My excellent Conversation with Steven Pinker
Here is the audio, video, and transcript. Here is part of the episode summary:
Tyler and Steven probe these dimensions of common knowledge—Schelling points, differential knowledge, benign hypocrisies like a whisky bottle in a paper bag—before testing whether rational people can actually agree (spoiler: they can’t converge on Hitchcock rankings despite Aumann’s theorem), whether liberal enlightenment will reignite and why, what stirring liberal thinkers exist under the age 55, why only a quarter of Harvard students deserve A’s, how large language models implicitly use linguistic insights while ignoring linguistic theory, his favorite track on Rubber Soul, what he’ll do next, and more.
Excerpt:
COWEN: Surely there’s a difference between coordination and common knowledge. I think of common knowledge as an extremely recursive model that typically has an infinite number of loops. Most of the coordination that goes on in the real world is not like that. If I approach a traffic circle in Northern Virginia, I look at the other person, we trade glances. There’s a slight amount of recursion, but I doubt if it’s ever three loops. Maybe it’s one or two.
We also have to slow down our speeds precisely because there are not an infinite number of loops. We coordinate. What percentage of the coordination in the real world is like the traffic circle example or other examples, and what percentage of it is due to actual common knowledge?
PINKER: Common knowledge, in the technical sense, does involve this infinite number of arbitrarily embedded beliefs about beliefs about beliefs. Thank you for introducing the title with the three dots, dot, dot, dot, because that’s what signals that common knowledge is not just when everyone knows that everyone knows, but when everyone knows that everyone knows that and so on. The answer to your puzzle — and I devote a chapter in the book to what common knowledge — could actually consist of, and I’m a psychologist, I’m not an economist, a mathematician, a game theorist, so foremost in my mind is what’s going on in someone’s head when they have common knowledge.
You’re right. We couldn’t think through an infinite number of “I know that he knows” thoughts, and our mind starts to spin when we do three or four. Instead, common knowledge can be generated by something that is self-evident, that is conspicuous, that’s salient, that you can witness at the same time that you witness other people witnessing it and witnessing you witnessing it. That can grant common knowledge in a stroke. Now, it’s implicit common knowledge.
One way of putting it is you have reason to believe that he knows that I know that he knows that I know that he knows, et cetera, even if you don’t literally believe it in the sense that that thought is consciously running through your mind. I think there’s a lot of interplay in human life between this recursive mentalizing, that is, thinking about other people thinking about other people, and the intuitive sense that something is out there, and therefore people do know that other people know it, even if you don’t have to consciously work that through.
You gave the example of norms and laws, like who yields at an intersection. The eye contact, though, is crucial because I suggest that eye contact is an instant common knowledge generator. You’re looking at the part of the person looking at the part of you, looking at the part of them. You’ve got instant granting of common knowledge by the mere fact of making eye contact, which is why it’s so potent in human interaction and often in other species as well, where eye contact can be a potent signal.
There are even species that can coordinate without literally having common knowledge. I give the example of the lowly coral, which presumably not only has no beliefs, but doesn’t even have a brain with which to have beliefs. Coral have a coordination problem. They’re stuck to the ocean floor. Their sperm have to meet another coral’s eggs and vice versa. They can’t spew eggs and sperm into the water 24/7. It would just be too metabolically expensive. What they do is they coordinate on the full moon.
On the full moon or, depending on the species, a fixed number of days after the full moon, that’s the day where they all release their gametes into the water, which can then find each other. Of course, they don’t have common knowledge in knowing that the other will know. It’s implicit in the logic of their solution to a coordination problem, namely, the public signal of the full moon, which, over evolutionary time, it’s guaranteed that each of them can sense it at the same time.
Indeed, in the case of humans, we might do things that are like coral. That is, there’s some signal that just leads us to coordinate without thinking it through. The thing about humans is that because we do have or can have recursive mentalizing, it’s not just one signal, one response, full moon, shoot your wad. There’s no limit to the number of things that we can coordinate creatively in evolutionarily novel ways by setting up new conventions that allow us to coordinate.
COWEN: I’m not doubting that we coordinate. My worry is that common knowledge models have too many knife-edge properties. Whether or not there are timing frictions, whether or not there are differential interpretations of what’s going on, whether or not there’s an infinite number of messages or just an arbitrarily large number of messages, all those can matter a lot in the model. Yet actual coordination isn’t that fragile. Isn’t the common knowledge model a bad way to figure out how coordination comes about?
And this part might please Scott Sumner:
COWEN: I don’t like most ballet, but I admit I ought to. I just don’t have the time to learn enough to appreciate it. Take Alfred Hitchcock. I would say North by Northwest, while a fine film, is really considerably below Rear Window and Vertigo. Will you agree with me on that?
PINKER: I don’t agree with you on that.
COWEN: Or you think I’m not your epistemic peer on Hitchcock films?
PINKER: Your preferences are presumably different from beliefs.
COWEN: No. Quality relative to constructed standards of the canon…
COWEN: You’re going to budge now, and you’re going to agree that I’m right. We’re not doing too well on this Aumann thing, are we?
PINKER: We aren’t.
COWEN: Because I’m going to insist North by Northwest, again, while a very good movie is clearly below the other two.
PINKER: You’re going to insist, yes.
COWEN: I’m going to insist, and I thought that you might not agree with this, but I’m still convinced that if we had enough time, I could convince you. Hearing that from me, you should accede to the judgment.
I was very pleased to have read Steven’s new book