Reading the Comics, April 18, 2019: Slow But Not Stopped Week Edition


The first, important, thing is that I have not disappeared or done something worse. I just had one of those weeks where enough was happening that something had to give. I could either write up stuff for my mathematics blog, or I could feel guilty about not writing stuff up for my mathematics blog. Since I didn’t have time to do both, I went with feeling guilty about not writing, instead. I’m hoping this week will give me more writing time, but I am fooling only myself.

Second is that Comics Kingdom has, for all my complaining, gotten less bad in the redesign. Mostly in that the whole comics page loads at once, now, instead of needing me to click to “load more comics” every six strips. Good. The strips still appear in weird random orders, especially strips like Prince Valiant that only run on Sundays, but still. I can take seeing a vintage Boner’s Ark Sunday strip six unnecessary times. The strips are still smaller than they used to be, and they’re not using the decent, three-row format that they used to. And the archives don’t let you look at a week’s worth in one page. But it’s less bad, and isn’t that all we can ever hope for out of the Internet anymore?

And finally, Comic Strip Master Command wanted to make this an easy week for me by not having a lot to write about. It got so light I’ve maybe overcompensated. I’m not sure I have enough to write about here, but, I don’t want to completely vanish either.

Man walking past a street sign for 52 Ludlow Avenue; the 5 falls down and hits him on the head. Woman with him: 'Numbers are hard.'
Dave Whamond’s Reality Check for the 15th of April, 2019. Appearances in these pages of Reality Check should be gathered at this link.

Dave Whamond’s Reality Check for the 15th is … hm. Well, it’s not an anthropomorphic-numerals joke. It is some kind of wordplay, making concrete a common phrase about, and attitude toward, numbers. I could make the fussy difference between numbers and numerals here but I’m not sure anyone has the patience for that.

Man in a cloudscape: 'I made it to heaven!' Angel: 'You sure did! Now you get to do the best stuff! You can design new systems of mathematics! You can attempt to create self-consistent physics systems. Beset of all, try to create a maximally complex reality using the simplest possible constructions!' Man: 'But that sounds terrible.' Angel: 'QUIET! He hears EVERYTHING.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 17th of April, 2019. I am surprised that this is the first time this strip has drawn a mention this month. Well, this and other Saturday Morning Breakfast Cereal posts are at this link.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 17th touches around mathematics without, I admit, necessarily saying anything specific. The angel(?) welcoming the man to heaven mentions creating new systems of mathematics as some fit job for the heavenly host. The discussion of creating self-consistent physics systems seems mathematical in nature too. I’m not sure whether saying one could “attempt” to create self-consistent physics is meant to imply that our universe’s physics are not self-consistent. To create a “maximally complex reality using the simplest possible constructions” seems like a mathematical challenge as well. There are important fields of mathematics built on optimizing, trying to create the most extreme of one thing subject to some constraints or other.

I think the strip’s premise is the old, partially a joke, concept that God is a mathematician. This would explain why the angel(?) seems to rate doing mathematics or mathematics-related projects as so important. But even then … well, consider. There’s nothing about designing new systems of mathematics that ordinary mortals can’t do. Creating new physics or new realities is beyond us, certainly, but designing the rules for such seems possible. I think I understood this comic better then I had thought about it less. Maybe including it in this column has only made trouble for me.

First chicken: 'What do you want for your birthday?' Second chicken: 'I want everybody to ignore my birthday!' First: 'But if I ignore your birthday I'll be giving the perfect birthday gift, which means I'll be celebrating your birthday, which means I won't be ignoring it!!! AAAAUGH! BIRTHDAY PARADOX!!'
Doug Savage’s Savage Chickens for the 17th of April, 2019. Essays inspired by something from Savage Chickens should be at this link.

Doug Savage’s Savage Chickens for the 17th amuses me by making a strip out of a logic paradox. It’s not quite your “this statement is a lie” paradox, but it feels close to that, to me. To have the first chicken call it “Birthday Paradox” also teases a familiar probability problem. It’s not a true paradox. It merely surprises people who haven’t encountered the problem before. This would be the question of how many people you need to have in a group before there’s a 50 percent (75 percent, 99 percent, whatever you like) chance of at least one pair sharing a birthday.

And I notice on Wikipedia a neat variation of this birthday problem. This generalization considers splitting people into two distinct groups, and how many people you need in each group to have a set chance of a pair, one person from each group, sharing a birthday. Apparently both a 32-person group of 16 women and 16 men, or a 49-person group of 43 women and six men, have a 50% chance of some woman-man pair sharing a birthday. Neat.

Man speaking to a teacher: 'There are two angry parents outside. One's upset that you're teaching multiplication ... the other us upset you're teaching division.' Outside the door are an angry bunny and an angry amoeba.
Mark Parisi’s Off The Mark for the 18th of April, 2019. And essays inspired by Off The Mark should appear at this link.

