Reading the Comics, September 24, 2019: I Make Something Of This Edition


I trust nobody’s too upset that I postponed the big Reading the Comics posts of this week a day. There’s enough comics from last week to split them into two essays. Please enjoy.

Scott Shaw! and Stan Sakai’s Popeye’s Cartoon Club for the 22nd is one of a yearlong series of Sunday strips, each by different cartoonists, celebrating the 90th year of Popeye’s existence as a character. And, I’m a Popeye fan from all the way back when Popeye was still a part of the pop culture. So that’s why I’m bringing such focus to a strip that, really, just mentions the existence of algebra teachers and that they might present a fearsome appearance to people.

Popeye and Eugene popping into Goon Island. Popeye: 'Thanks for bringing us to Goon Island! Watch out, li'l Jeep! Them Goons are nutty monskers that need civilizin'! Here's Alice the Goon!' Alice: 'MNWMNWMNMN' . Popeye: 'Whatever you sez, Alice! --- !' (Sees a large Goon holding a fist over a baby Goon.) Popeye: 'He's about to squash that li'l Goon! That's all I can stands, I can't stands no more!' Popeye slugs the big Goon. Little Goon holds up a sign: 'You dummy! He's my algebra teacher!' Popeye: 'Alice, I am disgustipated with meself!' Alice: 'MWNMWN!'
Scott Shaw! and Stan Sakai’s Popeye’s Cartoon Club for the 22nd of September, 2019. This is the first (and likely last) time Popeye’s Cartoon Club has gotten a mention here. But appearances by this and by the regular Popeye comic strip (Thimble Theatre, if you prefer) should be gathered at this link.

Lincoln Pierce’s Big Nate for the 22nd has Nate seeking an omen for his mathematics test. This too seems marginal. But I can bring it back to mathematics. One of the fascinating things about having data is finding correlations between things. Sometimes we’ll find two things that seem to go together, including apparently disparate things like basketball success and test-taking scores. This can be an avenue for further research. One of these things might cause the other, or at least encourage it. Or the link may be spurious, both things caused by the same common factor. (Superstition can be one of those things: doing a thing ritually, in a competitive event, can help you perform better, even if you don’t believe in superstitions. Psychology is weird.)

Nate, holding a basketball, thinking: 'If I make this shot it means I'm gonna ace the math test!' He shoots, missing. Nate: 'If I make *this* shot I'm gonna ace the math test!' He shoots, missing. Nate: 'If *this* one goes in, I'll ace the math test!' He shoots, missing. Nate: 'THIS one COUNTS! If I make it it means I'll ace the math test!' He shoots, missing. Nate: 'OK, this is IT! If I make THIS, I WILL ace the math test!' It goes in. Dad: 'Aren't you supposed to be studying for the math test?' Nate: 'Got it covered.'
Lincoln Pierce’s Big Nate for the 22nd of September, 2019. Essays inspired by something in Big Nate, either new-run or the Big Nate: First Class vintage strips, are at this link.

But there are dangers too. Nate shows off here the danger of selecting the data set to give the result one wants. Even people with honest intentions can fall prey to this. Any real data set will have some points that just do not make sense, and look like a fluke or some error in data-gathering. Often the obvious nonsense can be safely disregarded, but you do need to think carefully to see that you are disregarding it for safe reasons. The other danger is that while two things do correlate, it’s all coincidence. Have enough pieces of data and sometimes they will seem to match up.

Norm Feuti’s Gil rerun for the 22nd has Gil practicing multiplication. It’s really about the difficulties of any kind of educational reform, especially in arithmetic. Gil’s mother is horrified by the appearance of this long multiplication. She dubs it both inefficient and harder than the way she learned. She doesn’t say the way she learned, but I’m guessing it’s the way that I learned too, which would have these problems done in three rows beneath the horizontal equals sign, with a bunch of little carry notes dotting above.

Gil: 'Mom, can you check my multiplication homework?' Mom: 'Sure .. is THIS how they're teaching you to do it?' (eg, 37x22 as 14 + 60 + 140 + 600 = 814) Gil: 'Yes.' Mom: 'You know, there's an easier way to do this?' Gil: 'My teacher said the old way was just memorizing an algorithm. The new way helps us understand what we're doing.' Mom: '*I* always understood what I was doing. It seems like they're just teaching you a less efficient algorithm.' Gil: 'Maybe I should just check my work with a calculator.' Mom: 'I have to start going to the PTA meetings.'
Norm Feuti’s Gil rerun for the 22nd of September, 2019. Essays inspired by either the rerun or the new Sunday Gil strips should be gathered at this link.

Gil’s Mother is horrified for bad reasons. Gil is doing exactly the same work that she was doing. The components of it are just written out differently. The only part of this that’s less “efficient” is that it fills out a little more paper. To me, who has no shortage of paper, this efficiency doens’t seem worth pursuing. I also like this way of writing things out, as it separates cleanly the partial products from the summations done with them. It also means that the carries from, say, multiplying the top number by the first digit of the lower can’t get in the way of carries from multiplying by the second digits. This seems likely to make it easier to avoid arithmetic errors, or to detect errors once suspected. I’d like to think that Gil’s Mom, having this pointed out, would drop her suspicions of this different way of writing things down. But people get very attached to the way they learned things, and will give that up only reluctantly. I include myself in this; there’s things I do for little better reason than inertia.

People will get hung up on the number of “steps” involved in a mathematical process. They shouldn’t. Whether, say, “37 x 2” is done in one step, two steps, or three steps is a matter of how you’re keeping the books. Even if we agree on how much computation is one step, we’re left with value judgements. Like, is it better to do many small steps, or few big steps? My own inclination is towards reliability. I’d rather take more steps than strictly necessary, if they can all be done more surely. If you want speed, my experience is, it’s better off aiming for reliability and consistency. Speed will follow from experience.

