But cultures have not been known to adopt Christianity, Islam, or any other particular religion which has been developed elsewhere, independent of contact with carriers of that religion.
if you define "science" as carrying on in the tradition of Bacon, sure. But that didn't stop the greeks from making the antikythera device long before he existed. Astronomy has been independently discovered by druids, mesoamerican cultures, the far east, and countless others where "independent" is more vague. If you consider "science" as a process of invention as well as research and discovery there are also tons of examples in eg http://en.wikipedia.org/wiki/History_of_science_and_technology_in_China#Magnetism_and_metallurgy ... (read more)
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.