Hofstadterian Loops

I Am a Strange Loop

Reading a book by Douglas Hofstadter is the intellectual equivalent of eating the most satisfyingly delicious meal imaginable in the most enjoyable company ever. I've only read three so far and my favourite has definitely been "Le Ton Beau de Marot", because I don't think it'll ever be possible for a book's subject matter to be so broad in scope and yet so perfectly match my own areas of deepest interest. His most recent book, I Am a Strange Loop, was a thoroughly enjoyable read as well and extremely thought-provoking: it has really whetted my appetite for literature in the field of philosophy of mind.

The book begins with Hofstadter giving a brief history of his own personal grapplings with the idea of consciousness, an inevitable question arising from which is whether non-human animals have consciousness in any analogous way to humans. This is a question I've done much grappling with myself, resulting in my decision several years ago not to eat the flesh of animals (human or otherwise!). By far the most difficult thing to deal with since making that decision has been the attitudes of others, with expressions of anger, mock sympathy ("oh, you poor deluded half-wit!"), and derision being the most common reactions among those most "anti-vegetarian" of my acquaintances. I've had many a conversation with people whose minds I admire and opinions I respect, who clearly believe strongly that I am just wrong on this subject, though it has always proven equally clear that I am the one who has done more thinking on the matter. Anyway, I fully believed Hofstadter was someone who would always represent some sort of conflict for me in this way: he was an intellectual hero of mine, yet he ate meat. Or so I thought. In this early section of the book he explains the meandering path that his own thoughts and feelings on this matter took over the years, from becoming vegetarian as a teenager, to going back to eating meat for several years, to allowing himself only chicken and fish, and finally to being completely vegetarian for the past several years. If this wasn't wonderful enough reading for me, imagine how I felt reading this passage:

In those days, I often wondered how some of my personal idols - Albert Einstein, for instance - could have been meat-eaters. I found no explanation, although recently, to my great pleasure, a Web search yielded hints that Einstein's sympathies were, in fact, toward vegetarianism, and not for health reasons but out of compassion towards living beings. But I didn't know that fact back then, and in any case many other heroes of mine were certainly carnivores who knew exactly what they were doing. Such facts saddened and confused me.

I don't know but to me that seems like quite the Hofstadterian loop: actually experiencing what the author of what you're reading is describing having experienced.

At any rate, the central thesis of this book is that consciousness arises when a system that perceives and responds to external stimuli becomes so complex as to develop symbols or concepts representative of itself, which results in a "strange loop" akin to that devised by Kurt Gödel when he proved the incompleteness of Russel and Whitehead's Principia Mathematica. We are introduced to the idea of a strange loop through the example of audio and video feedback loops which, though not "strange" in the sense of the book's title, provide a taste of the weird and wonderful effects of loopiness in general. Photographs in the centre section of the book show the magical-looking portals Hofstadter and his cohort achieved by pointing a video camera at the screen that was outputting what it picked up and then adding other objects and tilts of the camera into the mix. It's a great introduction to the power of a loop.

Of course, anyone involved in programming is already familiar with this kind of concept - just think of a recursive function, e.g.:

function infinite_loop() {

It is only when we encounter Gödel's incompleteness theorem, however, that we get a real taste of "strange" loopiness, the key to the strangeness being self-reference. What Gödel did in his famous and devastating (to many mathematicians and logicians of the time) proof was to construct a sentence, in his codified version of the symbols of Russell and Whitehead's Principia Mathematica (PM), that spoke about itself. What it said was, "I am unprovable in PM". It is important to be clear on what sets this apart from the video camera being pointed at the screen it's outputting to - there is no meaning in what the video camera is picking up, it is merely receiving and rendering, then receiving what it has rendered, then rendering that, then receiving that, and on and on... Gödel's sentence, on the other hand, is talking about itself in a meaningful way. The sentence has to be either true or false. If it is false, then its negation is true: the sentence is provable in PM. But that means a false statement is provable in PM, which means PM is inconsistent. This cannot be the case, and so the sentence must be true, which means there's a true sentence in PM which cannot be proved - thus, the system is incomplete. The ability of Gödel's sentence to talk about itself is what makes it truly strange.

