Reading the Comics, June 15, 2019: School Is Out? Edition

This has not been the slowest week for mathematically-themed comic strips. The slowest would be the week nothing on topic came up. But this was close. I admit this is fine as I have things disrupting my normal schedule this week. I don’t need to write too many essays too.

On-topic enough to discuss, though, were:

Lalo Alcaraz’s La Cucaracha for the 9th features a teacher trying to get ahead of student boredom. The idea that mathematics is easier to learn if it’s about problems that seem interesting is a durable one. It agrees with my intuition. I’m less sure that just doing arithmetic while surfing is that helpful. My feeling is that a problem being interesting is separate from a problem naming an intersting thing. But making every problem uniquely interesting is probably too much to expect from a teacher. A good pop-mathematics writer can be interesting about any problem. But the pop-mathematics writer has a lot of choice about what she’ll discuss. And doesn’t need to practice examples of a problem until she can feel confident her readers have learned a skill. I don’t know that there is a good answer to this.

Also part of me feels that “eight sick waves times eight sick waves” has to be “sixty-four sick-waves-squared”. This is me worrying about the dimensional analysis of a joke. All right, but if it were “eight inches times eight inches” and you came back with “sixty-four inches” you’d agree something was off, right? But it’s easy to not notice the units. That we do, mechanically, the same thing in multiplying (oh) three times $1.20 or three times 120 miles or three boxes times 120 items per box as we do multiplying three times 120 encourages this. But if we are using numbers to measure things, and if we are doing calculations about things, then the units matter. They carry information about the kinds of things our calculations represent. It’s a bad idea to misuse or ignore those tools. Paul Trap’s Thatababy for the 14th is roughly the anthropomorphized geometry cartoon of the week. It does name the three ways to group triangles based on how many sides have the same length. Or if you prefer, how many interior angles have the same measure. So it’s probably a good choice for your geometry tip sheet. “Scalene” as a word seems to have entered English in the 1730s. Its origin traces to Late Latin “scalenus”, from the Greek “skalenos” and meaning “uneven” or “crooked”. “Isosceles” also goes to Late Latin and, before that, the Greek “isoskeles”, with “iso” the prefix meaning “equal” and “skeles” meaning “legs”. The curious thing to me is “Isosceles”, besides sounding more pleasant, came to English around 1550. Meanwhile, “equilateral” — a simple Late Latin for “equal sides” — appeared around 1570. I don’t know what was going on that it seemed urgent to have a word for triangles with two equal sides first, and a generation later triangles with three equal sides. And then triangles with no two equal sides went nearly two centuries without getting a custom term. But, then, I’m aware of my bias. There might have been other words for these concepts, recognized by mathematicians of the year 1600, that haven’t come to us. Or it might be that scalene triangles were thought to be so boring there wasn’t any point giving them a special name. It would take deeper mathematics history knowledge than I have to say. Those are all the mathematically-themed comic strips I can find something to discuss from the past week. There were some others with mentions of mathematics, though. These include: Tony Rubino and Gary Markstein’s Daddy’s Home for the 9th, in which mathematics is the last class of the school year. Francesco Marciuliano and Jim Keefe’s Sally Forth for the 11th has a study session with “math charades” mentioned. Mark Andersons Andertoons for the 11th wants in on some of my sweet Thatababy exposition. Harley Schwadron’s 9 to 5 for the 14th is trying to become the default pie chart joke around here. It won’t beat out Randolph Itch, 2 am without a stronger punch line. And Mark Tatulli’s Heart of the City for the 15th sees Dean mention hiding sleeping in algebra class. This closes out a week’s worth of comic strips. My next Reading the Comics post should be at this link next Sunday. And now I need to think of something to post for the Thursday and, if I can, Tuesday publication dates. Reading the Comics, April 24, 2019: Mic Drop Edition Edition I can’t tell you how hard it is not to just end this review of last week’s mathematically-themed comic strips after the first panel here. It really feels like the rest is anticlimax. But here