I’m again falling behind the comic strips; I haven’t had the writing time I’d like, and that review of last month’s readership has to go somewhere. So let me try to dig my way back to current. The happy news is I get to do one of those single-day Reading the Comics posts, nearly.
Harley Schwadron’s 9 to 5 for the 7th strongly implies that the kid wearing a lemon juicer for his hat has nearly flunked arithmetic. At the least it’s mathematics symbols used to establish this is a school.
Jef Mallett’s Frazz for the 7th has kids thinking about numbers whose (English) names rhyme. And that there are surprisingly few of them, considering that at least the smaller whole numbers are some of the most commonly used words in the language. It would be interesting if there’s some deeper reason that they don’t happen to rhyme, but I would expect that it’s just, well, why should the names of 6 and 8 (say) have anything to do with each other?
There are, arguably, gaps in Evan and Kevyn’s reasoning, and on the 8th one of the other kids brings them up. Basically, is there any reason to say that thirteen and nineteen don’t rhyme? Or that twenty-one and forty-one don’t? Evan writes this off as pedantry. But I, admittedly inclined to be a pedant, think there’s a fair question here. How many numbers do we have names for? Is there something different between the name we have for 11 and the name we have for 1100? Or 2011?
There isn’t an objectively right or wrong answer; at most there are answers that are more or less logically consistent, or that are more or less convenient. Finding what those differences are can be interesting, and I think it bad faith to shut down the argument as “pedantry”.
Dave Whamond’s Reality Check for the 7th claims “birds aren’t partial to fractions” and shows a bird working out, partially with diagrams, the saying about birds in the hand and what they’re worth in the bush.
The narration box, phrasing the bird as not being “partial to fractions”, intrigues me. I don’t know if the choice is coincidental on Whamond’s part. But there is something called “partial fractions” that you get to learn painfully well in Calculus II. It’s used in integrating functions. It turns out that you often can turn a “rational function”, one whose rule is one polynomial divided by another, into the sum of simpler fractions. The point of that is making the fractions into things easier to integrate. The technique is clever, but it’s hard to learn. And, I must admit, I’m not sure I’ve ever used it to solve a problem of interest to me. But it’s very testable stuff.
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:
Comic Strip Master Command started the summer vacation early this year. There have been even slower weeks for mathematically-themed comics, but not many, and not much slower. Well, it’s looking like a nice weekend anyway. We can go out and do something instead.
And I’m doing a little experiment to see what happens if I publish posts a bit earlier in the day. My suspicion is nothing that reaches statistical significance. But statistical significance isn’t everything. I can devote a month or two to a lark.
Piers Baker’s Ollie and Quentin for the 2nd is a rerun. The strip ended several years ago, and has not been one of those formerly syndicated comics gone to web-only publication. And it’s one that I’ve discussed before, in a 2014 repeat and briefly in 2015. I don’t know why it reran six months apart. Having a particular daily strip repeat so often is usually a sign I should retire the strip from this blog. Likely I won’t retire it from my reading. I like its style a bit too much.
The joke is built on Quentin hearing that only 50% of people are not happy. And as he is happy, and he and Ollie are two people, it follows Ollie can’t be. The joke builds on the logic of the gambler’s fallacy. This is the idea that the probability of some independent event depends on what has recently happened. Here “event” means what it does to statisticians, what it turns out something is. This can be the result of a coin toss. This can be finding out whether a person is happy or not. The gambler’s fallacy has a hard-to-resist logic to it. We know it is unlikely that a coin tossed fairly ten times will come up tails each time. We also know it is even more unlikely that a coin tossed fairly eleven times will turn up tails every time. So if the coin has already come up tails ten times? It’s easy in the abstract to sneer at people who make this mistake. But at some point or other we all think some unpredictable event is “due”.
There is a catch here, though. The gambler’s fallacy covers independent events. One coin’s toss does not affect whether the next toss should be heads or tails. But personal happiness? That is something affected by other people. Perhaps not dramatically. But one person’s mood can certainly alter another’s, just as the strip demonstrates. In past appearances of this strip I’ve written about it as though the mathematical comedy element were obvious. Now I realize I may have under-explored what is happening here.
