## Reading the Comics, June 6, 2020: Wrapping Up The Week Edition

Let’s see if I can’t close out the first week of June’s comics. I’d rather have published this either Tuesday or Thursday, but I didn’t have the time to write my statistics post for May, not yet. I’ll get there.

One of Gary Larson’s The Far Side reprints for the 4th is one I don’t remember seeing before. The thing to notice is the patient has a huge right brain and a tiny left one. The joke is about the supposed division between left-brained and right-brained people. There are areas of specialization in the brain, so that the damage or destruction of part can take away specific abilities. The popular imagination has latched onto the idea that people can be dominated by specialties of the either side of the brain. I’m not well-versed in neurology. I will hazard the guess that neurologists see “left-brain” and “right-brain” as amusing stuff not to be taken seriously. (My understanding is the division of people into “type A” and “type B” personalities is also entirely bunk unsupported by any psychological research.)

Samson’s Dark Side of the Horse for the 5th is wordplay. It builds on the use of “problem” to mean both “something to overcome” and “something we study”. The mathematics puzzle book is a fanciful creation. The name Lucien Kastner is a Monty Python reference. (I thank the commenters for spotting that.)

Dan Collins’s Looks Good on Paper for the 5th is some wordplay on the term “Möbius Strip”, here applied to a particular profession.

Bud Blake’s Tiger rerun for the 6th has Tiger complaining about his arithmetic homework. And does it in pretty nice form, really, doing some arithmetic along the way. It does imply that he’s starting his homework at 1 pm, though, so I guess it’s a weekend afternoon. It seems like rather a lot of homework for that age. Maybe he’s been slacking off on daily work and trying to make up for it.

John McPherson’s Close To Home for the 6th has a cheat sheet skywritten. It’s for a geometry exam. Any subject would do, but geometry lets cues be written out in very little space. The formulas are disappointingly off, though. We typically use ‘r’ to mean the radius of a circle or sphere, but then would use C for its circumference. That would be $c = 2\pi r$. The area of a circle, represented with A, would be $\pi r^2$. I’m not sure what ‘Vol.C’ would mean, although ‘Volume of a cylinder’ would make sense … if the next line didn’t start “Vol.Cyl”. The volume of a circular cylinder is $\pi r^2 h$, where r is the radius and h the height. For a non-circular cylinder, it’s the area of a cross-section times the height. So that last line may be right, if it extends out of frame.

Granted, though, a cheat sheet does not necessarily make literal sense. It needs to prompt one to remember what one needs. Notes that are incomplete, or even misleading, may be all that one needs.

And this wraps up the comics. This and other Reading the Comics posts are gathered at this link. Next week, I’ll get the All 2020 A-to-Z under way. Thanks once again for all your reading.

## Reading the Comics, May 15, 2020: Squared Away Edition

The end of last week offered just a few more comic strips, and some pretty casual mathematics content. Let me wrap that up.

Daniel Beyer’s Long Story Short for the 13th has the “math department lavatory” represented as a door labelled $1 \pm 2$. It’s an interesting joke in that it reads successfully, but doesn’t make sense. To match the references to the commonly excreted substances they’d want $\frac32 \pm \frac12$.

On funny labels, though, I did once visit a mathematics building in which the dry riser had the label N Bourbaki. Nicholas Bourbaki was not a member of that college’s mathematics department, of course. This is why the joke was correctly formed and therefore funny.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 13th features the rounding-up-sheep joke.

Gary Larson’s The Far Side strips for the 14th includes the famous one of Albert Einstein coming so close to working out $E = mc^2$. The usual derivations for $E = mc^2$ don’t start with that and then explore whether it makes sense, which is what Einstein seems to be doing here. Instead they start from some uncontroversial premises and find that they imply this $E = mc^2$ business. Dimensional analysis would also let you know that, if c is involved, it’s probably to the second power rather than anything else.

But that doesn’t mean we can’t imagine Einstein assuming there must be a relationship between energy and mass, finding one that makes sense, and then finding a reason it’s that rather than something else. That’s a common enough pattern of mathematical discovery. Also, a detail I hadn’t noticed before, is that Einstein tried out $E = mc^3$, rejected it, and then tried it again. This is also a common pattern of discovery.

