## 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.

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.

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 11, 2020: Half Week Edition

There were a good number of comic strips mentioning mathematical subjects last week, as you might expect for one including the 14th of March. Most of them were casual mentions, though, so that’s why this essay looks like this. And is why the week will take two pieces to finish.

Jonathan Lemon and Joey Alison Sayer’s Little Oop for the 8th is part of a little storyline for the Sunday strips. In this the young Alley Oop has … travelled in time to the present. But different from how he does in the weekday strips. What’s relevant about this is Alley Oop hearing the year “2020” and mentioning how “we just got math where I come from” but being confident that’s either 40 or 400. Which itself follows up a little thread in the Sunday strips about new numbers on display and imagining numbers greater than three.

Maria Scrivan’s Half Full for the 9th is the Venn Diagram strip for the week.

Paul Trap’s Thatababy for the 9th is a memorial strip to Katherine Johnson. She was, as described, a NASA mathematician, and one of the great number of African-American women whose work computing was rescued from obscurity by the book and movie Hidden Figures. NASA, and its associated agencies, do a lot of mathematical work. Much of it is numerical mathematics: a great many orbital questions, for example, can not be answered with, like, the sort of formula that describes how far away a projectile launched on a parabolic curve will land. Creating a numerical version of a problem requires insight and thought about how to represent what we would like to know. And calculating that requires further insight, so that the calculation can be done accurately and speedily. (I think about sometime doing a bit about the sorts of numerical computing featured in the movie, but I would hardly be the first.)

I also had thought the Mathematical Moments from the American Mathematical Society had posted an interview with her last year. I was mistaken but in, I think, a forgivable way. In the episode “Winning the Race”, posted the 12th of June, they interviewed Christine Darden, another of the people in the book, though not (really) the movie. Darden joined NASA in the late 60s. But the interview does talk about this sort of work, and how it evolved with technology. And, of course, mentions Johnson and her influence.

Graham Harrop’s Ten Cats for the 9th is another strip mentioning Albert Einstein and E = mc2. And using the blackboard full of symbols to represent deep thought.

Patrick Roberts’s Todd the Dinosaur for the 10th showcases Todd being terrified of fractions. And more terrified of story problems. I can’t call it a false representation of the kinds of mathematics that terrify people.

Stephen Beals’s Adult Children for the 11th has a character mourning that he took calculus as he’s “too stupid to be smart”. Knowing mathematics is often used as proof of intelligence. And calculus is used as the ultimate of mathematics. It’s a fair question why calculus and not some other field of mathematics, like differential equations or category theory or topology. Probably it’s a combination of slightly lucky choices (for calculus). Calculus is old enough to be respectable. It’s often taught as the ultimate mathematics course that people in high school or college (and who aren’t going into a mathematics field) will face. It’s a strange subject. Learning it requires a greater shift in thinking about how to solve problems than even learning algebra does. And the name is friendly enough, without the wordiness or technical-sounding language of, for example, differential equations. The subject may be well-situated.

Tony Rubino and Gary Markstein’s Daddy’s Home for the 11th has the pacing of a logic problem, something like the Liar’s Paradox. It’s also about homework which happens to be geometry, possibly because the cartoonists aren’t confident that kids that age might be taking a logic course.

I’ll have the rest of the week’s strips, including what Comic Strip Master Command ordered done for Pi Day, soon. And again I mention that I’m hosting this month’s Playful Math Education Blog Carnival. If you have come across a web site with some bit of mathematics that brought you delight and insight, please let me know, and mention any creative projects that you have, that I may mention that too. Thank you.

## Reading the Comics, January 27, 2020: Alley Oop Followup Edition

I apologize for missing Sunday. I wasn’t able to make the time to write about last week’s mathematically-themed comic strips. But I’m back in the swing of things. Here are some of the comic strips that got my attention.

Jonathan Lemon and Joey Alison Sayers’s Little Oop for the 26th has something neat in the background. Oop and Garg walk past a vendor showing off New Numbers. This is, among other things, a cute callback to one of the first of Lemon and Sayers’s Little Oop strips.. (And has nothing to do with the daily storyline featuring the adult Alley Oop.) And it is a funny idea to think of “new numbers”. I imagine most of us trust that numbers are just … existing, somewhere, as concepts independent of our knowing them. We may not be too sure about the Platonic Forms. But, like, “eight” seems like something that could plausibly exist independently of our understanding of it.

Still, we do keep discovering things we didn’t know were numbers before. The earliest number notations, in the western tradition, for example, used letters to represent numbers. This did well for counting numbers, up to a large enough total. But it required idiosyncratic treatment if you wanted to handle large numbers. Hindu-Arabic numerals make it easy to represent whole numbers as large as you like. But that’s at the cost of adding ten (well, I guess eight) symbols that have nothing to do with the concept represented. Not that, like, ‘J’ looks like the letter J either. (There is a folk etymology that the Arabic numerals correspond to the number of angles made if you write them out in a particular way. Or less implausibly, the number of strokes needed for the symbol. This is ingenious and maybe possibly has helped one person somewhere, ever, learn the symbols. But it requires writing, like, ‘7’ in a way nobody has ever done, and it’s ahistorical nonsense. See section 96, on page 64 of the book and 84 of the web presentation, in Florian Cajori’s History of Mathematical Notations.)

