## Reading the Comics, April 10, 2022: Quantum Entanglement Edition

I remember part of why I stopped doing Reading the Comics posts regularly was their volume. I read a lot of comics and it felt like everyone wanted to do a word problem joke. Since I started easing back into these posts it’s seemed like they’ve disappeared. When I put together this week’s collection, I only had three interesting ones. And one was Andertoons for the 10th of April. Andertoons is a stalwart here, but this particular strip was one I already talked about, back in 2019.

Another was the Archie repeat for the 10th of April. And that only lists mathematics as a school subject. It would be the same joke if it were English lit. Saying “differential calculus” gives it the advantage of specificity. It also suggests Archie is at least a good enough student to be taking calculus in high school, which isn’t bad. Differential calculus is where calculus usually starts, with the study of instantaneous changes. A person can, and should, ask how a change can be instantaneous. Part of what makes differential calculus is learning how to find something that matches our intuition about what it should be. And that never requires us to do something appalling like divide zero by zero. Our current definition took a couple centuries of wrangling to find a scheme that makes sense. It’s a bit much to expect high school students to pick it up in two months.

Ripley’s Believe It Or Not for the 10th of April, 2022 was the most interesting piece. This referenced a problem I didn’t remember having heard about, the “36 Officers puzzle” of Leonhard Euler. Euler’s name you know as he did foundational work in every field of mathematics ever. This particular puzzle ates to 1779, according to an article in Quanta Magazine which one of the Ripley’s commenters offered. Six army regiments each have six officers of six different ranks. How can you arrange them in a six-by-six square so that no row or column repeats a rank or regiment?

The problem sounds like it shouldn’t be hard. The two-by-two version of this is easy. So is three-by-three and four-by-four and even five-by-five. Oddly, seven-by-seven is, too. It looks like some form of magic square, and seems not far off being a sudoku problem either. So it seems weird that six-by-six should be particularly hard, but sometimes it happens like that. In fact, this happens to be impossible; a paper by Gaston Terry in 1901 proved there were none.

The solution discussed by Ripley’s is of a slightly different problem. So I’m not saying to not believe it, just, that you need to believe it with reservations. The modified problem casts this as a quantum-entanglement, in which the rank and regiment of an officer in one position is connected to that of their neighbors. I admit I’m not sure I understand this well enough to explain; I’m not confident I can give a clear answer why a solution of the entangled problem can’t be used for the classical problem.

The problem, at this point, isn’t about organizing officers anymore. It never was, since that started as an idle pastime. Legend has it that it started as a challenge about organizing cards; if you look at the paper you’ll see it presenting states as card suits and values. But the problem emerged from idle curiosity into practicality. These turn out to be applicable to quantum error detection codes. I’m not certain I can explain how myself. You might be able to convince yourself of this by thinking how you know that someone who tells you the sum of six odd numbers is itself an odd number made a mistake somewhere, and you can then look for what went wrong.

And that’s as many comics from last week as I feel like discussing. All my Reading the Comics posts should be gathered at this link. Thanks for reading this and I hope to do this again soon.