Reading the Comics, May 1, 2019: Not Perfectly Certain Edition


There’s several comics from the first half of last week that I can’t perfectly characterize. They seem to be on-topic enough for my mathematical discussions. It’s just how exactly they are on-topic that I haven’t quite got. Some weeks are like that.

Dave Whamond’s Reality Check for the 28th circles around being a numerals joke. It’s built on the binary representation of numbers that we’ve built modern computers on. And on the convention that “(Subject) 101” is the name for an introductory course in a subject. This convention of course numbering — particularly, three-digit course numbers, with the leading digit representing the year students are expected to take it — seems to have spread in American colleges in the 1930s. It’s a compromise, as many things are. As college programs of study become more specialized there’s the need for a greater number of courses in each field. And there’s a need to give people some hint of the course level. “Numerical Methods” could be a sophomore, senior, or grad-student course; how should someone from a different school know what to expect? But the pull of the serial number, and the idea that ’01’ must be the first in a field, is hard to resist.

Woman looking at college classroom doors: English 101 and then Computers 101 0101001 101010100 0110110011 100100100.
Dave Whamond’s Reality Check for the 28th of April, 2019. Essays which include Reality Check should be gathered at this link.

Anyway, the long string of zeroes and ones after the original ‘101’ is silliness and that’s all it has to be. The number one-hundred-and-one in binary would be a mere “1100101”, which doesn’t start with the important one-oh-one, and isn’t a big enough string of digits to be funny. Maybe this is a graduate course. The number given, if we read it as a single long binary number, would be 182,983,026,468. I’ve been to schools which use four-digit course codes. Twelve digits seems excessive.

Man carrying a large numeral 8 walks to a man sitting on a recliner in a field. The man with the eight asks, 'Is this nine?' The sitting man says, 'No. Eight.' The man with the eight says, 'I've got the wrong number'. And he walks away, carrying the 8, in a silent final panel.
John Deering’s Strange Brew for the 29th of April, 2019. Other appearances by Strange Brew are at this link.

John Deering’s Strange Brew for the 29th circles around being an anthropomorphic numerals joke. At least it is a person using a large representation of the number eight. I’m not sure how to characterize it, or why I find the strip amusing. It’s a strange one.

Cop, presenting a handcuffed 2, 3, 5, and 7 to his supervisor at the Vice Squad: 'We're breaking up the numbers racket. These are some of the prime suspects.'
Thaves’s Frank and Ernest for the 1st of May, 2019. This is the first time in maybe a month that I’ve written about Thaves’s strip. But last time, and other earlier appearances, of Frank and Ernest should be gathered at this link.

Thaves’s Frank and Ernest for the 1st is, finally, a certain anthropomorphic numerals joke. With wordplay about prime numbers being unavoidably prime suspects. … And when I was a kid, I had no idea what “numbers rackets” were, other than a thing sometimes mentioned on older sitcoms. That it involved somehow literally taking numbers and doing … something … that the authorities didn’t like was mysterious. I don’t remember what surely hilarious idea the young me had for what that might even mean. I suspect that, had I seen this strip at the time, I would have understood this wasn’t really whatever was going on. But I would have explained to my parents what a prime number was, and they would put up with my doing so, because that’s just what our relationship was.

Fish standing at a podium with a laptop, and behind, a screen with a string of overlapping circles. It says to the other: 'These are Venn diagras for my presentation. And no, I'm not tooting.'
Dave Whamond’s Reality Check for the 1st of May, 2019. And it’s a bit odd to have two Reality Check strips in the same essay. But I’m glad to have the strip back at all, since I discovered I had somehow lost the comic for a couple of months.

Dave Whamond’s Reality Check for the 1st is more or less the Venn Diagram joke for this essay. It’s a bit of a fourth-wall-breaking strip: the joke wouldn’t really work from the other goldfish’s perspective. Anyway, only two of those figures are proper Venn diagrams. The topmost figure, with five circles, and the bottommost, with three, aren’t proper Venn diagrams. Only some of the possible intersections between sets exist there. They are proper Euler diagrams, though.

Person giving a presentation: 'As this slide indicates, the most popular pies are apple, chocolate, and pumpkin.' The slide is a pie chart, showing (in decreasing popularity) apple, chocolate, pumpkin, pecan, cherry, lemon meringue, coconut cream, banana cream, key lime, and blueberry. Caption; 'Metadata'.
Wayno’s WaynoVision for the 1st of May, 2019. This appears to be the first time I’ve mentioned this comic. Well. This and any future essays mentioning WaynoVision should be at this link.

Wayno’s WaynoVision for the 1st is the pie-chart joke for the essay. It’s not as punchy as that Randolph Itch strip I kept bringing back around. But it’s on the same theme, mixing the metaphor of the pie chart with literal pies.


There’s one more Reading the Comics post before I’ve got all last week’s strips covered. That, I hope to have published and available at this link for Tuesday.

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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.

Let Me Tell You How Interesting March Madness Could Possibly Be


I read something alarming in the daily “Best of GoComics” e-mail this morning. It was a panel of Dave Whamond’s Reality Check. It’s a panel comic, although it stands out from the pack by having a squirrel character in the margins. And here’s the panel.

Three mathematicians standing around chalkboards. One says: 'My pick is (9 +/- sqrt(5)). What's your bracket?' '(x + 3).' '(n - 1).' Caption: 'March Mathness'.
Dave Whamond’s Reality Check for the 2nd of March, 2019. Edge City inspires discussions in the essays at this link. I don’t know when or how Reality Check dropped off my comics page. It must have been after October 2018. Here’s essays including Reality Check, to serve as proof. I probably won’t go reading five months’ worth of the strip to get all the strips I’d missed. But the strip should return to my regular Reading the Comics posts now.

Certainly a solid enough pun to rate a mention. I don’t know of anyone actually doing a March Mathness bracket, but it’s not a bad idea. Rating mathematical terms for their importance or usefulness or just beauty might be fun. And might give a reason to talk about their meaning some. It’s a good angle to discuss what’s intersting about mathematical terms.

And that lets me segue into talking about a set of essays. The next few weeks see the NCAA college basketball tournament, March Madness. I’ve used that to write some stuff about information theory, as it applies to the question: is a basketball game interesting?

Along the way here I got to looking up actual scoring results from major sports. This let me estimate the information-theory content of the scores of soccer, (US) football, and baseball scores, to match my estimate of basketball scores’ information content.

  • How Interesting Is A Football Score? Football scoring is a complicated thing. But I was able to find a trove of historical data to give me an estimate of the information theory content of a score.
  • How Interesting Is A Baseball Score? Some Partial Results I found some summaries of actual historical baseball scores. Somehow I couldn’t find the detail I wanted for baseball, a sport that since 1845 has kept track of every possible bit of information, including how long the games ran, about every game ever. I made do, though.
  • How Interesting Is A Baseball Score? Some Further Results Since I found some more detailed summaries and refined the estimate a little.
  • How Interesting Is A Low-Scoring Game? And here, well, I start making up scores. It’s meant to represent low-scoring games such as soccer, hockey, or baseball to draw some conclusions. This includes the question: just because a distribution of small whole numbers is good for mathematicians, is that a good match for what sports scores are like?

Reading the Comics, October 27, 2018: Surprise Rerun Edition


While putting together the last comics from a week ago I realized there was a repeat among them. And a pretty recent repeat too. I’m supposing this is a one-off, but who can be sure? We’ll get there. I figure to cover last week’s mathematically-themed comics in posts on Wednesday and Thursday, subject to circumstances.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 26th is a joking reminder that educational texts, including in mathematics, don’t have to be boring. We can have narrative thrust and energy. It’s a good reminder.

Caption: 'I wish all educational texts were written like Epictetus wrote.' Textbook: 'What, hapless wretch? Do you suppose int(sqrt(x^2 + x)dx = (x^2 + x)^{-1/2}? And when you eat, do you carry the food to your mouth or to your eyes? Slave!
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 26th of October, 2018.

As fits the joke, the bit of calculus in this textbook paragraph is wrong. \int \sqrt{x^2 + x} dx does not equal \left(x^2 + x\right)^{-\frac12} . This is even ignoring that we should expect, with an indefinite integral like this, a constant of integration. An indefinite integral like this is equal to a family of related functions. But it’s common shorthand to write out one representative function. But the indefinite integral of \sqrt{x^2 + x} is not \left(x^2 + x\right)^{-\frac12} . You can confirm that by differentiating \left(x^2 + x\right)^{-\frac12} . The result is nothing like \sqrt{x^2 + x} . Differentiating an indefinite integral should get the original function back. Here are the rules you need to do that for yourself.

As I make it out, a correct indefinite integral would be:

\int{\sqrt{x^2 + x} dx} = \frac{1}{4}\left( \left(2x + 1\right)\sqrt{x^2 + x} + \log \left|\sqrt{x} + \sqrt{x + 1} \right| \right)

Plus that “constant of integration” the value of which we can’t tell just from the function we want to indefinitely-integrate. I admit I haven’t double-checked that I’m right in my work here. I trust someone will tell me if I’m not. I’m going to feel proud enough if I can get the LaTeX there to display.

Berle: 'It was just a happy stroll through the gloomy graveyard when suddenly ... ' Spivak's Calculus, 3rd Edition appears. Berle: 'Math jumped out of nowhere!' Harvey: 'Drink it off.'
Stephen Beals’s Adult Children rerun for the 27th of October, 2018. It also appeared the 31st of March, 2018. I’m surprised it was that recent. I can’t blame Beals if he needed a break. This is a Halloween-ready example of the comic.

Stephen Beals’s Adult Children for the 27th has run already. It turned up in late March of this year. Michael Spivak’s Calculus is a good choice for representative textbook. Calculus holds its terrors, too. Even someone who’s gotten through trigonometry can find the subject full of weird, apparently arbitrary rules. And formulas like those in the above paragraph.