Mark Parisi’s Off The Mark for the 18th sports a bit of wordplay. It’s built on how multiplication and division also have meanings in biology. … If I’m not mis-reading my dictionary, “multiply” meant any increase in number first, and the arithmetic operation we now call multiplication afterwards. Division, similarly, meant to separate into parts before it meant the mathematical operation as well. So it might be fairer to say that multiplication and division are words that picked up mathematical meaning.


And if you thought this week’s pickings had slender mathematical content? Jef Mallett’s Frazz, for the 19th, just mentioned mathematics homework. Well, there were a couple of quite slight jokes the previous week too, that I never mentioned. Jenny Campbell’s Flo and Friends for the 8th did a Roman numerals joke. The rerun of Richard Thompson’s Richard’s Poor Almanac for the 11th had the Platonic Fir Christmas tree, rendered as a geometric figure. I’ve discussed the connotations of that before.

And there we are. I hope to have some further writing this coming week. But if all else fails my next Reading the Comics essay, like all of them, should be at this link.

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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, March 14, 2019: Pi Day 2019 Edition


Some weeks there’s an obvious theme. Most weeks there’s not. But mid-March has formed a traditional theme for at least one day. I’m going to excerpt that from the rest of the week’s comics, because I’ve noticed what readership around here is like for stuff tagged “Pi Day” in mid-March. You all can do what you like with your pop-mathematics blogs.

Pi Day seems to have brought out fewer comics than in years past. The ones that were made, among the set I read, were also less on point. There was a lot of actual physical pie involved, too, suggesting the day might be escaping the realm of pop-mathematics silliness straight into pun nobody thinks about. Or maybe cartoonists just didn’t have a fresh angle this year.

John Hambrock’s The Brilliant Mind of Edison Lee shows off a nerd kind of mistake. At least one I think of as particularly nerdy. Wanting to calculate is a natural urge, especially for those who do it well. But to calculate the circumference of a pie from its diameter? What is exciting about that? More, does Grandpa recognize what a circumference is? It’s relatively easy to see the diameter of a pie. Area, also. But circumference? I’m not sure people are good at estimating the circumference of things, not by sight. You’d need a tape measure, or a similar flexible ruler, to start with and we don’t see that. Without the chance to measure it himself, Grandpa has to take the circumference (and, for that matter, diameter) at Edison Lee’s word. What would convince Grandpa of anything?

Edison: 'Happy Pi Day, Grandpa.' Grandpa: 'Is that today?' Edison: 'I'll demonstrate Pi by using it to calculate the circumference of this pie. [ He sets a pie on the table and calculates. ] If the diameter is 12 inches and we multiply by pi, which is 3.14, we'll end up with ... [ he looks up ] nothing.' Grandpa, who's already eaten the whole pie: 'Sorry, were you saying something?'
John Hambrock’s The Brilliant Mind of Edison Lee for the 14th of March, 2019. This and other essays inspired by Edison Lee can be found at this link.

For example, even if Grandpa accepted that Edison Lee had multiplied one number by 3.14 and gotten another number he might ask: how do we know pi is the same for pies of all sizes? Could a small pie’s circumference be only three times the diameter’s length, while a large pie’s is four times that? Could Edison offer an answer for why 3.14, or some nearby number, is all that interesting?

Hamster, holding up a pie: 'Guess what? It's national pie day!' Capybara: 'It's also my birthday.' Hamster: 'uh ... aand I got you this pie!'
Liz Climo’s Cartoons for the 14th of March, 2019. I haven’t had reason to discuss this comic here before. This and any future essays discussing Liz Climo Cartoons should appear at this new tag.

Liz Climo’s Cartoons is an example of the second kind of strip I mentioned during my introductory paragraphs. While it’s nominally built on Pi Day, any mathematics is gone. It’s just about the pun. And, well, the fun of having a capybara around.

Mark Parisi’s Off The Mark is the most on-topic strip for the day. And the anthropomorphic numerals joke for the day, too. It’s built on there being infinitely many digits to π, which, true enough. There are also infinitely many digits to \frac{1}{3} , mind; they’re just not so interesting a set. π being irrational gives us a never-ending variety of digits. It’s almost certainly normal, too. Any finite string of digits most likely appears infinitely often in this string.

Anthropomorphic 3, holding up a selfie stick; a decimal and the digits 1, 4, 1, 5, 9, 2, etc, all waving hands. 3: 'I don't think I can fit everyone in ... '
Mark Parisi’s Off The Mark for the 14th of March, 2019. The essays inspired by Off The Mark should appear at this link.

We won’t ever know enough digits of π to depict all of them. But we can depict the digits we know, and many different ways. Here’s a 2015 Washington Post article with several pictures representing the digits, including some neat “random walk” ones. In those the digits are used to represent directions and distances for a thing to move, and it represents the number as this curious wispy structure. There’s amazing pictures to be made of this.

