Are you saying that China isn't a civ because economic centres move from time to time? I'm also fairly sure you're not quite characterizing either western or eastern fairly during the years 0 to ~1500.
What is Chinese Culture? If nothing else, the writing system? Putonghua was only adopted in all of current China under Mao.
I could also talk of the "western culture" and take Sanskrit and all indu-germanic languages that are descendant from it - so basically nearly all of the European languages" as "one culture".
I don't know a lot about the specific languages of either the "cultures" you mentioned, but you'd have to assert that culture didn't exist before writing for writing to be the definition of culture. That's not supported in cultural anthropology or history and is a bit contrived, perhaps unless your view is only that of a cunning linguist ;)
I could also talk of the "western culture" and take Sanskrit and all indu-germanic languages that are descendant from it - so basically nearly all of the European languages" as "one culture".