Reading the Comics, March 9, 2019: In Which I Explain Eleven Edition


I thought I had a flood of mathematically-themed comic strips last week. On reflection, many of them were slight enough not to need further context. You’ll see in the paragraph of not-discussed strips at the end of this. What did rate discussion turned out to get more interesting to me the more I wrote about them.

Stephen Beals’s Adult Children for the 6th uses mathematics as icon of things that are indisputably true. Two plus two equals four is a good example of such. If we take the ordinary meanings of ‘two’ and ‘plus’ and ‘equals’ and ‘four’ there’s no disputing it. The result follows from some uncontroversial-seeming axioms and a lot of deduction. By the rules of logic, the conclusion has to be true, whoever makes it. Even, for that matter, if nobody makes it. It’s difficult to imagine a universe in which nobody ever notices two plus two equals four. But we can imagine that there are mathematical truths that will never be noticed by anyone. (Here’s one. There is some largest finite whole number that any human-created project will ever use in any context. Consider the equation represented by “that number plus two equals (even bigger number)”.)

Harvey: 'Everyone ignores facts! Two plus two equals four, you know what I mean?' Friend: 'Yes. In your opinion, two plus two equals four.' Harvey: 'Noooo! Facts aren't opinions! There are no true facts, fake facts, iffy facts ... just facts! Let's judge things based on the facts!' Friend: 'And how do these facts make you feel?' Harvey, clutching his chest. 'Like you're giving me a fact attack.'
Stephen Beals’s Adult Children for the 6th of March, 2019. Essays inspired by something mentioned in Adult Children appear at this link.

But you see cards palmed there. What do we mean by ‘two’? Have we got a good definition? Might there be a different definition that’s more useful? Probably not, for ‘two’ anyway. But a part of mathematics, especially as a field develops, is working out what are the important concepts, and what their definitions should be. What a ‘function’ is, for example, went through a lot of debate and change over the 19th century. There is an elusiveness to facts, even in mathematics, where you’d think epistemology would be simpler.

Lauren's problem: '(x^2 y - 3y^2 + 5xy^2) - (-x^2 y + 3xy^2 - 3y^2). Which of the following is equivalent to the expression above? a. 4x^2 y^2. b. 8xy^2 - 6y^2. c. 2x^2 + 2xy^2. d. 2x^2 y + 8xy^2 - 6y^2.' Next problem: 'If a/b = 2 what's the value of 4b/a? a. 0. b. 1. c. 2. d. 4.' Bob, holding up empty ice trays: 'If a and b are empty because Lauren is selfish and not thinking of Bob, what are the chances he gets to have an iced drink? a. slim, b. none, c. all of the above?'
Frank Page’s Bob the Squirrel for the 6th of March, 2019. When I’m moved to write something based on Bob the Squirrel the essays should be tagged to appear at this link.

Frank Page’s Bob the Squirrel for the 6th continues the SAT prep questions from earlier in the week. There’s two more problems in shuffling around algebraic expressions here. The first one, problem 5, is probably easiest to do by eliminating wrong answers. (x^2 y - 3y^2 + 5xy^2) - (-x^2 y + 3xy^2 - 3y^2) is a tedious mess. But look at just the x^2 y terms: they have to add up to 2x^2 y , so, the answer has to be either c or d. So next look at the 3y^2 terms and oh, that’s nice. They add up to zero. The answer has to be c. If you feel like checking the 5xy^2 terms, go ahead; that’ll offer some reassurance, if you do the addition correctly.

The second one, problem 8, is probably easier to just think out. If \frac{a}{b} = 2 then there’s a lot of places to go. What stands out to me is that 4\frac{b}{a} has the reciprocal of \frac{a}{b} in it. So, the reciprocal of \frac{a}{b} has to equal the reciprocal of 2 . So \frac{a}{b} = \frac{1}{2} . And 4\frac{b}{a} is, well, four times \frac{b}{a} , so, four times one-half, or two. There’s other ways to go about this. In honestly, what I did when I looked at the problem was multiply both sides of \frac{a}{b} = 2 by \frac{b}{a} . But it’s harder to explain why that struck me as an obviously right thing to do. It’s got shortcuts I grew into from being comfortable with the more methodical approach. Someone who does a lot of problems like these will discover shortcuts.