This idea of a self-referential loop seems to me a very powerful tool for explaining phenomenal consciousness. It could explain why we don't react to pain the way the Terminator does (something like, "I sense damage; the data could be interpreted as pain") but have such a deep response to it. We sense the injury, then sense ourselves sensing the injury, and now that we are sensing ourselves there are all of the associations that go along with that (fears about being hurt, death, etc) and that in turn gets fed in to our consciousness and on and on until we have this phenomenal experience (or "quale") of pain. I cannot help but try to imagine how this might look as a recursive function:

function consciousness($perception) {
  static $quale = array();
  $quale[] = $perception;

I realise the use of an array for the $quale variable seems a bit odd but I just wanted to get across the idea that this is going to keep ballooning as the function gets called over and over again.

Anyway, I really love this basic idea of the book - the concept of a strange loop as the fundamental ingredient that makes our consciousness the bizarre thing that it is. There are other ideas in the book I'm not so convinced by though. For example, Hofstadter talks about us each having multiple strange loops manifested in our brains, especially the strange loops constituting the "I-ness" of the people we are closest to and have most empathy with. He gives an example of his sister describing to him over the phone a meal she had just had - I think it was falafel or something. And he felt that he could experience exactly what she had experienced just by being told about the meal and through his ability to conjure up in his mind what it tasted like. He seems to be saying that his sister's "I" was manifested in him when he did that. To me this seems like quite an extreme idea and I didn't feel it was adequately backed up.

Hofstadter's view here is in opposition to the more traditional view of the mind, which is as a "caged bird", the idea being that one brain = one mind, and that mind is essentially trapped inside the brain, with no space for any others. He strongly refutes this idea of trappedness, claiming that a person's "I" can be manifested in multiple brains and that one brain can house multiple "I"s.

To me it seems that only very abstract thoughts can be multiply realisable. Everything else is pretty much trapped within the hard-wiring of the brain. Now, I don't claim to know a whole lot about the physics or chemistry of the human brain but I think I'm on fairly safe ground in making the simple assertion that we are born with certain faculties and these are not identical from individual to individual. Then, as we grow older, we develop other faculties, as well as tendencies, likes and dislikes, and so on. Something that for me might well fit into the first category (i.e. something I was born with, as I have no memory of things being otherwise) is my dislike of apples. When I see somebody eating an apple with obvious pleasure it looks like something really good and tasty, and yet when I try it myself there is no pleasure at all - rather, the combination of taste and texture is distinctly unpleasant to me. My older brother, on the other hand, loves apples. If he called me up sometime and mentioned that he had just been to an orchard and eaten the most delicious sweet apples, my reaction would be to his general expression of pleasure at having eaten something tasty and wholesome, for the actual experience of enjoying the taste of an apple will forever be denied to me. In this way I am limited by something in my brain that will not allow me, ever, to reproduce my brother's experience. I can only share in the more abstract, intellectual appreciation of it.

Other experiences that I feel are denied to me have to do with contexts that I'll never be able to get into. For example, I'll never know what my Irish accent sounds like to my Canadian colleagues (apparently it's "charming" and "mesmerising" but alas I will never hear it like that) because I can never enter a context where my own accent is other than the norm.

In general I would say that the more intellectual or abstract our ideas and experiences are, the easier they are to share. As an example, when I was reading Hofstadter's "Le Ton Beau de Marot" he talked about his acquisition of both the German and French languages and how important it was to him to be able to sound like a native speaker. I could really relate to this, having studied both German and French myself and always having been pretty obsessive about my accent being perfect. Similarly, my delight in discovering that Hofstadter was vegetarian meant I had a particularly accurate grasp of the delight he was expressing in the paragraph I quoted earlier.

Below this level of thought, though, surely there's an extent to which I am indeed trapped inside a cage of sorts, where the experiences that have formed me are the bars I will never get beyond: I'll never know what it's like to hear Bach's ciaconne as just a jumble of sounds; I'll never know what it's like to enjoy eating an apple; and I'll never know what it's like to be charmed by the manner in which I speak the English language.

On the other hand, apart from my experience of music, none of the above examples are particularly central to who I am, to "me-ness", and so perhaps those facets of me that are most central are the ones that are more easily realisable in other people's brains - my appreciation of language, my compassion for animals, my interest in programming, etc. But I don't think we can make such a clear-cut distinction between my raw experience facets and my more intellectual facets, music being a case in point. How intellectual is our appreciation of music and to what extent is it bound up with raw experience? If it is just about the intellectual process of understanding and appreciating patterns, as Hofstadter seems to claim at one point (quoted below), then why aren't people content just to read music scores rather than attend performances? The question of what makes music special (and I think it is very special) is one that interests me greatly and I've done some thinking about it here.