Profesor showing multiple paths from A to B on the chalkboard: 'The universe wants particles to take the easiest route from point A to point B. Mysteriously, the universe accomplishes this by first considering *every* possible path. It's doing an enormous amount of calculation just to be certain it's not taking a suboptimal route.' Caption: 'You can model reality pretty well if you imagine it's your dad planning a road trip.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 22nd of September, 2019. Essays which go into some aspect of Saturday Morning Breakfast Cereal turn up all the time, such as at this link.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 22nd builds on mathematical physics. Lagrangian mechanics offers great, powerful tools for solving physics problems. It also offers a philosophically challenging interpretation of physics problems. Look at the space made up of all the possible configurations of the system. Take one point to represent the way the system starts. Take another point to represent the way the system ends. Grant that the system gets from that starting point to that ending point. How does it do that? What is the path in this configuration space that goes in-between this start and this end?

We can find the path by using the Lagrangian. Particularly, integrate the Lagrangian over every possible curve that connects the starting point and the ending point. This is every possible way to match start and end. The path that the system actually follows will be an extremum. The actual path will be one that minimizes (or maximizes) this integral, compared to all the other paths nearby that it might follow. Yes, that’s bizarre. How would the particle even know about those other paths?

This seems bad enough. But we can ignore the problem in classical mechanics. The extremum turns out to always match the path that we’d get from taking derivatives of the Lagrangian. Those derivatives look like calculating forces and stuff, like normal.

Then in quantum mechanics the problem reappears and we can’t just ignore it. In the quantum mechanics view no particle follows “a” “path”. It instead is found more likely in some configurations than in others. The most likely configurations correspond to extreme values of this integral. But we can’t just pretend that only the best-possible path “exists”.

Thus the strip’s point. We can represent mechanics quite well. We do this by pretending there are designated starting and ending conditions. And pretending that the system selects the best of every imaginable alternative. The incautious pop physics writer, eager to find exciting stuff about quantum mechanics, will describe this as a particle “exploring” or “considering” all its options before “selecting” one. This is true in the same way that we can say a weight “wants” to roll down the hill, or two magnets “try” to match north and south poles together. We should not mistake it for thinking that electrons go out planning their days, though. Newtonian mechanics gets us used to the idea that if we knew the positions and momentums and forces between everything in the universe perfectly well, we could forecast the future and retrodict the past perfectly. Lagrangian mechanics seems to invite us to imagine a world where everything “perceives” its future and all its possible options. It would be amazing if this did not capture our imaginations.

Billy, pointing a much older kid out to his mother: 'Mommy, you should see HIS math! He has to know numbers AND letters to do it!'
Bil Keane and Jeff Keane’s Family Circus for the 24th of September, 2019. I’m surprised there are not more appearance of this comic strip here. But Family Circus panels inspire essays at these links.

Bil Keane and Jeff Keane’s Family Circus for the 24th has young Billy amazed by the prospect of algebra, of doing mathematics with both numbers and letters. I’m assuming Billy’s awestruck by the idea of letters representing numbers. Geometry also uses quite a few letters, mostly as labels for the parts of shapes. But that seems like a less fascinating use of letters.


The second half of last week’s comics I hope to post here on Wednesday. Stick around and we’ll see how close I come to making it. Thank you.

Reading the Comics, March 13, 2019: Ziggy Rerun Scandal Edition


I do not know that the Ziggy printed here is a rerun. I don’t seem to have mentioned it in previous Reading the Comics posts, but that isn’t definite. How much mathematical content a comic strip needs to rate a mention depends on many things, and a strip that seems too slight one week might inspire me another. I’ll explain why I’ve started to get suspicious of the quite humanoid figure.

Tom II Wilson’s Ziggy for the 12th is framed around weather forecasts. It’s the probability question people encounter most often, unless they’re trying to outsmart the contestants on Let’s Make A Deal. (And many games on The Price Is Right, too.) Many people have complained about not knowing the meaning of a “50% chance of rain” for a day. If I understand it rightly, it means, when conditions have been like this in the recorded past, it’s rained about 50% of the time. I’m open to correction from meteorologists and it just occurred to me I know one. Mm.

Few people ask about the probability a forecast is correct. In some ways it’s an unanswerable question. To say there is a one-in-six chance a fairly thrown die will turn up a ‘1’ is not wrong just because it’s rolled a ‘1’ eight times out of the last ten. But it does seem like a forecast such as this should include a sense of confidence, how sure the forecaster is that the current weather is all that much like earlier times.

Weather forecaster on the TV Ziggy watches: 'Tomorrow's weather, there's a 50% chance of rain, and a 50% chance I'm even right about the 50%!!'
Tom II Wilson’s Ziggy for the 12th of March, 2019. When I do find a mathematical context to discuss Ziggy the results should appear at this link. Speculating about the comic’s rerun schedule isn’t really my business.

I’m not sure how much of the joke is meant to be the repetition of “50% chance”. The joke might be meant to say that if he’s got a 50% chance of being wrong, then, isn’t the 50% chance of rain “correctly” a 50% chance of not-rain … which is the same chance of rain? The logic doesn’t hold up, if you pay attention, but it sounds like it should make sense, and having the “wrong” version of something be the same as the original is a valid comic construction.

So now for the promised Ziggy rerun scandal. To the best of my knowledge Ziggy is presented as being in new run. It’s done by the son of the comic strip’s creator, but that’s common enough for long-running comic strips. This Monday, though, ran a Ziggy-at-the-psychiatrist joke that was, apart from coloring, exactly the comic run the 2nd of March, barely two weeks before. (Compare the scribbles in the psychiatrist’s diploma.) It wouldn’t be that weird if a comic were accidentally repeated; production mistakes happen, after all. It’s slightly weird that the daily, black-and-white, original got colored in two different ways, but I can imagine this happening by accident.