Manfred: 'How do you want to divide up the bill?' Wink: 'Lemme see it .. add that and that ... carry the two ... let's just split it htree ways.' Manfred: 'Nice try.' Dusty: 'Mr Surf 'n' Turf needs a calculator!'
Rob Harrell’s Big Top rerun for the 27th of October, 2018. It originally appeared the 13th of December, 2008.

Rob Harrell’s Big Top for the 27th is a strip about the difficulties of splitting a restaurant bill. And they’ve not even got to calculating the tip. (Maybe it’s just a strip about trying to push the group to splitting the bill a way that lets you off cheap. I haven’t had to face a group bill like this in several years. My skills with it are rusty.)

Jack-o-lantern standing on a scale: 'Hey! I weigh exactly 3.14 pounds!' Caption: 'Pumpkin Pi'.
Dave Whamond’s Reality Check for the 27th of October, 2018. Does the weight count if the jack-o-lantern is wearing sneakers?

Dave Whamond’s Reality Check for the 27th is a Pi Day joke shifted to the Halloween season.


And I have more Reading the Comics post at this link. Since it’s not true that every one of these includes a Saturday Morning Breakfast Cereal mention, you can find those that have one at this link. Essays discussing Adult Children, including the first time this particular strip appeared, are at this link. Essays with a mention of Big Top are at this link. And essays with a mention of Reality Check are at this link. Furthermore, this month and the rest of this year my Fall 2018 Mathematics A-To-Z should continue. And it is open for requests for more of the alphabet.

Reading the Comics, September 24, 2018: Carnival Delay Edition


It’s unusual for me to have a Reading the Comics post on Monday, but that’s what fits my schedule. The Playful Mathematics Education Blog Carnival took my Sunday spot, and Tuesday and Friday I hope to continue the A to Z posts. It’s going to be a rather full week. I’m looking forward to, I hope, surviving. Meanwhile, here’s some comics.

Mike Thompson’s Grand Avenue for the 23rd resumes its efforts to become my archenemy with a strip about why learn arithmetic. Michael is right that we don’t need people to do multiplication. So why should we learn it? Grandmom Kate offers only the answer that he’ll be punished if he doesn’t learn them. This could motivate Michael to practice multiplication tables. But it’ll never convince him that learning multiplication tables is something of value.

Michael: 'You once told me: what you don't know won't hurt you. So I figure that means I don't need to know my multiplication tables!' Grandmom: 'You're right. Not knowing your multiplication tables won't hurt you. It will hurt both you and your allowance.' Michael: 'Wait! You're saying there's a possibility I might not get my allowance?' Grandmom: 'What you don't know won't hurt you.'
Mike Thompson’s Grand Avenue for the 23rd of September, 2018. So, not to nitpick the writing of these strips. Comic strip dialogue is subject to a great number of constraints that aren’t obvious, and that constrain how naturalistic it can be. But the dialogue flow is a slight wreck. Third panel to fourth, Grandmom goes from saying not knowing the multiplication tables won’t hurt you to saying it will hurt you and your allowance. Then, fourth panel to fifth, Michael goes from hearing he and his allowance will be hurt to wondering if there’s a possibility he might not get his allowance. It’s like they’re having different drafts of the conversation.

That said, what would convince him? It’s ridiculous to suppose Michael would be in a spot where he’d need to know eight times seven right away and without a computer to tell him. I find a certain amount of arithmetic-doing fun. But I already like doing it. (I admit a bootstrapping problem. Do I find it fun because I do it well, or do I do arithmetic well because I find it fun? I don’t know.) And that I find something fun is a lousy argument that everyone should learn to do it. I can argue that practicing multiplication tables is practice for finding neat patterns in other things, in higher mathematics. But is that reason to care? If Michael isn’t interested in eight times seven, is he going to be interested in the outer products of the set of symmetries on the octagon and the permutations of the heptagon?

I don’t have an actual answer here. I think it’s worth learning to do arithmetic. But not because we need people to do arithmetic. At least not except when we’re too lazy to take out our phones. But “or else you’ll lose money” is a terrible reason.

Things You Should Never, Ever Say To A Cartoonist. (It's nine panels of things they likely hear often, including 'Do you ever do any *real* art?' and 'You should try making your comics funnier' and 'You should do comics about my family, let me tell you about them!' Only one sends him running.) Questioner: 'What's the square root of 64 ? Why are you running away? Why are you screaming?' Corner Squirrel: 'Wait! Where do you get your ideaaaaas?!'
Dave Whamond’s Reality Check for the 23rd of September, 2018. That fourth panel happens to me, by the way, anytime I recount some odd, slightly awkward interaction that I have. And my family heritage is such that I’m a carrier of awkward interactions. Not to brag, but include a Nebus in your social circle and you’re more than ten times more likely than you ever imagined you could be to have responsibility for a styrofoam-peanut whirlwind, for example.

Dave Whamond’s Reality Check for the 23rd is a smorgasbord strip of things cartoonists get told too often. It comes in here because I like the strip, and because the punch line is built in the fear of arithmetic. It’s traditional to think that cartoonists, as artists, haven’t got an interest in mathematics or science. I can’t deny that the time it takes to learn how to draw, and the focus it takes to make a syndication-worthy comic strip, hurt someone’s ability to study much mathematics. And vice-versa. But people are a varied bunch. Bill Amend, of FoxTrot, and Bud Grace, of the discontinued The Piranha Club, were both physics majors. Darrin Bell, of Candorville and Rudy Park, writes well about mathematical (and scientific) topics. Crockett Johnson, of the renowned 1940s comic strip Barnaby and the Harold and the Purple Crayon books, was literate enough in mathematics to do over a hundred paintings based on geometry theorems. Part of why I note when the mathematics put into the background of a strip is that I do like pointing out there’s no reason artists and mathematicians or scientists need to be separate people.

Teacher: 'Question number three: you have twelve apples, but your friend Timmy only has two. How do you convince Timmy that this is a fair arrangement?'
Tony Carrillo’s F Minus for the 24th of September, 2018. Question four is about how many people named Timmy are in class.

Tony Carrillo’s F Minus for the 24th uses the form of the story problem. This one of the classic form of apples distributed amongst people. The problem presented makes its politics bare. But any narrative, however thin, carries along with it cultural values. That mathematicians may work out things whose truth is (we believe) independent of the posed problem doesn’t mean the posed problem is universal.

Tortoise: 'Y'know, I'm embarrassed to tell you how old I am.' Dog: 'Can you whisper it?' Tortoise: 'I'll write my age in the sand real temporary-like.' Dog: 'Don't spell it out, I can't read words!' Tortoise: 'Those are Roman numerals!'
Steve Boreman’s Little Dog Lost rerun for the 24th of September, 2018. This is a rerun from the 8th of September, 2009. Little Dog Lost has ended its run, and of gentle comic strips it’s one that I particularly miss.

Steve Boreman’s Little Dog Lost rerun for the 24th is the Roman Numerals joke for the week. There is a connotation of great age to anything written in Roman Numerals. Likely because we are centuries past the time they were used for anything but ornament. And even in ornament they seem to be declining in age. I do wonder if the puniness of, say, ‘MMI’ or ‘MMXX’ as a sequence of numerals, compared to (say) ‘MCMXLVII’ makes it look better to just write ‘2001’ or ‘2020’ instead.


The full set of Reading the Comics posts should be at this link. Essays that discuss Grand Avenue should be at this link. This and other appearances by Reality Check should be at this link. Appearances by F Minus are at this link. And other essays with Little Dog Lost should be at this link. Thanks for reading along.

Reading the Comics, August 24, 2018: Delayed But Eventually There Edition


Now I’ve finally had the time to deal with the rest of last week’s comics. I’ve rarely been so glad that Comic Strip Master Command has taken it easy on me for this week.

Tom Toles’s Randolph Itch, 2am for the 20th is about a common daydream, that of soap bubbles of weird shapes. There’s fun mathematics to do with soap bubbles. Most of these fall into the “calculus of variations”, which is good at finding minimums and maximums. The minimum here is a surface with zero mean curvature that satisfies particular boundaries. In soap bubble problems the boundaries have a convenient physical interpretation. They’re the wire frames you dunk into soap film, and pull out again, to see what happens. There’s less that’s proven about soap bubbles than you might think. For example: we know that two bubbles of the same size will join on a flat common surface. Do three bubbles? They seem to, when you try blowing bubbles and fitting them together. But this falls short of mathematical rigor.

Randolph blows several soap bubbles. One is a perfect cube. Caption; 'But naturally nobody was around.' Footer joke: Randolph has a video camera but asks, 'What does 'battery, battery, battery' mean?'
Tom Toles’s Randolph Itch, 2am for the 20th of August, 2018. Little does Randolph realize that the others are all five-dimensional hyperspheres too.

Parker and Hart’s Wizard of Id Classics for the 21st is a joke about the ignorance of students. Of course they don’t know basic arithmetic. Curious thing about the strip is that you can read it as an indictment of the school system, failing to help students learn basic stuff. Or you can read it as an indictment of students, refusing the hard work of learning while demanding a place in politics. Given the 1968 publication date I have a suspicion which was more likely intended. But it’s hard to tell; 1968 was a long time ago. And sometimes it’s just so easy to crack an insult there’s no guessing what it’s supposed to mean.

King: 'I'm addressing a bunch of students tomorrow. What can I tell them that they don't already know?' Speechwriter: 'How about, two and two is four?'
Parker and Hart’s Wizard of Id Classics for the 21st of August, 2018. I’m curious when the speechwriter character disappeared from the comic strip. I remember it doing inexplicable election-year jokes at least to 1980 or maybe 1984. (I mean, he is a King, and we know he’s not King of Poland, so, you know?)