Roy, who has a pie tin and mess on his face: 'It's OK, Norm. Kath and I agreed we both deserve to wear gag pies for forgetting what yesterday was.' Norm: 'My gosh, Roy --- you mean you both forgot your anniversary?' Roy: 'Oh, that's not yet. No, we forgot it was Pi day!' Norm: 'I'm officially in over my head ... '
John Zakour and Scott Roberts’s Working Daze for the 15th of March, 2019. And this comic appears often enough. Working Days strips should appear in discussions at this link.

John Zakour and Scott Roberts’s Working Daze for the 15th is built more around the pie pun. I was relieved to see this. The kind of nerd jokes routinely made in Working Daze made me think it was bizarre the comic strip didn’t do a Pi Day joke. They were saving the setup.

Pierpoint, porcupine, to Gunther, bear: 'Heh! Heh! If I baked 13 apple pies and gave you half of them, how many would you have?' Gunther: 'Obviously I'd have all of them.' Pierpoint, dejected: 'Obviously.'
Bill Schorr’s The Grizzwells for the 13th of March, 2019. I’ve had a few chances to mention The Grizzwells and those essays are at this link.

And last, a comic strip that I don’t think was trying to set up a Pi Day joke. But Bill Schorr’s The Grizzwells for the 13th is a routine story problem joke. But that the setup mentions pies? If this ran on the 14th I would feel confident Schorr was going for a Pi Day comic. But it didn’t, so I don’t know if Schorr was going for that or not.


And those are the surprisingly few Pi Day 2019 comic strips. Later this week I should post, at this link, other recent mathematically-themed comic strips. Thanks for reading.

Reading the Comics, February 23, 2019: Numerals Edition


It’s happened again: another slow week around here. My supposition is that Comic Strip Master Command was snowed in about a month ago, and I’m seeing the effects only now. There’s obviously no other reason that more comic strips didn’t address my particular narrow interest in one seven-day span.

Samson’s Dark Side of the Horse for the 18th is a numerals joke. The mathematics content is slight, I admit, but I’ve always had a fondness for Dark Side of the Horse. (I know it sounds like I have a fondness for every comic strip out there. I don’t quite, but I grant it’s close.) Conflating numerals and letters, and finding words represented by numerals, is an old tradition. It was more compelling in ancient days when letters were used as numerals so that it was impossible not to find neat coincidences. I suppose these days it’s largely confined to typefaces that make it easy to conflate a letter and a numeral. I mean moreso than the usual trouble telling apart 1 and l, 0 and O, or 5 and S. Or to special cases like hexadecimal numbers where, for ease of representation, we use the letters A through F as numerals.

Samson, counting sheep in bed. #198 leaps over the fence; the numbers are written as might appear on a 14-segment LED. #199 follows. The next panel #200, makes the numerals look like the word ZOO, and an elephant marches through, uprooting the fence.
Samson’s Dark Side of the Horse for the 18th of February, 2019. I don’t always discussDark Side of the Horse but when I do, it should appear at this link.

Jef Mallett’s Frazz for the 18th is built on an ancient problem. I remember being frustrated with it. How is “questions 15 to 25” eleven questions when the difference between 15 and 25 is ten? The problem creeps into many fields. Most of the passion has gone out of the argument but around 1999 you could get a good fight going about whether the new millennium was to begin with January 2000 or 2001. The kind of problem is called a ‘fencepost error’. The name implies how often this has complicated someone’s work. Divide a line into ten segments. There are nine cuts on the interior of the line and the two original edges. I’m not sure I could explain to an elementary school student how the cuts and edges of a ten-unit-long strip match up to the questions in this assignment. I might ask how many birthdays someone’s had when they’re nine years old, though. And then flee the encounter.

Kid: 'If 25 minus 10 is 15, how is *doing* questions 15-25 eleven questions? I should get credit for answering one extra question.' Teacher: 'Two extra questions, if you can answer the one you just brought up.'
Jef Mallett’s Frazz for the 18th of February, 2019. Essays with a mention of Frazz appear at this link.

Mark Parisi’s Off The Mark for the 19th is another numerals joke. This one’s also the major joke to make about an ice skater doing a figure eight: write the eight some other way. (I’d have sworn there was an M-G-M Droopy cartoon in which Spike demonstrates his ability to skate a figure 8, and then Droopy upstages him by skating ‘4 + 4’. I seem to be imagining it; the only cartoon where this seems to possibly fit is 1950’s The Chump Champ, and the joke isn’t in that one. If someone knows the cartoon I am thinking of, please let me know.) Here, the robot is supposed to be skating some binary numeral. It’s nothing close to an ‘8’, but perhaps the robot figures it needs to demonstrate some impressive number to stand out.

An ice-staking woman does a figure 8. An ice-skating robot does a figure 1110101101.
Mark Parisi’s Off The Mark for the 19th of February, 2019. When I have discussed Off The Mark I’ve tried to tag it so the essays appear at this link.

