There’s three more comics from last week I want to talk about. To ease my workload I’m going to put those off until Saturday. This is not an attempt to inflate the number of posts I make so that I can do a post-a-day-for-a-month again, as has happened in previous A-to-Z series. I already missed yesterday anyway. I just didn’t have time to think of things to write about six comics yesterday.
Morrie Turner’s Wee Pals for the 3rd has an interesting description of a circle. Definitions are a big part of mathematical work. This is especially so as we tend to think of mathematical objects as things that relate to one another in different ways. You want a definition that includes the relationships that are important, and excludes the ones you don’t want.
Nipper’s definition of a circle … well, eh. I wouldn’t say that captures a circle. A ‘closed smooth curve’, yes. It’s closed because the ends join up. It’s smooth because there aren’t any corners, any kinks in it. It’s a curve because … well, there you go. There are many interesting shapes that are closed smooth curves. You can find some by tossing a rubber band in the air and seeing what it looks like when it lands. But I think what most people find important about circles are ideas like all the points on a curve being the same distance from some single “center” point. Nipper would probably realize his definition didn’t work by experimenting. Try drawing shapes that meet the rule he set out, but that aren’t what he thinks a circle ought to be.
This can be fruitful. It can develop a sharper idea of what a definition ought to have. Or it might force you to accept, in order to get the cases you want included, that something which seems wrong has to count too. This mathematicians faced in the late 19th and early 20th centuries. We learned that the best definition we’ve had for an idea like “a continuous function” means we have to allow weird conclusions, like that it’s possible to have a function continuous at a single point and nowhere else. But any other definition rules out things we absolutely have to call continuous, so, what’s there to do?
Jenny Campbell’s Flo and Friends for the 4th presents algebra as one of the burdens of youth. And one that’s so harsh that it makes old age more pleasant. I get the unpleasantness of being stuck in a class one doesn’t understand or like. But my own slight experience with that thing where you wake up, and a thing hurts, and there’s no good reason but eventually it either goes away or you get so used to it you don’t realize it still actually hurts? I would take the boring class, most of the time.
John Zakour and Scott Roberts’s Maria’s Day for the 4th is a joke about how hard mathematics is. Maria’s finding the monsters in her room less frightening than arithmetic. Well, as long as she’s picking up a couple useful things about multiplication.
I do at least one Reading the Comics post per week, and often two.They’ll be at this link. Other appearances by Wee Pals should be at this link. Topics raised by Flo and Friends are discussed at this link. And essays mentioning Maria’s Day are at this link. Thanks as ever for reading. I’m trusting that you did, or you wouldn’t be seeing this.
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