This is what I don't understand. The Great Wall is over 5,000 miles long. Surely it would have been a nightmare to defend?

Firstly, how many troops would be needed to constantly man the wall? Some rough calculations I did is that, even if you had 100,000 men constantly on the wall, presumably a huge amount of troops for the time, you'd still only have one soldier every 80-100 metres (on average). This doesn't seem enough. Surely attacking armies can simply concentrate a force and overwhelm the few troops within a few miles.

Secondly, even if it were to be effectively manned, this just spreads your army thin, doesn't it? If an attacker concentrated their force onto one part of the wall, it would be far too long to communicate to other parts to redistribute forces. Any breach would be unknown by troops on the other side of the wall for days, or even weeks, meanwhile the attacking army is pillaging its way across the countryside to the capital.

My knowledge of ancient far-eastern military tactics is lacking, but I simply don't see a wall of that length as being logistically useful as a defensive structure. Surely it would be pointless, and a simple single mobile force would be better?