The Magnet 061: Favorite Math(ish) Books
Flatland, the fourth dimension, and infinity
I didn’t enjoy the math classes I took in high school and college. (The one expectation was geometry proofs, which were fun.) But I love books about math, especially ones that aren’t textbooks but rather about the history, philosophy, and wonder of mathematics.
In this (and upcoming issues of) The Magnet, I’ll recommend some of my favorite math(ish) books.
All three books below have links to places where you can read them for free.
Flatland, A Romance of Many Dimensions
Flatland, A Romance of Many Dimensions is a delightful little illustrated novella from 1884 by Edwin Abbott. It's told from the perspective of a two-dimensional being, A. Square (he's square-shaped), who travels to a one-dimensional world (Lineland) and a three-dimensional world (Spaceland). A being from Spaceland introduces him to the concept of an additional dimension, but at first, A. Square cannot grasp it. Eventually, he comes to understand that there are worlds of not only three dimensions but of four and beyond.
The book centers around the idea that our perceptions and ability to understand the world are determined by our senses and our brains’ ability to process information. Our brains have evolved to make us good at understanding the world in the ways that help us survive. But the reality of the world is not limited by our perceptions.
The writing is very accessible, given the fact that it was written 138 years ago. Here are the book’s first two paragraphs:
I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.
Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows — only hard and with luminous edges and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said “my universe”: but now my mind has been opened to higher views of things.
The world of Flatland itself is fascinating, with its complex social interactions among shapes, biological functioning of flat creatures, and architectural innovations.
[Update 5-17-22. François says “I just wanted to draw your attention to the Standard Ebooks version of Flatland. It is a modern digital edition, available for free in several formats, including as a web page, and probably more practical than the Internet Archive version you originally linked to. Flatland deserves more exposure and I’m sure your readers will appreciate the convenience of the SE edition.”]