We all have two parents, four grandparents, eight great-grandparents, sixteen great-great grandparents . . . and so on. But how many ancestors do we have if we go back far enough? It is quite an easy calculation (if you have a calculator) and gives some surprising results.
Number of generations |
Years |
Number of Ancestors |
1 |
25 |
2 |
2 |
50 |
4 |
3 |
75 |
8 |
4 |
100 |
16 |
5 |
125 |
32 |
6 |
150 |
64 |
7 |
175 |
128 |
8 |
200 |
256 |
9 |
225 |
512 |
10 |
250 |
1024 |
20 |
500 |
1,048,576 |
30 |
750 |
1,073,741,824 |
40 |
1000 |
1,099,511,627,776 |
80 |
2000 |
1.20892582 x 10^24 |
Go back 10 generations, about 250 years, and we have a mere thousand or so ancestors. Go back another 250 years and the number jumps to a little over a million. Another 250 years and the number is more than a thousand million (roughly the current population of India). Going back 40 generations, or 1000 years, the number has increased exponentially to more than a trillion (almost 17 times the current population of the world). Two thousand years ago the number has become too large to express conventionally - it is approximately 12 with 23 zeros following.
Of course, these numbers are impossible. Until fairly recently, people didn't move around much. For most of the past two thousand years people were effectively bound to the village they were born in. Marriage partners came from the same village, or the village a mile or two down the road. There was a lot of interbreeding. If you want to follow this line of thought a little further, Brian Pears has an amusing, and thought-provoking, article on his website at www.bpears.org.uk/Misc/AncestorsParadox - and if you find that interesting, there are links to a couple of follow-up articles at the foot of his first page.
Are we all descended from royalty? Almost certainly. The problem is proving it.
