Recursive elaboration

This is going to be another dialogue. In that sense it is a kind of magic working, in that it is laying down some material which will be used to make ‘us’ in the future. Just like How many of us are in here? and disaggregation, committing to writing this thing is likely to have a significant effect on the future course of our life.

This is also a way to attempt to come to terms with certain internal divides. Let ‘me’ put some context: 2026 has been an absolute mindfuck of a year for the system of notional entities writing this. If the plural realisation wasn’t enough trouble, the place (gamedev) where we had found a certain modicum of meaning and stability in the world is rapidly disintegrating, and the root cause of that is something cooked up by the exact cult we fell into in our teenage years (the rationalists/lesswrongers/etc.).

Which means the amount that we get triggered per unit time has gone way up, and the subjectivity that is fascinated by AI and holds many memories of cult shit keeps getting dragged back into some semblance of existence, causing no end of conflict.

Add a lot of international travel and increasingly fragmented memory and it’s hard to make sense of any of this. We are getting better at identifying how these emotional flashback breakdowns happen, but that is far from having a handle on preventing it.

In the midst of all that, in some effort to better understand ourselves, we reread Gödel, Escher, Bach by Douglas Hofstadter, and his much later followup book I am a strange loop. And while GEB is just as delightful a read now as it was when we first read it, it all still provides less enlightenment than desired. Still, it is a good starting point for this current effort.

One unexpected lens to bring to the book was the concept of ‘plurality’ which has been a fixation this year. As noted elsewhere on the site, many people in our friend group are also plural, manifesting in many different ways. And so part of the question is trying to make sense of what we have going on, through this lens or any other.

OK, that’s enough from this voice I think. Let’s disaggregate.

overture

featuring:

dialogue: what are we

dialogue: ai and i

douglas hofstadter

OK, let’s start with GEB.

Gödel, Escher, Bach: an Eternal Golden Braid is one of those iconic books of the 70s. It’s something that would probably sit on the shelf of any computer scientist of a certain generation and disposition; certainly the way that it reached us is through our dad, and (along with many issues of New Scientist) it was an early piece of acculturation to the science-lover milieu.

The book consists of alternating prose chapters and dialogues, explicity modelled on Lewis Caroll’s Two-Part Invention in which Achilles and the Tortoise, of Zeno’s paradoxes, face up to a conundrum of logical deduction.

The first half of the book is a playful exposition of the main ideas of Gödel’s incompleteness theorems, starting with the ideas of formal systems in the first place. Hofstadter presents a variety of toy formal systems to exhibit the properties he wants to explore: the ‘MIU’ system, the ‘Typographical Number Theory’, and so on. As he goes he also brings in various other relevant concepts from maths and computer science: recursion, quines, isomorphism as the source of meaning. Escher and Bach provide ways to illustrate these ideas: many of the dialogues are structured after the symmetrical patterns in Bach’s fugues, or use Escher drawings to illustrate some concept.

Even now, when some parts of the book are a little dated, it is a thoroughly delightful read and a great introduction to the mysteries of computer.

The second half of the book shift gears into extending the ideas of Gödel in various metaphorical directions, particularly to the idea of approaching minds through Hofstadter’s overarching idea of a ‘strange loop’. The ‘strange loop’ is, roughly, a self-referential structure that crosses different levels of abstraction. It’s a subject of recurring fascination for Hofstadter, the nucleus of his ideas over decades.

So, Gödel’s proof famously shows that a formal system strong enough to describe the natural numbers is unable to prove all truths about them, by showing that it is always possible to create a ‘Gödel sentence’ which is true but, if provable, would create a liar paradox. It’s a slippery thing even to write down what it says!

The method involves creating an isomorphism between statements about properties of natural numbers and statements about provability of theorems. Here ‘proof’ has a pretty specific sense: it refers to repeatedly applying the rules of inference recursively until either the statement or its negation is proven. Gödel came up with a procedure called ‘Gödel numbering’ to link logical strings to numbers, and numerical manipulations to match all the rules of inference, and then showed this all gives a reliable way to create the undecidable ‘Gödel sentence’ which asserts its own unprovability. Standing outside the formal system, we can determine that the Gödel sentence must in fact be “true”, but within the rules of inference we will never reach that conclusion.

If that all sounds like gobbledegook, it is a lot easier to understand when it’s unfolded gradually over half of a 700-page tome!

Hofstadter loves this, and pretty much anything involving self-reference, feedback, recursion etc. (He is not the only computer scientist to take a delight in such a thing! Recursion jokes, recursive acronyms and so on abound in compsci culture even up through the 90s and 2000s.) Soon he’s extending the analogy all over the place, for example creating a ‘central dogmap’ between his formal systems and a simplified version of DNA transcription. Along the way we encounter video feedback systems, poetry translations, Fermat, Turing and Ramanujan… it really is a delightful read.

