Reading the Comics, April 25, 2020: Off Brand Edition

Comic Strip Master Command decided I should have a week to catch up on things, and maybe force me to write something original. Of all the things I read there were only four strips that had some mathematics content. And three of them are such glancing mentions that I don’t feel it proper to include the strip. So let me take care of this.

Mark Anderson’s Andertoons for the 20th is the Mark Anderson’s Andertoons for the week. Wavehead apparently wants to know whether \frac{3}{4} or \frac{6}{8} is the better of these equivalent forms. I understand the impulse. Rarely in real life do we see two things that are truly equivalent; there’s usually some way in which one is better than the other. There may be two ways to get home for example, both taking about the same time to travel. One might have better scenery, though, or involve fewer difficult turns or less traffic this time of day. This is different, though: \frac{3}{4} or \frac{6}{8} are two ways to describe the same number. Which one is “better”?

Wavehead is at the blackboard; on it are written 3/4 and 6/8. The teacher explains, 'They're just equivalent. Neither one is the off-brand.'
Mark Anderson’s Andertoons for the 20th of April, 2020. Essays featuring some mention of Andertoons are gathered at this link.

The only answer is, better for what? What do you figure to do with this number afterwards? I admit, and suppose most people have, a preference for \frac{3}{4} . But that’s trained into us, in large part, by homework set to reduce fractions to “lowest terms”. There’s honest enough reasons behind that. It seems wasteful to have a factor in the numerator that’s immediately divided out by the denominator.

If this were 25 years ago, I could ask how many of you have written out a check for twenty-two and 3/4 dollars, then, rather than twenty-two and 75/100 dollars? The example is dated but the reason to prefer an equivalent form is not. If I know that I need the number represented by \frac{3}{4} , and will soon be multiplying it by eight, then \frac{6}{8} may save me the trouble of thinking what three times two is. Or if I’ll be adding it to \frac{5}{8} , or something like that. If I’m measuring this for a recipe I need to cut in three, because the original will make three dozen cookies and I could certainly eat three dozen cookies, then \frac{3}{4} may be more convenient than \frac{6}{8} . What is the better depends on what will clarify the thing I want to do.

A significant running thread throughout all mathematics, not just arithmetic, is finding equivalent forms. Ways to write the same concept, but in a way that makes some other work easier. Or more likely to be done correctly. Or, if the equivalent form is more attractive, more likely to be learned or communicated. It’s of value.

Jan Eliot’s Stone Soup Classics rerun for the 20th is a joke about how one can calculate what one is interested in. In this case, going from the number of days left in school to the number of hours and minutes and even seconds left. Personally, I have never had trouble remembering there are 24 hours in the day, nor that there are 86,400 seconds in the day. That there are 1,440 minutes in the day refuses to stick in my mind. Your experiences may vary.

Thaves’s Frank and Ernest for the 22nd is the Roman Numerals joke for the week, shifting the number ten to the representation “X” to the prefix “ex”.

Harry Bliss’s Bliss for the 23rd speaks of “a truck driver with a PhD in mathematical logic”. It’s an example of signifying intelligence through mathematics credentials. (It’s also a bit classicist, treating an intelligent truck driver as an unlikely thing.)

I’m caught up! This coming Sunday I hope to start discussingthis week’s comics in a post at this link. And for this week? I don’t know; maybe I’ll figure something to write. We’ll see. Thanks for reading.

Reading the Comics, April 4, 2020: Ruling Things Out Edition

This little essay should let me wrap up the rest of the comic strips from the past week. Most of them were casual mentions. At least I thought they were when I gathered them. But let’s see what happens when I actually write my paragraphs about them.

Darrin Bell and Theron Heir’s Rudy Park rerun for the 1st of April uses arithmetic as emblematic of things which we know with certainty to be true.

Thaves’s Frank and Ernest for the 2nd is a bit of wordplay, having Euclid and Galileo talking about parallel universes. I’m not sure that Galileo is the best fit for this, but I’m also not sure there’s another person connected who could be named. It’d have to be a name familiar to an average reader as having something to do with geometry. Pythagoras would seem obvious, but the joke is stronger if it’s two people who definitely did not live at the same time. Did Euclid and Pythagoras live at the same time? I am a mathematics Ph.D. and have been doing pop mathematics blogging for nearly a decade now, and I have not once considered the question until right now. Let me look it up.

It doesn’t make any difference. The comic strip has to read quickly. It might be better grounded to post Euclid meeting Gauss or Lobachevsky or Euler (although the similarity in names would be confusing) but being understood is better than being precise.

Stephan Pastis’s Pearls Before Swine for the 2nd is a strip about the foolhardiness of playing the lottery. And it is foolish to think that even a $100 purchase of lottery tickets will get one a win. But it is possible to buy enough lottery tickets as to assure a win, even if it is maybe shared with someone else. It’s neat that an action can be foolish if done in a small quantity, but sensible if done in enough bulk.

Chalkboard problem 10 - 7, with answers given and crossed out of 0, 5, 7, 4, 17, 9, 1, 2, and 70. Wavehead, to teacher: 'OK, the good news is we've ruled these out.'
Mark Anderson’s Andertoons for the 3rd of April, 2020. This is actually the first time I’ve mentioned this strip in two months. But any time I discuss a topic raised by Andertoons should appear at this link.

Mark Anderson’s Andertoons for the 3rd is the Mark Anderson’s Andertoons for the week. Wavehead has made a bunch of failed attempts at subtracting seven from ten, but claims it’s at least progress that some thing have been ruled out. I’ll go along with him that there is some good in ruling out wrong answers. The tricky part is in how you rule them out. For example, obvious to my eye is that the correct answer can’t be more than ten; the problem is 10 minus a positive number. And it can’t be less than zero; it’s ten minus a number less than ten. It’s got to be a whole number. If I’m feeling confident about five and five making ten, then I’d rule out any answer that isn’t between 1 and 4 right away. I’ve got the answer down to four guesses and all I’ve really needed to know is that 7 is greater than five but less than ten. That it’s an even number minus an odd means the result has to be odd; so, it’s either one or three. Knowing that the next whole number higher than 7 is an 8 says that we can rule out 1 as the answer. So there’s the answer, done wholly by thinking of what we can rule out. Of course, knowing what to rule out takes some experience.

Mark Parisi’s Off The Mark for the 4th is roughly the anthropomorphic numerals joke for the week. It’s a dumb one, but, that’s what sketchbooks are for.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th is the Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th for the week. It shows in joking but not wrong fashion a mathematical physicist’s encounters with orbital mechanics. Orbital mechanics are a great first physics problem. It’s obvious what they’re about, and why they might be interesting. And the mathematics of it is challenging in ways that masses on springs or balls shot from cannons aren’t.

How To Learn Orbital Mechanics. Step 1: Gauge Difficulty. Person reading a text: 'It's Newtonian! Piece of cake. Just a bunch of circles and dots.' Step 2: Correction. 'OK, *ellipses* and dots.' Step 3: Concern. 'Oh, Christ, sometimes there are more than two dots.' Step 4: Pick an easier subject. 'I'm gonna go study quantum computing.' The textbook is in the trash.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th of April, 2020. This is actually the first time I’ve mentioned this strip ina week. But any time I discuss a topic raised in Saturday Morning Breakfast Cereal should appear at this link.

A few problems are very easy, like, one thing in circular orbit of another. A few problems are not bad, like, one thing in an elliptical or hyperbolic orbit of another. All our good luck runs out once we suppose the universe has three things in it. You’re left with problems that are doable if you suppose that one of the things moving is so tiny that it barely exists. This is near enough true for, for example, a satellite orbiting a planet. Or by supposing that we have a series of two-thing problems. Which is again near enough true for, for example, a satellite travelling from one planet to another. But these is all work that finds approximate solutions, often after considerable hard work. It feels like much more labor to smaller reward than we get for masses on springs or balls shot from cannons. Walking off to a presumably easier field is understandable. Unfortunately, none of the other fields is actually easier.

Pythagoras died somewhere around 495 BC. Euclid was born sometime around 325 BC. That’s 170 years apart. So Pythagoras was as far in Euclid’s past as, oh, Maria Gaetana Agnesi is to mine.

I did a little series looking into orbital mechanics, not necessarily ones that look like planetary orbits, a couple years ago. You might enjoy that. And I figure to have more mathematically-themed comic strips in the near future. Thanks for reading.

Reading the Comics, March 28, 2020: Closing A Week Edition

I know; I’m more than a week behind the original publication of these strips. The Playful Math Education Blog Carnival took a lot of what attention I have these days. I’ll get caught up again soon enough. Comic Strip Master Command tried to help me, by having the close of a week ago being pretty small mathematics mentions, too. For example:

Thaves’s Frank and Ernest for the 26th is the anthropomorphic numerals joke for the week. Also anthropomorphic letters, for a bonus.

Craig Boldman and Henry Scarpelli’s Archie for the 27th has Moose struggling in mathematics this term. This is an interesting casual mention; the joke, of Moose using three words to describe a thing he said he could in two, would not fit sharply for anything but mathematics. Or, possibly, a measuring class, but there’s no high school even in fiction that has a class in measuring.

Bud Blake’s Vintage Tiger for the 27th has Tiger and Hugo struggling to find adjective forms for numbers. We can giggle at Hugo struggling for “quadruple” and going for something that makes more sense. We all top out somewhere, though, probably around quintuple or sextuple. I have never known anyone who claimed to know what the word would be for anything past decuple, and even staring at the dictionary page for “decuple” I don’t feel confident in it.

Hilary Price’s Rhymes With Orange for the 28th uses a blackboard full of calculations as shorthand for real insight into science. From context they’re likely working on some physics problem and it’s quite hard to do that without mathematics, must agree.

Ham’s Life On Earth for the 28th uses E = mc^2 as a milestone in a child’s development.

John Deering’s Strange Brew for the 28th name-drops slide rules, which, yeah, have mostly historical or symbolic importance these days. There might be some niche where they’re particularly useful (besides teaching logarithms), but I don’t know of it.

And what of the strips from last week? I’ll discuss them in an essay at this link, soon, I hope. Take care, please.