Still, that got me primed to look for Ziggy repeats. I couldn’t find this one having an earlier appearance. But I did find that the 9th of January this year was a reprint of the Ziggy from the 11th of January, 2017. I wrote about both appearances, without noticing they were reruns. Here’s the 2017 essay, and over here is the 2019 essay, from before I was very good at remembering what the year was. Mercifully I didn’t say anything contradictory on the two appearances. I’m more interested in how I said things differently in the two appearances. Anyway this earlier year seems to have been part of a week’s worth of reruns, noticeable by the copyright date. I can’t begrudge a cartoonist their vacation. The psychiatrist strip doesn’t seem to be part of that, though, and its repetition is some as-yet-unexplained event.

Pete: 'Have you seen my ... ' Peggy: 'Top drawer, dresser.' Pete: 'What day is the ... ' Peggy: 'Monday.' Pete: 'Do we have any ... ' Peggy: 'Middle cabinet, kitchen.' Pete: 'What's the square root of 532?' Peggy: '23.06512518.' (In the last panel Peggy looks smugly at the reader.)
Tony Rubino and Gary Markstein’s Daddy’s Home for the 13th of March, 2019. The steadily growing number of essays with a mention of Daddy’s Home are at this link.

Tony Rubino and Gary Markstein’s Daddy’s Home for the 13th has a much more casual and non-controversial bit of mathematics. Pete tosses out a calculate-the-square-root problem as a test of Peggy’s omniscience. One of the commenters points out that the square root of 532 is closer to 23.06512519 than it is Peggy’s 23.06512818. It suggests the writers found the square root by something that gave plenty of digits. For example, the macOS Calculator program offers me “23.065 125 189 341 592”. But then they chopped off, rather than rounding off, digits when the panel space ran out.

Teacher: 'Nancy, Esther, I'm making you partners for classwork today.' Nancy, thinking: 'How are we supposed to work together? We're fighting!' Nancy, tearing a page of mathematics problems down the center: 'Here, you take the right side of the equals sign and I'll take the left.'
Olivia Jaimes’s Nancy for the 13th of March, 2019. Essays mentioning Nancy, either current-run or the “classic” vintage reprints, should appear here.

Olivia Jaimes’s Nancy for the 13th has Nancy dividing up mathematics problems along the equals sign. That’s cute and fanciful enough. One could imagine working out expressions on either side of the equals sign in the hopes of getting them to match. That wouldn’t work for these algebra problems, but, that’s something.

This isn’t what Nancy might do, unless she flashed forward to college and became a mathematics or physics major. But one great trick in differential equations is called the separation of variables. Differential equations describe how quantities change. They’re great. They’re hard. A lot of solving differential equations amounts to rewriting them as simpler differential equations.

Separation is a trick usable when there’s two quantities whose variation affect each other. If you can rewrite the differential equation so that one variable only appears on the left side, and the other variable only appears on the right? Then you can split this equation into two simpler equations. Both sides of the equation have to be some fixed number. So you can separate the differential equations of two variables into two differential equations, each with one variable. One with the first variable, one with the other. And, usually, a differential equation of one variable is easier than a differential equation with two variables. So Nancy and Esther could work each half by themselves. But the work would have to be put together at the end, too.


And for a truly marginal mathematics topic: Lincoln Pierce’s Big Nate: First Class for the 13th, reprinting the 2nd of March, 1994, mentions a mathematics test for Nate’s imminent doom.


And this wraps up the comic strips for the previous week. Come Sunday there should be a fresh new comic post. Yes, Andertoons is scheduled to be there.

Reading the Comics, December 15, 2018: Early Holiday Edition


So then this happened: Comic Strip Master Command didn’t have much they wanted me to write about this week. I made out three strips as being relevant enough to discuss at all. And even they don’t have topics that I felt I could really dig into. Coincidence, surely, although I like to think they were trying to help me get ahead of deadline on my A To Z essays for this last week of the run. It’s a noble thought, but doomed. I haven’t been more than one essay ahead of deadline the last three months. I know in past years I’ve gotten three or even four essays ahead of time and I don’t know why it hasn’t worked this time. I am going ahead and blaming that this these essays have been way longer than previous years’. So anyway, I thank Comic Strip Master Command for trying to make my Monday and my Thursday this week be less packed. It won’t help.

Darrin Bell and Theron Heir’s Rudy Park for the 10th uses mathematics as shorthand for a deep, thought-out theory of something. In this case, Randy’s theory of how to interest women. (He has rather a large number of romantic events around him.) It’s easy to suppose that people can be modeled mathematically. Even a crude model, one supposing that people have things they like and dislike, can give us good interesting results. This gets into psychology and sociology though. And probably requires computer modeling to get slightly useful results.

Rudy: 'You're wearing your lab coat. What's up?' Randy: 'Something big. Amending my unified theory of picking up chicks. Check it out.' (It's a blackboard filled with physics equations, as well as a sketch of a woman in a bikini.) Rudy: 'Explain, Doctor.' Randy: 'To start, you'll need a notepad and a gym membership.'
Darrin Bell and Theron Heir’s Rudy Park for the 10th of December, 2018. This strip is a rerun. It originally ran the 11th of January, 2010. Essays mentioning topics raised by Rudy Park are at this link.

Randy’s blackboard has a good number of legitimate equations on it. They’re maybe not so useful to his problem of modeling people, though. The lower left corner, for example, are three of Maxwell’s Equations, describing electromagnetism. I’m not sure about all of these, in part because I think some might be transcribed incorrectly. The second equation in the upper left, for example, looks like it’s getting at the curl of a conserved force field being zero, but it’s idiosyncratic to write that with a ‘d’ to start with. The symbols all over the right with both subscripts and superscripts look to me like tensor work. This turns up in electromagnetism, certainly. Tensors turn up anytime something, such as electrical conductivity, is different in different directions. But I’ve never worked deeply in those fields so all I can confidently say is that they look like they parse.

Nate's story: 'Barky the sheepdog stared in horror at the bloody foot on the barn floor. It was the fifth piece of Farmer Wobblewheel he'd found today. 'And don't forget about the three pieces we found yesterday!' said Winky the wonder monkey.' Franklin: 'What's a monkey doing on a farm?' Nate: 'Helping Barky discover who dismembered Farmer Wobblewheel *and* teaching us about numbers!' Story: ''Five pieces plus three pieces,' barked Barkey. 'That makes ... ' 'Eight,' chuckled Winky.' Francis: 'Ew.'
Lincoln Pierce’s Big Nate for the 14th of December, 2018. Other essays mentioning topics raised by Big Nate, both the current run — like this — and vintage 1990 are at this link.

