Gödel, Escher, Bach - a long climb worth making

This one took me a very long time to read, and I already know I’ll need to reread it to fully understand it.

That sounds like a warning, but it’s a 5/5 from me. I picked it up out of personal interest and read it in the background alongside other things, which suited it, because it is not a book you race through. By the end I could genuinely say I understand what Gödel’s incompleteness theorem is about, and I walked away with some great takeaways about the nature of consciousness. It takes a long time to get there, and there are a lot of tangents on the way. Some of them didn’t help me, but others really clicked and made the whole theorem far easier to grasp.

The tangents are the strange charm of the book. They’re all interesting and in depth. I’ve read several biology books and even one specifically on genes, and I still learned new things here about DNA and how it works in cells.

What surprised me most was the AI section. It’s amazing that this was written before any chess AI could beat a grandmaster, back in the “prolog” and rules based phase, long before neural networks took off. The author nailed the problem LLMs would eventually have: an inability to think across multiple levels of abstraction. It’s why ChatGPT struggles to tell you “how many r’s are in strawberry”, it only can “think” on the token level.

I struggled with the math heavy parts, but the author explains the same concepts in overlapping ways, so even when I didn’t properly follow the maths the other angles made up for it. I loved most of the dialogues, especially “Ant Fugue”, which blew my mind a bit and finally made me understand what he meant by “thinking in symbols”. The story of the ant colony has stuck with me ever since, the way a colony behaves as one mind while no single ant is in charge, much like the brain’s synapses. It even shifts how I think about AI: I can imagine an LLM gaining some form of consciousness just through a sheer number of parameters, the same way the ant fugue emerges, though its consciousness would be nothing like mine.

Read this if you want to really understand Gödel’s incompleteness theorem, and to pick up a lot along the way about Escher, AI, music, information theory, DNA and plenty more. Anyone really interested in AI will get a lot out of it. Don’t despair in the first half. The second half is easier to follow and much less math heavy.