbers. There’s a bit of scientific notation in the last panel. The “1 x” part isn’t necessary. It doesn’t change the value of the expression “1 x 1026”. But it might be convenient to use the “1 x” anyway. Scientific notation is about separating the size of the number from the interesting digits that the number has. Often when you compare numbers you’re interested in the size or else you’re interested in the important digits. Get into that habit and it’s not worth making an exception just because the interesting digits turn out to be boring in this case.

Reading the Comics, July 28, 2012


I intend to be back to regular mathematics-based posts soon. I had a fine idea for a couple posts based on Sunday’s closing of the Diaster Transport roller coaster ride at Cedar Point, actually, although I have to technically write them first. (My bride and I made a trip to the park to get a last ride in before its closing, and that lead to inspiration.) But reviews of math-touching comic strips are always good for my readership, if I’m readin the statistics page here right, so let’s see what’s come up since the last recap, going up to the 14th of July.

Continue reading “Reading the Comics, July 28, 2012”