I just finished reading ‘I am a strange loop’ by Douglas Hofstadter, and before I say anything else about the book, I’ll say that I really did want to like it.
I’m a huge fan of his better known book ‘Godel, Escher, Bach’ for which Hofstadter won a Pulitzer Prize, I’m also very interested in the subject area – maths, logic, self-reference, cognitive science. However there were just too many things that rubbed me up the wrong way, in no particular order here were all the things I didn’t like about the book:
We are treated to the following:
I did a very quick check and across the 433 pages of my edition there were 921 question marks, an average of 2.1 per page. A few other references points:
So Hofstadter is frankly off the chart.
And this may appear to be a fairly silly analysis, but I think it gets to the heart of the issue I have with the book. I just don’t find Hoftstadter to be a very clear writer. When reading GEB, I was happy to just explore some ideas, and like I said at the start, I’m a huge fan of that book. But what I was looking for in this book, were three main things:
Understand what a strange loop is
Problem 1 - after finishing the book, frankly I’m still not 100% sure what a strange loop is - I get the general idea, but what I'm not sure 100% sure about are the fringe cases. You see, Hofstadter never gives a final definition – the closest we come to it right at the start of the book where we get the following which Hoftstadter refers to as a provisional ‘first stab’:
“not a physical circuit but an abstract loop in which, in the series of stages that constitute the cycling-around, there is a shift from one level of abstraction (or structure) to another, which feels like an upwards movement in an hierarchy, and yet somehow the successive "upward" shifts turn out to give rise to a closed cycle. That is, despite one's sense of departing ever further from one's origin, one winds up, to one's shock, exactly where one had started out. In short, a strange loop is a paradoxical level-crossing feedback loop”
Let’s take the final sentence at face value: ‘a strange loop is a paradoxical level-crossing feedback loop’
Godel’s incompleteness theorem clearly meets this criteria – it is a paradox, it involves level crossing, and feedback loops, great.
What about the ‘chicken and the egg’, often given as another example of a strange loop – this is where I think the thinking becomes unclear. The concept of a chicken and egg cycle is simply not a paradox on its own – there is no self-contradictory element to a chicken being hatched from an egg, which goes on to become a chicken and lay more eggs. The question ‘what comes first, the chicken or the egg’ is a popular philosophical musing, which is a paradox – i.e. to give one of the answers seems to imply the other and so on. But then it is the question of precedence itself which is the paradox, but the question has no level-crossing, also the question never refers to itself so has no self-reference. The level crossing does occur in the idea of a chicken laying an egg which in turn becomes a chicken and so on, but then this particular phenomenon is not a paradox as we mentioned. So the ‘chicken and egg’ does not satisfy all of Hofstadter’s definition simultaneously. It is only when you allow a large amount of poetic licence and metaphor that the ‘chicken and egg’ becomes a strange loop – all the elements are involved somehow, but not in a unified way.
So maybe I’m being too literal about his use of the word ‘paradoxical’ here, maybe it is paradoxical simply by definition since we are ending up back where you started having tried to move strictly upwards hierarchally in the system. Okay, so now we can restate Hofstadter’s sentence above to read:
‘a strange loop is a level-crossing feedback loop’
This then is a lot closer to what Wikipedia uses to explain the concept "A strange loop is a cyclic structure that goes through several levels in a hierarchical structure.... [it] may involve self-reference and paradox'. So self-reference and paradox are not necessary conditions of a strange loop. Why have I seized on this one sentence of Hofstadter's as if I'm expecting it to explain what a strange loop is, when the entire book is about strange loops? The problem is, this is the only time in the entire book that Hofstadter does give an actual definition.
My issue then is I really don’t feel like I should have to work this hard just to understand the basic concept the book is about – just give us a definition, give examples, explain why the examples meet the criteria of the definition, maybe even chuck in some examples which don’t meet the definition to make it even clearer. Hofstadter only ever really explains what a strange loop is through the use of examples and analogy, however this makes it very unclear when his favourite example - Godel's theorem - involves both self-reference and paradox, whereas it seems these are possible features but not necessary features of his general definition.
So goal 1 - understand what a Strange loop is – I think this was finally accomplished, but only with the help of outside sources, and even then I do wonder if everyone who is using this term is using it in the same (limited) way, I feel like when I've read other people on the subject they act like self reference and paradox are fundamental to the defintion.
