Although of course I knew from a very young age that a baby has two parents, it wasn't until I was nearly middle aged that I understood the implications of what I knew. Family history taught me that my number of direct ancestors doubled as I went back each generation: two parents, four grandparents, eight great-grandparents, sixteen great-great grandparents. It doesn't take a genius to work out the maths.
The working forward of that thought didn't come until later. I have twice as many ancestors as my mother...she had twice as many as my grandmother...who had twice as many as her mother. My children have twice as many as me. Their children will have twice as many as them.
The trouble is, that much like the old story of the mathematician's payment, where a ruler was asked to pay one grain of rice, or wheat (depending upon who tells the story) on the first square of a chessboard, and two grains on the second, doubling up with each square, you soon get into the realms where you feel as though someone is slowly tryng to turn your brain inside out.
Three greats: 32; four:64; five:128; six:256; and so on: 512; 1024; 2048; 4096; 8192; 16, 384; 32, 768; 65,536; 131,072. 17 generations back and you have one hundred thousand ancestors, and the numbers seem unimaginably huge. But actually, allowing for 30 years a generation on average, seventeen generations only takes you back to about 1500... and the beginning of a problem. The numbers appear to accelerate enormously quickly over the next few generations: 18 is 262, 144. 19 generations back comes to 524,288; and 20 comes to over a million... 1,048,576. So your total ancestry going back to around 1380, would be around a million people. Hold...on...though.
In 1377 the adult population (over 15 years of age) were subject to a poll tax, and so we have good records about the number of people in England at that time. There were 1,355,201. So go back another generation... to around 1350... you will have 2,097,152 ancestors in theory. Which is many more than the adult population of England at the time.
Even allowing for the ravages of the Black Death, which removed about a third of the population of London in the course of 1348-50, there are still too many ancestors for the number of adults.
Now it is already obvious from my own family that the same people turn up in the family tree over and over again. If cousins marry, then the lines of family ancestry will join together with the same couple appearing as grandparents on both sides of the family. This has to account for the conundrum that although you have in theory twice as many ancestors each time you go back a generation, the maths doesn't add up once you are in the 14th century.
My feeling is that anyone with an English ancestry is probably related in some unknown way to any other person with an English ancestry. We are all cousins, and family. Probably that's true of all people, everywhere, because once you go back a few more generations, you need the adult population of the world to account for all the ancestors.
I enjoy family history because it moves me in a way that political history never could. Initially I thought it was the thrill of finding out about my own ancestors... but it isn't, because I feel every bit as thrilled about researching other people's families. I think it is simply that history on a personal level; the history of people, their story, is touching because you can always project yourself into the person's place, and understand their lives in a much more empathetic way than the wars and machinations of government.
Family history research has convinced me that we are all connected, and that time is much shorter than we think. Where once I would have thought of 14th century England as a place far removed from my daily life, and the people as being a long way from the people of today, I see that there are no real differences: the people living then were not much different from the people living today. 500 years, in the context of the history of the world, is hardly an intake of breath, it is no time at all.
It always amuses me when I hear someone from a documented ancient lineage say: of course my family goes back to the time of the conqueror.... Yes, so does my family - and your family - and the next person's family. By dint of us being in existence, we all have ancestors who were alive back then, and the chances are, they were related. In fact the population of England must have been fairly static for a few centuries, because there are estimated to have been about 1,250,000 to 2,000,000 people around the time of the Domesday survey.
So next time you see a picture in a gallery of an illustrious 15th century merchant, or a peasant in the fields, don't look upon them as a stranger. The likelihood is, if you have English ancestry, that they are your grandfather or grandmother - or aunt or uncle, cousin or sister. We are all related, and all connected, and we should celebrate that.