So, as the title implies, what and how would it take to make the Muslim world and Western world switch positions ? So the Muslim world (not to be called Muslim World, at least officially) would be as powerful as the Western world today, while Western World(not to be called Western World, but "Christian World"/"Frank World" instead. Unless you have a better name which would make things more interesting...) would be in a screwed position as much as the Muslim World today, both in relatively very much the same ways as their equivalent IOTL.