I just heard a fascinating talk by Enrico Spolaore of this paper on what predicts local growth rates over the very long run. He considers three periods: before the farming revolution, from farming to 1500, and from 1500 to today. The results:
More like the Persians living under Arab rule and even that had ended in the 13th century (destruction of Baghdad). Sadly the scientists in Bagdad never got the resources and support they needed to actually change their societies.
Before Galileo science was largely the business of Arabs.
Science (for the post 1500 era): Galileo, Newton, Lavoisier, Euler, Gauss, Maxwell, Einstein, Planck, they all lived in one particular part of the world where (some) smart people had the opportunity and were allowed to engage in real science and not only did other parts of the world have virtually no scientists, they barely even copied the knowledge of European scientists. Find out why that happened (probably something cultural, like the age of enlightenment, but also the competition between the many small European states) and you will know why European culture dominates the world today.