This is a line of thought I've been tinkering with a little bit. China shares quite a bit of history with the Muslim world. First of all, both of these are ancient civilizations, with quite a lot of cultural coherence. In recent history, since WWII, they have followed similar paths. Both civilizations see themselves as having lost out as a result of that war. China, after having being ravaged by Japan, watched as the US built Japan into a first-world country. Muslims, on the other hand, were not happy that problems originating from Europe resulted in the creation of Israel. So in both cases it was external influences that disrupted the balance of power, reigniting rifts between closely related cultures - the most dangerous kinds of rifts.

Both Chinese and Muslim culture are very different from the West - more different even than Russian culture. During the Cold War, they therefore lacked the background necessary to take Communism to its logical conclusion. So the US played them both off the Soviet Union, never committing itself to a head-on battle with either ideology. As a result, today both civilizations are too strong to fight on an ideological level, and they have to be negotiated with more on an item-by-item basis. It is unrealistic to expect the Chinese Communist government to fall, or suddenly change to a Western democracy. Likewise with the Muslim world, we will have to put up with political Islam, and maybe even tolerate some radical versions to a certain extent. The radicals seem to be the only people capable of exerting any leadership in the Muslim world, and changes can't be forced externally. At least according to this logic.

An example. In 2006 political Islam (the Islamic Courts Union) swept into Somalia. The US suspected al-Qaeda ties, and deposed of them, via Somalia. Now, the situation looks even more chaotic, making al-Qaeda incursions even more difficult to control. (The piracy problem might not be so serious now, but it could be a sign of things to come.) The thing is, the Islamists actually did manage to clean the place up, and bring the only peace in almost 2 decades to what the UN now calls the worst humanitarian emergency in the world. (More info here and here.) One wonders if it would have been possible to keep the ICU and work on moderating them, rather than eliminating the Muslim influence without any idea who else could keep order there.

There might be present applications for this line of thinking in places like Afghanistan and Pakistan. Also, it could be an effective communication strategy for decisions that have already been made in these areas. Of course, this is a very general way of thinking about things, and any conclusions should be taken with a heavy dose of common sense. How would anyone else apply this logic?