Reading the Comics, December 21, 2019: My Favorite Kind Of Explanation Edition

And here’s the other half of last week’s comic strips that name-dropped mathematics in such a way that I couldn’t expand it to a full paragraph. We’ll likely be back to something more normal next week.

David Malki’s Wondermark for the 20th is built on the common idiom of giving more than 100%. I’m firmly on the side of allowing “more than 100%” in both literal and figurative uses of percent, so there’s not much more to say.

Brian Boychuk and Ron Boychuk’s The Chuckle Brothers rerun for the 20th has a wall full of mathematical scribbles and plays on the phrase “calculating killer”. The strip originally ran the 7th of January, 2011.

Samson’s Dark Side of the Horse for the 19th is wordplay on “the thought that counts”. The joke demands Horace be pondering arithmetic, as we see.

Maria Scrivan’s Half Full for the 20th is the Venn Diagram joke for this week.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 20th uses Big Numbers as the sort of thing that need a down-to-earth explanation. The strip is about explanations that don’t add clarity. It shows my sense of humor that I love explanations that are true but explain nothing. The more relevant and true without helping the better. Right up until it’s about something I could be explaining instead.

Tom Batiuk’s vintage Funky Winkerbean for the 21st is part of a week of strips from the perspective of a school desk. It includes a joke about football players working mathematics problems. The strip originally ran the 8th of February, 1974, looks like.

Thaves’s Frank and Ernest for the 21st is the anthropomorphic-numerals (and letters) joke for the week.

And there we go; thank you for looking over a quick list of things. I should be back with more comic strips on Sunday, barring surprises.

Reading the Comics, August 30, 2019: The Ones Not Worth Mentioning Edition

Each week Comic Strip Master Command sends out some comics that mention mathematics, but that aren’t substantial enough to write miniature essays about. This past week, too. Here are the comics that just mention mathematics. You may like them; there’s just not more to explain is all.

Thaves’s Frank and Ernest for the 25th is a bunch of cafeteria lunch jokes. Geometry and wordplay about three square meals a day comes up.

Jeffrey Caulfield and Brian Ponshock’s Yaffle for the 26th has a bunch of jokes about representing two, as part of a “tattwo parlor”. I’m not sure how to categorize this. Wordplay, I suppose.

Brian Anderson’s Dog Eat Doug for the 27th uses “quantum entanglement equations” to represent deep thought on a complicated subject. Calculations are usually good for this.

Dan Collins’s Looks Good On Paper rerun for the 27th uses a blackboard of mathematics — geometry-related formulas — to stand in for all classwork. This strip also ran in 2017 and in 2015. I haven’t checked 2013. I know the strip is still in original production, as it’ll include strips referring to current events, so I’ll keep reading it a while yet.

Rick Detorie’s One Big Happy for the 27th mentions the “Old Math”, but going against Comic Strip Law, not as part of a crack about the New Math. This is just a simple age joke.

Bill Schorr’s The Grizzwells for the 29th is a joke about rabbit arithmetic. You know, about how well rabbits multiply and all.

Ernie Bushmiller’s Nancy Classics for the 29th, which originally ran the 23rd of November, 1949, is a basic cheating-in-class joke. It works for mathematics in a way it wouldn’t for, say, history. Mathematics has enough symbols that don’t appear in ordinary writing that you could copy them upside-down without knowing that you transcribe something meaningless. Well, not realizing an upside-down 4 isn’t anything is a bit odd, but anyone can get pretty lost in symbols.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 29th builds on the phrase “do the math” representing the process of thinking something out.

Percy Crosby’s Skippy for the 30th originally ran the 4th of May, 1932. It’s one of those jokes subverting the form of a story problem, one about rates of completion.

This wraps up the past week’s mathematics comic strips. I should have the next Reading the Comics essay here Sunday. And starting tomorrow: the Fall 2019 Mathematics A To Z. The benefit of this sort of schedule is I have to publish whether I’m happy with the essay or not!

Reading the Comics, May 16, 2019: Two and Two Edition

It might be more fair to call this a blackboard edition, as three of the strips worth discussing feature that element. But I think I’ve used that name recently. And two of the strips feature specifically 2 + 2, so I’ll use that instead.

And here’s a possible movie heads-up. Turner Classic Movies, United States feed, is showing Monday at 9:30 am (Eastern/Pacific) All-American Chump. All I know about this 1936 movie is from its Leonard Maltin review:

[ Stuart ] Erwin is funny, in his usual country bumpkin way, as a small-town math whiz known as “the human adding machine” who is exploited by card sharks and hustlers. Fairly diverting double-feature item.

People with great powers of calculation were — and still are — with us. Before calculating machines were common they were, pop mathematicians tell us, in demand for doing the kinds of arithmetic mathematicians and engineers need a lot of. They’d also have value in performing, if they can put together some good patter. And, sure, gambling is just another field that needs calculation done well. I have no idea the quality of the film (it’s rated two and a half stars, but Leonard Maltin rates many things two and a half stars). But it’s there if you’re curious. The film also stars Robert Armstrong. I assume it’s not the guy I know but, you know? We live in a strange world. Now on to the comics.

Glenn McCoy and Gary McCoy’s The Flying McCoys for the 13th uses the image of a blackboard full of mathematics symbols to represent deep thought. The equations on the board are mostly nonsense, although some, like E = mc^2 , have obvious meaning. Many of the other symbols have some meaning to them too. In the upper-right corner, for example, is what looks like E = \hbar \omega . This any physics major would recognize: it’s the energy of a photon, which is equal to Planck’s constant (that \hbar stuff) times its frequency.

Pair of scientist or mathematician types standing in front of a blackboard full of symbols. One says to the other: 'You're overthinking this.'
Glenn McCoy and Gary McCoy’s The Flying McCoys for the 13th of May 2019. I had thought I was just writing about this strip, and no, yesterday I posted a mention that I was not writing about it. You can see that and other mentions of The Flying McCoys at this link.

And there are other physics-relevant symbols. In the bottom center is a line that starts \oint \vec{B} . The capital B is commonly used to represent a magnetic field. The arrow above the capital B is a warning that this is a vector, which magnetic fields certainly are. (Mathematicians see vectors as a quite abstract concept. Physicists are more likely to see them as an intensity and direction, like forces, and the fields that make fields.) The \oint symbol comes from vector calculus. It represent an integral taken along a closed loop, a shape that goes out along some path and comes back to where it started without crossing itself. This turns out to be useful all the time in dynamics problems. So the McCoys drew something that doesn’t mean anything, but looks ready to mean things.

“Overthinking this” is a problem common to mathematicians, even at an advanced level. Real problems don’t make clear what their boundaries are, the things that are important and the things that aren’t and the things that are convenient but not essential. Making mistakes picking them out, and working too hard on the wrong matters, will happen.

Chesney, cat: 'Question: Are there more stars in the sky or grains of sand on all the beach of the world?' Annie: 'I would say definitely stars.' Jack, cat: 'That settles it.' Chesney, walking away, to Jack: 'Sand it is.' Jack: 'She's never right.'
Graham Harrop’s Ten Cats for the 14th of May 2019. This is a new tag; a strip about a girl and the ten cats she caretakes doesn’t get much into mathematics. I did mention it once, years ago, before I was tagging essays by comic strip name. Anyway, this and future mentions of Ten Cats should be at this link.

Graham Harrop’s Ten Cats for the 14th sees the cats pondering the counts of vast things. These are famous problems. Archimedes composed a text, The Sand Reckoner, which tried to estimate how much sand there could be in the universe. To work on the question he had to think of new ways to represent numbers. Grains of sand become numerous by being so tiny. Stars become numerous by the universe being so vast. Comparing the two quantities is a good challenge. For both numbers we have to make estimates. The volume of beaches in the world. The typical size of a grain of sand. The number of galaxies in the universe. The typical number of stars in a galaxy. There’s room to dispute all these numbers; we really have to come up with a range of possible values, with maybe some idea of what seems more likely.

Student, waving to two adults behind him, and explaining to his nonplussed arithmetic teacher (the blackboard has a big 2 + 2 = on it): 'This is a mathematics professor and my attorney. They'll explain why my answer is technically and legally correct.'
Thaves’s Frank and Ernest for the 15th of May 2019. Essays which mention some aspect of Frank and Ernest should appear at this link.

Thaves’s Frank and Ernest for the 15th has the student bringing authority to his answer. The mathematician is called on to prove an answer is “technically” correct. I’m not sure whether the kid is meant to be prefacing the answer he’s about to give, or whether his answer was rewriting the horizontal “2 + 2 = ” in a vertical form.

Serf: 'How much would you charge to draw up my will?' Lawyer: 'I take one-third of your estate.' Serf: 'That's impossible.' Lawyer: 'Why?' (The serf's children enter.) Serf: 'Three don't go into *five*.'
Brant Parker and Johnny Hart’s The Wizard of Id Classics for the 15th of May 2019. By the way the lawyer’s name is Larsen E Pettifogger, in case that ever comes up. I don’t know that the Serf has a name. This particular strip is from 1969. Essays inspired by something in either new-run Wizard of Id strips or 50-year-old repeats should be at this link.

Brant Parker and Johnny Hart’s The Wizard of Id Classics for the 15th is built around the divisibility of whole numbers, and of relative primes. Setting the fee as some simple integer fraction of the whole has practicality to it. It likely seemed even more practical in the days before currencies decimalized. The common £sd style currency Europeans used before decimals could be subdivided many ways evenly, with one-third of a pound (livre, Reichsgulden, etc) becoming 80 pence (deniers, Pfennig, etc). Unit fractions, and combinations of unit fractions, could offer interesting ways to slice up anything to a desired amount.

Kid, to the teacher, after answering the blackboard's 2+2 as 5: 'I make mistakes to keep you on your toes!'
Jim Unger’s Herman for the 16th of May 2019. This strip is also a repeat; Unger retired from regularly drawing new strips in 1992, and died in 2012. (From 1997 he occasionally updated old ones or drew new ones.) I have no idea when this first ran. The strip gets little attention from me, but the essays — with this, two of them — mentioning Herman should appear at this link.