Bud Blake’s Tiger for the 21st has Tiger trying to teach his brother arithmetic. Working it out with fingers seems like a decent path to try, given Punkinhead’s age and background. And Punkinhead has a good point: why is the demonstration the easy problem and the homework the hard problem? I haven’t taught in a while, but do know I would do that sort of thing. My rationalization, I think, would be that a hard problem is usually hard because it involves several things. If I want to teach a thing, then I want to highlight just that thing. So I would focus on a problem in which that thing is the only tricky part, and everything else is something the students are so familiar with they don’t notice it. The result is usually an easy problem. There isn’t room for toughness. I’m not sure if that’s a thing I should change, though. Demonstrations of how to work harder problems are worth doing. But I usually think of those as teaching “how to use these several things we already know”. Using a tough problem to show one new thing, plus several already-existing tricky things, seems dangerous. It might be worth it, though.

Tiger, holding up his fingers: 'Look, one plus one is two, two plus two is four. So then what's four plus four?' Punkinhead: 'How come YOU do the easy ones and you save the tough oens for me?'
Bud Blake’s Tiger rerun for the 21st of February, 2019. I have no information about when it first appeared. Essays inspired by Tiger should appear at this link.

This was not a busy week for comic strips. If it had been, I likely wouldn’t have brought in Dark Side of the Horse. Still there were a handful of comics too slight to get a write-up, even so. John Zakour and Scott Roberts’s Maria’s Day on the 19th just mentioned mathematics homework as hard, for example. Eric the Circle for the 22nd has a binary numeral written out. That one was written by ‘urwatuis’. Maybe that would have been a good, third, numeral comic strip to discuss.


That’s all the mathematically-themed comic strips for the week, though. Next Sunday I should have a fresh Reading the Comics post at this link.

Reading the Comics, February 9, 2019: Garfield Outwits Me Edition


Comic Strip Master Command decreed that this should be a slow week. The greatest bit of mathematical meat came at the start, with a Garfield that included a throwaway mathematical puzzle. It didn’t turn out the way I figured when I read the strip but didn’t actually try the puzzle.

Jim Davis’s Garfield for the 3rd is a mathematics cameo. Working out a problem is one more petty obstacle in Jon’s day. Working out a square root by hand is a pretty good tedious little problem to do. You can make an estimate of this that would be not too bad. 324 is between 100 and 400. This is worth observing because the square root of 100 is 10, and the square root of 400 is 20. The square of 16 is 256, which is easy for me to remember because this turns up in computer stuff a lot. But anyway, numbers from 300 to 400 have square roots that are pretty close to but a little less than 20. So expect a number between 17 and 20.

Jon swipes his card at a supermarket checkout. The reader asks: 'Would you like to donate a dollar to charity today?' (Boop.) 'Enter PIN.' (boop boop boop boop.) 'Your total is $3.24. Is this correct?' (Boop.) 'What is the square root of 324? Please show your work.' Jon: 'ALL I WANT IS A BAG OF CHEESE DOODLES!' Garfield: 'DON'T WE ALL?!!'
Jim Davis’s Garfield for the 3rd of February, 2019. Other essays featuring Garfield would be at this link. But somehow this is the first time I’ve had something to write about based in Garfield. Huh.

But after that? … Well, it depends whether 324 is a perfect square. If it is a perfect square, then it has to be the square of a two-digit number. The first digit has to be 1. And the last digit has to be an 8, because the square of the last digit is 4. But that’s if 324 is a perfect square, which it almost certainly is … wait, what? … Uh .. huh. Well, that foils where I was going with this, which was to look at a couple ways to do square roots.

One is to start looking at factors. If a number is equal to the product of two numbers, then its square root is the product of the square roots of those numbers. So dividing your suspect number 324 by, say, 4 is a great idea. The square root of 324 would be 2 times the square root of whatever 324 ÷ 4 is. Turns out that’s 81, and the square root of 81 is 9 and there we go, 18 by a completely different route.

So that works well too. If it had turned out the square root was something like 2\sqrt{82} then we get into tricky stuff. One response is to leave the answer like that: 2\sqrt{82} is exactly the square root of 328. But I can understand someone who feels like they could use a numerical approximation, so that they know whether this is bigger than 19 or not. There are a bunch of ways to numerically approximate square roots. Last year I worked out a way myself, one that needs only a table of trigonometric functions to work out. Tables of logarithms are also usable. And there are many methods, often using iterative techniques, in which you make ever-better approximations until you have one as good as your situation demands.

Anyway, I’m startled that the cheese doodles price turned out to be a perfect square (in cents). Of course, the comic strip can be written to have any price filled in there. The joke doesn’t depend on whether it’s easy or hard to take the square root of 324. But that does mean it was written so that the problem was surprisingly doable and I’m amused by that.

