There was a very good (charitable) takedown of some of the content of GEB referenced on Hacker News a few months ago, but I can't find it :-( Can anyone help please?
Gödel, Escher, Bach: an in-depth explainer
61–70 of 252 posts
Re: Gödel, Escher, Bach: an in-depth explainer
#62I wonder how experienced the author of GEB is with psychedelics, that book always felt fairly trippy to me.
commitment to the material in that depth is not the product of drugs
He doesn't say it was written while high. He is wondering if H knew the effects of psychedelics and maybe tried to replicate the feeling in the reader.
Re: Gödel, Escher, Bach: an in-depth explainer
#63> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable. This is only half of it! Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people p…
How can a statement that is unprovable be true? I always had the impression that unprovable means you could add either the statement or its negation as an axiom, and both resulting systems are as consistent as the system you started with
> How can a statement that is unprovable be true?
If you are a platonist and believe in some preferred model where every statement is decided this makes perfect sense. For the rest of us, this just means that in a sufficiently complex system there will be undecided statements. Which is not such a big surprise – but a rather awesome technical exercise!
Re: Gödel, Escher, Bach: an in-depth explainer
#64Earlier quoted context omitted.
Zen and the Art of Motorcycle Maintenance comes to mind immediately. It works on several levels and is very accessible as a result. If you wanted to stray from the spirit of GEB into narrative prose, there are a number of books I could recommend, especially in science fiction.
ZMM is a great philosophy intro book. It's captivating and will get you in that "deep thinking mode" while never getting too overly dense. The actual core philosophy is a bit meh, but it really doesn't matter since the book is loaded with general good insight. +1
I liked the book, but didn't like Pirsig in it. I felt sorry for him for sure, but i'm not sure I could understand him and his reasoning for things.
Re: Gödel, Escher, Bach: an in-depth explainer
#65Earlier quoted context omitted.
Thank you so much for saying this, I find this misconception deeply insulting
It's not an insult. Psychedelics can profoundly change how someone perceives things. GEB has that sort profound shift in POV that many would associate with psychedelics.
The insult is the implication that thinking like this is somehow due to use of and exposure to psychedelics. Maybe some people need assistance in thinking deeply, Hofstadter certainly is not one of them.
Re: Gödel, Escher, Bach: an in-depth explainer
#66Earlier quoted context omitted.
Thank you so much for saying this, I find this misconception deeply insulting
(upvoted!) can you say more about this sensibility of yours? I'm genuinely intrigued, as I haven't heard a take like that before :) At risk of asking a leading question: is it some idea that deep truth should come from reason rather than the noise and chaos of psychedelics? (I don't do them myself, but hold them in very high regard as a force in the world)
I have no problems with psychedelics or their use. I took issue with the implication that they are needed in order to think in the way Hofstadter does - it's kind of like asking what flippers Michael Phelps uses when he swims in the olympics.
Re: Gödel, Escher, Bach: an in-depth explainer
#67An incredible piece of work. Shaped my life trajectory in many ways. Introduced me to thinkers like Daniel Dennett and Stanislaw Lem. Every generation or so a book comes along that, in retrospect, seems almost clairvoyant. This is one of those books.
I was introduced to both Dennett and Lem through 'The Mind's I: Fantasies And Reflections On Self & Soul', an anthology edited by Hofstadter and Dennett that I chanced upon in the university library. I recognized Hofstadter from GEB. I found 'I' very digestible, I admit that I still haven't finished GEB. It beckons me from the bookshelf.
Re: Gödel, Escher, Bach: an in-depth explainer
#68> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable. This is only half of it! Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people p…
How can a statement that is unprovable be true? I always had the impression that unprovable means you could add either the statement or its negation as an axiom, and both resulting systems are as consistent as the system you started with
Because as soon as you have a system that includes that new axiom, _new_ true statements can be created that are not provable. It's true for every formal system with any finite number of axioms.
Re: Gödel, Escher, Bach: an in-depth explainer
#69> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable. This is only half of it! Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people p…
How can a statement that is unprovable be true? I always had the impression that unprovable means you could add either the statement or its negation as an axiom, and both resulting systems are as consistent as the system you started with
"This statement is false".
GEB is a marvellous work that is accessible to anyone with reasonably good school grade maths. I chanced upon it by accident in the school library one day and was hooked after a few pages.
Anyway the crux of the matter is that you can very carefully construct a statement about a system that can't be either proven or disproven by that system! I don't have anything like the formal knowledge to really get to grips with it and the discussions on infinities and so on are pretty mind blowing. However, you feel that DH is imparting glimpses into the sheer beauty of the ideas he covers.
Wait 'til you discover what ricercar and quining is all about - bloody lovely. Just read it but take your time. There is something in there for everyone. You often get told by clever people about the links between maths, music and art. Mr H easily gives the best argument I've ever seen that attests to that being true, whilst giving your brain a right good kicking.
There was a Dutchman, a German and an Austrian who walked into a book ...
Re: Gödel, Escher, Bach: an in-depth explainer
#70Am I the only one who did not find this book that interesting? I studied CS so it just felt like reading my class textbooks again, except with random trippy stories in between that try to shoehorn theory into a poor metaphor. The fundamentals of CS (strings, automata, graphs) are elementary building blocks. This is by design. You can apply them to almost anything. Almost everything "is a graph", or "recursion" if you…
I read it before studying cs and I thought it was fascinating and made me want to study it. After studying it at the grad school level I re read it and found the book somewhat pedantic. It’s a bit like the black swan in the regard: it package advanced under grad level stem topics with colorful anecdotes and musings.