## Reading the Comics, June 27, 2019: Closing A Slow Month Edition

Some months stretch my pop-mathematics writing skills, tasking me with finding new insights into the things I thought I understood and new ways to present them. Some months I’ve written about comic strips a lot. This was one of the latter. Here, let me nearly finish writing about the comic strips of June 2019 that had some mathematical content.

Jonathan Lemon’s Rabbits Against Magic for the 23rd is the Venn Diagram meta-joke for the week. Properly speaking, yes, Eight-Ball hasn’t drawn a Venn Diagram here. Representing two sets in a Venn Diagram, by the proper rules, requires two circles with one overlap. Indicating that both sets have the same elements means noting that there are no elements outside the intersection of these circles. One point of a Venn Diagram is showing all the possible logical relations between sets and maybe then marking off the ones that happen to be relevant to the problem. What Eight-Ball is drawing is an Euler Diagram, which has looser requirements. There’s no sense fighting this terminology battle, though. It makes cleaner pictures to draw a Venn Diagram modified to only show the relations that actually exist. If the goal is to communicate information, clarity counts. A joke counts as information.

Eight-Ball’s propositions are … well, a bit muddled. His first set is “people who like to think they are good at math”. His second set is “which of those people like Venn Diagrams”. This implies the second set can’t be anything but a subset of the first. So this we’d represent as one circle inside another, at least if we allow that there exists at least one person who likes to think they’re good at math, but still doesn’t like Venn Diagrams. It’s fine for the purposes of comic hyperbole to claim there is no such thing, of course, and I don’t quarrel with that.

Why not have the second group be “people who like Venn Diagrams”, without the restriction that they already think they’re good at math? Here I think there is a serious logical constraint. My suspicion is that Venn Diagrams are liked by people who don’t think they’re good at math. Also by people who aren’t good at math. Venn Diagrams are a wonderful tool because they present the relationships of sets in a way that uses our spatial intuitions. They wouldn’t make a good Internet joke format if they were liked only by people who think they’re good at math. Which is why Jonathan Lemon had to write the joke that way. It’s plausible comic hyperbole to say everyone who thinks they’re good at math likes Venn Diagrams. But there are too many people who react to explicit mathematics content with a shudder, but who like Venn Diagram jokes, to make “everyone who likes Venn Diagrams thinks they’re good at math” plausible.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 23rd is a lying-with-statistics joke. The median is an average of a data set. It’s “an” average because, in English, we mean several different things by “average”. Translated into mathematics these different things are, really, completely unrelated. The “median” is the midpoint of the ordered list of the data set. So, as the Man In Black says, half the data in the set is below that value, and half is above. This can be a better measure of “average” than the arithmetic mean is. It tells us a slight something about the distribution, about how the data is arranged. Not much, but then, it’s just one number. What do you want? It has an advantage over the arithmetic mean, which is the thing normal people intend when they say “average”. That advantage is that it’s relatively insensitive to outliers. One or two really large, or tiny, data points can throw the mean way off. The classic example we use these days is to look at the average wealth of twenty people in the room. If Bill Gates enters the room, the mean jumps way up. The median? Doesn’t alter much. (Bill Gates is the figure I see used these days, but it could be anyone impossibly wealthy. I imagine there are versions where it’s Jeff Bezos entering the room. I imagine a century ago, the proposition would be to imagine J P Morgan entering the room, except that a century ago he had been dead six years.)

Steve Skelton’s 2 Cows and a Chicken for the 26th shows off a counting chicken as a wonder. Animals do have some sense of mathematics. We know in some detail how well crows and ravens can count, and do simple arithmetic. This is partly because we know good ways to test crow and raven arithmetic skills. And we’ve come to appreciate their intelligence as deep and surprising. Chickens, to my knowledge, have gotten less study. But I would expect they’ve got skills. If nothing else, I would expect chickens to have a good understanding of the transitive property. This is the rule that if ‘a’ is greater than ‘b’, and ‘b’ is greater than ‘c’, then it follows that ‘a’ is greater than ‘c’. Chickens have a pecking order, and animals with that kind of hierarchy tend to know transitivity. I don’t know that the reasons for that link have been proven, but, c’mon. And animals doing arithmetic, like the cook says, have been good sideshow attractions or performances for a long while. They’ve also been good starts for scientific study, as people try to work out questions like how intelligence formed, and what other ways it might have formed.

Greg Cravens’s The Buckets for the 27th is a joke about the representation of numbers. Cravens has a good observation here about learning the differences between representations, and of not being able to express just what representation you want. I love Eddie’s horrified face as his mother (Sarah) tries to spell out the word. There’s probably a good exercise to be done in thinking of as many ways to represent fifteen as possible.

Etymologically, “fifteen” has exactly the origin you would say if you were dragged out of a sound sleep by someone demanding the history of the word RIGHT NOW, THERE’S NO TIME TO EXPLAIN. In Old English it was “fiftyne”, with “fif” meaning “five” and “tyne” meaning “ten more than”. This construction, pretty much five-and-ten, has fallen out of favor in English. Once we get past nineteen we more commonly write out, like, “twenty-one” and “thirty-five” and such. The alternate construction, which would be, like, one-and-twenty, or nine-and-sixty, or such, seems to have fallen out of use except as a more poetic way to express the idea. I don’t know why, say, five-and-twenty would have shifted to twenty-five while the equivalent five-and-ten didn’t shift to … teenfive(?). I would make an uninformed guess that words used more commonly tend to be more stable, and we tend to need smaller numbers more than bigger ones.

