Gödel, Escher, Bach by Douglas Hofstadter
Rating - 2.5: parts of it are worth reading once (borrow it from a library)
You will notice that it has been a long time since my last review. This is a long book that does not go quickly. Some parts are mind-numbingly tedious, so I was stuck on one chapter for more than a week. Other parts are very insightful, and you pause after the chapter to contemplate them. Some require re-reading to get their full meaning, and you are encouraged to pause and do some sample problems from number theory. This book is not a small project.
GEB explores how recursion and self-reference allow meaning and complexity to arise from the operation of very simple units. Number theory is a window on how formal statements can mirror reality and how we impart meaning to the manipulation of symbols. We see similar patterns in our neurons and DNA, suggesting this as a path to understanding how consciousness and identity arise.
The structure and content of the book mirror each other. An idea will be explained in a way that uses the idea. Each chapter is proceeded by a dialogue that demonstrates this. Bach is our musical structure, Escher is our visual representation, and Gödel is our guide to its formal logic; all three (and others) deal with recursion, so the ideas bend back onto themselves.
Yes, this book gets two paragraphs of summary. It is that hardcore.
I wanted to like this book more than I did. I found myself at the usual 20% point realizing that I was not enjoying it, but I stuck it out because this is one of the most highly recommended books that I know. I find that I would have few people to whom I could recommend it, and even then I might recommend using a summary for some chapters. In the spirit of the book: the chunked version is more valuable.
Great attention to detail is both its strength and its failing. The book does an excellent job of showing, not telling. Rather than just saying that number theory proves x, Mr. Hofstadter walks through the steps. Better yet, he goes back one step earlier to show how you derive number theory. The chapter on DNA takes you down to the base pairs. If you want all that, it is there. If you do not want all that, it is still there. This is healthy. To really get the ideas, you should work through them. Most audiences, however, probably do not need to get the ideas that deeply, and it makes it seem suspect when there is any hand-waving about what is assumed but not demonstrated.
The best example is Typographical Number Theory. Mr. Hofstadter demonstrates a notation for number theory by which all derivations are simply manipulations of symbols according to rules. No thought is necessary, just the repeated application of a set of tools to a set of theorems. If number theory is too wild for you, this could be a way to calm things. You might want to skip TNT, but it is a central part of the book, so you need to have at least some understanding of what he is talking about. A later dialogue inadvertently reflects TNT in asking why we do not read books one letter at a time: "Well, it sounds like that would turn the experience of 'reading' The Pickwick Papers into an indescribably boring nightmare. It would be an exercise in meaninglessness, no matter what concept I associated with each letter." (I presume that Mr. Hofstadter thinks otherwise, since the next dialogue cites number theory as a great entertainment for an evening, explicitly not something that will help you get to sleep.)
So that is why we have a *.5 rating: punishing detail. It is good intellectual vigor to read through it, but it is going to be far more detail than you need in your life, and it is not clear what is skimable.
The book is clever, too clever by half. There are anagrams and puns everywhere. The structure mirrors the content, which helps and leads to some very interesting bits. In one dialogue, the lines of the second half mirror the first half. Another discusses music and arranges the characters' lines to act out the fugue elements as they come up. There are nested dialogues, nested pictures, and theorems that represent themselves. Typographical Number Theory sets up a bit that reaches an unexpected punchline a few hundred pages later. One bit uses six letters to make a kind of joke about DNA, the periodic table, music, and the book itself.
That is a lot to pack into six letters. The book is very densely packed, like DNA. This is another way that form follows function, because the book so often shows how many (and self-reflecting) layers of meaning are packed into simple-seeming structures.
At the extreme, we have an unreliable narrator. That can be great in fiction, but it is troubling in non-fiction. One never knows if we can fully trust the author. Is this next bit a joke that we are meant to catch? An intentional mistake or trap, which may or may not be pointed out? Mr. Hofstadter discusses how a message may or may not successfully signal that there is a message to be decoded there. Have you ever sent signals that no one realized were signals? It seemed so obvious to the author... The joke bibliography and index entries are some of the most visible, and some puzzles are pointed out along the way. Add thirty years of progress since the book was written to whatever gaps in knowledge the author had at the time, and we really cannot trust the book to be fully accurate. (Think of computers in 1979, although the important fundamentals are the same.)