Gene Mora’s Graffiti for the 22nd mentions what’s probably the most famous equation after that thing with two times two in it. It does cry out something which seems true, that E = mc^2 was there before Albert Einstein noticed it. It does get at one of those questions that, I say without knowledge, is probably less core to philosophers of mathematics than the non-expert would think. But are mathematical truths discovered or invented? There seems to be a good argument that mathematical truths are discovered. If something follows by deductive logic from the axioms of the field, and the assumptions that go into a question, then … what’s there to invent? Anyone following the same deductive rules, and using the same axioms and assumptions, would agree on the thing discovered. Invention seems like something that reflects an inventor.

On a cement wall: 'e = mc^2 was there before Einstein discovered it'
Gene Mora’s Graffiti for the 22nd of August, 2018. Still have no idea whether this comic is still in production.

But it’s hard to shake the feeling that there is invention going on. Anyone developing new mathematics decides what things seem like useful axioms. She decides that some bundle of properties is interesting enough to have a name. She decides that some consequences of these properties are so interesting as to be named theorems. Maybe even the Fundamental Theorem of the field. And there was the decision that this is a field with a question interesting enough to study. I’m not convinced that isn’t invention.

On the blackboard: 49. 40% is ___. 50% is ___. 60% is ___. Non-Wavehead kid: 'I say we wait a few days and see if it doesn't hit 70%'.
Mark Anderson’s Andertoons for the 23rd of August, 2018. Ew, I wouldn’t want to do that problem on the board either.

Mark Anderson’s Andertoons for the 23rd sees Wavehead — waaait a minute. That’s not Wavehead! This throws everything off. Well, it’s using mathematics as the subject that Not-Wavehead is trying to avoid. And it’s not using arithmetic as the subject easiest to draw on the board. It needs some kind of ascending progression to make waiting for some threshold make sense. Numbers rising that way makes sense.

Leader of a (sideways) V-flock of birds: 'Roman ya newbies! A Roman five!' The other flock of birds is in a (sideways) 5 shape.

Scott Hilburn’s The Argyle Sweater for the 24th of August, 2018. Of course, we’re assuming that they’re flying off to the right. If they’re flying towards the lower left corner, then the 5-birds are doing a bit better.

Scott Hilburn’s The Argyle Sweater for the 24th is the Roman numerals joke for this week. Oh, and apparently it’s a rerun; I hadn’t noticed before that the strip was rerunning. This isn’t a complaint. Cartoonists need vacations too.

That birds will fly in V-formation has long captured people’s imaginations. We’re pretty confident we know why they do it. The wake of one bird’s flight can make it easier for another bird to stay aloft. This is especially good for migrating birds. The fluid-dynamic calculations of this are hard to do, but any fluid-dynamic calculations are hard to do. Verifying the work was also hard, but could be done. I found and promptly lost an article about how heartbeat monitors were attached to a particular flock of birds whose migration path was well-known, so the sensors could be checked and data from them gathered several times over. (Birds take turns as the lead bird, the one that gets no lift from anyone else’s efforts.)

So far as I’m aware there’s still some mystery as to how they do it. That is, how they know to form this V-formation. A particularly promising line of study in the 80s and 90s was to look at these as self-organizing structures. This would have each bird just trying to pay attention to what made sense for itself, where to fly relative to its nearest-neighbor birds. And these simple rules created, when applied to the whole flock, that V pattern. I do not know whether this reflects current thinking about bird formations. I do know that the search for simple rules that produce rich, complicated patterns goes on. Centuries of mathematics, physics, and to an extent chemistry have primed us to expect that everything is the well-developed result of simple components.

God, on a cloud, holding a lightning bolt: 'Whenever someone talks about the odds of winning the lottery, I like to hit 'em with one of these bad boys.'
Dave Whamond’s Reality Check for the 24th of August, 2018. Well, I guess the squirrel didn’t have anything to add to this one either.

Dave Whamond’s Reality Check for the 24th is apparently an answer to The Wandering Melon‘s comic earlier this month. So now we know what kind of lead time Dave Whamond is working on.


My next, and past, Reading the Comics posts are available at this link. Other essays with Randolph Itch, 2 a.m., are at this link. Essays that mention The Wizard of Id, classic or modern, are at this link. Essays mentioning Graffiti are at this link. Other appearances by Andertoons are at this link, or just read about half of all Reading the Comics posts. The Argyle Sweater is mentioned in these essays. And other essays with Reality Check are at this link. And what the heck; here’s other essays with The Wandering Melon in them.

Reading the Comics, August 14, 2018: Condensed Books Edition


The title of this installment has nothing to do with anything. My love and I just got to talking about Reader’s Digest Condensed Books and I learned moments ago that they’re still being made. I mean, the title of the series changed from “Condensed Books” to “Select Editions” in 1997, but they’re still going on, as far as anyone can tell. This got us wondering things like how they actually do the abridging. And got me wondering whether any abridged book ended up being better than the original. So I have reasons for only getting partway through last week’s mathematically-themed comics. I don’t say they’re good reasons.

Scott Hilburn’s The Argyle Sweater for the 13th is the Roman Numerals joke for the week, the first one of those in like five days. Also didn’t know that there were still sidewalk theaters that still showed porn movies. I thought they had all been renovated into either respectable neighborhood-revitalization projects that still sometimes show Star Wars films or else become incubator space for startup investment groups.

Couple in Roman togas at the ticket booth for XXX movies. Woman: 'We'd like a refund. Not only was our movie obscene --- there clearly are NOT 30 screens here.'
Scott Hilburn’s The Argyle Sweater for the 13th of August, 2018. Because I compulsively rewrite other people’s stuff: would the joke read stronger if the woman had said ‘are NOT thirty screens here’, instead of using the Arabic numerals?

Corey Pandolph’s The Elderberries for the 13th is a joke about learning fractions. They don’t see to be having much fun thinking about them. Fair enough, I suppose. Once you’ve got the hang of basic arithmetic here come fractions to follow rules for addition and subtraction that are suddenly way more complicated. Multiplication isn’t harder, at least, although it is longer. Same with division. Without a clear idea why this is anything you want to do, yeah, it seems to be unmotivated complicating of stuff.

Dusty: 'How was school, Ben?' Ben: 'Not good. We learned fractions, today.' Dusty: 'It's all downhill from there, my friend.' Ben: 'That's what I told Mr Fogarty. And he didn't seem to argue.'
Corey Pandolph’s The Elderberries rerun for the 13th of August, 2018. I’m sure it’s a wild coincidence but ‘Mr Fogarty’ was the teacher’s name in Luann back when the strip was officially set in high school. The strip originally ran the 8th of November, 2010.

Dave Whamond’s Reality Check for the 13th is trying to pick a fight with me. I’m not taking the bait. Although by saying ‘likelihood’ the question seems to be setting up a probability question. Those tend to use ‘p’ and ‘q’ as a generic variable name, rather than ‘x’. I bet you imagine that ‘p’ gets used to represent a possibly-unknown ‘probability’ because, oh yeah, first letter. Well … so far as I know that’s why. I’m away from my references right now so I can’t look them over and find no quite satisfactory answer. But that sure seems like it. ‘q’ gets called in if you need a second probability, and don’t want to deal with subscripts, then it’s a nice convenient letter close to ‘p’ in the alphabet. Again, so far as I know.

Exam question: 'Solve the equation where x equals the likelihood you will ever use algebra after high school.' The squirrel mascot who usually has a side joke in the corner is just looking over the edge of the paper, wordless.
Dave Whamond’s Reality Check for the 13th of August, 2018. Little surprised that the squirrel didn’t have any corner comment this day.

Thaves’s Frank and Ernest for the 13th is the anthropomorphic-numerals joke for the week.

Corporate Accounting Dept. A bunch of anthropomorphic numerals are inside a jail. Man with the key: 'investors will be interested in this --- we're going to release the numbers today.'
Thaves’s Frank and Ernest for the 13th of August, 2018. Somehow, the ‘8’ looks especially sinister by not having a mouth.

You can see this and more essays about comic strips by following this link. Other essays describing The Argyle Sweater are at this link. Essays inspired by The Elderberries are at this link. Essays about Reality Check are at this link. And times when I’ve talked about Frank and Ernest you should find at this link.. I can’t be perfectly sure about The Argyle Sweater and The Elderberries because I keep forgetting whether I had decided to include the ‘the’ of their titles as part of their tags. I keep figuring I’ll check which one I’ve used more often and then edit tags to make things consistent. And make a little style guide so that I remember. This will never happen.

Reading the Comics, August 4, 2018: August 4, 2018 Edition


And finally, at last, there’s a couple of comics left over from last week and that all ran the same day. If I hadn’t gone on forever about negative Kelvin temperatures I might have included them in the previous essay. That’s all right. These are strips I expect to need relatively short discussions to explore. Watch now as I put out 2,400 words explaining Wavehead misinterpreting the teacher’s question.

Dave Whamond’s Reality Check for the 4th is proof that my time spent writing about which is better, large numbers or small last week wasn’t wasted. There I wrote about four versus five for Beetle Bailey. Here it’s the same joke, but with compound words. Well, that’s easy to take care of.

[ Caption: Most people have a forehead --- Dave has a Five-Head. ] (Dave has an extremely tall head with lots of space between his eyebrows and his hair.) Squirrel in the corner: 'He'll need a 12-gallon hat.'
Dave Whamond’s Reality Check for the 4th of August, 2018. I’m sure it’s a coincidence that the tall-headed person shares a name with the cartoonist.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th is driving me slightly crazy. The equation on the board looks like an electrostatics problem to me. The ‘E’ is a common enough symbol for the strength of an electric field. And the funny-looking K’s look to me like the Greek kappa. This often represents the dielectric constant. That measures how well an electric field can move through a material. The upside-down triangles, known in the trade as Delta, describe — well, that’s getting complicated. By themselves, they describe measuring “how much the thing right after this changes in different directions”. When there’s a x symbol between the Delta and the thing, it measures something called the “curl”. This roughly measures how much the field inspires things caught up in it to turn. (Don’t try passing this off to your thesis defense committee.) The Delta x Delta x E describes the curl of the curl of E. Oh, I don’t like visualizing that. I don’t blame you if you don’t want to either.

