Reading the Comics, November 20, 2018: What Mathematics Is For Edition


The first half of last week’s comics offered another bunch of chances to think about what mathematics is for. Before I do get into all that, though, may I mention the most recent update of Gregory Taylor’s serial:

It does conclude with a vote about the next direction to take. So it’s a good chance for people who like to see authors twisting to their audience’s demands.

Mort Walker and Dik Browne’s Hi and Lois for the 23rd of May, 1961 builds off a major use of arithmetic. Budgeting doesn’t get much attention from mathematicians. I suppose it seems to us like all the basic problems are solved: adding? Subtracting? Multiplication? All familiar things. Especially now with decimal currency. There are great unsolved problems in mathematics, but they get into specialized areas of financial mathematics and just don’t matter for ordinary household budgeting.

Lois: 'How much is 7 plus 19, Hi?' Hi: 'Golly! Don't you know how to add?' Lois: 'I guess I've forgotten.' (She's holding up a book marked Home Budget.) 'All I usually get to do is subtract.'
Mort Walker and Dik Browne’s Hi and Lois for the 23rd of May, 1961 and rerun the 19th of November, 2018. Essays that mention topics raised by Hi and Lois, both current-run and vintage, should be at this link.

Hi comes across a bit harsh here. I’m going to suppose he was taken so by surprise by Lois’s problem that he spoke without thinking.

Scott Hilburn’s The Argyle Sweater for the 19th is the anthropomorphic numerals strip for the week. With the title of “improper fractions” it’s wordplay on the common meaning for a mathematical term. Two times over, come to it. That negative refers to a class of numbers as well as disapproval of something is ordinary enough. I’ve mentioned it, I estimate, 840 times this month alone.

Caption: Improper Fractions. An anthropomorphic -5, teacher, dragging a 3/2: 'After I wash your mouth out, you're going down to the principal's office!' 3/2: 'Don't be so negative!'
Scott Hilburn’s The Argyle Sweater for the 19th of November, 2018. The many essays with mention of The Argyle Sweater will be at this link.

Jokes about the technical and common meanings of “improper” are rarer. In a proper fraction, the numerator is a smaller number than the denominator. In an improper fraction, we don’t count on that. I remember a modest bit of time in elementary and middle school working on converting improper fractions into mixed fractions — a whole number plus a proper fraction. And also don’t remember anyone caring about that after calculus. In most arithmetic work, there’s not much that’s easier about “1 + 1/2” than about “3/2”. The one major convenience “1 + 1/2” has is that it’s easy to tell at a glance how big the number is. It’s not mysterious how big a number 3/2 is, but that’s because of long familiarity. If I asked you whether 54/17 or 46/13 was the larger number, you’d be fairly stumped and maybe cranky. So there’s not much reason to worry about improper fractions while you’re doing work. For the final presentation of an answer, proper or mixed fractions may well be better.

Whoever colored that minus symbol before the 5 screwed up and confused the joke. Syndicated cartoonists give precise coloring instructions for Sunday strips. But many of them don’t, or aren’t able to, give coloring instructions for weekday strips like this. And mistakes like that are the unfortunate result.

A sign at the split in the road reads, 'Diversion'. It's a large sudoku, with stopped cars and people gathered around.
Pascal Wyse and Joe Berger’s Berger and Wyse for the 19th of November, 2018. Essays that bring up topics raised by Berger and Wyse will be this link.. It’s a new tag, though.

Pascal Wyse and Joe Berger’s Berger and Wyse for the 19th features a sudoku appearance. It’s labelled a diversion, and so it is, as many mathematics and logic puzzles will be. The lone commenter at GoComics claims to have solved the puzzle, so I will suppose they’re being honest about this.

Mom in Mathematic Land: 'One dimension, line A is 2 times as long as line B. Two dimensions: area varies with the square of length. The area of square A is 4 times that of square B. Three dimensions: Volume varies with the cube of length. Cube A has volume 8 times that of cube B. So when you see that two months of hard-fought chemotherapy and radiation have transformed THIS ... into THIS ... your crushing disappointment only betrays your mathematical ignorance.'
Brian Fies’s Mom’s Cancer for the 19th of November, 2018. The handful of essays inspired by Mom’s Cancer are at this link.