Lincoln Pierce’s Big Nate for the 14th is part of a bit where Nate’s trying to write a gruesome detective mystery for kids. I’m not sure that’s a ridiculous idea, at least if the gore could be done at a level that wouldn’t be too visceral. Anyway, Nate has here got the idea of merging some educational value into the whole affair. It’s not presented as a story problem, just as characters explaining stuff to one another. There probably would be some room for an actual problem where Barky and Winky wanted to know something and had to work out how to find it from what they knew, though.

Playing in a cardboard box labelled SS Nora Dish. Jingles: 'Take the controls while I make the calculations for hyperspace.' Cecil: 'Wookie noise.' Jingles: 'Let's see. Bob has two bananas. He gives one to Joe who eats half and returns the remainder along with half a cantaloupe ... this ship needs a modern supercomputer.' Cecil: 'Wookie noise.'
Mel Henze’s Gentle Creatures for the 14th of December, 2018. All the essays where I’ve discussed Gentle Creatures are at this link although I suspect it’s mostly the same three comics discussed over and over.

Mel Henze’s Gentle Creatures for the 14th uses a story problem to stand in for science fictional calculations. The strip’s in reruns and I’ve included it here at least four times, I discover, so that’s probably enough for the comic until it gets out of reruns.


And since it was a low-volume week, let me mention strips I didn’t decide fit. Ray Kassinger asked about Tim Rickard’s Brewster Rockit for the 12th. Might it be a play on Schrödinger’s Cat, the famous thought-experiment about how to understand the mathematics of quantum mechanics? It’s possible, but I think it’s more likely just that cats like sitting in boxes. Thaves’s Frank and Ernest for the 13th looks like it should be an anthropomorphic numerals joke. But it’s playing on the idiom about three being a crowd, and the whole of the mathematical content is that three is a number. John Zakour and Scott Roberts’s Maria’s Day for the 15th mentions mathematics. Particularly, Maria wishing they weren’t studying it. It’s a cameo appearance; it could be any subject whose value a student doesn’t see. That’s all I can make of it.


This and my other Reading the Comics posts should all be available at this link. And please check back in Tuesday to see whether I make deadline for the letter ‘Y’ in my Fall 2018 Mathematics A To Z glossary.

Reading the Comics, May 30, 2018: Spherical Photos Edition


Last week’s offerings from Comic Strip Master Command got away from me. Here’s some more of the strips that had some stuff worth talking about. I should have another installment this week. I’m back to nonsense edition names; sorry.

Lincoln Pierce’s Big Nate for the 29th of May is about the gambler’s fallacy. Everyone who learns probability learns about it. The fallacy builds on indisputable logic: your chance of losing at something eighteen times in a row is less than the chance of your losing at that thing seventeen times in a row. So it makes sense that if you’ve lost seventeen times in a row then you must be due.

And that’s one of those lies our intuition tells us about probability. What’s important to Nate here is not the chance he’s in an 18-at-bat losing streak. What’s important is the chance that he’s in an 18-at-bat losing streak, given that he’s already failed 17 times in a row. These are different questions. The chance of an 18th at-bat in a row being a failure (for him) is much larger than the chance of an 18-at-bat losing streak starting from scratch.

Nate: 'Time for me to break this 0-and-17 stretch.' Teddy: 'Exactly! You're due, Nate! You're due!' Francis: 'Not necessarily. The chances of Nate getting a hit aren't enhanced by the fact that he's gone five games without one.' Teddy: 'I lied. You're not due.' Francis: 'But miracles happen, so go for it.'
Lincoln Pierce’s Big Nate rerun for the 29th of May, 2018. The strip first ran the 18th of May, 2010. I’ve not heard anything about why Pierce has been away from the strip since the start of the year.

That said I can’t go along with Francis’s claim that the chance of Nate getting a hit isn’t enhanced by his long dry spell. We can, and often do, model stuff like at-bats as though they’re independent. That is, that the chance of getting a hit doesn’t depend on what came before. Doing it this way gives results that look like real sports matches do. But it’s very hard to quantify things like losing streaks or their opposite, hot hands. It’s hard to dismiss the evidence of people who compete, though. Everyone who does has known the phenomenon of being “in the zone”, where things seem easier. I was in it for two games out of five just last night at pinball league. (I was dramatically out of it for the other three. I nearly doubled my best-ever game of Spider-Man and still came in second place. And by so little a margin my opponent thought the bonus might make the difference. Such heartbreak.)

But there is a huge psychological component to how one plays at a game. Nate thinks differently about what he’s doing going up to bat after seventeen failures in a row than he would after, say, three home runs in a row. It’s hard to believe that this has no effect on how he plays, even if it’s hard to track down a consistent signal through the noise. Maybe it does wash out. Maybe sometimes striking out the first three at-bats in a game makes the batter give up on the fourth. Meanwhile other times it makes the batter focus better on the fourth, and there’s no pinning down which effect will happen. But I can’t go along with saying there’s no effect.

Melvin: 'Hold on now --- replacement? Who could you find to do all the tasks only Melvin can perform?' Rita: 'A macaque, in fact. Listen, if an infinite number of monkeys can write all the great works, I'm confident that one will more than cover for you.'
John Zakour and Scott Roberts’s Working Daze for the 29th of May, 2018. Earlier in the sequence they had the Zootopia sloth replacing Ed, but there’s no making that on topic for my blog here.

John Zakour and Scott Roberts’s Working Daze for the 29th is an infinite-monkeys joke. Well, given some reasonable assumptions we can suppose that sufficiently many monkeys on typewriters will compose whatever’s needed, given long enough. Figuring someone’s work will take fewer monkeys and less time is a decent probability-based insult.