Jim Unger’s Herman for the 16th is a student-talking-back-to-the-teacher strip. It also uses the 2 + 2 problem. It’s a common thing for teachers to say they learn from their students. It’s even true, although I son’t know that people ever quite articulate how teachers learn. A good mistake is a great chance to learn. A good mistake shows off a kind of brilliant twist. That the student has understood some but not all of the idea, and has filled in the misunderstood parts with something plausible enough one has to think about why it’s wrong. And why someone would think the wrong idea might be right. There is a kind of mistake that inspires you to think closely about what “right” has to be, and students who know how to make those mistakes are treasures.

And for comic strips that aren’t quite worth a paragraph. Julia Kaye’s Up and Out for the 13th uses mathematics as stand-in for the sort of general education that anybody should master. David Waisglass and Gordon Coulthart’s Farcus for the 17th I don’t think is trying to be a mathematics joke. It’s sufficient joke that the painter’s spelled ‘sign’ wrong. But it did hit on the spelling that would encourage mathematics teachers to notice the strip. Patrick Roberts’s Todd the Dinosaur for the 18th mentions sudoku.

And with that I am caught up on the past week’s mathematically-themed comic strips. My next Reading the Comics post should be next Sunday, and at this link. Oh, I could have made the edition name something bragging about being on time.

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.

Reading the Comics, December 15, 2018: Early Holiday Edition

So then this happened: Comic Strip Master Command didn’t have much they wanted me to write about this week. I made out three strips as being relevant enough to discuss at all. And even they don’t have topics that I felt I could really dig into. Coincidence, surely, although I like to think they were trying to help me get ahead of deadline on my A To Z essays for this last week of the run. It’s a noble thought, but doomed. I haven’t been more than one essay ahead of deadline the last three months. I know in past years I’ve gotten three or even four essays ahead of time and I don’t know why it hasn’t worked this time. I am going ahead and blaming that this these essays have been way longer than previous years’. So anyway, I thank Comic Strip Master Command for trying to make my Monday and my Thursday this week be less packed. It won’t help.

Darrin Bell and Theron Heir’s Rudy Park for the 10th uses mathematics as shorthand for a deep, thought-out theory of something. In this case, Randy’s theory of how to interest women. (He has rather a large number of romantic events around him.) It’s easy to suppose that people can be modeled mathematically. Even a crude model, one supposing that people have things they like and dislike, can give us good interesting results. This gets into psychology and sociology though. And probably requires computer modeling to get slightly useful results.

Rudy: 'You're wearing your lab coat. What's up?' Randy: 'Something big. Amending my unified theory of picking up chicks. Check it out.' (It's a blackboard filled with physics equations, as well as a sketch of a woman in a bikini.) Rudy: 'Explain, Doctor.' Randy: 'To start, you'll need a notepad and a gym membership.'
Darrin Bell and Theron Heir’s Rudy Park for the 10th of December, 2018. This strip is a rerun. It originally ran the 11th of January, 2010. Essays mentioning topics raised by Rudy Park are at this link.

Randy’s blackboard has a good number of legitimate equations on it. They’re maybe not so useful to his problem of modeling people, though. The lower left corner, for example, are three of Maxwell’s Equations, describing electromagnetism. I’m not sure about all of these, in part because I think some might be transcribed incorrectly. The second equation in the upper left, for example, looks like it’s getting at the curl of a conserved force field being zero, but it’s idiosyncratic to write that with a ‘d’ to start with. The symbols all over the right with both subscripts and superscripts look to me like tensor work. This turns up in electromagnetism, certainly. Tensors turn up anytime something, such as electrical conductivity, is different in different directions. But I’ve never worked deeply in those fields so all I can confidently say is that they look like they parse.

Nate's story: 'Barky the sheepdog stared in horror at the bloody foot on the barn floor. It was the fifth piece of Farmer Wobblewheel he'd found today. 'And don't forget about the three pieces we found yesterday!' said Winky the wonder monkey.' Franklin: 'What's a monkey doing on a farm?' Nate: 'Helping Barky discover who dismembered Farmer Wobblewheel *and* teaching us about numbers!' Story: ''Five pieces plus three pieces,' barked Barkey. 'That makes ... ' 'Eight,' chuckled Winky.' Francis: 'Ew.'
Lincoln Pierce’s Big Nate for the 14th of December, 2018. Other essays mentioning topics raised by Big Nate, both the current run — like this — and vintage 1990 are at this link.

Lincoln Pierce’s Big Nate for the 14th is part of a bit where Nate’s trying to write a gruesome detective mystery for kids. I’m not sure that’s a ridiculous idea, at least if the gore could be done at a level that wouldn’t be too visceral. Anyway, Nate has here got the idea of merging some educational value into the whole affair. It’s not presented as a story problem, just as characters explaining stuff to one another. There probably would be some room for an actual problem where Barky and Winky wanted to know something and had to work out how to find it from what they knew, though.

Playing in a cardboard box labelled SS Nora Dish. Jingles: 'Take the controls while I make the calculations for hyperspace.' Cecil: 'Wookie noise.' Jingles: 'Let's see. Bob has two bananas. He gives one to Joe who eats half and returns the remainder along with half a cantaloupe ... this ship needs a modern supercomputer.' Cecil: 'Wookie noise.'
Mel Henze’s Gentle Creatures for the 14th of December, 2018. All the essays where I’ve discussed Gentle Creatures are at this link although I suspect it’s mostly the same three comics discussed over and over.

Mel Henze’s Gentle Creatures for the 14th uses a story problem to stand in for science fictional calculations. The strip’s in reruns and I’ve included it here at least four times, I discover, so that’s probably enough for the comic until it gets out of reruns.

And since it was a low-volume week, let me mention strips I didn’t decide fit. Ray Kassinger asked about Tim Rickard’s Brewster Rockit for the 12th. Might it be a play on Schrödinger’s Cat, the famous thought-experiment about how to understand the mathematics of quantum mechanics? It’s possible, but I think it’s more likely just that cats like sitting in boxes. Thaves’s Frank and Ernest for the 13th looks like it should be an anthropomorphic numerals joke. But it’s playing on the idiom about three being a crowd, and the whole of the mathematical content is that three is a number. John Zakour and Scott Roberts’s Maria’s Day for the 15th mentions mathematics. Particularly, Maria wishing they weren’t studying it. It’s a cameo appearance; it could be any subject whose value a student doesn’t see. That’s all I can make of it.

This and my other Reading the Comics posts should all be available at this link. And please check back in Tuesday to see whether I make deadline for the letter ‘Y’ in my Fall 2018 Mathematics A To Z glossary.

Reading the Comics, November 27, 2018: Multiplication Edition

Last week Comic Strip Master Command sent out just enough on-theme comics for two essays, the way I do them these days. The first half has some multiplication in two of the strips. So that’s enough to count as a theme for me.

Aaron Neathery’s Endtown for the 26th depicts a dreary, boring school day by using arithmetic. A lot of times tables. There is some credible in-universe reason to be drilling on multiplication like this. The setting is one where the characters can’t expect to have computers available. That granted, I’m not sure there’s a point to going up to memorizing four times 27. Going up to twelve-times seems like enough for common uses. For multiplying two- and longer-digit numbers together we usually break the problem up into a string of single-digit multiplications.

A classroom teacher drills: 4 times 20 is 80. 4 times 21 is 84. 4 times 22 is 88. 4 times 23 is 92. Students struggle to stay awake. One, an anthropomorphic cat, glares at the insect companion of an anthropomorphic bird.
Aaron Neathery’s Endtown for the 26th of November, 2018. Other essays mentioning topics brought up by Endtown should go here. If there ever are any. This is a new tag, and the strip’s setting — adventures in a post-apocalyptic world that’s left what remains of humanity turned into anthropomorphized animals and clinging to subterranean shelters against the global wasteland — makes it kind of a hard one to fit in any good jokes about algebra.

There are a handful of bigger multiplications that can make your life easier to know, like how four times 25 is 100. Or three times 33 is pretty near 100. But otherwise? … Of course, the story needs the class to do something dull and seemingly pointless. Going deep into multiplication tables communicates that to the reader quickly.

Ernest: 'You say more people are watching your online arithmetic classes?' Frank: 'No, I said the audience is multiplying.'
Thaves’s Frank and Ernest for the 26th of November, 2018. Other appearances by Frank and/or Ernest should be at this link. This strip’s premise makes it rather easier to toss in a couple jokes about algebra.

Thaves’s Frank and Ernest for the 26th is a spot of wordplay. Also a shout-out to my friends who record mathematics videos for YouTube. It is built on the conflation between the ideas of something multiplying and the amount of something growing. It’s easy to see where the idea comes from; just keep hitting ‘x 2’ on a calculator and the numbers grow excitingly fast. You get even more exciting results with ‘x 3’ or ‘x π’. But multiplying by 1 is still multiplication. As is multiplying by a number smaller than 1. Including negative numbers. That doesn’t hurt the joke any. That multiplying two things together doesn’t necessarily give you something larger is a consideration when you’re thinking rigorously about what multiplication can do. It doesn’t have to be part of normal speech.

Edison, to his friend: 'Math problem: if my mom bakes 24 cookies, and I eat twenty ...' (He scarfs them down) ' ... how many cookies does she have left?' Mom: 'HEY!' Later, Edison, to Dad: 'Being a teacher is a thankless job.'
John Hambrock’s The Brilliant Mind of Edison Lee for the 27th of November, 2018. Essays mentioning topics raised by Edison Lee are at this link. The strip’s premise that Edison Lee is some kind of genius always doing weird stuff in science and computers make it fairly likely it’ll turn up.

John Hambrock’s The Brilliant Mind of Edison Lee for the 27th uses the form of a word problem to show off Edison’s gluttony. Edison tries to present it as teaching. We all have rationalizations for giving in to our appetites.

Anthropomorphized numeral 1 sitting at a bar. In the background a 3 is saying to a 5: 'Por fellow. One really is the loneliest number.'
Nate Frakes’s Break of Day for the 27th of November, 2018. And this and other appearances by Break of Day should be at this link. The strip’s premise as a Far Side-esque strange-joke-a-day means it ought to be a common presence here, but somehow it doesn’t appear as much as I’d expect.

