These days I’ve been preparing these comics posts by making a note of every comic that seems like it might have a mathematical topic. Then at the end of the week I go back and re-read them all and think what I could write something about. This past week’s had two that seemed like nice juicy topics. And then I was busy all day Saturday so didn’t have time to put the thought into them that they needed. So instead I offer some comic strips with at least mentions of mathematical subjects. If they’re not tightly on point, well, I need to post something, don’t I?
Jeffrey Caulfield and Brian Ponshock’s Yaffle for the 24th is the anthropomorphic numerals joke for the week. It did get me thinking about the numbers which (in English) are homophones to other words. There don’t seem to be many, though: one, two, four, six, and eight seem to be about all I could really justify. There’s probably dialects where “ten” and “tin” blend together. There’s probably a good Internet Argument to be had about whether “couple” should be considered the name of a number. That there aren’t more is probably that there, in a sense, only a couple of names for numbers, with a scheme to compound names for a particular number of interest.
Scott Hilburn’s The Argyle Sweater for the 25th mentions algebra, but is mostly aimed at the Reading the Comics for some historian blogger. I kind of admire Hilburn’s willingness to go for the 70-year-old scandal for a day’s strip. But a daily strip demands a lot of content, especially when it doesn’t have recurring characters. The quiz answers as given are correct, and that’s easy to check. But it is typically easy to check whether a putative answer is correct. Finding an answer is the hard part.
I’m not aware of any etymological link between the term algebra and the name Alger. The word “algebra” derivate from the Arabic “al-jabr”, which the Oxford English Dictionary tells me literally derives from a term for “the surgical treatment of fractures”. Less literally, it would mean putting things back together, restoring the missing parts. We get it from a textbook by the 9th century Persian mathematician Muhammad ibn Musa al-Khwarizmi, whose last name Europeans mutated into “algorithm”, as in, the way to solve a problem. That’s thanks to his book again. “Alger” as in a name seems to trace to Old English, although exactly where is debatable, as it usually is. (I’m assuming ‘Alger’ as a first name derives from its uses as a family name, and will angrily accept correction from people who know better.)
Daniel Shelton’s Ben for the 25th has a four-year-old offering his fingers as a way to help his older brother with mathematics work. Counting on fingers can be a fine way to get the hang of arithmetic and at least I won’t fault someone for starting there. Eventually, do enough arithmetic, and you stop matching numbers with fingers because that adds an extra layer of work that doesn’t do anything but slow you down.
Catching my interest though is that Nicholas (the eight-year-old, and I had to look that up on the Ben comic strip web site; GoComics doesn’t have a cast list) had worked out 8 + 6, but was struggling with 7 + 8. He might at some point get experienced enough to realize that 7 + 8 has to be the same thing as 8 + 7, which has to be the same thing as 8 + 6 + 1. And if he’s already got 8 + 6 nailed down, then 7 + 8 is easy. But that takes using a couple of mathematical principles — that addition commutes, that you can substitute one quantity with something equal to it, that you addition associates — and he might not see where those principles get him any advantage over some other process.
Ed Allison’s Unstrange Phenomena for the 25th builds its Dadaist nonsense for the week around repeating numbers. I learn from trying to pin down just what Allison means by “repeating numbers” that there are people who ascribe mystical significance to, say, “444”. Well, if that helps you take care of the things you need to do, all right. Repeating decimals are a common enough thing. They appear in the decimal expressions for rational numbers. These expressions either terminate — they have finitely many digits and then go to an infinitely long sequence of 0’s — or they repeat. (We rule out “repeating nothing but zeroes” because … I don’t know. I would guess it makes the proofs in some corner of number theory less bothersome.)
You could also find interesting properties about numbers made up of repeating strings of numerals. For example, write down any number of 9’s you like, followed by a 6. The number that creates is divisible by 6. I grant this might not be the most important theorem you’ll ever encounter, but it’s a neat one. Like, a strong of 4’s followed by a 9 is not necessarily divisible by 4 or 9. There are bunches of cute little theorem like this, mostly good for making one admit that huh, there’s some neat coincidences(?) about numbers.
Although … Allison’s strip does seem to get at seeing particular numbers over and over. This does happen; it’s probably a cultural thing. One of the uses we put numbers to is indexing things. So, for example, a TV channel gets a number and while the station may have a name, it makes for an easier control to set the TV to channel numbered 5 or whatnot. We also use numbers to measure things. When we do, we get to pick the size of our units. We typically pick them so our measurements don’t have to be numbers too big or too tiny. There’s no reason we couldn’t measure the distance between cities in millimeters, or the length of toes in light-years. But to try is to look like you’re telling a joke. So we get see some ranges — 1 to 5, 1 to 10 — used a lot when we don’t need fine precision. We see, like, 1 to 100 for cases where we need more precision than that but don’t have to pin a thing down to, like, a quarter of a percent. Numbers will spill past these bounds, naturally. But we are more likely to encounter a 20 than a 15,642. We set up how we think about numbers so we are. So maybe it would look like some numbers just follow you.
Over the next few days I should have more chance to think. I’ll finish Reading the Comics from the past week and put an essay up at this link.