T-Rex: 'Say the average person can expect to live for 81 years. That's a little over 2.5 billion seconds. 2.5 billion is not that much! I thought I'd compare the seconds in a life to the molecules in a glass of water, but even a gram of water has over ten sextillion molecules in it. Even if I measure my life in NANOSECONDS I'm still not on par with a gram of boring ol' WATER.' Dromiceiomimus: 'Molecules are super tiny, T-Rex! You should measure yourself in bigger units.' T-Rex: 'like ... cubic millimeters?' Utahraptor: 'That'd give you 2500 litres, that's a lot!' T-Rex: 'Dude, that's just a GIANT BATHTUB! I want to visualize my lifespan as something impressive!' Utahraptor: 'OK. 2.5 billion kilometers is enough to make a one-way trip to Saturn and get most of the way back before dying, OR to travel part of the way to Uranus, but again, dying well before you arrive.' LATER: T-Rex: 'Dear audio diary! Today I learned why we measure lifetimes in years and not in 'failed trips to Uranus where only corpses show up at the end'. It's, um, for the reasons you'd expect, basically.'
Ryan North’s Dinosaur Comics for the 4th of February, 2019. Some of the many essays inspired by Dinosaur Comics appear at this link.

Ryan North’s Dinosaur Comics for the 4th goes in some odd directions. But it’s built on the wonder of big numbers. We don’t have much of a sense for how big truly large numbers. We can approach pieces of that, such as by noticing that a billion seconds is a bit more than thirty years. But there are a lot of truly staggeringly large numbers out there. Our basic units for things like distance and mass and quantity are designed for everyday, tabletop measurements. The numbers don’t get outrageously large. Had they threatened to, we’d have set the length of a meter to be something different. We need to look at the cosmos or at the quantum to see things that need numbers like a sextillion. Or we need to look at combinations and permutations of things, but that’s extremely hard to do.

Tube Sock: a white cylinder with two blue stripes near the top. Inner Tube Sock: a white torus with two blue stripes around the narrow radius.
Tom Horacek’s Foolish Mortals for the 4th of February, 2019. This is a new tag. When I am next moved to write about Foolish Mortals the results should be this link. This might be a while. I can find some examples of writing about this strip in 2014, before I tagged the comic strips by name, but not since then.

Tom Horacek’s Foolish Mortals for the 4th is a marginal inclusion for this week’s strips, but it’s a low-volume week. The intended joke is just showing off a “tube sock” and an “inner tube sock”. But it happens to depict these as a cylinder and a torus and those are some fun shapes to play with. Particularly, consider this: it’s easy to go from a flat surface to a cylinder. You know this because you can roll a piece of paper up and get a good tube. And it’s not hard to imagine going from a cylinder to a torus. You need the cylinder to have a good bit of give, but it’s easy to imagine stretching it around and taping one end to the other. But now you’ve got a shape that is very different from a sheet of paper. The four-color map theorem, for example, no longer holds. You can divide the surface of the torus so it needs at least seven colors.

Wiley's Dictionary, as read by Peter: 'Logarithm. A downed tree with dance moves.'
Mastroianni and Hart’s B.C. for the 5th of February, 2019. Essays describing some aspect of B.C., whether the current run or the vintage 1960s reruns, appear at this link.

Mastroianni and Hart’s B.C. for the 5th is a bit of wordplay. As I said, this was a low-volume week around here. The word “logarithm” derives, I’m told, from the modern-Latin ‘logarithmus’. John Napier, who advanced most of the idea of logarithms, coined the term. It derives from ‘logos’, here meaning ‘ratio’, and ‘re-arithmos’, meaning ‘counting number’. The connection between ratios and logarithms might not seem obvious. But suppose you have a couple of numbers, and we’ll reach deep into the set of possible names and call them a, b, and c. Suppose a ÷ b equals b ÷ c. Then the difference between the logarithm of a and the logarithm of b is the same as the difference between the logarithm of b and the logarithm of c. This lets us change calculations on numbers to calculations on the ratios between numbers and this turns out to often be easier work. Once you’ve found the logarithms. That can be tricky, but there are always ways to do it.

Mother: 'Maggot, help Otis with his math homework. Explain fractions to him.' Maggot, to Otis: 'Well, it's like when you drop a beer bottle and it breaks into a lot of pieces.'
Bill Rechin’s Crock rerun for the 8th of February, 2019. I have no information about when this strip previously appeared. Essays based on things mentioned in Crock appear at this link. Somehow this isn’t the first time I’ve tagged this comic.

Bill Rechin’s Crock for the 8th is not quite a bit of wordplay. But it mentions fractions, which seem to reliably confuse people. Otis’s father is helpless to present a concrete, specific example of what fractions mean. I’d probably go with change, or with slices of pizza or cake. Something common enough in a child’s life.