Nate Frakes’s Break of Day for the 27th is the anthropomorphic numerals joke for the week. I don’t know that there’s anything in the other numerals being odds rather than evens, or a mixture of odds and evens. It might just be that they needed to be anything but 1.

All of my regular Reading the Comics posts should all be at this link. The next in my Fall 2018 Mathematics A To Z glossary should be posted Tuesday. I’m glad for it if you do come around and read again.

Reading the Comics, November 11, 2018: November 11, 2018 Edition

There were just enough mathematically-themed comic strips last week to make two editions for this coming week. All going well I’ll run the other half on either Wednesday or Thursday. There is a point that isn’t quite well, which is that one of the comics is in dubious taste. I’ll put that at the end, behind a more specific content warning. In the meanwhile, you can find this and hundreds of other Reading the Comics posts at this link.

Thaves’s Frank and Ernest for the 11th is wordplay, built on the conflation of “negative” as in numbers and “negative” as in bad. I’m not sure the two meanings are unrelated. The word ‘negative’ itself derives from the Latin word meaning to deny, which sounds bad. It’s easy to see why the term would attach to what we call negative numbers. A number plus its negation leaves us zero, a nothing. But it does make the negative numbers sound like bad things to have around, or to have to deal with. The convention that a negative number is less than zero implies that the default choice for a number is one greater than zero. And the default choice is usually seen as the good one, with everything else a falling-away. Still, -7 is as legitimate a number as 7 is; it’s we who think one is better than another.

Alien Frank: 'The first Earthling election confused me. I expected campaign signs with things like '-5 + -2'.' Alien Ernest: 'The term is 'negative ads', not 'negative adds'.' Frank: 'I thought the pier would be crowded with people casting ballots. I heard there are voting machines so I expected to see a line of robots waiting at the polls. At least there were no natural disasters. I was worried about actual landslides because of all the mudslinging.'
Thaves’s Frank and Ernest for the 11th of November, 2018. Other essays mentioning Frank and Ernest will be at this link.

J C Duffy’s Lug Nuts for the 11th has the Dadaist panel present prime numbers as a way to communicate. I suspect Duffy’s drawing from speculations about how to contact alien intelligences. One problem with communicating with the truly alien is how to recognize there is a message being sent. A message too regular will look like a natural process, one conveying no more intelligence than the brightness which comes to most places at dawn and darkness coming at sunset. A message too information-packed, peculiarly, looks like random noise. We need an intermediate level. A signal that it’s easy to receive, and that is too hard to produce by natural processes.

Caption: 'Don's first, primitive attempt at communication was limited to prime numbers.' Don, speaking to an angered woman: '2 ... 3 ... 5 ... 7 ... 11 ... 13 ... 17 ...'
J C Duffy’s Lug Nuts for the 11th of November, 2018. This and other essays mentioning Lug Nuts will be at this link.

Prime numbers seem like a good compromise. An intelligence that understands arithmetic will surely notice prime numbers, or at least work out quickly what’s novel about this set of numbers once given them. And it’s hard to imagine an intelligence capable of sending or receiving interplanetary signals that doesn’t understand arithmetic. (Admitting that yes, we might be ruling out conversational partners by doing this.) We can imagine a natural process that sends out (say) three pulses and then rests, or five pulses and rests. Or even draws out longer cycles: two pulses and a rest, three pulses and a rest five pulses and a rest, and then a big rest before restarting the cycle. But the longer the string of prime numbers, the harder it is to figure a natural process that happens to hit them and not other numbers.

We think, anyway. Until we contact aliens we won’t really know what it’s likely alien contact would be like. Prime numbers seem good to us, but — even if we stick to numbers — there’s no reason triangular numbers, square numbers, or perfect numbers might not be as good. (Well, maybe not perfect numbers; there aren’t many of them, and they grow very large very fast.) But we have to look for something particular, and this seems like a plausible particularity.

Lucy: 'Charlie Brown, how much is zero times zero?' Charlie Brown: 'Zero.' Lucy: 'ZERO? Oh come on, Charlie Brown, it's *got* to be *something*. I'll put down three. That sounds just about right. 'Zero', he says ... ha!' Charlie Brown: 'Things like that make my stomach hurt.'
Charles Schulz’s Peanuts Begins for the 11th of November, 2018. It originally ran the 11th of August, 1954. Essays discussing topics raised by Peanuts will be at this link. That’s for either the “current” newspaper run, currently doing strips from 1971, or for the “vintage” reruns as here, showing strips from 1954.

Charles Schulz’s Peanuts Begins for the 11th is an early strip, from the days when Lucy would look to Charlie Brown for information. And it’s a joke built on conflating ‘zero’ with ‘nothing’. Lucy’s right that zero times zero has to be something. That’s how multiplication works. That the number zero is something? That’s a tricky concept. I think being mathematically adept can blind one to how weird that is. If you’re used to how zero is the amount of a thing you have to have nothing of that thing, then we start to see what’s weird about it.

But I’m not sure the strip quite sets that up well. I think if Charlie Brown had answered that zero times zero was “nothing” it would have been right (or right enough) and Lucy’s exasperation would have flowed more naturally. As it is? She must know that zero is “nothing”; but then why would she figure “nothing times nothing” has to be something? Maybe not; it would have left Charlie Brown less reason to feel exasperated or for the reader to feel on Charlie Brown’s side. Young Lucy’s leap to “three” needs to be at least a bit illogical to make any sense.

Now to the last strip and the one I wanted to warn about. It alludes to gun violence and school shootings. If you don’t want to deal with that, you’re right. There’s other comic strips to read out there. And this for a comic that ran on the centennial of Armistice Day, which has to just be an oversight in scheduling the (non-plot-dependent) comic.

Continue reading “Reading the Comics, November 11, 2018: November 11, 2018 Edition”

Reading the Comics, October 19, 2018: More Short Things Edition

At least, I’d thought the last half of last week’s comics were mostly things I could discuss quickly. Then Frank and Ernest went and sprawled on me. Such will happen.

Before I get to that, I did want to mention that Gregory Taylor’s paneling for votes for the direction his mathematics-inspired serial takes:

You may enjoy; at least, give it a try.

Thaves’s Frank and Ernest for the 18th is a bit of wordplay. There’s something interesting culturally about phrasing “lots of math, but no chemistry”. Algorithms as mathematics makes sense. Much of mathematics is about finding processes to do interesting things. Algorithms, and the mathematics which justifies them, can at least in principle be justified with deductive logic. And we like to think that the universe must make deductive-logical sense. So it is easy to suppose that something mathematical simply must make logical sense.

Frank: 'It didn't go well? That date was selected for you by a sophisticated statistical algorithm.' Ernest: 'Lots of math, but no chemistry.'
Thaves’s Frank and Ernest for the 18th of October, 2018. One might argue this just represents the algorithm not having enough data. That there are aspects to both people which were poorly modelled. Could happen.

Chemistry, though. It’s a metaphor for whatever the difference is between a thing’s roster of components and the effect of the whole. The suggestion is that it is mysterious and unpredictable. It’s an attitude strange to actual chemists, who have a rather good understanding of why most things happen. My suspicion is that this sense of chemistry is old, dating to before we had a good understanding of why chemical bonds work. We have that understanding thanks to quantum mechanics, and its mathematical representations.

But we can still allow for things that happen but aren’t obvious. When we write about “emergent properties” we describe things which are inherent in whatever we talk about. But they only appear when the things are a large enough mass, or interact long enough. Some things become significant only when they have enough chance to be seen.

Zeno: 'Honey, I'd love to, but it's not as if I can traverse infinite regions in finite time!' Caption: 'Fun Fact: Zeno never took out the garbage.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th of October, 2018. I wrote all this text assuming Weinersmith meant Zeno of Elea. It’d be a heck of a thing if he meant Zeno, the Omni-King of the 12 Universes that I’m told is a thing in Dragon Ball. I guess they have different character designs.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th is about mathematicians’ favorite Ancient Greek philosopher they haven’t actually read. (In fairness, Zeno is hard to read, even for those who know the language.) Zeno’s famous for four paradoxes, the most familiar of which is alluded to here. To travel across a space requires travelling across half of it first. But this applies recursively. To travel any distance requires accomplishing infinitely many partial-crossings. How can you do infinitely many things, each of which take more than zero time, in less than an infinitely great time? But we know we do this; so, what aren’t we understanding? A callow young mathematics major would answer: well, pick any tiny interval of time you like. All but a handful of the partial-crossings take less than your tiny interval time. This seems like a sufficient answer and reason to chuckle at philosophers. Fine; an instant has zero time elapse during it. Nothing must move during that instant, then. So when does movement happen, if there is no movement during all the moments of time? Reconciling these two points slows the mathematician down.

Teacher: 'Todd, please come up to the chalkboard and do this fraction problem.' Todd: 'Uh-oh! It's late October, almost November! And hibernation is kicking in! I'll have the answer for ya next spring! Well, see ya!' Teacher: 'Todd! Get up here right now!' Student: 'Teacher, it's not safe to wake a hibernating T-Rex! Especially when I'm the first one he'll see!'
Patrick Roberts’s Todd the Dinosaur for the 19th of October, 2018. I’d imagine he would have a sufficient excuse in his arms not being able to reach the chalkboard, actually.

Patrick Roberts’s Todd the Dinosaur for the 19th mentions fractions. It’s only used to list a kind of mathematics problem a student might feign unconsciousness rather than do. And takes quite little space in the word balloon to describe. It’d be the same joke if Todd were asked to come up and give a ten-minute presentation on the Battle of Bunker Hill.

Penny: 'It says here the Rubik's Cube is still a top-selling gift for kids at Christmas.' Earl: 'Why for kids?? *I* can't even do it!' Burl: 'But it's great for kids. It keeps Timmy busy for hours, even though the poor kid doesn't realize yet that it's impossible to do.
Julie Larson’s The Dinette Set for the 19th of October, 2018. It ran originally the 12th of December, 2007. Among the stray, side, filler jokes, I like best that both Earl and Burl have mugs reading “And Dumber”.

