Can math predict the rise and fall of empires? Math explains history. Researchers solve mystery behind evolution of complex societies using math model. The history of mankind as explained by math.

These are just some of the headlines about a recent article in a prestigious physics journal. Here is what the article supposedly does:

In a study out today in the journal Proceedings of the National Academy of Sciences, Gavrilets and his colleagues sought to create computer model that could predict the locations where empires would rise based on just three criteria. Despite the simplicity, their model reflected reality with 65 percent accuracy, showing that question of human social evolution could be quantitatively answered.

Wow! That sounds amazing. So how did they achieve this impressive result?

Spanning three millennia (1500 BCE to 1500 CE), the model used these three criteria to run simulations: the presence of agriculture, the ruggedness of the terrain, and most importantly, the distance from the Steppe geographical area, a belt that extends throughout Eurasia. “It appears that a lot of military technologies were invented in this Steppe area,” Gavrilets says, including combat on horseback and metal weaponry. Nomads in this Steppe area developed war tech to pillage nearby agricultural societies, he says. As centuries pass, these military advancements spread, and play a key role in the rise of new powers.

In other words: they used information that we know historically contributed to the rise and fall of complex societies to model the evolution of complex societies. The inclusion of distance from the Steppe is especially problematic given that this is a geographic variable that is used to “predict” the geographic spread of something that we know spread around areas close to the Steppe.

Much of the work here is not done by ‘math,’ but by understanding what factors contributed historically to the evolution of state formation. The math is used to model how these factors come together in a way that best fits the data. The math is important, but by itself cannot predict anything.

The authors of the study know this, of course, but every time a study like this comes out, there are media reports suggesting that some new algorithm can now be applied to solve the world’s major social questions. More often than not, the results are disappointing upon further review (see here for another example).

In this case, the authors develop an “agent-based model” that models how societies evolve, based on some assumptions about how warfare leads smaller societies to form larger organizational units. It is an interesting article. The contribution is to model with math what others have said in words. I don’t want to diminish the importance of that contribution. But it is not about “math explaining history” or “math predicting the rise and fall of complex societies.”

(h/t Tyler Cowen)