Just a few points I'd like to throw out there before I pack it in for the evening:
1) "Trouble is, a trawl of sci-fi fans and wargamers rarely results in a crop of historians. So most of us are arguing from a pretty incomplete recollection of what is (at best) a very patchy body of evidence to begin with..." (orginally posted by Rigelian) No need to be modest, you all are making some great historical points (even you Fyron
)
2) If you're interested in the impact of non-Western influences on modern science, check out Dick Teresi's "Lost Discoveries: The Ancient Roots of Modern Science - From the Babylonians to the Maya" I haven't gotten to it quite yet - too much other stuff to read at the moment - but I'm looking forward to reading it over the summer.
3) Yes, the Ancients were in many ways more advanced in science than their Medieval successors - thus the importance of the Renaissance rediscovery (in the Near East) of texts lost after the decline of Rome. Just a few examples:
Hipparchus of Nicea (196-126 BCE) calculated the Lunar month at 29 days, 12 hours, 44 minutes, 3 1/3 seconds (less than a minute off our current calculation). He also calculated the year within 6.5 minutes.
Aristarchus of Samos (310-230 BCE) proposed that the sun is the center of the cosmos, and that the Earth and other planets circle the sun. Copernicus knew of Aristarchus' idea - it wasn't original to Copernicus.
Eratosthenes of Alexandria (276-196 BCE), librarian at Alexandria, calculated (using sundials and wells in Egypt) the circumference of the Earth to within 200 miles. He was one of the first to suggest the possibility of sailing west to get to the East.
Tying that into our main argument, it's not necessarily bad to hold on to old authorities, because they can be useful. So, the copying of ancient texts, while it did promote perhaps an overzealous devotion to them, was an important Medieval function of the RCC.
Why, then, didn't the Medieval period continue to expand on the work of the Ancients? Conditions just weren't there for it. Philosophizing - and that's what science was until recently - takes free time. There were really only two Groups of people in the Medieval period who had the time to contemplate the universe - the clergy and the nobles.
The clergy sought answers that agreed with the Ancients and their theology. The nobles were too busy fighting to think of much else (with some exceptions, of course). It wasn't until Europeans got wealthy again (in the Renaissance) that they could afford to patronize someone to investigate the heavens on a regular basis. Therefore, I would argue, it was the basic underlying socio-economic structure of feudalism - not the intellectual rigidness of the RCC - that slowed scientific advancement.
PS For those who are interested in sources
all my information comes from Judith G. Coffin, et al.
Western Civilizations volume I.