Say that, with whatever POD you think is most appropriate, the Byzantine Empire doesn't collapse, and in 1453 is in a reasonably stable condition and controls most of modern-day Greece and Turkey. Assuming that the rest of Europe develops more-or-less as IOTL -- i.e., the Renaissance still happens, as do the Reformation and the Enlightenment -- how do you think the Byzantine Empire would develop? Would they end up stagnating like IOTL's Ottoman Empire, or would having a religion and culture more similar to the West's make them more likely to adopt and adapt to new Western ideas and technologies? What would their attitude to their Muslim neighbours be like, and how far could they expand, if that is they wanted to? And come the age of exploration, would we see the Byzantines trying to set up trading posts and colonies in distant lands?