MIRI course list book reviews, part 1: Gödel, Escher, Bach

bySo8res6y1st Sep 201310 comments

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I'm Nate. I was recently introduced to the ideas of existential risk and unfriendly AI. I've decided to read the books suggested in the MIRI course list. I'll review the books as I read them. Repeating the knowledge is expected to help solidify it. Public accountability is expected to help keep me on track. Hopefully my notes will also be useful to others. This is the first such review.

Gödel, Escher, Bach

I'll be reviewing this book from memory. I started it in 2010 at the recommendation of a friend. I got frustrated early on when Hofstadter introduced topics that I already knew well (such as recursion). This turned out to be a mistake; the book picks up shortly thereafter. I finished the rest of it maybe four months ago, around the time that I finished the sequences.

Overview

Gödel, Escher, Bach is an incredibly well-written foray into the intersection of art, mathematics, philosophy, and biology. It explores the border between syntax and semantics. It's not a textbook, but you'll learn more about logic than most introductory courses will teach you.

The book is composed of alternating dialogs and chapters. The dialogs are witty narratives which take on the structure of concepts discussed in the following chapter. It's hard to describe how this works, but it's very effective. The dialogs are brilliantly designed and are by far the most entertaining part of the book.

What I didn't like

I'd already been exposed to many of the topics in GEB. I have an aversion to being taught things I already understand, so some chapters frustrated me. The new-signal to old-signal ratio was lowest in chapters 5-8. Computer scientists beware: the book will feel slow early on. Chapter 5 is skippable. 6-8 are not, because the specific variants of propositional calculus and number theory that Hofstadter sets up are used (to brilliant effect) in later chapters.

One of the late sections of GEB discusses reductionism. The discussion is quite good, and I would recommend it to people who misunderstand the reductionist argument. But personally I found it boring, as I need no further convincing (and it didn't introduce any Nate!novel arguments).

The final section of GEB is a discussion of the artificial intelligence field, including predictions made decades ago. While most of the predictions were solid, the chapter is no longer relevant. For some reason, temporally-irrelevant text in narratives makes me feel uncomfortable.

These concerns were dwarfed by the wit, fun, and knowledge embedded in the rest of the book.

What I learned

GEB didn't introduce that many new concepts to me. What it did was bring old concepts to life. Before reading GEB, I knew about incompleteness and could state the theorem. After reading GEB, I can construct actual Gödel sentences. GEB will take you from superficial knowledge to full grok.

A number of tidbits stuck with me:


Every message has many levels:

  1. The framing (Whatever makes you recognize a message)
  2. The outer message (The symbols/words)
  3. The intended meaning

I hadn't thought about the frame message as a layer of the message before GEB.


There's a hard distinction between the symbol-game of formal logic and the interpretation of those symbols. (The difference between the symbol ∧ and its meaning as a conjunction).

Before GEB, I would nod my head at this fact, but it sounded silly. Of course the symbols were just symbols: but they were created with human meanings in mind, alongside rules that preserve said meanings. I didn't see a need to enforce the distinction.

In reading GEB I saw firsthand the different ways that the symbols could be interpreted, and the power available when multiple interpretations are considered simultaneously. Now the distinction is of paramount importance to me.

(As a side note, this realization helped me retroactively gain a higher understanding of Type Theory, which is all about making use of many different levels of interpretation at once.)


Some questions must be unasked.

Have you stopped beating your wife?

The word 'mu' unaskes a question. I really wish the word 'mu' was better known, so I could use it in daily conversation without drawing strange looks.


Though you may find this to be obvious, I cannot assert its truth:

Nate Soares cannot consistently assert this sentence.

This is my new favorite way to illustrate incompleteness.


There were many more little things that clicked, and a lot of pleasant surprises which aren't coming to mind. Also, the book isn't only about Gödel: I learned a lot about Escher and Bach along the way. If you read this book, I definitely recommend having a means to play Bach's music on-hand: many of the chapters are more powerful while listening to the Bach compositions that they allude to.

Conclusions

If nothing else, I recommend reading GEB for the sake of art. It's masterfully constructed. It will hopefully help you understand math that you know superficially. Even if it can't teach you the math it can probably teach you about art and music.

If you're new to the fields of math / logic / computer science, then Gödel, Escher, Bach is a must. However, I can't guarantee that the new-signal to old-signal ratio is favorable for people already knowledgeable in relevant fields.

Side question: Is this the sort of thing people want to see in main?

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