Reading the Comics, February 19, 2020: 90s Doonesbury Edition

The weekday Doonesbury has been in reruns for a very long while. Recently it’s been reprinting strips from the 1990s and something that I remember producing Very Worried Editorials, back in the day.

Garry Trudeau’s Doonesbury for the 17th reprints a sequence that starts off with the dread menace and peril of Grade Inflation, the phenomenon in which it turns out students of the generational cohort after yours are allowed to get A’s. (And, to a lesser extent, the phenomenon in which instructors respond to the treatment of education as a market by giving the “customers” the grades they’re “buying”.) The strip does depict an attitude common towards mathematics, though, the idea that it must be a subject immune to Grade Inflation: “aren’t there absolute answers”? If we are careful to say what we mean by an “absolute answer” then, sure.

Dean: 'Sir, you're going to have to speak to the faculty about grade inflation. Standards are just falling off the chart. The pressure to pander is even beginning to affect the math department.' President: 'Math? How can that be? Aren't there absolute answers in math?' Dean: 'Well, yes and no.' President, thinking: 'Yes and now?' [ Math Class ] Student: '17!' Other Student: '39!' Math Professor: 'Excellent guesses! Well done!'
Garry Trudeau’s Doonesbury rerun for the 17th of February, 2020 of February, 2020. It originally ran the 20th of December, 1993. I have few essays which mention this long-running strip, oddly. What essays are inspired by something in Doonesbury appear at this link.

But grades? Oh, there is so much subjectivity as to what goes into a course. And into what level to teach that course at. How to grade, and how harshly to grade. It may be easier, compared to other subjects, to make mathematics grading more consistent year-to-year. One can make many problems that test the same skill and yet use different numbers, at least until you get into topics like abstract algebra where numbers stop being interesting. But the factors that would allow any course’s grade to inflate are hardly stopped by the department name.

Mathematician: 'I went massively into debt to build a machine that generates holographic numbers and equations whenever I wish to appear thoughtful.' Friend: 'Was that a good use money?' [ Panel of the mathematician looking thoughtful with equations spread out in space behind and in front of her. ] Mathematician: 'Yes.' Friend: 'A thousand times yes.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th of February, 2020. I have a few essays which don’t mention this long-running web strip, oddly. What essays are inspired by something in Saturday Morning Breakfast Cereal appear at this link.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th is a strip about using a great wall of equations as emblem of deep, substantial thought. The equations depicted are several meaningful ones. The top row is from general relativity, the Einstein Field Equations. These relate the world-famous Ricci curvature tensor with several other tensors, describing how mass affects the shape of space. The P = NP line describes a problem of computational science with an unknown answer. It’s about whether two different categories of problems are, in fact, equivalent. The line about L = -\frac{1}{4} F_{\mu \nu} F^{\mu \nu} is a tensor-based scheme to describe the electromagnetic field. The next two lines look, to me, like they’re deep in Schrödinger’s Equation, describing quantum mechanics. It’s possible Weinersmith has a specific problem in mind; I haven’t spotted it.

Guy Walks Into A Bar comics. Man holding a horse's reins, to the bartender: 'I'll bet $50 my horse can do arithmetic!' Bartender: 'OK, what's 2 + 2?' Horse: '10.' Horse, to the angry guy, outside the bar: 'Well, think about it. Why would a horse use base ten?'
Ruben Bolling’s Super-Fun-Pak Comix for the 18th of February, 2020. There are a fair number of essays inspired by one of the Super-Fun-Pak Comics, and they’re gathered at this link. All the Super-Fun-Pak Comics first ran in Tom The Dancing Bug, essays about which appear here.

Ruben Bolling’s Super-Fun-Pak Comix for the 18th is one of the Guy Walks Into A Bar line, each of which has a traditional joke setup undermined by a technical point. In this case, it’s the horse counting in base four, in which representation the number 2 + 2 is written as 10. Really, yes, “10 in base four” is the number four. I imagine properly the horse should say “four” aloud. But it is quite hard to read the symbols “10” as anything but ten. It’s not as though anyone looks at the hexadecimal number “4C” and pronounces it “76”, either.

