I first learned about recursion in the context of computer programming. The output of some code was fed back as an input into the same code. This kept going until some criteria was met. I’m sure every novice programmer has made the mistake where the criteria was not specified, or specified incorrectly, leading to an eternal loop. It’s practically a rite of passage in learning programming.
I would be remiss not to quote the poet laureate of recursion, Douglas Hofstaedter:
WHAT IS RECURSION? It is…nesting, and variations in nesting. The concept is very general. (Stories inside stories, movies inside movies, paintings inside paintings, Russian dolls inside Russian dolls (even paranthetical comments inside paranthetical comments!)–these are just a few of the charms of recursion.)…
Sometimes recursion seems to brush paradox very closely. For example, there are recursive definitions. Such a definition may give the casual viewer the impression that something is being defined in terms of itself. That would be circular and lead to infinite regress, if not to paradox proper. Actually, a recursive definition (when properly formulated) never leads to infinite regress or paradox. This is because a recursive definition never defines something in terms of itself, but always in terms of simpler versions of itself. GEB, Chapter V
Here’s another great example of recursion: a commemorative plaque in Toronto commemorating its own installation: A recursive plaque honoring the installation of a plaque honoring the installation of a plaque honoring the installation of…(BoingBoing)
Thus, I will define recursion for our purposes as the nesting of like within like. Or, rules that can apply to their own output. A common image used to show this is the Russian Matryoshka dolls, which adorn the cover of The Recursive Mind by Michael C. Corballis, the book we’ll be considering today.
These dolls work in a pretty interesting way. Within each one, there is another doll that is exactly the same. You have multiple copies of the same doll, each within another, until eventually, you get to the smallest doll.
To Understand Recursion, You Must First Understand Recursion (Words and Code)
Another example is what’s called the Droste effect, after this can of Droste’s Cacao which references itself (which references itself, and…). This effect has subsequently been replicated in a number of product packages.
Another definition is, “a procedure which calls itself, or…a constituent that contains a constituent of some kind.” Thus, recursion can be understood as both a process and a structure.
In linguistics, recursion is the unlimited extension of language. It is the ability to embed phrases within phrases and sentences within sentences resulting in the potential of a never-ending sentence.
The Recursiveness of Language – A Linkfest (A Walk in the WoRds)
You can even have a book within a book—such as, for example, The Hipcrime Vocab, the book referenced inside John Brunner’s Stand on Zanzibar, from which this blog takes its name.
Often recursive processes produce recursive structures. Not always, though. For example, an iterative structure can be derived from a recursive process. Something like
AAAAAAABBBBBB can be generated using a recursive procedure. You just nest the AB’s like so:
But—and this turns out to be important—there is nothing in the above structure that indicates it must have been generated recursively. You could just have a series of A’s followed by a series of B’s. This may seem like a trivial point, but what it means is that there could be recursion behind something that does not seem recursive. And the reverse is also true—something might look recursive, but be generated via non-recursive means. The AB sequence shown above could be generated either way. This means that some apparent examples of recursion might actually be something else, such as repetition or iteration. As we’ll see, this means it can be quite tricky to determine whether there truly are examples of recursive thought in non-human animals or human ancestors.
Let’s start with a simple linguistic language. Let’s say I take a simple noun-verb phrase like, The dog has a ball. Let’s add another basic noun-verb phrase about the dog: The dog is brown. Each of these are standalone ideas. But I can nest them inside one another this way: The dog who is brown has a ball, or The brown dog has a ball, or The brown dog’s ball, etc.
Then let’s add this fact: The dog belongs to Erik. Therefore, Erik’s brown dog has a ball. Let’s say it’s my ball. Erik’s brown dog has my ball. Maybe the dog is barking at me right now. Erik’s brown dog, who has my ball, is barking at me right now. Do you get it? You get that Erik’s brown dog who has my ball is barking at me right now.
Anyway, we could go on doing this all day, but I think you get the point. Recursive structures can theoretically go on until infinity, but in reality are constrained. After all, there’s only so much time in the day. Corballis explains that recursive constructions need not involve embedding of exactly the same constituents, but constituents of the same kind—a process known as self-similar embedding. He gives the example of noun phrases. For example, Nusrat Fateh Ali Khan’s first album was entitled, “The Day, The Night, The Dawn, The Dusk” (you can listen to it here). That’s basically four noun phrases. From these constituents, one can make a new noun phrase like “The day gives way to night.” or perhaps a movie title like “From Dusk Till Dawn.”
Recursive language is needed to express recursive thoughts, and here’s a good case to be made that recursive thought is the key to our unique cognitive abilities. This is exactly the case Corballis makes.
…recursive processes and structures can in principle extend without limit, but are limited in practice. Nevertheless, recursion does give rise to the *concept* of infinity, itself perhaps limited to the human imagination. After all, only humans have acquired the ability to count indefinitely, and to understand the nature of infinite series, whereas other species can at best merely estimate quantity, and are accurate only up to some small finite number. Even in language, we understand that a sentence can in principle be extended indefinitely, even though in practice it cannot be–although the novelist Henry James had a damn good try…
Corbalis mentioned Henry James, above, and below is his longest sentence. Click on the link to see its structure diagrammed, whereupon you can see the recursive (embedded) nature of his language more clearly.