Hofstadter seems to wrap up questions about the mind and consciousness all too cleanly. That in itself may not be a valid objection - maybe it is that simple - but I find it hard to believe that the likes of David Chalmers, an eminent philosopher of mind and ex-student of Hofstadter's, whose theory of consciousness he caricatures fairly brutally for the sake of knocking it down, could really have it as wrong as Hofstadter makes out. I feel he makes the argument very black and white, especially in the section where he imagines a dialogue between himself and someone who opposes his view. I was disappointed by the content of this dialogue because I felt it left out the more difficult and challenging (and interesting!) counter-arguments to his ideas. His imagined interlocutor does not make particularly intelligent points. He keeps asking things like, "Why am I me and not someone else?" which, I think most people would accept, is a fairly nonsensical question. At one point during this dialogue, there is the following exchange regarding music:

SL#642: [...]Some other melody could be repulsive because it lacks logic, or because its logic is too simplistic or childish.
SL#641: That certainly sounds like a response to a pattern, not like raw sensation. A piece of music can have great emotional meaning despite being made of tiny atoms of sound that have no emotional meaning. What matters, therefore, is the pattern of organisation, not the nature of the constituents.

This is the quote I alluded to earlier and I just feel it ignores the fact that the substrate on which patterns of music supervene is a substrate of musical notes, which are something special in themselves, so transferring the pattern to a different substrate means losing the music. On the whole, I felt that this dialogue was slightly impoverished. I kept wanting it to do more justice to the other views of consciousness that are out there. I would love to read a real debate between Hofstadter and, say, Chalmers. Well, at least my appetite has been whetted and I can always go on and read more in the philosophy of mind debate on consciousness.

Overall, though, I did really enjoy the book. I love how Hofstadter thinks and so it is always a pleasure to read his ideas.

Finally, one clear limit on our brains' ability to manifest the minds of others is our intellectual capacity. I will never be able to see strange loops the way Hofstadter does, even if I somehow came to know him quite well, understand his likes, dislikes, etc., because I am "trapped" by the limits of the hardware in my head. Oh - does that not pose a loopy conundrum? If I am correct in that observation, it means Hofstadter is wrong about our not being trapped, which means I have made the wiser statement about our minds, which in turn undermines the assertion that I am trapped by my limited intellectual capacity. Hmm, the chances are I've got that wrong and can only hope that one day a more enlightened loop will manifest itself inside my head.


Just came upon this blog whilst reading up on jQuery and AHAH in Drupal. Funny to find such an intellectually stimulating post in this context! Thank you for reviewing this book in your blog - I will definitely be reading it. I have read 'Musicophilia' and think it's fascinating, but like other books by Sacks, somewhat reductionist in its orientation (to a neurologist, consciousness can be nothing other than quite literally 'trapped'/contained within the neurobiology of the brain).


Heya Katherine

Interesting piece. I wondered if Steve Reich might be a good musical tie in here? Also, not that I've read it myself, Oliver Sack's most recent book Musicophilia might be good to follow up on; that is if you haven't already read it.

Hi Brian, thanks for your

Hi Brian, thanks for your comment. To my shame I am woefully unfamiliar with Steve Reich's music, though he's one composer I've been meaning for a long time to get to know - perhaps you could suggest some works to start with? As regards Musicophilia, no I haven't read it but have noticed it in books stores and thought it looked interesting. Anyway, of course Hofstadter himself does a great job of tying music in with the idea of strange loops in his first book, Gödel, Escher, Bach - An Eternal Golden Braid, which is an absolute masterpiece.

Steve Reich

I would think that, although probably the most well known, "18" may not be the best first entry into Steve Reich world. I'd rather suggest the more melodic Tehilim, or Proverb both of which are sung, the latter on a Wittgenstein repeated stance: "How small it takes a thought to fill a whole life"... quite loopy and hofstaedtery ...


I'm interested to read this author. My reading list contains some fairly light material for the moment but as soon as I feel my concentration is up to it, I must try and catch up with the aforementioned piece.

As for Riech, hard to know. Purely as an intellectual exercise, it might be worth looking out for his very early works – such as 'It's gonna rain', or 'Come out'; all fairly dry.

His most popular piece – 'Music for 18 Musicians' – might be a bit more accessible and wet your appetite more.