Okay, so reading back.. everyone is thinking way, way too early.
"Modern science" in the sense of the materialist, empiricist method we use today, in the sense of having people who are scientists and who specialise in a field and whose entire job is to advance material understanding of the world is extremely recent. Like, a couple of centuries old at best. Before that, science is very, very different. Heck, let me give a few examples of scientific beliefs which were common in early modern Europe, and which illustrate weird features of early modern scientific thought.
In the sixteenth century, most literate people believed that women possessed the same sexual organs as men which had simply failed to manifest externally due to the body itself not having enough energy (or "vital heat"). This was not a common belief in the medieval period, but became increasingly popular as the church ban on dissections were relaxed and people started looking inside corpses. The reason was that people thought the reproductive organs of men and women looked visually similar when dissected, and therefore they must be the same (the law of resemblances). Weirdly, this remained the conventional medical opinion until the end of the 18th century.
This also shows another thing which was commonly believed well into the 19th century, that unseen forces or life energies could influence how things worked. For example, in the early 19th century many doctors and medical scientists believed that masturbation would make men ill, because their bodies had a finite supply of energy which losing semen would exhaust (vitalism)
For most of 19th century, it was considered entirely normal for a scientist to use their emotions or feelings as evidence, because feelings were thought to come from a kind of inherent sensitivity to the world (sentimentalism). For example, one Swiss-American evolutionist (Louis Agassiz) appears to have based a large part of his theory of human evolution on his experience of getting creeped out by his first meeting with a black person. This also manifested in the common belief that statements which were persuasive were more likely to be true, because the persuasiveness came from an interior emotional sensitivity to the truth.
So no. European science, and actually for the most part European technological superiority, is a fairly recent thing. It certainly can't be traced all the way back to the late medieval period or the feudal system, or even to the age of discovery or the renaissance. Until very recently, a lot of the conclusions produced by European science were complete rubbish, because the means by which they were derived were incredibly flawed.
Okay. So let's assume we're not talking about science, but rather about power. Because that's what we're really seeking to explain here, isn't it. How did Europeans achieve global dominance?
The answer is that noone definitively knows. There are many theories, but one thing we can almost completely rule out is technological determinism. Europeans did not become globally dominant because they had superior technology. It isn't because they had guns and non-Europeans didn't, for example, because wherever Europeans went they sold their guns. Guns were very quickly adopted by virtually every society which had even the slightest contact with Europeans. Likewise, it isn't just because they had printing presses. There were printing presses in China too.
Weirdly, one of the few possibilities for a technologically determinant explanation is eyeglasses, because glasses are one of the few pre-nineteenth century European inventions which did not also exist elsewhere. It might sound silly, but think about it.. with glasses, people could carry on reading well into old age, which meant they could effectively double the time they were able to be intellectually active throughout their lives.
But no, I'm not saying it's eyeglasses. I think the far more likely theory is the development of a stadial consciousness of time, which is not a technological development at all but rather a change in mentality.
Basically, in late medieval and early modern Europe you have these two horrendous events. The black death, and then the wars of religion. The latter in particular is, relative to the population size, the most destructive event in European history. Millions of people are massacred in wars and civil unrest between Catholics and Protestants. It is, essentially, like a nuclear war happening today, and like a nuclear war it destroys a lot of the institutions and culture which held the old order together. So what happens, after the wars of religion is that people have to start building a new society, and more importantly they have to start building a new kind of society, one which isn't going to be perpetually warring over religious differences. So you need new institutions, you need new ideas, you need new forms of government. Essentially, the old world has failed, and people start developing their sense that they're living in a new period of time, a time when everything is different before and where the old rules no longer apply.
That sense of being at a particular point in time which is unprecedented, of having a sense that the future and the past are different and that one is at the point of moving between them rather than simply repeating what your parents did before you is the essence of modernity. It's what it means for us to say we are "modern" people, because we live in a time which is different from the past. It's also immensely enabling, because it means you are no longer bound to the past. It's no longer necessary to keep doing the same things because they've always been done. If there's a better way of doing something, you can do that instead.