Ruthie on the phone: 'Hello, homework hotline? I have an arithmetic question. Why isn't eleven called oneteen, and twelve called twoteen? ... You don't know? ... May I speak to your supervisor, please?'
Rick Detorie’s One Big Happy for the 6th of March, 2019. This particular strip is several years old, but I can’t pin down its original run more precisely than that. Essays featuring One Big Happy should be at this link.

Rick Detorie’s One Big Happy for the 6th asks one of those questions you need to be a genius or a child to ponder. Why don’t the numbers eleven and twelve follow the pattern of the other teens, or for that matter of twenty-one and thirty-two, and the like? And the short answer is that they kind of do. At least, “eleven” and “twelve”, etymologists agree, derive from the Proto-Germanic “ainlif” and “twalif”. If you squint your mouth you can get from “ain” to “one” (it’s probably easier if you go through the German “ein” along the way). Getting from “twa” to “two” is less hard. If my understanding is correct, etymologists aren’t fully agreed on the “lif” part. But they are settled on it means the part above ten. Like, “ainlif” would be “one left above ten”. So it parses as one-and-ten, putting it in form with the old London-English preference for one-and-twenty or two-and-thirty as word constructions.

It’s not hard to figure how “twalif” might over centuries mutate to “twelve”. We could ask why “thirteen” didn’t stay something more Old Germanic. My suspicion is that it amounts to just, well, it worked out like that. It worked out the same way in German, which switches to “-zehn” endings from 13 on. Lithuanian has all the teens end with “-lika”; Polish, similarly, but with “-ście”. Spanish — not a Germanic language — has “custom” words for the numbers up to 15, and then switches to “diecis-” as a prefix to the numbers 6 through 9. French doesn’t switch to a systematic pattern until 17. (And no I am not going to talk about France’s 80s and 90s.) My supposition is that different peoples came to different conclusions about whether they needed ten, or twelve, or fifteen, or sixteen, unique names for numbers before they had to resort to systemic names.

Here’s some more discussion of the teens, though, including some exploration of the controversy and links to other explanations.

Caption: '4 out of 5 Doctors agree ... ' Four, of five, chickens dressed as doctors: 'We are 80% of the doctors!'
Doug Savage’s Savage Chickens for the 6th of March, 2019. And the occasional essay based on Savage Chickens should be gathered at this link.

Doug Savage’s Savage Chickens for the 6th is a percentages comic. It makes reference to an old series of (American, at least) advertisements in which four out of five dentists would agree that chewing sugarless gum is a good thing. Shifting the four-out-of-five into 80% riffs is not just fun with tautologies. Percentages have this connotation of technical precision; 80% sounds like a more rigorously known number than “four out of five”. It doesn’t sound as scientific as “0.80”, quite. But when applied to populations a percentage seems less bizarre than a decimal.


Oh, now, and what about comic strips I can’t think of anything much to write about?
Ruben Bolling’s Super-Fun-Pak Comix for the 4th featured divisibility, in a panel titled “Fun Facts for the Obsessive-Compulsive”. Olivia James’s Nancy on the 6th was avoiding mathematics homework. Jonathan Mahood’s Bleeker: The Rechargeable Dog for the 7th has Skip avoiding studying for his mathematics test. Bob Scott’s Bear With Me for the 7th has Molly mourning a bad result on her mathematics test. (The comic strip was formerly known as Molly And The Bear, if this seems familiar but the name seems wrong.) These are all different comic strips, I swear. Bill Holbrook’s Kevin and Kell for the 8th has Rudy and Fiona in mathematics class. (The strip originally ran in 2013; Comics Kingdom has started running Holbrook’s web comic, but at several years’ remove.) And, finally, Alex Hallatt’s Human Cull for the 8th talks about “110%” as a phrase. I don’t mind the phrase, but the comic strip has a harder premise.


And that finishes the comic strips from last week. But Pi Day is coming. I’ll be ready for it. Shall see you there.

