I have 928 friends on Facebook, and I follow 616 people on Twitter. But my speed dial on my iPhone contains just four people — my boyfriend, two close friends, and my mother. Apparently, that’s because even though social media has astronomically expanded our online networks, it hasn’t really expanded our capacity for friendship, according to a recent study published in the Proceedings of the National Academy of Sciences.

Researchers from the University of Oxford, Aalto University in Helsinki, Finland, and the University of Chester wondered whether the advent of social networks has actually increased our ability to stay in touch with people. It turns out that it really only makes it easier to be voyeurs. I may be connected with a high school friend on LinkedIn, but that only means I can watch her career grow, not that I speak with her any more frequently.

Most people have a small fixed number of close friends, and then a larger number of acquaintances, the researchers found. Different people can have different numbers of each — or more introverted person may have three close friends and 15 acquaintances, while a more social person could have six close friends and 25 acquaintances. The researchers also found that on average, females spent 48 percent of their time speaking to their three closest friends, while males spent 40 percent of their time with their closest three. But what the researchers found is that whatever your average number is, it’s likely to stay that way.

They proved this by following high school students around the time they were graduating and moving on to either college or the real world. They tracked the young adults’ phone calls and surveyed them every few months to see how they thought about the people in their lives and who they were spending time with. With the data they collected, the researchers graphed the connections as seen below.

Each yellow dot is a person, while the red lines show the friendship connections between them. The blue dashes show how many phone calls each participant made. They dubbed the patterns the data pointed out social signatures.

Over time, the researchers realized that though some of the connections evolved, the size and structure of each person’s social signature stayed roughly the same size. That means that if a close friend of yours moves to another city, it’s pretty likely she’ll shift out to the outer circle of acquaintances. The good news, though, is that you’ll likely find a replacement.

Why is this? Of the three reasons the researchers give, two are pretty obvious — we have limited time and emotional capacity. The last reason is that “cognitive limitations” actually dictate the number of close friendships we can have. This is built into our DNA, and can be observed in the habits of other primates as well.

It turns out that no matter how hard Facebook and Instagram and Twitter vie for our attention, they’re not better connecting us with friends, they’re just making it easier to watch.