Family Lessons 92: Numbers of Ancestors

The more observant of my readership will have noticed that in the past year, my family tree has gone further back, providing moderately interesting glimpses into the world of the dead and buried. I have officially got back 27 generations, with dear old Grandpa Waldeve who sadly departed this life in the 1150s. I was curious to know how many ancestors I had so far back; there is a mathematic formula to help calculate this: 2n= x, where n is the number of generations back and x equals the number of individuals in that generation. Now I’m a poor mathematician, but I can understand this much:

I am the first generation, and there is one of me.

My parents are the second generation, and there are two of them.

My grandparents are the third generation, and there are four of them.

My great-grandparents are the fourth generation, and there are eight of them.

So the numbers double with each generation. Thus, you have 1024 8x great-grandparents and therefore 2048 9x great-grandparents. If we go back to our 25x great grandparents, one of whose names I know to be dear old Waldeve, then the figure at which we arrive is…wait for it…


That’s right, in the 1100s, I am descended from one hundred and thirty-four million, two hundred and seventeen thousand and seven hundred and twenty eight people. Even allowing for the fact that some of these folk may have been Scandinavian Vikings, Normans, Saxons, Franks and even Moors…. the population of England in 1150 was less than two million and the whole of Europe was probably 63 million. Jean-Noel Birabe in 1980 estimated the global population in 1100 to be 301 million: were just under half of those folk my direct ancestors?? If we go back 40 generations (for which none of my ancestors’ names can be proved), the mathematical formula alone produces even greater absurdity: the number of ancestors is 1,099,511,627,776, which is ridiculously higher than the global population around forty generations back. Clearly, the maths alone cannot be trusted.

The solution is called pedigree collapse. Of my 1024 8x great-grandparents, it is likely that some of them ‘double up’, as cousins married cousins, and second-cousins married second-cousins, so the number grandparents and great- grandparents does not double; the same people pop up on multiple lines of a family tree. This means that, rather helpfully, we are all cousins to some degree or another. If we treated strangers as though they were family, we might better obey the Lord’s command to love our neighbours as we do ourselves. Secondly, we Bible believers know that we come from one man and one woman, Adam and Eve. One cannot trace a family tree back for ever; it does come to an end - or rather, a beginning:

And He has made from one blood every nation of men to dwell on all the face of the earth, and has determined their preappointed times and the boundaries of their dwellings, so that they should seek the Lord, in the hope that they might grope for Him and find Him, though He is not far from each one of us; for in Him we live and move and have our being, as also some of your own poets have said, ‘For we are also His offspring. Acts 17:26-28

Christ became a second Adam, that all who believe in Him might join a new family of God, the community of the redeemed, His Israel:

But as many as received Him, to them He gave the right to become children of God, to those who believe in His name: who were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God. John 1:12-13, NKJV