Julie Larson’s The Dinette Set for the 19th mentions the Rubik’s Cube. Sometime I should do a proper essay about its mathematics. Any Rubik’s Cube can be solved in at most 20 moves. And it’s apparently known there are some cube configurations that take at least 20 moves, so, that’s nice to have worked out. But there are many approaches to solving a cube, none of which I am competent to do. Some algorithms are, apparently, easier for people to learn, at the cost of taking more steps. And that’s fine. You should understand something before you try to do it efficiently.

Venn diagram of Content Warning. Bubble A: Violence. Bubble B: Mature Subject Matter. Bubble C: Coarse Language. Intersection of A and B: The Bible. Intersection of B and C: Thanksgiving Dinner. Intersection of C and A: Sports. Intersection of A, B, and C: Life.
John Atkinson’s Wrong Hands for the 19th of October, 2018. So … life is the intersection of Thanksgiving, the Bible, and Sports? … I could see the case for that.

John Atkinson’s Wrong Hands for the 19th is the Venn Diagram joke for the week. Good to have one around.

This and my other Reading the Comics posts are available at this link. The essays mentioning Frank and Ernest should be at this link. For just the Reading the Comics posts with Saturday Morning Breakfast Cereal content try this link. Essays which talk about things raised by Todd the Dinosaur are at this link. Posts that write about The Dinette Set are at this link. And the essays based on Wrong Hands should be at this link. And do please stick around for more of my Fall 2018 Mathematics A-To-Z, with another post due tomorrow that I need to write today.

Reading the Comics, October 18, 2018: Quick Half-Week Edition

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

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

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

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

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

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

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

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

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

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

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

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

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

Reading the Comics, September 5, 2018: Single Name Edition

For the second part of last week’s comics, there’s several strips whose authors prefer to use a single name. I’m relieved. Somehow my writing seems easier when I don’t have a long authorial credit to give. I can take writing “Zach Weinersmith” fourteen times a week. It’s all those appearances of, like, “Corey Pandolph and Phil Frank and Joe Troise” (The Elderberries) that slow me way up.

Darrin Bell’s Candorville for the 4th shows off one of the things statistics can do. Tracking some measurable thing lets one notice patterns. These patterns might signify something important. At the least they can suggest things that deserve more scrutiny. There’s dangers, of course. If you’re measuring something that’s rare, or that naturally fluctuates a lot, you might misinterpret changes. You could suppose the changes represent some big, complicated, and invariably scary pattern that isn’t actually there. You can take steps to avoid how much weight you give to little changes. For example, you could look at running averages. Instead of worrying about how often Lemont has asked for his clippers this year versus last, look at how often he’s asked for it, on average, each of the last three years, compared to the average of the three years before that. Changes in that are more likely to be meaningful. But doing this does mean that a sudden change, or a slight but persistent change, is harder to notice. There are always mistakes to be made, when analyzing data. You have to think about what kinds of mistakes you would rather make, and how likely you want to make them.

C-Dog: 'You might wanna get your hair checked, Bruh. Your ask-frequency is down 20% this year. That's a bad sign, Big L.' Lemont: 'My what?' C-Dog: 'This year you asked me, 'C'D-g, did you take my clippers?' five times. By this time last year, you done asked me 25 times. Guess how many times you asked the year before?' Lemont: 'GIVE. ME. BACK. MY. CLIPPERS.' C-Dog: 'Yo' hair growth be on a perfect negative-sloped linear Bezier curve, bruh. That #@$% serious.'
Darrin Bell’s Candorville for the 4th of September, 2018. All right, but 25 down to 5 is a drop of 80%. It’s a drop to 20%.

C-Dog talks about fitting Lemont’s hair growth to a curve. This means looking at the data one has as points in space. What kinds of curves will come as close as possible to including all those points? It turns out infinitely many curves will, and you can fit a curve to all the data points you have. (Unless you have some inconsistent data, like, in 2017 Lemont asked both 14 times and 18 times.) So to do an interpolation you need to make some suppositions. Suppose that the data is really a straight line, with some noise in it. Or is really a parabola. Really a sine wave. Or, drawing from a set of plausible curves, which of those best fits the data?

The Bézier Curve mentioned here is a family of shapes. They’re named for Pierre Bézier, an engineer with Renault who in the 1950s pioneered the using of these curves. There are infinitely many of them. But they’re nice to work with. You can make great-looking curves as sharply curved or as smoothly curved as you like, using them. Most modern fonts use Bézier Curves to compute the shapes of letters. If you have a drawing program, it’s got some kind of Bézier curve in there. It’s the weird tool with a bunch of little dots, most of which are nowhere near the curve they draw. But moving the dots changes the way the curve looks.

A Bézier curve can be linear; indeed, it can just be a line. C-Dog’s showing off by talking about a linear Bézier curve. Or he means something that looks a lot like a line, to the casual eye. Negative-sloped means what it would in high school algebra when you talk about lines: it’s a thing with a value that decreases as the independent variable increases. Something getting rarer in time, for example.

Samson, counting sheep in Roman Numerals. MCCCLXXXVII. MCCCLXXXVIII. Z.
Samson’s Dark Side of the Horse for the 4th of September, 2018. When I was younger I was upset that we had settled on ‘MCMXC’ as Roman Numerals for the year ‘1990’ when I couldn’t see any reason that ‘MXM’ wouldn’t do. Also now that I think about it I don’t see why 1950 wasn’t ‘MLM’ and why, like, 1989 was anything but ‘MLMXXXIX’.

Samson’s Dark Side of the Horse for the 4th is our Roman Numerals joke for the week. The Roman Numerals scheme has well-defined letters to represent the numbers up to 1,000. It doesn’t really have consistent schemes past that. But then the Roman Numeral scheme was a bit more ad hoc than really seems comfortable, to us. There could be a striking variety of ways to write larger numbers, particularly; MathWorld notes how letters like I or X or C would be framed in different ways to get at huge numbers like a hundred thousand or so. Roman Numerals standardized in the middle ages, long after the Roman Empire had reason to care about them, and for that matter as Arabic numerals got to be more accepted. Wikipedia also lists a bunch of Medieval abbreviations in a Roman Numerals scheme for things we just don’t use, like F for 40 or T for 160. I presume they have abundant manuscript examples of these, so that we aren’t making too much out of one person’s idiosyncratic notes.

Frank and Ernest in front of a chalkboard with basic addition on it. Frank: 'How does facing away from first-grade arithmetic simplify your life?' Ernest: 'It's 'Back to Basics'!'
Thaves’s Frank and Ernest for the 5th of September, 2018. Fine, but now he’s just facing the wall with the SRA Reading Laboratory posters on it.

Thaves’s Frank and Ernest for the 5th uses arithmetic, particularly simple addition, as emblematic of the basics of life. Hard to argue that this isn’t some of the first things anyone would learn, and that mathematics as it’s taught builds from that. A mathematician might see other fields — particularly set theory and category theory — as more fundamental than arithmetic. That is, that you can explain arithmetic in terms of set theory, and set theory in terms of category theory. So one could argue that those are the more basic. But if we mean basic as in the first things anyone learns, yeah, it’s arithmetic. Definitely.

Professor pointing to a chalkboard with a bunch of mathematical symbols, some of them cartoon fish. He presents in front of an audience of fish. Caption: 'Proving the existence of fish.'
Kliban’s Kliban Cartoons for the 5th of September, 2018. Based on the G#7 there I’m not sure this proof doesn’t include some music theory.

Kliban’s Kliban Cartoons for the 5th speaks of proofs. A good bit of mathematics is existence proofs, which is to say, showing that a thing with desired properties does exist. Sometimes they actually show you the thing. Such a “constructive proof” — showing how you make an example of the thing — pretty well proves the thing exists. But sometimes the best you can do is show that there is an answer. In any case, an example of a fish would convince all but the most hardcore skeptics that fish do exist.

I do at least one, and often several, Reading the Comics posts each week. They’re at this link. Essays that mention Candorville are at this link. Essays where I discuss Dark Side of the Horse are at this link. Appearances of Frank and Ernest should be at this link. Other essays with Kliban cartoons should be at this link.

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 11, 2018: Strips For The Week Edition

The other half of last week’s mathematically-themed comics were on familiar old themes. I’ll see what I can do with them anyway.

Scott Hilburn’s The Argyle Sweater for the 9th is the anthropomorphic numerals joke for the week. I’m curious why the Middletons would need multiple division symbols, but I suppose that’s their business. It does play on the idea that “division” and “splitting up” are the same thing. And that fits the normal use of these words. We’re used to thinking, say, of dividing a desired thing between several parties. While that’s probably all right in introducing the idea, I do understand why someone would get very confused when they first divide by one-half or one-third or any number between zero and one. And then negative numbers make things even more confusing.

5, looking out the window and speaking to 3: 'Oh dear. Looks like the Middletons are getting a divorce.' 3: 'How can you tell?' (Next door a 4 has driven up with two division obeluses in the car.)
Scott Hilburn’s The Argyle Sweater for the 9th of August, 2018. The division symbol ÷ is the “obelus”, by the way. And no, the dots above and below the line are not meant to represent where you would fit a numerator and denominator into a fraction. That’s a useful trick to remember what the symbol does, but it’s not how the symbol was “designed”.

Thaves’s Frank and Ernest for the 9th is the anthropomorphic geometric figures joke for the week. I think I can wrangle a way by which Circle’s question has deeper mathematical context. Mathematicians use the idea of “space” a lot. The use is inspired by how, you know, the geometry of a room works. Euclidean space, in the trade. A Euclidean space is a collection of points that obey a couple simple rules. You can take two points and add them, and get something in the space. You can take any scalar and multiply it by any point and get a point in the space. A scalar is something that acts like a real number. For example, real numbers. Maybe complex numbers, if you’re feeling wild.

Circle, and triangle, speaking to a cube: 'Three-dimensional, eh --- what makes you so spatial?
Thaves’s Frank and Ernest for the 9th of August, 2018. Idly curious if they’ve done this same joke in Eric the Circle.

