Reading the Comics, May 12, 2020: Little Oop Counts For More Edition


The past week had a fair number of comic strips mentioning some aspect of mathematics. One of them is, really, fairly slight. But it extends a thread in the comic strip that I like and so that I will feature here.

Jonathan Lemon and Joey Alison Sayers’s Little Oop for the 10th continues the thread of young Alley Oop’s time discovering numbers. (This in a storyline that’s seen him brought to the modern day.) The Moo researchers of the time have found numbers larger than three. As I’d mentioned when this joke was first done, that Oop might not have had a word for “seven” until recently doesn’t mean he wouldn’t have understood that seven of a thing was more than five of a thing, or less than twelve of a thing. At least if he could compare them.

Penelope, leading to the library: 'If you're going to keep coming to school with me, Alley, we've got to catch you up. You must learn to read.' Alley Oop: 'Hey! I can read.' Penelope: 'Really? How is that possible?' Alley: 'Well, letters are grouped into things called words, which in a certain order ... ' Penelope: 'OK, fine, what about numbers?' Alley: 'We just got numbers back home, so I know all about one, seven, five. All the numbers.' Penelope: 'Can you do *math*, though? What's three plus three?' Alley: 'Easy. It's threethree.' Penelope, to the librarian, with a mathematics book open in front of Alley: 'Can you put on a pot of coffee, Nancy? We're gonna be here a while.'
Jonathan Lemon and Joey Alison Sayers’s Little Oop for the 10th of May, 2020. So first, hey, neat: Little Alley Oop is a Javascript routine! Second, essays in which I talk about this comic, either the daily Alley Oop or the Sunday Little Oop pages, are at this link.

Sam Hurt’s Eyebeam for the 11th uses heaps of mathematical expressions, graphs, charts, and Venn diagrams to represent the concept of “data”. It’s spilled all over to represent “sloppy data”. Usually by the term we mean data that we feel is unreliable. Measurements that are imprecise, or that are unlikely to be reliable. Precision is, roughly, how many significant digits your measurement has. Reliability is, roughly, if you repeated the measurement would you get about the same number?

Nate Fakes’s Break of Day for the 12th is the anthropomorphic numerals joke for the week.

Ryan North’s Dinosaur Comics for the 12th talks about immortality. And what the probability of events means when there are infinitely many opportunities for a thing to happen.

We’re accustomed in probability to thinking of the expectation value. This is the chance that something will happen, given some number N opportunities to happen, if at each opportunity it has the probability p of happening. Let me assume the probability is always the same number. If it’s not, our work gets harder, although it’s basically the same kind of work. But, then, the expectation value, the number of times we’d expect to see the thing happen, is N times p. Which, as Utahraptor points out, we can expect has to be at least 1 for any event, however unlikely, given enough chances. So it should be.

But, then, to take Utahraptor’s example: what is the probability that an immortal being never trips down the stairs? At least not badly enough to do harm? Why should we think that’s zero? It’s not as if there’s a physical law that compels someone to go to stairs and then to fall down them to their death. And, if there’s any nonzero chance of someone not dying this way? Then, if there are enough immortals, there’s someone who will go forever without falling down stairs.

That covers just the one way to die, of course. But the same reasoning holds for every possible way to die. If there’s enough immortals, there’s someone who would not die from falling down stairs and from never being struck by a meteor. And someone who’d never fall down stairs and never be struck by a meteor and never fall off a cliff trying to drop an anvil on a roadrunner. And so on. If there are infinitely many people, there’s at least one who’d avoid all possible accidental causes of death.

