Why We Are All Descended From Royalty, According To Math

You! Yes, you there – did you know you’re related to Charlemagne? That’s right: you, a perfectly ordinary human being (no offense) without a kingdom or empire of your own, can trace back your ancestry to the Holy Roman Emperor himself, who was coronated on Christmas Day all the way back in the year 800 CE.

Well, you’re probably related to him, anyway, at least if you’re of European ancestry. Facts like this are not too surprising when you do the basic mathematics behind it, but whenever anything like this is mentioned in public, the media pick up on it. Understandably so, to be fair, because it’s initially hard to believe.

A BBC Documentary series named “Who Do You Think You Are?” recently featured a rather bemused human and actor by the name of Danny Dyer finding out that he was directly descended from the 14^th Century king Edward III.

Watching his brain explode in real time was quite fun to watch, but as geneticist, author, and science communication maestro Adam Rutherford pointed out at recently Chalke Farm History Festival, almost everyone born in the 1970s is a descendant of that very king. In fact, for his audience, it was a near-impossibility than none of them were of royal descent, at least in terms of that monarch.

^{The BAFTA-nominated moment in all its glory. BBC via YouTube}

So why is this? Well, fortunately, it’s not actually that complicated to explain. You, as a human, were presumably not created in a laboratory – we’d guess you had two parents that assembled you. Now, in that generation, you have two ancestors.

Each of your parents has two parents too, meaning in just two generations past, you have a total of 6 ancestors. Go a generation further, and you have 14 ancestors.

This is essentially a “power series” problem. If you want to know how ancestors you have descended from X number of generations ago, use this formula:

Number of ancestors = 2^X + 2^X-1 …

So say you want to know the total number of ancestors you have five generations ago. That works out to be:

2⁵ + 2⁴ + 2³ + 2² + 2¹ = 62 direct ancestors five generations ago.

For ten generations, you have 2,046 ancestors. For twenty generations, that’s 2,097,150 million direct ancestors.

Thirty generations back, just in that generation, there are 1.073 billion people. Considering that back in time there were fewer people on the planet to have been descended from than there are today, you can easily see how pretty much everyone is related to royalty at some point.

So, sadly, being of blue blood is not that special after all. If your grandparent is a monarch, then fair enough – but Charlemagne just isn’t that special these days.