My surname, Muir, is Celtic, but three of my four grandparents were born with Anglo-Saxon surnames: Smith, Pearson and Marshall. I therefore assumed I was one quarter Celtic, three-quarters Anglo-Saxon.
Recently, I discovered that after the Battle of Culloden, many Scots changed their surnames to Smith to escape persecution. This is one of the reasons why Smith is the most common surname in Scotland.
So I could be half Celtic, or more if some changed their names to Pearson or Marshall for the sake of variety.
Those who kept the surname, Muir, must have been living so obscurely that nobody bothered them, fought for the winning side, or were too stubborn to change.
When DNA testing kits are sold for about £10 at Lidl, I will have to test myself to see just how Celtic I am.
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Ancestry Update
Many years ago, I fell into conversation with some Austrians in Jugoslavia, before it became Croatia. I explained that I was wearing a shirt and trousers while everyone else was in T shirts and shorts because I tanned unevenly, developing dark patches on my arms and shoulders. One of the Austrians nodded and said, "Vikinger problem".I have discovered that he was probably right. I assumed that "Pearson" was an Anglo-Saxon name, but it turns out that the "Son" suffix is Viking. So as well as being descended from Celts, Anglo-Saxons and the unrecorded people who had rhesus negative blood, I am part Viking. Oh, well, the more the merrier. Hybrid vigour and all that sort of thing.
But most people in the British Isles can say the same, and if you go back far enough, we are all originally Africans. Some researchers believe that all us Europeans have a bit of Neanderthal in us as well. So we should regard the memory of the Neanderthals with a bit more respect, rather than thinking of them as a bunch of idiots.