# A Math-Free Guide to the Math of Alice in Wonderland

Image Credit: Photo by Annie Spratt on Unsplash

Alice in Wonderland got its start as a simple story, told by a mathematics professor to a colleague’s daughter. It’s a strange story that seems to be the result of a drug trip, but is actually a scathing satire of the new-fangled math that the professor was seeing invade his area of study.

Most of us just enjoy the White Rabbit and the hookah-smoking caterpillar. But now you can understand the math in Alice without needing to be a math whiz.

Some people who read Alice in Wonderland find it a whimsical adventure into a world of fun little paradoxes. Other people consider it a creepy march through a world of characters who seem to be set on making life as frustrating as possible as manically as they can. Which side you see might possibly have some bearing on your view of the world. Alice isn’t just fun and games. Charles Dodgson — the real name of Lewis Carroll — added all those paradoxes and puzzles as he was poring over the new math that was springing up in the middle of the 1800s.

Carroll liked good old-fashioned no nonsense algebra and Euclidean geometry — areas of study that could prove things about the natural world. Suddenly math students, and even teachers, were using different mathematical methods to prove things like one and one not equaling two. It seemed to Carroll that they were just being difficult on purpose, so he skewered them in prose.

Alice’s Mathematical Attempts at Control

Alice herself isn’t the focus of Carroll’s ire, so while she thinks circuitously about mathematics, and make mistakes, she’s mostly the straight man for the characters of Wonderland. She gets us started with mathematical concepts early on in the proceedings, when she’s still shrinking down. She wonders if she can shrink forever, getting smaller and smaller, or if she’ll eventually reach the point of nothingness. Where, exactly, is the mathematical partition between a very small something, and nothing at all?

Later, when she gets bigger and attempts to do math, she gets mixed up. She tries simple multiplication, but comes up with four times five equaling twelve, four times six becoming thirteen, and four times seven turning into fourteen.

In regular math, of course, this doesn’t work. If, however, you mess around with the base systems, things change. We work in base ten, meaning we have zero-through-nine digits, and then when we get to ten we move over and put a one in the next column. Alice was calculating in base ten, but her answers slipped into higher base systems. Four times five is twenty, which in base eighteen is one (1) group of eighteen, and two (2) extra singles, making 12. Four times six is twenty-four, got changed to a base twenty-one system, with one (1) group of twenty-one, plus three (3) extra singles, or 13. Four times seven is twenty-eight, but if you change that to a base twenty-four system, that’s one (1) group of twenty-four, and four (4) extra singles, or 14. When you change the system of measurement, but keep thinking of it as the original standard, you can pile on the numbers and never get anywhere, leaving you as lost as Alice.