Steven Pinker

and you know it, but in addition, I know that you know it, and you know that I know it, and I know that you know that I know it ad infinitum.

Of course, the reason that common knowledge is significant is that it is essential for coordination.

In a classic example from Thomas Schelling, a couple is separated in Manhattan, incommunicado, and somehow must find each other.

Well, he knows that she likes to browse the aisles of a certain bookstore, so he heads there, but then he realizes that she knows that he likes to hang out in a certain camera store, so he changes course, until he figures that she will anticipate that he will guess that she will opt for the bookstore, so he does another about-face, only for it to dawn on him that it will occur to her that he knows that she is aware that he likes to haunt the bookstore, so he pirouettes once again.

Meanwhile, she is whipsawed by the same futile empathy.

Nothing short of common knowledge can guarantee that they'll end up at the same place at the same time.

Of course, no one can think an infinite Russian doll of I know that she knows that I know that she knows thoughts.

Our heads start to spin with three or four layers, let alone an infinite number.

In a well-known episode of Friends, Phoebe says to Rachel, they don't know we know they know we know.

Joey, you can't say anything.

And he replies, I couldn't even if I wanted to.

Instead, common knowledge can be captured in a simple mental intuition that something is public or conspicuous or out there.

And that can be conveyed by direct speech, in the case of our separated couple, a cell phone call.

Indeed, solving coordination dilemmas may be the reason that language evolved in our species in the first place.

In the absence of a public event, the next best thing is conspicuous salience, or a focal point.

Schelling suggests that our couple might gravitate toward the big clock in Grand Central Station, even if it wasn't particularly close to the point at which they'd been separated, simply because each might anticipate that it would pop into the mind of the other.

A third solution is a convention, a tacit agreement to do something in a certain way for no other reason than they have agreed to do it that way, which is reason enough.

Our separated couple might agree that should they ever be separated in the future, they will adopt the convention of chivalry and go to the bookstore, or patriarchy and go to the camera store,

or whimsy and go to a lost and found in a department store, or fairness and take turns or flip coins.

At larger scales, common salience or focal points and conventions drive a lot of our legal and financial coordination.