(What does OP mean by "White Europe"? What will the academics in the replies take it to mean? Of course, they will take "White Europe" to mean the most extreme and uncharitable thing possible.)
The main response, from /u/Kelpie-Cat, is remarkable for the way in which it insists on reifying and prioritizing "non-white" racial categories, including in biological terms, while absolutely minimizing "European" as a category.
But how does any of this disprove the notion of "White Europe"? (Still unanswered: What exactly *does* /u/Kelpie-Cat think she was disproving? What is "White Europe" to her?) Are we supposed to believe that these merchants, diplomats, and slaves were the majority anywhere?
It's well-established that there was a long-term presence of European merchants in medieval China. Would anyone have the gall to say this "disproved" the "myth of an Asian China"?
No evidence is offered as to why these particular individuals found in England must be assumed to be of black African origin, or why it would have been any more likely in the Middle Ages when the vast majority of North Africans are not black today, either.
And all this from the an Anglo-Saxon's casual mention of "Huns" as some of the ancestors of the Anglo-Saxons. No matter that the Huns were likely a multiethnic confederation, no matter that we must be skeptical of the usage of such a charged ethnonym as "Hun".
(Notice how she carefully avoided saying "Anglo-Saxon" in the post above, instead opting for the potentially confusing and probably even more ahistorical "early English"?)
When dealing with words like "Anglo-Saxon", we must tread ever so carefully. But when trying to maximally read the presence of phenotypically black African and Asian people into medieval European history, throw caution to the wind—make those assumptions!
/u/Kelpie-Cat invites us to speculate on how we would perceive the phenotypes of putative Africans and Asians in medieval Europe—not considering that, perhaps, if we stepped into medieval Europe, almost all of the phenotypes we encountered we would "perceive as"... European?
In the end, /u/Kelpie-Cat does not make her argument clear, unless she really is just knocking down the strawman of "there were literally no non-Europeans in medieval Europe".
I believe the actual object of /u/Kelpie-Cat's argument, which she refrains from making explicit to avoid sounding absurd, is that there were so many non-Europeans in medieval Europe that no amount of non-European casting in a historical TV series could be regarded as inaccurate.
Since that was, of course, the context of OP's question—the casting of movies and TV shows.
For the illiterates encountering this thread: No, I am not mad at the user for correctly stating that there were, in fact, non-European people in medieval Europe. I am questioning her claim that these examples prove that "White Europe is a myth".
I am also highlighting the motivated and racialized assumptions she makes at various points—the very type of reasoning used by some 19th-century scholars to read their preferred racial narrative into various historical cultures, which is harshly criticized by historians today.
Namely, pleading with the reader to read all evidence in a manner that is "slanted" towards or against a particular racial group.
Human remains show evidence of geographic origin in North Africa? Well, we should remember that there were black people in North Africa. So we must take it as a "possibility" that they were black. Why we are to focus on this possibility over other, more likely ones is not clear.
A chronicler claimed that the Anglo-Saxons partially descend from Huns? Well, first we will give complete credibility to this statement. Then since Huns come from Asia, we will suppose that some of those who might have reached Britain "could be cast by an Asian actor today."
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