Professor Ridley: 'Imagine an infinitely thin rod. Visualize it but don't laugh at it. I know it's difficult. Now, the following equations hold for ... ' [ Caption: Professor Ridley's cry for help goes unnoticed. ]
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th of August, 2018. Really not clear what the cry for help would be about. Just treat the rod as a limiting case of an enormous number of small spheres placed end to end and you’re done.

Anyway. So all this looks like it’s some problem about a rod inside an electric field. Fine enough. What I don’t know and can’t work out is what the problem is studying exactly. So I can’t tell you whether the equation, so far as we see it, is legitimately something to see in class. Envisioning a rod that’s infinitely thin is a common enough mathematical trick, though. Three-dimensional objects are hard to deal with. They have edges. These are fussy to deal with. Making sure the interior, the boundary, and the exterior match up in a logically consistent way is tedious. But a wire? A plane? A single point? That’s easy. They don’t have an interior. You don’t have to match up the complicated stuff.

For real world problems, yeah, you have to deal with the interior. Or you have to work out reasons why the interiors aren’t important in your problem. And it can be that your object is so small compared to the space it has to work in that the fact it’s not infinitely thin or flat or smooth just doesn’t matter. Mathematical models, such as give us equations, are a blend of describing what really is there and what we can work with.

Lotto official looking over a burnt, shattered check: 'What are the ODDS?! First he wins the lottery and then he gets struck by lightning!'
Mike Shiell’s The Wandering Melon for the 4th of August, 2018. Still, impressive watchband that it’s stood up to all that trouble.

Mike Shiell’s The Wandering Melon for the 4th is a probability joke, about two events that nobody’s likely to experience. The chance any individual will win a lottery is tiny, but enough people play them that someone wins just about any given week. The chance any individual will get struck by lightning is tiny too. But it happens to people. The combination? Well, that’s obviously impossible.

In July of 2015, Peter McCathie had this happen. He survived a lightning strike first. And then won the Atlantic Lotto 6/49. This was years apart, but the chance of both happening the same day, or same week? … Well, the world is vast and complicated. Unlikely things will happen.


And that’s all that I have for the past week. Come Sunday I should have my next Reading the Comics post, and you can find it and other essays at this link. Other essays that mention Reality Check are at this link. The many other essays which talk about Saturday Morning Breakfast Cereal are at this link. And other essays about The Wandering Melon are at this link. Thanks.

Reading the Comics, June 19, 2018: Don’t Ask About The Hyperbolic Cosine Edition


Although the hyperbolic cosine is interesting and I could go on about it.

Eric the Circle for the 18th of June is a bit of geometric wordplay for the week. A secant is — well, many things. One of the important things is it’s a line that cuts across a circle. It intersects the circle in two points. This is as opposed to a tangent, which touch it in one. Or missing it altogether, which I think hasn’t got any special name. “Secant” also appears as one of the six common trig functions out there.

Small circle: 'Hey, Eric! There's a line on you!' Medium circle: 'Get it off!' Eric, with a line across his side: 'See? Can't!'
Eric the Circle for the 18th of June, 2018. This one was composed by Griffinetsabine. It originally appeared sometime in 2012.

In value the secant of an angle is just the reciprocal of the cosine of that angle. Where the cosine is never smaller than -1 nor larger than 1, the secant is always either greater than 1 or smaller than -1. It’s a useful function to have by name. We can write “the secant of angle θ” as sec(\theta) . The otherwise sensible-looking \cos^{-1}(\theta) is unavailable, because we use that to mean “the angle whose cosine is θ”. We need to express that idea, the “arc-cosine” or “inverse cosine”, quite a bit too. And \cos(\theta)^{-1} would look like we wanted the cosine of one divided by θ. Ultimately, we have a lot of ideas we’d like to write down, and only so many convenient quick shorthand ways to write them. And by using secant as its own function we can let the arc-cosine have a convenient shorthand symbol. These symbols are a point where you see the messy, human, evolutionary nature of mathematical symbols at work.

We can understand the cosine of an angle θ by imagining a right triangle with hypotenuse of length 1. Set that so the hypotenuse makes angle θ with respect to the x-axis. Then the opposite leg of that right triangle will be the cosine of θ away from the origin. The secant, now, that works differently. Again here imagine a right triangle, but this time one of the legs has length 1. And that leg is at an angle θ with respect to the x-axis. Then the far leg of that right triangle is going to cross the x-axis. And it’ll do that at a point that’s the secant of θ away from the origin.

Debbie: 'In this soap opera, Kimberly is trying to hide her past from Renaldo ... who has hired a detective to find out how many times (x) Kimberly has made love to how many lovers (y). ... Who says algebra has no use outside the classroom?'
Larry Wright’s Motley Classics for the 19th of June, 2018. It originally ran sometime in 1997.

Larry Wright’s Motley Classics for the 19th speaks of algebra as the way to explain any sufficiently complicated thing. Algebra’s probably not the right tool to analyze a soap opera, or any drama really. The interactions of characters are probably more a matter for graph theory. That’s the field that studies groups of things and the links between them. Occasionally you’ll see analyses of, say, which characters on some complicated science fiction show spend time with each other and which ones don’t. I’m not aware of any that were done on soap operas proper. I suspect most mathematics-oriented nerds view the soaps as beneath their study. But most soap operas do produce a lot of show to watch, and to summarize; I can’t blame them for taking a smaller, easier-to-summarize data set to study. (Also I’m not sure any of these graphs reveal anything more enlightening than, “Huh, really thought The Doctor met Winston Churchill more often than that”.)

Teacher: 'You two making progress on the math problem?' Nancy: 'We're making progress on *A* math problem.' (Nancy and Esther's paper: 'number of seconds left in school, 24 x 5 x 60 x 60'.)
Olivia Jaimes’s Nancy for the 19th of June, 2018. This one originally appeared in June of 2018.

Olivia Jaimes’s Nancy for the 19th is a joke on getting students motivated to do mathematics. Set a problem whose interest people see and they can do wonderful things.

Circle in the bar, speaking to another circle: 'You wanna get out of here, come back to my place and create a Venn diagram?' ... Squirrel in the corner, adding commentary: 'It'll never work ... they have nothing in common.'
Dave Whamond’s Reality Check for the 19th of June, 2018. Those seem like small drinks for circles that large.

Dave Whamond’s Reality Check for the 19th is our Venn Diagram strip for the week. I say the real punch line is the squirrel’s, though. Properly, yes, the Venn Diagram with the two having nothing in common should still have them overlap in space. There should be a signifier inside that there’s nothing in common, such as the null symbol or an x’d out intersection. But not overlapping at all is so commonly used that it might as well be standard.

Cardinal: 'Whatever you're thinking, don't say it.' Other bird has a thought balloon full of arithmetic expressions.
Teresa Bullitt’s Frog Applause for the 21st of June, 2018. It’s a Dadaist comic strip; embrace the bizarreness.

Teresa Bullitt’s Frog Applause for the 21st uses a thought balloon full of mathematical symbols as icon for far too much deep thinking to understand. I would like to give my opinion about the meaningfulness of the expressions. But they’re too small for me to make out, and GoComics doesn’t allow for zooming in on their comics anymore. I looks like it’s drawn from some real problem, based on the orderliness of it all. But I have no good reason to believe that.


If you’d like more of these Reading the Comics posts, you can find them in reverse chronological order at this link. If you’re interested in the comics mentioned particularly here, Eric the Circle strips are here. Frog Applause comics are on that link. Motley strips are on that link. Nancy comics are on that page. And And Reality Check strips are here.

Reading the Comics, May 5, 2018: Does Anyone Know Where The Infinite Hotel Comes From Edition


With a light load of mathematically-themed comic strips I’m going to have to think of things to write about twice this coming week. Fortunately, I have plans. We’ll see how that works out for me. So far this year I’m running about one-for-eight on my plans.

Mort Walker and Dik Browne’s Hi and Lois for the 1st of November, 1960 looks pretty familiar somehow. Having noticed what might be the first appearance of “the answer is twelve?” in Peanuts I’m curious why Chip started out by guessing twelve. Probably just coincidence. Possibly that twelve is just big enough to sound mathematical without being conspicuously funny, like 23 or 37 or 42 might be. I’m a bit curious that after the first guess Sally looked for smaller numbers than twelve, while Chip (mostly) looked for larger ones. And I see a logic in going from a first guess of 12 to a second guess of either 4 or 144. The 32 is a weird one.

Teacher: 'Chip, do you know the answer to number five?' Chip: 'Is it twelve? No, wait ... it's four. Or is it 32 ... it's either that or 144. No, wait a second ... I'll get it.' Teacher: 'I'm sure you will --- we're nearly out of numbers!'
Mort Walker and Dik Browne’s Hi and Lois for the 1st of November, 1960 and reprinted the 30th of April, 2018. Yeah, sure, eleven years later Charles Schulz would do basically the same joke. But comics snarkers get all smug when they notice that The Argyle Sweater is using the same premise as a Far Side from 1983 or something.

Tom Toles’s Randolph Itch, 2 am for the 30th of April, 2018 is on at least its third appearance around here. I suppose I have to retire the strip from consideration for these comics roundups. It didn’t run that long, sad to say, and I think I’ve featured all its mathematical strips. I’ll go on reading, though, as I like the style and Toles’s sense of humor.

