Yes, some people have millions of followers on Twitter. Lady Gaga was the first to hit 10 million. Justin Bieber, Barack Obama, and Britney Spears are close behind. But how many of these followers are really their friends? Our brains, it turns out, limits that number to around 150.

In the early 1990s, British anthropologist Robin Dunbar figured out that the human brain can only accommodate between about 100 and 200 stable relationships. That's essentially because we have so much to do in so little time that our brains limit the number of relationships we can manage.

But with the rise of social media, this premise, at a glance, seems to be changing. Many of us maintain hundreds, if not thousands, of connections on sites such as Facebook, Twitter, and Foursquare. Could it be that these networks are lifting our social capacity?

To find out, Bruno Goncalves and his colleagues at Indiana University gained temporary access to the Twitter "firehose," as they call it, and analyzed 380 million tweets sent by 3 million tweeters over a period of four years.

To be a friend instead of just a follower on Twitter, for the study at least, Goncalves's team worked out a formula that measures increasing bonds by the number of conversations, or exchange of tweets, between individuals.

A lot of tweets between you and Lady Gaga? Cool. You might be a true friend, not just one of her millions of followers.

What the researchers found was that when a person opens an account on Twitter, they have few friends and few interactions with them but as time goes by, stable users get more and more friends. Then they get overwhelmed.

"Eventually, a point is reached where the number of contacts surpasses the user's ability to keep in contact with them. This saturation process will necessarily lead to some relationships being more valued than others," the researchers write in their study posted on the preprint server Physics arXiv.

That point, it turns out, is between 100 and 200, as predicted by Dunbar.

"This finding suggests that even though modern social networks help us to log all the people with whom we meet and interact, they are unable to overcome the biological and physical constraints that limit stable social relations," they conclude.