In the ramping up of tensions between the Pentagon and North Korea, much is being made of China's supposed powerful influence over the Hermit Kingdom. We don't have much of a relationship with NK directly, but we do with China, and they have a strong relationship with NK, so if we pressure China, we can indirectly pressure NK.
The trouble with this argument is that China has rarely had control over the Korean Peninsula. Sure, they're the #1 destination by far for NK's exports, but by now we should know that economic sanctions rarely work, no matter how strong or how long, if the target is determined to resist.
What China would really need to have is geopolitical and military influence over NK. They do not. They don't even have a base in NK. Of course they have a larger and stronger military, but that's true for China and just about any other nation in the world, other than regional or super-powers. That doesn't mean those nations can be pushed around by China, or that they act as vassals of China.
And while China and NK have a history of Communism, so has China and the USSR -- and that didn't prevent the Sino-Soviet split. Just because they're ideological fellow travelers from the same rough part of the globe doesn't make the smaller one a satellite of the larger one. The closest European analogy would seem to be China as the USSR, NK as Yugoslavia, and SK as Greece.
In fact, when has China ever controlled Korea during its long history?
It turns out that it has only done so during one of its dynasties, the Han. China defeated what is now NK (though not SK) around 100 BC and left the Four Commanderies of Han, the principal and most enduring one being the Lelang Commandery, which was centered in what is now Pyongyang. Chinese rule lasted uncontested until roughly 100 AD, when the growing state of Goguryeo in northern Korea began chipping away at the Chinese presence until it was totally absorbed by 300.
That is the only long, stable period of Chinese control over Korea.
Northern Korea has been controlled by other states from mainland Northeast Asia, but they were not Chinese, even though some of them ruled over China as well as NK. They all belong to the nomadic Steppe empires that have flourished to the north of China for centuries -- Liao, Jurchen (Great Jin), and Mongol. And not all of these groups managed to conquer Korea if they also got China -- the Manchus ruled China from the 17th to 19th centuries, but did not get Korea.
China's first dynasty began around 1600 BC, so out of 3600 years it has only controlled NK for 200-400 of them, and even that was 2000 years ago.
Today's situation is the historical norm between China and NK. Expecting China to be able to pull on some puppet strings and have NK dancing however they want, at least in their geopolitical and military behavior, is writing a letter to Santa Claus.
The role of historical constraints on current foreign policy is not only unappreciated, it is not even thought of. See also: ignoring the long history of who has controlled who between Iraq and Iran. Since 500 BC, if the two were part of the same polity, Iran has always been the expanding power and Iraq the conquered power. Gee, what could possibly happen if we weaken the hell out of Iraq? Just maybe it will be Iran who fills the vacuum.
That is not to say that historical constraints are fixed forever. But it does require honesty about how unusual of a situation the Pentagon's plans are. Maybe they're well within historical norms, maybe they're mixed, maybe they're rare, and maybe they've never happened before. That has to be one of the first questions we ask when evaluating whether or not to proceed. Let's try to avoid what is a pipe dream from the perspective of thousands of years of history.