or like byzantins theologist who argued about the properties of angels, when the turkish empire was at their gates.
Not sure what that refers to specifically, but here’s a fun fact: The Turks didn’t just conquer Constantinople suddenly in 1453 and that was all. The conflict between the Byzantines and the Turks (either Seljuks or Ottomans) had lasted in some form for about 400 years by then. Even if we just look at the Ottomans, it took 150 years between Osman’s founding of the then-tiny empire and the Ottomans finally conquering Constantinople.
During that time, the relations between the Byzantines/Greeks and the Ottomans/Turks were actually rather complicated and fluid. Yes, they did fight, but at times they also cooperated. Furthermore, there were no simple sides there: it was actually rather common for there to be dynastic infighting and rebellions within each ‘side’, oftentimes resulting in, say, a Byzantine emperor or pretendent to the throne calling in the Ottomans to help him deal with his Byzantine opponents, in return for some benefit for the Ottomans.
There were many such moments, one of the most interesting being when a son of the Byzantine emperor and a son of the Ottoman sultan teamed up together to try deposing their ruling fathers! (They failed, though. The sultan then said he’d execute his son, and asked the emperor to do the same with his own. The emperor, though, IIRC just blinded his son on one eye, which later backfired when his son rebelled again).