## Reading the Comics, May 16, 2019: Two and Two Edition

It might be more fair to call this a blackboard edition, as three of the strips worth discussing feature that element. But I think I’ve used that name recently. And two of the strips feature specifically 2 + 2, so I’ll use that instead.

And here’s a possible movie heads-up. Turner Classic Movies, United States feed, is showing Monday at 9:30 am (Eastern/Pacific) All-American Chump. All I know about this 1936 movie is from its Leonard Maltin review:

[ Stuart ] Erwin is funny, in his usual country bumpkin way, as a small-town math whiz known as “the human adding machine” who is exploited by card sharks and hustlers. Fairly diverting double-feature item.

People with great powers of calculation were — and still are — with us. Before calculating machines were common they were, pop mathematicians tell us, in demand for doing the kinds of arithmetic mathematicians and engineers need a lot of. They’d also have value in performing, if they can put together some good patter. And, sure, gambling is just another field that needs calculation done well. I have no idea the quality of the film (it’s rated two and a half stars, but Leonard Maltin rates many things two and a half stars). But it’s there if you’re curious. The film also stars Robert Armstrong. I assume it’s not the guy I know but, you know? We live in a strange world. Now on to the comics.

Glenn McCoy and Gary McCoy’s The Flying McCoys for the 13th uses the image of a blackboard full of mathematics symbols to represent deep thought. The equations on the board are mostly nonsense, although some, like $E = mc^2$, have obvious meaning. Many of the other symbols have some meaning to them too. In the upper-right corner, for example, is what looks like $E = \hbar \omega$. This any physics major would recognize: it’s the energy of a photon, which is equal to Planck’s constant (that $\hbar$ stuff) times its frequency.

And there are other physics-relevant symbols. In the bottom center is a line that starts $\oint \vec{B}$. The capital B is commonly used to represent a magnetic field. The arrow above the capital B is a warning that this is a vector, which magnetic fields certainly are. (Mathematicians see vectors as a quite abstract concept. Physicists are more likely to see them as an intensity and direction, like forces, and the fields that make fields.) The $\oint$ symbol comes from vector calculus. It represent an integral taken along a closed loop, a shape that goes out along some path and comes back to where it started without crossing itself. This turns out to be useful all the time in dynamics problems. So the McCoys drew something that doesn’t mean anything, but looks ready to mean things.

“Overthinking this” is a problem common to mathematicians, even at an advanced level. Real problems don’t make clear what their boundaries are, the things that are important and the things that aren’t and the things that are convenient but not essential. Making mistakes picking them out, and working too hard on the wrong matters, will happen.

Graham Harrop’s Ten Cats for the 14th sees the cats pondering the counts of vast things. These are famous problems. Archimedes composed a text, The Sand Reckoner, which tried to estimate how much sand there could be in the universe. To work on the question he had to think of new ways to represent numbers. Grains of sand become numerous by being so tiny. Stars become numerous by the universe being so vast. Comparing the two quantities is a good challenge. For both numbers we have to make estimates. The volume of beaches in the world. The typical size of a grain of sand. The number of galaxies in the universe. The typical number of stars in a galaxy. There’s room to dispute all these numbers; we really have to come up with a range of possible values, with maybe some idea of what seems more likely.

Thaves’s Frank and Ernest for the 15th has the student bringing authority to his answer. The mathematician is called on to prove an answer is “technically” correct. I’m not sure whether the kid is meant to be prefacing the answer he’s about to give, or whether his answer was rewriting the horizontal “2 + 2 = ” in a vertical form.

Brant Parker and Johnny Hart’s The Wizard of Id Classics for the 15th is built around the divisibility of whole numbers, and of relative primes. Setting the fee as some simple integer fraction of the whole has practicality to it. It likely seemed even more practical in the days before currencies decimalized. The common £sd style currency Europeans used before decimals could be subdivided many ways evenly, with one-third of a pound (livre, Reichsgulden, etc) becoming 80 pence (deniers, Pfennig, etc). Unit fractions, and combinations of unit fractions, could offer interesting ways to slice up anything to a desired amount.

Jim Unger’s Herman for the 16th is a student-talking-back-to-the-teacher strip. It also uses the 2 + 2 problem. It’s a common thing for teachers to say they learn from their students. It’s even true, although I son’t know that people ever quite articulate how teachers learn. A good mistake is a great chance to learn. A good mistake shows off a kind of brilliant twist. That the student has understood some but not all of the idea, and has filled in the misunderstood parts with something plausible enough one has to think about why it’s wrong. And why someone would think the wrong idea might be right. There is a kind of mistake that inspires you to think closely about what “right” has to be, and students who know how to make those mistakes are treasures.

And for comic strips that aren’t quite worth a paragraph. Julia Kaye’s Up and Out for the 13th uses mathematics as stand-in for the sort of general education that anybody should master. David Waisglass and Gordon Coulthart’s Farcus for the 17th I don’t think is trying to be a mathematics joke. It’s sufficient joke that the painter’s spelled ‘sign’ wrong. But it did hit on the spelling that would encourage mathematics teachers to notice the strip. Patrick Roberts’s Todd the Dinosaur for the 18th mentions sudoku.

And with that I am caught up on the past week’s mathematically-themed comic strips. My next Reading the Comics post should be next Sunday, and at this link. Oh, I could have made the edition name something bragging about being on time.