God: 'T-Rex let's assume somehow you never die of natural causes. That's still not immortality.' T-Rex: 'Impossible!' T-Rex: 'You're still mortal. The difference is you won't die from your body getting old. Instead everything around you will be trying to kill you. You know. Accidents.' T-rex: 'PRETTY Sure I can avoid tripping down stairs if it means LIVING FOREVER.' Utahraptor: 'Pretty sure I can prove you can't!' T-Rex: 'Pretty sure I can get a book on how to hold the handrail!' Utahraptor: 'Forever is INFINITELY LONG. Say you have a 1 in 10 trillion chance of dying on the stairs. How often can you expect that happens if you life, oh, 10 trillion years?' T-Rex: 'O-once?' Utahraptor: 'And if you live INFINITY YEARS the chance of you dying from it becomes : total certainty. With an infinite natural lifespan the chance you die of ANYTHING rises to 1. Literally the entire universe will kill you if you give it enough time.' T-Rex: 'That means if I live long enough YOU'LL kill me too! Oh man! This friendship just got ... dangerous!
Ryan North’s Dinosaur Comics for the 12th of May, 2020. I often talk about this strip and when I do, Dinosaur Comics appears among the essays at this link.

More. If there’s infinitely many immortals, then there are going to be a second and a third — indeed, an infinite number — of people who happen to be lucky enough to never die from anything. Infinitely many immortals die of accidents, sure, but somehow not all of them. We can’t even say that more immortals die of accidents than don’t.

My point is that probability gets really weird when you try putting infinities into it. Proceed with extreme caution. But the results of basic, incautious, thinking can be quite heady.

Bill Amend’s FoxTrot Classics for the 12th has Paige cramming for a geometry exam. Don’t cram for exams; it really doesn’t work. It’s regular steady relaxed studying that you need. That and rest. There is nothing you do that you do better for being sleep-deprived.

Bob Weber Jr and Jay Stephens’s Oh Brother for the 12th has Lily tease her brother with a story problem. I believe the strip’s a rerun, but it had been gone altogether for more than a year. It’s nice to see it returned anyway.

And while I don’t regularly cover web-only comics here, Norm Feuti has carried on his Gil as a Sunday-only web comic. The strip for the 10th of May has Gil using a calculator for mathematics homework, with a teacher who didn’t say he couldn’t. I’m surprised she hadn’t set a guideline.


This carries me through half a week. I’ll have more mathematically-themed comic strips at this link soon. 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, October 24, 2018: Frazz Really Wants To Be My Friend Edition


It’s another week with several on-topic installments of Frazz. Again, Jef Mallet, you and I live in the same metro area. Wave to me at the farmer’s market or something. I’m kind of able to talk to people in real life, if I can keep in view three different paths to escape and know two bathrooms to hide in. Horrock’s is great for that.

Jef Mallet’s Frazz for the 22nd is a bit of wordplay. It’s built on the association between “negative” and “wrong”. And the confusing fact that multiplying a negative number by a negative number results in a positive number. It sounds like a trick. Still, negative numbers are tricky. The name connotes something that’s gone a bit wrong. It took time to understand what they were and how they should work. This weird multiplication rule follows from that. If we don’t suppose this to be true, then we break other ideas we have about multiplication and comparative sizes and such. Mathematicians needed to get comfortable with negative numbers. For a long time, for example, mathematicians would treat x^2 - 4x + 4 = 0 and x^4 + 4x + 4 = 0 as different kinds of polynomials to solve. Today we see a -4 as no harder than a +4, now that we’re good at multiplying it out. And I have read, but have not seen explained, that there was uncertainty among the philosophers of mathematics about whether we should consider negative numbers, as a group, to be greater than or less than positive numbers. (I have reasons for thinking this a mighty interesting speculation.) There’s reasons to doubt them, is what I have to say.

Mrs Olsen: 'Any questions? Goody. Caulfield.' Caulfield: 'If a negative times a negative is a positive, how come two wrongs don't make a right?' [Later] Frazz: 'Maybe negative isn't the same as wrong.' Caulfield: 'You are not incorrect.'
Jef Mallet’s Frazz for the 22nd of October, 2018. Good thing to learn, really.

Bob Weber Jr and Jay Stephens’s Oh Brother for the 22nd reminds me of my childhood. At some point I was pairing up the counting numbers and the letters of the alphabet, and realized that the alphabet ended while the numbers did not. Something about that offended my young sense of justice. I’m not sure how, anymore. But that it was always possible to find a bigger number than whatever you thought was the biggest caught my imagination.