Randolph, thinking in bed: 'Algebra pretty much put pirates out of business.' Pirate teacher: 'If ax^2 + bx + c = 0, what is x?' And a pirate sweats. Footer joke: '15 men on a dead man's chest, you ho ho, and a bottle of rum equals what?'
Tom Toles’s Randolph Itch, 2 am for the 30th of April, 2018. I think I’ve mentioned not knowing whether the legendary X on pirate maps is related to the use of X as the thing-to-be-found in algebra. My understanding is the X on a pirate map thing is mostly a matter of storytelling rather than something anyone really did.

Mark Tatulli’s Heart of the City for the 3rd of May is a riff on the motivation problem. For once, not about the motivation of the people in story problems to do what they do. It’s instead about why the student should care what the story people do. And, fair enough, really. It’s easy to calculate something you’d like to know the answer to. But give the teacher or textbook writer a break. There’s nothing that’s interesting to everybody. No, not even what minimum grade they need on this exam to get an A in the course. After a moment of clarity in fifth grade I never cared what my scores were. I just did my work and accepted the assessment. My choice not to worry about my grades had more good than bad results, but I admit, there were bad results too.

Heart: 'This homework is ridiculous! How are we supposed to know this? OK, so Julio has eleven apples! Why is it any of my business how many he shares with Allisa and Wesley? Why should I care how he divides them or what fraction he keeps for himself?' Dean: 'They're just math word problems. I don't think we have to explain motivation.' Heart: 'I guess I just can't get past why exactly a kid has eleven apples in the first place!'
Mark Tatulli’s Heart of the City for the 3rd of May, 2018. How does Heart know that Julio is a kid? Adults will go out and buy a dozen apples without that seeming strange, and we’ll eat as many as four of them before forgetting they’re on the counter and letting them rot by accident.

John McNamee’s Pie Comic for the 4th of May riffs on some ancient story-problems built on infinite sets. I don’t know the original source. I assume a Martin Gardiner pop-mathematics essay. I don’t know, though, and I’m curious if anyone does know.

[ You arrive at the Infinite Hotel ... but the concierge says *all* infinity of their rooms are booked. Luckily, you know MATH. 'Infinity = Infinity + 1'. You explain that if you just ask each guest to move one room over ... ] There's a large man in diapers with a sock puppet on his hand in the first door. [ Yeah ... math's not solving that. ] You drive away.
John McNamee’s Pie Comic for the 4th of May, 2018. Also you know how long it’d take to re-code everybody’s door access card? It’d be like forever.

Often I see these kinds of problem as set at the Hilbert Hotel. This references David Hilbert, the late-19th/early-20th century mastermind behind the 20th century’s mathematics field. They try to challenge people’s intuitions about infinitely large sets. Ponder a hotel with one room for each of the counting numbers. Suppose it’s full. How many guests can you add to it? Can you add infinitely many more guests, and still have room for them all? If you do it right, and if “infinitely many more guests” means something particular, yes. If certain practical points don’t get in the way. I mean practical for a hotel with infinitely many rooms.

This is a new-tag comic.

Medieval monks, talking about the one who's written down E = mc^2. 'God only knows what it means. This guy isn't all that swift.'
Dave Whamond’s Reality Check for the 4th of May, 2018. Yeah, I heard the sequel to A Canticle for Leibowitz was disappointing.

Dave Whamond’s Reality Check for the 4th is a riff on Albert Einstein’s best-known equation. He had some other work, granted. But who didn’t?

Reading the Comics, April 25, 2018: Coronet Blue Edition


You know what? Sometimes there just isn’t any kind of theme for the week’s strips. I can use an arbitrary name.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st of April, 2018 would have gone in last week if I weren’t preoccupied on Saturday. The joke is aimed at freshman calculus students and then intro Real Analysis students. The talk about things being “arbitrarily small” turns up a lot in these courses. Why? Well, in them we usually want to show that one thing equals another. But it’s hard to do that. What we can show is some estimate of how different the first thing can be from the second. And if you can show that that difference can be made small enough by calculating it correctly, great. You’ve shown the two things are equal.

Delta and epsilon turn up in these a lot. In the generic proof of this you say you want to show the difference between the thing you can calculate and the thing you want is smaller than epsilon. So you have the thing you can calculate parameterized by delta. Then your problem becomes showing that if delta is small enough, the difference between what you can do and what you want is smaller than epsilon. This is why it’s an appropriately-formed joke to show someone squeezed by a delta and an epsilon. These are the lower-case delta and epsilon, which is why it’s not a triangle on the left there.

Mad scientist cackling at a man being crushed between giant delta and epsilon figure: 'And now, good doctor, we will see how you fit between this delta and this epsilon!' Caption: Soon, soon the calculus teacher would become arbitrarily small.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 21st of April, 2018. I feel vaguely personally called out by the calculus teacher wearing cargo shorts, tall white socks, and sandals.

For example, suppose you want to know how long the perimeter of an ellipse is. But all you can calculate is the perimeter of a polygon. I would expect to make a proof of it look like this. Give me an epsilon that’s how much error you’ll tolerate between the polygon’s perimeter and the ellipse’s perimeter. I would then try to find, for epsilon, a corresponding delta. And that if the edges of a polygon are never farther than delta from a point on the ellipse, then the perimeter of the polygon and that of the ellipse are less than epsilon away from each other. And that’s Calculus and Real Analysis.

John Zakour and Scott Roberts’s Maria’s Day for the 22nd is the anthropomorphic numerals joke for this week. I’m curious whether the 1 had a serif that could be wrestled or whether the whole number had to be flopped over, as though it were a ruler or a fat noodle.

Maria at her desk challenges a giant number 4 to arm wrestling; she slams its 'arm' down easily. Other numerals flee as she yells out: 'Okay, anyone else wanna take me on? Huh? --- Yeah, didn't think so!' Reality: she's at her desk with a book and some paper and says, "Whew! This math homework was tough --- but I think I got it down.'
John Zakour and Scott Roberts’s Maria’s Day for the 22nd of April, 2018. I’m curious whether Zakour and Roberts deliberately put 2 and 3 to the left, with pain stars indicating they’ve been beaten already, while the bigger numbers are off to the side. Or was it just an arbitrary choice? The numbers are almost in order, left to right, except that the 7’s out of place. So maybe the ordering is just coincidence?

Anthony Blades’s Bewley for the 23rd offers advice for what to do if you’ve not got your homework. This strip’s already been run, and mentioned here. I might drop this from my reading if it turns out the strip is done and I’ve exhausted all the topics it inspires.

Bea: 'Aaaah! I forgot to do my maths homework!' Tonus: 'I did mine.' Bea: 'Can I copy yours?' Tonus: 'Of course you can. I didn't know the answers so I drew a picture of a scary dinosaur.' [ Silent penultimate panel. ] Bea: 'Better than nothing.' Tonus: 'Remember the big teeth. Big teeth make it scary.'
Anthony Blades’s Bewley for the 23rd of April, 2018. Whenever a comic strip with this setup begins I think of the time in geometry class when I realized I hadn’t done any homework and wondered if I could get something done in the time it took papers to be passed up. This in a class of twelve students. No, there was not, even though the teacher started from the other side of the classroom.

Dave Whamond’s Reality Check for the 23rd is designed for the doors of mathematics teachers everywhere. It does incidentally express one of those truths you barely notice: that statisticians and mathematicians don’t seem to be quite in the same field. They’ve got a lot of common interest, certainly. But they’re often separate departments in a college or university. When they do share a department it’s named the Department of Mathematics and Statistics, itself an acknowledgement that they’re not quite the same thing. (Also it seems to me it’s always Mathematics-and-Statistics. If there’s a Department of Statistics-and-Mathematics somewhere I don’t know of it and would be curious.) This has to reflect historical influence. Statistics, for all that it uses the language of mathematics and that logical rigor and ideas about proofs and all, comes from a very practical, applied, even bureaucratic source. It grew out of asking questions about the populations of nations and the reliable manufacture of products. Mathematics, even the mathematics that is about real-world problems, is different. A mathematician might specialize in the equations that describe fluid flows, for example. But it could plausibly be because they have interesting and strange analytical properties. It’d be only incidental that they might also say something enlightening about why the plumbing is stopped up.

[ Clown Statistician vs Clown mathematician. ] The Clown Statistician holds up a pie chart, ready to throw it. The mathematician holds up a pi symbol, ready to throw it. Corner squirrel's comment: 'There's always room for more pi.'
Dave Whamond’s Reality Check for the 23rd of April, 2018. I’m not sure I’ve laughed more at a dumb joke than I have at this in a long while.

Neal Rubin and Rod Whigham’s Gil Thorp for the 24th seems to be setting out the premise for the summer storyline. It’s sabermetrics. Or at least the idea that sports performance can be quantized, measured, and improved. The principle behind that is sound enough. The trick is figuring out what are the right things to measure, and what can be done to improve them. Also another trick is don’t be a high school student trying to lecture classmates about geometry. Seriously. They are not going to thank you. Even if you turn out to be right. I’m not sure how you would have much control of the angle your ball comes off the bat, but that’s probably my inexperience. I’ve learned a lot about how to control a pinball hitting the flipper. I’m not sure I could quantize any of it, but I admit I haven’t made a serious attempt to try either. Also, when you start doing baseball statistics you run a roughly 45% chance of falling into a deep well of calculation and acronyms of up to twelve letters from which you never emerge. Be careful. (This is a new comic strip tag.)

