from the 11th through early 16th century. There’s very little to distinguish what passed for science in Europe at the time from what had been going on in the Muslim world a few centuries earlier.
a) If this is so, then how was it that by 1500 already the Latin West was so far ahead of the House of Submission? Answer: study the logistic curve and note carefully its shape. Or watch a house being built. The initial phases seem to take forever with very little obvious change to a naive observer, while the final phases seem go lickety-split. But it might could be that laying a firm foundation is more important than the bells and whistles later added.
b) The muslim world in its early phase, before natural philosophy sputtered and died, can also be called the Eastern Christian world with such Christian centers of learning as Alexandria and Antioch and Constantinople. The House of Wisdom in old Baghdad was staffed and run by Nestorian Christians (e.g., Hunayn ibn Ishaq and his nephews) and the translation of Greek works into Arabic was facilitated by their earlier translation from Greek into Syriac. The East remained largely Christian for a long time: at the time of the “first crusade”, Egypt was still 50% Christian and Antioch was still both Greek and Christian. (Hence, Baybar’s massacre of Antioch.)
Of course, what lies in the distance often blurs together, so you may not discern the differences between what a handful of muslim faylasuf wrote in the teeth of societal opposition and what the Latin West did after the Volkerwanderungen came to an end. Meanwhile, the science of the 2010s seem vastly different from the science of say the 1970s. Being closer, we can pick out details. But “all that ancient stuff” looks pretty much the same.
One answer to your question can be found in Toby Huff’s book The Rise of Early Modern Science. The Latin West was the first society to embed the study of logic, reason, and the natural world into the society at large. Everywhere else we have brilliant individuals in isolated splendor, coming and going, but no societal interest. The Chinese had no word for “logic.” (Their current word is a borrowing from European languages.) And their term for “teaching” is the same term used to describe force-feeding a duck to make it fat and plump for Peking Duck.
A primary barrier was the inability to measure anything much beyond lengths and weights. Even mechanical clocks (a Latin West innovation) could measure time only in the broadest increments prior to the invention of the vernier. But a fruitful comparison could be made between the impact of the telescope in the Latin West (a Scientific Revolution) and its impact when taken to China, Mughal India, and the Osmanli Empire (nothing). Huff’s second book, Intellectual Curiosity, covers the history and importance of the look-glass.
+ + +