Brian Fies’s Mom’s Cancer for the 19th I have mentioned before, although not since I started including images for all mentioned comics. It’s set a moment when treatment for Mom’s cancer has been declared a great success.

The trouble is, as Feis lays out, volume is three-dimensional. We are pretty good at measuring the length, or at least the greatest width of something. You might call that the “characteristic length”. A linear dimension. But volume scales as the cube of this characteristic length. And the sad thing is that 0.8 times 0.8 times 0.8 is, roughly, 0.5. This means that the characteristic length dropping by 20% drops the volume by 50%. Or, as Feis is disappointed to see in this strip and its successor, the great news of a 50% reduction in the turmor’s mass is that it’s just 20% less big in every direction. It doesn’t look like enough.

One of Fi's audience: 'Why do I need to learn math? In the computer age, I just have to know ones and zeroes.' (Fi fumes, smoke steaming from her ears.) At the office Dethany reports: 'Fi texts 'every time I consider giving up these math seminars, I'm reminded why I can't'.'
Bill Holbrook’s On The Fastrack for the 20th of November, 2018. This and other essays inspired by On The Fastrack are at this link.

Bill Holbrook’s On The Fastrack for the 20th presents one of Fi’s seminars about why mathematics is a good thing. The offscreen student’s question about why one should learn mathematics goes unanswered. As often happens the question is presented as though it’s too absurd to deserve answering. The questioner is conflating “mathematics” with “calculating arithmetic”, yes. And a computer will be better at these calculations. A related question, sometimes asked (and rarely on-topic for my essays here), is why one needs to learn any specific facts when a computer is so much better at finding them.

Knowing facts is not understanding them, no. But it is hard to understand a thing without knowing facts. More, without loving the knowing of facts. If we don’t need to be good at calculating, we do still need to know what to have calculated. And why to calculate that instead of something else. In calculating we can learn things of great beauty. And some of us do go on to mathematics which cannot be calculated. There is software that will do very well at computing, say, the indefinite integral of functions. I don’t know of any that will even start on a problem like “find the kernel of this ring”. But these are problems we see, and think interesting, because our experience in arithmetic trains us to notice them. Perhaps there is new interesting mathematics that we would notice if we didn’t have preconceptions set by times tables and long division. But it is hard to believe that we can’t find it because we’re not ignorant enough. I wouldn’t risk it.


This and more Reading the Comics posts should all be at this link.

And for the rest of the calendar year my Fall 2018 Mathematics A To Z should continue posting new essays. I’m still looking for topics for the last half-dozen letters of the alphabet. Give your mathematics term a try.

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Reading the Comics, September 4, 2018: No Henry This Week Edition


There won’t be, this week, any mathematically-themed comic strips featuring the long-running, Carl Anderson-created character Henry. You’ll come to see why I find this worth mentioning soon enough. Not today.

Hart, Mastroianni, and Parker’s Wizard of Id for the 2nd features the blackboard full of symbols to represent the difficult and unsolved problem. And sometimes it does seem like it takes magic to solve an equation. That magic usually takes the form of a transformation. That is, we find a way to rewrite the problem as something different, and find that this different problem is solvable. And then that the solution to this altered problem can be transformed into a solution of the original. This is normal magic, the kind any trained mathematician can do, if haltingly. But sometimes it’ll be just a stroke of imaginative genius, solving a problem that seems at first to have nothing to do with the original. This is genius work, and we all hope we can find a problem on which we can do that.

Establishing shot: SECRET LAB. Wizard, to lab guy: 'I feel like you could do without the sign.' (That closes the throwaway top row.) (Main strip, now.) Secret Lab Guy: 'We are never going to solve this equation.' Wizard: 'I got this.' He casts a spell that sprays a whirlwind of colors and shapes that splash into the board, revealing 'x = 27'. Guy: 'That's not even close to the right answer.' Wizard: 'True, but those graphics were pretty cool, yeah?'
Hart, Mastroianni, and Parker’s Wizard of Id for the 2nd of September, 2018. Also I like the throwaway gag on the top row. Feels like it could be a minor beat in a spy comedy not quite as good as Get Smart, but trying.

