Thanks for explaining. I agree with you about the ascendancy of the West from around then and maybe up to now. But here is my problem. If you took out the Muslim contribution towards science (from that point) say, give or take, 800 years do you think we would be at the same level we are at now, higher or lower?
First of all, what you call "Muslim contribution towards science" I call "contribution towards science from people who happened to be Muslims". There is nothing inherently scientific about Islam, or Christianity, or most religions. But, as they turned out to be of extreme significance in the societies of the time, any progress was inevitably made by people with some connection to the prevailing faith.
Secondly, I'd like to turn the question on its head. There was certainly particularly one period of great scientific progress from the Muslim world, but dogmatic and fundamentalist religion vanquished it. If that progress had been allowed to continue, I believe the entire world would be both more secular and more advanced, and certainly the Muslim world.
To me, this and other examples, some recent such as stem cell research, signify that while religion doesn't always get in the way of science, when it does the consequences are invariably detrimental to science and progress.