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There are several argumentations already included in previous threads such as the betrayal. Plus, let me remind you that the # was 150,000 Arabs (I read that # somewhere) to 70,000 Tang pro soldiers. With these factors of influence and economy, I really don't see how the Byzantium was a comparable international power.
It was actually 30,00 Tang forces and around 40,000 Ghazis with an unknown number of allies.
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Ok, then why Mongols conquered half on then known world with a tiny population and almost non-existing economy? The key is tactics, military organization and military know-how. And both Mongols and Byzantines had these assets.
No, the key here is that the Mongols have a different system of organization; they are nomads, while the Byzantine empire was not. The comparison here is hence invalid.
You need to understand how nomadic empires function and how they are fundamentally different from sedentary empires. Nomadic empires rely on agricultural states for sufficiency through trade or pillage. They are not self sufficient. Yet because they have no need of farmers to produce surplus to feed their army, a much larger portion of their total population could join the military. While around 1/50 individuals in an sedentary empire were enlisted as soldiers, as much as 1/4 of the entire nomadic population could participate in the army.
The second advantage of these nomadic armies was their mobility. This can be attributed to two factors; the abundance of horse and their wandering lifestyle. According to estimate, Mongolia has over 3 million horses, which constitute around half of the entire world's horse supply, every soldier has 5 mounts which enables them to cover long distances without the need to worry about remounts. Secondly, the lack of cities in nomadic territories allows them to be elusive and maintain a strategic(not tactical) advantage. Whenever the nomadic armies actually faced Chinese armies on the battlefield, victory could easily go to either side. But on the big picture, nomads could easily gather a large force and concentrate their attack on isolated Chinese strongholds, and due to their mobility, they can easily retreat when sedentary reserve forces come to the rescue. Hence in most battles, nomadic forces outnumber Chinese forces in that specific region. Chinese offensives against the nomads were made difficult due to logistic problems, Mongolia is a huge area with no cities to loot. Long supply lines were needed to conduct a campaign. The nomads, with their superior mobility and sparse population could easily avoid battle with the sedentary armies until the latter were exhausted of their supplies and were forced to retreat. Therefore, the initiative lies with the nomads.
The Byzantines has no such advantages. They are sedentary, with cities to be captured, they are more predicatable. And population plays a big role here. Their horse supply only numbered around 200,000 during Justinian's time. And significantly reduced by the 7th century. The Tang on the other hand had over 700,000 imperial stallions, with an even more impressive private horse breeding industry.
There were a few major factors in an objective assessment of the strength of ancient states. Population was one, terrain was another, crucial military resources such as iron and horse was important as well, yet administration was perhaps the most important. Smaller states were able to overwhelm bigger ones due to their greater centralization, their ability to effectively execute political and military actions, and the ability of the state to conscript its population. This was the major reason why states such as France lost in the initial phase of the 100 years war with England, they did not have the advanced bureucracy to utilize the advantage of their greater population and conscript them for war.
Yet in all these areas(except terrain), the Tang state was unrivaled.
Modern bureaucracies requires 6 fundamental aggregates; a board for foreign policy, aboard for economic policy, a board for administration matters, a board for civil matters, a board for military matters, and a board for legal matters.
The Sui-Tang empire's 6 Shang Shu already satisfy the requirements of a modern bureucracy; the board of rites dictate foreign policy, the board of punishment dictate law, the board of registration deal with registration and agricultural matters, the board of Shi deals with promotion of magistrates, the board of military deals with the military, and the board of work deals with construction projects.
The Tang state was more centralized than any in the world, its equal field system allowed it to keep a fairly accurate census of its population, which implies that it could conscript them readily for war. The Tang horse breeding industry was the most developed on earth, and the same can be said about its iron industry, which had the blast furnace technique that produced as much as 20,000 tons of pig iron. In none of these areas, does the Byzantine come even close.
And as I already asserted, Koguryo's strength in these areas makes it a power comparable to the Byzantine.
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Britain could defeat China in Opium Wars etc.
Besides, the Byzantine Empire was Caliphate's arch-enemy. It was prophet's command to take Constantinople. So, it was the main front where the Muslim armies fought. And Byzantines not only withstood the assault but also managed to get the upper hand and regain lots of territories.
The Opium War was a different story, we are entering the age of industrialization where weapons of advanced technology became the decisive factor. Prior to the industrial revolution, weapon disparity were miniscule over most of Eurasia and were not decisive in determining victory. Yet with the introduction of steam boats and the later breech loaders, technological disparity widened to a degree that was unprecedented.
The Byzantine military was only the caliph's major enemy in the 7th century, by the 8th century, enemies such as the Khazars and Turgis were already overtaking their importance.