I have another Reading the Comics post with a title that’s got nothing to do with the post. It has got something to do with how I spent my weekend. Not sure if I’ll ever get around to explaining that since there’s not much mathematical content to that weekend. I’m not sure whether the nonsense titles are any better than trying to find a theme in what Comic Strip Master Command has sent the past week. It takes time to pick something when anything would do, after all.
Scott Hilburn’s The Argyle Sweater for the 10th is the anthropomorphic numerals strip for the week. Also arithmetic symbols. The ÷ sign is known as “the division symbol”, although now and then people try to promote it as the “obelus”. They’re not wrong to call it that, although they are being the kind of person who tries to call the # sign the “octothorp”. Sometimes social media pass around the false discovery that the ÷ sign is a representation of a fraction, , with the numbers replaced by dots. It’s a good mnemonic for linking fractions and division. But it’s wrong to say that’s what the symbol means. ÷ started being used for division in Western Europe in the mid-17th century, in competition with many symbols, including / (still in common use), : (used in talking about ratios or odds), – (not used in this context anymore, and just confusing if you do try to use it so). And ÷ was used in northern Europe to mean “subtraction” for several centuries after this.
Tom Toles’s Randolph Itch, 2am for the 11th is a repeat; the too-short-lived strip has run through several cycles since I started doing these summaries. But it is also one of the great pie chart jokes ever and I have no intention of not telling people to enjoy it.
Pie charts, and the also-mentioned bar charts, come to us originally from the economist William Playfair, who in the late 1700s and early 1800s devised nearly all the good ways to visualize data. But we know them thanks to Florence Nightingale. Among her other works, she recognized in these charts good ways to represent her studies about Crimean War medicine and about sanitation in India. Nightingale was in 1859 named the first woman in the Royal Statistical Society, and was named an honorary member of the American Statistical Association in 1874.
Olivia Jaimes’s Nancy for the 12th uses arithmetic as iconic for classwork nobody wants to do. Algebra, too; I understand the reluctance to start. Simultaneous solutions; the challenge is to find sets of values ‘x’ and ‘y’ that make both equations true together. That second equation is a good break, though. makes it easy to write what ‘y’ has to be in terms of ‘x’. Then you can replace the ‘y’ in the first equation with its expression in terms of ‘x’. In a slightly tedious moment, it’s going to turn out there’s multiple sets of answers. Four sets, if I haven’t missed something. But they’ll be clearly related to each other. Even attractively arranged.
is an equation that’s true if the numbers ‘x’ and ‘y’ are coordinates of the points on a circle. This is if the coordinates are using the Cartesian coordinate system for the plane, which is such a common thing to do that mathematicians can forget they’re doing that. The circle has radius . So you can look at the first equation and draw a circle and write down a note that its radius is and you’ve got it. looks like an equation that’s true if the numbers ‘x’ and ‘y’ are coordinates of the points on a hyperbola. Again in the Cartesian coordinate system. But I have to feel a little uncomfortable saying this. If the equation were (say) then it’d certainly be a hyperbola, which mostly looks like a mirror-symmetric pair of arcs. But equalling zero? That’s called a “degenerate hyperbola”, which makes it sound like the hyperbola is doing something wrong. Unfortunate word, but one we’re stuck with.
The description just reflects that the hyperbola is boring in some way. In this case, it’s boring because the ‘x’ and ‘y’ that make the equation true are just the points on a pair of straight lines that go through the origin, the point with coordinates (0, 0). And they’re going to be mirror-images of each other around the x- and the y-axis. So it seems like a waste to use the form of a hyperbola when we could do just as well using the forms of straight lines to describe the same points. This hyperbola will look like an X, although it might be a pretty squat ‘x’ or a pretty narrow one or something. Depends on the exact equation.
So. The solutions for ‘x’ and ‘y’ are going to be on the points that are on both a circle centered around the origin and on an X centered around the origin. This is a way to see why I would expect four solutions. Also they they would look about the same. There’d be an answer with positive ‘x’ and positive ‘y’, and then three more answers. One answer has ‘x’ with the same size but a minus sign. One answer has ‘y’ with the same size but a minus sign. One has both ‘x’ and ‘y’ with the same values but minus signs.
Sorry I wasn’t there to partner with.
Dave Coverly’s Speed Bump for the 12th is a Rubik’s Cube joke. Here it merges the idea with the struggles of scheduling anything anymore. I’m not sure that the group-theory operations of lining up a Rubik’s cube can be reinterpreted as the optimization problems of scheduling stuff. But there are all sorts of astounding and surprising links between mathematical problems. So I wouldn’t rule it out.
John Allen’s Nest Heads for the 13th is a lotteries joke. I’m less dogmatic than are many mathematicians about the logic of participating in a lottery. At least in the ones as run by states and regional authorities the chance of a major payout are, yes, millions to one against. There can be jackpots large enough that the expectation value of playing becomes positive. In this case the reward for that unlikely outcome is so vast that it covers the hundreds of millions of times you play and lose. But even then, you have the question of whether doing something that just won’t pay out is worth it. My taste is to say that I shall do much more foolish things with my disposable income than buying a couple tickets each year. And while I would like to win the half-billion-dollar jackpot that would resolve all my financial woes and allow me to crush those who had me imprisoned in the Château d’If, I’d also be coming out ahead if I won, like, one of the petty $10,000 prizes.