I've been too busy to comment, I'm afraid. So here's my explanation.
The Caliphates had a strong intellectual tradition, as most freeish societies do, but most of its contributions were in math and institutions like universities, less in science and especially not engineering. Why not? They had editions of Hero of Alexandria - why not try aeleopiles themselves, to try pushing them beyond toy status? Why not mature early eyeglasses on the scene? Why not develop Kepler's Laws, and then Newton's as generalizations?
The only explanation I can think of that seems to fit the facts is that the scientific method - the mental habit of looking at facts before faith - had been lost since a century after the Roman Republic fell - with Hero of Alexandria having been the last great area scientist/engineer for a long time. Unchecked monarchies have a long history of hostility to technological advance, and the Roman Empire was no different.
The scientific method's been invented in several times and places. The first invention for which documentation persists was in Classical Greece - and that mostly in its results of several fields being creasted or revolutionized quickly, like astronomy, geometry, mapmaking, and our favorite history. I'd guess it also probably also happened in the Indian subcontinent and East Asia, at the least, but records in both places have been censored or destroyed.
That wiki page rather supports my case. It says Alhazen invented the scientific method - though, really, he was reinventing it. But, I'm thinking Alhazen must've sadly failed to convert many of his contemporaries, though, or physics and steam engines would've been far earlier. Maybe it's because he only had two students.