Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Why I Don't Love Gödel, Escher, Bach

blog.infinitenegativeutility.com

Post reply on HN
Print view View original

31–40 of 348 posts

Re: Why I Don't Love Gödel, Escher, Bach

#31

Post by stuntkite »

audunw wrote: post #29

I read and finished GEB first, and then read 'I am a Strange Loop'. I think the trick to reading GEB is to not take it so seriously. You can skim sections, you can skip parts, you don't have to understand everything, not everything has to make sense. I think the author here misses that when he complains such about the quality of the metaphors. They're not meant to help understand, as much as being there to give a vag…

I definitely think GEB is important to getting into IAASL, which is why after I got into the book a bit I put it down and really made an effort to get into GEB. IAASL can totally be read on it's own, but I think it's fair to say you at least want to have a copy of GEB around to look at while you're reading it.

I can't recommend that course enough too. I guess I couldn't find the book on my own. So anyone that can, great! But having someone who knows the book take your through it, at least for me, made it a lot more fun. It was, in my experience, kind of a rare book in how I wanted to share what I was looking at with someone but didn't have anyone to share it with really. Having the prof giving a breakdown made it a lot more digestable for me.

Re: Why I Don't Love Gödel, Escher, Bach

#32

Post by waserwill »

The reviewer has interests which are superficially discussed in the book, and even those about which readers may often express interest. I believe the book would have been several times less interesting to me had I not looked into the philosophy of mind and the problems of consciousness and neurobiology. I'd enjoyed the math, the music, the art, the cultural references, and the surreal metaphors; but those weren't the full story—Hofstadter says that the book is not about those things outrightly, albeit towards the latter chapters, iirc. These references, though generally enjoyable, serve as a path towards expressing a strange proposition, however indirectly. Perhaps it was done more clearly in IAASL, but I've not read it. However, personally, the rhetorical flourish with which it was done here was enjoyable.

Re: Why I Don't Love Gödel, Escher, Bach

#33

Post by zirkonit »

lolc wrote: post #28
muro wrote: post #5

tl;dr. Excellent first few chapters (which deserve the high praise and possibly are the cause of all the hype), gets less and less interesting. At some point, I dreaded returning to it and gave up.

Did you sum up your experience reading the book? Or did you try to sum up the critique we're discussing here? If it's the latter you failed.

"tl;dr" here actually means "Too long; didn't read", as in, GP's result of reading the book, and not the "here is the summary" we usually tend to associate with the abbreviation.

Re: Why I Don't Love Gödel, Escher, Bach

#34

Post by stan_rogers »

stuntkite wrote: post #21
zerr wrote: post #14

Earlier quoted context omitted.

Can you be more specific - exactly from what page should one start reading GEB?

It's been about 2 years I think since I did that. Skip the Socratic dialogs basically. I think the course I linked is the same one I went through. He covers it in the first video. Also once you get through the other parts, the Socratic discussions are easy to come back to. You just don't end up in nowhere taxed with his presentation before you really find the book.

Well, if you forget about the fact that Aunt Hillary is the thesis, I suppose.

Re: Why I Don't Love Gödel, Escher, Bach

#35

Post by fifticon »

jatsign wrote: post #20

Does anyone have a better metaphor, or a link to someplace with a better explanation, of the Incompleteness Theorem?

It proves, that it is impossible to design any formal system, within which it would be possible to prove every principle/aspect that applied to that same system ( aspects that nevertheless WERE true, and CAN be proven by using a 'bigger hammer'.) In a way, the problem is, that whenever you expand your system to make it 'more complete' (to be able to prove more stuff), you'll invariably introduce new aspects you THEN can't cover. You "can't pull yourself up by your own hair".

Re: Why I Don't Love Gödel, Escher, Bach

#36

Post by stuntkite »

jatsign wrote: post #20

Does anyone have a better metaphor, or a link to someplace with a better explanation, of the Incompleteness Theorem?

Here's a pretty good reddit discussion about it. That's the best I could find with a quick google.

https://www.reddit.com/r/rational/comments/30144c/geb_discus...

Re: Why I Don't Love Gödel, Escher, Bach

#37

Post by chriswarbo »

beaconstudios wrote: post #24
jatsign wrote: post #20

Does anyone have a better metaphor, or a link to someplace with a better explanation, of the Incompleteness Theorem?

I'm not familiar with directly, but if you're more familiar with comp-sci: based on my understanding of Curry-Howard correspondence, I would think it's the logic equivalent of the halting problem. I could be way off-base though, I'd appreciate a mathematician chiming in on whether my intuition is accurate here.

(Caveat: I'm a computer scientist, not a mathematician)

The halting problem, and universal computation itself, came directly out of work on incompleteness. Incompleteness is about being unable to prove statements in a particular system; it leaves open the possibility that a more powerful system might be able to prove that statement (but that more powerful system will have its own incompleteness, and so on).

Turing got involved after attending a series of lectures on Goedel's incompeteness theorem. He came up with turing machines, showed that they cannot decide their own halting problem, and proved that they're equivalent to lambda calculus. Goedel tried to make a more powerful alternative to lambda calculus, called general recursive functions, but it also turned out to be equivalent to turing machines and lambda calculus.

This lead to the Church-Turing thesis, which claims that any effective/physical/realisable system of logic cannot be more powerful than turing machines/lambda calculus/general recursive functions. In this sense, we can still "solve" the halting problem by using a more powerful logical system (e.g. oracle machines), but the Church Turing thesis says that we can never carry out those calculation to get a true/false answer.

I like to think of incompleteness as a mathematical property, applying to all systems but allowing the "escape hatch" of switching to a more powerful system; and I like to think of the Church Turing thesis as a law of physics, that there is a limit to the logical power of any physical system (i.e. Turing completeness).

There's a nice summary at https://www.youtube.com/watch?v=GnpcMCW0RUA

Re: Why I Don't Love Gödel, Escher, Bach

#38

Post by gota »

jimhefferon wrote: post #2

> The high-level, slightly handwavey description of this theorem is that, for any sufficiently expressive mathematical proof system, there are more true facts within the system than there are proofs for facts, which in turn means that not every fact can be proved No, no, no. The proof is not by cardinality. The proof is constructive. That is the point of the book, or at least a major theme of it. For example, that is…

If I recall, the point is that if you have a record player that can play _every record_, then it can play _a record that breaks it_.

I think the piece's statement is supposed to relate to the "enumerating all deductions" bit of the Godel-numbering

Re: Why I Don't Love Gödel, Escher, Bach

#39

Post by ZanyProgrammer »

audunw wrote: post #29

I read and finished GEB first, and then read 'I am a Strange Loop'. I think the trick to reading GEB is to not take it so seriously. You can skim sections, you can skip parts, you don't have to understand everything, not everything has to make sense. I think the author here misses that when he complains such about the quality of the metaphors. They're not meant to help understand, as much as being there to give a vag…

IAASL also has one of the best (and easiest to understand) descriptions of non human sentience-when he talks about why he’s a vegetarian.
Post reply on HN