Hazel, with mathematics book, asking a bored kid: 'Okay, now what's nine times eight?' Next panel: the kid's coming out and saying 'Next'; a sign reads, 'Need help with your homework? See Hazel 1 to 5 pm Saturdays'.
Ted Key’s Hazel rerun for the 30th of May, 2018. I can’t say when this first ran. I’m not sure what the kid’s name is, sorry.

Ted Key’s Hazel for the 30th has the maid doing a bit of tutoring work. That’s about all I can make of this either. Doesn’t seem like a lot of fun, but there is only so much to do with arithmetic computation like this. It’s convenient to know a times table by memory.

Accessories of Famous Teachers: Einstein's Chalkboard; Galileo's Compass; Confucius's Fortune Cookie; Socrates's Hemlock; Miss Othmar's Trombone.
Scott Hilburn’s The Argyle Sweater for the 30th of May, 2018. Are … Einstein, Galileo, and Confucius really famous teachers? Calling Socrates a teacher is a lesser stretch.

Scott Hilburn’s The Argyle Sweater for the 30th has a chalkboard full of mathematical symbols as iconic for deep thinking. And it’s even Einstein’s chalkboard. And it’s even stuff that could plausibly be on Einstein’s chalkboard at some point. Besides E = mc2 the other formulas are familiar ones from relativity. They’re about the ways our ideas of how much momentum or mass a thing has has to change if we see the thing in motion. (I’m a little less sure about that \Delta t expression, but I think I can work something out.) And as a bonus it includes the circle-drawing compass as Galileo might have used. Well, he surely used a compass; I’m just not sure that the model shown wouldn’t be anachronistic. As though that matters; fortune cookies, after all, are a 20th century American invention and we’re letting that pass.

Mathematical Fun Fact: For each of the possible espresso-to-milk ratios, there exists at least one Italian-sounding name: Just Milk; 1:3 'latte', 1:2 'Cappuccino', 1:1 'Antoccino', 2:1 'Macchiato', 3:1 'Antilatte', Just Espresso. Also: 1/c^2 'Relativisto'; (espresso + milk)/espresso = espresso/milk 'Phicetto'; i:1 'Imaginarati', pi:1 'Irratiognito'; 6.022*10^23 : 1, 'Avogadro'; lim_{milk->0} espresso/milk: 'Infiniccino'.
Zach Weinersmiths’s Saturday Morning Breakfast Cereal for the 30th of May, 2018. Kind of curious what sorts of drinks you get from putting in infinitesimals. (You get milk or espresso with a homeopathic bit of the other.)

Zach Weinersmiths’s Saturday Morning Breakfast Cereal for the 30th builds on a fun premise. Underneath the main line it gets into some whimsical ratios built on important numbers you’d never use for this sort of thing, such as π, and the imaginary unit \imath . The Golden Ratio makes an appearance too, sneaking a definition for φ in in terms of espresso and milk. Here’s a free question: is there a difference between the “infiniccino” and “just espresso” except for the way it’s presented? … Well, presentation can be an important part of a good coffee.

π is well-known. Not sure I have anything interesting to add to its legend. φ is an irrational number a bit larger than 1.6. I’m not sure if I’ve ever called it the Boba Fett of numbers, but I should have. It’s a cute enough number, far more popular than its importance would suggest. \imath is far more important. Suppose that there is some number, which we give that name, with the property that \imath^2 equals -1. Then we get complex-valued numbers, which let us solve problems we’d like to know but couldn’t do before. It’s a great advance.

The name tells you how dubiously people approached this number, when it was first noticed. I wonder if people would be less uneasy with “imaginary numbers” if it weren’t for being told how there’s no such thing as the square root of minus one for years before algebra comes along and says, well, yes there is. It’s hard to think of a way that, say, “negative four” is more real than \imath , after all, and people are mostly all right with -4. And I understand why people are more skeptical of -4 than they are of, say, 6. Still, I wonder how weird \imath would look if people weren’t primed to think it was weird.

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, February 11, 2018: February 11, 2018 Edition


And it’s not always fair to say that the gods mock any plans made by humans, but Comic Strip Master Command has been doing its best to break me of reading and commenting on any comic strip with a mathematical theme. I grant that I could make things a little easier if I demanded more from a comic strip before including it here. But even if I think a theme is slight that doesn’t mean the reader does, and it’s easy to let the eye drop to the next paragraph if the reader does think it’s too slight. The anthology nature of these posts is part of what works for them. And then sometimes Comic Strip Master Command sends me a day like last Sunday when everybody was putting in some bit of mathematics. There’ll be another essay on the past week’s strips, never fear. But today’s is just for the single day.

Susan Camilleri Konar’s Six Chix for the 11th illustrates the Lemniscate Family. The lemniscate is a shape well known as the curve made by a bit of water inside a narrow tube by people who’ve confused it with a meniscus. An actual lemniscate is, as the chain of pointing fingers suggests, a figure-eight shape. You get — well, I got — introduced to them in prealgebra. They’re shapes really easy to describe in polar coordinates but a pain to describe in Cartesian coordinates. There are several different kinds of lemniscates, each satisfying slightly different conditions while looking roughly like a figure eight. If you’re open to the two lobes of the shape not being the same size there’s even a kind of famous-ish lemniscate called the analemma. This is the figure traced out by the sun if you look at its position from a set point on the surface of the Earth at the same clock time each day over the course of the year. That the sun moves north and south from the horizon is easy to spot. That it is sometimes east or west of some reference spot is a surprise. It shows the difference between the movement of the mean sun, the sun as we’d see it if the Earth had a perfectly circular orbit, and the messy actual thing. Dr Helmer Aslasken has a fine piece about this, and how it affects when the sun rises earliest and latest in the year.

At a restaurant: 'It was always a challenge serving the lemniscate family'. Nine people each pointing to neighbors and saying 'I'll have what s/he's having', in a sequence that would make a figure-eight as seen from above or below the tables.
Susan Camilleri Konar’s Six Chix for the 11th of February, 2018. It’s not really worse than some of the Carioid Institute dinners.

