Byzantium: Does History Repeat Itself?

"The thing that has been is that which shall be." So said the great Greek historian Thucydides.
If Thucydides was right (or at least if I understand him correctly), this means history repeats itself; or at least historical patterns repeat themselves.
Given human nature, I find this believable. So why, then, do we never seem to learn from it? If we did, wouldn't that prevent a world of pain?
The answer to the second, rhetorical question clearly is "Yes." The answers to why we never seem to learn from it are multiple, I think.
First, we clearly are not as smart as we think we are. Otherwise the planet most likely would be in a better state. Second, we may be confused by the costume changes. I am only half frivolous about this. In our historical memory Romans look a lot different from Huns, who look a lot different from Edwardians. Things like this can be just enough to make us believe that the people in the costumes are doing different things, when in reality they are doing the same things underneath it all.
Then there are small but deadly ideas that get in the way--things like skin color or theology.
Especially theology.
It could be theology, more than anything else, that has prevented the average person from being taught anything about the Byzantine Empire. And it's too bad. This story is an important one. It is the tale of how, for century after century, the West was threatened by the rise of militant Islam. But it had a bulwark to the east--a Christian empire, originally a mighty one. Call it the Eastern Roman Empire, Romai, whatever. These days people who have heard of it at all generally call it the Byzantine Empire, or Byzantium. Lars Brownworth's book, "Lost To The West" provides a fascinating survey of its thousand-plus-year history, its culture, its 88 emperors, its military triumphs and defeats.
The threat of Islam arose, for both Byzantium and the West, as early as the late 7th century--during or soon after the life of Mohammed, the new faith's prophet. Both recognized the onslaught from the East as a threat to their way of life. Religion, or rather theology, kept them from working together as effectively as they might have. Indeed, at one point Crusaders from the Latin West overran Constantinople, the Byzantine capital, and weakened the Orthodox Christian eastern empire beyond possible recovery.
On Tuesday, May 29, 1453 Constantinople, the great, the storied, fell before the onslaught of Ottoman Turks. The Byzantine Empire was dead. It fell almost unaided in its hour of agony. Western Europe was left to cope with generations of Turkish incursions that swept as far west as the gates of Vienna.
Looking at Europe today, it seems--to me, at least--that the incursions of Islam have never really stopped.
How different might things have been if those long-ago Christians of the West and of the East had decided to throw away theological differences and unite against the common threat? Would history now be repeating itself, or at least seeming to do so?
We'll never know.