goes. John Deering’s Strange Brew for the 20th is one of those strips that’s not on your mathematics professor’s office door only because she hasn’t seen it yet. The intended joke is obvious, mixing the tropes of the Old West with modern research-laboratory talk. “Theoretical reckoning” is a nice bit of word juxtaposition. “Institoot” is a bit classist in its rendering, but I suppose it’s meant as eye-dialect. What gets it a place on office doors is the whiteboard, though. They’re writing out mathematics which looks legitimate enough to me. It doesn’t look like mathematics though. What’s being written is something any mathematician would recognize. It’s typesetting instructions. Mathematics requires all sorts of strange symbols and exotic formatting. In the old days, we’d handle this by giving the typesetters hazard pay. Or, if you were a poor grad student and couldn’t afford that, deal with workarounds. Maybe just leave space in your paper and draw symbols in later. If your university library has old enough papers you can see them. Maybe do your best to approximate mathematical symbols using ASCII art. So you get expressions that look something like this:  / 2 pi | 2 | x cos(theta) dx - 2 F(theta) == R(theta) | / 0  This gets old real fast. Mercifully, Donald Knuth, decades ago, worked out a great solution. It uses formatting instructions that can all be rendered in standard, ASCII-available text. And then by dark incantations and summoning of Linotype demons, re-renders that as formatted text. It handles all your basic book formatting needs — much the way HTML, used for web pages, will — and does mathematics much more easily. For example, I would enter a line like: \int_{0}^{2\pi} x^2 \cos(\theta) dx - 2 F(\theta) \equiv R(\theta)  And this would be rendered in print as: $\int_{0}^{2\pi} x^2 \cos(\theta) dx - 2 F(\theta) \equiv R(\theta)$ There are many, many expansions available to this, to handle specialized needs, hardcore mathematics among them. Anyway, the point that makes me realize John Deering was aiming at everybody with an advanced degree in mathematics ever with this joke, using a string of typesetting instead of the usual equations here? The typesetting language is named TeX. Mark Anderson’s Andertoons for the 21st is the Mark Anderson’s Andertoons for the week. It’s about one of those questions that nags at you as a kid, and again periodically as an adult. The perimeter is the boundary around a shape. The circumference is the boundary around a circle. Why do we have two words for this? And why do we sound all right talking about either the circumference or the perimeter of a circle, while we sound weird talking about the circumference of a rhombus? We sound weird talking about the perimeter of a rhombus too, but that’s the rhombus’s fault. The easy part is why there’s two words. Perimeter is a word of Greek origin; circumference, of Latin. Perimeter entered the English language in the early 15th century; circumference in the 14th. Why we have both I don’t know; my suspicion is either two groups of people translating different geometry textbooks, or some eager young Scholastic with a nickname like ‘Doctor Magnifico Triangulorum’ thought Latin sounded better. Perimeter stuck with circules early; every etymology I see about why we use the symbol π describes it as shorthand for the perimeter of the circle. Why `circumference’ ended up the word for circles or, maybe, ellipses and ovals and such is probably the arbitrariness of language. I suspect that opening “circ” sound cues people to think of it for circles and circle-like shapes, in a way that perimeter doesn’t. But that is my speculation and should not be mistaken for information. Steve McGarry’s KidTown for the 21st is a kids’s information panel with a bit of talk about representing numbers. And, in discussing things like how long it takes to count to a million or a billion, or how long it would take to type them out, it gets into how big these numbers can be. Les Stewart typed out the English names of numbers, in words, by the way. He’d also broken the Australian record for treading water, and for continuous swimming. Gary Delainey and Gerry Rasmussen’s Betty for the 24th is a sudoku comic. Betty makes the common, and understandable, conflation of arithmetic with mathematics. But she’s right in identifying sudoku as a logical rather than an arithmetic problem. You can — and sometimes will see — sudoku type puzzles rendered with icons like stars and circles rather than numerals. That you can make that substitution should clear up whether there’s arithmetic involved. Commenters at GoComics meanwhile show a