[Read the full essay in Aeon Magazine.]
Putting the “B” Bach in GEB
Gödel, Escher, Bach by Douglas Hofstadter turns 40 this year. Bach’s music never had a justified place in the book – but could it find one?
By Ilari Kaila
Achilles: Frankly, I’m a little confused by the title. After all, what do Copper, Silver, and Gold have to do with each other? … Now if the title were, say, Giraffes, Silver, Gold, or Copper, Elephants, Gold, why, I could see it…
Tortoise: Perhaps you would prefer Copper, Silver, Baboons?
Achilles: Oh, absolutely! But that original title is a loser. No one would understand it.
Tortoise: I’ll tell my friend. He’ll be delighted to have a catchier title (as will his publisher).
(From Gödel, Escher, Bach: An Eternal Golden Braid (1979) by Douglas Hofstadter)
Twenty years ago, in the preface to the 20th-anniversary edition of his classic book, Douglas Hofstadter marvelled at how misunderstood its thesis has been. A treatise on the nature of consciousness, it is often wildly misconstrued as an exploration of how ‘math, art, and music are really all the same’. But one likely source of the confusion is in the name – which is, at the same time, a big reason for the book’s lasting popularity: Gödel, Escher, Bach: An Eternal Golden Braid, or GEB for short, sounds like a promise of just such a dazzling, cosmic counterpoint. Another likely culprit is Hofstadter’s own musings about music. While M C Escher’s artwork elegantly (and literally) illustrates many of the book’s themes, Hofstadter’s attempts at justifying the inclusion of Bach are mostly banal and often badly off the mark.
There are good reasons for GEB’s fame besides the sexy and marketable title, though. In its attempt to build a grand theory of minds and meanings, the book discusses an eclectic range of topics and, at its best, does it in a genuinely enlightening way. It is obviously an inspired work, even if the fundamental case it sets out to make falls flat. Like most attempts at ‘explaining’ consciousness, GEB is rooted in a category mistake: it treats our phenomenological core as just another phenomenon, making the book an 800-page exercise in begging the question. But it’s a stimulating 800 pages, riffing on fractals, Zen koans, computer languages, quantum physics and much more. To his credit, Hofstadter at least senses that the volume of a phonebook is required if you claim to be adding something to this perennial conversation.
At the centre of GEB’s thesis is a concept that Hofstadter calls the ‘strange loop’, a system of tangled hierarchies, often self-referential and paradoxical – and one that, in his view, gives rise to our sense of selfhood. Like with any complex system of logically governed symbols, his argument goes, the symbol-manipulation of our brains leads (as the 20th-century mathematician Kurt Gödel showed) inevitably to self-reference. This is what self-awareness is, in Hofstadter’s final analysis: the ability of our internal, neurally processed formal system to reference itself, to ‘talk about itself’, as a property that is mathematically predetermined to emerge.
An important strand in GEB’s exploration of such strange and loopy entities is recursion. A simple and intuitive illustration of the concept, and one that the book starts out with, is of a story inside a story: a self-similar structure, in which each new hierarchical level is nested within a lower one. This recursive nesting can either continue indefinitely (as in fractal geometry) or until the levels ‘bottom out’ (as with the leaves of a fern, or the 1,001 tales of Arabian Nights). Nature and human artifacts abound with examples of recursion and self-similarity, and Hofstadter exploits a great many to explain the concept. With his third titular character, however, he struggles.
In an effort to keep Bach relevant to the discussion, Hofstadter takes an oddly specific example (‘the gigue from the French Suite No 5’) and goes on to give descriptions that are so general they could apply to any number of tonal pieces. His main point is that the way the music moves through different keys – a process known as modulation – is recursive. But key changes are not organised in anything resembling stacks in computer languages, as Hofstadter would have it, with each new level nested within the previous one; nor do they create the expectation of ‘returning back in a reverse order’. Modulation is a defining characteristic of tonal music: it is not unique to Bach, nor is it a recursive phenomenon.
Ferns and fractals: recursion in nature and in the abstract. (Mandelbrot set animation created by Wolfgang Beyer with the program Ultra Fractal.)
Music is full of recursion, though. Schenkerian analysis – one of the dominant theoretical frameworks for tonal music (since before GEB was published) – deals with hierarchical harmonic structures that follow similar principles from the deepest levels to the surface. Other musical parameters, such as rhythm, exhibit recursion too. It would be easy to come up with any number of better examples than key changes in a random gigue. On the other hand, as GEB takes pains to demonstrate, recursion is everywhere: in plants, computer code, quantum particles, human languages. So whence the ‘B’?
More than anything, Bach’s name in the title represents a missed opportunity: his music could, in fact, beautifully serve the role that Hofstadter wanted to assign it. Beyond its relevance to recursion, it can help us think about the book’s biggest underlying subject matter, that of meaning – though it might lead us to a very different perspective from the one Hofstadter intended.
Continue reading at Aeon Magazine.
