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Please begin with an informative title:

Last year the Maya, this year Romans.This is the draft I submitted to the conference for acceptance. I will add to it prior to the 2014 International System Dynamics Conference, provided I am invited (which I expect to be).

This paper simulates the rise, stability, and fall of the Roman Empire from 500 BC to 1500 AD. Building on the 1995 ISDC Paper “Sustainable Civilization: Cohesion, Capacity, and External contacts,” the author considers the extraordinarily long life of the Roman state as it grew for half a millennium; sustained itself at its maximum extent for another half a millennium; persisted for another half a millennium as one of the strongest Western states with some successors; and finally declined and ended in yet more successor states two thousand years after it started. The Roman Empire grew via its competitive advantages of resilience and strength, bounded by Persia to the East and by environment and tribal societies to the West, South and North. While its powers waxed and waned, it declined only when the people to its north overcame the western half of the state. The eastern half persisted until other states met its strength, and even then a vestige lasted for several centuries. The rise, uniquely high climax, and fall are interesting, but even more interesting is the long persistence. This paper explores all of those dynamics in a historical and sociological context.

By legend, Rome was founded on April 21, 753 BC by Romulus and Remus. The first significant verifiable date however is 510 BC, with the expulsion of its last king Tarquinius Superbus and the foundation of the Republic. This innovation was a key to its gradually spectacular growth and uniquely long life. The Roman state grew at the expense of its neighbors for five centuries until it had only one neighboring state, the Parthian Empire in present-day Iran. Though at its peak it changed its form of government to Empire, still the republican institutions and the framework of state persisted to provide the basis for its resilience throughout its long maturity and decline.

This paper applies a version of the model from “Sustainable Civilization,” ultimately itself derived from “Limits to Growth,” to the specifics of Roman history. But rather than being driven by resource constraints, the dynamics are driven by the relative social power of societies and the economic ecosystems they exist within. In ancient times, only Parthia and its successor Persia were strong enough and different enough to resist Rome. The stateless peoples beyond the frontier were too weak to provide a basis for imperial rule until the fifth century AD in the west, the seventh century AD in the southeast, the eleventh century AD in the east, and the thirteenth century AD in the eastern core. The Roman story is ultimately one of the conduction and convection of power from Rome, with conduction predominating for a thousand years and convection afterwards, but both punctuating long periods of relative equilibria.

Problem Statement
Of all the world’s states – East and West, New World and Old – the Roman state had by far the longest duration. From the beginning of the Republic in 510 BC to the fall of Constantinople in 1453 AD, Rome existed for almost two millennia and over two millennia if the uncertain length of the kingship dating back to the seventh or eighth century BC is included. While Chinese and ancient Egyptian states covered at least that much time, there were interregna of decades and centuries when the states ceased to exist as a whole, or even at all. India, Iran, and elsewhere in Africa, Mesoamerica and Europe had no states of even interrupted comparable duration.

How did Rome manage to rise so far, and persist so long? Its rise was not continuous or without reversals, though they were short-lived. Its persistence at its imperial peak was eventful, yet they remained the dominant European and Mediterranean power until the rise of the Caliphate in the seventh century, and were a considerable force in the Balkans and Anatolia into the fourteenth. Its most comparable successor, the Ottoman Empire, lasted six centuries. Its most persistent rival, in Iran, went through Parthian, Sassanian, Arab, and Turkish states in the millennium of the rivalry.

In form a republic during its rise, the Roman state kept many of its republican institutions in place even after Augustus, who referred to himself as first citizen and said that he had saved and preserved the Republic – which in some ways he had.  It was only in the third century that emperors referred to themselves as lords and the Imperium Romanum became overt and explicit. That state, that name, that organization – they all remained in place continuously, in one part of the Mediterranean or another, for another thousand years.

Rome started as a small city-state in central Italy, founded by Etruscans. It grew in its first few centuries in a peninsula full of comparably-sized cities in varying alliance configurations. Over three centuries it overcame them all, and ruled them for many more centuries. They went on to conquer every pre-existing state on the Mediterranean and in Europe, and added territory that had never before been part of a state – and ruled it all for centuries, some for a thousand years and more. How did they do it?

Follow beyond the glycon, beyond the limes...


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Literature Review
There is a tremendous body of literature on the Roman Empire – its rise and fall; its functioning; its commerce, art, and literature. For Westerners it is a benchmark, a pervasive influence. The territorial expansion and contraction are well-documented, as is the political and economic organization, much of it in original sources.  This paper focuses on a handful of more recent works that discuss its rise, fall, and frontiers.

