I lack the time to address all your points, but here are some thoughts related most of your comments.
Uiler said:
You must be joking. Chinese cities were heavily fortified esp. in the border regions (and note most of the Jin cities were actually Chinese cities). These cities were constantly attacked by barbarian raiders. As such they were heavily fortified. Read Chinese history. Song was militarily weak but often many of these border cities were nothing more than big military colonies almost totally populated by soldiers and their families. You often hear about seiges that lasted for years and years and years. Seige warfare is part of standard Chinese military tactics. Before the Mongolian invasion, Chinese had practised sophisticated seige warfare for 1000s of years (mainly due to constantly breaking up into smaller states that would then wage constant war on each other's cities). I would say that they had a lot more experience with it than the Westerners. In fact, by the time of the Mongolian invasion the Chinese were using gunpowder to make bombs (which make a regular appearance in description of battles in Chinese fiction after the Song period even if said battle were 1000 years in the past)! In fact I think they even had a rudimentary cannon. I'd like to see how European walled cities of the time would stand up to dozens of bombs being ignited at their base and a few (admittedly crude) cannons. Somehow I doubt that they'd last. In fact the Mongolians took cities by press-ganging Chinese who were experts at seige warfare into their army. This is also how they managed to cross the Yangtze defeating the Song navy. Basically the Mongolians would have simply got the Chinese engineers they press-ganged into their service to blow up any walls in the European cities. Europe at the time had absolutely nothing to defefnd against bombs, gunpowder and cannons. The Mongolians not only had the warrior ethic, the great cavalry, they also appropriated extremely sophisticated Chinese military technology.
I believe most larger fortifications in Europe could withstand any siege, be it Mongol or European. By the mid-13th c. the art of masonry reached great perfection in Europe. European siege engineers were basically using the same machinery as their Saracen and even Mongol counterparts - mangonels, trebuchets, mining and so forth. Similarly, European fortifications were designed with all these threats in mind. The only exception may have been gunpowder which the Mongols seem to have used to a very limited extent. But it was primarily a psychological weapon at that time and the Mongols made no use of gunpowder artillery whatsoever. Not to mention, The concentration of fortifications was much higher in Europe than in the Middle East, even if most European fortifications were smaller. To subdue Europe, the Mongols would need to destroy castle after castle, town after town, all that probably against fierce resistance. The number of such fortifications in Europe was enormous, not to mention that they were often built in extremely difficult terrain where the Mongols would have been at a distinct disadvantage, being forced to fight on foot. So Even if the Mongols succeeded in defeating opposing armies in the field, they would still have to take the strongholds one by one. Worse yet, the defenders could choose to avoid battle for some time, waiting for a more opportune moment. More importantly, even the best fortification is worthless without determined troops to defend it. Baghdad may have been a huge city with an excellent system of walls. But the Abbasid caliphate had been in decline since the 9th c. And the Seljuks who took Baghdad in 1055 and effectively ruled it since then had lost much of their power during the 12th c. (particularly with the Crusades). They were in no position to resist the Mongol invasion. So while Baghdad may have been very heavily fortified indeed, it was poorly defended and its capture was no great feat. And China was a huge country at the time, technologically advanced and with a prospering economy, but it was not particularly strong militarily. This seems particularly true in case of the Song dynasty.
Almost all warfare in medieval Europe revolved around the siege and a more static style of warfare that the Mongols had with in their experience to deal with. And yes, they of course ensured that all metalworkers, carpenters and gunpowder makers in northern China were registered as catapult operators. They had previous and subsequent success in sieges elsewhere; and clearly knew of siege equipment and engineering. There were obviously skilled siege engineers in Batu's army who were capable of constructing catapults. In fact, we know that Batu had brought a train of minghan engineers, since he was able to field seven ho catapults to hurl firebombs against the unfortunate Hungarians at the Sajo bridge, teaching them a deadly lesson in the tactical use of artillery. But events showed that these werent heavy enough to breach the high stonewalls of the Hungarian castles, which Batu had to bypass. Gunpowder wasnt used during the Mongol campaigns in Russia and Europe, and the primitive projectile technology then in use wouldnt have made much of an impression. And unlike other Mongol dynasties, Batu couldnt draw on the quantity of artillery necessary for the reduction of the great towers and cities of Christendom. Weapons of sufficient quantity and quality could only have been manufactured and maintained by a sedentary population with the kind of advanced engineering skills available to China or Persia. On a later campaign it would take Hülegü three years to transport a thousand crews of Chinese artillerymen and their siege equipment two and a half thousand miles from the steppes of western Mongolia in 1253 to Khurasan in 1256, and another two years before they could topple the walls of Baghdad a thousand miles farther west. The lands of Western Europe were even more remote, over four thousand miles from Mongolia, and boasted an array of fortifications even more formidable than those of Persia or Mesopotamia. The Mongols could never draw on the quantity of artillery necessary for the reduction of the great towers and cities of Europe. Even had the Batu had access to Chinese and Persian artillery, the logistical problems of transporting and supplying a sufficient train would have been still more immense, and bringing such a siege train would have inevitably slowed the Mongols down to the extent of negating the surprise effect and superior mobility. And since no such attempt was ever made, even in the face of hostilities, such a stupendous leaguer would appear to have been quite beyond the Mongols' strategic capabilities.
So, could the Mongols have penetrated into the heart of Europe and wreaked havoc? Yes, they could have. Would this have been a mortal blow to Europe, or ended in conquest? No, given Europe's political character and general characteristics of European military development, I don't think the Mongols ever stood a realistic chance of conquering and holding territories in the West. For instance, whenever steppe horsemen came from the east they took Europe by surprise. There were several such waves; Huns, Avars, Magyars and finally Mongols. These were instances when large bands of nomadic horsemen successfully operated in Western Europe; most notably the Avars and Magyars who reached as far west as France. However, most of these attacks, even when made in strong force, were nonetheless only mere raids: advance, destroy, retreat to base. The lack of skill in siege warfare meant their invasions tended to consist of large-scale raids and thus made no real strategic impression. Take for example, the Second Punic War. How many battles and armies did Rome lose to Hannibal? Yet somehow, despite his genius and his superlative army, Hannibal could not win? Because he could not take all of the fortified cities with the forces at his disposal; nor could he be reinforced or resupplied sufficiently from the great distance to Carthage. Consequently, his offensives soon ran out of steam due to logistical problems and low morale. Over time, Hannibal realized the key to defeating Rome was not annihilating its armies in the field, but by laying siege to its strongholds and cities, something that was far beyond their capabilities to do so. Arguably for this same reason, neither the Avars nor the Magyars ever managed to gain a firm foothold in Western Europe. The only time when a body of steppe horsemen of any real size attempted to operate in Western Europe was the Hunnish campaigns, which ended catastrophically. These events demonstrate that while small, dispersed groups of steppe raiders could pester Western Europe, no large army of steppe horsemen which lacked siege equipment, stood the chance of operating there on a prolonged campaign.
Whew! These are getting long. If we keep up this debate, I'm going to have to publish a book.