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Gödel, Escher, Bach: an in-depth explainer

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

#121

Post by Zanni »

dtgriscom wrote: post #109
dinobones wrote: post #56

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…

I plowed my way through about two thirds of it. Lots of interesting stuff, but I finally gave up because it seemed just too self-involved and self-referential. Building up this enormous edifice, just to be able to say "Hey! Check out my edifice!" I guess I'm just too much of an applied engineering kinda guy.

Oh, the irony of dismissing GEB as "too self-referential."

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

#122

Post by gernb »

dinobones wrote: post #56

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…

I'm with you. I've heard so many raves but I've always found it a slog and sadly never was able to get into it.

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

#123

Post by schoen »

frimsah wrote: post #110
fao_ wrote: post #59

Earlier quoted context omitted.

Without a telescope I can't prove to you that andromeda is a galaxy, but it is.

following this analogy: is it possible with the proper instrumentation, or axioms, that a mathematical statement might become provable?

Yes, you can add more axioms and produce a more powerful system which can resolve more questions. In some cases you actually have a choice about whether to assume that something is true or that it's false (for example you can assume the continuum hypothesis or its negation!), and neither choice on its own produces an inconsistency, but either choice makes a different set of conclusions provable.

However, Gödel made explicit in the very first statement of his incompleteness theorem that assuming more axioms cannot ever eliminate incompleteness (except by the extremely undesirable event of eliminating consistency). Gödel shows that, if a set of axioms (including additional axioms on top of your original set) doesn't allow you to prove everything (by virtue of being inconsistent, something called the "principle of explosion"), then there are necessarily statements that those axioms can't resolve the truth of.

So you can add more axioms and that will either make your system more powerful or inconsistent (depending on whether you chose inconsistent axioms to add), but you still can't get rid of the incompleteness phenomenon that way!

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

#124

Post by robswc »

davesque wrote: post #10

I've read GEB over many years rather in the way someone would read the Bible. I pick it up from time to time and enjoy chewing on one or two chapters of material. But I've yet to figure out if the book actually has a specific thesis. I know it's all about the power of interpretation and the way in which interpreting a formal system as self-referencing has the effect of completely blowing up the intended design of tha…

He's said he wasn't great at conveying the thesis in GEB. If you want the thesis of GEB, you can read "A Strange Loop." It's a bit more narrative, less technical but still pretty good book, imo.

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

#125

Post by robswc »

dinobones wrote: post #56

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…

I think you have to be in the right mindset. Not to say its beyond anyone's level, but I think you have to be in the "mood" to learn about the material. I can assure you, there's been times where I would have hated reading it and times where I wouldn't have been able to put it down.

When I'm more focused on the here and now, I think I would find it a chore to get through. When I feel like I have less on my plate and looking for "interesting observations" it would work really well.

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

#127

Post by cfraenkel »

mxkopy wrote: post #83
Brusco_RF wrote: post #29

Earlier quoted context omitted.

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.

For someone who is complaining about someone supposedly not reading the exact words you wrote - you're awfully quick in putting words in their mouth. I don't see "alcohol" or "cocaine" mentioned, and yes, the public does put psychedelics in the generic term 'drugs'.

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

#128

Post by bo1024 »

red_trumpet wrote: post #51
jstanley wrote: post #39

> 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

Oof @ many of these answers. The reason is that there are multiple "models" of the natural numbers that satisfy the axioms, and the statement is true in the usual model that we all know, but in some other models the statement is false.

See https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_... and https://en.wikipedia.org/wiki/Peano_axioms#Nonstandard_model...

Godel's "completeness" theorem gives a converse. If the statement were true about all possible models, then it would be provable.

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

#129

Post by cfraenkel »

mxkopy wrote: post #105
widowlark wrote: post #100

Earlier quoted context omitted.

I truly am not intending this upcoming statement as an insult: I did not struggle with 'looking behind the curtain' while reading GEB, nor did I find the concepts silly - I was rapt with curiosity the whole reading and came to many profound conclusions about the book and it's ideas - and I was not on LSD. Whatever helps you personally understand the world in a more meaningful light is wonderful, but it certainly was…

I don't find that insulting. It's wonderful for you. What I find insulting is saying that calling GEB trippy is an insult. It's genuinely trippy and there's nothing wrong with that.

You explicitly "wondered" if H was "experienced" with psychedelics, implying that you thought so since you found it "trippy". Go back and read your original comment. No one here is saying psychedelics are morally suspect, they're saying that your explicit suggestion that H was "experienced" is insulting.

Because it is. And your trying to move the goalposts after the fact is just digging that hole deeper.

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