Mark Litzler’s Joe Vanilla for the 14th has a vague recollection of the Pythagorean Theorem be all that someone says he remembers of mathematics.

Niklas Eriksson’s Carpe Diem for the 15th depicts a couple ancient Greek deep-thinkers. A bit of mathematics, specifically geometry, is used as representative of that deep thinking.

This wraps up the past week’s mathematically-themed comics. Read this and next week’s comic strips at this link. Thank you.

## Reading the Comics, April 17, 2020: Creating Models Edition

And now let me close out a week ago, in the comics. It was a slow week and it finished on a bunch of casual mentions of mathematical topics.

Gary Larson’s The Far Side compilation “Hands Off My Bunsen Burner” features this panel creating a model of how to get rights out of wrongs. The material is a joke, but trying to find a transformation from one mathematical object to another is a reasonable enough occupation.

Ted Shearer’s Quincy rerun for the 15th is one in the lineage of strips about never using mathematics in later life. Quincy challenges us to think of a time a reporter asks the President how much is 34 times 587.

That’s an unpleasant multiplication to do. But I can figure some angles on it. 34 is just a bit over one-third of 100. 587 is just a bit under 600. So, 34 times 587 has to be tolerably near one-third of 100 times 600. So it should be something around 20,000. To get it more exact: 587 is 13 less than 600. So, 587 times one-third of a hundred will be 600 times one-third of a hundred minus 13 times one-third of a hundred. That’s one-third of 130, which is about 40. So the product has to be something close to 19,960. And the product has be some number which ends in an 8, what with 4 times 7 being 28. So the answer has to be one of 19,948, 19,958, or 19,968. And, indeed, it’s 19,958. I doubt I could do that so well during a press conference, I’ll admit. (If I wanted to be sure about that second digit, I’d have worked out: the tens unit in 34 times the ones in 587 is three times seven which is 21; the ones unit in 34 times the tens unit in 587 is four times eight which is 32; and the 4 times 7 being 28 gives me a 2 in the tens unit. So, 1 plus 2 plus 2 is 5, and there we go.)

Brian Anderson’s Dog Eat Doug for the 15th uses blackboards full of equations to represent deep thinking. I can’t make out what the symbols say. They look quite good, though, and seem to have the form of legitimate expressions.

Terri Liebenson’s The Pajama Diaries for the 17th imagines creating a model for the volume of a laundry pile. The problem may seem trivial, but it reflects an important kind of work. Many processes are about how something that’s always accumulating will be handled. There’s usually a hard limit to the rate at which whatever it is gets handled. And there’s usually very little reserve, in either capacity or time. This will cause, for example, a small increase in traffic in a neighborhood to produce great jams, or how a modest rain can overflow the whole city’s sewer systems. Or how a day of missing the laundry causes there to be a week’s backlog of dirty clothes.

And a little final extra comic strip. I don’t generally mention web comics here, except for those that have fallen in with a syndicator like GoComics.com. (This is not a value judgement against web comics. It’s that I have to stop reading sometime.) But Kat Swenski’s KatRaccoon Comics recently posted this nice sequence with a cat facing her worst fear: a calculus date.

And that’s my comics for a week ago. Later this week I’ll cover the past week’s handful of comics, in an essay at this link. Thanks for reading.

## Reading the Comics, March 20, 2020: Running from the Quiz Edition

I’m going to again start the week with the comics that casually mentioned mathematics. Later in the week I’ll have ones that open up discussion topics. I just don’t want you to miss a comic where a kid doesn’t want to do a story problem.

John Graziano’s Ripley’s Believe It or Not for the 15th mentions the Swiss mint issuing a tiny commemorative coin of Albert Einstein. I mention just because Einstein is such a good icon for mathematical physics.

Ashleigh Brilliant’s Pot-Shots for the 16th has some wordplay about multiplication and division. I’m not sure it has any real mathematical content besides arithmetic uniting multiplication and division, though.

