The Power of two
Recently I read a book titled “Irish Ancestors — A pocket guide to your family history” by John Grenham. I really liked the explanation he provided on the number of ancestors one would have during a 1000 year period. I have provided a summary below.
Within our mobile app (Android, iOS) we display a pedigree view of your ancestry. This tree shows three generations of ancestors allowing one to see their great grandparents in one view. On larger screens, such as a desktop computer, we also support displaying more generations in one view. However, a common feature request is to display all generations in one view. Whilst technically this is possible, the amount of people to render doubles for each generation you go back. You have two biological parents, four grandparents, eight great-grandparents, 16 great-great-grandparents and so on. Let’s pick a famous date in English history — 1066, the battle of Hastings. If we were to render a person from today showing all of their direct ancestors for 1,000 years we would have to determine how many generations of family a person has in that 1,000 year period. Let’s guess and say three generations per century that would be 30 generations. Two to the power of 30 (2³⁰) is 1,073,741,824 — more than one billion! This is why we do not currently support rendering all generations on a tree.
This means that you have over one billion direct ancestors over a 1000 year period. What is even more fascinating about this is the world population in the year 1066 was not one billion people. It is several times less. The United Nations Department of Economic and Social Affairs put this estimate at 310,000,00 in 2008. Wait a minute, if the population in 1066 was only 310 million then how can I have over one billion ancestors at the same time? Well, the original calculation assumes that none of the couples in those 30 generations was related in any way. If you were to marry your first cousin, your children would have only six great-grandparents, not eight; 12 great-great-grandparents not 16; and so on. By marrying a first cousin you have removed more than 600 million of these ancestors and that is assuming none of the other generations married relations. In fact, the chances are that almost all of your ancestors were related to each other in some way. In settled rural societies everyone was at least a fourth or fifth cousin.
On a slightly related and personal note, the date 1066 is when William I of England (AKA William the Conqueror) became the first Norman King of England. Through Ancestry and the help of Ancestry member Sue Dieckbernd (my mother in law) I have been able to trace my son’s roots back to William.
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