To return to Orthodox Christianity, it was not just because Constantinople was at the center of the empire that Byzantines thought it had a special relationship with God. Its power was derived from the sheer number of churches and relics present in the city, which in turn represented an enormous amount of potentia (holy power). Byzantines believed that God oversaw Constantinople and that the Virgin Mary interceded before God on the behalf of the city. Many priests taught that Constantinople was the New Jerusalem that would be at the center of events during the second coming of Christ, rather than the actual Jerusalem(!).
The piety of the empire sometimes undermined secular learning, however. Over time, the church grew increasingly suspicious of learning that did not have either center on the Bible and religious instruction or have direct practical applications in crafts or engineering. Thus, there was a marked decline in scholarship throughout the empire. Eventually, the whole body of ancient Greek learning was concentrated in a small academic elite in Constantinople and a few other important Greek cities. What was later regarded as the founding body of thought of Western Civilization - ancient Greek philosophy and literature - was thus largely analyzed, translated, and recopied outside of Greece itself in the Arab kingdoms of the Middle Ages. Likewise, almost no one in Byzantium understood Latin well by the ninth century, so even Justinian’s law code was almost always referenced in a simplified Greek translation.
This was a period in which, in both the Arab kingdoms and in Byzantium, there was a bewildering mixture of language, place of origin, and religious affiliation. For example, a Christian in Syria, a subject of the Muslim Arab kingdoms by the eighth century, would be unable to speak to a Byzantine Christian, nor would she be welcomed in Constantinople since she was probably a Monophysite Christian (one of the many Christian heresies, at least from the Orthodox perspective) instead of an Orthodox one. Likewise, men in her family might find themselves enlisted to fight against Byzantium despite their Christian faith, with political allegiances outweighing religious ones.