Edward Said would have a heart attack at the way this thread's gone. Everything's there: the "essential unchanging" Chinese
The Chinese see themselves as essential and unchanging in many respects.
The Chinese themselves use premodern history to think about strategy and politics.
The Chinese see China as a single, continuous entity, and it is more true than it is for most other nations.
Right now the Indian and Chinese economies are somewhat complementary but as India moves into manufacturing and China moves into services that may become less so in the future. There will be more trade and growth, however. And economic competition won't necessarily translate into political confrontation. Both sides know there is too much to lose from a confrontation.
The one complicating factor is Pakistan. Everyone is worried about Pakistan becoming a failed state. I wonder if China would ever allow itself to get dragged into a conflict over Pakistan.