Bud: 'Lily! Lily! What's the biggest number?' Lily: 'It's the same as the number of times you bug me.' Bud: 'But that's an ongoing, never-ending number.' Lily: 'Exactly!' Bud: 'Thanks for explaining math in practical terms!'
Bob Weber Jr and Jay Stephens’s Oh Brother for the 22nd of October, 2018. This may be a rerun; I don’t know if the strip is still in original production.

There is, surely, a largest finite number that anybody will ever use for something, even if it’s just hyperbole. I’m curious what it will be. Surely we can’t have already used it. A number named Skewes’s Number was famous, for a while, as the largest number actually used in a proof of something. The fame came from Isaac Asimov writing an essay about the number, and why someone might care, and how hard it is just describing how big the number is in a comprehensible way. Wikipedia tells me this number’s far been exceeded by, among other things, something called Rayo’s Number. It’s “the smallest number bigger than any finite number named by an expression in the language of set theory with a googol symbols or less” (plus some technical points to keep you from cheating). Which, all right, but I’d like to know if we think the first digit is a 1, maybe a 2? Somehow I don’t demand that of Skewes, perhaps because I read that Asimov essay when I was at an impressionable age.

Caulfield: 'If a fraction divided by a fraction is just a fraction times a flipped fraction, what happens if you fish with a fly for flying fish?' Mrs Olsen: 'You can't wade that far out in the ocean.' [ Later ] Frazz: 'So, nothing.' Caulfield: 'I don't think you can divide a fraction by a fraction and get zero.'
Jef Mallet’s Frazz for the 23rd of October, 2018. I appreciate when Mrs Olsen is given the chance to show she does know things.

Jef Mallet’s Frazz for the 23rd has Caulfield talk about a fraction divided by a fraction. And particularly he says “a fraction divided by a fraction is just a fraction times a flipped fraction”. This offends me, somehow. This even though that is how I’d calculate the value of the division, if I needed to know that. But it seems to me like automatically going to that process skips recognizing that, say, \frac{2}{5} \div \frac{1}{10} shouldn’t be surprising if it turns out not to be a fraction. Well, Caulfield’s just looking to cause trouble with a string of wordplay. I can think of how to divide a fraction by a fraction and get zero.

One is really the only number there is! All other numbers are simply collections of ones.
Ashleigh Brilliant’s Pot-Shots for the 23rd of October, 2018. This is a rerun, but from 1977; the strip is not in regular production anymore.

Ashleigh Brilliant’s Pot-Shots for the 23rd promises to recapitulate the whole history of mathematics in a single panel. Ambitious bit of work. It’s easy to picture going from the idea of 1 to any of the positive whole numbers, though. It’s so easy it doesn’t even need humans to do it; animals can count, at least a bit. We just carry on to a greater extent than the crows or the raccoons do, so far as we’ve heard. From those, it takes some squinting, but you can think of negative whole numbers. And from that you get zero pretty quickly. You can also get rational numbers. The western mathematical tradition did this by looking at … er … ratios, that something might be to another thing as two is to five. Circumlocutions like that. Getting to irrational numbers is harder. Can be harder. Some irrational numbers beg you to notice them: the square root of two, for example. Square root of three. Numbers that come up from solving polynomial equations. But there are more number than those. Many more numbers. You might suspect the existence of a transcendental number, that isn’t the root of any polynomial that’s decently behaved. But finding one? Or finding that there are more transcendental number than there are real numbers? This takes a certain brilliance to suspect, and to prove out. But we can get there with rational numbers — which we get to from collections of ones — and the idea of cutting sets of numbers into those smaller than and those bigger than something. Ashleigh Brilliant has more truth than, perhaps, he realized when he drew this panel.

Goldfish, in a tank, to its peers: 'This may seem weird, but my research indicates that the universe has the shape of a perfect cuboid.
Niklas Eriksson’s Carpe Diem for the 24th of October, 2018. I’m curious how the ground is accounted for.

Niklas Eriksson’s Carpe Diem for the 24th has goldfish work out the shape of space. A goldfish in this case has the advantage of being able to go nearly everywhere in the space. But working out what the universe must look like, when you can only run local experiments, is a great geometric problem. It’s akin to working out that the Earth must be a sphere, and about how big a sphere, from the surveying job one can do without travelling more than a few hundred kilometers.