Mark Pett’s Mr Lowe rerun for the 17th has the students bored during arithmetic class. Fractions; of course it would be fractions.

Justin Boyd’s Invisible Bread for the 18th> has an exhausted student making the calculation of they’ll do better enough after a good night’s sleep to accept a late penalty. This is always a difficult calculation to make, since you make it when your thinking is clouded by fatigue. But: there is no problem you have which sleep deprivation makes better. Put sleep first. Budget the rest of your day around that. Take it from one who knows and regrets a lot of nights cheated of rest. (This seems to be the first time I’ve mentioned Invisible Bread around here. Given the strip’s subject matter that’s a surprise, but only a small one.)

John Deering’s Strange Brew for the 18th is an anthropomorphic-objects strip, featuring talk about mathematics phobia.

One of Gary Larson’s The Far Side reruns for the 19th is set in a mathematics department, and features writing a nasty note “in mathematics”. There are many mathematical jokes, some of them written as equations. A mathematician will recognize them pretty well. None have the connotation of, oh, “Kick Me” or something else that would belong as a prank sign like that. Or at least nobody’s told me about them.

Tauhid Bondia’s Crabgrass for the 20th sees Kevin trying to find luck ahead of the mathematics quiz.

Bob Weber Jr and Jay Stephens’s Oh, Brother! for the 20th similarly sees Bud fearing a mathematics test.

Thanks for reading. And, also, please remember that I’m hosting the Playful Math Education Blog Carnival later this month. Please share with me any mathematics stuff you’ve run across that teaches or entertains or more.

## Reading the Comics, January 25, 2020: Comic Strip Master Command Is Making This Hard For Me Edition

Or they’re making it easy for me. But for another week all the comic strips mentioning mathematics have done so in casual ways. Ones that I don’t feel I can write a substantial paragraph about. And so, ones that I don’t feel I can fairly use the images of here. Here’s strips that at least said “math” somewhere in them:

Mark Pett’s Mr Lowe rerun for the 18th had the hapless teacher giving out a quiz about fractions.

Greg Cravens’s The Buckets for the 19th plays on the conflation of “zero” and “nothing”. The concepts are related, and we wouldn’t have a zero if we weren’t trying to worth with the concept of nothing. But there is a difference that’s quite hard to talk about without confusing matters.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 19th has a student accused of cheating on a pre-algebra test.

Liniers’s Macanudo for the 21st has a kid struggling with mathematics while the imaginary friend goes off and plays.

Lincoln Peirce’s Big Nate: First Class for the 21st has Nate struggling with mathematics. The strip is a reprint of the Big Nate from the 23rd of January, 1995.

Greg Curfman’s Meg for the 21st has Meg doing arithmetic homework.

Scott Hilburn’s The Argyle Sweater for the 23rd is a wordplay joke, with a flash card that has an addition problem on it.

One of Gary Larson’s The Far Side reprints for the 24th has a man demanding the answer to one question: the square root of an arbitrary number. It’s a little over 70, and that’s as far as anyone could reasonably expect to answer off the top of their head.

James Beutel’s Banana Triangle for the 24th quotes The Wizard Of Oz’s famous garbled version of the Pythagorean Theorem.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 25th presents a sinister reading of the fad of “prove you’re human” puzzles that demanded arithmetic expressions be done. All computer programs, including, like, Facebook group messages are arithmetic operations ultimately. The steps could be translated into simple expressions like this and be done by humans. It just takes work which, I suppose, could also be translated into other expressions.

And with that large pile of mentions I finish off the mathematical comic strips for the day. Also for the month: next Sunday gets us already into February. Sometime then I should post at this link a fresh Reading the Comics essay. Thank you for reading this one.

## Reading the Comics, January 4, 2020: The Little Things Edition

Today’s essay is just to mention the comic strips which, last week, said mathematics but in some incidental way. Or some way that I can’t write a reasonable blog entry for.

Gary Larson’s The Far Side reruns for the 30th of December, 2019, included this classic about curiosity killing cats. This 1985 strip rates a mention because a blackboard of mathematical symbols gets used to represent their intellectual inquiries.

