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I was at home on a recent Sunday when one of my twin 6-year-old sons did something absolutely adorable, but you’ll have to take my word for it. I’m not showing you the picture. He had spent the whole morning making a complete superhero costume out of paper, and when it was time for him to try it on, I pointed my phone at him, as so many 21st-century parents do. He immediately—and definitively—told me he was not okay with that. “Don’t put that online!”

He didn’t entirely object to digital sharing: After I pleaded for a bit, he gave me permission to send it to a group text of grandparents and cousins. “It’s okay if it’s only family,” he said. I later asked him to tell me a little more about why he didn’t want his photo online, and he explained, “I’m shy. I might get embarrassed if other people saw it who aren’t our friends. Or it got on the news.”

It’s tempting to dismiss these attitudes as naïveté—after all, my son doesn’t yet know what Facebook is, and what he knows about how the internet works, he says, is largely based on an episode of The Magic School Bus. But he is aware of technology and the influence it can have on his life, even if that’s primarily being upset when the Wi-Fi goes down and he can’t watch Pixar on Apple TV.

A child of the ’80s, I too was subjected to parental technological documentation; there are plenty of photographs of me around my mom’s house. But what I endured is nothing like the unblinking surveillance my own children face. Gigabytes and gigabytes of photos and videos are on hard drives and the cloud, chronicling them from birth and even before. Many parents have begun to consider what it means to amass their child’s digital identity before the kid knows what a digital identity is. And even if some technological concepts come easy—my kids seemed to know how to use a touch screen before they could speak or read—they sometimes struggle with forms of media that felt hardwired into my 20th-century brain. The first time we watched a movie on live TV, in a hotel room while on vacation, my kids got upset when we couldn’t rewind to the beginning and were utterly baffled (and annoyed) by commercial breaks. (We don’t allow them to watch YouTube, where they would have become well acquainted with such interruptions.)

Technological change is often measured in terms of new features, specs, and business models. But what people do with the technologies they have is not just about what’s technically possible; it’s a product of zigzagging cultural and psychological moods. Although my son doesn’t use a smartphone much (yet), he is constructing an attitude about what technology should do (bring stuff to him) and not do (transmit his personal details) that I am noticing more lately. Indeed, later that same day, as my family tried a new restaurant near our house, I snapped a photo of my wife enjoying dinner. “Don’t post that to Instagram!” she told me, protesting that she wasn’t wearing makeup. But she said it was fine to text it to some neighbors who were curious about the new place.

The most obvious lesson from all this may be simple: I need to put down my phone. But I also—optimistically, I admit—choose to see these moments as signs of a cultural transformation afoot. The age of sharing is ending, and just as I scoff at the disco era of my parents’ generation, I am hopeful that one day my kids will, after unearthing one of my cringey-er social-media posts, ask me, “You really just put that out on the internet, Dad? What were you thinking?”

Part of my reasoning comes from the fact that I see this happening well beyond my family. Digital trendsetters are all about iMessage groups and email newsletters these days. Even Mark Zuckerberg, the man who’s done more to persuade the world to post its every mood, brunch plate, and family photo online (“We decided that these would be the social norms now and we just went for it,” he once said) has now concluded that “the future is private.”

The past 20 or so years have been a wild cultural experiment. Many of the things that we tend to think of as permanent additions to our collective cultural habits—publishing a steady stream of short opinions about news, sports, and celebrities and sharing photos and videos of babies, pets, meals, and everyday life with the world—are only a few years old.

Before 1999, few people aside from the most eager of computer enthusiasts would have thought to maintain a digital identity—and fewer still would have known how to even if they wanted to. So it is by no means a stretch of the imagination that all these things that seem so lodged into our culture will change yet again, and all the ingrained habits of the past few years of exploding social media—the YouTube life-streamers, the Instagram influencers, the raging tweetstormers—will be as outmoded and embarrassing to teens and 20-somethings of the future as Disco Stu, clinging to his chest hair and gold medallions.

And while much worthy discussion is being had about the role of the biggest player in social media, Facebook, and whether it’s polluting our media and democracy, I am reasonably sure that my kids will never sign up for a Facebook account. Now, I am not predicting that Facebook or social media will disappear, anymore than the last days of disco meant the end of nightclubs, dancing, cocaine, or casual sex. But even if I don’t know much about the future, I do know this: Kids are never going to think their parents are cool.

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