Much like what the Japanese did in the Meiji Era with European customs and economics.
True. But my point still stands- there is continuous cultural intermingling and inter-marriages. Why do people rule this out ? From total societerial perspective, this is what happened with the Byzantine-Turkish empire transition: The ethnic Turks gradually moved westwards, into Turkey over several centuries and they gradually absorbed most/many ethnic communities into their fold. There is evidence from Ottoman Turkish writings itself that there was considerable inter-marriage in society, as significant % of byzantines married into the Turks, especially since a significant % converted to Islam ( the protection to Orthodox church wasnt extended at first, so many Byzantines converted to Islam. Turks were Muslim at this point and Muslims rarely discriminate based on race on marriage issues- its usually limited to religion only). Yes, there were some killings, some tensions, etc. but most of anatolia was effectively converted(except for Armenia & Georgia, both kingdoms in the Caucasus back then & quite hard to control) and intermarriage was extensive. Particularly since most byzantines were fairly rich (having a settled & trade based civ for 1000+ years).
This makes it a common heritage- many turks today in reality are mixed byzantines, ( they wern't exactly Greeks- more like few Romans mixed with Greeks & anatolians- who at that time, from know history, were mix of Iranians, Greeks, Hittite & possible semetic tribes) atleast, in some part.
I am sure there are some 'pure-bred Turks' in Turkey but i am also fairly confident that if each person from Turkey today looked back atleast 30-40 generations(if they can, i doubt many can), they will find atleast some Byzantine descendence to the story. A lot of Ottoman art & architecture is directly influenced by Byzantine architecture- and stuff like that you don't just learn from mimicry or holding a slave army at swordpoint for X # of years.
Stuff like that is learnt when your people mix with ( live side by side, sometimes, marry into, etc) the conquered people over time. That is the vehicle of cultural exchange- intermingling.
All this 'ethnic nationalism' forgets one thing - we are all mixed people- nobody is 'pure' anything, unless you happened to be a tiny tribe stuck on some dot in the middle of the pacific for the last 10,000 years, that is, you somehow got there during low sea levels of ice-ages and then got stranded once sea level rose.
Its just a question of who mixed with whom and how far back our historical knowledge goes on cultural basis.
Look back far enough and you will find practically every major old world tribal/ethnic/cultural imprint.
Turkey's people should be proud of their Byzantine heritage really- and its rather saddening that there are some who'd define history so narrowly on who sat on the throne and who didn't to form an opinion on an entire society.
Rather saddening to see people deny a part of their identity & heritage for silly and weird reasons.