On the System Dynamics side there is precious little to draw from directly. There have been a handful of papers on the lifecycle of states. In 1978 Jack Homer wrote a paper for the System Dynamics Group at MIT entitled “Civilization as Enterprise: The Lifecycle of Cultural Production.” At the 1995 ISDC Tom Lum Forest presented a paper entitled “Sustainable Civilization: Cohesion, Capacity, and External Contacts.”  Both papers discuss the problem generally, but do not specifically expand on the Roman state. Forest wrote some additional papers that discuss other areas – most recently the Maya at the 2013 ISDC – but none on Rome.

Also of interest is John Sterman’s 1992 paper for the System Dynamics Group at MIT entitled “Self-Organization, Competition, and Succession in the Dynamics of Scientific Revolution.” The structures are directly analogous to the current work, with Roman area taking the place of paradigm adherents. Further afield, there are works on product lifecycles that are less directly analogous, and they are not cited here.

Model Description and Simulation Results
The model simulates the period 500 BC – 1500 AD. It has four central state variables: Roman State Territory, Non- Roman State Territory, Potential State Territory, and Non-State Territory.  These are all areas, measured in square miles. Roman and Non- Roman State Territory can flow from one to the other, and both can acquire land from Potential State Territory. The latter is territory that is settled and developed far enough to economically and socially support incorporation into a state. Non-State Territory, however, is not settled and developed far enough. It gradually becomes so, though the process takes centuries.

Roman and Non- Roman State Territory growth is constrained by its current levels, and by the available land in the other category and in potential land. Those constraints are expressed as maximum possible and maximum available rates, respectively. The flow between Roman and Non- Roman State Territory is constrained by their levels, and by the relative advantage between them.  

Figure 1 shows the essentials of the stock-and-flow diagram. Click for full size version.

Stock and Flow diagram of Roman Territorial Extent simulation

Figure 1: Stock and Flow Diagram

The various time constants:

Time to Double Empire 200 yr Restricts assimilation to Rome, whether barbarians or other states
Time to Conquer Other States 25 yr Restricts acquisitions of one state by another, which cannot happen all at once
Time for Rome to Conquer Barbarians 250 yr Restricts barbarians acquisition by Rome, which cannot happen all at once
Time to Double Non-Roman States 200 yr Restricts assimilation to non-Roman states, whether barbarians or Rome
Time for non-Romans to Conquer Barbarians 250 yr Restricts barbarians acquisition by non-Roman states, which cannot happen all at once
Time to Develop State Potential 750 yr Required for non-state areas to become potentially able to support states economically and socially
The conquest rates are constrained by available conquests as well as assimilation capabilities, and so are the lesser of conquest and assimilation. Roman comparative advantage also affects the conquest rates. The time constants > 100 years are that long as a result of the high level of aggregation, and the assumption of continuous process. A discrete element model or other more granular analysis would have a series of shorter delays. Time to Develop State Potential, for instance, would be a series of 30x25 year delays.

The first simulation run is a baseline with no changes in levels – all adjustment times have been set  > 106 years

Figure 2: Base Run – equilibrium run
Initial (Equilibrium) values:
Roman State Territory 20,000 mi2
Non-Roman State Territory 230,000 mi2
Potential State Territory 250,000 mi2
Non-State Territory 1,500,000 mi2
The second simulation shows monotonic growth with a persistent Roman advantage.
Figure 3: Permanent Roman advantage
The third run shows an initial Roman advantage, which disappears at 100 AD and becomes a disadvantage at 400 AD.
Figure 4: Advantage to 100 AD; neutral to 400 AD; disadvantage post-400 AD
Here’s the corresponding advantage.
Figure 5: Advantage Over Time
The fourth run shows the same as before to 600 AD, but then a revival from 800-1000 AD.
Figure 6: Advantage to 100 AD; neutral to 400 AD; varied advantage post-400 AD
This is the advantage used.
Figure 7: Graph of persistent early advantage and transitory late medieval advantage
Validation and Verification
The territorial extent of the Roman state, its conquests, and losses are copiously documented in the archaeological and historical records.  The following lists, while not exhaustive, are sufficient to indicate the pattern.

