Plato's Great...Great Grandchildren

I met Nick last week at a friend's party. We talked about this and that for a while until I noticed that his big smile never left him. At such hard times, how did he manage to keep on smiling?

“It's finally official,” he told me. “Seventy years ago, the registrar made a mistake. My real family name is Paleologos, not Paleologou, as we are called.”

“Can a single letter make such a big deal?”

“A huge one. You see, my family's origin is from a village close to upper Kardamili in Mani. And that's where the brother of the last Emperor of Byzantium hid from the Turks and settled down. The dynasty of Paleologos was the longest in Byzantium. I must be their direct descendant!”

Reader, I am not a young man any more so I have watched myself bleed many times. And even though I don't suffer from colour blindness, I can't be certain if my blood colour is closer to pink than black. There is one thing however I am damn sure of: not once did it appear to be blue. Unlike smiling Nick I have no claims to royalty. But ever since I was in high school, I had this bug inside me. Where did I come from?

Because curiosity drives me, I wasted little time. First I interviewed my two surviving grandparents, then I found a couple of local books with family information. Finally I checked town registries, old books and property titles. Soon I had part of my story. Although my dad had always insisted that I would only find farmers and the like, I managed to put him wrong with a few surpises. It was only when the trail run cold, somewhere in the 1780's, that I noticed the obvious.

Every time we go back a generation, our ancestors double. We have 2 parents, 4 grandparents, 8 great grandparents, and so on. Generations are roughly 25 years apart. I have no degrees in genealogy, but I do know some math from engineering. Given the two facts: (a) that my friend Nick was probably born around 1965 and (b) that Wikipedia states that the last Emperor of Byzantium was born in 1404, this gives us 561 years or roughly 22 generations. I pushed a couple of buttons on my scientific calculator and I was terrified. Even if smiling Nick's great...great grandfather was the last emperor of Byzantium, another 4.194.303 original great...great grandparents (all in the same generation) had contributed to his ancestry. A century back when people thought that male parentage was what determined descent, it would have been great. But today we know that both parents contribute. Were all of Nick's ancestors of noble blood? Had the dynasty only intermarried? Of course not. And what about bastard children with the maids, pirates who raped ladies and so forth? Let's face it, smiling Nick is as much of a blue blood as me or you.

But let's carry the numbers game a step further. Plato, the Greek philosopher was born in 423 BC and I was born in 1953. This gives us 2.375 years and roughly 95 generations. So when I plug those numbers in my scientific calculator I get 3.9 with 28 zeros after it! In Plato's time, ancient Greece had a population of roughly a million, and the world perhaps a hundred million at most. So where did this huge number with 20 extra zeros come from? What's wrong with my reasoning?

The mistake is not that difficult to see. Many persons who appear at different spots on the table (in the same generation) are brothers and sisters. Therefore their parents, even though they appear in different places, are identical. The percentage of identical people appearing in different places increases more and more as you go back. I don't know enough math or genealogy to contrive correction factors. They would depend on the average number of children, community size, social and physical mobility and the like. This was a far more complicated a problem than I had bargained for, so I did the sensible thing. I quit.

What can parentage possibly mean anyway? Einstein has been declared last century's most important man. He had a daughter and two sons. One of his sons did some sediment research. Except for that, all of his offspring disappeared into anonymity. So having a great ancestor doesn't make you great at all. If anything, the comparison diminishes you! Of course in genealogy, the game being played does not involve much thinking. It's called snobbery!

Still, my simple calculation had showed me one thing. As we go back the centuries, our parentage base becomes so large that it embraces most of the population. The numbers might not be as large as the ones I have stated. My friend Nick, for example, has more royal blood than I have given him credit for, and I do hope that he keeps the smile on his face.

But for all practical purposes, we are all Plato's great ...great grandchildren.