conflation of mathematics with logic. Certainly every mathematician uses logic, and some of them study logic. But is logic mathematics? I’m not sure it is, and our friends in the philosophy department are certain it isn’t. But then, if something that a recognizable set of mathematicians study as part of their mathematics work isn’t mathematics, then we have a bit of a logic problem, it seems. Come Sunday I should have a fresh Reading the Comics essay available at this link. Reading the Comics, May 28, 2016: Visual Interest Will Never Reappear Edition OK, that’s three weeks in a row in which all my mathematically-themed comic strips are from Gocomics. Maybe I should commission some generic Reading The Comics art from the cartoonists and artists I know. It could make things more exciting on a visually dull week like this. Mark Anderson’s Andertoons got its entry on the 25th. We draw the name “exponents” from the example of Michael Stifel, a 16th-century German theologian/mathematician. He’d described them as exponents in his influential 1544 book Arithmetica Integra. But I don’t know why he picked the name “exponent” rather than some other word. Nate Fakes’s Break of Day for the 25th is the anthropomorphic numerals gag for this week. Dave Blazek’s Loose Parts for the 25th is not quite the anthropomorphic shapes joke for this week. The word “isosceles” does trace back to Greek, of course. The first part comes from “isos”, meaning equal; you see the same root in terms like “isobar” and “isometric view”. The “sceles” part comes from “skelos”, meaning leg. Say what you will about an isosceles triangle, and you may as they’ve got poor hearing, but they do have two legs with the same length. If you want to say an equilateral triangle, which has three legs the same length, is an isosceles triangle you can do that. You’ll be right. But you will look like you’re trying a little too hard to make a point, the way you do if you point to a square and start off by calling it a rhombus. Donna A Lewis’s Reply All Lite for the 25th tries doing a joke about doing mathematics by hand being a sign of old age. If we’re talking about arithmetic … I could go along with that, grudgingly. Calculator applications are so reliable and so quick that it’s hard to justify doing arithmetic by hand unless it’s a very simple problem. If you have fun doing that, good. But if we’re doing real mathematics, the working out of a model and the implications of that, or working out calculus or group theory or graph theory or the like? There are surely some people who can do all this work in their heads and I am impressed by that. But much of real mathematics is working out implications of ideas, and that’s done so very well by hand. I haven’t found a way of typing in strings of expressions which makes it easier for me to think about the mathematics rather than the formatting. And I would believe in a note-taking program that was as sensitive and precise as pen on paper. I haven’t seen one yet, though. (I have small handwriting, and the applications I’ve tried turn all my writing into tiny, disconnected dots and scribbles.) Ralph Hagen’s The Barn for the 27th is superficially about Olbers’s Paradox. If there’s an infinitely large, infinitely old universe, then how can the night sky by dark? The light of all those stars should come together to make night even more brilliantly blazing than the daytime sun. This is a legitimate calculus problem. The reasoning is sound. The light of a star trillions upon trillions of light-years away may be impossibly faint. But there are so many stars that would be that far away that they would be, on average, about as bright as the sun is. Integral calculus tells us what happens when we have infinitely large numbers of impossibly tiny things added together. In the case of stars, infinitely many impossibly faint stars would come together to an infinitely bright night sky. That night is dark tells us: the universe can’t be infinitely large and infinitely old. There must be limits to how far away anything can be. The Barn reappears in my attention on the 28th, with a subverted word problem joke. Reading the Comics, February 14, 2015: Valentine’s Eve Edition I haven’t had the chance to read today’s comics, what with it having snowed just enough last night that we have to deal with it instead of waiting for the sun to melt it, so, let me go with what I have. There’s a sad lack of strips I feel justified including the images of, since they’re all Gocomics.com representatives and I’m used to those being reasonably stable links. Too bad. Eric the Circle has a pair of strips by Griffinetsabine, the first