Flatterland: Like Flatland, Only More So - Ian Stewart
I begin to despair that anyone will ever be able to combine mathematics with social satire as well as Edwin Abbott did in the original. Flatterland covers much more in the way of mathematics and physics—after all, things have changed quite a bit in the century-and-some when Abbott was writing. Stewart introduces the reader to much higher dimensions, fractional dimensions, dimensions with a finite number of points. Without really saying so, he teaches you a bit of topology and group theory, curvature of a space, and then plays a bit with wormholes and time travel. And if that weren't enough, we also get a dose of Relativity, quantum theory, and string theory. It's like a college education in math and physics, in one easy dose!
Granted, with so much to cover in a short book (quite a bit longer than Flatland, but far from being a textbook), Stewart glosses over a lot of it. If you still feel a little hazy about Relativity when you're done, it's not entirely your fault. The biggest drawback to this light treatment of so many subjects: I'm not sure somebody who doesn't already know a little about each subject would really learn that much. I mean, I majored in math, and my brain felt a little knotted while I read.
But a bigger complaint isn't so much the math, but the story—he tries to keep the spirit of the original, but it felt like Alice in Wonderland was a much bigger influence, and the resulting puns could get a bit wearisome. Don't get me wrong; Alice in Wonderland is a fantastic book, but Stewart is no Lewis Carroll, and the result is a "Mathiverse" that is neither Flatland nor Wonderland.
My biggest beef, though, is a pretty minor thing that just irked me more and more. The characters know of a world called "Planiturth," in a dimension somewhat like Spaceland. The Space Hopper (who's guiding Flatlander Vikki Line through these strange dimensions) often refers to Planiturthians and their mathematical discoveries (e.g. Relativity). But for whatever reason, these Mathiverse beings (who themselves have multiple names) insist on conflating the names. It gets quite tiring reading about Alberteinstein and Maxplanck and Henripoincare, especially when there's no good narrative reason for it. After all, they know it's Planck's constant, not Maxplanck's constant, etc.
The verdict: if you're wanting a light overview of a broad swath of math and physics (and you really like math-based puns), give it a shot. But don't expect it to be as good as Flatland. If you prefer to keep your fiction and your science education from intermingling, skip this one.

Fed to jonathan's brain | August 28, 2003