Using Math to Explore the Fall of the Roman Empire

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I am firmly committed to the idea that there is great value in exploring change over time in Roman history using mathematical models. Since antiquity itself, scholars have debated broad questions concerning the forces responsible for the rise and fall of the Roman Empire.  But in the status quo, fundamental elements of the debate seem relegated to the realm of the pseudo-scientific, since it seems impossible to either confirm or deny broad claims such as “barbarian pressure along the frontier was more responsible for the ultimate decline of Roman civilization than the long-term effects of civil war.” In fact, historians making precisely opposite claims can point to compelling data from archaeological and literary records to bolster their hypotheses. Preferring one explanation over another sometimes becomes a matter of personal taste or academic politics rather than an empirical exercise, which is only exacerbated by the fact that so much information from the ancient world itself is lacking. The fact that medievalists and classicists often interpret and answer major questions about antiquity and the early Middle Ages so differently is the clearest indication of this trend. Indeed, in the tradition of certain historians like Irene Barbiera and Gianpiero Dalla-Zuanna, some have even gone so far as to question whether the very disintegration of the Roman Empire should be interpreted as a fundamentally regressive phenomenon at all, with historians of the Early Middle Ages increasingly challenging simplistic models of decline and fall.

How can all of these narratives be reconciled, let alone evaluated against each other in an objective context?

Originally, I hoped to engage in a novel approach to these questions, making use of tools traditionally employed in fields outside of the Classics. Imagine we were looking at a map of the Roman Empire, divided into many quadrants.

These are the elements that would be tracked:

1) the locations of iron deposits and other natural resources that can be pinned down with a fair degree of accuracy, including the locations of major mines (these are, of course, static)

2) the locations of where the Roman emperor was declared, and where he was physically during each month of his reign, which can be tracked with great accuracy over several centuries

3) The locations of recorded battles

4) the locations of the Roman legions themselves; their movement can be crudely mapped out over the course of five centuries

5) the location of the city of Rome itself, major roads, and other geographical features (Mediterranean sea and the Rhine-Danube frontier)

I tentatively hypothesize that times of plague, rebellion, and civil war should show statistically significant changes in the relationships between the static and dynamic data sets as such periods would lend themselves to efforts to seize control of local mineral deposits and resource-distribution-centers.  By contrast, in times of relative internal stability, the Rhine-Danube frontier is more likely to attract dynamic movement in response to external pressure along the borders. Permanent changes in spatial relationships can suggest watershed moments in Roman history.

The upshot of all this is that using the right mathematical tools, the relationship between these variables can be systematically evaluated, and we can investigate what various causal forces (internal or external) seem to have been responsible for violence at different points in time. For example, considering a specific span of time, do major battles and troop movements statistically clump along the Rhine-Danube frontier, or do things like the locations of local resources and the physical location of men proclaimed the Roman emperor play weightier role as a source of attraction? The former would suggest the long term influence of external pressures during this era, and the latter internal dynamics. At the same time, do relationships among major variables change after major events in Roman history such as the advent of the Antonine Plague, the establishment of a new capital, or the rise of Christianity? What is statistically likelier to attract battles at any given point in time—cities, mineral deposits, or geographical features along the border? The answer to this question reveals something fundamental about the texture of the decline and fall of the Roman Empire.

Once all of this work was done for the Roman Empire itself, it would be fascinating to employ similar methods to explore Mediterranean history in the period of the Republic, when I predict that the major causal networks determining troop movements would be quite different, perhaps oriented more around features of the Mediterranean coastline and the locations of major mineral deposits as opposed to the case of the Empire, when unity was achieved and the focus turned to defense rather than offense. If the data were compared to information from Han China, I hypothesize that the “particles” representing armies and battles would move synchronously across the continent at certain times in response to pan-Eurasian forces such as plague, the spread of technologies, and the movement of barbarian tribes. This would provide strong support for the idea of macrohistorical forces at work in determining causal outcomes in history.

Nevertheless, after a great deal of soul searching and wavering, I have decided to focus my dissertation on orgiastic display, violence, and politics. There were several reasons for this.

  1. As I said above, I think that exploring change over time in Roman history using mathematical models would be incredibly interesting. However, because the nature of my work in this field is experimental, I am worried that the success of my dissertation would be largely contingent on whether or not my mathematical hypotheses in fact bore fruit. I can’t guarantee anything of the sort, however, until I actually examine the data. It may be that mineral deposits attract battles, for example, or it may not be. It might be the case that Han and Roman data line up nicely, but again, there is nothing to guarantee this.
  2. Writing the quantitative dissertation might have alienated me in the eyes of others in the field and on the job market. The topic seems iconoclastic, to say the least, and I think that there would exist great skepticism about my new methodology. At first glance, my idea seems simultaneously too traditional and too futuristic. Because it seems to touch upon universalizing schematizations about the nature of historical change and is focused on military history and troop movement, it seems like a throwback; at the same time, because it deals with mathematical regressions and computer modelling, it seems too out there.
  3. I would prefer to leave the option open to me of co-authoring a tight, focused article using quantitative methods with colleagues who are already familiar with the available software so that we could learn and work together on the project; by contrast, I think that the dissertation should necessarily involve strictly independent research. At this point, guaranteeing that I could master the mapping software quickly enough to write a great dissertation seemed too risky a prospect.
  4. The dissertation should be immersed in and enriched by existing discourse on the subject, making a specific informed contribution to an ongoing conversation. However, there is in fact very little existing discourse on the mathematical relationships between the locations of battles, emperors, and geographic features/natural resources and the significance of these changing correlations over time. If I did something like make the dissertation a broader study of “decline and change” in Roman history and relegated the quantitative methods to an appendix, it would be a shame—the quantitative methods require a great deal of work, and probably deserve to shine in their own paper.

Ultimately, staking the entire dissertation on something so novel seemed riskier to me than utilizing my quantitative methods in a separate project.

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