Why I Don't Love Gödel, Escher, Bach • Hacker News Board

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

#91

Post by jkabrg » Thu, Jul 05, 2018, 3:06 PM UTC

giantsloth wrote: post #54

This is a perfect opportunity to whip out one of my favorite quotes by Simone de Beauvoir: “Proust observed with astonishment that a great doctor or a great professor often shows himself, outside of his specialty, to be lacking in sensitivity, intelligence, and humanity. The reason for this is that having abdicated his freedom, he has nothing else left but his techniques. In domains where his techniques are not appli…

What does "fulfill himself as a flight" mean?

Is the lesson that since professors are "less free" than everyone else, they criticize everyone else out of bitterness? Or is it that since they're so specialized and able to make a living only in their specialty, they don't need to practise good judgement outside their discipline? Is it that they live in an ivory tower and don't know the difference between theory and practise? What does that quote mean?

...

Maybe they "abdicate their freedom" when they have to teach students and battle administration. I seriously don't know what that quote means.

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

#92

Post by guiambros » Thu, Jul 05, 2018, 3:06 PM UTC

greggarious wrote: post #53

stuntkite wrote: post #6

I'd owned this book for many years and had a similar experience to OP. But one day someone gave me `I am a Strange Loop`, which I started reading and enjoyed way more. After getting in a little bit Hofstadter makes some apologies for GEB saying it was the sum of work of a very young person. I think he was 24? I think it's pretty incredible considering his age. The things that lead him to thinking critically about con…

Thanks for sharing this course, very interesting. I wish HN had an easy way to save comments like Reddit, but this reply should do the trick :)

Pinboard [0] solves it for me. I tag all the interesting stories with "hackernews", so I can easily go back and search.

I noticed over the years that my use of Pinboard is very asymmetrical: I save several URLs every month, but retrieve at most a handful per year. But knowing that my memories are safely stored gives me peace of mind (and, just to be safe, I make a backup every year or so).

[0] https://pinboard.in

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

#93

Post by stuntkite » Thu, Jul 05, 2018, 3:07 PM UTC

vanderZwan wrote: post #86

stuntkite wrote: post #6

I'd owned this book for many years and had a similar experience to OP. But one day someone gave me `I am a Strange Loop`, which I started reading and enjoyed way more. After getting in a little bit Hofstadter makes some apologies for GEB saying it was the sum of work of a very young person. I think he was 24? I think it's pretty incredible considering his age. The things that lead him to thinking critically about con…

> I'd owned this book for many years and had a similar experience to OP. But one day someone gave me `I am a Strange Loop`, which I started reading and enjoyed way more. Thank you for sharing your experience, I may have to give `I am a Strange Loop` a try after all, and do the skip-300-pages trick with GEB. I've tried to get through it multiple times, but I never managed to get far into the later chapters without lit…

I also live with ADHD. I think that's maybe why the dialogs at the beginning were so impenetrable to me without context. They are important and do a great job of illustrating what he's getting to, but for me it just felt like reading nonsense until I had some context about why they were exploring. I found myself in my initial readings not just bored but kind of offended by how wanky they were. Once I got a better understanding of what he was trying to say, I could see the weave of the thing and even have a few laughs along the way.

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

#94

Post by lisper » Thu, Jul 05, 2018, 3:07 PM UTC

jatsign wrote: post #20

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

Excerpted from http://www.flownet.com/ron/chaitin.html:

Proof of the undecidability of the halting problem in six sentences:

Assume that there exists a program H that solves the halting problem, that is, H takes two input parameters, a program P and an input I and returns true if P halts when run on input I, false otherwise.

Construct a program B that does the following: B accepts as input a program P and computes H(P,P), that is, it calls H as a subroutine to determine if program P halts when run on a copy of itself as the input. If the result from H is true then B enters an infinite loop, otherwise B halts (that is, B does the opposite of what P would do when run on a copy of itself).

Now consider what happens if we run B on a copy of itself. B will halt iff H(B,B) is false. But H(B,B) is false iff B doesn't halt, which is a contradiction. Therefore, our assumption is false, and H is impossible. QED.

Turing's original proof of this theorem was remarkable (and complicated) because in his day there were no computers. Not only did Turing have to more or less invent the idea of a program, but he had to conceive of the rather mind-bending idea of running a program with a copy of itself as input. Nowadays this is commonplace. The unix command "cat `which cat`" is one of the simplest examples of a program operating on itself as input. A compiler that compiles itself is another.

