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Why I Don't Love Gödel, Escher, Bach

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

#111

Post by pfortuny »

inputcoffee wrote: post #104

This was a pre-internet book though. The internet has made explanations hyper competitive. At this point I can find dozens -- perhaps hundreds -- of explanations of Godel's theorem. But in the pre-internet days I could go to the library, or have my friend Kent explain it to me. (He had to explain first that languages were either complete or true -- he called it sound if I recall. soundness was the property -- and the…

“The best explanation”... That is something which you should reconsider. Few problems have a single optimal solution. And knowledge is more a matter of cumulative subjective experiences than a single event.

What is good for me is bad for you (as a matter of fact I find Gödel’s proof unmistakeaby clear).

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

#112

Post by danharaj »

The treatment of Godel's theorems in GEB always struck me as gratuitous: It treats a technical result as having great philosophical import. The philosophical content of Godel's theorems is already found in the Liar paradox, "This statement is false." and incompleteness in a grand sweeping sense involving language in its entirety can be found in works as early as the Daoists and the Greeks.

Edit: I should say that this wasn't at all obvious to me when I was in college and thinking hard about incompleteness. The limitations of mathematics disturbed me deeply. These days, I think it's part of the beauty of mathematics that its limitations are its own result.

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

#113

Post by inputcoffee »

pfortuny wrote: post #111
inputcoffee wrote: post #104

This was a pre-internet book though. The internet has made explanations hyper competitive. At this point I can find dozens -- perhaps hundreds -- of explanations of Godel's theorem. But in the pre-internet days I could go to the library, or have my friend Kent explain it to me. (He had to explain first that languages were either complete or true -- he called it sound if I recall. soundness was the property -- and the…

“The best explanation”... That is something which you should reconsider. Few problems have a single optimal solution. And knowledge is more a matter of cumulative subjective experiences than a single event. What is good for me is bad for you (as a matter of fact I find Gödel’s proof unmistakeaby clear).

I concede the point: the "best" explanation is best in a context.

The best explanation for a PhD candidate about to defend their thesis the next day is not the same as it is for, say, me.

But that reinforces the point I am making.

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

#114

Post by beaconstudios »

lisper wrote: post #102
beaconstudios wrote: post #95

Earlier quoted context omitted.

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 rem…

> the properties that separate the 3 But that is exactly my point: what separates these three classes is the state of our current mathematical knowledge, and that obviously changes over time. > Which is pretty self-evident No, that is not at all self-evident. (If it were, someone would have proven it long before Turing, and he wouldn't be famous for it.) I don't know what you mean by a "bounding" problem, but we can…

it's self-evident _at this point in time_, given you could feed such a machine the collatz conjecture as an algorithm and we just don't know if any arbitrary input will halt. I'm not claiming it is self-evident in perpetuity. By bounding problem I guess I mean the mathematical equivalent of knowing it can halt. I'm not a mathematician as I previously stated so I don't know the terminology.

I don't think the space I'm talking about is equivalent to the state of all of our mathematical knowledge, as AFAIK not all problems relate directly to this space. But a subset of all mathematics, sure (perhaps computability, or logic in general although of a higher kind than first-order). My interest is in creating a static analyser based on the set of axioms or deductions that can be derived from that space.

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

#115

Post by dnautics »

fao_ wrote: post #10
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…

This. 100 times, this. GEB is an alright book, but nobody I know has actually managed to finish it. I Am A Strange Loop discusses the exact same thing, but does so with the experience of years of writing in metaphor, and more importantly, entirely in metaphor . All of the metaphors are well-crafted in that they are both a pleasure to imagine, can be recalled rather easily, and accurately map to what the author is try…

You're not supposed to finish GEB, there's even a section in the book about that.

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

#117

Post by _jal »

stuntkite wrote: post #85
perl4ever wrote: post #81

Earlier quoted context omitted.

I have a simple rule - I don't eat any creature that is sentient enough to choose to be vegan...

That's kind of you. I assume your coworkers appreciate that.

All of them? I have my doubts about the sentience of some of mine, although at first blush that appears uncorrelated with eating habits.

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

#118

Post by kranner »

usrusr wrote: post #66
stuntkite wrote: post #47

Earlier quoted context omitted.

I am not a vegan, but his consciousness cone is something I seem to bring up frequently with people. Usually by the end of the conversation I don't quite know why I'm not vegan aside from habit. Last time I brought it up I was eating sushi and talking about how I had decided to quit eating cephalopods because they might be smarter than humans... But then ate pork belly and just didn't really know what I stood for any…

Pigs are awesome and most of them (all except for wild boar) would not be around if not for us eating them. We should strive for avoiding unnecessary hardship and unsustainably high numbers, not for extermination through total disuse.

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

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

#120

Post by jjcc »

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 have both books. I read the books using the exact the same approach you suggested. I often skipped parts when I don't want to read.

GEB is not a book for consume only once. I came back again and again. The profound meaning of the book and Godel theorem goes beyond many people can imaging. GEB itself is a metaphor.

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