Gödel, Escher, Bach: An Eternal Golden Braid

January 4, 2014

by Douglas Hoftstadter

I first read GEB about 25 years ago, as far as I can remember. I’m not sure how much I took from it then (I was about 16 years old and knew a little bit of maths, but it was my first exposure to logic and the theory of computation), although I do remember the dialogues and all the wonderful Escher pictures.

I picked up a copy again recently as a result of reading an interview with Hofstadter in The Atlantic. The book has aged really well, with just a few technological fossils from the 1970s (record players playing records that they cannot play, for instance). Hofstadter has a timeless and almost overwhelmingly fecund imagination, bubbling over with novel ideas that seem to pop up from nowhere. His description of the thought process that led to the construction of one of the dialogues (each of which is modelled on a piece of Bach’s music and attempts to explore questions of linguistics or metamathematics on a number of levels at once) gives an impression of a mind of almost obsessional twistiness, trying to pack as many ideas as possible into the smallest possible amount of text using puns, structure and patterns at all available levels. It’s quite wonderful.

I’m not going to attempt any sort of comprehensive review of GEB. I’m not sure that it is reviewable in any real sense without writing something that’s even longer than the book itself (a conclusion that would doubtless please Hofstadter!). Instead I want to concentrate on three things that struck me most on this reading: one on content, one on form, and one meta-level aspect.

The content that most interested me was Hofstadter’s insistence that self-awareness and consciousness arise directly from what he calls “strange loops”, i.e. self-referential structures in formal systems, of which human minds are just one example (what else could they be?). It’s a very difficult subject to think about in a reasonable way. We all have that sensation of the homunculus inside our heads, somehow driving us from a seat just behind our eyes, and we naturally ascribe the same sense of self-awareness to other systems like ourselves, other people. But where does that sense of self-awareness really come from? There isn’t a homunculus driving us! All there is in our heads is a kilogram or two of glucose-fueled computing machinery, and yet somehow, from the fluctuations and vacillations of that tissue, our sense of I arises. How on earth does that happen? And if it can happen in our brains, can it happen in other systems? In a lot of discussions of artificial intelligence, there is a failure to appreciate the scale issues at work in this problem (Searle’s Chinese Room is a particularly egregious example). There are tens or hundreds of billions of neurons in the human brain with hundreds of trillions of connections. How do we begin to imagine or understand what epiphenomena might arise from that scale of complexity? Hofstadter tries to get at this scale problem a little using the example of a self-aware ant colony called Aunt Hilary, a friend of one of the characters in the dialogues, an Anteater.

Aunt Hilary knows little and cares less about ants, and the Anteater even now and then eats some of the ants composing the computing substrate on which Aunt Hilary’s personality runs. The other participants in the dialogue where this is discussed are a little horrified and not a little sceptical, but the Anteater insists that Aunt Hilary is just as self-aware as they are, and that there’s nothing particularly surprising about the whole setup. The analogies ants : ant colony :: neurons : brain and ant colony : Aunt Hilary :: brain : you or me are whimsical and a little silly, but render the central issue of consciousness in real clarity: how can the collective interactions of a large number of (more or less) simple elements lead to complex emergent behaviour?

There’s much more in this vein in the book, and Hofstadter’s presentation of these questions is extremely engaging.

Which brings me to form. Reading GEB, one gets the impression that Hofstadter’s imagination is not like the imagination of other people. He overflows with ideas. The edifices of invention he can create from a single simple tangent to a single simple idea are often enough to fill a whole other book. What’s most interesting to me about this is that this enormous power of imagination is expressed in very straightforward and readable language, almost casually. Hofstadter’s writing is clear and simple enough that you could almost imagine that he dictated the whole book in a couple of sessions, a cup of coffee in one hand, a stick of chalk in the other, never once needing to refer to a source or pause for thought. Of course, the reality is comically different from this. GEB is a masterpiece of careful construction, obsessional attention to detail, rewriting, rethinking and reworking. That the end result reads as such a smooth and seamless whole is a testimony to Hofstadter’s skill as a writer – the scaffolding that supported the construction of this marvellous thing has all been taken down. In the best traditions of mathematics, there’s no sign of the sausage-making machinery left. That this was Hofstadter’s first book, completed (and winning a Pulitzer Prize) before he was 35, is rather extraordinary.