Reading the Comics, April 19, 2018: Late Because Of Pinball Edition


Hi, all. I apologize for being late in posting this, but my Friday and Saturday were eaten up by pinball competition. Pinball At The Zoo, particularly, in Kalamazoo, Michigan. There, Friday, I stepped up first thing and put in four games on the Classics, pre-1985, tournament bank and based on my entry scores was ranked the second-best player there. And then over the day my scores dwindled lower and lower on the list of what people had entered until, in the last five minutes of qualifying, they dropped off the roster altogether and I was knocked out. Meanwhile in the main tournament, I was never even close to making playoffs. But I did have a fantastic game of Bally/Midway’s World Cup Soccer, a game based on how much the United States went crazy for soccer that time we hosted the World Cup for some reason. The game was interrupted by one of the rubber straps around one of the kickers (the little triangular table just past the flippers that you would think would be called the bumpers) breaking, and then by the drain breaking in a way that later knocked the game entirely out of the competition. So anyway besides that glory I’ve been very busy trying to figure out what’s gone wrong and stepping outside to berate the fox squirrels out back, and that’s why I’m late with all this. I’m sure you relate.

Danielle Rabbit as a lion tamer whipping a 2. Danielle as orchestra conductor leading a 4 playing violin. As a puppet-master holding up an 8 and 3 as marionettes. Juggling the numerals 0 through 9. Nursing a 7. Then reality: Kevin saying, 'Danielle, thanks for doing our taxes.' Danielle: 'Well, you just have to know how to handle numbers.'
Bill Holbrook’s Kevin and Kell rerun for the 15th of April, 2018. The strip is this enormously tall format because at the time it originally ran (in 2012) the strip appeared in print in the Atlanta Journal-Constitution, sharing the page with Wiley Miller’s similarly-formatted Non Sequitur. The strip has since resumed more normal dimensions.

Bill Holbrook’s Kevin and Kell rerun for the 15th is the anthropomorphic numerals strip for the week. Also the first of the anthropomorphic strips for the week. Calculating taxes has always been one of the compelling social needs for mathematics, arithmetic especially. If we consider the topic to be “accounting” then that might be the biggest use of mathematics in society. At least by humans; I’m not sure how to rate the arithmetic that computers do even for not explicitly mathematical tasks like sending messages back and forth. New comic strip tag for around here, too.

Fauna, to her brother Tucker: 'I learned a valuable lesson in trigonometry class today. The next time I sign up for a class, it will have nothing to do with numbers.'
Bill Schorr’s The Grizzwells for the 17th of April, 2018. Yeah, people say that, but then they get into Abstract Algebra and then they see any proof whatsoever that involves ideals of rings.

Bill Schorr’s The Grizzwells for the 17th sees Fauna not liking trigonometry class. I’m sympathetic. I remember it as seeming to be a lot of strange new definitions put to vague purposes. On the bright side, when you get into calculus trigonometry starts solving more problems than it creates. On the dim side, at least when I took it they tried to pass off “trigonometric substitution” as a thing we might need. (OK, it’s come in useful sometimes, but not as often as the presentation made it look.) Also a new comic strip tag.

A two-circle Venn diagram. In one circle: 'Eric's friends'. In the other: 'Eric's enemies'. In the intersection: 'Eric's cat'.
Eric the Circle for the 18th of April, 2018, this one by sdhardie. It’s a rerun, yes, although I don’t know just from when. The copyright date of 2012 suggests I’ve probably already covered this in a Reading the Comics post before. (If I have I can’t find it.)

Eric the Circle for the 18th, this one by sdhardie, is a joke in the Venn Diagram mode. The strip’s a little unusual for not having one of the circles be named Eric. Not a new comic strip tag.

A trophy room. Behind the adult are the heads of an elephant and a tiger . Behind the child are Maths Teacher Year 1 and Maths Teacher Year 2.
Ham’s Life on Earth for the 19th of April, 2018. I suppose that Ham is a pseudonym but I have no information about the cartoonist other than that I guess she’s not American.

Ham’s Life on Earth for the 19th leaves me feeling faintly threatened. Maybe it’s just me. Also not a new comic strip tag, somehow.

Mostly a list of '6 Daydreams That Will Immediately Improve Your Mood'. Relevant is #3, 'Oh hey professor who failed me in college math I'm doing pretty well thanks MATH SLAP.'
Lord Birthday’s Dumbwitch Castle for the 19th of April, 2018. I … I would swear when this comic first started appearing it was by a less absurd pseudonym. I don’t remember, though.

Lord Birthday’s Dumbwitch Castle for the 19th is a small sketch and mostly a list of jokes. This is the normal format for this strip, which tests the idea of what makes something a comic strip. I grant it’s a marginal inclusion, but I am tickled by the idea of a math slap so here you go. This one’s another new comic strip tag.