Since antiquity Europe has been the world's center of technological, educational, and social development. I know there were developed societies in Asia and the Americas that predate European exploration but it is undeniable that by the end of the Middle Ages Europeans were far more advanced than any other group.

That's quite a sweeping statement, one which not many historians would agree with. It conjures up images of a Sid Meier's Civilization-type tech tree in which "Europe" is an era ahead of everyone else. This is not how history works. There is not a single path of development, and there is not a single end-point ("future tech"). Simply stating that Europeans were more advanced is a disservice to the innovations and developments of other cultures. It almost reeks of racism, with - only slightly exaggerated - superior Europeans showing the stupid others how things should be done. Furthermore, your reasoning ignores how European nations spread their power; they often did so with the help of locals, using a divide-and-conquer strategy. There is no technological superiority needed for that.

In short, your premise is deeply flawed, to the point where it would be very difficult to answer your question.