When the little boy said the emperor was naked, he wasn't telling them anything they didn't already know. But he added to their knowledge nonetheless. By blurting out what everyone could see within earshot of the others, he ensured that everyone knew that everyone else knew what they knew, that everyone knew that, and so on. And that changed their relationship with the emperor from obsequious deference to ridicule and scorn.当那个小男孩说皇帝没穿衣服时，他并没有告诉大家他们原本不知道的事情。但他仍然在一定程度上增加了他们的认知。因为他当众喊出大家都能看到的事实，让所有人都知道了其他人也知道他们所知道的，而所有人也知道这一点，如此循环往复。于是，这改变了他们对皇帝的态度——从谄媚恭敬转为嘲笑与蔑视。

Hans Christian Andersen's immortal story draws on a momentous logical distinction. With private knowledge, I know something, and you know it. With common knowledge, I know that fact, 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.安徒生这篇不朽的故事揭示了一个重要的逻辑区别：在“私有知识”中，我知道某件事，你也知道它。而在“公共知识”中，我知道这个事实，你也知道，但除此之外，我知道你知道它，你也知道我知道它，我还知道你知道我知道它，如此无限递归。当然，“公共知识”之所以重要，是因为它对于协调行动至关重要。

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 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 and at the same time.托马斯·谢林的一个经典例子是：一对情侣在曼哈顿走散，无法联系，但必须想办法找到对方。男方知道女方喜欢逛某家书店，于是往那边走；但他又想到，女方知道他喜欢待在某家相机店，于是改道过去；接着他又推测，女方可能会预料到他会猜她会选择书店，于是他再次掉头；然而他又意识到，女方可能会想到他知道她清楚他喜欢去书店，于是他又转回去。与此同时，女方也在被同样无休止的推测折腾着。除了“公共知识”，没有任何东西能确保他们在同一时间出现在同一地点。

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.当然，没有人能在脑中无限套娃地思考“我知道她知道我知道她知道”这种想法。三四层就足以让人头晕，更别说无限层了。

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!"在著名美剧《老友记》的一集中，菲比对瑞秋说：“他们不知道我们知道他们知道我们知道。乔伊，你什么也不能说！”

And he replies, "I couldn't even if I wanted to!"乔伊回答：“我就算想说，也说不出来！”

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.实际上，“公共知识”可以通过一种简单的心理直觉来获得——某事是公开的、显而易见的、众所周知的——而这种状态可以通过直接的语言传递。在走散情侣的例子中，一个电话就足够了。事实上，解决协调困境可能正是人类语言最初演化的原因之一。

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.如果没有公共事件，次优的选择是明显的“显著性”或“焦点”。谢林建议，这对情侣可能会选择去中央车站的大钟下见面，即使它离他们走散的地方并不近，仅仅是因为他们都可能想到对方会首先想到这个地方。

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.第三种解决方式是“约定”。即双方默契地同意以某种方式行事，唯一的理由就是他们已经同意了这样做，而这本身就足够了。这对走散的情侣可能会约定，如果以后再走散，就按照“骑士精神”去书店；或者按照“男权主义”去相机店；又或者凭“异想天开”去百货商店的失物招领处；或者讲求“公平”，轮流决定或抛硬币来定。