Last week I posed the mystery of why the Great Wall of China was so small at the top of the hills but so large at the bottom. Anyone can jump right onto it at the top. Where Europeans built castles designed to keep even a single attacker out, something else was going on with this Wall. Lots of people took up the challenge to think of something and the answer you will see below has pretty much been given by several contributors.
Before giving you an answer, let me admit right here that it is actually hard to find out what the ‘official answer’ is. Mainly this is because the true deliberations are based on strategic assessments that, even in China, are not usually part of open debate: they are usually unrecorded. The interpretation of later historians is just an informed guess, often tainted by the wish to glorify this or that commander, or, if the interpretations come from memoirs or writings by the military commander itself, by political and self-esteem considerations. As Tolstoy (not Dostoyevsky as a reader helpfully reminded me of!) and Von Clausewitz pointed out, the reality of war and the real considerations are a million miles away from how most military writers depict them. So as far as I am concerned, there is no ‘official’ answer (apart from the obvious throw-away answers that this was how the architects designed it), merely answers with different levels of plausibility.
Mainly, the Wall seems designed to keep out horses, not people, and to itself serve as a road to move troops between different segments of the wall. The main purpose of fortifications half-way up hills was then to make it hard for a large group of foot soldiers to go over the wall and overtake the garrisons at the gate in order to open it up for horses. At the top of steep hills, where horses could not come anyway, all this Wall was for was to move foot soldiers and building material around, much like you use the previous bits of a railway track to build the next bit.
The deeper question is why it was sufficient to stop horses. Mainly it was a matter of mobilisation: the Chinese empire had many more people in it than the Mongols (easily a 100:1 advantage in terms of total population), but the overwhelming majority of the Chinese were farmers whilst the Mongols were with their horses all the time and could assemble in larger numbers unnoticed by the Chinese.
Was there no standing army large enough to repel invaders? Yes, there was a large standing army but it had many duties. The standing Chinese imperial army was now and then stretched to its limits in quelling uprisings or in battles with other imperial factions, so it often occurred that the centres of power (such as the forbidden city) had limited standing protection. And of course there was a lot of Wall to guard.
So yes, once alerted, the military might of the Empire was immense as tens of millions of farmers could be mobilised into troops (and Wall builders!) within a few weeks and months. So the Chinese did not have to fear a slow invasion by all the Mongols. Similarly, they did not need to fear Mongols on foot as they were much less of a threat than Mongols on horses, so it did not matter much if some Mongols would scale the hills and jumped over the short Wall there: without horses they could not quickly reach something critical, nor bring back their loot.
Yet, an invasion by a mobile cavelry like that of the Mongols could at times have decapitated the Chinese Empire before it had time to mobilise. And once you control a bureaucracy like the Chinese, you dont need to fear mobilisation and can enjoy the fat of the land. Just read what Kublai Khan (descendant of the most successful Mongol raid ever) was up to in China with all the pleasure houses he got them to build for him and you will realise what China had to offer the Mongols. What goes for massive invasions also goes for less ambitious raids, in which smaller bands of horse-riding Mongols would sweep in and steal something of value (women and luxury goods).
So the strategic situation for a long time was one whereby the Chinese had enough of a standing army to station large numbers of guards at the foots of the hills of this Great Wall, i.e. where there were gates, but not enough to continuously guard all parts of the Wall such that no-one on foot could come in or to repel a concentrated mass-attack. Yet, the Wall meant that even any large attack would be slowed down considerably. Even if a garrison would be overwhelmed, it could collapse part of the Wall to make the gates useless or to prevent the Wall itself from being used as a road. Given that respite, the Mongols would face overwhelming numbers once they finally managed to come in with their horses.
So the answer involves a bit of military strategy, a bit of economics (pastoralist Mongols versus peasant Chinese), and a bit of technology.
Champagne to the many who clearly said the same thing last week. Diet water for the rest.