Recursion may be responsible for the concept of self

WHAT is it that makes humans so dominant on Planet Earth? Clearly, the answer does not lie in our physical attributes, for other species are stronger, faster or capable of such superhuman feats as flight or long-distance travel under water. The answer surely lies in our mental capacities.
According to evolutionary psychologists, we acquired our mental superiority during the Pleistocene, that period from around 1.8 million years ago when our forebears were forced to adapt to a perilous hunter-gatherer existence on the African savannah. Rather than compete directly with the killer cats that roamed the plains, the Pleistocene hominins adapted to what has been termed the "cognitive niche", relying on brains rather than brawn to survive.
Evolutionary psychologists also argue that the human mind evolved as a basketful of separate components, or "modules", ranging from language and its sub-components to the ability to detect freeloaders or the capacity for jealous love. This is known as the "Swiss army knife" view of the mind, with a mental blade for every purpose.
Although the modules of the mind are generally regarded as independent, or "encapsulated", there is one capacity that seems to underlie several of them. That capacity is recursion. In terms of computer programming, recursion may be defined as a principle whereby a routine can invoke itself, or a similar routine. It is the main characteristic that distinguishes human language from other forms of animal communication, and endows it with unlimited variability and expressive power.
Take, for example, the sentence "I know a woman who was kissed by Elvis Presley" (true, as it happens). Recursion can extend this sentence to include a line of female acquaintances: "I know a woman who knows a woman who knows a woman who was kissed by Elvis." In principle, at least, there is no limit to the length of sentences that can be generated using recursion, as readers of Henry James will probably appreciate.
In language, a distinction can be drawn between end recursion, in which constituents are added to the end of a sentence, and centre-embedded recursion, in which constituents are inserted within a sentence. A good example of end recursion is the children's story "The House that Jack Built", a portion of which runs as follows: "This is the dog that worried the cat that killed the rat that ate the malt that lay in the house that Jack built." We can rearrange it to illustrate centre-embedded recursion: "The malt that the rat ate lay in the house that Jack built."
Too much centre-embedded recursion, though, boggles the mind. Consider the following: "The malt that the rat that the cat killed ate lay in the house that Jack built" and "The malt that the rat that the cat that the dog worried killed ate lay in the house that Jack built." The first of these sentences may just be manageable, but the second, though grammatically correct, is almost impossible to unpack, probably because it is difficult to keep track of which verb goes with which noun.
A relatively trivial form of recursion is repetition, as in this sentence from A. A. Milne's Winnie the Pooh: "It rained and it rained and it rained." At this level, recursion is probably not unique to humans. Birdsong, for instance, is often relentlessly repetitive. But there is no evidence that non-human species can use recursion to flexibly and progressively qualify and add meaning, in the way that we humans can.
Recursion is not restricted to language, but appears to be a fairly general property of human thought. Knowing a woman who knows a woman who knows a woman who was kissed by Elvis is a prerequisite to the sentence that declares that fact. Language presumably evolved in order to express the recursive nature of human thought.
Recursive thought is evident especially in what has been termed theory of mind, which is our ability to understand what is going on in the minds of others: I may think that you think I'm a fool. In principle, theory of mind may be extended to any number of levels of recursion: I may think that you think that I think you are a fool. In Shakespeare's Twelfth Night, 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. Each verb in italics after the first shows the addition of another level of recursion.
Recursion may even be responsible for the concept of self. Descartes is famous for the phrase cogito ergo sum - "I think, therefore I am" - from which he inferred that he existed. Descartes' insight was fundamentally recursive, since it implies not just thinking, but thinking about thinking. The fact that we can be aware of our own thinking (and not just of our thoughts) implies a concept of self.
Recursion may also be a characteristic of a certain kind of memory, known as episodic memory, which involves mentally reliving events from the past. In this sense, "remembering" may be distinguished from "knowing": I know when I was born, but I certainly don't remember it. We all know many thousands of words, but with very few possible exceptions have no memory of where and when we first encountered them. Remembering is fundamentally recursive, because it involves inserting a past mental state into the present one.
It seems likely that episodic memory is part of a more general ability to travel mentally in time, so that we imagine not only events from the past, but also possible events in the future. We can use mental time travel at several levels of recursion, as when I remember thinking yesterday that I would go to the beach today. Mental time travel is responsible for the very concept of time, which itself may be characteristically human, and responsible for such uncomfortable phenomena as awareness of death, anxiety about future events, or embarrassment about past episodes, and it may even be one of the factors leading to belief in religions that promise a life after death. Mental time travel can scarcely have evolved purely to burden our lives. What it does, though, is allow us to plan future events in meticulous detail.
So far, there is no convincing evidence for recursion in any non-human species. In one recent study, reported in the journal Nature, a group of researchers claimed that starlings were able to distinguish sequences characterized by centre-embedded recursion from those not so characterized, but the behavior of these admittedly clever birds is easily explained by simpler principles. My guess, then, is that recursion provides the key to the human mind, and unifies several capacities that have hitherto been regarded as independent.