Reading the Comics, December 17, 2015: Caught Up Edition


And now, after a little effort, I’m caught up to the current day’s comic strips. Unless someone did something mathematical in Saturday’s strips. I suppose I’ll find out soon enough.

Johnny Hart’s Back to B.C. for the 14th of December reprints the strip for the 26th of May, 1958. It’s about parallel lines and how they might meet. It does bring up something that bothered me as a kid: how do you know parallel lines never do meet? You might know by definition. If parallel lines are “lines that never meet”, then they can’t meet, any more than a square can have eight sides. But that doesn’t seem like a “proof” exactly.

When we look at non-Euclidean geometries — the way shapes look on the surface of a sphere, or other non-flat shapes — we do start seeing things that look like they should be parallel lines that do come together anyway. Look at lines of longitude on the globe, all of which come together at the north and south pole. I think most folks try to resist calling them parallel, though, because we don’t want to muddy the word. There are some problems — the ones I know come from calculus — where it’s convenient to declare that two parallel lines really intersect somewhere infinitely far off. That’s patching the logic behind a tool so we can apply it somewhere novel.

John Atkinson’s Wrong Hands for the 14th of December I could swear had been here before. But I don’t seem to find it in past Reading the Comics posts. Maybe I’ve seen the pun being passed around on Twitter or WordPress. The Wrong Hands for the 16th of December is certainly one that hasn’t featured here before. It does suggest the question of why right angles are called “right”. According to a Math Forum post from 2002, the “right” comes from the Indo-European root reg-, meaning “to move in a straight line”. And it’s supposed to reflect the way a weight on a string making a right angle with the ground or horizon lines. (The post, by Doctor Sarah, quotes Steven Schwartzman’s The Words Of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English. It’s a book I didn’t specifically know existed or I’d have put it on my wish lists.)

Richard Thompson’s Poor Richard’s Almanac for the 15th of December (a rerun, and I’m not sure from when) is a guide to Christmas trees. One is “so asymmetrical it not longer inhabits Euclidean space”. Properly speaking neither do we. But the difference between the geometry of our living room and a true Euclidean space is too tiny to notice. And just being Euclidean is no guarantee against weird stuff happening. A four-dimensional (or more-dimensional) object in a three-dimensional space can produce wild effects, as a good Flatlander would point out. But “non-Euclidean” is still, and probably will stay, a good term to describe bizarre shapes. We need something to say about, like, an object that you can rotate 360 degrees and have it not quite back to the way you started.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 15th of December is a calculus pun. It’s playing on the term u-substitution. The u-substitution is a calculus trick that makes a lot of integrals possible to do. The trick is one of replacing parts of an integral we can’t do with a new variable. The rules of how we can change variables within an integral mean we can remake the integral into something simpler. Well, we (typically) wouldn’t be doing the substitution if we weren’t making something simpler. Typically the integral starts out with x or z or maybe y as the original variable. So we use ‘u’ as the new, substituted-in, variable name. The use of ‘u’ isn’t important. It can be any letter not already doing some work. The technique’s also called “integration by substitution”. But that doesn’t lend itself to puns so easily.

Mark Anderson’s Andertoons stops in on the 17th of December for its visit and for this essay’s students-resisting-blackboard-work joke. Anyway, data mining is the matter of looking for patterns in the data. here, for example, I’d wonder: are students more likely to get right problems where two even numbers are added together? Two odd numbers? An even and an odd? How does having to carry numbers affect how well students do? Are sevens and eights just trouble all around? Are students better on the first problems in a set, or the last?

There may be no way to tell. Suppose we only had these eight problems and these three students to draw from. It would be impossible to say whether the students are better at some of these problems or if they just got lucky. But there might be some useful information that might help us understand students, and what students don’t understand, in there. Still, it’s not something the kids need to worry about right now.

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Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

6 thoughts on “Reading the Comics, December 17, 2015: Caught Up Edition”

    1. It would, if you’re careful in saying what you mean by a line. On the surface of a sphere what we usually mean by ‘line’ is what’s also called a ‘great circle’. That’s a circle around the whole shape and it has the same diameter as the original sphere. So, using the Earth, the equator is a great circle, and all the lines of longitude are. There are many other great circles. Airplanes flying great distances follow, more or less, these great circle routes. (There’s some digressions to reflect local airspace rules, the use of jet streams, that sort of thing. They’re still approximately great circle routes.) But the equator and the longitudes are the great circles that are included on most every globe.

      The lines of latitude, meanwhile, are not ‘great circles’. They have a radius that’s smaller than the Earth’s radius. And those we don’t consider to be ‘lines’ for the surface of the sphere.

      Anyway, the great circles do intersect. Any two lines of longitude meet up at the north and south poles. An equator and a line of longitude meet up twice also, although not at a pole. And this allows for a geometry that works quite a bit like our everyday geometry, with some curious variations.

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