There’s also a thing called the “polynomial lemniscate”. This is a level curve of a polynomial. That is, what are all the possible values of the independent variable which cause the polynomial to evaluate to some particular number? This is going to be a polynomial in a complex-valued variable, in order to get one or more closed and (often) wriggly loops. A polynomial of a real-valued variable would typically give you a boring shape. There’s a bunch of these polynomial lemniscates that approximate the boundary of the Mandelbrot Set, that fractal that you know from your mathematics friend’s wall in 1992.

Mark Anderson’s Andertoons took care of being Mark Anderson’s Andertoons early in the week. It’s a bit of optimistic blackboard work.

Lincoln Pierce’s Big Nate features the formula for calculating the wind chill factor. Francis reads out what is legitimately the formula for estimating the wind chill temperature. I’m not going to get into whether the wind chill formula makes sense as a concept because I’m not crazy. The thinking behind it is that a windless temperature feels about the same as a different temperature with a particular wind. How one evaluates those equivalences offers a lot of room for debate. The formula as the National Weather Service, and Francis, offer looks frightening, but isn’t really hard. It’s not a polynomial, in terms of temperature and wind speed, but it’s close to that in form. The strip is rerun from the 15th of February, 2009, as Lincoln Pierce has had some not-publicly-revealed problem taking him away from the comic for about a month and a half now.

Jim Scancarelli’s Gasoline Alley included a couple of mathematics formulas, including the famous E = mc2 and the slightly less famous πr2, as part of Walt Wallet’s fantasy of advising scientists and inventors. (Scientists have already heard both.) There’s a curious stray bit in the corner, writing out 6.626 x 102 x 3 that I wonder about. 6.626 is the first couple digits of Planck’s Constant, as measured in Joule-seconds. (This is h, not h-bar, I say for the person about to complain.) It’d be reasonable for Scancarelli to have drawn that out of a physics book or reference page. But the exponent is all wrong, even if you suppose he mis-wrote 1023. It should be 6.626 x 10-34. So I don’t know whether Scancarelli got things very garbled, or if he just picked a nice sciencey-looking number and happened to hit on a significant one. (There’s enough significant science numbers that he’d have a fair chance of finding something.) The strip is a reprint from the 4th of February, 2007, as Jim Scancarelli has been absent for no publicly announced reason for four months now.

Greg Evans and Karen Evans’s Luann is not perfectly clear. But I think it’s presenting Gunther doing mathematics work to support his mother’s contention that he’s smart. There’s no working out what work he’s doing. But then we might ask how smart his mother is to have made that much food for just the two of them. Also that I think he’s eating a potato by hand? … Well, there are a lot of kinds of food that are hard to draw.

Greg Evans’s Luann Againn reprints the strip from the 11th of February (again), 1990. It mentions as one of those fascinating things of arithmetic an easy test to see if a number’s a multiple of nine. There are several tricks like this, although the only ones anybody can remember are finding multiples of 3 and finding multiples of 9. Well, they know the rules for something being a multiple of 2, 5, or 10, but those hardly look like rules, and there’s no addition needed. Similarly with multiples of 4.

Modular arithmetic underlies all these rules. Once you know the trick you can use it to work out your own add-up-the-numbers rules to find what numbers are multiples of small numbers. Here’s an example. Think of a three-digit number. Suppose its first digit is ‘a’, its second digit ‘b’, and its third digit ‘c’. So we’d write the number as ‘abc’, or, 100a + 10b + 1c. What’s this number equal to, modulo 9? Well, 100a modulo 9 has to be equal to whatever a modulo 9 is: (100 a) modulo 9 is (100) modulo 9 — that is, 1 — times (a) modulo 9. 10b modulo 9 is (10) modulo 9 — again, 1 — times (b) modulo 9. 1c modulo 9 is … well, (c) modulo 9. Add that all together and you have a + b + c modulo 9. If a + b + c is some multiple of 9, so must be 100a + 10b + 1c.

The rules about whether something’s divisible by 2 or 5 or 10 are easy to work with since 10 is a multiple of 2, and of 5, and for that matter of 10, so that 100a + 10b + 1c modulo 10 is just c modulo 10. You might want to let this settle. Then, if you like, practice by working out what an add-the-digits rule for multiples of 11 would be. (This is made a lot easier if you remember that 10 is equal to 11 – 1.) And if you want to show off some serious arithmetic skills, try working out an add-the-digits rule for finding whether something’s a multiple of 7. Then you’ll know why nobody has ever used that for any real work.

J C Duffy’s Lug Nuts plays on the equivalence people draw between intelligence and arithmetic ability. Also on the idea that brain size should have something particularly strong link to intelligence. Really anyone having trouble figuring out 15% of $10 is psyching themselves out. They’re too much overwhelmed by the idea of percents being complicated to realize that it’s, well, ten times 15 cents.

Reading the Comics, November 8, 2017: Uses Of Mathematics Edition


Was there an uptick in mathematics-themed comic strips in the syndicated comics this past week? It depends how tight a definition of “theme” you use. I have enough to write about that I’m splitting the week’s load. And I’ve got a follow-up to that Wronski post the other day, so I’m feeling nice and full of content right now. So here goes.

Zach Weinersmith’s Saturday Morning Breakfast Cereal posted the 5th gets my week off to an annoying start. Science and mathematics and engineering people have a tendency to be smug about their subjects. And to see aptitude or interest in their subjects as virtue, or at least intelligence. (If they see a distinction between virtue and intelligence.) To presume that an interest in the field I like is a demonstration of intelligence is a pretty nasty and arrogant move.

And yes, I also dislike the attitude that school should be about training people. Teaching should be about letting people be literate with the great thoughts people have had. Mathematics has a privileged spot here. The field, as we’ve developed it, seems to build on human aptitudes for number and space. It’s easy to find useful sides to it. Doesn’t mean it’s vocational training.

