A few months ago, when searching for some information I found a reference to one of my ancestors on a site called Royal Blood. Royal Blood was a site that claimed to list people who can trace their ancestry to European Royalty, in particular Charlemagne the Great - Holy Roman Emperor (742-814).1
The ancestor I was searching for information about was “William Dawtrey” who was my 12th great grandfather.
According to Royal Blood, William Dawtrey married Margaret Roper (who would therefore be my 12th great grandmother) and she was identified as the 22nd great grandchild of Charlemagne.
This would make Charlemagne my 36th great grandfather.
Now, I don’t trust all the information in this site but it set my math brain thinking.
I have 2 parents, 4 grandparents, 8 great grandparents, 16 great great grandparents - which in binary is 21, 22, 23, 24.
Taking this further this would mean I should have 238 36th great grandparents.
As a computer programmer I know that this is a very big number - after all 232 is 4 billion.2 Well 238 is over 274 billion.
It is thought that the world’s population first exceded 1 billion in ~ 1800, and Europe’s population was less than 80 million in the 8th century.3
So given that the math says I should have 274 billion possible 36th great grandparents - even accounting for the fact that cousins and second cousins often married - the mathematical odds that Charlemagne is NOT my ancestor (or yours if you are of Western European descent) is quite slim.
The only challenge is proving it!!