## Reading the Comics, December 23, 2016: Weak Pretexts Edition

I’ve set the cutoff for the strips this week at Friday because you know how busy the day before Christmas is. If you don’t, then I ask that you trust me: it’s busy. If Comic Strip Master Command sent me anything worthy of comment I’ll report on it next year. I had thought this week’s set of mathematically-themed comics were a weak bunch that I had to strain to justify covering. But on looking at the whole essay … mm. I’m comfortable with it.

Bill Amend’s FoxTrot for the 18th has two mathematical references. Writing “three kings” as “square root of nine kings” is an old sort of joke at least in mathematical circles. It’s about writing a number using some elaborate but valid expression. It’s good fun. A few years back I had a calendar with a mathematics puzzle of the day. And that was fun up until I noticed the correct answer was always the day of the month so that, say, today’s would have an answer of 25. This collapsed the calendar from being about solving problems to just verifying the solution. It’s a little change but it is one that spoiled it for me.

And a few years back an aunt and uncle gave me an “Irrational Watch”, with the dial marked only by irrational numbers — π, for example, a little bit clockwise of where ‘3’ ought to go. The one flaw: it used the Euler-Mascheroni constant, a number that’s about 0.57, to designate that time a little past 12:30. The Euler-Mascheroni constant isn’t actually known to be irrational. It’s the way to bet, but it might just be a rational number after all.

A binary tree, mentioned in the bottom row, is a tree for which every vertex is connected to at most three others. We’ve seen trees recently. And there’s a specially designated vertex known as the root. Each vertex (except the root) is connected to exactly one vertex that’s closer to the root. The structure looks like either the branches or the roots of a tree, depending whether the root is put at the top or bottom. And if you accept a strikingly minimal, Mid-Century Modern style drawing of a (natural) tree.

Ted Shearer’s Quincy for the 26th of October, 1977. Reprinted the 20th of December, 2016. There’s much that’s expressive here, although what most catches my eye is the swoopy curves of the soda straw.

Ted Shearer’s Quincy for the 26th of October, 1977 mentions mathematics. So I’m using that as an excuse to include it. Mostly I like it for the artwork. But the mention of mathematics was strikingly arbitrary; the joke would be the same were it his English homework or Geography or anything else. I suppose mathematics got the nod because it can be written with so few letters. (Art is even more compact, but it would probably distract the reader trying to think of what would be hard to understand about an Art project homework. Difficult, if it were painting or crafting something, sure, but that’s not a challenge in understanding.)

I don’t know what Marty Links’s Emmy Lou for the 20th was getting at. The strip originally ran the 15th of September, 1964. It seems to be referring to some ephemeral trivia passed around the summer of that year. My guess is it refers to some estimation of the unattached male and female populations of some age set and finding that there were very different numbers. That sort of result is typically done by clever definition, sometimes assisted by double-counting and other sleights of hand. It’s legitimate if you accept the definition. But before reacting too much to any surprising claim one should know just what the claim is, and why it’s that.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 20th is mathematics wordplay. Simpson’s Approximation, mentioned here, is a calculus thing. It’s about integrals. We use it to estimate the value of an integral. We find a parabola that resembles the original function. And then the integral of the parabola should be close to the integral of the original function. The advantage of using a parabola is that we know exactly how to integrate that. You may have noticed a lot of calculus is built on finding a problem that we can do that looks enough like the one we want to do. There’s also a Simpson’s 3/8th Approximation. It uses a cubic polynomial instead of a parabola for the approximation. We can integrate cubics exactly too. It’s called the 3/8 Approximation, or the 3/8 Rule, because the formula for it starts off with a 3/8. So now and then a mathematics thing is named appropriately. Simpson’s Approximation is named for Thomas Simpson, an 18th century mathematician and textbook writer who did show the world the 3/8 Approximation. But other people are known to have used Simpson’s non-3/8 Approximation a century or more before Simpson was born .

Jason Poland’s Robbie and Bobby seeks much but slight attention from me this week. The first, from the 21st, riffs on the “randomness” of the random acts of kindness. Robbie strives for a truly random act. Randomness is tricky. We’re pretty sure we know what it ought to look like, but it’s so very hard to ever be sure we have randomness. We have a set of possible outcomes of whatever we’re doing; but, should every one of those outcomes be equally likely? Should some be more likely than others? Should some be almost inevitable but a few have long-shot chances? I suspect that when we say “truly random” we are thinking of a uniform distribution, with every different outcome being equally likely. That isn’t always what fits the situation.

And then on the 23rd the strip names “Zeno’s Paradoxical Pasta”. There are several paradoxes; this surely refers to the one about not being able to cross a distance because one must always get halfway across the distance first. It’s a reliably funny idea. It’s not a paradox by itself, though. What makes the paradox is that Zeno presents several scenarios which ask that we decide whether space and time and movement can be infinitely subdivided or not, and either decision brings up new difficulties.