The brilliant atomic physicist Enrico Fermi was notorious for unnerving PhD candidates during their oral examinations by asking ‘How many piano tuners are there in the city of Chicago?’ The point of the question, besides the psychological effect, was to gauge how well the candidate could estimate (and justify!) an apparently inestimable quantity. This is something experimental physicists routinely do to estimate whether a physical effect can be measured. Even in the absence of a neighborhood particle accelerator, Fermi questions are fun ways to pass the time on a long car trip (‘How many trees are in the state of Washington?’, ‘How many gallons of water are there in the ocean?’).
Most Fermi questions typically estimate a static quantity but some Fermi questions ask about whether and how a complex system might reach some state. We employ these sort of exercises every day when we ask what the weather will be like in a few hours, whether a stock might do well in a year, or if it is mate in ten. Answering these questions often requires thinking about events that might impact the main underlying processes and about when they might occur. But depending on the complexity of the processes and the odds of the events, people just aren’t very good at keeping track of the alternative paths and hence estimating the likely outcomes.
This is why computers have become indispensable for answering such dynamical questions with any time depth. Of course you have to have a pretty logical, often quantitative understanding of the processes to be able to run such simulations. A lot of work in weather forecasting, climate change modeling, and chess playing involves encoding the ‘rules’ of the process and ensuring the steps are modeled at sufficient resolution to not miss important impacts.
What about Fermi questions applied to history? There have been many well-known questions about events and the dynamics of history, including wondering about the fall of states and the rise of subsequent or invading states. A recent, excellent example of one such investigation is Walter Scheidel’s The Escape from Rome, in which he asks why another Roman empire never arose in Europe after the fall of the original in 476 CE while, for example, vast Chinese empires consistently reformed in spite of various dynastic collapses. His far-ranging investigations asked what other societies might plausibly have taken Rome’s place in the centuries following the fall and the factors that checked each in turn. Could a computer model help illuminate such long-standing historical quandaries?
In a paper published in PLOS ONE last week I did just this, building a sophisticated computer model of agrarian states and nomadic confederations that substantially accounts for the dynamics of societies in Europe and Asia across three thousand years of history, from 1500 BCE to 1500 CE. Originally inspired by work of Turchin et al. 2013, my model combines elements of different popular theories to predict not only the number of states, their location and size but also their population, which drives their military might. The model predicts how a state’s military expansion would be checked logistically and hence when warriors would turn from interstate to civil war, causing new states to appear and spread. Using historically accurate timing, locations and estimates of the severity of the threat from nomadic groups (who used military means to extort tribute from states), the model can, for the first time, account for the rapidly increased size and proper timing of different mega-empires. These include the Achaemenid, Roman, Mauryan, and Han Empires, along with various large ‘mirror’ nomadic confederations such as the Scythians and the Xiongnu, as suggested by Turchin’s 2009 conjecture about an arms race along the agrarian/steppe meta-ethnic boundary.
But the modeling framework goes further. It allowed me to identify a host of key events and developments that are required to account for observed history. For instance, had it not been for the invention of large, fast, and reliable ships throughout the Mediterranean in the first millennium BCE and the use of camels as transport animals in the deserts of Egypt and southwest Asia, our world would look radically different today. By eliminating, delaying or changing the scale of these contingent events, the model can pump our intuitions about what might have occurred ‘but for’ these events. In one experiment, for example, if agrarian states had arisen in 1500 BCE in the Mekong and Ganges river valleys, rather than in the Nile, Mesopotamian, and Yellow River valleys, the time before the nomadic pressure enabled the rise of very large European empires west of Persia would have been delayed by ~600 years. Interestingly, in this case the first Chinese empire would have arisen from the south as the associated military technology would have ‘boomeranged’ back from Persia through India and then via the Mekong states, allowing a very large southern Chinese state to expand north into the remaining hinterland and finally engage with the nomads there a millennium later than observed. The model also suggests that no Persian, Mauryan or Cambodian empire would have arisen in those regions because they were already well-saturated with many smaller, militarily-balanced states, none of which could effectively exploit the improved military technology before their neighbors also adopted it.
Along the way, I was able to answer some other important Fermi questions. How much more agriculturally productive were large-scale Eurasian states compared with non-states? Roughly three times, then doubling to six times starting in the late Middle Ages. How much more logistically effective did the militaries of ancient states become because of the threat of nomadic confederations? Roughly twice. How much longer did the very large mega-empires survive before internal collapse than smaller empires? Roughly not at all – as the figure below shows, the historical data and model predictions agree that increased size appears to be no cure for the threat of internal instability and civil war!
This type of computer model is a crucial step in consolidating and testing causal theories about the pulse of societies in the past as they rose, spread, and, ultimately, fell. Models built to scrutinize the collected insights of historians will continue to pump our intuitions about why and how history unfolded.