-    343-303 BC Rome conquers Campania and Latium
-    280-267 BC Pyrrhic War; Rome conquers South Italy
-    264-238 BC: First Punic War; Rome conquers Sicily, Sardinia, and Corsica
-    222 BC Conquest of Cisalpine Gaul
-    218-201 BC Second Punic War. Rome conquers southern Spain
-    168 BC Conquest of Adriatic Balkan coast
-    146 BC  Carthage and Macedon (including Greece) are annexed
-    133 BC Pergamon (W. Anatolia) bequeathed to Rome
-    121 BC Rome conquers southern France
-    63 BC Rome completes conquest of Anatolia and Syria
-    58-50 BC Rome conquers northern France
-    30 BC Egypt annexed
-    19 BC Roman conquest of Spain completed
-    13 BC Roman frontier in Balkans extended to the Danube
-    43-84 AD Roman conquest of Britain
-    106 AD Roman conquest of Dacia (Romania)

-    272 AD Withdrawal from Dacia (Romania)
-    275 AD Withdrawal from Upper Germany
-    409 AD Vandals conquer Spain
-    417 AD Visigoths conquer Aquitaine
-    439 AD Vandals conquer N. Africa
-    476 AD Ostrogoths conquer Italy
-    486 AD Franks conquer Gaul (France)
-    636-642 AD Arabs conquer Syria and Egypt
-    568 AD Lombards conquer N and  central Italy
-    621 AD Visigoths conquer S Spain
-    680 AD Bulgarian independence in Thrace
-    698 AD Arabs conquer North Africa

-    534 AD Reconquest of Sicily, Sardinia, Corsica, N Africa and S Spain
-    554 AD Reconquest of Italy
-    873 AD Reconquest of S Italy
-    965 AD Reconquest of Cyprus
-    965 AD Reconquest of Antioch
-    1018 AD Reconquest of Thrace (Bulgaria ) and Serbia
-    1045 AD Reconquest of Armenia

-    901 AD Arabs Conquer Sicily
-    1071 AD Normans Conquer S Italy
-    1071 AD Turks conquer eastern Anatolia
-    1185 AD Bulgarian independence; loss of Cyprus and Antioch
-    1204 AD Frankish conquest of much of Greece and Aegean islands; Empire split into three
-    1204–1261 AD Frankish occupation of Constantinople
-    1320 AD Ottomans complete conquest of Anatolia
-    1346 AD Serbian conquest of Epirus and Thessaly
-    1453 AD Ottomans take Constantinople
-    1460 AD Ottomans conquer Despotate of Mistra
-    1461 AD Ottomans take Trebizond, last Roman outpost.

Much more problematic to interpret is the nature of the frontiers themselves and the nature of Roman state control. A limes marked a zone, not an exact boundary as we now think of it, and was often a road for efficient transport well inside the limit of military and political control.  As Whittaker says, “[We] can see how in Algeria, for example, many of the sectors of the limes in the fourth century AD were simply lines or roads through the difficult mountains, such as the Grand Kabylie, which lay well to the north of the line of military control” [p. 200]. Additionally, there were penumbral client states like the Kingdom of Bosporos in the Crimea and southern Ukraine. Any measurement of area is difficult to compare over time, and cannot be done with the degree of precision possible in modernity.

Analysis, Inferences and Implications
The model reproduces the aggregate behavior observed – the territorial variations in the Roman state.  Yet it relies on explicitly stated variations in the Roman competitive advantage as it varied over the centuries. Initially, against its early peers, its resilience, persistence, and discipline were unmatched. In the Imperial heyday its challenge slowly increased as its neighbors developed and adapted in reference to the Romans. The Romans themselves responded in turn, and for a few centuries were able to maintain a status quo while losing their margin for safety, error – and civil war. A follow-up version of this model could include variations – dips, or punctuations – in the Roman advantage during leadership changes.

After the western half of the empire was overrun by Germans in the fifth and sixth centuries, much of the eastern half was overrun by Arabs and Slavs in the seventh. The Imperium Romanum eventually adapted to the Slavs, and even to a lesser extent to the Arabs, particularly with themata, but was ultimately undone by Venetians and Turks to whom they had too little time and too few resources to adapt.

There is, then, considerable room for further research as to what exactly the competitive advantage was and why its dynamics were as they were. Rome started with some advantages that helped it in Latium, the immediate neighborhood of its origins, stemming from its distinctive Republican governance.  Those advantages helped it for over six centuries. But its success created another environment entirely, an environment that Germans, Slavs, Arabs, Venetians, and to a lesser extent Turks developed in. Nothing fails like success: Rome created the soil for growing the seeds of its own destruction.