One famous idea from GEB is how an author can hide the true ending of a book. A reader can always see how many pages are left, so the author needs to pad the end of the book with other stuff after the true ending. The lengthy bibliography and index can serve that function here, but we have an explicit statement about including extraneous ideas and characters. Of course this is demonstrated in the dialogue that proposes it, but would you care to guess where the real ending of GEB is?
Or, given the structure of the book, the real beginning? Note that odd first word, and the last dialogue.
You should have the feeling that you are missing something. You probably are. I surely did. The next question would be if that is an important something, or just another instance of Mr. Hofstadter subtly hiding his name in the book (the index gives some pointers there). There could be a variety of esoteric messages hidden within. You could spend a long while sifting through and playing. Any demand for an obvious payoff defeats the purpose of it all.
That is how clever things are: wonderful to get, but you can usually do without them. You do not get the full meaning from a book if you do not catch its allusions, but I would be hard-pressed to say what you lose other than some ill-defined "flavor." While I may appreciate Buffy the Vampire Slayer on a much deeper level than you, you will somehow get by without extensive knowledge of pop culture, classical mythology, and in-jokes. I may get slightly more utility from the show, but it takes me much longer to explain the full impact of a scene with many references. If you have to explain the joke, it isn't funny.
See, that was an example. I just spent too long explaining why it is a bad idea to spend too long explaining. And there I go again. The book rubs off.
I have mostly addressed structure and the way of telling, rather than the content. Given the book, that might mean that I have adequately covered the content. I think the clever tricks are probably too distracting, so most people talk about GEB as an exercise in self-reference, rather than really addressing self-reference and the emergence of meaning from complexity. Mr. Hofstadter may have thought so, since he has a recent book that goes back to the core topic in a purer way. Gödel's Incompleteness Theorem is meant to be deeply meaningful, not a clever trick.
There book yields much, but you must put much work into it. I think that's called learning.
Amazon link
Gödel
Escher
Bach
You will notice that it has been a long time since my last review. This is a long book that does not go quickly. Some parts are mind-numbingly tedious, so I was stuck on one chapter for more than a week. Other parts are very insightful, and you pause after the chapter to contemplate them. Some require re-reading to get their full meaning, and you are encouraged to pause and do some sample problems from number theory. This book is not a small project.
GEB explores how recursion and self-reference allow meaning and complexity to arise from the operation of very simple units. Number theory is a window on how formal statements can mirror reality and how we impart meaning to the manipulation of symbols. We see similar patterns in our neurons and DNA, suggesting this as a path to understanding how consciousness and identity arise.
The structure and content of the book mirror each other. An idea will be explained in a way that uses the idea. Each chapter is proceeded by a dialogue that demonstrates this. Bach is our musical structure, Escher is our visual representation, and Gödel is our guide to its formal logic; all three (and others) deal with recursion, so the ideas bend back onto themselves.
Yes, this book gets two paragraphs of summary. It is that hardcore.
I wanted to like this book more than I did. I found myself at the usual 20% point realizing that I was not enjoying it, but I stuck it out because this is one of the most highly recommended books that I know. I find that I would have few people to whom I could recommend it, and even then I might recommend using a summary for some chapters. In the spirit of the book: the chunked version is more valuable.
Great attention to detail is both its strength and its failing. The book does an excellent job of showing, not telling. Rather than just saying that number theory proves x, Mr. Hofstadter walks through the steps. Better yet, he goes back one step earlier to show how you derive number theory. The chapter on DNA takes you down to the base pairs. If you want all that, it is there. If you do not want all that, it is still there. This is healthy. To really get the ideas, you should work through them. Most audiences, however, probably do not need to get the ideas that deeply, and it makes it seem suspect when there is any hand-waving about what is assumed but not demonstrated.
