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Gödel, Escher, Bach: an in-depth explainer

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Re: Gödel, Escher, Bach: an in-depth explainer

#82

> 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

True, but if you add too many axioms, the resulting set of axioms will not be computable anymore. If you allow your set of axioms to not be computable you can of course just use the set of statements that are true for whatever model of the natural numbers you have in mind. The whole point is that it's not possible to write down any sensible definition of what natural numbers are supposed to be.

Re: Gödel, Escher, Bach: an in-depth explainer

#83
post #19

Earlier quoted context omitted.

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.

Getting hit in the head can also change how someone perceives things. I think the above commenter was expressing frustration with the popular notion that taking drugs is some sort of shortcut to understanding consciousness, dynamic systems, etc

Note that I said "profound change" not "arbitrary change". What a faithful argument you've blessed us with.

If you think drinking alcohol or taking cocaine has the same mental effects as psychedelics, then, I guess all I can say is don't talk about what you don't know.

Re: Gödel, Escher, Bach: an in-depth explainer

#84
post #38

Earlier quoted context omitted.

(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.

I didn't mean to imply that and certainly don't think it is required. My question had little to do with the content and much more to do with the style, and the author's intended effects upon the reader.

Re: Gödel, Escher, Bach: an in-depth explainer

#85
Every socially awkward person who obsesses about their intellect is an in-depth explainer of Goedel, Escher, Bach. It's a fun read, and clever enough, but the relation between the work of the three is pretty shallow, and if you understand only what the book contains, you haven't gotten very deep into their valuable work. The book is more an act of self-indulgence on the author's part, or at best a tribute to the brilliance of his subjects, than a profound intellectual achievement in itself.

Re: Gödel, Escher, Bach: an in-depth explainer

#87

Am 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…

Middle ground opinion here. I found roughly the first third of GEB interesting. It's mind-expanding to think about self-reference and recursive structure in the context of all the other fields besides computer science, like natural language, music, art. GEB is a fun exploration of that for the first few chapters... but it doesn't get better after that, after a while it just keeps doing the same things and repeating the same stuff, and becomes a chore rather than fun to get through.

Re: Gödel, Escher, Bach: an in-depth explainer

#88

Is there a good book that is similar in spirit, but doesn't require the maturity of GEB? I know an 8th grader that would be a great target, but I don't know if they have the mathematical/logical maturity to get through it.

Try Raymond Smullyan. He has books at a range of levels of accessibility; I'm not sure if there's anything great for your 8th grader, but I remember first getting into The Lady or the Tiger? as a teen.

Re: Gödel, Escher, Bach: an in-depth explainer

#89
post #19

Earlier quoted context omitted.

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.

Do you think that you feel better than others for not taking drugs, and that this superiority is assailed when people who take drugs find common ground with one of your favorite thinkers? Because that's the only explanation I can think of for this blatant assholeishness and gatekeeping.

Hofstadter doesn't own thinking about consciousness, thinking deeply, or thinking philosophically. As a matter of fact these sorts of things, to many people - many more than who have even heard of Hofstadter - associate them with psychedelics. So it's not unreasonable, it's not an insult, to think Hofstadter going pretty deeply into questions of meaning, putting mind-bending Escher works in his book, referring to the person that wrote GEB as different from Hofstadter himself, etc... is psychedelic. These are things that most people find eccentric, and what psychedelic users find psychedelic.

The only way I could find insult in such comparisons is if I felt psychedelics themselves were morally inferior or insulting. I would examine that.

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