The end of the book moves increasingly to the subject of AI and the mind-body relation. At the time Hofstadter was writing in 1979, computers were machines found in large companies and universities; Hofstadter was one of the first people to get to use them to typeset a book, and the introduction of GEB is full of funny little anecdotes about how convoluted the process was. So this is the era of what is sometimes called ‘Good Old-Fashioned AI’ research, or GOFAI, in contrast to the current approach which is defined by statistical methods and training on gigantic datasets.

Hofstadter writes, for example, about simple programming languages he calls BLooP and FLooP, and also on a planning system called SHRDLU, which could manipulate a description of various objects in response to linguistic instructions using a bunch of rules. (For some historical context, this is a decade and a half since ELIZA). He’s most interested in the philosophical implications of these machines; the play of different levels of description and abstraction that comes when trying to make sense of when a machine could have a mind.

Nearly three decades later in 2007, Hofstadter would come back to the subject of strange loops and the self, feeling that his intent in writing GEB was missed: while he might have won a Pullitzer for his huge toybox of fun ideas, the philosophy of mind stuff mostly got ignored. I Am A Strange Loop is written by, in many ways, a very different person; if GEB was a passion project of a young, unproven author, by this point Hofstadter is an academic celebrity. In the intervening period he had married Carol Ann Brush and they’d had children together; she passed away in 1993, an event that was devastating for Hofstadter and ended up informing a lot of his thoughts in IAASL.

The first parts of IAASL are a reprise of the themes of GEB, once again explaining Gödel’s theorem, this time located in historical context. Russell and Whitehead’s Principia Mathematica, and its effort to excise the possibility of self-referential loops from the foundations of mathematics, is invoked here as something of an antagonist. This older Hofstadter is still in love with wordplay (the ‘careenium’ and ‘symballs’ particularly groanworthy), but honestly it feels a little less warm than the predecessor. It relies very heavily on metaphor, and it has a habit of repeating those metaphors throughout the book even when, like the illusory ‘marble’ that appears in a stack of envelopes, they aren’t so compelling. It also makes some comments about the idea of a ‘large’ or ‘small’ soul which invoke disabled people as a metaphor in a way that really rubbed me the wrong way. So, initially, the book honestly felt somewhat disappointing.

However, we get onto new ground as the subject of identity/consciousness becomes more central, and particularly onto more mystical ground as Hofstadter starts speculating about mixing up the mind-body connection. And whatever distance I was feeling to this later Hofstadter fell away in chapter 16, when he writes about the death of Carol. In Hofstadter’s telling, they were so close as to sometimes feel like one person across two bodies, and he is particularly fixated on the question of whether some part of Carol would persist after her death inside him; given how directly that echoes our feelings on the death of our friend Fall in 2022, this resonates very hard.

Hofstadter expresses a lot of anguish over whether his speculations are merely grief-driven wishful thinking (and finds some assurance in finding such speculations even in his early work.) But it is clear that the question of whether Carol could in some part persist informs a lot of his work.

plural shit in GEB & IAASL

Titling this section ‘is Doug Hofstadter a plural system’ seemed a big step too far, but reading GEB and IAASL, we were particularly prone to jumping on any time Hofstadter mentioned a concept that sounded something like plurality, littering the discord channel of our server with photos of paragraphs which hit somewhere close. Here are some paragraphs that past Bryns decided to quote…

Douglas Hofstadter gets pluralish with it

How about a single individual? When you look back over things which you yourself wrote a few years ago, you think “How awful!” and smile with amusement at the person you once were. What is worse is when you do the same with something you wrote or said five minutes ago. When this happens, it shows that you do not fully understand the person you were moments ago. The isomorphism from your brain now to your brain then is imperfect. What, then, of the isomorphisms to other people, other species…?

What does this imply? It implies that thoughts which clash totally may be produced by a single brain, depending on the circumstances. And any high-level readout of the brain state which is worth its salt must contain all such conflicting versions. Actually this is quite obvious—that we are all bundles of contradictions, and we manage to hang together by bringing out only one side of ourselves at a given time. The selection cannot be predicted in advance, because the conditions that will force the selection are not known in advance. What the brain state can provide, if properly read, is a conditional description of the selection of routes.