I can also take the strip to represent one of those things I’m curmudgeonly about. That is that I tend to look at big special-effects-laden attempts to make mathematics look beautiful as … well, they’re nice. But I don’t think they help anyone learn how to do anything. So that the Wizard’s work doesn’t actually solve the problem feels true to me.

Tiger: 'We studied times tables today.' Punkinhead: 'Okay, so what's six times two?' Tiger: 'I said we studied it --- not learned it.'
Bud Blake’s Tiger rerun for the 3rd of September, 2018. I have no information about when it originally ran.

Bud Blake’s Tiger rerun for the 3rd is an exclusive peek into my experience every time I decide to finally learn non-Euclidean geometry properly.

Chip: 'I hate arithmetic.' Hi; 'That's not the right attitude. Think of arithmetic as a puzzle. If I ask you, 'what's 246 divided by 3?' it's just like asking you the riddle, 'what has four wheels and flies?'.' Chip: 'Except that 82 isn't as funny an answer.'
Mort Walker and Dik Browne’s Hi and Lois for the 3rd of September, 2018. It originally ran the 8th of March, 1961.

Mort Walker and Dik Browne’s vintage Hi and Lois for the 3rd sees Chip struggling with mathematics. His father has a noble idea, that it’ll be easier if he tries to see the problems as fun puzzles. Maybe so, but I agree with Chip: there’s not a punch line to 246 ÷ 3. Also, points to Chip for doing that division right away. Clearly he isn’t bad at arithmetic; he just doesn’t like it. We’ve all got things like that.

Baldo: 'How'd you do on your algebra quiz?' Cruz: 'I got nine wrong. ... Or maybe it was 19.' Baldo: 'So numbers are not your strength.' Cruz: '10 ... it was 10.'
Hector D Cantu and Carlos Castellanos’s Baldo for the 4th of September, 2018. How … how many questions was the quiz? I guess at least 19 questions but that’s breaching the walls between “quiz” and “endurance marathon”.

Hector D Cantu and Carlos Castellanos’s Baldo for the 4th is a joke about being helpless with numbers. … Actually, from the phrasing, I’m not positive that Cruz doesn’t mean he got question number 9, or maybe 19, or maybe number 10 wrong. It’s a bit sloppy to not remember which question was, but I certainly know the pain of remembering having done a problem wrong.


My other Reading the Comics posts should appear at this link. Other essays with The Wizard of Id are at this link. More essays with Tiger are at this link. Both current-run and vintage-run Hi and Lois strips are in essays on this link. And Baldo comics should be at this link.

Reading the Comics, May 5, 2018: Does Anyone Know Where The Infinite Hotel Comes From Edition


With a light load of mathematically-themed comic strips I’m going to have to think of things to write about twice this coming week. Fortunately, I have plans. We’ll see how that works out for me. So far this year I’m running about one-for-eight on my plans.

Mort Walker and Dik Browne’s Hi and Lois for the 1st of November, 1960 looks pretty familiar somehow. Having noticed what might be the first appearance of “the answer is twelve?” in Peanuts I’m curious why Chip started out by guessing twelve. Probably just coincidence. Possibly that twelve is just big enough to sound mathematical without being conspicuously funny, like 23 or 37 or 42 might be. I’m a bit curious that after the first guess Sally looked for smaller numbers than twelve, while Chip (mostly) looked for larger ones. And I see a logic in going from a first guess of 12 to a second guess of either 4 or 144. The 32 is a weird one.

Teacher: 'Chip, do you know the answer to number five?' Chip: 'Is it twelve? No, wait ... it's four. Or is it 32 ... it's either that or 144. No, wait a second ... I'll get it.' Teacher: 'I'm sure you will --- we're nearly out of numbers!'
Mort Walker and Dik Browne’s Hi and Lois for the 1st of November, 1960 and reprinted the 30th of April, 2018. Yeah, sure, eleven years later Charles Schulz would do basically the same joke. But comics snarkers get all smug when they notice that The Argyle Sweater is using the same premise as a Far Side from 1983 or something.

