Was Byzantium a continuation of the Roman Empire, or was it a whole new political entity?

1) During the late Roman Empire and the late antiquity of the Byzantine Empire, Christianity as we know it took recognizable form through endless debate and much political force. Based upon your readings about the numerous controversies outlined in the text, how do you think Christianity by the year 600 or so differed from the original little movement in Roman Judea, and how recognizable would the great religious divisions within Christianity today be to those early Christian-movement Jews who still practiced circumcision, Jewish dietary laws, and worshipped in the synagogues after the crucifixion of their leader?

2) Was Byzantium a continuation of the Roman Empire, or was it a whole new political entity?

3) The word ‘iconoclasm’ has survived to this day to describe people who smash the traditions of the past. The iconoclasts of Byzantium smashed cherished traditions when they smashed the icons of Christian worship. What kinds of iconoclastic behavior do we see in our own culture?

4) Islam was born in the same part of the world as Judaism and Christianity, and yet we seldom view it as a “Western” religion. Why is this? (Is there no way that the three major religions of the West can cohabit without endless violence?) Your thoughts are most welcome.