[ With rain delaying (baseball) practice, Kevin Pelwecki expounds on his new favorite subject --- ] Kevin: 'Launch angle! You want the ball coming off the bat at 25 degrees.' Teammate: 'Anyone else notice we're taking math lessons --- from a guy who barely passed geometry?'
Neal Rubin and Rod Whigham’s Gil Thorp for the 24th of April, 2018. Are … both word balloons coming from the same guy? In the last panel there. I understand one guy starting and another closing a thought but that’s usually something you do with an established in-joke that anyone can feed and anyone else can finish. A spontaneous insult like this seems like it only needs the one person, but the word balloon tails are weird if they’re both from the same guy.

Randy Glasbergen’s Glasbergen Cartoons rerun for the 25th feels a little like a slight against me. Well, no matter. Use the things that get you in the mood you need to do well. (Not a new comic strip tag because I’m filing it under ‘Randy Glasbergen’ which I guess I used before?)

Kid with guitar: 'I start every song by counting 1-2-3-4 because it reminds me of math. Math depresses me and that helps me sing the blues.'
Randy Glasbergen’s Glasbergen Cartoons rerun for the 25th of April, 2018. OK, but what’s his guitar plugged in to?

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Reading the Comics, December 9, 2017: Zach Weinersmith Wants My Attention Edition


If anything dominated the week in mathematically-themed comic strips it was Zach Weinersmith’s Saturday Morning Breakfast Cereal. I don’t know how GoComics selects the strips to (re?)print on their site. But there were at least four that seemed on-point enough for me to mention. So, okay. He’s got my attention. What’s he do with it?

On the 3rd of December is a strip I can say is about conditional probability. The mathematician might be right that the chance someone will be murdered by a serial killer are less than one in ten million. But that is the chance of someone drawn from the whole universe of human experiences. There are people who will never be near a serial killer, for example, or who never come to his attention or who evade his interest. But if we know someone is near a serial killer, or does attract his interest? The information changes the probability. And this is where you get all those counter-intuitive and somewhat annoying logic puzzles about, like, the chance someone’s other child is a girl if the one who just walked in was, and how that changes if you’re told whether the girl who just entered was the elder.

On the 5th is a strip about sequences. And built on the famous example of exponential growth from doubling a reward enough times. Well, you know these things never work out for the wise guy. The “Fibonacci Spiral” spoken of in the next-to-last panel is a spiral, like you figure. The dimensions of the spiral are based on those of golden-ratio rectangles. It looks a great deal like a logarithmic spiral to the untrained eye. Also to the trained eye, but you knew that. I think it’s supposed to be humiliating that someone would call such a spiral “random”. But I admit I don’t get that part.

The strip for the 6th has a more implicit mathematical content. It hypothesizes that mathematicians, given the chance, will be more interested in doing recreational puzzles than even in eating and drinking. It’s amusing, but I’ll admit I’ve found very few puzzles all that compelling. This isn’t to say there aren’t problems I keep coming back to because I’m curious about them, just that they don’t overwhelm my common sense. Don’t ask me when I last received actual pay for doing something mathematical.

And then on the 9th is one more strip, about logicians. And logic puzzles, such as you might get in a Martin Gardner collection. The problem is written out on the chalkboard with some shorthand logical symbols. And they’re symbols both philosophers and mathematicians use. The letter that looks like a V with a crossbar means “for all”. (The mnemonic I got was “it’s an A-for-all, upside-down”. This paired with the other common symbol, which looks like a backwards E and means there exists: “E-for-exists, backwards”. Later I noticed upside-down A and backwards E could both be just 180-degree-rotated A and E. But try saying “180-degree-rotated” in a quick way.) The curvy E between the letters ‘x’ and ‘S’ means “belongs to the set”. So that first line says “for all x that belong to the set S this follows”. Writing out “isLiar(x)” instead of, say, “L(x)”, is more a philosopher’s thing than a mathematician’s. But it wouldn’t throw anyway. And the T just means emphasizing that this is true.

And that is as much about Saturday Morning Breakfast Cereal as I have to say this week.

Sam Hurt’s Eyebeam for the 4th tells a cute story about twins trying to explain infinity to one another. I’m not sure I can agree with the older twin’s assertion that infinity means there’s no biggest number. But that’s just because I worry there’s something imprecise going on there. I’m looking forward to the kids learning about negative numbers, though, and getting to wonder what’s the biggest negative real number.

Percy Crosby’s Skippy for the 4th starts with Skippy explaining a story problem. One about buying potatoes, in this case. I’m tickled by how cranky Skippy is about boring old story problems. Motivation is always a challenge. The strip originally ran the 7th of October, 1930.

Dave Whamond’s Reality Check for the 6th uses a panel of (gibberish) mathematics as an example of an algorithm. Algorithms are mathematical, in origin at least. The word comes to us from the 9th century Persian mathematician Al-Khwarizmi’s text about how to calculate. The modern sense of the word comes from trying to describe the methods by which a problem can be solved. So, legitimate use of mathematics to show off the idea. The symbols still don’t mean anything.

Joe: 'Grandpa, what's 5x7?' Grandpa: 'Why do you wanna know?' Joe: 'I'm testing your memory.' Grandpa: 'Oh! The answer's 35.' Joe: 'Thanks! Now what is 8x8?' Grandpa: 'Joe, is that last night's homework?' Joe: 'We're almost done! Only 19 more!'
Rick Detorie’s One Big Happy for the 7th of December, 2017. And some attention, please, for Ruthie there. She’s completely irrelevant to the action, but it makes sense for her to be there if Grandpa is walking them to school, and she adds action — and acting — to the scenes.

Rick Detorie’s One Big Happy for the 7th has Joe trying to get his mathematics homework done at the last minute. … And it’s caused me to reflect on how twenty multiplication problems seems like a reasonable number to do. But there’s only fifty multiplications to even do, at least if you’re doing the times tables up to the 10s. No wonder students get so bored seeing the same problems over and over. It’s a little less dire if you’re learning times tables up to the 12s, but not that much better. Yow.

Olivia Walch’s Imogen Quest for the 8th looks pretty legitimate to me. It’s going to read as gibberish to people who haven’t done parametric functions, though. Start with the plane and the familiar old idea of ‘x’ and ‘y’ representing how far one is along a horizontal and a vertical direction. Here, we’re given a dummy variable ‘t’, and functions to describe a value for ‘x’ and ‘y’ matching each value of ‘t’. The plot then shows all the points that ever match a pair of ‘x’ and ‘y’ coordinates for some ‘t’. The top drawing is a shape known as the cardioid, because it kind of looks like a Valentine-heart. The lower figure is a much more complicated parametric equation. It looks more anatomically accurate,

Still no sign of Mark Anderson’s Andertoons and the drought is worrying me, yes.

But they’re still going on the cartoonist’s web site, so there’s that.

Reading the Comics, September 9, 2017: First Split Week Edition, Part 2


I don’t actually like it when a split week has so many more comics one day than the next, but I also don’t like splitting across a day if I can avoid it. This week, I had to do a little of both since there were so many comic strips that were relevant enough on the 8th. But they were dominated by the idea of going back to school, yet.

Randy Glasbergen’s Glasbergen Cartoons rerun for the 8th is another back-to-school gag. And it uses arithmetic as the mathematics at its most basic. Arithmetic might not be the most fundamental mathematics, but it does seem to be one of the parts we understand first. It’s probably last to be forgotten even on a long summer break.

Mark Pett’s Mr Lowe rerun for the 8th is built on the familiar old question of why learn arithmetic when there’s computers. Quentin is unconvinced of this as motive for learning long division. I’ll grant the case could be made better. I admit I’m not sure how, though. I think long division is good as a way to teach, especially, the process of estimating and improving estimates of a calculation. There’s a lot of real mathematics in doing that.

Guy Gilchrist’s Nancy for the 8th is another back-to-school strip. Nancy’s faced with “this much math” so close to summer. Her given problem’s a bit of a mess to me. But it’s mostly teaching whether the student’s got the hang of the order of operations. And the instructor clearly hasn’t got the sense right. People can ask whether we should parse “12 divided by 3 times 4” as “(12 divided by 3) times 4” or as “12 divided by (3 times 4)”, and that does make a major difference. Multiplication commutes; you can do it in any order. Division doesn’t. Leaving ambiguous phrasing is the sort of thing you learn, instinctively, to avoid. Nancy would be justified in refusing to do the problem on the grounds that there is no unambiguous way to evaluate it, and that the instructor surely did not mean for her to evaluate it all four different plausible ways.

By the way, I’ve seen going around Normal Person Twitter this week a comment about how they just discovered the division symbol ÷, the obelus, is “just” the fraction bar with dots above and below where the unknown numbers go. I agree this is a great mnemonic for understanding what is being asked for with the symbol. But I see no evidence that this is where the symbol, historically, comes from. We first see ÷ used for division in the writings of Johann Henrich Rahn, in 1659, and the symbol gained popularity particularly when John Pell picked it up nine years later. But it’s not like Rahn invented the symbol out of nowhere; it had been used for subtraction for over 125 years at that point. There were also a good number of writers using : or / or \ for division. There were some people using a center dot before and after a / mark for this, like the % sign fell on its side. That ÷ gained popularity in English and American writing seems to be a quirk of fate, possibly augmented by it being relatively easy to produce on a standard typewriter. (Florian Cajori notes that the National Committee on Mathematical Requirements recommended dropping ÷ altogether in favor of a symbol that actually has use in non-mathematical life, the / mark. The Committee recommended this in 1923, so you see how well the form agenda is doing.)

Dave Whamond’s Reality Check for the 8th is the anthropomorphic-numerals joke for this week. A week without one is always a bit … peculiar.

Mark Leiknes’s Cow and Boy rerun for the 9th only mentions mathematics, and that as a course that Billy would rather be skipping. But I like the comic strip and want to promote its memory as much as possible. It’s a deeply weird thing, because it has something like 400 running jokes, and it’s hard to get into because the first couple times you see a pastoral conversation interrupted by an orca firing a bazooka at a cat-helicopter while a panda brags of blowing up the moon it seems like pure gibberish. If you can get through that, you realize why this is funny.

