Take your young kid with you as you commute through Penn Station and you’ll find that you have a lot to explain. Walking through the Long Island Railroad concourse, my son was perplexed by the close proximity of three chicken-themed restaurants—Chick-fil-A, Raising Cane’s, and Pollo Campero—and by the fact that a shop called Gotham News mainly seemed to sell candy and bottled water. He also wanted to know why some people, as they strolled or waited, drank out of cans in brown paper bags. “Why do they use those bags?” he asked.

Where to begin? Brown bagging is one of those social practices that continues to feel senseless even after it’s been explained. As we all know, the idea is that the bags obscure the beverage being consumed, allowing drinkers and police officers to ignore prohibitions on drinking alcohol in public places. Of course, the bags don’t actually hide anything; in fact, they are reserved specifically for, and definitively signal, the drinking of alcohol. (It would never occur to you to sip a bottle of Fiji water that was in a paper bag.) Spelled out, the thought process is bizarre. The drinkers know that the cops know that they’re drinking, and the cops know that the drinkers know that they know. But the cops pretend they don’t know, while reserving the right to suddenly “realize” what’s going on, if a drinker becomes disruptive. Nondrinkers, meanwhile, benefit from a train station that seems more genteel than it really is.

These weird eddies of tangled logic can’t be typical of how we think; surely human affairs are usually more straightforward. But this is exactly the assumption that Steven Pinker questions in his new book, “When Everyone Knows That Everyone Knows . . . : Common Knowledge and the Mysteries of Money, Power, and Everyday Life.” The puzzle of who-knows-who-knows-what, always fascinating to fans of mystery novels and spy thrillers, has long preoccupied psychologists and game theorists. “As a cognitive scientist, I have spent my life thinking about how people think,” Pinker writes. “So the ultimate subject of my fascination would have to be how people think about what other people think, and how they think about what other people think they think, and how they think about what other people think they think they think.” Such recursive loops of thought, Pinker argues, aren’t just brainteasers for specialists; they’re central to how we live.

“Common knowledge” is generally how we describe those ideas or facts that we all know: say, the Pledge of Allegiance, or the meaning of LOL. But Pinker has a more specific definition in mind. Common knowledge, he explains, isn’t just what we know but what we know is known. It’s different from “mutual knowledge,” which is held by multiple people but not openly. If you know that the emperor has no clothes, and I know that the emperor has no clothes, that’s mutual knowledge: neither of us can be sure that the other knows. In contrast, if I know for sure that you know, and you know for sure that I know, that knowledge is common between us. “When the little boy said the emperor was naked, he wasn’t telling anyone anything they didn’t already know,” Pinker writes. Still, “by blurting out what every onlooker could see”—Pinker cites idioms such as “letting the cat out of the bag,” or getting it “out there”—he made the emperor’s nakedness into common knowledge, which was enough to shift everyone’s view of the emperor “from obsequious deference to ridicule and scorn.”

The story of the emperor with no clothes shows how common knowledge empowers collective action. Everyone in the imperium knows the emperor is a nincompoop—and yet no one wants to go out on a limb to criticize him. It’s everyone for himself. This is what game theorists call a coördination problem. If everyone acted together, revolution would be possible, but when individuals act alone they face punishment; what’s worse, they have incentive to work against the common good, for example, by ratting one another out or by denying reality to one another. Once the emperor’s nakedness becomes common knowledge, however, the coördination problem can be solved.

Life is full of coördination problems that are addressed through common knowledge, Pinker writes. In the simplest of examples, two people trying to pass through a narrow doorway simultaneously can coördinate with each other most efficiently if they knowingly hold the same conventions about who should have priority. (They might know that they agree that priority goes to whoever arrived earliest, or to whoever is the boss, or to “ladies first.”) In America, it’s common knowledge that you drive on the right, not the left. Reading Pinker, I thought of how, in New York City, it’s common knowledge that pedestrians will often wait to cross by standing in the street, rather than on the curb. City drivers know to take this into account, and pedestrians know they know, and vice versa. Try doing it elsewhere and you take your life in your hands.

Big groups of people, Pinker writes, often solve the coördination problem of holding themselves together by cultivating beliefs that are “commonly held but not easily verified.” Pinker cites a belief on the American right “that the 2020 presidential election was stolen” and the view “among the young educated left” that “being a man or a woman has nothing to do with biology.” It’s precisely because such ideas are contentious and nonobvious—they’re a far cry from asserting “that the sun rises in the east,” Pinker writes—that they serve as reliable signals of group membership. If someone tells you that he believes in Pizzagate, you can be fairly sure that he holds many related beliefs, and coördination can begin.

These sorts of ideas allow people who are actually quite different to feel similar. Common knowledge is taken very seriously; it becomes a litmus test of belonging and a driver of division. It shapes the course of society and affects us as individuals. Yet, in Pinker’s analysis, it has a lot in common with more innocuous beliefs and conventions, such as the rules of the road. For fans of “KPop Demon Hunters,” it’s an article of faith that the singer EJAE is a generational talent because of her extraordinary vocal range, which seems to span two and a half octaves; within MAGA, it’s common knowledge that the radical left is trying to indoctrinate kids with gender ideology; within certain groups of artificial-intelligence researchers, everyone knows that everyone thinks that a superintelligence might soon take over the world. How might life be different if we saw such beliefs not as ideas that are necessarily attractive in themselves but as uniquely potent solutions to coördination problems?

If people who seek to work together cultivate common knowledge, they also police, repress, and elide it, both to maintain group cohesion and to avoid being grouped with people they don’t like. The members of a religious community may punish heretics who question common knowledge; in the process, they sometimes create opportunities for people to affirm their membership in the group by contributing to the act of punishment. The more people join the mob, the more everyone believes that everyone believes in the dogma. (Pinker argues that this is the dynamic behind cancel culture.) “The inner circle of a doddering leader may act as if all is normal”; perhaps those inside the circle are trying to prevent mutual knowledge of his doddering (everyone knows about it) from becoming common knowledge (everyone knows that everyone knows about it). Similarly, when an unstable leader makes autocratic statements, his acolytes may insist that he’s “only joking.” One could say that they’re putting a brown bag over the beer.

And yet, in other circumstances, the evasion of common knowledge can be subtle, even enjoyable. Consider two people who like each other: they may arrange to hang out but do so in a way that keeps their mutual attraction from becoming common knowledge between them. (Two friends can enjoy a hike, right?) What the pair conceals might amplify the electricity between them—or provide cover if the charge dissipates. Pinker recounts an episode of “Seinfeld” in which George tells Jerry and Elaine about a recent date. “She invites me up at twelve o’clock at night, for ‘coffee,’ ” George recalls. “And I don’t go up. ‘No, thank you. I don’t want coffee. It keeps me up. Too late for me to drink coffee.’ I said this to her. People this stupid shouldn’t be allowed to live!” Why wasn’t his date more up front in her proposition? Pinker ultimately characterizes this kind of indirectness as providing “plausible deniability of common knowledge.” George knows where he wants the evening to go, and presumably so does she, but her performative ignorance gives both parties a chance to de-escalate. It can be useful to pretend that you’re just friends.