Tom Toles’s Randolph Itch, 2 am for the 30th of April, 2018 is on at least its third appearance around here. I suppose I have to retire the strip from consideration for these comics roundups. It didn’t run that long, sad to say, and I think I’ve featured all its mathematical strips. I’ll go on reading, though, as I like the style and Toles’s sense of humor.

Randolph, thinking in bed: 'Algebra pretty much put pirates out of business.' Pirate teacher: 'If ax^2 + bx + c = 0, what is x?' And a pirate sweats. Footer joke: '15 men on a dead man's chest, you ho ho, and a bottle of rum equals what?'
Tom Toles’s Randolph Itch, 2 am for the 30th of April, 2018. I think I’ve mentioned not knowing whether the legendary X on pirate maps is related to the use of X as the thing-to-be-found in algebra. My understanding is the X on a pirate map thing is mostly a matter of storytelling rather than something anyone really did.

Mark Tatulli’s Heart of the City for the 3rd of May is a riff on the motivation problem. For once, not about the motivation of the people in story problems to do what they do. It’s instead about why the student should care what the story people do. And, fair enough, really. It’s easy to calculate something you’d like to know the answer to. But give the teacher or textbook writer a break. There’s nothing that’s interesting to everybody. No, not even what minimum grade they need on this exam to get an A in the course. After a moment of clarity in fifth grade I never cared what my scores were. I just did my work and accepted the assessment. My choice not to worry about my grades had more good than bad results, but I admit, there were bad results too.

Heart: 'This homework is ridiculous! How are we supposed to know this? OK, so Julio has eleven apples! Why is it any of my business how many he shares with Allisa and Wesley? Why should I care how he divides them or what fraction he keeps for himself?' Dean: 'They're just math word problems. I don't think we have to explain motivation.' Heart: 'I guess I just can't get past why exactly a kid has eleven apples in the first place!'
Mark Tatulli’s Heart of the City for the 3rd of May, 2018. How does Heart know that Julio is a kid? Adults will go out and buy a dozen apples without that seeming strange, and we’ll eat as many as four of them before forgetting they’re on the counter and letting them rot by accident.

John McNamee’s Pie Comic for the 4th of May riffs on some ancient story-problems built on infinite sets. I don’t know the original source. I assume a Martin Gardiner pop-mathematics essay. I don’t know, though, and I’m curious if anyone does know.

[ You arrive at the Infinite Hotel ... but the concierge says *all* infinity of their rooms are booked. Luckily, you know MATH. 'Infinity = Infinity + 1'. You explain that if you just ask each guest to move one room over ... ] There's a large man in diapers with a sock puppet on his hand in the first door. [ Yeah ... math's not solving that. ] You drive away.
John McNamee’s Pie Comic for the 4th of May, 2018. Also you know how long it’d take to re-code everybody’s door access card? It’d be like forever.

Often I see these kinds of problem as set at the Hilbert Hotel. This references David Hilbert, the late-19th/early-20th century mastermind behind the 20th century’s mathematics field. They try to challenge people’s intuitions about infinitely large sets. Ponder a hotel with one room for each of the counting numbers. Suppose it’s full. How many guests can you add to it? Can you add infinitely many more guests, and still have room for them all? If you do it right, and if “infinitely many more guests” means something particular, yes. If certain practical points don’t get in the way. I mean practical for a hotel with infinitely many rooms.

This is a new-tag comic.

Medieval monks, talking about the one who's written down E = mc^2. 'God only knows what it means. This guy isn't all that swift.'
Dave Whamond’s Reality Check for the 4th of May, 2018. Yeah, I heard the sequel to A Canticle for Leibowitz was disappointing.

Dave Whamond’s Reality Check for the 4th is a riff on Albert Einstein’s best-known equation. He had some other work, granted. But who didn’t?

Reading the Comics, February 7, 2018: Not Taking Algebra Too Seriously Edition


There were nearly a dozen mathematically-themed comic strips among what I’d read, and they almost but not quite split mid-week. Better, they include one of my favorite ever mathematics strips from Charles Schulz’s Peanuts.

