Ask YC: Do you know of any good attempts at using a social network as a brain to solve problems?
What do you receive from your connections? Ideas, partial solutions, etc. If someone is not contributing in this way, then people would disconnect from him/her.
Moreover, once the problem is solved, you can have some sort of credit assignment so that people/neurons who have contributed to the solution in a meaningful way receive more points.
Finally, you can have a real-time global visualization of the network so that the more active regions are easily found and you might consider connecting to people in those regions. You could even have summaries of what those active regions are thinking about (so that you can join a region that's working on a subproblem that interests you most).