The Mathematics of Groups

The most interesting thing about Shirky's book, Here Comes Everybody, is that it demonstrates that the mathematics behind group forming is inherently tied to that group's structure, longevity, and purpose. His book outlines the power law distribution, Metcalfe's Law, and Reed's law, and shows in a down-to-earth fashion that these theoretical and discreet principles of mathematics profoundly impact the formation of groups in our world. That there are basic, guiding principles which govern complex phenomenon is an idea which feels timeless; yet, interestingly, this idea is younger than the computer itself. This idea was a revolutionary idea in mathematics, and was put forth by Benoit Mandelbrot, famous for discovering fractals. Mandelbrot discovered that some shapes looked similar at different levels of magnification, and also discovered that a relatively simple formula governed this complex and sometimes erratic shape. This self-similar design appears in Shirky's book also, on page thus-and-so, when he starts to talk about how small-world networks look similar to itself at different scales. Thus, he ties into Mandelbrot's fractals, and hence that complex phenomenon can be described by simple rules, but also shows that in spite of that, these phenomenon are still relatively unpredictable. Though he did not mean to do so, Shirky showed how social networks relate to the mathematical framework of fractal geometry pioneered by Mandelbrot, giving us hope that there is a way to examine social phenomena in a mathematically rigorous way.