Jimmy Halto’s Little Iodine for the 4th of December, 1956 was rerun the 2nd of February. Little Iodine seeks out help with what seems to be story problems. The rate problem — “if it takes one man two hours to plow seven acros, how long will it take five men and a horse to … ” — is a kind I remember being particularly baffling. I think it’s the presence of three numbers at once. It seems easy to go from, say, “if you go two miles in ten minutes, how long will it take to go six miles?” to an answer. To go from “if one person working two hours plows seven acres then how long will five men take to clear fourteen acres” to an answer seems like a different kind of problem altogether. It’s a kind of problem for which it’s even wiser than usual to carefully list everything you need.

Iodone, going into a department store. 'Boy, we got tough homework for tomorrow.' At Information: 'If it takes one man two hours to plow seven acres, how long will it take five men and a horse to --- etc' Clerk: 'Wha? Uh ... let me get a pencil. Will you repeat that, please? ... Cipher ... two o carry ... mmm ... times x ... minus ... mmm ... now let me think ... ' NEXT DAY; Teacher: 'Sharkey Shannon, 92, very good, Sharkey. Shalimar Shultz, 94, excellent, Shalimar. Iodine Tremblechin ... zero ... every problem wrong! Iodine ... I just can't understand it ... not one single answer correct!' Iodine, at the Complaint Department: 'Somebody in this store has to write a hundred times 'I will henceforth study harder'!
Jimmy Halto’s Little Iodine for the 2nd of December, 1956 and rerun the 4th of February, 2018. It’s the rare Little Iodine where she doesn’t get her father fired!

Kieran Meehan’s Pros and Cons for the 5th uses a bit of arithmetic. It looks as if it’s meant to be a reminder about following the conclusions of one’s deductive logic. It’s more common to use 1 + 1 equalling 2, or 2 + 2 equalling 4. Maybe 2 times 2 being 4. But then it takes a little turn into numerology, trying to read more meaning into numbers than is wise. (I understand why people should use numerological reasoning, especially given how much mathematicians like to talk up mathematics as descriptions of reality and how older numeral systems used letters to represent words. And that before you consider how many numbers have connotations.)

Judge: 'Members of the jury, before retiring to consider your verdict, I shall give you my summing-up. 3 + 3 = 6. There are six letters in the word 'guilty'. Coincidence? I don't believe in coincidences.'
Kieran Meehan’s Pros and Cons for the 5th of February, 2018. I grant the art is a bit less sophisticated than in Little Iodine. But the choice of two features to run outside the panels and into the white gutters is an interesting one and I’m not sure what Meehan is going for in choosing one word balloon and the judge’s hand to run into the space like that.

Charles Schulz’s Peanuts for the 5th of February reruns the strip from the 8th of February, 1971. And it is some of the best advice about finding the values of x and y, and about approaching algebra, that I have ever encountered.

Trixie: 'Look at all the birds!! I wonder how many there are! Sic, nine, five, 'leven, eight, fwee, two! Only two! It sure looked like there were more!'
Mort Walker and Dik Browne’s Hi and Lois for the 10th of August, 1960 was rerun the 6th of February, 2018. And I do like Trixie’s look of bafflement in the last panel there; it’s more expressive than seems usual for the comic even in its 1960s design.

Mort Walker and Dik Browne’s Hi and Lois for the 10th of August, 1960 was rerun the 6th of February. It’s a counting joke. Babies do have some number sense. At least babies as old as Trixie do, I believe, in that they’re able to detect that something weird is going on when they’re shown, eg, two balls put into a box and four balls coming out. (Also it turns out that stage magicians get called in to help psychologists study just how infants and toddlers understand the world, which is neat.)

John Zakour and Scott Roberts’s Maria’s Day for the 7th is Ms Payne’s disappointed attempt at motivating mathematics. I imagine she’d try going on if it weren’t a comic strip limited to two panels.

Reading the Comics, August 9, 2017: Pets Doing Mathematics Edition


I had just enough comic strips to split this week’s mathematics comics review into two pieces. I like that. It feels so much to me like I have better readership when I have many days in a row with posting something, however slight. The A to Z is good for three days a week, and if comic strips can fill two of those other days then I get to enjoy a lot of regular publication days. … Though last week I accidentally set the Sunday comics post to appear on Monday, just before the A To Z post. I’m curious how that affected my readers. That nobody said anything is ominous.