And I grant there have been several comic strips here of marginal mathematics value. There was still one of such marginal value. Mark Parisi’s Off The Mark for the 7th has anthropomorphized numerals, in service of a temperature joke.


These are all the mathematically-themed comic strips for the past week. Next Sunday, I hope, I’ll have more. Meanwhile please come around here this week to see what, if anything, I think to write about.

Reading the Comics, July 14, 2018: County Fair Edition


The title doesn’t mean anything. My laptop’s random-draw of pictures pulled up one from the county fair last year is all. I’m just working too close to deadline to have a good one. Pet rabbit has surgery scheduled and we are hoping that turns out well for everyone involved.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 12th has the blackboard of mathematical symbols. Familiar old shorthand of conflating mathematics ability with genius, or at least intelligence. The blackboard isn’t particularly full of expressions, possibly because Caulfield and Rouillard’s art might not be able to render too much detail clearly. It’s also got a sort-of appearance of Einstein’s most famous equation. Although with perhaps an extra joke to it. Suppose we’re to take ‘E’ and ‘M’ and ‘C’ to mean what they do in Einstein’s use. Then E - mc^2 has to equal zero. And there are many things you can safely do with zero. Dividing by it, though, isn’t one. I shan’t guess whether Caulfield and Rouillard were being that sly, though.

Blackboard with 'a^2 x 333 / E - MC^2 = 1,333' on it. Nerd: 'Ah! See, I've proved it!' Bully: 'That's nice, now let's step outside and settle this like men.'
Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 12th of July, 2018. Must say that’s some really nice canvas grain and I wonder whether they actually work on media like that for their thrice-a-week comic strip or whether they simply use that texture in their art programs.

Marty Links’s Emmy Lou rerun for the 13th tries to be a paradox. How can one like mathematics without liking figures? But arithmetic is just one part of mathematics. Surely the most-used part, if we go by real-world utility. But not everything. Arithmetic is often useful, yes. But you can do good work in (say) logic or knot theory or geometry with only a slight ability to add or subtract or multiply. There’s not enough emphasis put on that in early education. I suppose it reflects the reasonable feeling that people do need to be competent at arithmetic, which is useful. But it gives one a distorted view of what mathematics can be.

Emmy Lou, looking over her homework, and complaining to her mother: 'Mathematics in itself isn't so hard! It's all these figures ... '
Marty Links’s Emmy Lou rerun for the 13th of July, 2018. Apparently it previously ran the 21st of October, 1971. (I make no claims about even earlier runs of the strip and am just going by what I can make out in the copyright information.)

Mark Parisi’s Off The Markfor the 13th is the anthropomorphic numerals joke for the week. And it presents being multiplied by zero as a terrifying fate for other numbers. This seems to reflect the idea that being multiplied by zero is equivalent to being made into nothing. That it’s being killed. Zero enjoys this dual meaning, culturally, representing both a number and the concept of a thing that doesn’t exist and the concept of non-existence. If being turned from one number to another is a numeral murder, then a 2 sneaking in with a + sign would be at least as horrifying. But that joke wouldn’t work, and I know that too.

Numerals, sweating as a suspenseful scene in a numerals movie: a 9 whistling happily, unsuspecting that a 0 is sneaking into the room and carrying a x sign.
Mark Parisi’s Off The Mark for the 13th of July, 2018. In a moment of comic relief the x slips in the 0’s hand, and it temporarily becomes a + and everybody sighs with relief.

Olivia Jaimes’s Nancy for the 14th is another recreational-mathematics puzzle. I know nothing of Jaimes’s background but apparently it involves a keen interest in that kind of play that either makes someone love or hate mathematics. (Myself, I’m only slightly interested in these kinds of puzzles, most of the time.) This one — add one line to ‘fix’ the equation 5 + 5 + 5 + 5 = 555 — I hadn’t encountered before. Took some fuming to work it out. The obvious answer, of course, is to add a slash across the = sign so that it means “does not equal”.

Teacher: 'Here's today's brainteaser. Can you add just one line to this equation to fix it?' [ 5 + 5 + 5 + 5 = 555 ] Nancy: 'Yep.' (She scribbles a line across the whole equation.)
Olivia Jaimes’s Nancy for the 14th of July, 2018. They … do seem to be spending a lot of time in class for it being July.

But that answer’s dull. What mathematicians like are statements that are true and interesting. There are many things that 5 + 5 + 5 + 5 does not equal. Why single out 555 from that set? So negating the equals sign meets the specifications of the problem, slightly better than Nancy does herself. It doesn’t have the surprise of the answer Nancy’s teacher wants.

If you don’t get how to do it, highlight over the paragraph below for a hint.

There are actually three ways to add the stroke to make this equation true. The three ways are equivalent, though. Notice that the symbols on the board comprise strokes and curves and consider that the meaning of the symbol can be changed by altering the composition of those strokes and curves.