A Euclidean space can be two-dimensional. This is the geometry of stuff you draw on paper. It can be three-dimensional. This is the geometry of stuff in the real world, or stuff you draw on paper with shading. It can be four-dimensional. This is the geometry of stuff you draw on paper with big blobby lines around it. Each of these is an equally good space, though, as legitimate and as real as any other. Context usually puts an implicit “three dimensional” before most uses of the word “space”. But it’s not required to be there. There’s many kinds of spaces out there.

And “space” describes stuff that doesn’t look anything like rooms or table tops or sheets of paper. These are spaces built of things like functions, or of sets of things, or of ways to manipulate things. Spaces built of the ways you can subdivide the integers. The details vary. But there’s something in common in all these ideas that communicates.

Wavehead at the blackboard, speaking to his teacher. On the board is '14 - x = 5'. Wavehead: 'I'm just saying --- sooner or later X is going to have to solve these things for itself.'
Mark Anderson’s Andertoons for the 11th of August, 2018. Why do they always see it as x needing solving, and not, say, 14 needing solving?

Mark Anderson’s Andertoons for the 11th is the Mark Anderson’s Andertoons for the week. I think we’ve all seen this joke go across our social media feed and it’s reassuring to know Mark Anderson has social media too. We do talk about solving for x, using the language of describing how we help someone get past a problem. I wonder if people might like this kind of algebra more if we talked more about finding out what values ‘x’ could have that make the equation true. Well, it won’t stop people feeling they don’t like the mathematics they learned in school. But it might help people feel like they know why they’re doing it.

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 Frank and Ernest are at this link. And some of the very many essays about Andertoons are at this link. Enjoy responsibly.

Reading the Comics, June 1, 2018: His First Name Is Tom For What That’s Worth Edition

And now I’ve got caught up with last week’s comics. I can get to readying for this coming Sunday looking at … so far … nine comic strips that made the preliminary cut. Whimper.

This time the name does mean something.

Thaves’s Frank and Ernest for the 31st complains about not being treated as a “prime number”. There’s a lot of linguistic connotation gone into this strip. The first is the sense that to be a number is to be stripped of one’s humanity, to become one of a featureless horde. Each number is unique, of course; Iva Sallay’s Find the Factors page each day starts with some of the features of each whole number in turn. But one might look at, oh, 84,644 and not something very different from 84,464.

Frank: 'The boss treats me like a number, and not a prime one.'
Thaves’s Frank and Ernest for the 31st of May, 2018. In the past I’ve gone out trying to find and print Thaves’s first name, on the grounds that I should fully credit people. I’m coming around on this, first because I keep forgetting his first name and looking it up every time is tiresome. But more important, if Thaves wants to be known simply as ‘Thaves’ what am I doing arguing that? Is there a different Thaves, possibly his evil twin, producing another comic strip named Frank and Ernest that I have to make clear I’m not talking about? So that’s my level of overthinking these captions right now.

And yet there’s the idea that there are prime numbers, celebrities within the anonymous counting numbers. The name even says it; a prime something is especially choice. And we speak of prime numbers as somehow being the backbone of numbers. This reflects that we find unique factorizations to be a useful thing to do. But being a prime number doesn’t make a number necessarily better. There are reasons most (European) currencies, before decimalization, divided their currency unit into 20 parts of 12 parts each. And nobody divided them into 19 parts of 13 parts each. As often happens, whether something is good depends on what you’re hoping it’s good for.

[ Movie showing the digits of Pi marching out of a flying saucer.] Guy in movie: 'What are they?' Woman in movie: 'They appear to be numbers.' Guy watching movie: 'I just love sci-pi movies.'
Nate Fakes’s Break of Day for the 1st of June, 2018. Sure, but what do you do for the sequel? No, τ is not a thing.

Nate Fakes’s Break of Day for the 1st of June is more or less the anthropomorphized numerals installment for the week. It’s also a bit of wordplay, so, good on them. There’s not so many movies about mathematics. Darren Aronofsky’s Pi, Ron Howard’s A Beautiful Mind, and Theodore Melfi’s Hidden Figures are the ones that come to mind, at least in American cinema. And there was the TV detective series Numbers. It seems odd that there wasn’t, like, some little studio prestige thing where Paul Muni played Évariste Galois back in the day. But a lot of the mathematical process isn’t cinematic. People scribbling notes, typing on a computer, or arguing about something you don’t understand are all hard to make worth watching. And the parts that anyone could understand — obsession, self-doubt, arguments over priority, debates about implications — are universal to any discovery or invention. Note that the movies listed are mostly about people who happen to be doing mathematics. You could change the specialties to, say, chemical engineering without altering the major plot beats. Well, Pi would need more alteration. But you could make it about any process that seems to offer reliable forecasting in a new field.

Bernice, whispering: 'Luann! Did you hear? Tiffany asked Aaron Hill to the dance but he turned her down! He said he's inviting 'someone else'!' Teacher: 'So if x is 1/4 y over 42.6 minus (Q^2 R)/19 ...' Bernice: 'And we know WHO that 'someone else' is, don't we?' [ Luann is wide-eyed with joy. ] Teacher: 'Can anyone tell me what 'R' is?' Luann: 'YES!' Teacher: 'Good! Come up here to the board, Luann.'
Greg Evans’s Luann Againn for the 1st of June, 2018. It originally ran the 1st of June, 1990.

Greg Evans’s Luann Againn for the 1st takes place in mathematics class. The subject doesn’t matter for the joke. It could be anything that doesn’t take much word-balloon space but that someone couldn’t bluff their way through.

Mr Barrows: 'You're pretty good at numbers, Quincy. Are you going to work with figures when you grow up?' Quincy: 'I'm not sure yet, Mr Barrows. I'm either gonna be a very tall accountant or a very short basketball player.'
Ted Shearer’s Quincy for the 7th of April, 1979 and reprinted the 1st of June, 2018. I get why Quincy would figure he’d grow up to be a very tall accountant, but why does he just assume he’d be a very short basketball player? Isn’t it as easy to imagine you’ll grow up to be a typically-sized basketball player? Does he know something we don’t?

Ted Shearer’s Quincy for the 7th of April, 1979 has Quincy thinking what he’ll do with his head for figures. He sees accounting as plausible. Good for him. Society always needs accountants. And they probably do more of society’s mathematics than the mathematicians do.

Scientist type pointing to the blackboard full of arithmetic: 'Cutting-edge formula? No, that's the wi-fi password.'
Bill Abbott’s Spectickles for the 1st of June, 2018. So, is this all the characters that have to be typed in, or is it one of those annoying things where you have to solve the puzzle to get the password?

Bill Abbott’s Spectickles for the 1st features the blackboard-full-of-mathematics to represent the complicated. It shows off the motif that an advanced mathematical formula will be a long and complicated one. This has good grounds behind it. If you want to model something interesting that hasn’t been done before, chances are it’s because you need to consider many factors. And trying to represent them will be clumsily done. It takes reflection and consideration and, often, new mathematical tools to make a formula pithy. Famously, James Clerk Maxwell introduced his equations about electricity and magnetism as a set of twenty equations. By 1873 Maxwell, making some use of quaternions, was able to reduce this to eight equations. Oliver Heaviside, in the late 19th century, used the still-new symbols of vector mechanics. This let him make an attractive quartet. We still see that as the best way to describe electromagnetic fields. As with writing, much of mathematics is rewriting.

Reading the Comics, March 10, 2018: I Will Get To Pi Day Edition

There were fewer Pi Day comic strips than I had expected for this year. It’s gotten much more public mention than I had expected a pop-mathematics bit of whimsy might. But I’m still working off last week’s strips; I’ll get to this week’s next week. This makes sense to me, which is as good as making sense at all.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 7th is a percentages joke, as applied to hair. Lard doesn’t seem clear whether this would be 10% off the hair by individual strand length or by total volume. Either way, Lard’s right to wonder about the accuracy.

Mark Pett’s Mr Lowe rerun for the 7th is a standardized test joke. Part of the premise of Pett’s strip is that Mister Lowe is a brand-new teacher, which is why he makes mistakes like this problem. (This is touchy to me, as in grad school I hoped to make some spare money selling questions to a standardized testing company. I wasn’t good enough at it, and ultimately didn’t have the time to train up to their needs.) A multiple-choice question needs to clear and concise and to have one clearly best answer. As the given question’s worded, though, I could accept ‘2’ or ’12’ as a correct answer. With a bit of experience Lowe would probably clarify that Tommy and Suzie are getting the same number of apples and that together they should have 20 total.

Then on the 9th Mr Lowe has a joke about cultural bias in standardized tests. It uses an arithmetic problem as the type case. Mathematicians like to think of themselves as working in a universal, culturally independent subject. I suppose it is, but only in ways that aren’t interesting: if you suppose these rules of logic and these axioms and these definitions then these results follow, and it doesn’t matter who does the supposing. But start filtering that by stuff people care about, such as the time it takes for two travelling parties to meet, and you’ve got cultural influence. (Back when this strip was new the idea that a mathematics exam could be culturally biased was a fresh new topic of mockery among people who don’t pay much attention to the problems of teaching but who know what those who do are doing wrong.)

Ralph Hagen’s The Barn for the 8th — a new tag for my comics, by the way — lists a bunch of calculation tools and techniques as “obsolete” items. I’m assuming Rory means that longhand multiplication is obsolete. I’m not sure that it is, but I have an unusual perspective on this.

Thaves’s Frank and Ernest for the 8th is an anthropomorphic-numerals joke. I was annoyed when I first read this because I thought, wait, 97 isn’t a prime number. It is, of course. I have no explanation for my blunder.

Jon Rosenberg’s Scenes from a Multiverse has restarted its run on GoComics. The strip for the 8th is a riff on Venn Diagrams. And, it seems to me, about those logic-bomb problems about sets consisting of sets that don’t contain themselves and the like. You get weird and apparently self-destructive results pondering that stuff. The last time GoComics ran the Scenes from a Multiverse series I did not appreciate right away that there were many continuing stories. There might be follow-ups to this Former Venn Prime Universe story.

