GEB is a great book, and I've probably read it at least 3.33333333... times over the years. As a late teen it blew my mind. But I'm not sure I'd recommend it as a route into Gödel's proofs [1]. The book covers a lot of other ground too, and is notoriously digressive and quirky (looking at you, dialogues).
Instead I'd recommend Gödel's Proof by Nagel and Newman for a conceptual intro.
[1] I'm not a mathematician, so my understanding is necessarily informal.
Most proof of the Gödel theorem use the primes encoding that is makes all the operations very unintuitive. But GEB uses just ascii and a lot of the side task get obvious. (It uses base 20 instead of 256, but it's the same idea.)
> is¨notoriously digressive and quirky
It is super mega ultra notoriously digressive and quirky.
I’ll never understand how GEB was using math, art, and music to explain consciousness (and Hofstadter himself still thinks no one understood it), but Nagel and Newman did a great job explaining why logic as a mechanical thing has only a tenuous relationship to concepts we understand, and that helped me crack at least a little bit of the mystery I was after when giving up on GEB.
I have not read GEB but I thought his second book, I am a Strange Loop, did a pretty good job of connecting the idea of self referential loops (like in godels proof) to consciousness and art and such.
Thanks for the suggestions. Just checked out some of Le Ton Beau de Marot, will most likely read the rest.
Actually, I was recently wondering whether poems can be interpreted as "efficient" computer programs. Words in a sentence/essay just connect different objects in space and time (syntactically and semantically) to form some concept, kind of like a program. A poem just uses higher order abstractions (imagery) to express the same concepts in fewer words.
> I’ll never understand how GEB was using math, art, and music to explain consciousness
As Flannery O'Connor wrote, "The result of the proper study of a novel should be contemplation of the mystery embodied in it, but this is a contemplation of the mystery in the whole work and not or some proposition or paraphrase. It is not the tracking down of an expressible moral or a statement about life." We don't read literature with the hopes of a book laying out a precise thesis and incontrovertibly demonstrating it.
If you come into GEB expecting a scientific explanation of consciousness (like I did, when I first read it) you walk away confused and maybe disappointed. Hofstadter observed something transcendentally beautiful about self-reference and had a spiritual or religious revelation that, for him, related it to consciousness, and he attempted to convey that beauty and spiritual revelation in - appropriately self-referentially - a book that embodied it. You're meant to appreciate it in your heart and soul, not (just) in your mind. It's literature, not science.
It’s actually an interesting fact that every person who was programming in the 80s owns a copy of GEB, which they flipped through a bit and then put on the bookshelf and never actually read.
while it is a groovy into to recursion and other cool ideas, GEB annoys me in that I feel like the three figures in the title are ill matched. Godel proves a super important result in math, sure... Escher was a skilled draughtsman who had a feel for tesselation. An OK artist IMO but no special insights. Bach on the other hand was an expressive genius who in the volume, power and beauty of his productions just seemed to drop out the sky like a meteor. Escher does not belong in the same breath frankly. if Bach made a crab canon or did other marginally math-y things that is just not the point - the work lives or dies in entirely different terms...
Yeah. My brother was really into GEB but for the exact reason you laid out I never even gave it a chance because just from the title it really seems to trivialise the artistic achievements of Bach to have him be included in that list.
The only mathematical figure I feel you could reasonably compare to Bach would be Euler. I would read that book if someone wrote it.
And Bach did indeed write variations on B-A-C-H[1]. But lots of composers have self-referencing cryptograms and other riddles in music. You would find far more in Scriabin, Bartok or Alban Berg for example.
It also doesn’t fit the narrative but the idea of self-reference in art didn’t start with Escher either. For example the Arnolfini wedding portrait by van Eyck[2]
[2] https://en.wikipedia.org/wiki/Arnolfini_Portrait
The artist can be seen in a reflection in the central mirror that he has ostentatiously signed his name above. It’s an incredible painting and worth a trip to the National Gallery to see if you’re ever in London.
GEB is a great book, and I've probably read it at least 3.33333333... times over the years. As a late teen it blew my mind. But I'm not sure I'd recommend it as a route into Gödel's proofs [1]. The book covers a lot of other ground too, and is notoriously digressive and quirky (looking at you, dialogues).
Instead I'd recommend Gödel's Proof by Nagel and Newman for a conceptual intro.
[1] I'm not a mathematician, so my understanding is necessarily informal.
I really like GEB.