“The house had a name and a history; the old gentleman taking his tea would have been delighted to tell you these things: how it had been built under Edward the Sixth, had offered a night’s hospitality to the great Elizabeth (whose august person had extended itself upon a huge, magnificent and terribly angular bed which still formed the principal honour of the sleeping apartments), had been a good deal bruised and defaced in Cromwell’s wars, and then, under the Restoration, repaired and much enlarged; and how, finally, after having been remodelled and disfigured in the eighteenth century, it had passed into the careful keeping of a shrewd American banker, who had bought it originally because (owing to circumstances too complicated to set forth) it was offered at a great bargain: bought it with much grumbling at its ugliness, its antiquity, its incommodity, and who now, at the end of twenty years, had become conscious of a real aesthetic passion for it, so that he knew all its points and would tell you just where to stand to see them in combination and just the hour when the shadows of its various protuberances—which fell so softly upon the warm, weary brickwork—were of the right measure.” (James 2003, 60)
The Henry James Sentence: New Quantitative Approaches (Jonathan Reeve)
The appealing aspect of recursion is that it can in principle extend indefinitely to create thoughts (and sentences) of whatever complexity is required. The idea has an elegant simplicity, giving rise to what Chomsky called “discrete infinity,” or Wilhelm Humboldt famously called “the infinite use of finite means.” And although recursion is limited in practice, we can nevertheless achieve considerable depths of recursive thought, arguably unsurpassed in any other species. In chess, for example, a player may be able to think recursively three or four steps ahead, examining possible moves and countermoves, but the number of possibilities soon multiplies beyond the capacity of the mind to hold them.
Deeper levels of recursion may be possible with the aid of writing, or simply extended time for rehearsal and contemplation, or extended memory capacity through artificial means. The slow development of a complex mathematical proof, for example, may require subtheorems within subtheorems. Plays or novels may involve recursive loops that build slowly—in Shakespeare’s Twelfth Night, for example, Maria foresees that Sir Toby will eagerly anticipate that Olivia will judge Malvolio absurdly impertinent to suppose that she wishes him to regard himself as her preferred suitor. (This is recursive embedding of mental states, in that Sir Toby’s anticipation is embedded in what Maria foresees, Olivia’s judgement is embedded in what Sir Toby anticipates, and so on).
As in fiction, so in life; we all live in a web of complex recursive relationships, and planning a dinner party may need careful attention of who things what of whom. pp. 8-9
We do indeed live in a web of complex social relationships, but some of us live in a more complex web than others. A small village in the jungle is vastly different than a medieval free city, and certainly different from a modern city of millions of people. Similarly, where one lives and what one does for a living have an effect also. A politician or businessman lives in a much more complex social world than a painter or a ratcatcher. People who grow up in a village where everyone is related to another have a much easier cognitive task than a traveling salesman, or an international diplomat.
I point all this out to prepare the way for an argument I’m going to make later on, which is my own, but loosely based on ideas from Julian Jaynes. I’m going to make the case that increasing social complexity in human societies over time selected for recursive thinking abilities. I will also argue that such abilities led to the creation of things like writing and mathematics, which emerged only several thousand years ago, and were initially the province of a small number of elites (indicating that such abilities may be quite recent). I will also argue that recursive thinking allowed for advanced organization and planning abilities, which early leaders used to justify their elevated social status. Furthermore, I will argue that the type of “reflective self” that Jaynes saw developing during the Axial Age was due to increasingly recursive modes of thought. It was not caused by social breakdown, but rather by the increasing cognitive challenges demanded by social structures, as opposed to the primarily environmental challenges that earlier humans faced. This should become clearer as we discuss the social benefits of recursive thinking below.
In other words, consciousness did not arise so much from the breakdown of the bicameral mind, as it did from the rise of the recursive mind. That’s my argument, anyway.
As recursive thinking advanced, so too did the abilities which Jaynes notes as giving rise to the construction of the reflective, vicarial self—extended metaphor, mental time travel, higher-order theory of mind, and so on, as we’ll see. The lack or paucity of recursive thought, in contrast, prior to this period, is what prevented reflective self-consciousness (or, in Jaynes’s parlance, “consciousness”) from developing. Thus my timeline is similar to Jaynes’s, as are the conclusions, but the underlying reasons differ. We’ll get into this in more depth later.
