Here, Peter Turchin is talking about cliodynamics - I will let him explain that himself (you can also download a pdf of his recent Nature essay here):
Empires rise and fall, populations and economies boom and bust, world religions spread or wither... What are the mechanisms underlying such dynamical processes in history? Are there 'laws of history'? We do not lack hypotheses to investigate - to take just one instance, more than two hundred explanations have been proposed for why the Roman Empire fell. But we still don't know which of these hypotheses are plausible, and which should be rejected. More importantly, there is no consensus on what general mechanisms explain the collapse of historical empires. What is needed is a systematic application of the scientific method to history: verbal theories should be translated into mathematical models, precise predictions derived, and then rigorously tested on empirical material. In short, history needs to become an analytical, predictive science (see my essay Arise cliodynamics in the sidebar)
Cliodynamics (from Clio, the muse of history, and dynamics, the study of temporally varying processes) is the new transdisciplinary area of research at the intersection of historical macrosociology, economic history/cliometrics, mathematical modeling of long-term social processes, and the construction and analysis of historical databases. Mathematical approaches - modeling historical processes with differential equations or agent-based simulations; sophisticated statistical approaches to data analysis - are a key ingredient in the cliodynamic research program (see "Why do we need mathematical history?" in the side bar). But ultimately the aim is to discover general principles that explain the functioning and dynamics of actual historical societies.
It is interesting to see Ibn Khaldun's work on social cohesion (Asabiyyah) and on the rise and fall of empires show up in his talk. He also brings up religion at the end as a possible social glue that allowed empires to grow for the first time between 800 and 200BC, and the period of prophets and philosophers (coined the Axial Age by Karl Jaspers). Peter is explicit in saying that he is not talking about the supernatural component of religion, but rather its emphasis of social integration. An interesting idea and merges nicely with the some of the work that David Sloan Wilson has been doing (see the video of his lecture at Hampshire College here).