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

#95

Post by beaconstudios » Thu, Jul 05, 2018, 3:08 PM UTC

lisper wrote: post #84

beaconstudios wrote: post #61

Earlier quoted context omitted.

the question that fascinates me is - what is the property of a program that makes it undecidable? I've been playing around with the idea of trying to make a program that determines halts/doesn't halt/don't know, given some representation of a program. I'm running into some interesting implications when I incorporate dependent typing, but it feels like there must be something theoretical that's already out there.

> what is the property of a program that makes it undecidable? That is itself an undecidable question! There are a lot of programs for which you can tell that they halt (programs with no loops, for example). Likewise there are a lot of programs for which you can tell that they do not halt (any program whose main body is a WHILE TRUE loop in a language that does not have exceptions, for example.) And then there are lo…

but that's exactly my point - there are clear-cut halting, clear-cut non-halting, and "we don't know yet" programs. My interest is in delineating the properties that separate the 3. The collatz conjecture is exactly the example I use when explaining the "we don't know yet" programs. If I could build a logic system that can positively prove halting, and one that can positively prove non-halting, then anything that remains is "dunno".

The halting problem is basically showing that you can never prove the category of "dunno" to be empty. Which is pretty self-evident given there are unsolved bounding problems like the collatz conjecture in mathematics.

For a minimal example, if I create a program that takes an AST and runs it through two truth functions, one that checks if the AST === "return;" and prints "it halts" and one that checks if the AST === "while(true) {}" and prints "it never halts", then we've already created such an application, just with a "dunno" space containing the majority of programs. Adding practical axioms to a logic system could grow the "halts" and "never halts" spaces to the point where only a subset of applications cannot be excluded from the "dunno" space, and my question is: what are the unique properties of those applications?

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

#96

Post by j2kun » Thu, Jul 05, 2018, 3:11 PM UTC

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…

> "the proof"

As if there can only be one. (And it seems OP is describing the theorem, not a proof)

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

#97

Post by jlarcombe » Thu, Jul 05, 2018, 3:12 PM UTC

Yes, an irritatingly-written book, very hard to enjoy despite seemingly being perfectly designed for my interests. I feel the same way about Iain Sinclair's books, which I kept on buying until I eventually admitted defeat that they're just not for me, despite the amount of fascinating stuff within

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

#98

Post by iafisher » Thu, Jul 05, 2018, 3:12 PM UTC

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.

> Skip the Socratic dialogs basically.

I agree, except make sure not to skip the SHRDLU [1] one, which isn't actually Hofstadter's writing at all, but a demo of the SHRDLU system which is fascinating and should not be missed.

[1] https://en.wikipedia.org/wiki/SHRDLU

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

#99

Post by nabla9 » Thu, Jul 05, 2018, 3:13 PM UTC

pmoriarty wrote: post #74

jhbadger wrote: post #26

A couple of comments: 1) The author complains that the Socratic dialogs are contrived and largely consist of one character explaining something and the other saying "I see" and so on. Well, that's true, but that's kind of how the format works. You could make a similar complaint about Plato's _Republic_. 2) I think the author totally misses that the reference to not hearing the silverware during 4'33" in a cafe is a j…

"The author complains that the Socratic dialogs are contrived and largely consist of one character explaining something and the other saying "I see" and so on. Well, that's true, but that's kind of how the format works. You could make a similar complaint about Plato's _Republic_." Plato is widely criticized by philosophers for doing just that. We cut him some slack, however, as he was one of the first to do so. Hofst…

(Socratic dialog as literary device should not be confused with Socratic method/questioning as a thinking device)

Socratic dialog's have different uses. On the one end it can be used to consider serious existing counterarguments and provide answers to them. One is to explain one point of view and not to provide balanced opinion.

One-sided Socratic dialog that is like a 'happy path' without hairy counterarguments falls into the latter category. Hofstadter uses them to illustrate a concepts, not to go question them.

In fact the hole book is just attempt to repeat the same ideas again and again.

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

#100

Post by floatboth » Thu, Jul 05, 2018, 3:14 PM UTC

> decided to explain its working by coming up with a metaphor involving record-players and records that are designed to physically break the record-players they’re played on

Wait... I've seen this style of explanation somewhere...

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