I have just finished reading a short history of Byzantium and it has left me with a lot of 'what if' questions. To name one, what if the Crusades never happened? To my mind there is nothing inherent in Christianity that would produce vast military expeditions to fight the Saracen. It's not like the kingdoms of Christendom were ever really on good terms with each other given all the wars between them. So here's the question: If there are no crusades does this ultimately help Byzantium last longer? Remember that the while the crusaders did found some states in formerly Muslim lands for a time, they also sacked Constantinople, and generally were a problem while they traveled through the Empire. Heck, they even took control of Constantinople for a over have a century.
Part of me admires Byzantium and would want to construct a timeline where they are more victorious. But a part of me would be curious about the opposite outcome. For example, what if Constantinople fell to the Caliphate in the 8th century instead of the Turks in the 15th? Byzantium was a strangely long-lived civilization as it was. This question might be impossible given the butterflies involved but would you rather live in a world where Byzantium lasted longer, perhaps without the Crusades and the disaster at Manzikert or would you rather live in a world where the seemingly invincible armies of Dar al Islam crushed Byzantium just as they did to the Sassanid Empire?