An example of the infinitely extensible nature of language a novelties like one-sentance novels. of which there are a surprisingly large amount. Here is a good review of three of the best ones where the review itself is written as a single sentence (providing yet another example of recursion!):
Awe-Inspiring One-Sentence Novels You Never Knew Existed (The GLOCAL Experience)
In 2016, an Irish novelist won a literary prize for a one-sentence novel. To me, this novel is exemplary of the kinds of recursive thinking we’re describing here, and how it’s necessary to construct the vicarial self (the Analog ‘I’ and Metaphor ‘me’). The novel demonstrates not only a highly embedded (recursive) sentence, but mental time travel, and advanced theory of mind (the ability to extrapolate the mental states of other characters by inserting oneself into their experience; a requirement of good fiction), and autobiographical narratization (about which, more below). We’ll cover each of these concepts in more depth:
It stutters into life, like a desperate incantation or a prose poem, minus full-stops but chock-full of portent: “the bell / the bell as / hearing the bell as / hearing the bell as standing here / the bell being heard standing here / hearing it ring out through the grey light of this / morning, noon or night”…The speaker hearing the bell is one Marcus Conway, husband, father and a civil engineer in some small way responsible for the wild rush of buildings, roads and bridges that disrupted life in Ireland during the boom that in the book has just gone bust. Marcus is a man gripped by “a crying sense of loneliness for my family”. We don’t quite know why until the very end of the novel, which comes both as a surprise and a confirmation of all that’s gone before.
Among its many structural and technical virtues, everything in the book is recalled, but none of it is monotonous. Marcus remembers the life of his father and his mother, for example, a world of currachs and Massey Fergusons. He recalls a fateful trip to Prague for a conference. He recalls Skyping his son in Australia, scenes of intimacy with his wife, and a trip to his artist daughter’s first solo exhibition, which consists of the text of court reports from local newspapers written in her own blood, “the full gamut from theft and domestic violence to child abuse, public order offences, illegal grazing on protected lands, petty theft, false number plates, public affray, burglary, assault and drunk-driving offences”. Above all, he remembers at work being constantly under pressure from politicians and developers, “every cunt wanting something”, the usual “shite swilling through my head, as if there weren’t enough there already”. He recalls when his wife got sick from cryptosporidiosis, “a virus derived from human waste which lodged in the digestive tract, so that […] it was now the case that the citizens were consuming their own shit, the source of their own illness”.
Single sentence novel wins Goldsmiths prize for books that ‘break the mould’ (The Guardian)
Solar Bones by Mike McCormack review – an extraordinary hymn to small-town Ireland (The Guardian)
In the example above, we can see how recursive thought is intrinsically tied to self-identity, which is in turn connected with episodic memory, which is also tied to recursion as we will see. In brief, I will argue that recursive thought is tied to the kind of reflective self-consciousness that Jaynes was describing, and, as such, we are not as much concerned with the beginnings of language as the origin of consciousness, as much as the beginnings of recursive thought as the beginning of consciousness (as I will argue). It is quite possible for spoken language to have existed for communicative purposes for thousands of years prior to recursive thought and its subsequent innovations.
I focus on two modes of thought that are recursive, and probably distinctively human. One is mental time travel, the ability to call past episodes to mind and also to imagine future episodes. This can be a recursive operation in that imagined episodes can be inserted into present consciousness, and imagined episodes can even be inserted into other imagined episodes. Mental time travel also blends into fiction, whereby we imagine events that have never occurred, or are not necessarily planned for the future. Imagined events can have all of the complexity and variability of language itself. Indeed I suggest that language emerged precisely to convey this complexity, so that we can share our memories, plans and fictions.
The second aspect of thought is what has been called theory of mind, the ability to understand what is going on in the minds of others. This too, is recursive. I may know not only what you are thinking, but I may also know that you know what I am thinking. As we shall see, most language, at least in the form of conversation, is utterly dependent on this capacity. No conversation is possible unless the participants share a common mind-set. Indeed, most conversation is fairly minimal, since the thread of conversation is largely assumed. I heard a student coming out of a lecture saying to her friend, “That was really cool.” She assumed, probably rightly, hat her friend knew exactly what “that” was, an what she meant by “cool.” pp. ix-x
It goes beyond that, however. Later, we’ll look at work by Robin Dunbar which suggests that both organized religion and complex kinship groupings are dependent upon these same recursive thought processes. Given how important these social structures are to human dominance of the planet (perhaps the most important), we can see that recursion might be the skeleton key to all the things that make us uniquely human. This is especially true given the evidence (although it is disputed) that our predecessor species (i.e. Archaic Humans and earlier) were unable to engage in this kind of thinking.
2 thoughts on “The Recursive Mind (Review) – 1”
I’m old enough to remember the sudden incursion of fractals into mass consciousness some time in the 80s. It’s hard to describe the mind-boggling feeling of what is now common enough to be a lyric in that song from Frozen (originally by Journey, of course ;D)
Double the angle, square the distance and add the number you first thought of. That generates the Mandelbrot set. Who’da thunk it? I remember grokking that and a world of possibility opening up. And then that Dawkins fella got completely the wrong end of the stick.
Not only human social patterns, but also human habitation (i.e. cities) can be understood using fractals: http://zeta.math.utsa.edu/~yxk833/connecting.html
Also, from the same author, it appears that fractal-derived patterns and designs are shown to empirically reduce stress in the human habitat, something completely ignored by modernist architecture: