I’ve gotten enough comics, I think, to justify a fresh roundup of mathematics appearances in the comic strips. Unfortunately the first mathematics-linked appearance since my most recent entry is also the most badly dated. Pab Sugenis’s The New Adventures of Queen Victoria took (the appropriate) day to celebrate the birthday of Tom Lehrer, but fails to mention his actual greatest contribution to American culture, the “Silent E” song for The Electric Company. He’s also author of the humorous song “Lobachevsky”, which is pretty much the only place to go if you need a mathematics-based song and can’t use They Might Be Giants for some reason. (I regard Lehrer’s “New Math” song as not having a strong enough melody to count.)

Six Chix, written by a rotation of six female artists (in this case, Rina Piccolo, who also draws the comic strip Tina’s Groove), featured a blackboard full of equations. This one interests me as the first several lines are clearly meaningful: they’re recognizable as the Schrödinger Equation, which describes how a quantum mechanical system evolves in time, as well as the start of a Hamiltonian, describing the forces and energies within a system. The latter two lines I’m less sure about, as they seem to be incomplete — the first term in the third line, for example, seems to want to have a quantity within the double vertical lines representing an absolute value, but hasn’t got the second line — which suggests to me that Piccolo found a set of equations roughly appropriate to the topic of the cartoon, even if she made (minor) mistakes in transcribing them.

There’s been an interesting minor shift in using mathematics or physics stuff in comic strips over the decades. The first place I noticed this was in Bill Amend’s FoxTrot, where Amend — a physics major — would use correct mathematics and physics details even though the joke makes sense without it. I appreciate the effort put in to making background details like this, which really don’t matter in the joke, as correct as possible. Often jokes have a stronger punch when they have a stronger factual base behind them.

Willy and Ethel, one of an estimated 65 daily comic strips drawn by Joe Martin, mentioned the (actual) million-dollar prize to be awarded to anyone able to prove the Poincaré Conjecture in three dimensions. I haven’t got the confidence in my narrative abilities to explain what the Poincaré Conjecture is in a couple of paragraphs. However, the conjecture was proved by a trio of papers presented by Grigori Perelman in 2002 and 2003. The proofs have been accepted, and Perelman was awarded the million dollars — and a Fields Medal — in 2010, although Perelman rejected both. Willy and Ethel are probably better off trying to prove Fermat’s Last Theorem using the ordinary shuffling around of polynomials, anyway; it won’t work, but it’s easy to produce very satisfying reams of manipulations in that subject. I’m not even sure what I’d start scribbling down to make a stab at the Poincaré Conjecture.

Gil, by Norm Feuti, who also draws Retail, attacked the problem of solving a Rubik’s Cube. While Gil’s father here shows the way I actually solved it when I knew where mine was (peeling stickers off I rejected because it was too easy to tear a patch of green), the problem of how to solve a Rubik’s Cube can be a good way to get into group theory. Group Theory is, in a way, the study of how to do things that look like multiplication and addition on things which aren’t necessarily numbers, and it turns out that rotating objects, such as blocks on a Rubik’s Cube, can be represented in this way.

If you don’t believe me, I don’t blame you, but imagine this: suppose you have a square, as in the top side of the cube, sitting on top of an analog clock face. Have one corner at 12:00. We can say how the face has been put down by drawing a line from the center of the face to that particular corner. The line is pointing at 12:00. If we rotate the face, we change the time this line is pointing to; we might increase it, say, by three hours — rotating the face by 90 degrees clockwise. Or we might decrease it by one hour — rotating the face 30 degrees counterclockwise. Suddenly, rotating the face is the same as adding or subtracting hours to the time this face represents. We have to figure out some way of handling how hours only run up to 12 and then loop back around to 1, and there’s a lot more figuring out to do to handle having three axes of rotation in the actual cube, but the basic idea is right there.

It’s incidentally proven that there are configurations of the Rubik’s Cube which require at least 18 moves to solve. The maximum number of face turns needed can’t be more than 20, although whether it is 18, 19, or 20 remains an open question.

Eric the Circle, a fan-written comic strip had a panel mentioning an arc of “approximately π/180 * 94 – sin 94 degrees”, although I’d admit to not measuring it. And I’m not sure whether that justifies inclusion in this roundup, but, what the heck. I have publication space here.

Dana Simpson’s Heavenly Nostrils just began publication today, and it hasn’t got any mathematics content at all, but Dana Simpson is a friend so the least I can do is mention it. It’s the story of a unicorn and her girl.

Actually, the maximum number of moves to solve a Rubik’s cube, also known as ‘God’s number’ is now known. The upper and lowers bounds converged on 20 moves. eg. See http://www.cube20.org

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I hadn’t heard the news! Thank you.

I suppose now I can’t feel mildly smug over Joe Martin not having heard about the Poincare conjecture’s proof a couple years back. (I didn’t feel all that smug about it.)

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