Most proof of the Gödel theorem use the primes encoding that is makes all the operations very unintuitive. But GEB uses just ascii and a lot of the side task get obvious. (It uses base 20 instead of 256, but it's the same idea.)
> is¨notoriously digressive and quirky
It is super mega ultra notoriously digressive and quirky.
I can second this as a wonderful introduction to the proofs. This is the book that got me into logic and formal methods.
I’ll never understand how GEB was using math, art, and music to explain consciousness (and Hofstadter himself still thinks no one understood it), but Nagel and Newman did a great job explaining why logic as a mechanical thing has only a tenuous relationship to concepts we understand, and that helped me crack at least a little bit of the mystery I was after when giving up on GEB.
I have not read GEB but I thought his second book, I am a Strange Loop, did a pretty good job of connecting the idea of self referential loops (like in godels proof) to consciousness and art and such.
I am a Strange Loop is basically GEB but written properly instead of being a random collation of ideas.
Unrusprisingly, since many years went by. But I still love the quirkiness of GEB
(Also, he has other books between the two, I deeply enjoyed Le Ton Beau de Marot, about translations)
Thanks for the suggestions. Just checked out some of Le Ton Beau de Marot, will most likely read the rest.
Actually, I was recently wondering whether poems can be interpreted as "efficient" computer programs. Words in a sentence/essay just connect different objects in space and time (syntactically and semantically) to form some concept, kind of like a program. A poem just uses higher order abstractions (imagery) to express the same concepts in fewer words.
So this book should be great!
> I’ll never understand how GEB was using math, art, and music to explain consciousness
As Flannery O'Connor wrote, "The result of the proper study of a novel should be contemplation of the mystery embodied in it, but this is a contemplation of the mystery in the whole work and not or some proposition or paraphrase. It is not the tracking down of an expressible moral or a statement about life." We don't read literature with the hopes of a book laying out a precise thesis and incontrovertibly demonstrating it.
If you come into GEB expecting a scientific explanation of consciousness (like I did, when I first read it) you walk away confused and maybe disappointed. Hofstadter observed something transcendentally beautiful about self-reference and had a spiritual or religious revelation that, for him, related it to consciousness, and he attempted to convey that beauty and spiritual revelation in - appropriately self-referentially - a book that embodied it. You're meant to appreciate it in your heart and soul, not (just) in your mind. It's literature, not science.
Thanks, that's a fantastic quote that gets at the heart of how to appreciate GEB.
“Godel’s Proof”[1] is also a great and shorter read if the scale of GEB is intimidating(I know it was for me at first).
https://nyupress.org/9780814758014/godels-proof/
It’s actually an interesting fact that every person who was programming in the 80s owns a copy of GEB, which they flipped through a bit and then put on the bookshelf and never actually read.
> which they put on the bookshelf and never actually read.
Much like the many unread copies of Knuth's TAOCP.
I would say "never actually finished", but I think this is quite true.
while it is a groovy into to recursion and other cool ideas, GEB annoys me in that I feel like the three figures in the title are ill matched. Godel proves a super important result in math, sure... Escher was a skilled draughtsman who had a feel for tesselation. An OK artist IMO but no special insights. Bach on the other hand was an expressive genius who in the volume, power and beauty of his productions just seemed to drop out the sky like a meteor. Escher does not belong in the same breath frankly. if Bach made a crab canon or did other marginally math-y things that is just not the point - the work lives or dies in entirely different terms...
Yeah. My brother was really into GEB but for the exact reason you laid out I never even gave it a chance because just from the title it really seems to trivialise the artistic achievements of Bach to have him be included in that list.
The only mathematical figure I feel you could reasonably compare to Bach would be Euler. I would read that book if someone wrote it.
the linking thread for all three is self-reference, either in the form of a fugue or in a painting showing its own creation. Doug is a loop guy
And Bach did indeed write variations on B-A-C-H[1]. But lots of composers have self-referencing cryptograms and other riddles in music. You would find far more in Scriabin, Bartok or Alban Berg for example.
It also doesn’t fit the narrative but the idea of self-reference in art didn’t start with Escher either. For example the Arnolfini wedding portrait by van Eyck[2]
[1] Bb A C B in modern notation https://en.wikipedia.org/wiki/BACH_motif
[2] https://en.wikipedia.org/wiki/Arnolfini_Portrait The artist can be seen in a reflection in the central mirror that he has ostentatiously signed his name above. It’s an incredible painting and worth a trip to the National Gallery to see if you’re ever in London.
A Strange Loop guy, to be precise.
(It's the title of his follow up work after GEB.)