Dave Blazek’s Loose Parts for the 9th uses chalkboards full of stuff as the sign of a professor doing serious thinking. Mathematics is will-suited for chalkboards, at least in comic strips. It conveys a lot of thought and doesn’t need much preplanning. Although a joke about the difficulties in planning out blackboard use does take that planning. Yes, there is a particular pain that comes from having more stuff to write down in the quick yet easily collaborative medium of the chalkboard than there is board space to write.

Brian Basset’s Red and Rover for the 9th also really only casually mentions mathematics. But it’s another comic strip I like a good deal so would like to talk up. Anyway, it does show Red discovering he doesn’t mind doing mathematics when he sees the use.

Reading the Comics, April 6, 2017: Abbreviated Week Edition


I’m writing this a little bit early because I’m not able to include the Saturday strips in the roundup. There won’t be enough to make a split week edition; I’ll just add the Saturday strips to next week’s report. In the meanwhile:

Mac King and Bill King’s Magic in a Minute for the 2nd is a magic trick, as the name suggests. It figures out a card by way of shuffling a (partial) deck and getting three (honest) answers from the other participant. If I’m not counting wrongly, you could do this trick with up to 27 cards and still get the right card after three answers. I feel like there should be a way to explain this that’s grounded in information theory, but I’m not able to put that together. I leave the suggestion here for people who see the obvious before I get to it.

Bil Keane and Jeff Keane’s Family Circus (probable) rerun for the 6th reassured me that this was not going to be a single-strip week. And a dubiously included single strip at that. I’m not sure that lotteries are the best use of the knowledge of numbers, but they’re a practical use anyway.

Dolly holds up pads of paper with numbers on them. 'C'mon, PJ, you hafta learn your numbers or else you'll never win the lottery.'
Bil Keane and Jeff Keane’s Family Circus for the 6th of April, 2017. I’m not familiar enough with the evolution of the Family Circus style to say whether this is a rerun, a newly-drawn strip, or an old strip with a new caption. I suppose there is a certain timelessness to it, at least once we get into the era when states sported lotteries again.

Bill Bettwy’s Take It From The Tinkersons for the 6th is part of the universe of students resisting class. I can understand the motivation problem in caring about numbers of apples that satisfy some condition. In the role of distinct objects whose number can be counted or deduced cards are as good as apples. In the role of things to gamble on, cards open up a lot of probability questions. Counting cards is even about how the probability of future events changes as information about the system changes. There’s a lot worth learning there. I wouldn’t try teaching it to elementary school students.

The teacher: 'How many apples will be left, Tillman?' 'When are we going to start counting things more exciting than fruit?' 'What would you like to count, Tillman?' 'Cards.'
Bill Bettwy’s Take It From The Tinkersons for the 6th of April, 2017. That tree in the third panel is a transplant from a Slylock Fox six-differences panel. They’ve been trying to rebuild the population of trees that are sometimes three triangles and sometimes four triangles tall.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 6th uses mathematics as the stuff know-it-alls know. At least I suppose it is; Doctor Know It All speaks of “the pathagorean principle”. I’m assuming that’s meant to be the Pythagorean theorem, although the talk about “in any right triangle the area … ” skews things. You can get to stuf about areas of triangles from the Pythagorean theorem. One of the shorter proofs of it depends on the areas of the squares of the three sides of a right triangle. But it’s not what people typically think of right away. But he wouldn’t be the first know-it-all to start blathering on the assumption that people aren’t really listening. It’s common enough to suppose someone who speaks confidently and at length must know something.

Dave Whamond’s Reality Check for the 6th is a welcome return to anthropomorphic-numerals humor. Been a while.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 6th builds on the form of a classic puzzle, about a sequence indexed to the squares of a chessboard. The story being riffed on is a bit of mathematical legend. The King offered the inventor of chess any reward. The inventor asked for one grain of wheat for the first square, two grains for the second square, four grains for the third square, eight grains for the fourth square, and so on, through all 64 squares. An extravagant reward, but surely one within the king’s power to grant, right? And of course not: by the 64th doubling the amount of wheat involved is so enormous it’s impossibly great wealth.

The father’s offer is meant to evoke that. But he phrases it in a deceptive way, “one penny for the first square, two for the second, and so on”. That “and so on” is the key. Listing a sequence and ending “and so on” is incomplete. The sequence can go in absolutely any direction after the given examples and not be inconsistent. There is no way to pick a single extrapolation as the only logical choice.

We do it anyway, though. Even mathematicians say “and so on”. This is because we usually stick to a couple popular extrapolations. We suppose things follow a couple common patterns. They’re polynomials. Or they’re exponentials. Or they’re sine waves. If they’re polynomials, they’re lower-order polynomials. Things like that. Most of the time we’re not trying to trick our fellow mathematicians. Or we know we’re modeling things with some physical base and we have reason to expect some particular type of function.

In this case, the $1.27 total is consistent with getting two cents for every chess square after the first. There are infinitely many other patterns that would work, and the kid would have been wise to ask for what precisely “and so on” meant before choosing.

Berkeley Breathed’s Bloom County 2017 for the 7th is the climax of a little story in which Oliver Wendell Holmes has been annoying people by shoving scientific explanations of things into their otherwise pleasant days. It’s a habit some scientifically-minded folks have, and it’s an annoying one. Many of us outgrow it. Anyway, this strip is about the curious evidence suggesting that the universe is not just expanding, but accelerating its expansion. There are mathematical models which allow this to happen. When developing General Relativity, Albert Einstein included a Cosmological Constant for little reason besides that without it, his model would suggest the universe was of a finite age and had expanded from an infinitesimally small origin. He had grown up without anyone knowing of any evidence that the size of the universe was a thing that could change.

Anyway, the Cosmological Constant is a puzzle. We can find values that seem to match what we observe, but we don’t know of a good reason it should be there. We sciencey types like to have models that match data, but we appreciate more knowing why the models look like that and not anything else. So it’s a good problem some of the cosmologists have been working on. But we’ve been here before. A great deal of physics, especially in the 20th Century, has been driven by looking for reasons behind what look like arbitrary points in a successful model. If Oliver were better-versed in the history of science — something scientifically minded people are often weak on, myself included — he’d be less easily taunted by Opus.

Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 7th thinks that we forgot they ran this same strip back on the 17th of March. I spotted it, though. Nyah.

Reading the Comics, February 15, 2017: SMBC Does Not Cut In Line Edition


On reflection, that Saturday Morning Breakfast Cereal I was thinking about was not mathematically-inclined enough to be worth including here. Helping make my mind up on that was that I had enough other comic strips to discuss here that I didn’t need to pad my essay. Yes, on a slow week I let even more marginal stuff in. Here’s the comic I don’t figure to talk about. Enjoy!

Jack Pullan’s Boomerangs rerun for the 16th is another strip built around the “algebra is useless in real life” notion. I’m too busy noticing Mom in the first panel saying “what are you doing play [sic] video games?” to respond.

Ruben Bolling’s Super-Fun-Pak Comix excerpt for the 16th is marginal, yeah, but fun. Numeric coincidence and numerology can sneak into compulsions with terrible ease. I can believe easily the need to make the number of steps divisible by some favored number.

Rich Powell’s Wide Open for the 16th is a caveman science joke, and it does rely on a chalkboard full of algebra for flavor. The symbols come tantalizingly close to meaningful. The amount of kinetic energy, K or KE, of a particle of mass m moving at speed v is indeed K = \frac{1}{2} m v^2 . Both 16 and 32 turn up often in the physics of falling bodies, at least if we’re using feet to measure. a = -\frac{k}{m} x turns up in physics too. It comes from the acceleration of a mass on a spring. But an equation of the same shape turns up whenever you describe things that go through tiny wobbles around the normal value. So the blackboard is gibberish, but it’s a higher grade of gibberish than usual.

Rick Detorie’s One Big Happy rerun for the 17th is a resisting-the-word-problem joke, made fresher by setting it in little Ruthie’s playing at school.

T Lewis and Michael Fry’s Over The Hedge for the 18th mentions the three-body problem. As Verne the turtle says, it’s a problem from physics. The way two objects — sun and planet, planet and moon, pair of planets, whatever — orbit each other if they’re the only things in the universe is easy. You can describe it all perfectly and without using more than freshman physics majors know. Introduce a third body, though, and we don’t know anymore. Chaos can happen.

Emphasis on can. There’s no good way to solve the “general” three-body problem, the one where the star and planets can have any sizes and any starting positions and any starting speeds. We can do well for special cases, though. If you have a sun, a planet, and a satellite — each body negligible compared to the other — we can predict orbits perfectly well. If the bodies have to stay in one plane of motion, instead of moving in three-dimensional space, we can do pretty well. If we know two of the bodies orbit each other tightly and the third is way off in the middle of nowhere we can do pretty well.

But there’s still so many interesting cases for which we just can’t be sure chaos will not break out. Three interacting bodies just offer so much more chance for things to happen. (To mention something surely coincidental, it does seem to be a lot easier to write good comedy, or drama, with three important characters rather than two. Any pair of characters can gang up on the third, after all. I notice how much more energetic Over The Hedge became when Hammy the Squirrel joined RJ and Verne as the core cast.)

Dave Whamond’s Reality Check for the 18th is your basic mathematics-illiteracy joke, done well enough.

Reading the Comics, February 2, 2017: I Haven’t Got A Jumble Replacement Source Yet


If there was one major theme for this week it was my confidence that there must be another source of Jumble strips out there. I haven’t found it, but I admit not making it a priority either. The official Jumble site says I can play if I activate Flash, but I don’t have enough days in the year to keep up with Flash updates. And that doesn’t help me posting mathematics-relevant puzzles here anyway.

