Early this morning, my youngest woke me up. This is not a new Sunday event, so I quickly took her to our basement where her noise and activity wouldn't wake up the rest of the family. We started reading a book she loves about Greek mythology, and I mentioned to her that she was 1/16 Greek on her father's side.
This spawned a long discussion over many hours about our ancestors, genealogy, progenitors, and so on. At one point in mapping our pedigree on my office wall, she asked why she couldn't draw everyone in our bloodline. "Because", I told her, "if you go back ten generations, it's 512 great grandparents, and we dont have enough room to write that at the top of the whiteboard."
How I arrived at 512 is easy. Audrey (my daughter), has two biological parents. In turn, my wife and I both had two parents each (4), who also had two parents each (8), and so on (1,2,4,8,16,32,64,128,256,512) until you arrive at 512 great-great-great-great progenitors (I know, I missed a few greats in there).
Ten iterations is about 300 years in my bloodline, roughly a generation every 30 years. Jean Georges Renaud of Audincourt France was born right around 1700, and he's tenth generation exactly on my paternal pedigree.
Audrey made the astute observation that this was a lot of people, and if you went back another 300 years, it'd be a much larger number (1048576 progenitors in 1400, to be exact). She followed up her question by asking what the population of the world was in 1700, and in 1400 (640M and 374M respectively).
If you extrapolate progenitors far enough, and take consensus population figures going far back enough, the number of my forebears crosses over the total world population line, around 1150 AD. There were 300-400M people on the entire planet in 1150, and the extrapolation of forebears crosses over somewhere between 1200 and 100 AD.
Yes I know that it's unrealistic to assume that there were always two discrete individuals (childbirth mortality was very high until the last two hundred years, so many males remarried and sired additional children) but all this does is reduce the population number further. This also discounts wars, pandemics, and so on.
There is no way that 100% of the people on the planet in 1150 were my/your ancestors, so there is a logical error in my reasoning. Help me out, where is it?