Reading the Comics, December 11, 2015: So, That Didn’t Work Edition
I’d hoped that running a slightly-too-soon edition of Reading the Comics would let me have a better-sized edition for later in this week. Then everybody did comics for the 11th of December. I can have a series of awkward-sized essays or just run what I have. I wonder which I’ll do.
Aaron McGruder’s The Boondocks for the 6th of December is a student-resisting-the-problem joke. It ran originally the 24th of September, 2000, if the copyright information is right. The original problem — “what is 24 divided by 4 minus 2” — is a reasonable one for at least some level of elementary school. (I’m vague on just what grade Caesar is supposed to be in. It’s a problem for any strip with wise-beyond-their-years children. Peanuts plays with this by having the kids give book reports on Peter Rabbit and Tess of the d’Urbervilles.) What makes it a challenge is that you know to know the order of operations. Should you divide 24 by 4 first, and subtract 2 from that, or should you take 4 minus 2 and then divide 24 by whatever that number is?
Absent any confounding information, you should always do multiplication and division before you do addition and subtraction. So this suggests 24 divided by 4, giving us 6, and then subtract 2, giving us 4. The only relevant confounding information, though, would be the direction to do something else first. That’s indicated by putting something in parentheses. (Or brackets, if you have so many parentheses the symbols are getting confusing.) A thing in parentheses has higher priority and should be calculated first. But there’s no way to tell parentheses in dialogue. The best the teacher could do is say something like “24 divided by the quantity four minus two”, or even, “24 divided by parenthesis four minus two close parenthesis”. That’s awkward but it is what we resort to even in the mathematics department.
Eric the Circle for the 6th of December, this one by “Scooterpiggy”, is the anthropomorphic-numerals joke this essay. You might fuss that there’s a difference between a circle and zero. The earliest examples of zero seem to have been simple dots. But the circle, or at least elliptical, shape of zero grew pretty fast. Maybe in a couple of centuries. Maybe there’s something in the empty loop that suggests what it stands for.
Tom Thaves’s Frank and Ernest for the 6th of December tosses in a statistics pun for the final panel. The statistics use of “median” is the number that half the data is less than and half the data is greater than. It’s one of several quantities that get called an “average”. In this case it’s average because if you picked a data point at random you’d be as likely to be above as below the median. In data sets that aren’t too weird, that will usually be pretty close to the arithmetic mean. The arithmetic mean is the thing normal people mean by “average”. It’ll also typically be near the most common value. That most common value mathematicians and statisticians call the “mode”.
I don’t know if the use of “median” for the middle strip of a divided road shares an etymology with the statistics use of the word. It might be one use might have inspired the other, perhaps as metaphor. But the similarity between “being in the middle of the data” and “being in the middle of the street” is straightforward for English.
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 6th of December pinpoints a common failure mode of experts. (The strip almost surely ran before, sometime. The only method I have to find out when, though, is to post an incorrect date and make someone correct me. So let me say it originally ran on Singapore National Day, 2009.) Mathematics is especially prone to it. It’s so seductive to teach something the way an expert sees it. This is usually in a rigorously thought-out, open-ended, flexible method. After all, why would you ever teach something that wasn’t exactly right, with “right” being “the ways experts see things”? A teacher knows the answer: the expert understanding of a thing is hard to get to. That’s why having it takes expertise. The comic strip’s explanation of fractions is correct and reasonable. But it brings up why Bertrand Russell and Alfred North Whitehead needed over four hundred pages to establish 1 + 1 equals 2. That’s a lot of intellectual scaffolding for the quality of paint job required. Sometimes it’s easier to start with a quick and dirty explanation, and then go back later and rebuild the understanding if a student needs it.
Rick Stromoski’s Soup to Nutz for the 7th of December puts forth a kind of Zeno’s paradox problem in the guise of compound interest. If doing something increases life expectancy by a certain percentage, then, how much of the extra time one gets do you need to be immortal? I’m amused by this although I can’t imagine modest alcohol consumption increasing lifespan by 20 percent. (I assume 20 percent of the average expected lifespan.) If the effect were anything near that big the actuaries would have noticed and ordered people to drink long ago.
On looking at all this, I think I’ll save the December 11th strips for later. This is enough text for this early in the morning.