The idea of limitless growth gives sleepless nights to environmentalists, but not to Facebook founder Mark Zuckerberg. He espouses a law of social sharing, which predicts that every year, for the foreseeable future, the amount of information you share on the Web will double.

That rule of thumb can be visualized mathematically as a rapidly growing exponential curve. More simply, our online social lives are set to get significantly busier. As for Facebook, more personal data means better ad targeting. If things work out, Zuckerberg’s net worth will follow a similar trajectory to that described in his law of social sharing.

That law is said to be mathematically derived from data inside Facebook. In ambition, it is closely modeled on Moore’s Law, which was conceived by the computer-processor pioneer Gordon Moore in 1965 and has been at work in every advance in computing since. Also an exponential curve, it states that every two years twice as many transistors can be fitted onto a chip of any given area for the same price, allowing processing power to get cheaper and more capable.

There’s a hint of vanity in Zuckerberg’s attempt to ape Moore. But it makes sense to try to describe the mechanisms that have raised Facebook and other social-Web companies to power. The Web defines our time and is being rapidly reshaped by social content—from dumb viral videos to earnest pleas on serious issues. Facebook’s success has left older companies like Google scrambling to add social features to their own products (see Q&A, November­/December 2011). Zuckerberg’s Law can help us understand such a sudden change of tack from a seemingly dominant company, just as Moore’s Law has long been used to plan and explain new strategies and technologies.

Inasmuch as Facebook is the company most invested in ­Zuckerberg’s Law, its every move can be understood as an effort to sustain the graceful upward curve of its founder’s formula. The short-term prospects look good for Zuckerberg. The original Moore’s Law is on his side; faster, cheaper computers and mobile devices have made sharing easier and allowed us to do it wherever we go. Just as important, we are willing to play along, embracing new features from Facebook and others that lead us to share things today that we wouldn’t or couldn’t have yesterday.

Facebook’s most recent major product launch, last September, is clearly aimed at validating Zuckerberg’s prophecy and may provide its first real test. An upgrade to the Open Graph platform that unleashed the now ubiquitous Like button onto the Web (see “You Are the Ad,” May/June 2011), it added a feature that allows apps and Web sites to automatically share your activity via Facebook as you go about your business. Users must first give a service permission to share automatically on their behalf. After that, frictionless sharing, as it has become known, makes sharing happen without your needing to click a Like button, or to even think about sharing. The most prominent early implementation was the music-streaming service Spotify, which can now automatically post on Facebook the details of every song you listen to. In the first two months of frictionless sharing, more than 1.5 billion “listens” were shared through Spotify and other music apps. News organizations like the Washington Post use the feature, making it possible for them to share every article a person reads on their sites or in a dedicated app. Frictionless sharing is also helping Facebook drag formerly offline activities onto the Web. An app for runners can now automatically post the time, distance, and path of a person’s morning run.

Frictionless sharing sustains ­Zuckerberg’s Law by automating what used to be a manual task, thus removing a brake on the rate at which we can share. It also shows that we are willing to compromise our previous positions on how much sharing is too much. Facebook introduced a form of automatic sharing four years ago with a feature called Beacon, but it retreated after a strong backlash from users. Beacon automatically shared purchases that Facebook members made through affiliated online retailers, such as eBay. Frictionless sharing reintroduces the same basic model with the difference that it is opt-in rather than opt-out. Carl ­Sjogreen, a computer scientist who is a product director overseeing Open Graph, says it hasn’t elicited anything like the rage that met Beacon’s debut. “Everyone has a different idea of what they want to share, and what they want to see,” says Sjogreen. Moreover, judging by the number of Spotify updates from my Facebook friends, frictionless sharing is pretty popular.

Privacy concerns will surely arise again as Facebook and others become able to ingest and process more of our personal data. Yet our urge to share always seems to win out. The potential for GPS-equipped cell phones to become location trackers, should the government demand access to our data, has long concerned some people. A South Park episode last year even portrayed an evil caricature of Apple boss Steve Jobs standing before a wall-sized map labeled “Where Everybody in the World Is Right Now.” Six months later, to a mostly positive reception, Apple debuted a new iPhone feature called Find My Friends, which encourages users to let Apple track their location and share it.

It’s not hard to explain why we seem eager to do our bit to maintain the march of Zuckerberg’s Law. Social sites are like Skinner boxes: we press the Like button and are rewarded with attention and interaction from our friends. It doesn’t take long to get conditioned to that reward. Frictionless sharing can now push the lever for us day and night, in hopes of drawing even more attention from others.

Unfortunately for Zuckerberg and his law, not every part of that feedback loop can be so easily boosted. Frictionless sharing helps, but getting others to care is the bigger challenge. In 2009 a new social site called Blippy was launched; it connected with your credit card to create a Twitter-style online feed of everything you bought. That stream could be made public or shared with particular contacts. Blippy got a lot of press but not the wide adoption its cofounder Philip Kaplan had hoped for. “Most people thought Blippy’s biggest challenge would be getting users to share their purchases,” he says. “Turns out the hard part was getting users to look at other people’s purchases. Getting people to share is a small hump. Getting them to obsess over the data—making it fun, interesting, or useful—is the big hump.”

Sjogreen has that problem in his sights. He says he is working on ways to turn the impending flood of daily trivialities coming from frictionless sharing into something fun, interesting, and useful. Repackaging the raw information to make it more compelling to others is one tactic. “It’s the patterns and anomalies that matter to us,” he says. For example, if you notice that a friend just watched 23 episodes of Breaking Bad in a row, you may decide you should check out that show after all. Or if he sets a new personal record on his morning run, the app in the phone strapped to his arm could automatically tout it to friends. Perhaps Blippy would have thrived if it highlighted significant purchases like vacations, instead of simply blasting people with everything from grocery lists to fuel bills.

We can only guess at the effectiveness of Sjogreen’s future tactics, but it is certain that they can sustain Zuckerberg’s Law for only so long. Gordon Moore put it well in 2005 when reflecting on the success of his own law: “It can’t continue forever. The nature of exponentials is that you push them out and eventually disaster happens.”

Facebook’s impending problem is that even if the company enables future pacemakers to share our every heartbeat, the company cannot automate caring—the most important part of the feedback loop that has driven the social Web’s ascent. Nothing can support exponential growth for long. No matter how cleverly our friends’ social output is summarized and highlighted for us, there are only so many hours in the day for us to express that we care. Today, the law of social sharing is a useful way to think about the rise of social computing, but eventually, reality will make it obsolete.

Paul Boutin is a freelance writer in Los Angeles. He writes about technology for the New York Times and contributes to Wired.