What do Gödel, Escher, and Bach Have In Common?
Reviewing the book masterpiece written by Douglas R. Hofstadter
I was really looking forward to this book, seeing it mentioned many times. It’s a Pulitzer Prize-winning book that explores the connections between mathematics, music, and intelligence through the works of mathematician Kurt Gödel, artist M.C. Escher, and composer Johann Sebastian Bach. The intersection of fields alluded to directly in the title is what drew me into it.
The book argues that Gödel, Escher, and Bach are all connected by the theme of self-reference and self-referential systems, with Gödel’s incompleteness theorem, Escher’s paradoxical art, and Bach’s fugues all serving as examples of this phenomenon in different domains.
I was immediately hooked when he dived into Godel’s incompleteness theorems, which I’ve longed been fascinated by but always felt I could never understand on a deep level. I enjoyed his description of the topic, and I understand the topic much better. I particularly liked the connection to the history of mathematics itself, mentioning Rusell’s and Whitehead’s Principia Mathematica, which tried to derive all mathematics from logic.
Beyond Godel, the other two key figures are Escher and Bach. It’s not like they are all related or saying the same thing, but he does use it to explore the topic he wants to explain, often being self-reference. I really enjoyed the connections between mathematics and Escher, and it’s great that there are so many pictures in the book. Bach was equally fascinating, but harder to grasp due to my music illiteracy.
The book heavily relies on logic, and sometimes mathematics. I was quite hesitant about this, but at least in the beginning, I was pleasantly surprised about how they were introduced. It made me view logic differently, and it doesn’t look as intimidating as it once was.
At the beginning of each chapter, Douglas tells a little narrative that exemplifies the concepts he will cover later. I was mind-blown by how good some of these were. Not only were they incredibly enjoyable to read by themselves as just short stories, but I was amazed by his creativity to put such complex logical notions in a narrative form that doesn’t require math. Some were better than others, but overall it was fantastic and it made the book super fun to read and felt incredibly original. It’s most definitely unique, and that alone makes it super valuable, even if it’s not your cup of tea.
Despite being topics that I enjoy and I liked the authors writing, as the book progressed, it got harder and harder. It wasn’t the type of hard that it seemed impossible for me to get, although at times it was the case, most of the time it just required an insane amount of concentration and re-reading. And this killed the mood for me at some point.
The beginning was honestly fun, and while I love non-fiction, it isn’t an adjective that fits very often. But slowly, that fun faded away, and I got increasingly demotivated to read it. The way I had to approach the book felt like I was studying for an exam, and it just wasn’t worth it. I took a break halfway and hoped that I’d be more motivated later, but I never had the motivation to get back to it.
I felt bad quitting the book because I’m sure that there are many interesting ideas that I’d get to, but I just couldn’t justify the hassle. However, perhaps the book got a bit better later on. And if you’re more inclined towards mathematics and logic than I am, I think you will get a lot more out the book and find it easier to read.
I don’t regret reading the first half that I did, and in the beginning, it was super fun, and I understood Godel’s theorem much better, but overall it just wasn’t for me. Nevertheless, I was impressed by the author’s creativity and the emphasis on self-reference. Perhaps I will pick up a newer book from him, as this one was quite old, published in 1979.
It’s worth mentioning that MIT has an online course for free based on the book, which is 8h long or so (not very long considering GEB is 700 pages), and it might be a good alternative instead of the book. You can access it here: https://ocw.mit.edu/courses/es-258-goedel-escher-bach-spring-2007/
“Achilles: …But I’m still a bit puzzled about this business of going round and round in circles. Suppose I take ten paces due north, then ten paces due east, then ten paces due south, and then ten paces due west. What will I be?
Tortoise: What a silly thing to ask! You’ll be back where you started, of course.
Achilles: Back where I started? Not at all! I’ll have described a square, and have returned to my starting point.
Tortoise: But you will have been round all four sides of it, and therefore will have turned round, so to speak.
Achilles: Nonsense! Turning round is going round in a circle. What I’ve done is describe a square.
Tortoise: But, my dear chap, that’s just what going round in a circle is: describing a square.”
Thanks for reading! If you read non-fiction and you’d like to try out a more efficient note-taking system, check out the app I’m developing, Raven: https://www.ravenotes.com/
