Other forms: convergently
If you're a Red Sox fan and your cousin loves the Yankees but you both agree baseball is a wonderful game, that's a convergent idea — in other words an idea that brings you together.
Convergent applies to anything that is arrived at from different paths, not just an idea. Two trains, for example, arriving at the same station from different directions are said to be convergent; or two species of animals inhabiting the same environment that grow more and more alike in habit are also said to be convergent. The opposite of convergent is divergent — as in a Red Sox fan and a Yankees fan arguing about which is the better team.