Border collies are, as we know, highly intelligent. (Looking over a chalkboard diagramming 'fetch', with symbols.) 'There MUST be some point to it, but I guess we don't have the mathematical tools to crack it at the moment.'
Niklas Eriksson’s Carpe Diem for the 7th of August, 2017. I have to agree the border collies haven’t worked out the point of fetch. I also question whether they’ve worked out the simple ballistics of the tossed stick. If the variables mean what they suggest they mean, then dimensional analysis suggests they’ve got at least three fiascos going on here. Maybe they have an idiosyncratic use for variables like ‘v’.

Niklas Eriksson’s Carpe Diem for the 7th of August uses mathematics as the signifier for intelligence. I’m intrigued by how the joke goes a little different: while the border collies can work out the mechanics of a tossed stick, they haven’t figured out what the point of fetch is. But working out people’s motivations gets into realms of psychology and sociology and economics. There the mathematics might not be harder, but knowing that one is calculating a relevant thing is. (Eriksson’s making a running theme of the intelligence of border collies.)

Nicole Hollander’s Sylvia rerun for the 7th tosses off a mention that “we’re the first generation of girls who do math”. And that therefore there will be a cornucopia of new opportunities and good things to come to them. There’s a bunch of social commentary in there. One is the assumption that mathematics skill is a liberating thing. Perhaps it is the gloom of the times but I doubt that an oppressed group developing skills causes them to be esteemed. It seems more likely to me to make the skills become devalued. Social justice isn’t a matter of good exam grades.

Then, too, it’s not as though women haven’t done mathematics since forever. Every mathematics department on a college campus has some faded posters about Emmy Noether and Sofia Kovalevskaya and maybe Sophie Germaine. Probably high school mathematics rooms too. Again perhaps it’s the gloom of the times. But I keep coming back to the goddess’s cynical dismissal of all this young hope.

Mort Walker and Dik Browne’s Hi and Lois for the 10th of February, 1960 and rerun the 8th portrays arithmetic as a grand-strategic imperative. Well, it means education as a strategic imperative. But arithmetic is the thing Dot uses. I imagine because it is so easy to teach as a series of trivia and quiz about. And it fits in a single panel with room to spare.

Dot: 'Now try it again: two and two is four.' Trixie: 'Fwee!' Dot: 'You're not TRYING! Do you want the Russians to get AHEAD of US!?' Trixie looks back and thinks: 'I didn't even know there was anyone back there!'
Mort Walker and Dik Browne’s Hi and Lois for the 10th of February, 1960 and rerun the 8th of August, 2017. Remember: you’re only young once, but you can be geopolitically naive forever!

Paul Trap’s Thatababy for the 8th is not quite the anthropomorphic-numerals joke of the week. It circles around that territory, though, giving a couple of odd numbers some personality.

Brian Anderson’s Dog Eat Doug for the 9th finally justifies my title for this essay, as cats ponder mathematics. Well, they ponder quantum mechanics. But it’s nearly impossible to have a serious thought about that without pondering its mathematics. This doesn’t mean calculation, mind you. It does mean understanding what kinds of functions have physical importance. And what kinds of things one can do to functions. Understand them and you can discuss quantum mechanics without being mathematically stupid. And there’s enough ways to be stupid about quantum mechanics that any you can cut down is progress.

Reading the Comics, January 21, 2017: Homework Edition


Now to close out what Comic Strip Master Command sent my way through last Saturday. And I’m glad I’ve shifted to a regular schedule for these. They ordered a mass of comics with mathematical themes for Sunday and Monday this current week.

Karen Montague-Reyes’s Clear Blue Water rerun for the 17th describes trick-or-treating as “logarithmic”. The intention is to say that the difficulty in wrangling kids from house to house grows incredibly fast as the number of kids increases. Fair enough, but should it be “logarithmic” or “exponential”? Because the logarithm grows slowly as the number you take the logarithm of grows. It grows all the slower the bigger the number gets. The exponential of a number, though, that grows faster and faster still as the number underlying it grows. So is this mistaken?

