Well then, here is my continued discussion.
I think it was just a lack of powerful cultures present in the Scientific world. Any strong civilization follows the advancements in Science, there is no question about that, and the Islamic nations were no different. It is just basic human psyche. You get knowledge, as well as power and prestige. Science allows better war tactics, more methods to improve the economy, and a way to simply state your people to be more advanced for than anyone else, which is a thing in its own right.
The thing is, most centres of intellect were under Muslim influence, Spain, southern Italy, Persia, etc. Byzantium was already doing good in science, and I don't think it was that far behind, as it was also under political problems of Muslim expansion. The Catholic world, I think, was simply too politically disconnected from these areas, especially the Mediteranean. Most of the Catholic world, at least in that time period, primarily sprung up from Charlemagne's world, which was mostly based in Northern Europe. This area, I feel, just like the Russian plains and the Viking world, were not close enough for trade links to be set up, especially after the fall of Rome. It took time for ideas to seep in, which happened in the 16th century.
The papacy as well, did not try to advance scientific ideas, and the ideas of one simple group affected Europe in such a way, that the implications were long lasting. Also, I think, that how the clergy tried to be overly isolationist, contributed to this, such as monkhood, abstaining from marriage, they were separating themselves from this world too much. The head of the Islamic religion, was usually the most powerful feudal empire, and this made the religious authorities, give patronage to something that would help them. So the Catholic world was mostly based in areas that weren't so near the rest of civilization, and was too unified by the clergy and the kings. The entire dark age period helped this time of falling behind. It wasn't some overly complicated story, just a simple fold of history that took an era down with it.
As I said, what other civilization was there after Greco-Roman times? India was good, Byzantium was good, China was good, Islamdon (or something) was good, even Mediteranean Christian realms were good, such as Normal Scicily. The only nations behind were those in Northern Europe, which were just down on their time due to a few things.
Secondly, we come to the coherence between Science and Religion. I don't perceive religion by itself as against this method. Yes, religion deals in the absolute, but science also seeks to discover the absolute. The thing is, how much that religion uses statements that relate to science. The Bible, I believe, is too down-to-earth in its statements. It is somewhat hard to explain, but I think it is the writing style. The Bible simply states, the age of the earth, and the age of this, and the age of that. The Quran isn't like that, it doesn't simply tell us all the answers, like how to make a 4D dimension from virtual simulators. It is more free flowing, there is more natural discovery. It gives you the perspective of learning, finding out the answers. So do other scriptures, especially the Vedic ones. I feel they are written so you feel more closer to them. Like this is a sign, that is a sign, study it, and stuff.
If scientific knowledge was revealed to the Arabs, they would simply be mind blown and turn away. So you can call it a more timeless book. It is a great mixture between past and present, and eternity. It is more like a challenge, that combines the absolute with its study. Such as this:
"And We made the sky a protected ceiling, but they, from its signs, are turning away." (Quran 21: 32)
It isn't that apparent, but the more we study in science, the more it compliments the religion. It is aided, scientific discovery. How can you be a skeptic over that, there isn't anything that's wrong, in any science. But the more you study the sign, it hits you. What it means. The atmosphere protects us from radiation! The Quran simply speaks in a poetic, truthful manner, that tells you to learn about God's signs.
The very first revealed Quranic verses, amplify this chain of thought the most.
"Read! In the Name of your Lord Who has created (all that exists)… He has taught man that which he knew not." (Quran 96:1-5)