From Social Math to Social Networks

Shing-Tung Yau is best known for proving the Calabi conjecture and giving his name to the Calabi-Yau manifolds, later used in string theory. The so-called Calabi-Yau manifolds (a manifold is simply a higher dimension space, in this case 6 dimensions folded and curled up in every point of our macro fourdimensional space) are used because they provide symmetry for the strings wobbling around in them, as string theory claims.

Here’s my review of his book “The Shape of Inner Space“. He also seems to know his way around in social networking!

Large social networks foster connections by erasing national, geographic, and even linguistic barriers. But when it comes to fostering cooperation, global connectivity leaves something to be desired, new research says.

Working with colleagues at Emmanuel College, Harvard scientists have developed an algorithm that predicts whether a social structure is likely to favor cooperation, and the findings suggest that strong pairwise relationships—not loose networks scattered across the globe—are the most conducive to cooperation. The study is described in a March 29 paper in Nature.

“What we are able to do is calculate the critical benefit-to-cost ratio for cooperation to thrive on any fixed population structure,” said senior author Martin Nowak, a professor of mathematics and of biology and director of the Program for Evolutionary Dynamics. “And what we find is truly interesting. We can take any graph or social network, and if it has strong pairwise ties, that is what is most conducive for cooperation. This is a mathematical argument for stable families or for stable friendships.” … (

Shing-Tung Yau (from left), William Caspar Graustein Professor of Mathematics, Ben Allen, researcher at the Program for Evolutionary Dynamics (PED), and Martin Nowak, PED director, are co-authors of a new study that examines how cooperation emerges in social networks and debuts an algorithm that can calculate the likelihood that a network will foster cooperation. Credit: Kris Snibbe/Harvard Staff Photographer