# Learn This One Weird Trick (Part Two)

… that humans use, and now you can too! (Continued from the previous post.)

3) Recursion. What if you have one mirror facing a second mirror, so the first mirror shows what’s in the second mirror, which shows what’s in the first mirror …? What if you take a chameleon, which tries to take on the color of its surroundings, and put it on a mirror? What if you point a video camera at the very screen that’s showing what the video camera is pointing at? What if (getting mathematical) you use a function in defining that same function? What if you use the cleaning attachment from your vacuum cleaner to suck dust off the vacuum cleaner itself? (Okay, the last one is a bit lame.) The basic idea in each of these cases is called recursion, which is a major concept in mathematics and computer science. Douglas Hofstadter’s Gödel, Escher, Bach is all about recursion. Some people think recursion – nesting ideas about ideas inside one another in a potentially infinite hierarchy, or (for syntax) phrases inside phrases — is central to human uniqueness. Noam Chomsky has lately been pushing a hard-core version of this argument. Here he is with Robert Berwick defending his view.

Related to the idea of recursion is the idea of “meta-representation”: not just having ideas about the world but having ideas about ideas, being able to put a box around a proposition, and then attaching a tag to it that says the equivalent of “This is true” or “This is false” or “This will be true later” or “Suppose this were true,” and then manipulating it accordingly. A nice little essay in “imagination,” elaborating this idea, is here from Simon Baron-Cohen, best known as an authority on autism.

4) Shared intentionality. Suppose you and I are friends with a couple, Fred and Wendy Smith. I tell you “I saw Wendy Smith kissing a man in the park yesterday.” Logically speaking, there’s nothing to say the man wasn’t Fred. But you’ll probably assume that I meant she was kissing someone other than Fred. Why? Well if the man had been Fred I could just as easily have said “I saw Wendy Smith kissing Fred in the park yesterday.” Since I didn’t say that, you assume I mean to convey the man wasn’t Fred. Note this only works if both of us try to pack as much relevant information into our sentences as possible and know the other person is doing the same. (If you think this sounds like recursion, you’re right.) Back in the 1950s, Paul Grice, a philosopher, worked out a lot of how we pack non-literal meanings into sentences. But the same principles are at work even when people are communicating non-linguistically. This leads to another theory of human uniqueness: human beings are uniquely good at developing shared intentions with one another: each party knows the other party is trying to communicate something, so they converge on the correct answer. People may have been doing this even before language evolved. Following up on this can quickly get you into game theory, where a central concept is “common knowledge”: not just “I know X” and “You know X,” but “I know X,” and “I know X is common knowledge,” and similarly for you. Here’s a philosophical treatment.

But you can skip the philosophy if you want and move on to a telling little piece of anatomy that’s relevant here. In most mammals, including chimpanzees, the sclera (white of the eyes) is not visible. It’s hard to tell where a chimpanzee is looking, easy for a human. Human eyes make it easy to cooperate in sharing attention, a first step in developing shared intentions. If you know your card games, chimpanzees are playing poker, humans are playing bridge.

Our discussion of human uniqueness on Logarithmic History has been frustratingly short on specific dates. But human sclera are probably a fairly simple trait genetically, and we may soon enough discover the genes involved and even tell how long ago they mutated.