Brian Fies’s The Last Mechanical Monster for the 9th has the Mad Scientist, struggling his way into the climax of the story, testing his mind by calculating a Fibonacci Sequence. Whatever keeps you engaged and going. You can build a Fibonacci Sequence from any two starting terms. Each term after the first two is the sum of the previous two. If someone just says “the Fibonacci Sequence” they mean the sequence that starts with 0, 1, or perhaps with 1, 1. (There’s no interesting difference.) Fibonacci Sequences were introduced to the west by Leonardo of Pisa, who did so much to introduce Hindu-Arabic Numerals to a Europe that didn’t know it wanted this stuff. They touch on some fascinating stuff: the probability of not getting two tails in a row of a set number of coin tosses. Chebyshev polynomials. Diophantine equations. They also touch on the Golden Ratio, which isn’t at all important but that people like.

Nicholas Gurewitch’s Perry Bible Fellowship for the 9th just has a blackboard of arithmetic to stand in for schoolwork.

Reading the Comics, February 10, 2018: I Meant To Post This Thursday Edition

Ah, yes, so, in the midst of feeling all proud that I’d gotten my Reading the Comics workflow improved, I went out to do my afternoon chores without posting the essay. I’m embarrassed. But it really only affects me looking at the WordPress Insights page. It publishes this neat little calendar-style grid that highlights the days when someone’s posted and this breaks up the columns. This can only unnerve me. I deserve it.

Tom Thaves’s Frank and Ernest for the 8th of February is about the struggle to understand zero. As often happens, the joke has a lot of truth to it. Zero bundles together several ideas, overlapping but not precisely equal. And part of that is the idea of “nothing”. Which is a subtly elusive concept: to talk about the properties of a thing that does not exist is hard. As adults it’s easy to not notice this anymore. Part’s likely because mastering a concept makes one forget what it took to understand. Part is likely because if you don’t have to ponder whether the “zero” that’s “one less than one” is the same as the “zero” that denotes “what separates the count of thousands from the count of tens in the numeral 2,038” you might not, and just assume you could explain the difference or similarity to someone who has no idea.

John Zakour and Scott Roberts’s Maria’s Day for the 8th has maria and another girl bonding over their hatred of mathematics. Well, at least they’re getting something out of it. The date in the strip leads me to realize this is probably a rerun. I’m not sure just when it’s from.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 8th proposes a prank based on mathematical use of the word “arbitrarily”. This is a word that appears a lot in analysis, and the strip makes me realize I’m not sure I can give a precise definition. An “arbitrarily large number”, for example, would be any number that’s large enough. But this also makes me realize I’m not sure precisely what joke Weinersmith is going for. I suppose that if someone were to select an arbitrarily large number they might pick 53, or a hundred, or million billion trillion. I suppose Weinersmith’s point is that in ordinary speech an arbitrarily made choice is one selection from all the possible alternatives. In mathematical speech an arbitrarily made choice reflects every possible choice. To speak of an arbitrarily large number is to say that whatever selection is made, we can go on to show this interesting stuff is true. We’d typically like to prove the most generically true thing possible. But picking a single example can be easier to prove. It can certainly be easier to visualize. 53 is probably easier to imagine than “every number 52 or larger”, for example.

Quincy: 'Someday I'm gonna write a book, Gran.' Grandmom: 'Wonderful. Will you dedicate it to me?' Quincy: 'Sure. In fact, if you want, I'll dedicate this math homework to you.'
Ted Shearer’s Quincy for the 16th of December, 1978 and reprinted the 9th of February, 2018. I’m not sure just what mathematics homework Quincy could be doing to inspire him to write a book, but then, it’s not like my mind doesn’t drift while doing mathematics either. And book-writing’s a common enough daydream that most people are too sensible to act on.

Ted Shearer’s Quincy for the 16th of December, 1978 was rerun the 9th of February. It just shows Quincy at work on his mathematics homework, and considering dedicating it to his grandmother. Mathematics books have dedications, just as any other book does. I’m not aware of dedications of proofs or other shorter mathematics works, but there’s likely some. There’s often a note of thanks, usually given to people who’ve made the paper’s writers think harder about the subjects. But I don’t think there’s any reason a paper wouldn’t thank someone who provided “mere” emotional support. I just don’t have examples offhand.

Jef Mallet’s Frazz for the 9th looks like one of those creative-teaching exercises I sometimes see in Mathematics Education Twitter: the teacher gives answers and the students come up with story problems to match. That’s not a bad project. I’m not sure how to grade it, but I haven’t done anything that creative when I’ve taught. I’m sorry I haven’t got more to say about it since the idea seems fun.

Redeye: 'C'mon, Pokey. Time for your lessons. Okay, what do you get when you divide 5,967,342 by 973 ... ?' Pokey: 'A headache!'
Gordon Bess’s Redeye for the 30th of September, 1971 and reprinted the 10th of February, 2018. I realized I didn’t know the father’s name and looked it up, and Wikipedia revealed to me that he’s named Redeye. You know, like the comic strip implies right there in the title. Look, I just read the comics, I can’t be expected to think about the comics too.

Gordon Bess’s Redeye for the 30th of September, 1971 was rerun the 10th. It’s a bit of extremely long division and I don’t blame Pokey for giving up on that problem. Starting from 5,967,342 divided by 973 I’d say, well, that’s about six million divided by a thousand, so the answer should be near six thousand. I don’t think the last digits of 2 and 3 suggest anything about what the final digit should be, if this divides evenly. So the only guidance I have is that my answer ought to be around six thousand and then we have to go into actually working. It turns out that 973 doesn’t go into 5,967,342 a whole number of times, so I sympathize more with Pokey. The answer is a little more than 6,132.9311.

Reading the Comics, October 7, 2017: Rerun Comics Edition

The most interesting mathematically-themed comic strips from last week were also reruns. So be it; at least I have an excuse to show a 1931-vintage comic. Also, after discovering my old theme didn’t show the category of essay I was posting, I did literally minutes of search for a new theme that did. And that showed tags. And that didn’t put a weird color behind LaTeX inline equations. So I’m using the same theme as my humor blog does, albeit with a different typeface, and we’ll hope that means I don’t post stuff to the wrong blog. As it is I start posting something to the wrong place about once every twenty times. All I want is a WordPress theme with all the good traits of the themes I look at and none of the drawbacks; why is that so hard to get?

Castor Oyl: 'Hey, Popeye, handing out money is an easy job. Come, work on the books awhile. I'll take your place. yah. Figure up and see what the capital of our one-way bank is today.' Popeye: ? Oke. ! Eight times eight is eighty-eight ... six and' six is sixteen ... ahoy, Castor! Ya makes a nine like a six only up-side-down ain't it? ... Me figgers say we eighter got sixty thousing left of we was broke three days ago. I wonder which is right?' (At the vault.) Castor: 'What the heck are you doing?' Popeye: 'Blow me down - it's more easy to count it. 7627, 7628 ... '
Elzie Segar’s Thimble Theatre rerun for the 25th of April, 1931, and rerun the 5th of October, 2017. No, Kabibble Kabaret is not actually a joke and yes, it’s always like that, and no, I have no idea why Comics Kingdom includes these footers. I find them fascinating in their badness, but, yeah.

Elzie Segar’s Thimble Theatre rerun for the 5th originally ran the 25th of April, 1931. It’s just a joke about Popeye not being good at bookkeeping. In the story, Popeye’s taking the $50,000 reward from his last adventure and opened a One-Way Bank, giving people whatever money they say they need. And now you understand how the first panel of the last row has several jokes in it. The strip is partly a joke about Popeye being better with stuff he can hit than anything else, of course. I wonder if there’s an old stereotype of sailors being bad at arithmetic. I remember reading about pirate crews that, for example, not-as-canny-as-they-think sailors would demand a fortieth or a fiftieth of the prizes as their pay, instead of a mere thirtieth. But it’s so hard to tell what really happened and what’s just a story about the stupidity of people. Marginal? Maybe, but I’m a Popeye fan and this is my blog, so there.

Bill Rechin’s Crock rerun(?) from the 6th must have come before. I don’t know when. Anyway it’s a joke about mathematics being way above everybody’s head.

Vulture: 'How come you failed the math test?' Kid: 'Dad helped me study for it. I knew I was in trouble when he said the answer to 125 times 140 was 'a lot'.
Bill Rechin’s Crock from the 6th of October, 2017. Yeah, I don’t exactly get the vulture as a pack animal either, but it’s kind of a cute idea. Or I’m a soft touch for cartoon and comic strip vultures. I would like to identify the characters but I forget their names and Wikipedia and the official Comics Kingdom site don’t give me any help.

Norm Feuti’s Gil rerun for the 6th is a subverted word problem joke. And it’s a reminder of how hard story problems can be. You need something that has a mathematics question on point. And the question has to be framed as asking something someone would actually care to learn. Plus the story has to make sense. Much easier when you’re teaching calculus, I think.

Jason Chatfield’s Ginger Meggs for the 6th is a playing-stupid joke built in percentages. Cute enough for the time it takes to read.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 6th is a parent-can’t-help-with-homework joke, done with arithmetic since it’s hard to figure another subject that would make the joke possible. I suppose a spelling assignment could be made to work. But that would be hard to write so it didn’t seem contrived.

Thaves’ Frank and Ernest for the 7th feels like it’s a riff on the old saw about Plato’s Academy. (The young royal sent home with a coin because he asked what the use of this instruction was, and since he must get something from everything, here’s his drachma.) Maybe. Or it’s just the joke that you make if you have “division” and “royals” in mind.

Mark Tatulli’s Lio for the 7th is not quite the anthropomorphic symbols joke for this past week. It’s circling that territory, though.

Reading the Comics, September 16, 2017: Wait, Are Elviney and Miss Prunelly The Same Character Week

It was an ordinary enough week when I realized I wasn’t sure about the name of the schoolmarm in Barney Google and Snuffy Smith. So I looked it up on Comics Kingdom’s official cast page for John Rose’s comic strip. And then I realized something about the Smiths’ next-door neighbor Elviney and Jughaid’s teacher Miss Prunelly:

Pictures of Elviney and Miss Prunelly from the Barney Google And Snuffy Smith cast page. They look almost the same, except for Elviney wearing smaller glasses and having something that isn't a pencil in her hair bun.
Excerpt from the cast page of Barney Google and Snuffy Smith. Among the many mysteries besides that apparently they’re the same character and I never noticed this before? Why does Spark Plug, the horse Google owns that’s appeared like three times this millennium and been the source of no punch lines since Truman was President, get listed ahead of Elviney and Miss Prunelly who, whatever else you can say about them, appear pretty much every week?