If you’re interested in reading the comics, you might want to see Reading the Comics posts. They’re here. More essays mentioning Frazz should be at this link. Essays that discuss ideas brought up by Oh Brother! should be this link. Essays which talk about Frazz — wait. I said that. This and other appearances by Pot Shots should be at this link. And posts which feature Carpe Diem should be at link. Do please stick around for more of my Fall 2018 Mathematics A-To-Z, too. I’m trying to keep up at two essays a week through the end of the year, which is not precisely fall.

Reading the Comics, May 27, 2017: Panels Edition


Can’t say this was too fast or too slow a week for mathematically-themed comic strips. A bunch of the strips were panel comics, so that’ll do for my theme.

Norm Feuti’s Retail for the 21st mentions every (not that) algebra teacher’s favorite vague introduction to group theory, the Rubik’s Cube. Well, the ways you can rotate the various sides of the cube do form a group, which is something that acts like arithmetic without necessarily being numbers. And it gets into value judgements. There exist algorithms to solve Rubik’s cubes. Is it a show of intelligence that someone can learn an algorithm and solve any cube? — But then, how is solving a Rubik’s cube, with or without the help of an algorithm, a show of intelligence? At least of any intelligence more than the bit of spatial recognition that’s good for rotating cubes around?

'Rubik's cube, huh? I never could solve one of those.' 'I'm just fidgeting with it. I never bothered learning the algorithm either.' 'What algorithm?' 'The pattern you use to solve it.' 'Wait. All you have to do to solve it is memorize a pattern?' 'Of course. How did you think people solved it?' 'I always thought you had to be super smart to figure it out.' 'Well, memorizing the pattern does take a degree of intelligence.' 'Yeah, but that's not the same thing as solving it on your own.' 'I'm sure some people figured out the algorithm without help.' 'I KNEW Chad Gustafson was a liar! He was no eighth-grade prodigy, he just memorized the pattern!' 'Sounds like you and the CUBE have some unresolved issues.'
Norm Feuti’s Retail for the 21st of May, 2017. A few weeks ago I ran across a book about the world of competitive Rubik’s Cube solving. I haven’t had the chance to read it, but am interested by the ways people form rules for what would seem like a naturally shapeless feature such as solving Rubik’s Cubes. Not featured: the early 80s Saturday morning cartoon that totally existed because somehow that made sense back then.

I don’t see that learning an algorithm for a problem is a lack of intelligence. No more than using a photo reference shows a lack of drawing skill. It’s still something you need to learn, and to apply, and to adapt to the cube as you have it to deal with. Anyway, I never learned any techniques for solving it either. Would just play for the joy of it. Here’s a page with one approach to solving the cube, if you’d like to give it a try yourself. Good luck.

Bob Weber Jr and Jay Stephens’s Oh, Brother! for the 22nd is a word-problem avoidance joke. It’s a slight thing to include, but the artwork is nice.

Brian and Ron Boychuk’s Chuckle Brothers for the 23rd is a very slight thing to include, but it’s looking like a slow week. I need something here. If you don’t see it then things picked up. They similarly tried sprucing things up the 27th, with another joke for taping onto the door.

Nate Fakes’s Break of Day for the 24th features the traditional whiteboard full of mathematics scrawls as a sign of intelligence. The scrawl on the whiteboard looks almost meaningful. The integral, particularly, looks like it might have been copied from a legitimate problem in polar or cylindrical coordinates. I say “almost” because while I think that some of the r symbols there are r’ I’m not positive those aren’t just stray marks. If they are r’ symbols, it’s the sort of integral that comes up when you look at surfaces of spheres. It would be the electric field of a conductive metal ball given some charge, or the gravitational field of a shell. These are tedious integrals to solve, but fortunately after you do them in a couple of introductory physics-for-majors classes you can just look up the answers instead.

Samson’s Dark Side of the Horse for the 26th is the Roman numerals joke for this installment. I feel like it ought to be a pie chart joke too, but I can’t find a way to make it one.

Izzy Ehnes’s The Best Medicine Cartoon for the 27th is the anthropomorphic numerals joke for this paragraph.