Bill Amend’s FoxTrot for the 29th, a Sunday and thus new strip, is some wordplay based on the Disney+ line of entertainment product.

Jim Meddick’s Monty for the 29th has the time-travelling Professor Xemit (get it?) show a Times Square Ball Drop of the future. The ball gets replaced with a “demihypercube”, the idea being that the future will have some more complicated geometry than a mere “ball”. There is no such thing as “a” demihypercube, in the same way there is not “a” pentagon. There is a family of shapes, all called demihypercubes. There’s a variety of ways to represent them. A reasonable one, though, is a roughly spherical shape made of pointy triangles all over. It wouldn’t look absurd. There are probably time ball drops that use something like a demihypercube already.

Ruben Bolling’s Super-Fun-Pak Comix rerun for the 1st of January, 2020 features a Comics For The Elderly speaking of the advantages an abacus has over a spreadsheet.

Neal Rubin and Rod Whigham’s Gil Thorp for the 2nd has one of the student athletes working on calculus. And coach Mimi Thorp is doing the mathematics of studying athlete performance. If this strip makes you curious, too, my other blog should this Sunday recap what’s going on in Gil Thorp.

Also this coming Sunday I should look at more mathematically-themed comic strips. That should appear at this link, unless something urgent commands my attention first. Thank you.

## Reading the Comics, January 4, 2020: Representations Edition

The start of the year brings me comic strips I can discuss in some detail. There are also some that just mention a mathematical topic, and don’t need more than a mention that the strip exists. I’ll get to those later.

Jonathan Lemon’s Rabbits Against Magic for the 2nd is another comic strip built on a very simple model of animal reproduction. We saw one late last year with a rat or mouse making similar calculations. Any calculation like this builds on some outright untrue premises, particularly in supposing that every rabbit that’s born survives, and that the animals breed as much as could do. It also builds on some reasonable simplifications. Things like an average litter size, or an average gestation period, or time it takes infants to start breeding. These sorts of exponential-growth calculations depend a lot on exactly what assumptions you make. I tried reproducing Lemon’s calculation. I didn’t hit 95 billion offspring. But I got near enough to say that Lemon’s right to footnote this as ‘true’. I wouldn’t call them “baby bunnies”, though; after all, some of these offspring are going to be nearly seven years old by the end of this span.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 3rd justifies why “mathematicians are no longer allowed to [sic] sporting events” with mathematicians being difficult. Each of the signs is mean to convey the message “We’re #1”. The notations are just needlessly inaccessible, in that way nerds will do things.

$0.\bar{9}$ first. The bar over over a decimal like this means to repeat what is underneath the bar without limit. So this is the number represented by 0.99999… and this is another way to write the number 1. This sometimes makes people uncomfortable; the proof is to think what the difference is between 1 and the number represented by 0.999999 … . The difference is smaller than any positive number. It’s certainly not negative. So the difference is zero. So the two numbers have to be the same number.

$0^0$ is the controversial one here. The trouble is that there are two standard rules that clash here. One is the rule that any real number raised to the zeroth power is 1. The other is the rule that zero raised to any positive real number is 0. We don’t ask about zero raised to a negative number. These seem to clash. That we only know zero raised to positive real numbers is 0 seems to break the tie, and justify concluding the number-to-the-zero-power rule should win out. This is probably what Weinersmith, or Weinersmith’s mathematician, was thinking. If you forced me to say what I think $0^0$ should be, and didn’t let me refuse to commit to a value, I’d probably pick “1” too. But.

The expression $x^x$ exists for real-valued numbers x, and that’s fine. We can look at $\lim_{x \rightarrow 0 } x^x$ and that number’s 1. But what if x is a complex-valued number? If that’s the case, then this limit isn’t defined. And mathematicians need to work with complex-valued numbers a lot. It would be daft to say “real-valued $0^0$ is 1, but complex-valued $0^0$ isn’t anything”. So we avoid the obvious daftness and normally defer to saying $0^0$ is undefined.