Lincoln Peirce’s Big Nate on the 6th discovered mathematics puzzles. And this gave him the desire to create a new mathematical puzzle that he would use to get rich. Good luck with that. Coming up with interesting enough recreational mathematics puzzles is hard. Presenting it in a way that people will buy is another, possibly greater, challenge. It takes luck and timing and presentation, just as getting a hit song does. Sudoku, for example, spent five years in the Dell Magazine puzzle books before getting a foothold in Japanese newspapers. And then twenty years there before being noticed in the English-speaking puzzle world. Big Nate’s teacher tries to encourage him, although that doesn’t go as Mr Staples might have hoped. (The storyline continues to the 11th. Spoiler: Nate does not invent the next great recreational mathematics puzzle.)

Jef Mallett’s Frazz for the 7th start out in a mathematics class, at least. I suppose the mathematical content doesn’t matter, though. Mallett’s making a point about questions that, I confess, I’m not sure I get. I’ll leave it for wiser heads to understand.

Mike Thompson’s Grand Avenue for the 8th is a subverted word-problem joke. And I suppose a reminder about the need for word problems to parse as things people would do, or might be interested in. I can’t go along with characterizing buying twelve candy bars “gluttonous” though. Not if they’re in a pack of twelve or something like that. I may be unfair to Grand Avenue. Mind, until a few years ago I was large enough my main method of getting around was “being rolled by Oompa-Loompas”, so I could be a poor judge.

Keith Tutt and Daniel Saunders’s Lard’s World Peace Tips for the 8th does a rounding joke. It’s not much, but I’ve included appearances of this joke before and it seems unfair to skip it this time.

Reading the Comics, October 4, 2017: Time-Honored Traditions Edition


It was another busy week in mathematically-themed comic strips last week. Busy enough I’m comfortable rating some as too minor to include. So it’s another week where I post two of these Reading the Comics roundups, which is fine, as I’m still recuperating from the Summer 2017 A To Z project. This first half of the week includes a lot of rerun comics, and you’ll see why my choice of title makes sense.

Lincoln Pierce’s Big Nate: First Class for the 1st of October reprints the strip from the 2nd of October, 1993. It’s got a well-formed story problem that, in the time-honored tradition of this setup, is subverted. I admit I kind of miss the days when exams would have problems typed out in monospace like this.

Ashleigh Brilliant’s Pot-Shots for the 1st is a rerun from sometime in 1975. And it’s an example of the time-honored tradition of specifying how many statistics are made up. Here it comes in at 43 percent of statistics being “totally worthless” and I’m curious how the number attached to this form of joke changes over time.

The Joey Alison Sayers Comic for the 2nd uses a blackboard with mathematics — a bit of algebra and a drawing of a sphere — as the designation for genius. That’s all I have to say about this. I remember being set straight about the difference between ponies and horses and it wasn’t by my sister, who’s got a professional interest in the subject.

Mark Pett’s Lucky Cow rerun for the 2nd is a joke about cashiers trying to work out change. As one of the GoComics.com commenters mentions, the probably best way to do this is to count up from the purchase to the amount you have to give change for. That is, work out $12.43 to $12.50 is seven cents, then from $12.50 to $13.00 is fifty more cents (57 cents total), then from $13.00 to $20.00 is seven dollars ($7.57 total) and then from $20 to $50 is thirty dollars ($37.57 total).

It does make me wonder, though: what did Neil enter as the amount tendered, if it wasn’t $50? Maybe he hit “exact change” or whatever the equivalent was. It’s been a long, long time since I worked a cash register job and while I would occasionally type in the wrong amount of money, the kinds of errors I would make would be easy to correct for. (Entering $30 instead of $20 for the tendered amount, that sort of thing.) But the cash register works however Mark Pett decides it works, so who am I to argue?

Keith Robinson’s Making It rerun for the 2nd includes a fair bit of talk about ratios and percentages, and how to inflate percentages. Also about the underpaying of employees by employers.

Mark Anderson’s Andertoons for the 3rd continues the streak of being Mark Anderson Andertoons for this sort of thing. It has the traditional form of the student explaining why the teacher’s wrong to say the answer was wrong.

Brian Fies’s The Last Mechanical Monster for the 4th includes a bit of legitimate physics in the mad scientist’s captioning. Ballistic arcs are about a thing given an initial speed in a particular direction, moving under constant gravity, without any of the complicating problems of the world involved. No air resistance, no curvature of the Earth, level surfaces to land on, and so on. So, if you start from a given height (‘y0‘) and a given speed (‘v’) at a given angle (‘θ’) when the gravity is a given strength (‘g’), how far will you travel? That’s ‘d’. How long will you travel? That’s ‘t’, as worked out here.

(I should maybe explain the story. The mad scientist here is the one from the first, Fleischer Studios, Superman cartoon. In it the mad scientist sends mechanical monsters out to loot the city’s treasures and whatnot. As the cartoon has passed into the public domain, Brian Fies is telling a story of that mad scientist, finally out of jail, salvaging the one remaining usable robot. Here, training the robot to push aside bank tellers has gone awry. Also, the ground in his lair is not level.)

Tom Toles’s Randolph Itch, 2 am rerun for the 4th uses the time-honored tradition of Albert Einstein needing a bit of help for his work.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 4th uses the time-honored tradition of little bits of physics equations as designation of many deep thoughts. And then it gets into a bit more pure mathematics along the way. It also reflects the time-honored tradition of people who like mathematics and physics supposing that those are the deepest and most important kinds of thoughts to have. But I suppose we all figure the things we do best are the things it’s important to do best. It’s traditional.

And by the way, if you’d like more of these Reading the Comics posts, I put them all in the category ‘Comic Strips’ and I just now learned the theme I use doesn’t show categories for some reason? This is unsettling and unpleasant. Hm.

Reading the Comics, April 18, 2017: Give Me Some Word Problems Edition


I have my reasons for this installment’s title. They involve my deductions from a comic strip. Give me a few paragraphs.

