GEB: Exploring Douglas R. Hofstadter's Strange Loops

[PetSounds]

Lately, I've been hooked on Douglas R. Hofstadter's book Gödel, Escher, Bach. In it, he discusses the idea of "strange loops"—often apparent logical paradoxes—and argues that they are the key to understanding consciousness. He includes witty dialogues, as well as examples of "strange loops" in math, art, and music.

What are PF's thoughts on GEB? On one hand, I find myself nodding along as Hofstadter connects his loops to consciousness. On the other, I wonder if he doesn't stretch things and make assertions. I'm not always knowledgeable enough to make that judgement. (Still in high school—still learning the basics. )

It's a delightful read. But how seriously should I take it?

(Note to mods: Wasn't sure to which forum this topic belonged. Please move it if you think it's better suited elsewhere.)

 

[Svein]

I read it when it first came out, and I still think it is one of the best - and most thought-provoking -science books written. As a mathematician I loved his take on the proof of Gödel incompleteness theorem (the original version is not very readable).

 

[Stephen Tashi]

It's a delightful read. But how seriously should I take it?

This article: https://www.theatlantic.com/magazin...man-who-would-teach-machines-to-think/309529/ indicates Hoftstadter is not in the mainstream of current artificial intelligence techniques - but his interest is in consciousness, which is not necessarily the same thing as "thinking", if we allow that unconscious goings-on may accomplish thinking. Whether you should take Hofstadter seriously depends on your purposes.

 

[StatGuy2000]

I have read GEB, and agree that it is among the most thought-provoking books that I've read, and it was among the first places where I developed an understanding of Gödel's Incompleteness Theorem, as well as informative views on topics in areas of theoretical computer science, artificial intelligence, and cognitive science, with delightful diversions into music, art, philosophy, among others.

As a source of inspiration, it is a great book (and inspiration is important). In terms of how seriously to take it -- keep in mind that the book was written almost 40 years ago, so much of Hofstadter's speculations in various areas of science in the book has to be seen in that light.

 

[lpetrich]

I like his toy programming languages BlooP, FlooP, and GlooP.

BlooP: primitive recursive functions -- for every loop, one must set a maximum number of times that it can repeat.

FlooP: general recursive functions -- loops can repeat an arbitrary number of times, and it's possible to get stuck in an infinite loop. Equivalent to the lambda calculus and Turing completeness.

GlooP: hypothetical -- can solve problems like the Turing-machine halting problem.

Lambda calculus: doing everything with functions and uninterpreted variables.

 

[tholepin]

GED is a vast and glorious pun. I read a review in Scientific American and bought it - still re-read it.

 

[Klystron]

I read it when it first came out, and I still think it is one of the best - and most thought-provoking -science books written. As a mathematician I loved his take on the proof of Gödel incompleteness theorem (the original version is not very readable).

This thread inspires me to re-read the book; my copy was "borrowed" and never returned in the 1990's. A semi-joke in software engineering circles was when faced with a difficult problem to solve, review the requirements then play J.S. Bach and contemplate an Escher drawing while thinking like Godel. Or skip the art and ask for help.

While I used hyperbolic geometry at work on occasion, M. C. Escher allowed me to see it.