Quincy's Grandmother: 'Who has been your favorite teacher this year, Quincy?' Quincy: 'Well, Mrs Glover sure has made arithmetic relevant. Like this problem. If your pants need a new patch every month ... how many patches would you have in a year and a half?!'
Ted Shearer’s Quincy for the 14th of July, 2018. It originally ran the 21st of May, 1979.

Ted Shearer’s Quincy for the 21st of May, 1979, and rerun the 14th is a joke about making mathematics problems relevant. And, yeah, I’ll give Mrs Glover credit for making problems that reflect stuff students know they’re going to have to deal with. Also that they may have already dealt with and so have some feeling for what plausible answers will be. It’s tough to find many problems like that which don’t repeat themselves too much. (“If your pants need a new patch every two months how many would you have in three years?”).


I do many Reading the Comics posts. Others like this one are here. For other essays that mention Mustard and Boloney, look to this link. I admit I’m surprised there’s anything there; I didn’t remember having written about it before For other discussions of Emmy Lou, try this link. For this and other times I’ve written about Off The Mark try this link. For Nancy content, try this link. And for other Quincy essays you can read this link. Thank you.

Reading the Comics, March 17, 2018: Pi Day 2018 Edition


So today I am trying out including images for all the mathematically-themed comic strips here. This is because of my discovery that some links even on GoComics.com vanish without warning. I’m curious how long I can keep doing this. Not for legal reasons. Including comics for the purpose of an educational essay about topics raised by the strips is almost the most fair use imaginable. Just because it’s a hassle copying the images and putting them up on WordPress.com and that’s even before I think about how much image space I have there. We’ll see. I might try to figure out a better scheme.

Also in this batch of comics are the various Pi Day strips. There was a healthy number of mathematically-themed comics on the 14th of March. Many of those were just coincidence, though, with no Pi content. I’ll group the Pi Day strips together.

Counselor: 'Come in Funky! What seems to be troubling you?' Funky: 'We're nothing but computer numbers at this school, Mr Fairgood! Nobody cares about us as persons! I'm tired of being just a number! I want a chance to make some of my own decisions!' Counselor: 'Okay! What would you like to be, odd or even?'
Tom Batiuk’s Funky Winkerbean for the 2nd of April, 1972 and rerun the 11th of March, 2018. Maybe I’m just overbalancing for the depression porn that Funky Winkerbean has become, but I find this a funny bordering-on-existential joke.

Tom Batiuk’s Funky Winkerbean for the 2nd of April, 1972 is, I think, the first appearance of Funky Winkerbean around here. Comics Kingdom just started running the strip, as well as Bud Blake’s Tiger and Bill Hoest’s Lockhorns, from the beginning as part of its Vintage Comics roster. And this strip really belonged in Sunday’s essay, but I noticed the vintage comics only after that installment went to press. Anyway, this strip — possibly the first Sunday Funky Winkerbean — plays off a then-contemporary fear of people being reduced to numbers in the face of a computerized society. If you can imagine people ever worrying about something like that. The early 1970s were a time in American society when people first paid attention to the existence of, like, credit reporting agencies. Just what they did and how they did it drew a lot of critical examination. Josh Lauer’s recently published Creditworthy: a History of Consumer Surveillance and Financial Identity in America gets into this.

Bear: 'Can I come in?' Molly: 'Sure.' Bear: 'What happened?' Molly: 'I got an F on my math test.' Bear: 'But you're a genius at math.' Molly: 'I didn't have time to study.' Bear: 'Is it because I distracted you with my troubles yesterday?' Molly: 'No. Well, maybe. Not really. Okay, sure. Yes. I don't know. ARRGHHHH!!!'
Bob Scott’s Bear With Me for the 14th of March, 2018. Every conversation with a high-need, low-self-esteem friend.

Bob Scott’s Bear With Me for the 14th sees Molly struggling with failure on a mathematics test. Could be any subject and the story would go as well, but I suppose mathematics gets a connotation of the subject everybody has to study for, even the geniuses. (The strip used to be called Molly and the Bear. In either name this seems to be the first time I’ve tagged it, although I only started tagging strips by name recently.)

Jeff: 'Next November you and I will have appeared in this comic strip for 45 years!' Mutt: 'Mmm. 45 years! That's 540 months or 2,340 weeks! So, the boss drew us 1,436 times ... one each day of the year! Now, 16,436 until I'm 90 ... ' Jeff: 'What have you been working on?' Mutt: 'Oh, I'm just calculating what we'll be doing during the next 45 years!' (Jeff leaves having clobbered Mutt.) Mutt: 'No! Not this!'
Bud Fisher’s Mutt and Jeff rerun for the 14th of March, 2018. The comic strip ended the 26th of June, 1983 — I remember the announcement of its ending in the (Perth Amboy) News-Tribune, our evening paper, and thinking it seemed illicit that an ancient comic strip like that could end. It was a few months from being 76 years old then.