Garry Trudeau’s Doonesbury for the 19th twisted the Grade Inflation peril to something that felt new in the 90s: an attack on mathematics as “Eurocentric”. The joke depends on the reputation of mathematics as finding objectively true things. Many mathematicians accept this idea. After all, once we’ve seen a proof that we can do the quadrature of a lune, it’s true regardless of what anyone thinks of quadratures and lunes, and whether that person is of a European culture or another one.

Student: 'This B+ is wrong, man! You're dissin me big time here.' Professor: 'Mr Slocum, I merely gave you the grade you deserved.' Student: 'Can't be, man! This is WAY off base!' Professor: 'As was your entire first proof, in which you held the square root of 144 to be 15. It is, in fact, 12.' Student: 'Well, sure, from a narrow, absolutist, Eurocentric perspective, maybe it's 12.' Professor: 'So?' Student: 'So my culture teaches it's 15, man!' Professor: 'Fascinating. Would this be an advanced civilization?'
Garry Trudeau’s Doonesbury rerun for the 19th of February, 2020 of February, 2020. It originally ran the 22nd of December, 1993. I am reminded once again of a fellow grad student, doing his teaching-assistant duties, watching student after student on the calculus exam reduce 1002 to 10. When enough students make the same mistake you start to question your grading scheme. Which is sometimes fair: if everyone gets partway through a question and fails at the same step there’s a prima facie case that the problem was your instruction, not their comprehension. Doesn’t cover dumb arithmetic glitches, though.

But there are several points to object to here. The first is, what’s a quadrature? … This is a geometric thing; it’s finding a square that’s the same area as some given shape, using only straightedge and compass constructions. The second is, what’s a lune? It’s a crescent moon-type shape (hence the name) that you can make by removing the overlap from two circles of specific different radiuses arranged in a specific way. It turns out you can find the quadrature for the lune shape, which makes it seem obvious that you should be able to find the quadrature for a half-circle, a way easier (to us) shape. And it turns out you can’t. The third question is, who cares about making squares using straightedge and compass? And the answer is, well, it’s considered a particularly elegant way of constructing shapes. To the Ancient Greeks. And to those of us who’ve grown in a mathematics culture that owes so much to the Ancient Greeks. Other cultures, ones placing more value on rulers and protractors, might not give a fig about quadratures and lunes.

This before we get into deeper questions. For example, if we grant that some mathematical thing is objectively true, independent of the culture which finds it, then what role does the proof play? It can’t make the thing more or less true. It doesn’t eve matter whether the proof is flawed, or whether it convinces anyone. It seems to imply a mathematician isn’t actually needed for their mathematics. This runs contrary to intuition.

Anyway, this gets off the point of the student here, who’s making a bad-faith appeal to multiculturalism to excuse laziness. It’s difficult to imagine a culture that doesn’t count, at least, even if they don’t do much work with numbers like 144. Granted that, it seems likely they would recognize that 12 has some special relationship with 144, even if they don’t think too much of square roots as a thing.

And do please stop in later this Leap Day week. I figure to have one of my favorite little things, a Reading the Comics day that’s all one day. It should be at this link, when posted. Thank you.

Reading the Comics, April 24, 2017: Reruns Edition

I went a little wild explaining the first of last week’s mathematically-themed comic strips. So let me split the week between the strips that I know to have been reruns and the ones I’m not so sure were.

Bill Amend’s FoxTrot for the 23rd — not a rerun; the strip is still new on Sundays — is a probability question. And a joke about story problems with relevance. Anyway, the question uses the binomial distribution. I know that because the question is about doing a bunch of things, homework questions, each of which can turn out one of two ways, right or wrong. It’s supposed to be equally likely to get the question right or wrong. It’s a little tedious but not hard to work out the chance of getting exactly six problems right, or exactly seven, or exactly eight, or so on. To work out the chance of getting six or more questions right — the problem given — there’s two ways to go about it.