I say no. It depends what the logarithm is, and is of. If the number of kids is the logarithm of the difficulty of hauling them around, then the intent and the mathematics are in perfect alignment. Five kids are (let’s say) ten times harder to deal with than four kids. Sensible and, from what I can tell of packs of kids, correct.

'Anne has six nickels. Sue has 41 pennies. Who has more money?' 'That's not going to be easy to figure out. It all depends on how they're dressed!'
Rick Detorie’s One Big Happy for the 17th of January, 2017. The section was about how the appearance and trappings of wealth matter for more than the actual substance of wealth so everyone’s really up to speed in the course.

Rick Detorie’s One Big Happy for the 17th is a resisting-the-word-problem joke. There’s probably some warning that could be drawn about this in how to write story problems. It’s hard to foresee all the reasonable confounding factors that might get a student to the wrong answer, or to see a problem that isn’t meant to be there.

Bill Holbrook’s On The Fastrack for the 19th continues Fi’s story of considering leaving Fastrack Inc, and finding a non-competition clause that’s of appropriate comical absurdity. As an auditor there’s not even a chance Fi could do without numbers. Were she a pure mathematician … yeah, no. There’s fields of mathematics in which numbers aren’t all that important. But we never do without them entirely. Even if we exclude cases where a number is just used as an index, for which Roman numerals would be almost as good as regular numerals. If nothing else numbers would keep sneaking in by way of polynomials.

'Uh, Fi? Have you looked at the non-compete clause in your contract?' 'I wouldn't go to one of Fastrack's competitors.' 'No, but, um ... you'd better read this.' 'I COULDN'T USE NUMBERS FOR TWO YEARS???' 'Roman numerals would be okay.'
Bill Holbrook’s On The Fastrack for the 19th of January, 2017. I feel like someone could write a convoluted story that lets someone do mathematics while avoiding any actual use of any numbers, and that it would probably be Greg Egan who did it.

Dave Whamond’s Reality Check for the 19th breaks our long dry spell without pie chart jokes.

Mort Walker and Dik Browne’s Vintage Hi and Lois for the 27th of July, 1959 uses calculus as stand-in for what college is all about. Lois’s particular example is about a second derivative. Suppose we have a function named ‘y’ and that depends on a variable named ‘x’. Probably it’s a function with domain and range both real numbers. If complex numbers were involved then the variable would more likely be called ‘z’. The first derivative of a function is about how fast its values change with small changes in the variable. The second derivative is about how fast the values of the first derivative change with small changes in the variable.

'I hope our kids are smart enough to win scholarships for college.' 'We can't count on that. We'll just have to save the money!' 'Do you know it costs about $10,000 to send one child through college?!' 'That's $40,000 we'd have to save!' Lois reads to the kids: (d^2/dx^2)y = 6x - 2.
Mort Walker and Dik Browne’s Vintage Hi and Lois for the 27th of July, 1959. Fortunately Lois discovered the other way to avoid college costs: simply freeze the ages of your children where they are now, so they never face student loans. It’s an appealing plan until you imagine being Trixie.

The ‘d’ in this equation is more of an instruction than it is a number, which is why it’s a mistake to just divide those out. Instead of writing it as \frac{d^2 y}{dx^2} it’s permitted, and common, to write it as \frac{d^2}{dx^2} y . This means the same thing. I like that because, to me at least, it more clearly suggests “do this thing (take the second derivative) to the function we call ‘y’.” That’s a matter of style and what the author thinks needs emphasis.

There are infinitely many possible functions y that would make the equation \frac{d^2 y}{dx^2} = 6x - 2 true. They all belong to one family, though. They all look like y(x) = \frac{1}{6} 6 x^3 - \frac{1}{2} 2 x^2 + C x + D , where ‘C’ and ‘D’ are some fixed numbers. There’s no way to know, from what Lois has given, what those numbers should be. It might be that the context of the problem gives information to use to say what those numbers should be. It might be that the problem doesn’t care what those numbers should be. Impossible to say without the context.