Three of the strips I have for this installment feature kids around mathematics talk. That’s enough for a theme name.
Gary Delainey and Gerry Rasmussen’s Betty for the 23rd is a strip about luck. It’s easy to form the superstitious view that you have a finite amount of luck, or that you have good and bad lucks which offset each other. It feels like it. If you haven’t felt like it, then consider that time you got an unexpected $200, hours before your car’s alternator died.
If events are independent, though, that’s just not so. Whether you win $600 in the lottery this week has no effect on whether you win any next week. Similarly whether you’re struck by lightning should have no effect on whether you’re struck again.
Except that this assumes independence. Even defines independence. This is obvious when you consider that, having won $600, it’s easier to buy an extra twenty dollars in lottery tickets and that does increase your (tiny) chance of winning again. If you’re struck by lightning, perhaps it’s because you tend to be someplace that’s often struck by lightning. Probability is a subtler topic than everyone acknowledges, even when they remember that it is such a subtle topic.
Darrin Bell’s Candorville for the 23rd jokes about the uselessness of arithmetic in modern society. I’m a bit surprised at Lemont’s glee in not having to work out tips by hand. The character’s usually a bit of a science nerd. But liking science is different from enjoying doing arithmetic. And bad experiences learning mathematics can sour someone on the subject for life. (Which is true of every subject. Compare the number of people who come out of gym class enjoying physical fitness.)
If you need some Internet Old, read the comments at GoComics, which include people offering dire warnings about what you need in case your machine gives the wrong answer. Which is technically true, but for this application? Getting the wrong answer is not an immediately awful affair. Also a lot of cranky complaining about tipping having risen to 20% just because the United States continues its economic punishment of working peoples.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 25th is some wordplay. Mathematicians often need to find minimums of things. Or maximums of things. Being able to do one lets you do the other, as you’d expect. If you didn’t expect, think about it a moment, and then you expect it. So min and max are often grouped together.
Paul Trap’s Thatababy for the 26th is circling around wordplay, turning some common shape names into pictures. This strip might be aimed at mathematics teachers’ doors. I’d certainly accept these as jokes that help someone learn their shapes.
Since I took the Pi Day comics ahead of their normal sequence on Sunday, it’s time I got back to the rest of the week. There weren’t any mathematically-themed comics worth mentioning from last Friday or Saturday, so I’m spending the latter part of this week covering stuff published before Pi Day. It’s got me slightly out of joint. It’ll all be better soon.
Mark Anderson’s Andertoons for the 11th is the Mark Anderson’s Andertoons for this week. That’s nice to have. It’s built on the concept of story problems. That there should be “stories” behind a problem makes sense. Most actual mathematics, even among mathematicians, is done because we want to know a thing. Acting on a want is a story. Wanting to know a thing justifies the work of doing this calculation. And real mathematics work involves looking at some thing, full of the messiness of the real world, and extracting from it mathematics. This would be the question to solve, the operations to do, the numbers (or shapes or connections or whatever) to use. We surely learn how to do that by doing simple examples. The kid — not Wavehead, for a change — points out a common problem here. There’s often not much of a story to a story problem. That is, where we don’t just want something, but someone else wants something too.
Parker and Hart’s The Wizard of Id for the 11th is a riff on the “when do you use algebra in real life” snark. Well, no one disputes that there are fields which depend on advanced mathematics. The snark comes in from supposing that a thing is worth learning only if it’s regularly “useful”.
Rick Detorie’s One Big Happy for the 12th has Joe stalling class to speak to “the guy who invented zero”. I really like this strip since it’s one of those cute little wordplay jokes that also raises a legitimate point. Zero is this fantastic idea and it’s hard to imagine mathematics as we know it without the concept. Of course, we could say the same thing about trying to do mathematics without the concept of, say, “twelve”.
We don’t know who’s “the guy” who invented zero. It’s probably not all a single person, though, or even a single group of people. There are several threads of thought which merged together to zero. One is the notion of emptiness, the absense of a measurable thing. That probably occurred to whoever was the first person to notice a thing wasn’t where it was expected. Another part is the notion of zero as a number, something you could add to or subtract from a conventional number. That is, there’s this concept of “having nothing”, yes. But can you add “nothing” to a pile of things? And represent that using the addition we do with numbers? Sure, but that’s because we’re so comfortable with the idea of zero that we don’t ponder whether “2 + 1” and “2 + 0” are expressing similar ideas. You’ll occasionally see people asking web forums whether zero is really a number, often without getting much sympathy for their confusion. I admit I have to think hard to not let long reflex stop me wondering what I mean by a number and why zero should be one.
And then there’s zero, the symbol. As in having a representation, almost always a circle, to mean “there is a zero here”. We don’t know who wrote the first of that. The oldest instance of it that we know of dates to the year 683, and was written in what’s now Cambodia. It’s in a stone carving that seems to be some kind of bill of sale. I’m not aware whether there’s any indication from that who the zero was written for, or who wrote it, though. And there’s no reason to think that’s the first time zero was represented with a symbol. It’s the earliest we know about.
