Sorry if this is going really far back into history here but I need to disagree with this statement. The geographical condition of the Western Empire was infinitely greater than the Eastern Empire, not the other way around. The Western Empire had two borders, Hadrian's Wall to the North and the Rhine River to the East. Both formidable defensive barriers and both holding back mere barbarians.
In comparison the Eastern Empire was literally surrounded on all fronts by powerful adversaries. The Northern border of the Danube River held back the steppe barbarians such as the Avars and Alans. They also had the powerful Sassanid Persian Empire breathing down their neck on the Eastern Border. After the West fell the Empire's western border fell open to attacks by the various tribes that had conquered Rome.
Rather I feel that the Eastern Empire was able to outlast the Western for several reasons:
1) Adaptability
The Eastern Empire was quick to adapt the strategies of powerful adversaries. They transitioned from Rome's old heavy infantry system to a cavalry based army. They adapted such Hunnic inovations as the stirup and the composite recurve bow and would spend years training Hippo-Toxite that could rival those of the Steppe nomads. A Byzantine cavalry archer could bring down a fully armored enemy soldier while riding away from him at a range of 75 meters.
2) Leadership
In general, the Eastern Empire was far more stable than the West politically. While there were a few major rebellions (such as Phocas) that nearly killed the Empire superior leaders such as my namesake, Herakleios, were able to take back the reigns and restore the Empire in most cases. The Western Empire faced civil war after civil war during a time of barbarian incursion and as a result could not bring to bear the force necessary to hold back the horde.
3) Diplomacy and Force
The Western Roman Empire was built on a strategy of attack. Assemble a massive army, send it into the enemy's territory, devastate their army, and take control. This is not an effective long term strategy for dealing with threats as it weakens your armies while allowing another, potentially more powerful, adversary to take the place of the one you just destroyed.
The Eastern Empire pitted its neighbors against each other rather than sending in its own forces. While the Byzantine Army was powerful, it was not large enough to ensure continual victories against endless waves of steppe nomads and Persians. Attrition would eventually take its toll, as it did on Rome. Only on rare occasions, such as the attacks on Bulgaria and Persia, did the Byzantine main army launch a full scale attack on an enemy. More commonly the Byzantines would convince the enemy's neighbors to attack.
The Byzantines used diplomacy to compliment force, whereas the Romans used force to compliment diplomacy. Both tactics get the job done in the short term, but the latter quickly drains manpower and leads to an inevitable decline in the long term against unending waves of enemies.
In shorter terms, the Byzantine Empire outlasted the Western Roman Empire because they were in it for the long term. They used diplomacy and tactics that would ensure their long term survival, rather than trying to reach short term goals. While they did eventually fall in 1204 to the crusaders, they outlasted the Roman empire by a significant margin (and even then they recovered as a city state and lasted until 1453).
Luttwak, Charles. Grand Strategy of the Byzantine Empire. 1st. Cambridge: Harvard University Press, 2009. Print.




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