And which brings me to meta. The copy of GEB that I have is a 20th anniversary edition containing a retrospective preface by Hofstadter, looking back at the impact that GEB had, talking a little about his career and writing since then, and recounting a few anecdotes about the production of the book. In some ways, the content in the preface is as interesting as what’s in the rest of the book. Hofstadter typeset GEB himself, before this was a normal thing to do (TeX was first released in 1978, but Hofstadter was writing the book around this time, and used a different system written by a friend of his). In fact, he typeset it himself twice. The first set of galleys he produced faded because of a poorly maintained typesetting machine, rendering them unusable for reproduction. So he had to do it all again. That did mean that he got to do a full proof-read of the book from the first set of galleys, but it necessitated travelling back and forth between Stanford (where he was working) and Indiana (where he had access to a typesetting machine) every weekend to get the work done.

He also has some words to say about sexist language and translation that are very interesting. In the English editions of the book, the characters in the dialogues (apart from Aunt Hilary, who never appears in person, and one other minor part) are all male. This ended up being a matter of some regret for Hofstadter (he’s written about sexist language and the “default assumptions” that flow from it in his Metamagical Themas column in Scientific American as well as in other places) and he was tempted to update some of the dialogues in the newer edition. He didn’t do this, primarily through honesty, I think, and not wanting to whitewash a bad decision he knew that he’d made. However, translations of GEB into other languages provided an opportunity to make amends – in the French translation of GEB, the Tortoise becomes “Madame Tortue” and in the Italian “signorina Tartaruga”, both of which, to me, sound really good. The Italian, in particular, to my non-Italian-speaking ear, sounds like a perfect fit for the Tortoise’s rather tricksterish personality.

Hoftstadter is very interested in translation and analogy (most of his academic research in AI/cognitive science is about the representation of analogies and analogical reasoning), and in the preface he says that he thinks that the best book he has written and the best book he ever will write is not GEB, but Le Ton Beau de Marot, a book that is all about translation (in fact, mostly about the translation of a single rather short French poem). I think I need to read that. (As well as I Am A Strange Loop and Fluid Concepts and Creative Analogies, which is a record of the research of Hofstadter’s group at Indiana University.)

Hofstadter is one of the few people who has tried to stay true to the early goals of Artificial Intelligence research. Much of modern AI research is very instrumental, in the sense that it’s about building artefacts that perform functions that are, in some narrow sense, “intelligent”, without necessarily providing any insight into what “intelligence” really is. For example, a lot of AI problems turn out to be solvable using different forms of search, or statistical methods that, while they may very well be implemented by some part of the underlying machinery of intelligence, once you’ve seen how they work, no longer seem intelligent. There’s nothing intrinsically wrong with this, and the solutions and the artefacts that this research produces are useful. But they don’t tell us a whole lot about what “intelligence” is or might be, which was one of the original aims of AI. Hofstadter has tried to stick more to those original aims, working on very difficult problems about analogical reasoning and creativity that try to get at deeper questions about intelligence than are accessible via more “conventional” AI problems. I’m looking forward to reading more about this – I have a copy of Fluid Concepts and Creative Analogies on my bookshelf already…

In summary, Hofstadter is one of the most original thinkers and writers on intelligence and creativity that we have. Everyone should read GEB, even if some of the mind-bending computability stuff is hard to get through the first time you see it. It’s well worth the effort, and there are more than enough wild and wonderful flights of Hoftstadter’s fancy to leaven the dough.