Darrin Bell’s Candorville for the 12th has some talk about numbers, and favorite numbers. Lemont claims to have had 8 as his favorite number because its shape, rotated, is that of the infinity symbol. C-Dog disputes Lemont’s recollection of his motives. Which is fair enough; it’s hard to remember what motivated you that long ago. What people mostly do is think of a reason that they, today, would have done that, in the past.
The ∞ symbol as we know it is credited to John Wallis, one of that bunch of 17th-century English mathematicians. He did a good bit of substantial work, in fields like conic sections and physics and whatnot. But he was also one of those people good at coming up with notation. He developed what’s now the standard notation for raising a number to a power, that stuff, and showed how to define raising a number to a rational-number power. Bunch of other things. He also seems to be the person who gave the name “continued fraction” to that concept.
Wallis never explained why he picked ∞ as a shape, of all the symbols one could draw, for this concept. There’s speculation he might have been varying the Roman numeral for 1,000, which we’ve simplified to M but which had been rendered as (|) or () and I can see that. (Well, really more of a C and a mirror-reflected C rather than parentheses, but I don’t have the typesetting skills to render that.) Conflating “a thousand” with “many” or “infinitely many” has a good heritage. We do the same thing when we talk about something having millions of parts or costing trillions of dollars or such. But, Wallis never explained (so far as we’re aware), so all this has to be considered speculation and maybe mnemonic helps to remembering the symbol.
Terry LaBan and Patty LaBan’s Edge City for the 12th is another story problem joke. Curiously the joke seems to be simply that the father gets confused following the convolutions of the story. The specific story problem circles around the “participation awards are the WORST” attitude that newspaper comics are surprisingly prone to. I think the LaBans just wanted the story problem to be long and seem tedious enough that our eyes glazed over. Anyway you could not pay me to read whatever the comments on this comic are. Sorry not sorry.
For the second part of last week’s comics, there’s several strips whose authors prefer to use a single name. I’m relieved. Somehow my writing seems easier when I don’t have a long authorial credit to give. I can take writing “Zach Weinersmith” fourteen times a week. It’s all those appearances of, like, “Corey Pandolph and Phil Frank and Joe Troise” (The Elderberries) that slow me way up.
Darrin Bell’s Candorville for the 4th shows off one of the things statistics can do. Tracking some measurable thing lets one notice patterns. These patterns might signify something important. At the least they can suggest things that deserve more scrutiny. There’s dangers, of course. If you’re measuring something that’s rare, or that naturally fluctuates a lot, you might misinterpret changes. You could suppose the changes represent some big, complicated, and invariably scary pattern that isn’t actually there. You can take steps to avoid how much weight you give to little changes. For example, you could look at running averages. Instead of worrying about how often Lemont has asked for his clippers this year versus last, look at how often he’s asked for it, on average, each of the last three years, compared to the average of the three years before that. Changes in that are more likely to be meaningful. But doing this does mean that a sudden change, or a slight but persistent change, is harder to notice. There are always mistakes to be made, when analyzing data. You have to think about what kinds of mistakes you would rather make, and how likely you want to make them.
C-Dog talks about fitting Lemont’s hair growth to a curve. This means looking at the data one has as points in space. What kinds of curves will come as close as possible to including all those points? It turns out infinitely many curves will, and you can fit a curve to all the data points you have. (Unless you have some inconsistent data, like, in 2017 Lemont asked both 14 times and 18 times.) So to do an interpolation you need to make some suppositions. Suppose that the data is really a straight line, with some noise in it. Or is really a parabola. Really a sine wave. Or, drawing from a set of plausible curves, which of those best fits the data?
The Bézier Curve mentioned here is a family of shapes. They’re named for Pierre Bézier, an engineer with Renault who in the 1950s pioneered the using of these curves. There are infinitely many of them. But they’re nice to work with. You can make great-looking curves as sharply curved or as smoothly curved as you like, using them. Most modern fonts use Bézier Curves to compute the shapes of letters. If you have a drawing program, it’s got some kind of Bézier curve in there. It’s the weird tool with a bunch of little dots, most of which are nowhere near the curve they draw. But moving the dots changes the way the curve looks.
A Bézier curve can be linear; indeed, it can just be a line. C-Dog’s showing off by talking about a linear Bézier curve. Or he means something that looks a lot like a line, to the casual eye. Negative-sloped means what it would in high school algebra when you talk about lines: it’s a thing with a value that decreases as the independent variable increases. Something getting rarer in time, for example.
