I was watching a documentary on whether Zheng He's Chinese fleet discovered the world in 1421 (http://www.1421.tv/). I haven't read the book (but Amar may have) so can't really do a full blown review, just some thoughts instead.
It seems that everyone agrees that the fleet sailed to countries around the Indian Ocean, including possibly the northern tip of Australia. Gavin Menzies says the Chinese discovered the Americas, the Arctic ocean and Antarctica as well as circumnavigating the world. Now, if the Chinese were really visiting all those places, then why didn't they burge into the English Channel?
Actually, suppose Menzies is just a hack, and the accepted history is the truth - that the Eunuch Admiral's fleet sailed around the Indian Ocean and then went home. This still begs the question: why didn't they kick some Firangi arse after they sailed around the Cape of Good Hope?
I was at a talk by Angus Maddison the other day, and somebody asked a variation of the same question: why didn't the Chinese colonise Malindi or Ceylon (in the Emerald Island they did kick some arse, but then left)? Maddison's view is that the Chinese weren't particularly interested in dominating other countries.
Over the drinks after the talk, we discussed what the rise of China might mean for international politics. Perhaps the rise of China might not mean war with the US the way rise of Germany or Japan resulted in wars with the UK because the Chinese aren't as aggressive (of course, the Americans might just push China into a war - everyone agreed this was quite possible). Perhaps, after all, instead of just taking Aksai Chin and withdrawing from NEFA, the Chinese could have marched on to Calcutta and install a friendly communist government, but chose not to.