Reading the Comics, November 29, 2018: Closing Out November Edition


Today, I get to wrap up November’s suggested discussion topics as prepared by Comic Strip Master Command.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 27th mentions along its way the Liar Paradox and Zeno’s Paradoxes. Both are ancient problems. The paradoxes arise from thinking with care and rigor about things we seem to understand intuitively. For the Liar Paradox it’s about what we mean to declare a statement true or false. For Zeno’s Paradoxes it’s about whether we think space (and time) are continuous or discrete. And, as the strip demonstrates, there is a particular kind of nerd that declares the obvious answer is the only possible answer and that it’s foolish to think deeper. To answer a question’s literal words while avoiding its point is a grand old comic tradition, of course, predating even the antijoke about chickens crossing roads. Which is what gives these answers the air of an old stage comedian.

A man seeks the Wise Man atop a mountain. He asks: 'Wise master, if a man says 'I am lying' is he telling the truth?' Wise Man: 'Yes, if his name is 'lying'.' Seeker: 'But- ' Wise Man: 'NEXT.' Seeker departs, angrily. Other Seeker: 'Wise master, how can you cross infinite points in finite time?' Wise Man: 'By walking. NEXT!'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 27th of November, 2018. Other essays mentioning topics raised by Saturday Morning Breakfast Cereal are at this link. Well, all right, this link, if you want to avoid the maybe four times it hasn’t turned up.

Mark Tatulli’s Lio for the 28th features a cameo for mathematics. At least mathematics class. It’s painted as the most tedious part of the school day. I’m not sure this is quite right for Lio as a character. He’s clever in a way that I think harmonizes well with how mathematics brings out universal truths. But there is a difference between mathematics and mathematics class, of course.

Lio, on his ham radio, gets an ALIEN TRANSMISSION: 'INVASION UNDERWAY! TARGET ALL ELEMENTARY SCHOOLS!' Lio gets excited. Next ALIEN TRANSMITION: 'JK! JK! JK! ENJOY YOUR MATH CLASS, STUPID KID! LOL!' Lio grimaces; aliens laugh at their prank call.
Mark Tatulli’s Lio for the 28th of November, 2018. Essays discussing topics raised by Lio should be at this link.

Tom Toles’s Randolph Itch, 2am for the 28th shows how well my resolution to drop the strip from my rotation here has gone. I don’t seem to have found it worthy of mention before, though. It plays on the difference between a note of money, the number of units of currency that note represents, and between “zero” and “nothing”. Also I’m enchanted now by the idea that maybe some government might publish a zero-dollar bill. At least for the sake of movie and television productions that need realistic-looking cash.

Randolph, at a restaurant, asking his date as he holds open his wallet: 'Do you have a twenty? All I seem to have is zeroes.' Footer joke: 'And you can never have enough of those.'
Tom Toles’s Randolph Itch, 2am rerun for the 28th of November, 2018. It first appeared the 12th of April, 2000. Other instances of Randolph Itch, 2 am that I thought worth discussing are at this link.

In the footer joke Randolph mentions how you can never have enough zeroes. Yes, but I’d say that’s true of twenties, too. There is a neat sense in which this is true for working mathematicians, though. At least for those doing analysis. One of the reliable tricks that we learn to do in analysis is to “add zero” to a quantity. This is, literally, going from some expression that might be, say, “a – b” to “a + 0 – b”, which of course has the same value. The point of doing that is that we know other things equal to zero. For example, for any number L, “-L + L” is zero. So we get the original expression from “a + 0 – b” over to “a – L + L – b”. And that becomes useful is you picked L so that you know something about “a – L” and about “L – b”. Because then it tells you something about “a – b” that you didn’t know before. Picking that L, and showing something true about “a – L” and “L – b”, is the tricky part.

Caption: Mobius Comic Strip. Titled 'Down in the Dumpties with Humpty'; on it a pair of eggs argue about whether they're going in circles and whether they've done all this before and getting sick as the comic 'twists' over.
Dan Collins’s Looks Good On Paper for the 29th of November, 2018. Other appearances by Looks Good On Paper should be at this link.

Dan Collins’s Looks Good On Paper for the 29th is back with another Möbius Strip comic strip. Last time it was presented as the “Möbius Trip”, a looping journey. This time it’s a comic strip proper. If this particular Looks Good On Paper has run before I don’t seem to have mentioned it. Unlike the “Möbius Trip” comic, this one looks more clearly like it actually is a Möbius strip.

The Dumpties in the comic strip are presented as getting nauseated at the strange curling around. It’s good sense for the comic-in-the-comic, which just has to have something happen and doesn’t really need to make sense. But there is no real way to answer where a Möbius strip wraps around itself. I mean, we can declare it’s at the left and right ends of the strip as we hold it, sure. But this is an ad hoc placement. We can roll the belt along a little bit, not changing its shape, but changing the points where we think of the strip as turning over.

But suppose you were a flat creature, wandering a Möbius strip. Would you have any way to tell that you weren’t on the plane? You could, but it takes some subtle work. Like, you could try drawing shapes. These let you count a thing called the Euler Characteristic, which relates the numer of vertices, edges, and faces of a polyhedron. The Euler Characteristic for a Möbius strip is the same as that for a Klein bottle, a cylinder, or a torus. You could try drawing regions, and coloring them in, calling on the four-color map theorem. (Here I want just to mention the five-color map theorem, which is as these things go easy to prove.) A map on the plane needs at most four colors to have no neighboring territories share a color along an edge. (Territories here are contiguous, and we don’t count territories meeting at only a point as sharing an edge.) Same for a sphere, which is good for we folks who have the job of coloring in both globes and atlases. It’s also the same for a cylinder. On a Möbius strip, this number is six. On a torus, it’s seven. So we could tell, if we were on a Möbius strip, that we were. It can be subtle to prove, is all.


All of my regular Reading the Comics posts should all be at this link. The next in my Fall 2018 Mathematics A To Z glossary should be posted Tuesday. I’m glad for it if you do come around and read again.

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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. He/him.

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