The last expression is $e^{\frac{\pi}{2}} \imath^{\imath}$. This $\imath$ is that famous base of imaginary numbers, one of those numbers for which $\imath^2 = -1$. Complex-valued numbers can be multiplied and divided and raised to powers just like real-valued numbers can. And, remarkably — it surprised me — the number $\imath^{\imath}$ is equal to $e^{-\frac{\pi}{2}}$. That’s the reciprocal of $e^{\frac{\pi}{2}}$.

There are a couple of ways to show this. A straightforward method uses the famous Euler formula, that $e^{\imath x} = \cos(x) + \imath\sin(x)$. This implies that $e^{\imath \frac{\pi}{2}} = \imath$. So $\imath^{\imath}$ has to equal $(e^{\imath \frac{\pi}{2}})^{\imath}$. That’s equal to $e^{\imath^2 \frac{\pi}{2}})$, or $e^{- \frac{\pi}{2}})$. If you find it weird that an imaginary number raised to an imaginary number gives you a real number — it’s a touch less than 0.208 — then, well, you see how weird even the simple things can be.

Gary Larson’s The Far Side for the 4th references Abraham Lincoln’s famous use of “four score and seven” to represent 87. There have been many ways to give names to numbers. As we’ve gotten comfortable with decimalization, though, most of them have faded away. I think only dozens and half-dozens remain in common use; if it weren’t for Lincoln’s style surely nobody today would remember “score” as a way to represent twenty. It probably avoids ambiguities that would otherwise plague words like “hundred”, but it does limit one’s prose style. The talk about carrying the one and taking away three is flavor. There’s nothing in turning eighty-seven into four-score-and-seven that needs this sort of arithmetic.

I hope later this week to list the comic strips which just mentioned some mathematical topic. That essay, and next week’s review of whatever this week is mathematical, should appear at this link. Thanks for reading.

## Reading the Comics, December 16, 2019: The Far Side Is Back Edition, Part I

As will sometimes happen I write this without having read Saturday’s comic strips. Press of time and all that. But it has been a week of only casual mentions of mathematics, not enough to need much detail. There were a lot of strips with this kind of casual mention. But one is of special interest.

So, yes. Gary Larson’s The Far Side has an official online home, and is reprinting strips from the classic 80s-to-early-90s comic strip. I’m glad for this, not just to reacquaint myself with an old friend. The strip was a pioneer in the good sort of nerd humor. Jokes about topics of narrow, specific interest, but — generally — not told in an exclusionary way. One might not understand why a particular joke should be funny, but only because you don’t happen to know something in the background. I’m thinking here of a desert-island strip that Larson, in one of his collections, said went over almost everybody’s head. The characters remarked on their good luck that the island was covered with mussels (or something), so at least they wouldn’t get hungry. The thing that makes this funny is that the mussels (or whatever) only grow places that get covered in water every day; that is, the island sinks with the tides.

Anyway, the first official online Far Side is, as you can see, your generic mathematics anxiety joke, using a story problem — with trains leaving stations, even — as the premise. And I admit this particular strip might not convince a young reader to today that The Far Side was anything special. This is the fate of many pioneers. If you look at it and think, well, that could run in Bizarro or The Argyle Sweater or Brevity or F Minus or Non Sequitur a dozen other comics, it’s because those are comic strips that want to be like this.

I’m sorry to say that, as best I can tell, there isn’t a lasting archive of strips on the new site. This particular rerun was one of the selection printed the 19th of December, but when I go to the link that should have shown that day’s strips I get bounced to the front page. This is vexing to someone who hopes to use the strips to lead conversations about mathematics topics. I’ll have to deal with that in one way or another.

Well, so be it. Later this week I’ll carry on with the roster of comic strips mentioning mathematical topics. For now I am still enjoying seeing the comics back in a mass media.

## Reading the Comics, March 6, 2017: Blackboards Edition

I can’t say there’s a compelling theme to the first five mathematically-themed comics of last week. Screens full of mathematics turned up in a couple of them, so I’ll run with that. There were also just enough strips that I’m splitting the week again. It seems fair to me and gives me something to remember Wednesday night that I have to rush to complete.