Mark Anderson’s Andertoons for the 16th asks for attention from whatever optician-written blog reads the comics for the eye jokes. And meets both the Venn Diagram and the Mark Anderson’s Andertoons content requirements for this week. Good job! Starts the week off strong.

Lincoln Pierce’s Big Nate: First Class for the 16th, rerunning the strip from 1993, is about impossibly low-probability events. We can read the comic as a joke about extrapolating a sequence from a couple examples. Properly speaking we can’t; any couple of terms can be extended in absolutely any way. But we often suppose a sequence follows some simple pattern, as many real-world things do. I’m going to pretend we can read Jenny’s estimates of the chance she’ll go out with him as at all meaningful. If Jenny’s estimate of the chance she’d go out with Nate rose from one in a trillion to one in a billion over the course of a week, this could be a good thing. If she’s a thousand times more likely each week to date him — if her interest is rising geometrically — this suggests good things for Nate’s ego in three weeks. If she’s only getting 999 trillionths more likely each week — if her interest is rising arithmetically — then Nate has a touch longer to wait before a date becomes likely.

(I forget whether she has agreed to a date in the 24 years since this strip first appeared. He has had some dates with kids in his class, anyway, and some from the next grade too.)

J C Duffy’s Lug Nuts for the 16th is a Pi Day joke that ran late.

Jef Mallett’s Frazz for the 17th starts a little thread about obsolete references in story problems. It’s continued on the 18th. I’m sympathetic in principle to both sides of the story problem debate.

Is the point of the first problem, Farmer Joe’s apples, to see whether a student can do a not-quite-long division? Or is it to see whether the student can extract a price-per-quantity for something, and apply that to find the quantity to fit a given price? If it’s the latter then the numbers don’t make a difference. One would want to avoid marking down a student who knows what to do, and could divide 15 cents by three, but would freeze up if a more plausible price of, say, $2.25 per pound had to be divided by three.

But then the second problem, Mr Schad driving from Belmont to Cadillac, got me wondering. It is about 84 miles between the two Michigan cities (and there is a Reed City along the way). The time it takes to get from one city to another is a fair enough problem. But these numbers don’t make sense. At 55 miles per hour the trip takes an awful 1.5273 hours. Who asks elementary school kids to divide 84 by 55? On purpose? But at the state highway speed limit (for cars) of 70 miles per hour, the travel time is 1.2 hours. 84 divided by 70 is a quite reasonable thing to ask elementary school kids to do.

And then I thought of this: you could say Belmont and Cadillac are about 88 miles apart. Google Maps puts the distance as 86.8 miles, along US 131; but there’s surely some point in the one town that’s exactly 88 miles from some point in the other, just as there’s surely some point exactly 84 miles from some point in the other town. 88 divided by 55 would be another reasonable problem for an elementary school student; 1.6 hours is a reasonable answer. The (let’s call it) 1980s version of the question ought to see the car travel 88 miles at 55 miles per hour. The contemporary version ought to see the car travel 84 miles at 70 miles per hour. No reasonable version would make it 84 miles at 55 miles per hour.

So did Mallett take a story problem that could actually have been on an era-appropriate test and ancient it up?

Before anyone reports me to Comic Strip Master Command let me clarify what I’m wondering about. I don’t care if the details of the joke don’t make perfect sense. They’re jokes, not instruction. All the story problem needs to set up the joke is the obsolete speed limit; everything else is fluff. And I enjoyed working out variation of the problem that did make sense, so I’m happy Mallett gave me that to ponder.

Here’s what I do wonder about. I’m curious if story problems are getting an unfair reputation. I’m not an elementary school teacher, or parent of a kid in school. I would like to know what the story problems look like. Do you, the reader, have recent experience with the stuff farmers, drivers, and people weighing things are doing in these little stories? Are they measuring things that people would plausibly care about today, and using values that make sense for the present day? I’d like to know what the state of story problems is.

Lee: 'I'm developing a new theory about avocado intelligence.' Joules: 'You can't be serious.' Lee: 'Avocado, what is the square root of 8,649?' Avocado: 'That's easy. It's 92?' Lee: 'Wrong. It's 93.' Joules: 'See? It's just a dumb piece of fruit.' Lee: 'I honestly thought I was on to something.'
John Hambrock’s The Brilliant Mind of Edison Lee for the 18th of April, 2017. Before you ask what exactly the old theory of avocado intelligence was remember that Edison Lee’s lab partner there is a talking rat. Just saying.

John Hambrock’s The Brilliant Mind of Edison Lee for the 18th uses mental arithmetic as the gauge of intelligence. Pretty harsly, too. I wouldn’t have known the square root of 8649 off the top of my head either, although it’s easy to tell that 92 can’t be right: the last digit of 92 squared has to be 4. It’s also easy to tell that 92 has to be about right, though, as 90 times 90 will be about 8100. Given this information, if you knew that 8,649 was a perfect square, you’d be hard-pressed to think of a better guess for its value than 93. But since most whole numbers are not perfect squares, “a little over 90” is the best I’d expect to do.

Reading the Comics, July 1, 2012


This will be a hastily-written installment since I married just this weekend and have other things occupying me. But there’s still comics mentioning math subjects so let me summarize them for you. The first since my last collection of these, on the 13th of June, came on the 15th, with Dave Whamond’s Reality Check, which goes into one of the minor linguistic quirks that bothers me: the claim that one can’t give “110 percent,” since 100 percent is all there is. I don’t object to phrases like “110 percent”, though, since it seems to me the baseline, the 100 percent, must be to some standard reference performance. For example, the Space Shuttle Main Engines routinely operated at around 104 percent, not because they were exceeding their theoretical limits, but because the original design thrust was found to be not quite enough, and the engines were redesigned to deliver more thrust, and it would have been far too confusing to rewrite all the documentation so that the new design thrust was the new 100 percent. Instead 100 percent was the design capacity of an engine which never flew but which existed in paper form. So I’m forgiving of “110 percent” constructions, is the important thing to me.

Continue reading “Reading the Comics, July 1, 2012”