# Reading the Comics, July 12, 2022: Numerals Edition

The small set of comic strips with some interesting mathematical content for the first third of the month include an anthropomorphic numerals one and one about the representation of infinity. That’s enough to make a title.

Richard Thompson’s Cul de Sac repeat for the 3rd is making its third appearance in my column! I had mentioned it when it first ran, in July 2012, and then again in its July 2017 repeat. But in neither of those past times did I actually include the comic as I felt it likely GoComics would keep the link to it stable. I’m less confident now that they will keep the link up, as Thompson has died and his comic strip — this century’s best, to date — is in perpetual rerun.

I admit not having many thoughts which I haven’t said twice already. It’s a joke about making a character out of the representation of a number. Alice gives it personality and backstory and, as the kids say these days, lore. Anyway, be sure to check out this blog for the comic’s repeat the 4th of July, 2027. I hope to still be reading then.

I think mathematicians do tend to give, if not personality, at least traits to mathematical constructs. Like, 60, a number with abundant divisors, is likely to be seen as a less difficult number to calculate with than 58 is. A mathematician is likely to see $e^{\imath sin(x)}$ as a pleasant, well-behaved function, but is likely to see $\sin(e^{\frac{\imath}{x}})$ as a troublesome one. These examples all tie to how easy they are to do other stuff with. But it is natural to think fondly of things you see a lot that work nicely for you. These don’t always have to be “nice” things. If you want to test an idea about continuous curves, for example, it’s convenient to have handy the Koch curve. It’s this spiky fractal that’s nothing but corners, and you can use it to see if the idea holds up. Do this enough, and you come to see a reliable partner to your work.

Bill Amend’s FoxTrot for the 3rd is the one built on representing infinity. Best that one could hope for given Peter’s ambitious hopes here. I know the characters in this strip and I just little brother Jason wanted a Möbius-strip burger.

Tauhid Bondia’a Crabgrass for the 7th — a strip new to newspaper syndication, by the way — is a cryptography joke. This sort of thing is deeply entwined into mathematics, most deeply probability. This because we know that a three-letter (English) word is more likely to be ‘the’ or ‘and’ or ‘you’ than it is to be ‘qua’ or ‘ado’ or ‘pyx’. And either of those is more likely than ‘pqd’. So, if it’s a simple substitution, a coded word like ‘zpv’ gives a couple likely decipherings. The longer the original message, and the more it’s like regular English, the more likely it is that we can work out the encryption scheme.

But this is simple substitution. What’s a complex substitution? There are many possible schemes here. Their goal is to try to make, in the code text, every set of three-letter combinations to appear about as often as every other pair. That is, so that we don’t see ‘zpv’ happen any more, or less, than ‘sgd’ or ‘zmc’ do, so there’s no telling which word is supposed to be ‘the’ and which is ‘pyx’. Doing that well is a genuinely hard problem, and why cryptographers are paid I assume big money. It demands both excellent design of the code and excellent implementation of it. (One cryptography success for the Allies in World War II came about because some German weather stations needed to transmit their observations using two different cipher schemes. The one which the Allies had already cracked then gave an edge to working out the other.)

It also requires thinking of the costs of implementation. Kevin and Miles could work out a more secure code, but would it be worth it? They just need people to decide their message is too much effort to be worth cracking. Mrs Campbell seems to have reached that conclusion, at a glance. Not sure what Principal Sanders would have decided, were Miles not eager to get out of there. Operational security is always a challenge.

And that’s enough for the start of the month. All my Reading the Comics posts should be at this link,. I hope to have some more of them to discuss next week. We’ll see what happens.

## 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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