I got pulled up by the mods earlier for asking this question in a way that I thought was humorous but which they found distinctly unfunny. Hopefully it'll not rile the mods this time. Any political incorrectness reflected in this question should be attributed to naivete and not malice - I hope you'll let me edit the question than outright remove it.
Let me get to the point. We live in a world dominated by artefacts of Western origin. I am not a historian so I may be way off the mark here, but most of the intellectual underpinnings of these things (which range from technological products to ideas such as democracy, socialism and liberty to entire fields such as modern Science and Mathematics) I think can be traced to have originated in the past 600 years of history in Europe. Not that they didn't exist in some form or the other in other cultures till then, but the pace of production of discoveries and ideas took off at an unprecedented rate in Europe starting from 1500s or so. We're still living in the shadow of this explosive growth of Western civilization.
My question is, what are the distinct philosophical positions or cultural attitudes of the West, i.e., what was in the cultural and intellectual DNA of the West, that caused this Cambrian explosion of ideas to happen specifically there, and not elsewhere?
Or is that even a wrong question to ask?
Perhaps this is the wrong question to ask, because both ancient Greeks and medieval Muslims engaged in studies which are recognizably scientific, and which were in fact the precursors of modern science. However, clearly science did develop differently in Europe than it did elsewhere in early modernity, so I'll give it a shot.
In this answer I'm relying heavily on Richard H Jones's "For the Glory of God," which revolves around the question of the development of modern science. Jones's argument is primarily negative: he argues that for many years debate over the origin of modern science has centered around what's known as the "dependency thesis," which argued that core Christian theological beliefs were the root of Western science. Advocates of the dependency thesis argue that Christianity postulated a benevolent, rational creator God who controlled the world, laying the groundwork for a belief in the clockwork universe -- a place in which cause and effect would reliably and consistently follow each other. Without a belief in God, there is no justification for an assumption that the universe is orderly; therefore, there is no justification for science. (This is related to Hume's argument that our idea of cause and effect is ultimately a result of custom, not rationality.) Christianity also features a linear sense of time and a natural world which exists on its own, without the ever-present influence of the divine.
However, Jones argues, I think convincingly, that there are substantial problems with that narrative. The dependency thesis ignores the absence of scientific exploration before the twelfth century, and it incorrectly places Christianity at the heart of the naturalistic doctrines described above. Instead, Jones writes, "Only after the introduction in the West in the 12th and 13th centuries of Greek thought as developed by Muslim natural philosophers did a 'new naturalism' become firmly planted -- one based on Plato's limitation of divine action to only the moment of creation" (16). Also, the dependency thesis argues without much justification that Christian scientists must have been scientists because they were Christian. Men like Francis Bacon and Isaac Newton were very religious and sought religious justification for their scientific work, but they weren't given theological marching orders.
So if Christianity wasn't responsible for the rise of science, what was? The biggest single cause is likely institutional support and the rise of the university in the 12th and 13th centuries. Independent centers of learning supported those with interest in natural philosophy and later science. In contrast, in the Muslim world, which had superior scientific and engineering achievements to those of the West in the 13th and 14th centuries, those kinds of institutions never formed, allowing conservative theology which opposed exploration of the natural world to dominate. Similarly, in China centers of higher education were tightly controlled by politicians who dissuaded scholars from scientific inquiry. Jones, then, essentially argues that it was the intellectual freedom created by the separation of the universities from the cathedral schools controlled by the church which allowed science to flourish. There are no doubt other substantial political and economic factors which influenced the development of science, but the key point to take away is that it was not an innate superiority of Western thinkers or of Christian culture which allowed science to flourish. In regard to natural philosophy and later science, European "cultural and intellectual DNA" were essentially borrowed from the Greeks, just like in the Islamic world.
People here seem to be saying that universities were the reason that scientific advancement took off, but that doesn't really satisfy me. The idea I hear is that wealthy people with lots of money = more time for learning and funding of education = science. However, why couldn't a place like China or an Indian kingdom do this (on a widespread scale) first? And this answer doesn't explain how the European mindset changed from spending money on stuff such as war and the church to investing in education.