The internet should facilitate chance encounters
You have somewhere you need to go so you head outside and a few blocks later you might bump into a friend or acquaintance. Good neighbourhoods facilitate chance encounters. If The internet is like a city, how could similar encounters could be facilitated through the internet?
Twitter (and likely other social networks) can facilitate chance encounters like these to an extent, but the analogy here would be closer to bumping into people in a very, very crowded public square full of conversations; it's loud, and everyone is trying to speak above everyone else to get their voice heard.
Perhaps a better approach would be to facilitate chance encounters on the quiet side-streets of the internet. If you're heading somewhere, you might bump into someone somewhere along the path. On the internet, you navigate the city through search, so this would be the ideal place to bump into friends and people in your network. By facilitating chance encounters, Search could be a social experience.