Harley Schwadron’s 9 to 5 for the 3rd is a student-at-the-blackboard joke. And a joke about the uselessness of learning arithmetic if there are computing devices around. There have always been computing devices around, though. I’d prefer them for tedious problems, or for problems in which mistakes have serious consequences. But I think it’s worth knowing at least what to do. But I like mathematics. Of course I would.
Mike Baldwin’s Cornered for the 6th is another student-at-the-blackboard joke. This one has the student excusing his wrong answer, a number too high, as a tip. In the student’s defense, I’ll say being able to come up with a decent approximate answer, even one you know is a little too high, is worth it. Often an important step in a problem is knowing about what a reasonable answer is. This can involve mental-mathematics tricks. For example, remembering that 7 times 7 is just under fifty, which would help with a problem like 7 times 6.
And that’s all the comic strips I found worth any mention last week. There weren’t even any that rated a “there’s a comic that said ‘math class’, so here you go” aside. This bodes well for an interesting week of content around here. My next Reading the Comics post should appear next Sunday at this link. All the past comic strip discussion should, too. If you should find a comics essay that doesn’t appear in those archives please let me know. I’ll fix it.
For this, the second of my Reading the Comics postings with all the comics images included, I’ve found reason to share some old and traditional mathematicians’ jokes. I’m not sure how this happened, but sometimes it just does.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th brings to mind a traditional mathematics joke. A dairy hires a mathematician to improve operations. She tours the place, inspecting the cows and their feeding and the milking machines. She speaks with the workers. She interviews veterinarians. She talks with the truckers who haul out milk. She interviews the clients. Finally she starts to work on a model of better milk production. The first line: “Assume a spherical cow.”
One big field of mathematics is model-building. When doing that you have to think about the thing you model. It’s hard. You have to throw away all the complicating stuff that makes your questions too hard to answer. But you can’t throw away all the complicating stuff or you have a boring question to answer. Depending on what kinds of things you want to know, you’ll need different models. For example, for some atmosphere problems you’ll do fine if you assume the air has no viscosity. For others that’s a stupid assumption. For some you can ignore that the planet rotates and is heated on one side by the sun. For some you don’t dare do that. And so on. The simplifications you can make aren’t always obvious. Sometimes you can ignore big stuff; a satellite’s orbit, for example, can be treated well by pretending that the whole universe except for the Earth doesn’t exist. Depends what you’re looking for. If the universe were homogenous enough, it would all be at the same temperature. Is that useful to your question? That’s the trick.
Mark Anderson’s Andertoons for the 20th is the Mark Anderson’s Andertoons for this essay. It’s just a student trying to distract the issue from fractions. I suppose mathematics was chosen for the blackboard problem because if it were, say, a history or an English or a science question someone would think that was part of the joke and be misled. Fractions, though, those have the signifier of “the thing we’d rather not talk about”.
Daniel Beyer’s Long Story Short for the 21st is a mathematicians-mindset sort of joke. Let me offer another. I went to my love’s college reunion. On the mathematics floor of the new sciences building the dry riser was labelled as “N Bourbaki”. Let me explain why is a correctly-formed and therefore very funny mathematics joke. “Nicolas Bourbaki” was the pseudonym used by the mathematical equivalent of an artist’s commune, in France, through several decades of the mid-20th century. Their goal was setting mathematics on a rigorous and intuition-free basis, the way mathematicians sometimes like to pretend it is. Bourbaki’s influential nonexistence lead to various amusing-for-academia problems and you can see why a fake office is appropriately named so, then. (This is the first time I’ve tagged this strip, looks like.)
Harley Schwadron’s 9 to 5 for the 21st is a name-drop of Einstein’s famous equation as a power tie. I must agree this meets the literal specification of a power tie since, you know, c2 is in it. Probably something more explicitly about powers wouldn’t communicate as well. Possibly Fermat’s Last Theorem, although I’m not sure that would fit and be legible on the tie as drawn.