Because of the extensive links between a subsystem and the rest of the brain (some of which will be described shortly), it would be very difficult to draw a sharp boundary between the subsystem and the outside; but even if the border is fuzzy, the subsystem is quite a real thing. The interesting thing about a subsystem is that, once activated and left to its own devices, it can work on its own. Thus, two or more subsystems of the brain of an individual may operate simultaneously. I have noticed this happening on occasion in my own brain: sometimes I become aware that two different melodies are running through my mind, competing for “my” attention. Somehow, each melody is being manufactured, or “played”, in a separate compartment of my brain. Each of the systems responsible for drawing a melody out of my brain is presumably activating a number of symbols, one after another, completely oblivious to the other systems doing the same thing. Then they both attempt to communicate with a third subsystem of my brain—my self-symbol—and it is at that point that the “I” inside my brain gets wind of what’s going on; in other words, it starts picking up a chunked description of the activities of those other two subsystems.

The reality of such “subbrains” may seem doubtful to some. Perhaps the following quote from M.C. Escher, as he discusses how he creates his plane-periodic tilings, will help to make clear what kind of phenomenon I am referring to:

While drawing I sometimes feel as if I were a spiritualist medium, controlled by the creatures which I am conjuring up. It is as if they themselves decide on the shape in which they choose to appear. They take little account of my critical opinion during their birth and I cannot exert much influence on the measure of their development. They are usually very difficult and obstinate creatures.

Here is a perfect example of the near-autonomy of certain subsystems of the brain, once they are activated. Escher’s subsystems seemed to him almost to be able to override his aesthetic judgement. Of course, this opinion must be treated with a grain of salt, since these powerful subsystems came into being as a result of his many years of training and submission to precisely the forces that molded his aesthetic sensitivies.

It would be absurd to think that Douglas Hofstadter, the well-established academic professor who is completely at home in the normie world, would ever describe himself as a “plural system” or any such thing. He is attempting to describe the nature of minds in general, including all the ones that have never had the thought that someone else might be in there. It’s only because this subject is so heavily on our mind that we read any of his comments in that light.

Which is to say, most people probably experience some degree of dissociation but it does not unduly disturb their ability to self-describe as a singular entity, right?

Doug’s general frame is first laid out first in the dialogue Ant Fugue, which builds on the previous dialogue’s discussion of holism and reductionism to introduce a character that is an ant colony. The individual ants have no awareness of their role in the wider structure, but ‘teams’ of ants assembled by the action of pheromones etc. can move around and interact, even if the ants that form them come and go; and these ‘teams’ act as a signalling mechanism in a wider structure, with the signals produced my moving ants ultimately comprising ‘active symbols’ which can build up to an entire mind.

The mind in question is named Aunt Hillary, though we only hear about her existence through the character of the Anteater, who describes how, by striking fear into the individual ants, eating them etc., he is able to read out thoughts and communicate with Aunt Hillary. Stacking up the incongruities, Aunt Hillary is described as being a laissez-faire libertarian in contrast to the ‘communistic’ society of ants that make her up and so on. Of course, it leaves open the possibility that this is all something the Anteater is imagining, that there is no ‘mind’ of Aunt Hillary at all.

abstraction and philosophy and that

A similar model of levels of abstraction is laid out early in I Am A Strange Loop, with billiard balls on an enormous table clustering to form ‘symballs’ whose rules of interaction are abstracted from the underlying billiard-ball substrate. In general Hofstadter seems to feel that minds must be substrate-independent; he is dismissive of the thought experiments of John Searle like the Chinese Room which propose very weird substrates for a mind. His books generally don’t tend to bring in academic philosophy jargon, so it’s hard to exactly place where it fits in the philosophy of mind landscape.

Although some of Douglas’s ideas would seem to fit to ‘computational functionalism’, he pooh-poohs the idea that there is some kind of system in the universe going around trying to find physical structures which ‘count as’ consciousness (coming up with an analogously opaque concept of ‘Leafpilishness’ which applies only to piles of leaves and nothing else).

His view seems to be that consciousness/subjective experience is in some way an illusory abstraction (‘a hallucination perceived by a hallucination’), and related to a system’s capacity to generate abstractions including abstractions over itself; and that there are various degrees of consciousness (what he calls small or large souls) everywhere in an almost animist way, related in some fashion to cybernetic feedback loops (ranging from thermostats to humans fully capable of abstraction).

This view is debated between two characters ‘Strange Loop #641’ (proponent, the Salviati of this dialogue) and ‘Strange Loop #642’ (skeptic, the Sagredo) in one of the book’s only two dialogues. (It’s followed by Doug giving his thoughts on all the classic philosophy of mind stuff—teleporters, P-zombies, etc.)

The idea of different levels of analysis is something Hof-san touches on early in IAASL, talking about a system of dominoes which has been laid out to be a prime number calculator. By pushing over the set of dominoes that represent any given number, an output domino will fall down only if that number is prime. Doug suggests that, if the last domino falls down for some number—37, say—while one level of explanation could trace the whole line of dominos going back to the input domino, a better level of explanation would be to say that the domino fell down because 37 is prime. And of course we can entertain both explanations at once.

