Sorry to be double posting, but as I said... fascinating...
It occurs to me that this may be part of the reason some of us have so much trouble with eye contact. When we look at someone else's face, we see their emotions, and when they look at our face, they see our responses. But our knowledge of each other's intimate feelings is not common knowledge at this point. However, when we look each other in the eyes, said to be windows to the soul, we each know that each of us is seeing each other's feelings. Our mutual knowledge becomes common knowledge. It is a big step from merely looking at the other's body or even face, to looking each other in the eye - and that big step is the transition from mutual knowledge to common knowledge. Common knowledge has an element of infinite recursion and infinite depth to it, and so when we make eye contact we are in a sense moving from a finite degree of knowledge, to an infinite degree. In that sense, it is understandable that it feels like such a huge and difficult transition, and that maintaining eye contact is for example a significant marker of intimacy among lovers.
Followup to: Belief in Belief
One of those insights that made me sit upright and say "Aha!" From The Uncredible Hallq:
The power of real deception - outright lies - is easy for even us nerds to understand.
The notion of a lie that the other person knows is a lie, seems very odd at first. Up until I read the Hallq's explanation of Pinker, I had thought in terms of people suppressing uncomfortable thoughts: "If it isn't said out loud, I don't have to deal with it."
Like the friends of a terminal patient, whose disease has progressed to a stage that - if you look it up online - turns out to be nearly universally fatal. So the friends gather around, and wish the patient best hopes for their medical treatment. No one says, "Well, we all know you're going to die; and now it's too late for you to get life insurance and sign up for cryonics. I hope it isn't too painful; let me know if you want me to smuggle you a heroin overdose."
So even that is possible for a nerd to understand - in terms of, as Vassar puts it, thinking of non-nerds as defective nerds...
But the notion of a lie that the other person knows is a lie, but they aren't sure that you know they know it's a lie, and so the social situation occupies a different state from common knowledge...
I think that's the closest I've ever seen life get to imitating a Raymond Smullyan logic puzzle.
Added: Richard quotes Nagel on a further purpose of mutual hypocrisy: preventing an issue from rising to the level where it must be publicly acknowledged and dealt with, because common ground on that issue is not easily available.