Thaves’s Frank and Ernest for the 5th uses arithmetic, particularly simple addition, as emblematic of the basics of life. Hard to argue that this isn’t some of the first things anyone would learn, and that mathematics as it’s taught builds from that. A mathematician might see other fields — particularly set theory and category theory — as more fundamental than arithmetic. That is, that you can explain arithmetic in terms of set theory, and set theory in terms of category theory. So one could argue that those are the more basic. But if we mean basic as in the first things anyone learns, yeah, it’s arithmetic. Definitely.
Kliban’s Kliban Cartoons for the 5th speaks of proofs. A good bit of mathematics is existence proofs, which is to say, showing that a thing with desired properties does exist. Sometimes they actually show you the thing. Such a “constructive proof” — showing how you make an example of the thing — pretty well proves the thing exists. But sometimes the best you can do is show that there is an answer. In any case, an example of a fish would convince all but the most hardcore skeptics that fish do exist.
Comic Strip Master Command had a slow week for everyone. This is odd since I’d expect six to eight weeks ago, when the comics were (probably) on deadline, most (United States) school districts were just getting back to work. So education-related mathematics topics should’ve seemed fresh. I think I can make that fit. No way can I split this pile of comics over two days.
Hector D Cantu and Carlos Castellanos’s Baldo for the 17th has Gracie quizzed about percentages of small prices, apparently as a test of her arithmetic. Her aunt has other ideas in mind. It’s hard to dispute that this is mathematics people use in real life. The commenters on GoComics got into an argument about whether Gracie gave the right answers, though. That is, not that 20 percent of $5.95 is anything about $1.19. But did Tia Carmen want to know what 20 percent of $5.95, or did she want to know what $5.95 minus 20 percent of that price was? Should Gracie have answered $4.76 instead? It took me a bit to understand what the ambiguity was, but now that I see it, I’m glad I didn’t write a multiple-choice test with both $1.19 and $4.76 as answers. I’m not sure how to word the questions to avoid ambiguity yet still sound like something one of the hew-mons might say.
Dan Thompson’s Brevity for the 19th uses the blackboard and symbols on it as how a mathematician would prove something. In this case, love. Arithmetic’s a good visual way of communicating the mathematician at work here. I don’t think a mathematician would try arguing this in arithmetic, though. I mean if we take the premise at face value. I’d expect an argument in statistics, so, a mathematician showing various measures of … feelings or something. And tests to see whether it’s plausible this cluster of readings could come out by some reason other than love. If that weren’t used, I’d expect an argument in propositional logic. And that would have long strings of symbols at work, but they wouldn’t look like arithmetic. They look more like Ancient High Martian. Just saying.
Dave Coverly’s Speed Bump for the 20th is designed with crossover appeal in mind and I wonder if whoever does Reading the Comics for English Teacher Jokes is running this same strip in their collection for the week.
Darrin Bell’s Candorville for the 21st sees Lemont worry that he’s forgotten how to do long division. And, fair enough: any skill you don’t use in long enough becomes stale, whether it’s division or not. You have to keep in practice and, in time, have to decide what you want to keep in practice about. (That said, I have a minor phobia about forgetting how to prove the Contraction Mapping Theorem, as several professors in grad school stressed how it must always be possible to give a coherent proof of that, even if you’re startled awake in the middle of the night by your professor.) Me, I would begin by estimating what 4,858.8 divided by 297.492 should be. 297.492 is very near 300. And 4,858.8 is a little over 4800. And that’s suggestive because it’s obvious that 48 divided by 3 is 16. Well, it’s obvious to me. So I would expect the answer to be “a little more than 16” and, indeed, it’s about 16.3.
(Don’t read the comments on GoComics. There’s some slide-rule-snobbishness, and some snark about the uselessness of the skill or the dumbness of Facebook readers, and one comment about too many people knowing how to multiply by someone who’s reading bad population-bomb science fiction of the 70s.)
I apologize for not writing as thoughtfully about the comics this week as I’d like, but it’s been a bit of a rushed week and I haven’t had the chance to do pop-mathematics writing of the kind I like, which is part of why you aren’t right now seeing a post about goldfish. All should be back to normal soon. I’m as ever not sure which is my favorite comic of the bunch this week; I think Bewley may have the strongest, if meanest, joke in it, though as you can see by the text Candorville gave me the most to think about.
Daniel Beyer’s Long Story Short (January 1) plays a little on the way a carelessly-written Z will morph so easily into a 2, and vice-versa, which serves as a reminder to the people who give out alphanumeric confirmation codes: stop using both 0’s and O’s, and 1’s and I’s, and 2’s and Z’s, in the same code already. I know in the database there’s no confusion about this but in the e-mail you sent out and in the note we wrote down at the airport transcribing this over the phone, there is. And now that it’s mentioned, why is the letter Z used to symbolize snoring? Nobody is sure, but Cecil Adams and The Straight Dope trace it back to the comics, with Rudolph Dirks’s The Katzenjammer Kids either the originator or at least the popularizer of the snoring Z.