on the 7th of February, and the next on February 13, both returning to “the Shape Single’s Bar” and both working on “complementary angles” for a pun. That all may help folks remember the difference between complementary angles — those add up to a right angle — and supplementary angles — those add up to two right angles, a straight line — although what it makes me wonder is the organization behind the Eric the Circle art collective. It hasn’t got any nominal author, after all, and there’s what appear to be different people writing and often drawing it, so, who does the scheduling so that the same joke doesn’t get repeated too frequently? I suppose there’s some way of finding that out for myself, but this is the Internet, so it’s easier to admit my ignorance and let the answer come up to me. Mark Anderson’s Andertoons (February 10) surprised me with a joke about the Dewey decimal system that I hadn’t encountered before. I don’t know how that happened; it just did. This is, obviously, a use of decimal that’s distinct from the number system, but it’s so relatively rare to think of decimals as apart from representations of numbers that pointing it out has the power to surprise me at least. Florian Cajori: A History Of Mathematical Notations I just noticed that over at archive.org they have Volume I of Florian Cajori’s A History Of Mathematical Notations. There’s a fair chance this means nothing to you, but, Dr Cajori did a great deal of work in writing the history of mathematics in the early 20th century, and with a scope and prose style that still leaves me a bit awed. (He also wrote a history of physics; I remember reading the book, originally written in the mid-1920s, with his description of one of the mysteries of the day. With the advantage of decades on my side I knew this to be the Zeeman effect, a way that magnetic fields affect spectral lines.) Archive.org has several of Cajori’s books, including the histories mentioned, but Mathematical Notations I like as it’s an indispensable reference. It describes, with abundant examples, the origins of all sorts of the ways we write out mathematical ideas, from numerals themselves to the choices of symbols like the + and x signs to how we got to using letters to represent quantities to something called alligation which was apparently practiced in 15th-century Venice. Unfortunately archive.org hasn’t yet got Volume II, which includes topics like where the$ symbol for United States currency came from — Cajori had some strong opinions about this, suggesting he was tired of tracking down false leads — but it’s a book you can feel confident in leafing through to find something interesting most any time. I think his description of the way historical opinions had changed particularly fascinating, and recommend particularly Paragraph 96 (pages 64 through 68 of the book, and not one enormous block of text), describing “Fanciful hypotheses on the origins of the numeral forms”, many of them based on ideas that the symbols for numbers contain the number of vertices or strokes or some other mnemonic to how big a number is represented. Of those hypothesis formers he says, “Nor did these writers feel that they were indulging simply in pleasing pastimes or merely contributing to mathematical recreations. With perhaps only one exception, they were as convinced of the correctness of their explanations as are circle-squarers of the soundness of their quadratures”.

Dover publishing, of course, reprints the entire book on paper if you want Volumes I and II together. I admit that’s the form I have, and enjoy, since it becomes one of those books you could use to beat off an intruder if need be.

Reading the Comics, July 5, 2013

I’m surprised to discover it’s been over a month since I had a roster of mathematics-themed comic strips to share, but that’s how things happen to happen. It’s also been a month with repeated references to “finding square roots”, I suppose because that sounds like a really math-y thing to do. It’s certainly computationally challenging; the task of finding such is even a (very minor) moment in Isaac Asimov’s magnificent short story about arithmetic, “The Feeling Of Power”. I remember reading the procedure for finding them when I was a kid, and finding that with considerable effort, I was able to, though I’d probably refuse to do more than give a rough estimate of such a root nowadays.

Bill Watterson’s Calvin and Hobbes (June 4, rerun) is another entry in the long string of jokes about “why bother studying mathematics”, but Watterson’s craft lifts it above average. Admire that fourth panel: that’s every resistant student in one pose.