Bud Fisher’s Mutt and Jeff rerun for the 14th is a rerun from sometime in 1952. I’m tickled by the problem of figuring out how many times Fisher and his uncredited assistants drew Mutt and Jeff. Mutt saying that the boss “drew us 14,436 times” is the number of days in 45 years, so that makes sense if he’s counting the number of strips drawn. The number of times that Mutt and Jeff were drawn is … probably impossible to calculate. There’s so many panels each strip, especially going back to earlier and earlier times. And how many panels don’t have Mutt or don’t have Jeff or don’t have either in them? Jeff didn’t appear in the strip until March of 1908, for example, four months after the comic began. (With a different title, so the comic wasn’t just dangling loose all that while.)

Diagram: Pie Chart, Donut Chart (pie chart with the center missing), Tart Charts (several small pie charts), Shepherd's Pie Chart (multiple-curve plot with different areas colored differently), Tiramisu Chart (multiple-curve plot with all areas colored the same), and Lobster Thermidor Chart (lobster with chunks labelled).
Doug Savage’s Savage Chickens for the 14th of March, 2018. Yeah, William Playfair invented all these too.

Doug Savage’s Savage Chickens for the 14th is a collection of charts. Not all pie charts. And yes, it ran the 14th but avoids the pun it could make. I really like the tart charts, myself.

And now for the Pi Day strips proper.

[PI sces ] Guy at bar talking to Pi: 'Wow, so you were born on March 14th at 1:59, 26 seconds? What're the odds?'
Scott Hilburn’s The Argyle Sweater for the 14th of March, 2018. Also a free probability question, if you’re going to assume that every second of the year is equally likely to be the time of birth.

Scott Hilburn’s The Argyle Sweater for the 14th starts the Pi Day off, of course, with a pun and some extension of what makes 3/14 get its attention. And until Hilburn brought it up I’d never thought about the zodiac sign for someone born the 14th of March, so that’s something.

Pi figure, wearing glasses, reading The Neverending Story.
Mark Parisi’s Off The Mark for the 14th of March, 2018. Really the book seems a little short for that.

Mark Parisi’s Off The Mark for the 14th riffs on one of the interesting features of π, that it’s an irrational number. Well, that its decimal representation goes on forever. Rational numbers do that too, yes, but they all end in the infinite repetition of finitely many digits. And for a lot of them, that digit is ‘0’. Irrational numbers keep going on with more complicated patterns. π sure seems like it’s a normal number. So we could expect that any finite string of digits appears somewhere in its decimal expansion. This would include a string of digits that encodes any story you like, The Neverending Story included. This does not mean we might ever find where that string is.

[ How ancient mathematicians amused themselves, AKA how to celebrate Pi Day today; third annual Pi-Easting Contest. Emcee: 'And HERE he is, our defending champ, that father of conic sections --- ARCHIMEDES!' They're all eating cakes shaped like pi.
Michael Cavna’s Warped for the 14th of March, 2018. Yes, but have you seen Pythagoras and his golden thigh?

Michael Cavna’s Warped for the 14th combines the two major joke threads for Pi Day. Specifically naming Archimedes is a good choice. One of the many things Archimedes is famous for is finding an approximation for π. He’d worked out that π has to be larger than 310/71 but smaller than 3 1/7. Archimedes used an ingenious approach: we might not know the precise area of a circle given only its radius. But we can know the area of a triangle if we know the lengths of its legs. And we can draw a series of triangles that are enclosed by a circle. The area of the circle has to be larger than the sum of the areas of those triangles. We can draw a series of triangles that enclose a circle. The area of the circle has to be less than the sum of the areas of those triangles. If we use a few triangles these bounds are going to be very loose. If we use a lot of triangles these bounds can be tight. In principle, we could make the bounds as close together as we could possibly need. We can see this, now, as a forerunner to calculus. They didn’t see it as such at the time, though. And it’s a demonstration of what amazing results can be found, even without calculus, but with clever specific reasoning. Here’s a run-through of the process.

[ To Stephen Hawking, Thanks for making the Universe a little easier for the rest of us to understand ] Jay: 'I suppose it's only appropriate that he'd go on Pi Day.' Roy: 'Not to mention, Einstein's birthday.' Katherine: 'I'll bet they're off in some far reach of the universe right now playing backgammon.'
John Zakour and Scott Roberts’s Working Daze for the 15th of March, 2018. No, you should never read the comments, but here, really, don’t read the comments.

John Zakour and Scott Roberts’s Working Daze for the 15th is a response to Dr Stephen Hawking’s death. The coincidence that he did die on the 14th of March made for an irresistibly interesting bit of trivia. Zakour and Roberts could get there first, thanks to working on a web comic and being quick on the draw. (I’m curious whether they replaced a strip that was ready to go for the 15th, or whether they normally work one day ahead of publication. It’s an exciting but dangerous way to go.)

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.