Jimmy Hatlo’s Little Iodine for the 1st of January, 1956 was rerun on the 5th of March. The setup demands Little Iodine pester her father for help with the “hard homework” and of course it’s arithmetic that gets to play hard work. It’s a word problem in terms of who has how many apples, as you might figure. Don’t worry about Iodine’s boss getting fired; Little Iodine gets her father fired every week. It’s their schtick.

Dana Simpson’s Phoebe and her Unicorn for the 5th mentions the “most remarkable of unicorn confections”, a sugar dodecahedron. Dodecahedrons have long captured human imaginations, as one of the Platonic Solids. The Platonic Solids are one of the ways we can make a solid-geometry analogue to a regular polygon. Phoebe’s other mentioned shape of cubes is another of the Platonic Solids, but that one’s common enough to encourage no sense of mystery or wonder. The cube’s the only one of the Platonic Solids that will fill space, though, that you can put into stacks that don’t leave gaps between them. Sugar cubes, Wikipedia tells me, have been made only since the 19th century; the Moravian sugar factory director Jakub Kryštof Rad got a patent for cutting block sugar into uniform pieces in 1843. I can’t dispute the fun of “dodecahedron” as a word to say. Many solid-geometric shapes have names that are merely descriptive, but which are rendered with Greek or Latin syllables so as to sound magical.

Bud Grace’s Piranha Club for the 6th started a sequence in which the Future Disgraced Former President needs the most brilliant person in the world, Bud Grace. A word balloon full of mathematics is used as symbol for this genius. I feel compelled to point out Bud Grace was a physics major. But while Grace could as easily have used something from the physics department to show his deep thinking abilities, that would all but certainly have been rendered as equation and graphs, the stuff of mathematics again.

Scott Meyer’s Basic Instructions rerun for the 6th is aptly titled, “How To Unify Newtonian Physics And Quantum Mechanics”. Meyer’s advice is not bad, really, although generic enough it applies to any attempts to reconcile two different models of a phenomenon. Also there’s not particularly a problem reconciling Newtonian physics with quantum mechanics. It’s general relativity and quantum mechanics that are so hard to reconcile.

Still, Basic Instructions is about how you can do a thing, or learn to do a thing. It’s not about how to allow anything to be done for the first time. And it’s true that, per quantum mechanics, we can’t predict exactly what any one particle will do at any time. We can say what possible things it might do and how relatively probable they are. But big stuff, the stuff for which Newtonian physics is relevant, involve so many particles that the unpredictability becomes too small to notice. We can see this as the Law of Large Numbers. That’s the probability rule that tells us we can’t predict any coin flip, but we know that a million fair tosses of a coin will not turn up 800,000 tails. There’s more to it than that (there’s always more to it), but that’s a starting point.

Michael Fry’s Committed rerun for the 6th features Albert Einstein as the icon of genius. Natural enough. And it reinforces this with the blackboard full of mathematics. I’m not sure if that blackboard note of “E = md3” is supposed to be a reference to the famous Far Side panel of Einstein hearing the maid talk about everything being squared away. I’ll take it as such.

## Reading the Comics, May 4, 2015: Hatless Aliens Edition

I have to make two confessions for this round of mathematics comic strips. First is that I was busy for like two days and missed about a jillion comic strips. So this is the first part of some catching-up to do. The second is that I don’t have a favorite of this bunch. The most interesting, I suppose, is the Mr Boffo, because it lets me get into a little trivia about Albert Einstein. But there’s not any in this bunch that made me smile much or that gave me a juicy topic to discuss. Maybe tomorrow.

Steve Breen and Mike Thompson’s Grand Avenue ran a week of snarky-answers-to-word-problems strips. April 28th, April 30th, and May 2nd featured mathematics questions. This must reflect how easy it is to undermine the logic of a mathematics question. The April 27th strip is about using Roman numerals, which I suppose is arithmetic. I’m not sure there’s much point to learning Roman numerals. We don’t do any calculations using the Roman numeral scheme except to show why Arabic numerals are better. All you get from Roman numerals is an ability to read building cornerstones and movie copyright dates. At least learning cursive handwriting provides the learner with a way to make illegible notes.