[Related articles:
The Art of Mixing Metaphors
Technology Bringing Dumb Ethical Questions to Life (Kind Of)
Ten Jokes, Explained]
Limited Hangout 
Found this via Aeon. Started reading for its critique of Hofstadter’s invocations of Bach in GEB – which is way beyond my expertise – but was pleasantly surprised at your insights into his takes on consciousness and AI.
I think AI enthusiasm has moved a bit beyond voodoo into the realm of cargo cult (or at least some of the stories associated with it), Rather than trying to emulate the ‘software’ of intelligence and consciousness many are now focused on the ‘hardware’. They think if they can simulate the connections between neurons in the human brain with transistors in a computer that intelligence and consciousness will spontaneously appear. Like building a copy of an airfield with vines and logs and waiting for the planes full of cargo to show up.
Other than religion, I think few other fields have messed themselves up so thoroughly with the reification of metaphors.
Glad to hear it! One of my objectives with the essay was to show how meaning and, by extension, consciousness aren’t things anyone can, or should, claim to have “expertise” in. We live in a time when people seem to accept that physicists have special insight into the existence/non-existence of God and computer geeks into consciousness. GEB provided a good pretext to show how you can discuss these topics from the point of view of an artist.
I like that description.
Alan Turing wrote in his famous paper, back in 1950, about a similar “superstition” (his word) already back then: that because computers work on electricity, and signals between neurons are electrical, we are somehow on our way to capturing consciousness. He goes on to point out that Babbage’s analytical engine would have been able to do the same things as a computer, just slower, and without electricity.
Trying to superficially imitate how neurons transmit signals seems similarly outdated to me. I’ve understood that a big problem in modern neuroscience is to figure out where the cognitive heavy lifting actually happens, since action potentials travel too slowly to account for much of it.
I pretty much agree with both those things, but I’ve gotta admit I’m not sure where the ‘by extension’ is coming from. I can’t see a necessary link between meaning and conscious myself (except maybe that you can’t have the former without the latter).
I do see the problems of consciousness as being an extension of incoherent theories of mind though (talking philosophical ToMs here, not the ToM that auties like me supposedly lack). I reckon pretty much all ‘mind science’ is compromised by that.
Also I’d make a distinction between expertise in consciousness and expertise in theories of consciousness (I’m not suggesting you fail to do so). So, for example, David Chalmers has a lot to say about theories of consciousness (whatever you may think of his p-zombie stuff) but his ontological anti-realism seems to hold him back from claiming expertise in consciousness itself. OTOH Daniel Dennett claims to understand consciousness itself. I don’t think I’m dumbing him down too much by summarising his position as “Science can explain everything in existence. Science can’t explain consciousness. Therefore consciousness doesn’t exist.”
I haven’t struck that before. Can you refer me to something about it? I’d reckon it’s gotta be dependent on how you’re modelling the physiological bases of cognition and how you think you’re measuring its speed.
This was one of the points I was trying to make in the essay. It’s not a super original thought; the term “aboutness” (popularized in the philosophy of mind by, I think, John Searle) gets at the same thing. But another reason I was itching to write about GEB is that Bach’s music is a manifestation of such dense “aboutness”, and thus serves as a perfect illustration of why Hofstadter’s grand theory is so wrong. He starts with meaning (symbols, information), without realizing that nothing can be meaningful unless you already postulate consciousness.
Another thing that plagues the study of mind is that the word “consciousness” has so many meanings. Sometimes it’s used synonymously with mind or cognition, and that creates misunderstandings.
A bigger issue is that a lot of these theories set about to solve an undefined problem. Chomsky often discusses this: that there is no mind-body problem. We have no coherent definition of what “matter” is anymore, and the mind-body problem vanished already with Newton and the collapse of the old mechanical models of the universe.
For sure. This is kind of the same as saying that an ethicist can be an expert on theories of right and wrong, but not an expert on what is right and wrong.
I don’t know much about his work, except that he recognizes naive reductionism for what it is. I hate the “philosophical zombie” counterfactual, though; to me, it’s like a mirror image of how the Turing Test is popularly — and totally incorrectly — understood and used. (A machine that “passes” the Turing Test would be a philosophical zombie, but it’s typically used to make the opposite argument, in favor of physicalism, from the one Chalmers makes.)
Yeah, that’s pretty much it.
I’m a bit out of my depth here, but this is related to things I’ve come across Chomsky musing about, and in discussions with my father who happens to be a neurophysiologist. It’s interesting that Chomsky has recently mentioned Roger Penrose positively when he says we’re looking at something pretty slow and crude when we study neurons; that not only are nerve impulses too slow, but neural circuits (which is what AI researchers claim to imitate with “neural networks”) don’t have the kind of architecture to make them a good candidate for the primary driver of thinking. Chomsky himself was saying already back in the 90s, though, that things like quantum indeterminacy that Penrose is bringing into the study of consciouness don’t add anything helpful or relevant (since, as I wrote above, there is no matter and hence no mind-body problem). But he seems to think that looking for superior computing power in the internal structure of the neuron makes Penrose’s current research interesting and potentially important.
Just more generally, there’s such a wealth of things going on in the brain that we have no clue about, even within the tiny sliver of things we’re able to observe, that it seems obvious that neurons are just a tiny, superficial part of the story.