The best example is Typographical Number Theory. Mr. Hofstadter demonstrates a notation for number theory by which all derivations are simply manipulations of symbols according to rules. No thought is necessary, just the repeated application of a set of tools to a set of theorems. If number theory is too wild for you, this could be a way to calm things. You might want to skip TNT, but it is a central part of the book, so you need to have at least some understanding of what he is talking about. A later dialogue inadvertently reflects TNT in asking why we do not read books one letter at a time: "Well, it sounds like that would turn the experience of 'reading' The Pickwick Papers into an indescribably boring nightmare. It would be an exercise in meaninglessness, no matter what concept I associated with each letter." (I presume that Mr. Hofstadter thinks otherwise, since the next dialogue cites number theory as a great entertainment for an evening, explicitly not something that will help you get to sleep.)
So that is why we have a *.5 rating: punishing detail. It is good intellectual vigor to read through it, but it is going to be far more detail than you need in your life, and it is not clear what is skimable.
The book is clever, too clever by half. There are anagrams and puns everywhere. The structure mirrors the content, which helps and leads to some very interesting bits. In one dialogue, the lines of the second half mirror the first half. Another discusses music and arranges the characters' lines to act out the fugue elements as they come up. There are nested dialogues, nested pictures, and theorems that represent themselves. Typographical Number Theory sets up a bit that reaches an unexpected punchline a few hundred pages later. One bit uses six letters to make a kind of joke about DNA, the periodic table, music, and the book itself.
That is a lot to pack into six letters. The book is very densely packed, like DNA. This is another way that form follows function, because the book so often shows how many (and self-reflecting) layers of meaning are packed into simple-seeming structures.
At the extreme, we have an unreliable narrator. That can be great in fiction, but it is troubling in non-fiction. One never knows if we can fully trust the author. Is this next bit a joke that we are meant to catch? An intentional mistake or trap, which may or may not be pointed out? Mr. Hofstadter discusses how a message may or may not successfully signal that there is a message to be decoded there. Have you ever sent signals that no one realized were signals? It seemed so obvious to the author... The joke bibliography and index entries are some of the most visible, and some puzzles are pointed out along the way. Add thirty years of progress since the book was written to whatever gaps in knowledge the author had at the time, and we really cannot trust the book to be fully accurate. (Think of computers in 1979, although the important fundamentals are the same.)
One famous idea from GEB is how an author can hide the true ending of a book. A reader can always see how many pages are left, so the author needs to pad the end of the book with other stuff after the true ending. The lengthy bibliography and index can serve that function here, but we have an explicit statement about including extraneous ideas and characters. Of course this is demonstrated in the dialogue that proposes it, but would you care to guess where the real ending of GEB is?
Or, given the structure of the book, the real beginning? Note that odd first word, and the last dialogue.
You should have the feeling that you are missing something. You probably are. I surely did. The next question would be if that is an important something, or just another instance of Mr. Hofstadter subtly hiding his name in the book (the index gives some pointers there). There could be a variety of esoteric messages hidden within. You could spend a long while sifting through and playing. Any demand for an obvious payoff defeats the purpose of it all.
That is how clever things are: wonderful to get, but you can usually do without them. You do not get the full meaning from a book if you do not catch its allusions, but I would be hard-pressed to say what you lose other than some ill-defined "flavor." While I may appreciate Buffy the Vampire Slayer on a much deeper level than you, you will somehow get by without extensive knowledge of pop culture, classical mythology, and in-jokes. I may get slightly more utility from the show, but it takes me much longer to explain the full impact of a scene with many references. If you have to explain the joke, it isn't funny.
See, that was an example. I just spent too long explaining why it is a bad idea to spend too long explaining. And there I go again. The book rubs off.
I have mostly addressed structure and the way of telling, rather than the content. Given the book, that might mean that I have adequately covered the content. I think the clever tricks are probably too distracting, so most people talk about GEB as an exercise in self-reference, rather than really addressing self-reference and the emergence of meaning from complexity. Mr. Hofstadter may have thought so, since he has a recent book that goes back to the core topic in a purer way. Gödel's Incompleteness Theorem is meant to be deeply meaningful, not a clever trick.
There book yields much, but you must put much work into it. I think that's called learning.
Amazon link
Gödel
Escher
Bach
posted by Zubon at 8:08 PM
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