Mark Anderson’s Andertoons for January 29th satisfies my Andertoons need for this week. And it name-drops the one bit of geometry everyone remembers. To be dour and humorless about it, though, I don’t think one could likely apply the Pythagorean Theorem. Typically the horizontal axis and the vertical axis in a graph like this measure different things. Squaring the different kinds of quantities and adding them together wouldn’t mean anything intelligible. What would even be the square root of (say) a squared-dollars-plus-squared-weeks? This is something one learns from dimensional analysis, a corner of mathematics I’ve thought about writing about some. I admit this particular insight isn’t deep, but everything starts somewhere.

Norm Feuti’s Gil rerun for the 30th is a geometry name-drop, listing it as the sort of category Jeopardy! features. Gil shouldn’t quit so soon. The responses for the category are “What is the Pythagorean Theorem?”, “What is acute?”, “What is parallel?”, “What is 180 degrees?” (or, possibly, 360 or 90 degrees), and “What is a pentagon?”.

Parents' Glossary Of Terms: 'Mortifraction': That utter shame when you realize you can no longer do math in your head. Parent having trouble making change at a volunteer event.
Terri Libenson’s Pajama Diaries for the 1st of February, 2017. You know even for a fundraising event $17.50 seems a bit much for a hot dog and bottled water. Maybe the friend’s 8-year-old child is way off too.

Terri Libenson’s Pajama Diaries for the 1st of February shows off the other major theme of this past week, which was busy enough that I have to again split the comics post into two pieces. That theme is people getting basic mathematics wrong. Mostly counting. (You’ll see.) I know there’s no controlling what people feel embarrassed about. But I think it’s unfair to conclude you “can no longer” do mathematics in your head because you’re not able to make change right away. It’s normal to be slow or unreliable about something you don’t do often. Inexperience and inability are not the same thing, and it’s unfair to people to conflate them.

Gordon Bess’s Redeye for the 21st of September, 1970, got rerun the 1st of February. And it’s another in the theme of people getting basic mathematics wrong. And even more basic mathematics this time. There’s more problems-with-counting comics coming when I finish the comics from the past week.

'That was his sixth shot!' 'Good! OK, Paleface! You've had it now!' (BLAM) 'I could never get that straight, does six come after four or after five?'
Gordon Bess’s Redeye for the 21st of September, 1970. Rerun the 1st of February, 2017. I don’t see why they’re so worried about counting bullets if being shot just leaves you a little discombobulated.

Dave Whamond’s Reality Check for the 1st hopes that you won’t notice the label on the door is painted backwards. Just saying. It’s an easy joke to make about algebra, also, that it should put letters in to perfectly good mathematics. Letters are used for good reasons, though. We’ve always wanted to work out the value of numbers we only know descriptions of. But it’s way too wordy to use the whole description of the number every time we might speak of it. Before we started using letters we could use placeholder names like “re”, meaning “thing” (as in “thing we want to calculate”). That works fine, although it crashes horribly when we want to track two or three things at once. It’s hard to find words that are decently noncommittal about their values but that we aren’t going to confuse with each other.

So the alphabet works great for this. An individual letter doesn’t suggest any particular number, as long as we pretend ‘O’ and ‘I’ and ‘l’ don’t look like they do. But we also haven’t got any problem telling ‘x’ from ‘y’ unless our handwriting is bad. They’re quick to write and to say aloud, and they don’t require learning to write any new symbols.

Later, yes, letters do start picking up connotations. And sometimes we need more letters than the Roman alphabet allows. So we import from the Greek alphabet the letters that look different from their Roman analogues. That’s a bit exotic. But at least in a Western-European-based culture they aren’t completely novel. Mathematicians aren’t really trying to make this hard because, after all, they’re the ones who have to deal with the hard parts.

Bu Fisher’s Mutt and Jeff rerun for the 2nd is another of the basic-mathematics-wrong jokes. But it does get there by throwing out a baffling set of story-problem-starter points. Particularly interesting to me is Jeff’s protest in the first panel that they couldn’t have been doing 60 miles an hour as they hadn’t been out an hour. It’s the sort of protest easy to use as introduction to the ideas of average speed and instantaneous speed and, from that, derivatives.

Reading the Comics, January 21, 2017: Homework Edition


Now to close out what Comic Strip Master Command sent my way through last Saturday. And I’m glad I’ve shifted to a regular schedule for these. They ordered a mass of comics with mathematical themes for Sunday and Monday this current week.

Karen Montague-Reyes’s Clear Blue Water rerun for the 17th describes trick-or-treating as “logarithmic”. The intention is to say that the difficulty in wrangling kids from house to house grows incredibly fast as the number of kids increases. Fair enough, but should it be “logarithmic” or “exponential”? Because the logarithm grows slowly as the number you take the logarithm of grows. It grows all the slower the bigger the number gets. The exponential of a number, though, that grows faster and faster still as the number underlying it grows. So is this mistaken?

I say no. It depends what the logarithm is, and is of. If the number of kids is the logarithm of the difficulty of hauling them around, then the intent and the mathematics are in perfect alignment. Five kids are (let’s say) ten times harder to deal with than four kids. Sensible and, from what I can tell of packs of kids, correct.

'Anne has six nickels. Sue has 41 pennies. Who has more money?' 'That's not going to be easy to figure out. It all depends on how they're dressed!'
Rick Detorie’s One Big Happy for the 17th of January, 2017. The section was about how the appearance and trappings of wealth matter for more than the actual substance of wealth so everyone’s really up to speed in the course.

Rick Detorie’s One Big Happy for the 17th is a resisting-the-word-problem joke. There’s probably some warning that could be drawn about this in how to write story problems. It’s hard to foresee all the reasonable confounding factors that might get a student to the wrong answer, or to see a problem that isn’t meant to be there.

Bill Holbrook’s On The Fastrack for the 19th continues Fi’s story of considering leaving Fastrack Inc, and finding a non-competition clause that’s of appropriate comical absurdity. As an auditor there’s not even a chance Fi could do without numbers. Were she a pure mathematician … yeah, no. There’s fields of mathematics in which numbers aren’t all that important. But we never do without them entirely. Even if we exclude cases where a number is just used as an index, for which Roman numerals would be almost as good as regular numerals. If nothing else numbers would keep sneaking in by way of polynomials.

'Uh, Fi? Have you looked at the non-compete clause in your contract?' 'I wouldn't go to one of Fastrack's competitors.' 'No, but, um ... you'd better read this.' 'I COULDN'T USE NUMBERS FOR TWO YEARS???' 'Roman numerals would be okay.'
Bill Holbrook’s On The Fastrack for the 19th of January, 2017. I feel like someone could write a convoluted story that lets someone do mathematics while avoiding any actual use of any numbers, and that it would probably be Greg Egan who did it.

Dave Whamond’s Reality Check for the 19th breaks our long dry spell without pie chart jokes.

Mort Walker and Dik Browne’s Vintage Hi and Lois for the 27th of July, 1959 uses calculus as stand-in for what college is all about. Lois’s particular example is about a second derivative. Suppose we have a function named ‘y’ and that depends on a variable named ‘x’. Probably it’s a function with domain and range both real numbers. If complex numbers were involved then the variable would more likely be called ‘z’. The first derivative of a function is about how fast its values change with small changes in the variable. The second derivative is about how fast the values of the first derivative change with small changes in the variable.

'I hope our kids are smart enough to win scholarships for college.' 'We can't count on that. We'll just have to save the money!' 'Do you know it costs about $10,000 to send one child through college?!' 'That's $40,000 we'd have to save!' Lois reads to the kids: (d^2/dx^2)y = 6x - 2.
Mort Walker and Dik Browne’s Vintage Hi and Lois for the 27th of July, 1959. Fortunately Lois discovered the other way to avoid college costs: simply freeze the ages of your children where they are now, so they never face student loans. It’s an appealing plan until you imagine being Trixie.

The ‘d’ in this equation is more of an instruction than it is a number, which is why it’s a mistake to just divide those out. Instead of writing it as \frac{d^2 y}{dx^2} it’s permitted, and common, to write it as \frac{d^2}{dx^2} y . This means the same thing. I like that because, to me at least, it more clearly suggests “do this thing (take the second derivative) to the function we call ‘y’.” That’s a matter of style and what the author thinks needs emphasis.

There are infinitely many possible functions y that would make the equation \frac{d^2 y}{dx^2} = 6x - 2 true. They all belong to one family, though. They all look like y(x) = \frac{1}{6} 6 x^3 - \frac{1}{2} 2 x^2 + C x + D , where ‘C’ and ‘D’ are some fixed numbers. There’s no way to know, from what Lois has given, what those numbers should be. It might be that the context of the problem gives information to use to say what those numbers should be. It might be that the problem doesn’t care what those numbers should be. Impossible to say without the context.

Reading the Comics, July 1, 2012


This will be a hastily-written installment since I married just this weekend and have other things occupying me. But there’s still comics mentioning math subjects so let me summarize them for you. The first since my last collection of these, on the 13th of June, came on the 15th, with Dave Whamond’s Reality Check, which goes into one of the minor linguistic quirks that bothers me: the claim that one can’t give “110 percent,” since 100 percent is all there is. I don’t object to phrases like “110 percent”, though, since it seems to me the baseline, the 100 percent, must be to some standard reference performance. For example, the Space Shuttle Main Engines routinely operated at around 104 percent, not because they were exceeding their theoretical limits, but because the original design thrust was found to be not quite enough, and the engines were redesigned to deliver more thrust, and it would have been far too confusing to rewrite all the documentation so that the new design thrust was the new 100 percent. Instead 100 percent was the design capacity of an engine which never flew but which existed in paper form. So I’m forgiving of “110 percent” constructions, is the important thing to me.

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