Still, in time we discovered, for example, that there were irrational numbers and those were useful to have. Negative numbers, and those are useful to have. That there are complex-valued numbers, and those are useful to have. That there are quaternions, and … I guess we can use them. And that we can set up systems that resemble arithmetic, and work a bit like numbers. Those are often quite useful. I expect Lemon and Sayers were having fun with the idea of new numbers. They are a thing that, effectively, happens.

Lincoln Peirce’s Big Nate: First Class for the 26th has Nate badgering Francis for mathematics homework answers. Could be any subject, but arithmetic will let Peirce fit in a couple answers in one panel.

Art Sansom and Chip Sansom’s The Born Loser for the 26th is another strip on the theme of people winning the lottery and being hit by lightning. And, as I’ve mentioned, there is at least one person known to have won a lottery and survived a lightning strike.

David Malki’s Wondermark for the 27th describes engineering as “like math, but louder”, which is a pretty good line. And it uses backgrounds of long calculations to make the point of deep thought going on. I don’t recognize just what calculations are being done there, but they do look naggingly familiar. And, you know, that’s still a pretty lucky day.

Mark Anderson’s Andertoons for the 27th is the Mark Anderson’s Andertoons for the week. It depicts Wavehead having trouble figuring where to put the decimal point in the multiplication of two decimal numbers. Relatable issue. There are rules you can follow for where to put the decimal in this sort of operation. But the convention of dropping terminal zeroes after the decimal point can make that hazardous. It’s something that needs practice, or better: though. In this case, what catches my eye is that 2.95 times 3.2 has to be some number close to 3 times 3. So 9.440 is the plausible answer.

Mike Twohy’s That’s Life for the 27th presents a couple of plausible enough word problems, framed as Sports Math. It’s funny because of the idea that the workers who create events worth billions of dollars a year should be paid correspondingly.

This isn’t all for the week from me. I hope to have another Reading the Comics installment at this link, soon. Thanks for reading.

## Reading the Comics, September 28, 2019: Laconic Edition

There were more mathematically-themed comic strips last week than I had time to deal with. This is in part because of something Saturday which took several more hours than I had expected. So let me start this week with some of the comics that, last week, mentioned mathematics in a marginal enough way there’s nothing to say about them besides yeah, that’s a comic strip which mentioned mathematics.

Joey Alison Sayers and Jonathan Lemon’s Little Oop — a variation of Alley Oop — for the 22nd has the caveman struggling with mathematics homework. It’s fun that he has an abacus. Also that the strip keeps with the joke from earlier this year about their only dreaming of a number larger than three.

Jef Mallett’s Frazz for the 22nd sees Caulfield stressing out over a mathematics test.

Ralph Dunagin and Dana Summers’s The Middletons for the 24th has more kids stressing out over a mathematics test. Also about how time is represented in numbers.

Mark Parisi’s Off The Mark for the 24th is a bit of animal-themed wordplay on the New Math.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 24th has a parent offering excuses for not helping with mathematics homework.

Eric the Circle for the 27th, by GeoMaker this time, tries putting out a formula for the area of Eric the circle.

Jef Mallett’s Frazz for the 27th has a kid wondering why they need in-person instruction for arithmetic. (I’d agree that rehearsing arithmetic skills is very easy to automate. You can make practice problems pretty near without limit. How much this has to do with mathematics is a point of debate.)

Glenn McCoy and Gary McCoy’s The Flying McCoys for the 27th is a bit of wordplay and numerals humor.

Daniel Beyer’s Long Story Short for the 28th uses arithmetic, the ever-famous 2 + 2 =, as symbol for knowing anything.

With that, I’ve cleared the easy part of comics for the past week. When I get to the comics needing discussion the essay should post here, likely on Monday. And the Fall 2019 A to Z series should post on Tuesday, with ‘I’. Thanks for reading and for your forbearance.

## Reading the Comics, January 26, 2019: The Week Ended Early Edition

Last week started out at a good clip: two comics with enough of a mathematical theme I could imagine writing a paragraph about them each day. Then things puttered out. The rest of the week had almost nothing. At least nothing that seemed significant enough. I’ll list those, since that’s become my habit, at the end of the essay.

Jonathan Lemon and Joey Alison Sayers’s Alley Oop for the 20th is my first chance to show off the new artist and writer team. They’ve decided to make Sunday strips a side continuity about a young Alley Oop and his friends. I’m interested. The strip is built on the bit of pop anthropology that tells us “primitive” tribes will have very few counting words. That you can express concepts like one, two, and three, but then have to give up and count “many”.

