Why I Don't Love Gödel, Escher, Bach

A lot of people think that the goal of the book was to explain Gödel's theorem. Some even think the book shows that "mathematics, art and music are the same". In fact, as Hofstadter says in the preface (to the 20th Anniversary Edition I think), this is utter nonsense and he intended no such thing: his goal with the book was to build up a certain philosophical argument about what consciousness is (and his answer was something like self-reference, or transcending "levels").

I might be misquoting this, because, like most people, I found the way he builds up this argument more fun and memorable and interesting than the argument itself.

Do not read the book to understand Gödel's theorem, or Escher, or Bach. In fact, Hofstadter is not even really interested in Gödel's theorem itself: his interest is more in the particular trick that Gödel used to prove the theorem (Gödel numbering), which allows Gödel to encode statements about the system as arithmetic statements (within the system). And although the explanation in GEB is surely not the best explanations of Gödel's theorem, it is one of the most enjoyable musings on things "like" Gödel numbering — something you won't find in other places that are more interested in Gödel's theorem itself.

I think if one tries to read the book expecting to learn or understand something, one can get frustrated. But like other Pulitzer-Prize winners for nonfiction (say The Soul of a New Machine), any learning is only incidental; what one can enjoy is the way the book is constructed. It is a work of literature, not mathematics. The dialogues are my favourite parts of the book — sure they may not be realistic, but they take surprising turns, they often have a lot hidden in them (I remember reading one half way through and suddenly suspecting something, then noticing that they formed an acrostic, reading the first letters down the page). Other things I most loved about the book is the way it is self-referential, the way everything fits together, elaborate puns seem to be set up over a course of 300 pages, etc.

All in all, it is a book just simply of Hofstadter having fun.

(I had the same impression of Hofstadter's translation of Pushkin's Eugene Onegin — I've read at least three other translations; Hofstadter's may not be most literal but it's surely enjoyable and with the most outrageous rhymes: who else would rhyme "debts" with "Till his creditors cast their nyets"! You can read online an article he wrote [1] before starting his own translation, then a very critical review of his translation [2] but whose "bad" examples (and the whole first chapter linked there) show what's actually fun.)

You can see him enjoying himself, and you can go along if you'd like to have fun as well, forgiving a few things here and there, skipping parts that you don't find as much fun.

[1]: https://archive.nytimes.com/www.nytimes.com/books/97/07/20/r...

[2]: https://archive.nytimes.com/www.nytimes.com/books/99/09/12/r...

Is it such a great thing to be born that we are doing something good for our children by causing them to come into existence?

I mean, c'mon. The only way for there to be something good, or great, from a first-person experience, is for there to be a first person to actually do the experiencing.

Caveat, of course, bringing something into an existence that is only suffering is probably not so great. This is why we need to treat our food animals well (not to mention our kids!)

Yes, I understand that. And what I'm saying is: you can't do that. The halting problem is formally equivalent to proving arbitrary mathematical theorems. For every program, there is a corresponding theorem which is true IFF the program halts, and for every theorem there is a corresponding program that halts IFF the theorem is true. So the question: for what programs can the halting problem be decided? is formally equivalent to the question: what theorems can we prove? And we can't prove any useful theorems about that because if we could, we could solve the halting problem!

[UPDATE] I want to revise my claim that if we could prove interesting theorems about which programs have decidable halting properties that we could solve the halting problem itself. That's not true, because the word "interesting" is too poorly defined. But what is true is that if we could do this then we could prove theorems that we could not previously prove (that has to be true for any reasonable definition of "interesting"). Furthermore, we could now prove these theorems in a purely mechanistic way with no need for human creativity. By any stretch of the imagination that would be a major breakthrough.

From what I can tell the book has no real beginning or end, but three threads each of which start and end in different places, none of which start or end at the beginning or ending of the book. That chapter seems to be the end of one of those threads as the rest of the chapter after that statement doesn't really make sense.

Let's say, like many people, you enjoy the occasional article from The Onion. You can very easily continue enjoying them without reading Animal Farm, Gulliver's Travels or the collected works of Aristophanes.

TAOCP, to me, is in a similar category - it's worth remembering Knuth essentially carved the field of study out himself. If you need a reference or textbook, there are by now better places to start. If you are interested in the field, you should definitely get a hold of TAOCP as well. But you can be a perfectly fine and educated programmer (let alone person) and never touch the thing.