In just a few short weeks, Google+, a new social network from the company that gave us the world’s most popular and profitable search engine, has signed up over 10 million members. While it remains to be seen whether Google+ will prove an enduring success, it has already demonstrated that Facebook, with over 750 million members, is not infallibly destined to dominate the social-networking landscape.

Though Google+ and Facebook appear similar on the surface, they are built around different animating principles. Google’s mission is often described as organizing the world’s information. That sounds like a noble enterprise in itself, but of …