Perhaps it’s so. Some societies have been found to have, what seem to us, rather few numerals. This doesn’t reflect on anyone’s abilities or intelligence or the like. And it doesn’t mean people who lack a word for, say, “forty-nine” would be unable to compute. It might take longer, but probably just from inexperience. If someone practiced much calculation on “forty-nine” they’d probably have a name for it. And folks raised in the western mathematics use, even enjoy, some vagueness about big numbers too. We might say there are “dozens” of a thing even if there are not precisely 24, 36, or 48 of the thing; “52” is close enough and we probably didn’t even count it up. “Hundred” similarly has gotten the connotation of being a precise number, but it’s used to mean “really quite a lot of a thing”. The words “thousands”, “millions”, and mock-numbers like “zillions” have a similar role. They suggest different ranges of what might be “many”.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 20th is a SABRmetrics joke! At least, it’s an optimization joke, built on the idea that you can find an optimum strategy for anything, whether winning baseball games or The War. The principle is hard to argue with. Nobody would doubt that different approaches to a battle affect how likely winning is. We can imagine gathering data on how different tactics affect the outcome. (We can easily imagine combat simulators running these experiments, particularly.)

The catch — well, one catch — is that this tempts one to reward a process. Once it’s taken for granted the process works, then whether it’s actually doing what you want gets forgotten. And once everyone knows what’s being measured it becomes possible to game the system. Famously, in the mid-1960s the United States tried to judge its progress in the Vietnam War by counting the number of enemy soldiers killed. There was then little reason to care about who was killed, or why. And reason to not care whether actual enemy soldiers were being killed. There’s good to be said about testing whether the things you try to do work. There’s great danger in thinking that the thing you can measure guarantees success.

Mark Anderson’s Andertoons for the 21st is a bit of fun with definitions. Mathematicians rely on definitions. It’s hard to imagine a proof about something undefined. But definitions are hard to compose. We usually construct a definition because we want a common term to describe a collection of things, and to exclude another collection of things. And we need people like Wavehead who can find edge cases, things that seem to satisfy a definition while breaking its spirit. This can let us find unstated assumptions that we should pay attention to. Or force us to accept that the definition is so generally useful that we’ll tolerate it having some counter-intuitive implications.

My favorite counter-intuitive implication is in analysis. The field has a definition for what it means that a function is continuous. It’s meant to capture the idea that you could draw a curve representing the function without having to lift the pen that does it. The best definition mathematicians have settled on allows you to count a function that’s continuous at a single point in all of space. Continuity seems like something that should need an interval to happen. But we haven’t found a better way to define “continuous” that excludes this pathological case. So we embrace the weirdness in exchange for general usefulness.

Charles Brubaker’s Ask A Cat for the 21st is a guest appearance from Brubaker’s other strip, The Fuzzy Princess. It’s a rerun and I did discuss it earlier. Soap bubbles make for great mathematics. They’re easy to play with, for one thing. That’s good for capturing imagination. And the mathematics behind them is deep, and led to important results analytically and computationally. It happens when this strip first ran I’d encountered a triplet of essays about the mathematics of soap bubbles and wireframe surfaces. My introduction to those essays is here.

Benita Epstein’s Six Chix for the 25th I wasn’t sure I’d include. But Roy Kassinger asked about it, so that tipped the scales. The dog tries to blame his bad behavior on “the algorithm”, bringing up one of the better monsters of the last couple years. An algorithm is just the procedure by which you do something. Mathematically, that’s usually to solve a problem. That might be finding some interesting part of the domain or range of a function. That might be putting a collection of things in order. that might be any of a host of things. And then we go make a decision based on the results of the algorithm.

What earns The Algorithm its deserved bad name is mindlessness. The idea that once you have an algorithm that a problem is solved. Worse, that once an algorithm is in place it would be irrational to challenge it. I have seen the process termed “mathwashing”, by analogy with whitewashing, and it’s a good one. The notion that because something is done by computer it must be done correctly is absurd. We knew it was absurd before there were computers as we knew them, as see anyone for the past century who has spoken of a “Kafkaesque” interaction with a large organization. It’s impossible to foresee all the outcomes of any reasonably complicated process, much less to verify that all the outcomes are handled correctly. This is before we consider that there will always be mistakes made in the handling of data. Or in the carrying out of the process. And that’s before we consider bad actors. I’m sure there must be research into algorithms designed to handle gaming of the system. I don’t know that there are any good results yet, though. We certainly need them.

There were a couple comics that didn’t seem to be substantial enough for me to write at length about. You might like them anyway. Connie Sun’s Connie to the Wonnie for the 21st shows off a Venn Diagram. Hector D Cantú and Carlos Castellanos’s Baldo for the 23rd is a bit of wordplay about what mathematicians do. Jonathan Lemon’s Rabbits Against Magic for the 23rd similarly is a bit of wordplay built around percentages. (Lemon is the new artist for Alley Oop.) And Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips features Albert Einstein, and a joke based on one of the symmetries which make relativity such a useful explanation of the world’s workings.

I don’t plan to have another Reading the Comics post until next Sunday. But when I do, it’ll be here.