One is the conceptually easy but tedious way. Work out the chance of getting exactly six questions right. Work out the chance of getting exactly seven questions right. Exactly eight questions. Exactly nine. All ten. Add these chances up. You’ll get to a number slightly below 0.377. That is, Mary Lou would have just under a 37.7 percent chance of passing. The answer’s right and it’s easy to understand how it’s right. The only drawback is it’s a lot of calculating to get there.

So here’s the conceptually harder but faster way. It works because the problem says Mary Lou is as likely to get a problem wrong as right. So she’s as likely to get exactly ten questions right as exactly ten wrong. And as likely to get at least nine questions right as at least nine wrong. To get at least eight questions right as at least eight wrong. You see where this is going: she’s as likely to get at least six right as to get at least six wrong.

There’s exactly three possibilities for a ten-question assignment like this. She can get four or fewer questions right (six or more wrong). She can get exactly five questions right. She can get six or more questions right. The chance of the first case and the chance of the last have to be the same.

So, take 1 — the chance that one of the three possibilities will happen — and subtract the chance she gets exactly five problems right, which is a touch over 24.6 percent. So there’s just under a 75.4 percent chance she does not get exactly five questions right. It’s equally likely to be four or fewer, or six or more. Just-under-75.4 divided by two is just under 37.7 percent, which is the chance she’ll pass as the problem’s given. It’s trickier to see why that’s right, but it’s a lot less calculating to do. That’s a common trade-off.

Ruben Bolling’s Super-Fun-Pax Comix rerun for the 23rd is an aptly titled installment of A Million Monkeys At A Million Typewriters. It reminds me that I don’t remember if I’d retired the monkeys-at-typewriters motif from Reading the Comics collections. If I haven’t I probably should, at least after making a proper essay explaining what the monkeys-at-typewriters thing is all about.

'This new math teacher keeps shakin' us down every morning, man ... what's she looking for, anyway?' 'Pocket calculators.'
Ted Shearer’s Quincy from the 28th of February, 1978. So, that FoxTrot problem I did? The conceptually-easy-but-tedious way is not too hard to do if you have a calculator. It’s a buch of typing but nothing more. If you don’t have a calculator, though, the desire not to do a whole bunch of calculating could drive you to the conceptually-harder-but-less-work answer. Is that a good thing? I suppose; insight is a good thing to bring. But the less-work answer only works because of a quirk in the problem, that Mary Lou is supposed to have a 50 percent chance of getting a question right. The low-insight-but-tedious problem will aways work. Why skip on having something to do the tedious part?

Ted Shearer’s Quincy from the 28th of February, 1978 reveals to me that pocket calculators were a thing much earlier than I realized. Well, I was too young to be allowed near stuff like that in 1978. I don’t think my parents got their first credit-card-sized, solar-powered calculator that kind of worked for another couple years after that. Kids, ask about them. They looked like good ideas, but you could use them for maybe five minutes before the things came apart. Your cell phone is so much better.

Bil Watterson’s Calvin and Hobbes rerun for the 24th can be classed as a resisting-the-word-problem joke. It’s so not about that, but who am I to slow you down from reading a Calvin and Hobbes story?

Garry Trudeau’s Doonesbury rerun for the 24th started a story about high school kids and their bad geography skills. I rate it as qualifying for inclusion here because it’s a mathematics teacher deciding to include more geography in his course. I was amused by the week’s jokes anyway. There’s no hint given what mathematics Gil teaches, but given the links between geometry, navigation, and geography there is surely something that could be relevant. It might not help with geographic points like which states are in New England and where they are, though.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 24th is built on a plot point from Carl Sagan’s science fiction novel Contact. In it, a particular “message” is found in the digits of π. (By “message” I mean a string of digits that are interesting to us. I’m not sure that you can properly call something a message if it hasn’t got any sender and if there’s not obviously some intended receiver.) In the book this is an astounding thing because the message can’t be; any reasonable explanation for how it should be there is impossible. But short “messages” are going to turn up in π also, as per the comic strips.

I assume the peer review would correct the cartoon mathematicians’ unfortunate spelling of understanding.