I’ll have some more comic strips for you later in the week. Before then should be a statistics review, as I figure out whether anyone is reading this blog after a month when I wrote basically nothing. The next Reading the Comics post should be at this link probably on Thursday. Thank you for reading any of this.

## Reading the Comics, March 18, 2017: Pi Day Edition

No surprise what the recurring theme for this set of mathematics-mentioning comic strips is. Look at the date range. But here goes.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 13th uses algebra as the thing that will stun a class into silence. I know the silence. As a grad student you get whole minutes of instructions on how to teach a course before being sent out as recitation section leader for some professor. And what you do get told is the importance of asking students their thoughts and their ideas. This maybe works in courses that are obviously friendly to opinions or partially formed ideas. But in Freshman Calculus? It’s just deadly. Even if you can draw someone into offering an idea how we might start calculating a limit (say), they’re either going to be exactly right or they’re going to need a lot of help coaxing the idea into something usable. I’d like to have more chatty classes, but some subjects are just hard to chat about.

Steve Skelton’s 2 Cows And A Chicken for the 13th includes some casual talk about probability. As normally happens, they figure the chances are about 50-50. I think that’s a default estimate of the probability of something. If you have no evidence to suppose one outcome is more likely than the other, then that is a reason to suppose the chance of something is 50 percent. This is the Bayesian approach to probability, in which we rate things as more or less likely based on what information we have about how often they turn out. It’s a practical way of saying what we mean by the probability of something. It’s terrible if we don’t have much reliable information, though. We need to fall back on reasoning about what is likely and what is not to save us in that case.

Scott Hilburn’s The Argyle Sweater lead off the Pi Day jokes with an anthropomorphic numerals panel. This is because I read most of the daily comics in alphabetical order by title. It is also because The Argyle Sweater is The Argyle Sweater. Among π’s famous traits is that it goes on forever, in decimal representations, yes. That’s not by itself extraordinary; dull numbers like one-third do that too. (Arguably, even a number like ‘2’ does, if you write all the zeroes in past the decimal point.) π gets to be interesting because it goes on forever without repeating, and without having a pattern easily describable. Also because it’s probably a normal number but we don’t actually know that for sure yet.

Mark Parisi’s Off The Mark panel for the 14th is another anthropomorphic numerals joke and nearly the same joke as above. The answer, dear numeral, is “chained tweets”. I do not know that there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. But there’s a Twitter bot posting the digits of π in an enormous chained Twitter feed. If there isn’t, there is now.

John Zakour and Scott Roberts’s Working Daze for the 14th is your basic Pi Day Wordplay panel. I think there were a few more along these lines but I didn’t record all of them. This strip will serve for them all, since it’s drawn from an appealing camera angle to give the joke life.

Dave Blazek’s Loose Parts for the 14th is a mathematics wordplay panel but it hasn’t got anything to do with π. I suspect he lost track of what days he was working on, back six or so weeks when his deadline arrived.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 15th is some sort of joke about the probability of the world being like what it seems to be. I’m not sure precisely what anyone is hoping to express here or how it ties in to world peace. But the world does seem to be extremely well described by techniques that suppose it to be random and unpredictable in detail. It is extremely well predictable in the main, which shows something weird about the workings of the world. It seems to be doing all right for itself.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th is built on the staggering idea that the Earth might be the only place with life in the universe. The cosmos is a good stand-in for infinitely large things. It might be better as a way to understand the infinitely large than actual infinity would be. Somehow thinking of the number of stars (or whatnot) in the universe and writing out a representable number inspires an understanding for bigness that the word “infinity” or the symbols we have for it somehow don’t seem to, at least to me.

Mikael Wulff and Anders Morgenthaler’s TruthFacts for the 17th gives us valuable information about how long ahead of time the comic strips are working. Arithmetic is probably the easiest thing to use if one needs an example of a fact. But even “2 + 2 = 4” is a fact only if we accept certain ideas about what we mean by “2” and “+” and “=” and “4”. That we use those definitions instead of others is a reflection of what we find interesting or useful or attractive. There is cultural artifice behind the labelling of this equation as a fact.

Jimmy Johnson’s Arlo and Janis for the 18th capped off a week of trying to explain some point about the compression and dilution of time in comic strips. Comic strips use space and time to suggest more complete stories than they actually tell. They’re much like every other medium in this way. So, to symbolize deep thinking on a subject we get once again a panel full of mathematics. Yes, I noticed the misquoting of “E = mc2” there. I am not sure what Arlo means by “Remember the boat?” although thinking on it I think he did have a running daydream about living on a boat. Arlo and Janis isn’t a strongly story-driven comic strip, but Johnson is comfortable letting the setting evolve. Perhaps all this is forewarning that we’re going to jump ahead to a time in Arlo’s life when he has, or has had, a boat. I don’t know.