Reading the Comics, April 11, 2018: Obscure Mathematical Terms Edition


I’d like to open today’s installment with a trifle from Thomas K Dye. He’s a friend, and the cartoonist behind the long-running web comic Newshounds, its new spinoff Infinity Refugees, and some other projects.

Dye also has a Patreon, most recently featuring a subscribers-only web comic. And he’s good enough to do the occasional bit of spot art to spruce up my work here.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 9th of April, 2018 is, for me, relatable. I think I’ve read off this anecdote before. The first time I took Real Analysis I was completely lost. Getting me slightly less lost was borrowing a library book on Real Analysis from the mathematics library. The book was in French, a language I can only dimly read. But the different presentation and, probably, the time I had to spend parsing each sentence helped me get a basic understanding of the topic. So maybe trying algebra upside-down isn’t a ridiculous idea.

Archie: 'I can't make any sense out of this algebra!' Jughead: 'Er, Arch! Your book is upside-down!' Archie: 'Yeah, I know! I already tried it the other way, and it didn't make sense then either!'
Henry Scarpelli and Craig Boldman’s Archie rerun for the 9th of April, 2018. Finally, an artistic explanation for putting the name of the book being read on house left!

Lincoln Pierce’s Big Nate rerun for the 9th presents an arithmetic sequence, which is always exciting to work with, if you’re into sequences. I had thought Nate was talking about mathematics quizzes but I see that’s not specified. Could be anything. … And yes, there is something cool in finding a pattern. Much of mathematics is driven by noticing, or looking for, patterns in things and then describing the rules by which new patterns can be made. There’s many easy side questions to be built from this. When would quizzes reach a particular value? When would the total number of points gathered reach some threshold? When would the average quiz score reach some number? What kinds of patterns would match the 70-68-66-64 progression but then do something besides reach 62 next? Or 60 after that? There’s some fun to be had. I promise.

Nate: 'Four quizzes ago, I got a 70. Three quizzes ago, I got a 68. Two quizzes ago, I got a 66, and last quiz I got a 64! See the pattern?' Francis: 'The pattern of academic incompetence?' Nate: 'No, the way it keeps decreasing by twos! Isn't that COOL?'
Lincoln Pierce’s Big Nate rerun for the 9th of April, 2018. Trick question: there’s infinitely many sequences that would start 70, 68, 66, 64. But when we extrapolate this sort of thing we tend to assume that it’ll be some simple sequence. These are often arithmetic — each term increasing or decreasing by the same amount — or geometric — each term the same multiple of the one before. They don’t have to be. These are just easy ones to look for and often turn out well, or at least useful.

Mike Thompson’s Grand Avenue for the 10th is one of the resisting-the-teacher’s-problem style. The problem’s arithmetic, surely for reasons of space. The joke doesn’t depend on the problem at all.

Teacher: 'Gabby, can you solve the problem?' [ '33 x 22' on the blackboard. ] Gabby: 'No, thank you. You're the adult, so I'll let you solve the problem. Why do you need a kid? Adults are able to solve problems on their own.' [ Gabby sits outside the Principal's office, thinking ] 'Looks like he solved his problem after all.'
Mike Thompson’s Grand Avenue for the 10th of April, 2018. My grudge against Grand Avenue is well-established and I fear it will make people think I am being needlessly picky at this. But Gabby’s protest would start from a logical stance if the teacher asked “Would you solve the problem?” Then she’d have reason to argue that adults should be able to solve the problem. “Can” you doesn’t reflect on who ought to solve arithmetic problems.

Dave Whamond’s Reality Check for the 10th similarly doesn’t depend on what the question is. It happens to be arithmetic, but it could as easily be identifying George Washington or picking out the noun in a sentence.

Dog reading an exam: 'Do you know the square root of 81? Do you? Do you? Yes, you do!'
Dave Whamond’s Reality Check for the 10th of April, 2018. I keep wanting to think the exam is playing on the pun between K-9 and canine but it’s not quite there.

Leigh Rubin’s Rubes for the 10th riffs on randomness. In this case it’s riffing on the unpredictability and arbitrariness of random things. Random variables are very interesting in certain fields of mathematics. What makes them interesting is that any specific value — the next number you generate — is unpredictable. But aggregate information about the values is predictable, often with great precision. For example, consider normal distributions. (A lot of stuff turns out to be normal.) In that case we can be confident that the values that come up most often are going to be close to the arithmetic mean of a bunch of values. And that there’ll be about as many values greater than the mean as there are less than the mean. And this will be only loosely true if you’ve looked at a handful of values, at ten or twenty or even two hundred of them. But if you looked at, oh, a hundred thousand values, these truths would be dead-on. It’s wonderful and it seems to defy intuition. It just works.

Door to the Randomness Research Institute. Sign hanging on the doorknob: 'Be Back In: (Your Guess Is As Good As Ours.)'
Leigh Rubin’s Rubes for the 10th of April, 2018. My guess, in the absence of other information, would be “back in about as long as the last time we were out”. In surprisingly many cases your best plausible guess about what the next result should be is whatever the last result was.

John Atkinson’s Wrong Hands for the 10th is the anthropomorphic numerals joke for the week. It’s easy to think of division as just making numbers smaller: 4 divided by 6 is less than either 4 or 6. 1 divided by 4 is less than either 1 or 4. But this is a bad intuition, drawn from looking at the counting numbers that don’t look boring. But 4 divided by 1 isn’t less than either 1 or 4. Same with 6 divided by 1. And then when we look past counting numbers we realize that’s not always so. 6 divided by ½ gives 12, greater than either of those numbers, and I don’t envy the teachers trying to explain this to an understandably confused student. And whether 6 divided by -1 gives you something smaller than 6 or smaller than -1 is probably good for an argument in an arithmetic class.

