History is filled with patterns that can be studied mathematically.  The rise and fall of empires can be analyzed as a dynamic system to understand how groups of people can come together and achieve complex goals.
In this video I offer a review of War and Peace and War by Peter Turchin to share some of his insights into the way civilizations change over time.  He brings the powerful tools of population ecology to the study of human group dynamics.
As we confront the need to change our civilization in the 21st Century, topics like this become extremely practical.  How do groups of people form strong social identities?  What are the underlying principles of group cohesion that make collective action possible?  Why does inequality arise and how does it influence the evolution of society?
These topics and more are explored in Turchin’s excellent book.