Mark Pett’s Lucky Cow rerun for the 21st has the generally inept Neil work out a geometry problem in his head. The challenge is having a good intuitive model for what the relationship between the shapes should be. I’m relieved to say that Neil is correct, to the number of decimal places given. I’m relieved because I’ve spent embarrassingly long at this. My trouble was missing, twice over, that the question gave diameters instead of radiuses. Pfaugh. Saving me was just getting answers that were clearly crazy, including at one point 21 1/3.
Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 21st mentions Euler’s Theorem in the first panel. Trouble with saying “Euler’s Theorem” is that Euler had something like 82 trillion theorems. If you ever have to bluff your way through a conversation with a mathematician mention “Euler’s Theorem”. You’ll probably have said something on point, if closer to the basics of the problem than people figured. But the given equation — — is a good bet for “the” Euler’s Theorem. It’s a true equation, and it ties together a lot of interesting stuff about complex-valued numbers. It’s the way mathematicians tie together exponentials and simple harmonic motion. It makes so much stuff easier to work with. It would not be one of the things presented in a Distinctly Useless Mathematics text. But it would be mentioned along the way to something fascinating and useless. It turns up everywhere. (This is another strip I’m tagging for the first time.)
Wulff and Morgenthaler’s WuMo for the 21st uses excessively complicated mathematics stuff as a way to signify intelligence. Also to name-drop Massachusetts Institute of Technology as a signifier of intelligence. (My grad school was Rensselaer Polytechnic Institute, which would totally be MIT’s rival school if we had enough self-esteem to stand up to MIT. Well, on a good day we can say snarky stuff about the Rochester Institute of Technology if we don’t think they’re listening.) Putting the “Sigma” in makes the problem literally nonsense, since “Sigma” doesn’t signify any particular number. The rest are particular numbers, though. π/2 times 4 is just 2π, a bit more than 6.28. That’s a weird number of apples to have but it’s perfectly legitimate a number. The square root of the cosine of 68 … ugh. Well, assuming this is 68 as in radians I don’t have any real idea what that would be either. If this is 68 degrees, then I do know, actually; the cosine of 68 degrees is a little smaller than ½. But mathematicians are trained to suspect degrees in trig functions, going instead for radians.
Well, hm. 68 would be between 11 times 2π and 12 times 2π. I think that’s just a little more than 11 times 2π. Oh, maybe it is something like ½. Let me check with an actual calculator. Huh. It is a little more than 0.440. Well, that’s a once-in-a-lifetime shot. Anyway the square root of that is a little more than 0.663. So you’d be left with about five and a half apples. Never mind this Sigma stuff. (A little over 5.619, to be exact.)
I’d been splitting Reading the Comics posts between Sunday and Thursday to better space them out. But I’ve got something prepared that I want to post Thursday, so I’ll bump this up. Also I had it ready to go anyway so don’t gain anything putting it off another two days.
Bill Amend’s FoxTrot Classics for the 27th reruns the strip for the 4th of May, 2006. It’s another probability problem, in its way. Assume Jason is honest in reporting whether Paige has picked his number correctly. Assume that Jason picked a whole number. (This is, I think, the weakest assumption. I know Jason Fox’s type and he’s just the sort who’d pick an obscure transcendental number. They’re all obscure after π and e.) Assume that Jason is equally likely to pick any of the whole numbers from 1 to one billion. Then, knowing nothing about what numbers Jason is likely to pick, Paige would have one chance in a billion of picking his number too. Might as well call it certainty that she’ll pay a dollar to play the game. How much would she have to get, in case of getting the number right, to come out even or ahead? … And now we know why Paige is still getting help on probability problems in the 2017 strips.
Sandra Bell-Lundy’s Between Friends for the 29th also gives me a bit of a break by just being a Venn Diagram-based joke. At least it’s using the shape of a Venn Diagram to deliver the joke. It’s not really got the right content.
Harley Schwadron’s 9 to 5 for the 29th is this week’s joke about arithmetic versus propaganda. It’s a joke we’re never really going to be without again.