Understand Hofstadter’s theory of self
Hofstadter’s theory is something along the line of - an ‘I’ is ultimately nothing more than the “pattern of symbols” that arises through a strange loop (feedback system) between our brain/mind and the world/other people. Here a 'symbol' refers to any recurring marks within a system left by a particular stimulus, so it's a lot broader than just physically symbols such as writing or pictures. Most of this feedback looping naturally happens within our own mind, so this is where most of our ‘I’ resides. The ‘I’ emerges over time as a result of the strange loop whereby our mental capacity to understand objects gets pointed at ourselves in such a way that a cyclical loop occurs.
One consequence of this theory is that in so far as our pattern of thought and self feeds-back through other people’s minds (which are themselves patterns of feedback…) we can be said to exist within their minds (remember that our ‘I’ is simply the name for this pattern nothing else, so there's no reason it can't exist in someone else's mind). So each of us carries a sort of low-fidelity version of everyone we interact with, and the version is stronger or weaker based on how close or distant we are with them.
This implies that it is literally true to say that people who have died live on in us after they are gone. Since an ‘I’ is simply a pattern of symbols that has this particular kind of strange loop, when we are sufficiently close to someone to take on some of their patterns of thought within us and start to feedback on them (as humans naturally do), that ‘I’ is not doing so only in their mind but in our mind as well, i.e. their ‘I’ exists within our brain.
You might ask yourself, why would anyone believe in a theory with a consequence as wacky as this? I’m fairly convinced that Hofstadter believes in this theory because of this consequence, not in spite. There is a rather tragic section in the book in which Hofstadter relates how his wife died suddenly and unexpectedly, leaving him to raise their two young children. Moreover he and his wife seemed exceptionally close and her death hit him, as you would expect, extremely hard. Hofstadter developed most of his theory of self after this point (though he does mention that its genesis was prior to her illness and explicitly claims that her death was not a motivating factor for developing it) I just find this quite a hard claim to swallow – that he didn’t at least partly, maybe subconsciously, develop this rather unusual theory of self, with its implications about living on in other people partly as a response to the trauma he suffered.
So goal 2 – understand his theory of self – yes… to a certain extent accomplished, however I just didn’t really find it very convincing.
Understand the link between Godel’s theory and consciousness
This is another intriguing idea however I feel like I needed to do the hard work to understand it again, rather than Hofstadter explaining it for me, and that once I did the link was more one of analogy rather than strict isomorphism.
First I’ll state what I agree with, both consciousness and Godel’s theorem involve a strange loop, this I can get on-board with. Consciousness in the way that our minds can think about itself, Godel’s theorem in the way that when we introduce Godel numbering, a axiomatic system such as Russell and Whitehead’s Principia Mathematica can encode statements which refer to the system, and the system in turn can make statements about Godel numbers.
I’ll also agree that there is another analogy between the two which is interesting. We can think about brains/minds as being two levels of meaning operating out of the same physical process - i.e. neurons firing in the brain in line with the laws of physics, and our thoughts interacting with each with a separate level of meaning emerging ut of the same underlying process.
In Godel’s theorem there are also two levels of meaning – one at the low-level (analogy to the level neurons), which are the strings of symbols within PM. So when Russell and Whitehead prove a theorem in Type Theory using PM they do so by manipulating strings of symbols according to the rules of the system (think the rules of physics), the second level of meaning is in Godel numbering - where meaning is encoded in numbers themselves (analogy to the level of mind rather than brain). So basically through Godel numbering, numbers are simultaneously numbers, and statements about numbers, just as in our brain neurons are simultaneously inanimate objects following the laws of physics but also thoughts in our mind.
Here is my problem with it – I always thought of Godel numbering as basically just a clever trick (maybe that should read a genius trick but a trick none the less), no one would actually reason at the level of Godel numbers – their incredible length just make it completely unfeasible to work with them. The fact that we can imbue them with meaning is certainly interesting, it allows for example of the proof of Godel's incompleteness theorem, and it’s a cool analogy that we’ve got a fairly mechanical system with one level of meaning, out of which by looking at it in a different way we get a different level of meaning. But that is basically where the isomorphism ends.
So goal 3 – understand the link between Consciousness and Godel’s theorem – achieved to a certain extent, but I’m just not convinced that it really leads to any insight about either consciousness or Godel’s theorem.
In summary, would I recommend this book - probably not, what I would suggest is that anyone who hasn't read GEB should think about reading that, because that was a fascinating read, and I think it still holds up well today even having been written back almost 50 years ago.
I work as a pricing actuary at a reinsurer in London.