Bingo Book Review 19: White Whale
I think it was about 3 years ago when I read How to Bake π, mostly liked it, and went out to get the author’s subsequent book Beyond Infinity. I started it, got bored after about a chapter, and it’s been sitting on my coffee table since then. I’ve promised myself every now and again that I’m going to finish off the 3-4 books that I’ve started at some point and not finished, so this time it was Beyond Infinity’s turn.
The author Eugenia Cheng’s books tend to be high-level abstract math stuff for non-math people, at least in theory. A lot of parts of how she explains things like how infinity plus one is not the same thing as one plus infinity and both are legitimately plausible mathematical concepts makes sense, but as she points out, that kind of abstraction is “only thought experiments, not logical arguments. That’s why they’re open to debate, and why we have to work hard to turn them into genuine mathematical arguments that are no longer open to debate, at least not by people who understand mathematics.” (240) I’m putting the page number in not just because I’m an English teacher, which I am, but also because I want to show how late in the book this admission is. I would have liked to have seen that much earlier as it would have helped make some of the main examples early on make more sense. Some examples, like Hilbert’s Hotel, are frequently brought up, so it would be useful to fully understand them. The basic gist of that one is that there’s a hotel with infinite rooms, it’s full, but then it can always manage to accommodate one more guest, often by shuffling guests around. I spent most of the book not accepting this because according to logic if a hotel is full, even one with infinite rooms, then it cannot have a spare room available. I still don’t quite buy it.
For me, the last quarter of the book, which deals far less directly with infinity, makes the most sense. Admittedly, I have not taken a math class since my freshman year of undergrad many years ago, but this is supposed to be a book for the non-mathy. One of my colleagues decided to take college algebra this year since he never took that during his own undergrad, and I wonder how much a book like this would make sense to someone currently working with the subject in a non-expert capacity. The later sections deal with things like dimensions, geometry, and matrices. These bits make the most sense but they are also the bits least directly connected to the main subject, infinity and all the stuff someone who wants or cares to can do with the concept.
I don’t especially care for general philosophy, and that’s a lot of what this book is: abstract, theoretical philosophy math-style. It’s not my kind of reasoning; as such, I didn’t get a whole lot out of this book, although I did learn an interesting thing I hadn’t know before: there is a mode of transport (kinda, in the sense that an elevator is transport) called the paternoster, which sounds like a cross between an escalator and revolving door. I’ve never seen or heard of this before, yet I would now rather like to meet one. That’s probably the most relevant thing in the book; I appreciated some of the culinary examples, but those were what drew me to the first book in the first place. I heard on the radio the other day Eugenia Cheng has a new book out on gender, which sounds interesting, but then again, she’s always made more sense to me on the radio than on paper.