Rome had a competitive advantage for many centuries over its neighbors, and expanded to the limits of the areas that could support Roman society economically and militarily.  That advantage faded in the Imperial period, and had reversed by the fifth century AD.  There was a significant revival in the eighth to eleventh centuries AD before ending altogether in the fifteenth. The wonder is still not that it ended, but that its ending was so long after its beginning. The Ottoman Empire, who most closely reproduced the Roman Empire after formally ending it, claimed to be its continuation: just the state religion had changed, to Islam, much like Constantine had established Christianity as the state religion. The Ottoman state lasted six centuries – a long time, but well short of Rome’s twenty.

Part of the answer is in the momentum of success. Rome had conquered the entire civilized world west of the Euphrates, so any successors had to come from a long way off, developmentally or geographically. Another part of the answer was in the nature of the advantage – more stability, continuity, efficiency, and inclusion. Anyone could become a Roman. To defeat Rome required outdoing them in those qualities, or undoing them despite those qualities. That took a very long time to develop. Such genius, however inadvertent and proximately intended, is exceedingly rare. Adaptation is hard, even when the consequences of not adapting are harder.

Simulations done with Vensim

Bringman, Klaus, 2007. A History of the Roman Republic. Malden, MA. Polity Press

Forest, Tom Lum “Sustainable Civilization: Cohesion, Capacity, and External Contacts”. Paper presented at International System Dynamics Conference, July 1995, Tokyo Japan
 –    “Byzantine, Bulgarian, and Ottoman: The Dynamics of Empire at the Crossroads of Asia and Europe” Paper presented at International System Dynamics Conference, August 19-22, 1997, Istanbul, Turkey
–     “The Perilous Frontier: East Asian Cultural Ecology and Two Millennia of Chinese Dynastic Succession” Paper presented at International System Dynamics Conference, July 20-23 1998, Québec City, Canada
–     “Maya Apocalypse: Warfare-Punctuated Equilibrium at the Limit of Growth” Paper presented at International System Dynamics Conference, July 29 – August 2, 2007, Boston, MA USA
–     “Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results” Paper presented at International System Dynamics Conference, July 21-25, 2013, Boston, MA USA

Heather, Peter, 2006. The Fall of the Roman Empire: a new history of Rome and the barbarians. New York, NY. Oxford University Press

Hodgson, Marshall G. S., 1974. The Venture of Islam. Chicago, IL. University of Chicago Press

Homer, Jack “Civilization as Enterprise: The Lifecycle of Cultural Production” in Sloan School of Management Working Papers (D-2951). Cambridge, Mass. Massachusetts Institute of Technology September 1978

Inalcik, Halil (Ed.) 1994. An Economic and Social History of the Ottoman Empire, Volume One 1300-1600. New York, NY. Cambridge University Press

Kafadar, Cemal, 1995. Between Two Worlds: Construction of the Ottoman State. Berkeley, CA. University of California Press

Lapidus, Ira M., 1988, A History of Islamic Societies. New York, NY. Cambridge University Press

Meadows, Donella; Meadows, Dennis; Randers, Jorgen. 1993. Beyond the Limits: Confronting Global Collapse, Envisioning a Sustainable Future. White River Junction, VT. Chelsea Green

Norwich, John Julius, 1988. Byzantium: The Early Centuries. New York, NY. Alfred A. Knopf, Inc.
-    Byzantium: The Apogee, 1991. New York, NY. Alfred A. Knopf, Inc.
-    Byzantium: The Decline and Fall, 1995. New York, NY. Alfred A. Knopf, Inc.

Ostrogorsky, George, 1969. History of the Byzantine State. New Brunswick, NJ.  Rutgers University Press

Smith, Julia M. H., 2005. Europe After Rome: A New Cultural History 500 1000. New York, NY. Oxford University Press

Sterman, John D. 2000. Business Dynamics. New York. McGraw-Hill
–   “Self-Organization, Competition, and Succession in the Dynamics of Scientific Revolution” in Sloan School of Management Working Papers (D-4367). Cambridge, Mass. Massachusetts Institute of Technology 1992

Ward-Perkins, Bryan, 2005. The Fall of Rome and the End of Civilization. New York, NY. Oxford University Press

Weisehofer, Josef, 2001. Ancient Persia, New York, NY. St. Martins Press

Whitaker, C. R, 1994 Frontiers of the Roman Empire: a social and economic study. Baltimore, MD. Johns Hopkins University Press

3:59 PM PT: Thank you for the posting to SciTech! This diary is word-for-word what I submitted to the conference. I'll post a DailyKos-targeted version later.

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Originally posted to Tom Lum Forest on Fri Mar 21, 2014 at 12:37 AM PDT.

Also republished by SciTech.

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