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

by So8res2 min read1st Sep 201310 comments

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Machine Intelligence Research Institute (MIRI)Book Reviews
Personal Blog

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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10 comments, sorted by Highlighting new comments since Today at 7:17 PM
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I will observe that

(and it didn't introduce any Nate!novel arguments)

Feels to me better than

(and it didn't introduce any novel arguments)

Or something similar, because it reminds the reader that the word 'novel' is a two-place word. I will be doing this in future.

I agree, except that by this point I had already forgotten the author was called Nate.

I'm not familiar with the exclamation point notation, and I'm not sure where it originates, though of course I could infer it from context. "Any arguments that were novel to me" seems to achieve the same thing in a less jargony, more accessible way. Is there any reason to go with the "Nate!novel" form over that?

It originates in fanfiction summaries, where authors have a limited number of characters to describe their characters.

GEB will take you from superficial knowledge to full grok.

A word of caution: there is a risk when reading popular science/math books like GEB of coming away feeling like one understands something at a higher level than one actually does, particularly if one hasn't already studied the subject formally.

If one has formally studied incompleteness before, it's easy to wave away standard primitive recursive derivations (e.g. the proof predicate) as tedious and trivial and beside the main point, but having this attitude the first time around could be dangerous.

I read GEB years ago, and recall liking it quite a bit, though I disagree with Louie Helm's endorsement of GEB as a course reference, at least not without supplementation from a "standard" source like these notes (or any formal logic textbook).

I agree that GEB should be supplemented with formal study for a deeper understanding.

To clarify my anecdote, my "formal study" of incompleteness allowed me to manipulate the symbols, follow the proofs, pass a test, and conclude that incompleteness is something I have to believe.

By contrast, GEB showed me incompleteness intuitively. It made incompleteness seem natural and inevitable. It convinced me, instead of forcing my beliefs.

("There's a difference between a proof and a why", as I like to say.)

This is likely due in part to the fact that my "formal study" of incompleteness was part of university courses, and was not self-motivated. I like to think I could have gleaned a "why" from the formal proofs -- but I didn't. It wasn't high priority.

GEB makes it fun and relatively easy, which is a huge part of its appeal. That said, reading about something is rarely a substitute for hands-on experience.

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

My book reviews have done well in Main, but I try to discuss the book in much more depth; this post feels right for Discussion for me. (You'll also notice from my reviews that the closer the book is to the main LW focus, the more upvotes it gets.)

I've found forcing myself to write something about every chapter to be rather useful in both making sure I've captured all that the book discusses and making it easy to recommend which sections of the book someone should read. That level of depth is also way better at convincing people that they should read the book, because they can visualize it as lots of small pieces each worth reading, and because it makes it easier for people to pick and choose which pieces to read. You have the start of this here, talking about Chapters 5-8 in a bit more depth, but more would be helpful.

Did you personally witness that this style is better at convincing people to read the book, or is it something you surmised? I'm asking because I've been thinking about the same style for my reviews, but found myself wondering whether a detailed summary wouldn't make people feel they've already got the gist of the book and it's therefore less important to actually read it.

Did you personally witness that this style is better at convincing people to read the book, or is it something you surmised?

I'm generalizing from a few examples. Matt_Simpson and beoShaffer both commented that the review convinced them to read the book, and in both of the comments I got the impression that the level of detail was what made the book interesting enough to read. I also had someone contact me privately to talk about the book, which I believe was because of the level of detail. I haven't gotten any feedback that said "now I don't have to read the book!" but I also would expect someone who felt that way to be less likely to give that feedback than someone who now wanted to read the book.

It also seems likely to me (this part I'm surmising) that most people will have had many of these books recommended to them before, and a detailed exploration is more likely to tip them from "I've heard it's good" to "I actually want to read it" than another recommendation.

I do think that there are summaries- like badger's summary of Epistemology and the Psychology of Human Judgment- that on net do substitute (partially) for reading the book, rather than complementing reading the book. (EPHJ is particularly easy to summarize for LW, because it's basically a philosopher and a philosopher/psychologist arguing "the point of philosophy should be to teach people how to live effectively given the minds they have," which is one of the foundational beliefs of LW.) I think whether or not this is possible is basically determined by the length/complexity of the book, and when it's possible it's generally desirable.

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

Slightly short for main, IMO, but no strong opinion. (I upvoted this in Discussion for useful information -- would probably not vote on it in Main as quality and quantity expectations are higher.)

As a note, I'm unlikely to respond to future children of this comment.