Actually, my philosophy teacher had an interesting slant on this one, which may even have something to do with it.
The reason Europe dominated the world was the Holy Roman Empire, or in a more general sense, Christianity.
WAIT! Don’t scream yet. Listen to the logic. It’s really rather fascinating.
In ancient Greece, they invented many devices similar to things Europe produced just before the industrial revolution. But in Greece, they never used them. They built it, said, “My, how interesting,” then shoved it into the Alexandrian Library and left it.
The reason Greece (and, by extension, many Eastern cultures) didn’t advance as quickly as the West is because of how the religion worked.
In the East, and Greece, the whole worldview was based on a cyclical view of things. In some areas, it was reincarnation, in others, like Greece, simply a feeling that “if it was good enough for our fathers, it is good enough for us”. The Christian world-view, though, is a line. We start at a point here, with original sin, and we are GOING to this point, redemption. Everything in between is the history of the world, as well as, on a smaller scale, personal life.
The point is that because of this, the Western, primarily Christian world, had the idea that advance is good. It is the DUTY of each generation to be better than the last one. In the Eastern culture, it’s the duty of each generation to copy the one before, to keep everything static. In the extreme form, this turns into the rigid caste system where you are born to your station and can never leave it.
In short, Europe dominated the world because they thought new ideas were a wonderful thing that should be encouraged, while many of the rest of the cultural centers were basically apathetic towards technology.