There were a healthy number of comic strips with at least a bit of mathematical content the past week. Enough that I would maybe be able to split them across three essays in all. This conflicts with my plans to post two A-To-Z essays, and two short pieces bringing archived things back to some attention, when you consider the other thing I need to post this week. Well, I’ll work out something, this week at least. But if Comic Strip Master Command ever sends me a really busy week I’m going to be in trouble.

Bud Blake’s **Tiger** rerun for the 7th has Punkinhead ask one of those questions so basic it ends up being good and deep. What *is* arithmetic, exactly? Other than that it’s the mathematics you learn in elementary school that isn’t geometry? — an answer that’s maybe not satisfying but at least has historical roots. The quadrivium, four of the seven liberal arts of old, were arithmetic, geometry, astronomy, and music. Each of these has a fair claim on being a mathematics study, though I’d agree that music is a small part of mathematics these days. (I first wrote a “minor” piece, and didn’t want people to think I was making a pun, but you’ll notice I’m sharing it anyway.) I can’t say what people who study music learn about mathematics these days. Still, I’m not sure I can give a punchy answer to the question.

Mathworld offers the not-quite-precise definition that arithmetic is the field of mathematics dealing with integers or, more generally, numerical computation. But then it also offers a mnemonic for the spelling of arithmetic, which I wouldn’t have put in the fourth sentence of an article on the subject. I’m also not confident in that limitation to integers. Arithmetic certainly is about things we do on the integers, like addition and subtraction, multiplication and division, powers, roots, and factoring. So, yes, adding five and two is certainly arithmetic. But would we say that adding one-fifth and two is not arithmetic? Most other definitions I find allow that it can be about the rational numbers, or the real numbers. Some even accept the complex-valued numbers. The core is addition and subtraction, multiplication and division.

Arithmetic blends almost seamlessly into more complicated fields. One is number theory, which is the posing of problems that anyone can understand and that nobody can solve. If you ever run across a mathematical conjecture that’s over 200 years old and that nobody’s made much progress on besides checking that it’s true for all the whole numbers below 2^{1,000,000,000} – 1, it’s probably number theory. Another is group theory, in which we think about structures that look like arithmetic without necessarily having all its fancy features like, oh, multiplication or the ability to factor elements. And it weaves into computing. Most computers rely on some kind of floating-point arithmetic, which approximates a wide range of the rational numbers that we’d expect to actually need.

So arithmetic is one of those things so fundamental and universal that it’s hard to take a chunk and say that this is it.

John Zakour and Scott Roberts’s **Maria’s Day** for the 8th has Maria fretting over what division means for emotions. I was getting ready to worry about Maria having the idea division means getting less of something. Five divided by one-half is not less than either five or one-half. My understanding is this unsettles a great many people learning division. But she does explicitly say, divide two, which I’m reading as “divide by two”. (I mean to be charitable in my reading of comic strips. It’s only fair.)

Still, even division into two things does not necessarily make things less. One of the fascinating and baffling discoveries of the 20th century was the Banach-Tarski Paradox. It’s a paradox only in that it defies intuition. According to it, one ball can be divided into as few as five pieces, and the pieces reassembled to make two whole balls. I would not expect Maria’s Dad to understand this well enough to explain.

Bob Weber Jr’s **Slylock Fox and Comics for Kids** for the 9th presents a logic puzzle. If you know the laws of Boolean algebra it’s a straightforward puzzle. But it’s light enough to understand just from ordinary English reading, too.

Rick Detorie’s **One Big Happy** for the 12th is a little joke about finding mathematics problems in everyday life. Or it’s about the different ways one can represent numbers.

There were naturally comic strips with too marginal a mention of mathematics to rate paragraphs. Among them the past week were these.

Stephen Bentley’s **Herb and Jamaal** rerun for the 11th portrays the aftermath of realizing a mathematics problem is easier than it seemed. Realizing this after a lot of work should feel good, as discovering a clever way around tedious work is great. But the lost time can still hurt.

Ernie Bushmiller’s **Nancy Classics** for the 11th, rerunning a strip from the 6th of December, 1949, has Sluggo trying to cheat in arithmetic.

**Eric the Circle** for the 13th, by “Naratex”, is the Venn Diagram joke for the week.

Jason Poland’s **Robbie and Bobby** for the 13th is a joke about randomness, and the old phrase about doing random acts of kindness.

And that’s where I’ll pause a while. Tuesday I hope to publish another in the Fall 2019 A To Z series, and Thursday the piece after that. I plan to have the other Reading the Comics post for the past week published here on Wednesday. The great thing about having plans is that without them, nothing can go wrong.