Are … are they the same character, just wearing different glasses? I’ve been reading this comic strip for like forty years and I’ve never noticed this before. I’ve also never heard any of you all joking about this, by the way, so I stand by my argument that if they’re prominent enough then, yes, glasses could be an adequate disguise for Superman. Anyway, I’m startled. (Are they sisters? Cousins? But wouldn’t that make mention on the cast page? There are missing pieces here.)

Mac King and Bill King’s Magic In A Minute feature for the 10th sneaks in here yet again with a magic trick based in arithmetic. Here, they use what’s got to be some Magic Square-based technology for a card trick. This probably could be put to use with other arrangements of numbers, but cards have the advantage of being stuff a magician is likely to have around and that are expected to do something weird.

Kid: 'I can't do this! I'll never be bale to figure out this stupid math homework!!!' Ollie the dog, thinking: 'Want me to eat it?' Caption: Ollie always dreamed of being a rescue dog.
Susan Camilleri Konair’s Six Chix for the 13th of September, 2017. It’s a small artistic touch, but I do appreciate that the kid is shown with a cell phone and it’s not any part of the joke that having computing devices is somehow wrong or that being on the Internet is somehow weird or awry.

Susan Camilleri Konair’s Six Chix for the 13th name-drops mathematics as the homework likely to be impossible doing. I think this is the first time Konair’s turned up in a Reading The Comics survey.

Thom Bluemel’s Birdbrains for the 13th is an Albert Einstein Needing Help panel. It’s got your blackboard full of symbols, not one of which is the famous E = mc2 equation. But given the setup it couldn’t feature that equation, not and be a correct joke.

Miss Prunelly: 'If Jughaid has twelve jelly beans an' he gives five of 'em to Mary Beth, how many does he have left?' Mary Beth: 'Prob'ly four, 'cuz he ain't all that good at counting'!''
John Rose’s Barney Google for the 14th of September, 2017. I admire Miss Prunelly’s commitment to ongoing professional development that she hasn’t run out of shocked or disapproving faces after all these years in a gag-a-day strip.

John Rose’s Barney Google for the 14th does a little more work than necessary for its subtraction-explained-with-candy joke. I non-sarcastically appreciate Rose’s dodging the obvious joke in favor of a guy-is-stupid joke.

Niklas Eriksson’s Carpe Diem for the 14th is a kind of lying-with-statistics joke. That’s as much as it needs to be. Still, thought always should go into exactly how one presents data, especially visually. There are connotations to things. Just inverting an axis is dangerous stuff, though. The convention of matching an increase in number to moving up on the graph is so ingrained that it should be avoided only for enormous cause.

At the hospital: 'We've inverted the Y-Axis so as not to worry the patient.'
Niklas Eriksson’s Carpe Diem for the 14th of September, 2017. It’s important the patient not panic thinking about how he’s completely flat under the blanket there.

This joke also seems conceptually close, to me, to the jokes about the strangeness of how a “negative” medical test is so often the good news.

Olivia Walch’s Imogen Quest for the 15th is not about solitaire. But “solving” a game by simulating many gameplays and drawing strategic advice from that is a classic numerical mathematics trick. Whether a game is fun once it’s been solved so is up to you. And often in actual play, for a game with many options at each step, it’s impossible without a computer to know the best possible move. You could use simulations like this to develop general guidelines, and a couple rules that often pan out.

Thaves’s Frank and Ernest for the 16th qualifies as the anthropomorphic-numerals joke for this week. I’m glad to have got one in.

Reading the Comics, August 5, 2017: Lazy Summer Week Edition

It wasn’t like the week wasn’t busy. Comic Strip Master Command sent out as many mathematically-themed comics as I might be able to use. But they were again ones that don’t leave me much to talk about. I’ll try anyway. It was looking like an anthropomorphic-symboles sort of week, too.

Tom Thaves’s Frank and Ernest for the 30th of July is an anthropomorphic-symbols joke. The tick marks used for counting make an appearance and isn’t that enough? Maybe.

Dan Thompson’s Brevity for the 31st is another entry in the anthropomorphic-symbols joke contest. This one sticks to mathematical symbols, so if the Frank and Ernest makes the cut this week so must this one.

Eric the Circle for the 31st, this installment by “T daug”, gives the slightly anthropomorphic geometric figure a joke that at least mentions a radius, and isn’t that enough? What catches my imagination about this panel particularly is that the “fractured radius” is not just a legitimate pun but also resembles a legitimate geometry drawing. Drawing a diameter line is sensible enough. Drawing some other point on the circle and connecting that to the ends of the diameter is also something we might do.

Scott Hilburn’s The Argyle Sweater for the 1st of August is one of the logical mathematics jokes you could make about snakes. The more canonical one runs like this: God in the Garden of Eden makes all the animals and bids them to be fruitful. And God inspects them all and finds rabbits and doves and oxen and fish and fowl all growing in number. All but a pair of snakes. God asks why they haven’t bred and they say they can’t, not without help. What help? They need some thick tree branches chopped down. The bemused God grants them this. God checks back in some time later and finds an abundance of baby snakes in the Garden. But why the delay? “We’re adders,” explain the snakes, “so we need logs to multiply”. This joke absolutely killed them in the mathematics library up to about 1978. I’m told.

John Deering’s Strange Brew for the 1st is a monkeys-at-typewriters joke. It faintly reminds me that I might have pledged to retire mentions of the monkeys-at-typewriters joke. But I don’t remember so I’ll just have to depend on saying I don’t think I retired the monkeys-at-typewriters jokes and trust that someone will tell me if I’m wrong.

Dana Simpson’s Ozy and Millie rerun for the 2nd name-drops multiplication tables as the sort of thing a nerd child wants to know. They may have fit the available word balloon space better than “know how to diagram sentences” would.

Mark Anderson’s Andertoons for the 3rd is the reassuringly normal appearance of Andertoons for this week. It is a geometry class joke about rays, line segments with one point where there’s an end and … a direction where it just doesn’t. And it riffs on the notion of the existence of mathematical things. At least I can see it that way.

Dad: 'How many library books have you read this summer, Hammie?' Hammie: 'About 47.' Zoe: 'HA!' Dad: 'Hammie ... ' Hammie: 'Okay ... two.' Dad: 'Then why did you say 47?' Hammie: 'I was rounding up.' Zoe: 'NOW he understands math!'
Rick Kirkman and Jerry Scott’s Baby Blues for the 5th of August, 2017. Hammie totally blew it by saying “about forty-seven”. Too specific a number to be a plausible lie. “About forty” or “About fifty”, something you can see as the result of rounding off, yes. He needs to know there are rules about how to cheat.

Rick Kirkman and Jerry Scott’s Baby Blues for the 5th is a rounding-up joke that isn’t about herds of 198 cattle.

Stephen Bentley’s Herb and Jamaal for the 5th tosses off a mention of the New Math as something well out of fashion. There are fashions in mathematics, as in all human endeavors. It startles many to learn this.

Reading the Comics, April 22, 2017: Thought There’d Be Some More Last Week Edition

Allison Barrows’s PreTeena rerun for the 18th is a classic syllogism put into the comic strip’s terms. The thing about these sorts of deductive-logic syllogisms is that whether the argument is valid depends only on the shape of the argument. It has nothing to do with whether the thing being discussed makes any sense. This can be disorienting. It’s hard to ignore the everyday meaning of words when you hear a string of sentences. But it’s also hard to parse a string of sentences if the words don’t make sense in them. This is probably part of why on the mathematics side of things logic courses will skimp on syllogisms, using them to give an antique flavor and sense of style to the introduction of courses. It’s easier to use symbolic representations for logic instead.

Randy Glasbergen’s Glasbergen Cartoons rerun for the 20th is the old joke about arithmetic being different between school, government, and corporate work. I haven’t looked at the comments — the GoComics redesign, whatever else it does, makes it very easy to skip the comments — but I’m guessing by the second one someone’s said the Common Core method means getting the most wrong answer.

Dolly, coming home: 'Rithmetic would be a lot easier if it didn't have all those different numbers.'
Bil Keane and Jeff Keane’s Family Circus for the 21st of April, 2017. In fairness, there aren’t a lot of things we need all of 6, 7, and 8 for and you can just use whatever one of those you’re good at for any calculations with the others. Promise.

Bil Keane and Jeff Keane’s Family Circus for the 21st I don’t know is a rerun. But a lot of them are these days. Anyway, it looks like a silly joke about how nice mathematics would be without numbers; Dolly has no idea. I can sympathize with being intimidated by numerals. At the risk of being all New Math-y, I wonder if she wouldn’t like arithmetic more if it were presented as a game. Like, here’s a couple symbols — let’s say * and | for a start, and then some rules. * and * makes *, but * and | makes |. Also | and * makes |. But | and | makes |*. And so on. This is binary arithmetic, disguised, but I wonder if making it look like something inconsequential would make it more pleasant to learn, and if that would transfer over to arithmetic with 1’s and 0’s. Normal, useful arithmetic would be harder to play like this. You’d need ten symbols that are easy to write that aren’t already numbers, letters, or common symbols. But I wonder if it’d be worth it.

Tom Thaves’s Frank and Ernest for the 22nd is provided for mathematics teachers who need something to tape to their door. You’re welcome.

Reading the Comics, June 13, 2012

Because there weren’t many math-themed comic strips, that’s why I went so long without an update in my roster of comic strips that mention math subjects. After Mike Peters’s Mother Goose and Grimm put in the start of a binomial expression the comics pages — through King Features Syndicate and — decided to drop the whole subject pretty completely for the rest of May. It picked up a little in June.

Continue reading “Reading the Comics, June 13, 2012”