This leads to exasperation, because in a server farm packed with social data, it’s hard to know what to count. What’s the value of a Facebook “like” or a Twitter follower? What do you measure to find out? In this way, marketing resembles other hot spots of data research, including brain science and genomics. In each one, scientists are combing through petabytes of data, trying to discern whether certain genes or groups of neurons cause something or simply correlate with it. It’s not clear, because these are immensely complex systems with millions of variables — much like our social networks. Even as researchers swim in data that previous generations would have swooned over, they struggle to answer crucial questions regarding cause and effect. What action can I take to get the response I want?

Debates rage as quants accuse one another of counting the wrong things. Take I.B.M.’s Black Friday study. While the numbers indicate that few shoppers clicked directly from a social network to buy a laptop or a fridge, some may have seen ads that later led to a purchase. If so, valuable influence went unmeasured. “I.B.M. is looking at a single point in time,” says Dan Neely, the chief executive of Networked Insights, a marketing analytics company. Neely’s team followed Macy’s Black Friday campaign on Twitter, which started weeks before the big day; it generated a viral flurry on the network, he says. Clearly, many big advertisers are still believers: last week, Facebook shares got a boost from reports that Walmart, Samsung and other boldfaced names have recently stepped up social-media advertising.

But gauging the effectiveness of these ads is still a challenge. “It’s hard to measure influence,” says Steve Canepa, I.B.M.’s general manager for media and entertainment.

That, in fact, may be the ultimate lesson to draw from the social media marketing miracle that wasn’t. The impact of new technologies is invariably misjudged because we measure the future with yardsticks from the past.

Dave Morgan, a pioneer in Internet advertising and the founder of Simulmedia, an ad network for TV, points to the early years of electricity. In the late 19th century, most people associated the new industry with one extremely valuable service: light. That was what the marketplace understood. Electricity would displace kerosene and candles and become a giant of illumination. What these people missed was that electricity, far beyond light, was a platform for a host of new industries. Over the following years, entrepreneurs would come up with appliances — today we might call them “apps” — for vacuuming, laundry and eventually radio and television. Huge industries grew on the electricity platform. If you think of Apple in this context, it’s a $496 billion company that builds the latest generation of electricity apps.

Social networks, like them or not, are fast laying out a new grid of personal connections. Even if this matrix of humanity sputters in advertising and marketing, it’s bound to spawn new industries in consulting, education, collaborative design, market research, media and loads of products and services yet to be imagined. Maybe, just maybe, it will even be able to sell soap.