Borges Magical Cat
Chomsky has famously argued that recursion is the distinguishing feature of human language. Other creatures, for example songbirds and dolphins, have systems of communication strikingly similar to human language. None, however, show evidence of recursive ability. Recursion, or to be more exact, syntactic recursion, is exclusive to the human species, enabling language and playing an essential role in the broader human cognitive apparatus.
But what is it? In some ways, the concept is remarkably simple and intuitive: recursion is the ability to limitlessly combine and recombine atomic elements—words—and produce an infinite number of sentences. Chomsky sometimes uses the phrase “discrete infinity” to describe it. Any child has this ability as part of its genetic endowment and it’s the only plausible explanation for the universal capacity to learn a language based on a limited set of examples. Recursion also implies a faculty of memory. The cognitive system underlying language acquisition and use must retain a record or pointer to a datum in order to modify it organically using syntactic recursion.
If Chomsky is right any machine claiming intelligence in the sense of general or strong AI must model recursion. Can artificial neural networks model recursion? Even more simply, can they model memory?
Memory presumes time. It presumes time past. You can’t have a memory of the future, nor of the present. And thus it follows that you have no memory at all if you live in the present. But the reverse also holds. Time presumes memory. Time wouldn’t exist without memory, or the perception of successiveness.
In his short story, The South, the esteemed Argentine writer, Jorge Luis Borges tells of a man entering a familiar cafe after a stay in a hospital. In the café was a large house cat:
There was the cat, asleep. He ordered a cup of coffee, slowly spooned sugar into it, tasted it (a pleasure that had been forbidden him in the clinic), and thought, while he stroked the cat’s black fur, that this contact was illusory, that he and the cat were separated as though by a pane of glass, because man lives in time, in successiveness, while the magical animal lives in the present, in the eternity of the instant.