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We are online. We select messages. We share information with others, press a button if we like what someone else has put on the Internet. Regardless of what we do online – each time, new data is created, data that has allowed digital companies like Facebook to become the most valuable companies in the world. The social network is said to have a total value of more than $400 billion. The four most valuable German firms – SAP, Siemens, Bayer and Allianz – cannot quite match that amount, although they have many times more employees and are active throughout the world.

So Facebook lives well, very well indeed – off our data. That is what the company feeds to its algorithms, which increase its knowledge daily and thus strengthens its market position. Shouldn’t we get a piece of the pie?

It wouldn’t be much, observes Andreas Weigend dryly. The man from Germany, formerly the top data expert at Amazon, a resident of San Francisco, has written a book, Data for the People. He calculates that in 2015, all of Facebook’s profits would have amounted to $3.50 per user—a latte macchiato, nothing more. He concludes: "We should demand in exchange for our raw data something far more valuable as a paltry compensation: We should insist on a place at the control points of the data refineries."

How Internet users can regain control of their data is a hot topic. Organizations such as CitizenMe offer us a sort of digital account on which, as private users or entrepreneurs, we can store all our data and easily specify with whom we want to share what and when. Moreover, they offer us the possibility of learning more about our own personality types and preferences.

That sounds like a solution. But Andreas Weigend believes it will be a long way until users in the digital world really have a say. Oil used to be the crucial raw material; today it is data. And the "data refineries," the Facebooks of this world, are doing well by receiving private information with no restriction and offering in return a service "at no charge"  – social contacts or search results. What is certain: They won’t give up their business models voluntarily. Mr. Weigend believes users will have to force them to make genuine changes.

Is a service worth handing over our private data? We don’t know.

Data researchers in Germany always get nervous when the Internet giants, in spite of their promises to be open and transparent, use technology to exclude others. For example, at the end of May, Mr. Weigend’s former employer Amazon patented a technology that can be used, for example, in conjunction with its newly acquired upscale grocery chain Whole Foods Market. The software registers when customers in the store search for the prices of competitors via the free-of-charge Internet connection—whereupon the connection is stopped. "For me, this is an example of data against the people," he says.

No one yet knows how the company really intends to use the patent. But increased alertness is required. Everyone should have access to the information on the Internet. That is certainly not the case if companies "selectively make accessing data more difficult," as the data scientist puts it.

Andreas Weigend studied physics and philosophy in Europe before he switched to Stanford University in the heart of Silicon Valley and never looked back. His focus is on all the data about us users. About our behavior, our movements, interests, relationships, values. Once that is out in the world, it is called social data. Mr. Weigend set up a "Laboratory for Social Data" and speaks about the "social data revolution." He spent three years writing this new book. Up to now, no one else has addressed with more depth and structure the question as to "how we can reacquire power over our data."