Oh what a tangled web we weave. Or so it may seem. Because many social networks eventually evolve into one of just two states. We either all get along. Or an unbridgeable divide develops. And a new mathematical model can predict which it will be, findings laid out in the Proceedings of the National Academy of Sciences. [Seth Marvel et al., Continuous-time model of structural balance]

Consider a relationship triangle. Arthur and Carl don’t like each other. But Bill is friendly with them both. Bill will probably try to convince Arthur and Carl to get along. But Arthur and Carl are telling Bill that the other guy’s no good. You don’t need to be a math whiz to see that, as time goes on, either everyone will be friends or Bill is going to have to pick a side.

Now picture a big network made of these triangles. Which is what scientists did in their computer model. And they found that this theoretical social network produced either global harmony or all-out war, depending on the initial triangles. The model even predicted almost exactly the identities of all the Allied and Axis forces during World War II. So one way to prevent global war may be to forge friendships between enough Arthurs and Carls.

—Karen Hopkin

[The above text is an exact transcript of this podcast.]