The Ancestral Numbers Game
The gene pool dwindles as we go back in time
The number of forbears all alive at one time surpasses the number of living persons on earth just 750 years ago.
Be fruitful, and multiply and replenish the earth. But the biological imperative to make more of ourselves has a catch. It takes two to tango.
The mean time span between human generations is something less than twenty-five years, judging from a count of the generations of one actual bloodline over the past three hundred years in the United States.
In spite of genocidal wars, and great floods, despite droughts and famines and the black death, man has come from a very few individuals alive in remote antiquity to billions today. Estimates of historical world populations during different times projected by many different demographers give very similar results; they are very consistent even into remote antiquity. This doesn’t mean the experts are correct; it means they all agree even though they may have used different methods.
In the year One, there were probably 170 million people on Earth. By the year 1000 there were 265 million. Population grew to 465 million by 1500 C.E., and continued its growth until today there are over 6 billion of us.
Two multiplied by itself becomes a very large number very quickly
It takes two to tango. To produce one human being, two human beings are needed. If your parents didn’t tell you about the birds and the bees this may come as surprise to you, but it is so. With each step back in time, twice as many progenitors are needed as are in the following generation.
You have two parents, and each of them had two parents, making for four grandparents. There were eight great-grandparents, and so on with each successive generation. There are twice as many people alive all at the same time with each step back into the past. It is a biological necessity.
With “A” equal to the number of ancestors all living at the same moment in time, and “n” being the number of generations from your own parents counted as the first generation, the formula for determining the number of ancestors living and breathing in any generation is A=2 to the power of n. As an example, your great-grandparents are the third generation removed from your parents: A=2e3=8.
Let’s go back to the year 1250, beginning from the year 2000. There are 30 generations between the two years. Two to the power of 30 yields 1,073,741,824.
Out of biological necessity, there must have been over one billion people, all alive at the same time, in the year 1250 C.E., who are your direct ancestors. But in the year 1500 there were only an estimated 465 million humans on all of Earth, and in the year 1000 there were only 265 million (the highest estimate is 345 million) people walking the face of the Earth.
Kremer (1993) estimates the world human population one million years ago at 125,000, which is a speculative figure at best but probably in the ball park. Those ancestors were not humans as you are, but one of the predecessor species of human, such as Homo heidelbergensis, or Homo antecessor.
And there is the riddle. With each step back in time, the more ancestors we need and the fewer people there are.
References:
http://www.uky.edu/AS/Geology/moecher/120/worldhis.html
http://www.j-bradford-delong.net/TCEH/1998_Draft/World_GDP/Estimating_World_GDP.html