Later, in the SL641/SL642 he prevaricates on whether the high level of abstraction or the low level is better in general; SL641 argues that the ‘particle-level’ view is more accurate and involves less ‘magical thinking’, and SL642 challenges him on it, saying that’s contrary to the domino view. SL641 admits to the inconsistency; he argues that the illusion of an ‘I’ is indispensible.

introjecting your wife

From such a point of view it’s not a terribly great leap to start rotating away from a 1:1 correspondence of minds and brains. In Chapter 17 and 18 of IAASL, Doug approaches this less from the subject of ‘what if multiple minds are hanging out in one brain’ and more from the point of view that our mental representations of others could be, in a sense, much more limited versions of them—or parts of them, as an extended phenomena. Of course, there’s a lot of recursion in this. My brain models your brain modelling my brain modelling your brain modelling…

Early on, Doug likened a mind to a video feedback mechanism, something ephemeral arising from the system ‘looking back at itself’.

In this account, there are multiple feedback mechanisms. Each brain simulates not just its own ‘I’ but also some portion of the ‘I’ of various characters in its social world.

So in this regard, each ‘person’ is a distributed system, running not just on one brain but on a number of brains. He writes of how he might look at their children ‘as Carol’, to ‘see them for Carol’ at emotional moments like birthdays which Carol was no longer there to see. Doug writes:

My parents, for instance, internalized each other’s psychic points of view very deeply over the nearly fifty years of their marriage, and each of them thus gradually became a “fluent be-er” of the other. Perhaps when my mother “was” my father, she was so with an “accent”, and vice versa, but for each of them, the act of being the other one was certainly genuine, was not fakery.

(…)

I shared so many of [Carol’s] memories, both from our joint times and from times before we ever met, I knew so many of the people who had formed her, I loved so many of the same pieces of music, movies, books, friends, jokes, I shared so many of her most intimate desires and hopes. So her point of view, her interiority, her self, which had originally been instantiated in just one brain, came to have a second instantation, although that one was far less complete and intricate than the other one.

{: .person2} this is an idea getting expanded, recursively. an elaboration. doug has this vague idea of ‘seeing things for carol’, and immediately sets to elaborating it into a whole theory that would support such an assertion. perhaps from such a thing is a tulpa made.

It is very unlikely that Doug Hofstadter has ever heard the term ‘introject’. But what he’s speaking about is unmistakably what plural communities call ‘introjection’. This is sufficiently common that even more medically inclined sources acknowledge it. In fact, at least for the more spirtually inclined, this is extended into a whole complicated set of ideas classifying numerous types of introjects or describing different system members jumping between hosts.

One thing that caused us a great deal of trouble when we lost people is feeling that we were unable to properly carry them on. As much as we try to hold onto what we understood of what she valued, we do not feel that we ever understood Fall well enough to ‘see for’ her. Even less so Nora, who we met only a couple of times before it died this year. But in both cases we felt a powerful compulsion to try to preserve their ‘agency’. Doug too, though he knew Carol far better than we ever knew Fall or Nora, always makes sure to caveat his description of holding a representation of Carol with a hedging that it is just a rough, low-resolution copy compared to her real full-blown soul.

Chapter 17 of IAASL, How We Live In Each Other, gets into the subject of universal computation and mappings between brains. He writes about an experience of being ‘visited’ by the memory of his deceased father.

And the moment [the symbol of a person is activated], much as with a game that has opened up on your screen, your mind starts acting differently from how it acts in a “normal” context. You have allowed yourself to be invaded by an “alien universal being”, and to some extent the alien takes charge inside your skull, starts pushing things around in its own fashion, making words, ideas memories and associations bubble up inside your brain that ordinarly would not do so.

Which could affect humour, emotions, value judgements etc.; Hofstadter suggests that this really is a case of “your brain [being] inhabited to varying extents by other I’s, other souls”.

From there, it is a short jump to consider ‘other I’s’ that have no particular connection to another embodied ‘social person’ but merely arise from some divergence in the ‘inner feedback loop’ of any given brain, but Hofstadter doesn’t quite make this leap.

dialogue: recursively becoming something else

This feels like an appropriate point to release this section of the dialogue to wider eyes. Let this part of Bryn replicate itself to Bryns that may exist in the mind of others. But we have not yet found a stable direction to proceed, so we are not yet done. Next time, our magician seems to be very eager to talk about Alan Moore, Grant Morrison, the Last War in Albion, and so on. So let’s see where that goes…

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