'The Great Divide'. Numeral 6, looking at an obelus, and speaking to a 4 and a 1; 'It's the guy from division. Looks like we're downsizing'.
John Atkinson’s Wrong Hands for the 10th of April, 2018. Oh yeah, remember a couple months ago when the Internet went wild about how ÷ was a clever way of representing fractions, with the dots representing the numerator and denominator? … Yeah, that wasn’t true, but it’s a great mnemonic.

Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 11th has an argument about predicting humans mathematically. It’s so very tempting to think people can be. Some aspects of people can. In the founding lore of statistics is the astonishment at how one could predict how many people would die, and from what causes, over a time. No person’s death could be forecast, but their aggregations could be. This unsettles people. It should: it seems to defy reason. It seems to me even people who embrace a deterministic universe suppose that while, yes, a sufficiently knowledgeable creature might forecast their actions accurately, mere humans shouldn’t be sufficiently knowledgeable.

Priti: 'Did you know that all human culture can be represented with GRAPHS?!' Sloan: 'Doubtful. Here. Read Machiavelli, Durkheim, and Montesquieu.' Priti: 'I see a lot of French and a lack of graphs.' Sloan: 'Not everything can be represented graphical [sic]. Plus it's full of CITATIONS! Wonderful, wonderful citations!' Priti: 'So, you don't think your behavior can be predicted mathematically?' Sloan: 'Correct.' Priti: 'Predictable'.
Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 11th of April, 2018. So when James Webb, later of NASA fame, was named Under-Secretary of State in 1949 one of his projects was to bring more statistical measure to foreign affairs. He had done much to quantify economic measures, as head of the Bureau of the Budget. But he wasn’t able to overcome institutional skepticism (joking about obvious nonsense like “Bulgaria is down a point!”), and spent his political capital instead on a rather necessary reorganization of the department. That said, I would not trust the wildly enthusiastic promises of any pop mathematics book proclaiming human cultures can be represented by any simple numerical structure.

No strips are tagged for the first time this essay. Just noticing.

Reading the Comics, March 21, 2018: Old Mathematics Jokes Edition


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.”

[Pro Tip: this is the answer to any thermodynamics question that requires you to determine an object's temperature: ] T = 2.73 K (assume well-mixed Cosmos)
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th of March, 2018. Temperature’s a great subject though, and I’ve been thinking for ages about doing a series on it just because I want to explain negative temperatures Kelvin.

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.

On the board: 1/2 - 1/8 = ?. Student: 'Apropos of nothing, I have two cats.'
Mark Anderson’s Andertoons for the 20th of March, 2018. Okay, but why the poster with the octopus on it?

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”.

Woman: 'And if you haven't figured it out yet, this is the math department lavatory'. The door reads 1 +/- 2
Daniel Beyer’s Long Story Short for the 21st of March, 2018. Not to nitpick but shouldn’t it be 1½ ± ½?

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.)

Employee: 'Cool 'power tie' boss'. The tie reads E = mc^2.
Harley Schwadron’s 9 to 5 for the 21st of March, 2018. I understand the tie has to face the audience to make the joke work, but isn’t it more fun to imagine that it’s actually a pyramidal tie, like, a solid triangular projection of tie material, and we see one side of it and maybe there’s another equation written on the other side? Please vote in the comments.

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.

Clare: 'How many cylinders with length 3 and diameter 1.5 equal the volume of a sphere with diameter 3?' Neil: 'Um ... 2.6. no, 2.7!' Clare: 'Neil, how on earth did you know that?' Neil: 'It's simple, Clare! I converted the cylinder to 'Ho Hos' and the sphere to Hostess 'Sno Balls', then I imagined eating them!' Clare: 'Um ... wow.' Neil: 'My brain's only average, but my tummy's a genius!'
Mark Pett’s Lucky Cow for the 21st of March, 2018. I preferred Ding Dongs eater myself. But my heart was with the Suzy Q’s, if we’re not letting Tastykake into the discussion.

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.

Professor in girl's daydream: 'But don't take my word for it. It's Euler's theorem.' (Points to e^{i pi} + 1 = 0 on the board.) Girl: 'Greg! Greg! I've changed my mind! Let's be colleagues again! ... Greg?' (Sees a closet jammed shut by a door.) Person inside: 'Help! I'm stuck!' (She unjams the door.) Person inside: 'Did she leave? Where's ray? Someone has to stop her!' Girl: 'That's like trying to stop a yeti!' Person inside: 'By my calculations it's far worse.' (Looks over sheet labelled 'Monster Unit Conversions', with Wray worked out to be 8 orcs or 3 trolls or 6 werewolves or werebears or 2.788 Yetis.)
Zach Weinersmith, Chris Jones and James Ashby’s Snowflakes for the 21st of March, 2018. I would like to give you more context for this but I confess I haven’t been able to follow the storyline. I don’t know why but this is one of the strips I don’t get the flow of.

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 — e^{\imath \pi} + 1 = 0 — 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.)

[ Cybil used to teach at MIT ] Cybil, teaching: 'If you've got pi/2 x 4 apples, and you eat Sigma x square root of cos(68) apples, how many apples do you have?' The class looks baffled.
Wulff and Morgenthaler’s WuMo for the 21st of March, 2018. Fun fact: since 68 is a rational number, the cosine of 68 has to be transcendental. All right, but it’s fun to me and whose blog is this? Thank you. But the cosine of any rational number other than zero is transcendental. Ditto the sine and the tangent.

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.)