The Mathematics of Genealogy

The mathematics of genealogy is not a concept I created, but I will explain it in my own words. This topic covers two subjects I find interesting, so it is only natural that I would find the subject of the mathematics of genealogy very interesting as well.

At this point in time, you are probably wondering what math has to do with genealogy. Let me explain. Everyone has two parents, their mother and father, right? Each of your parents has two parents of their own, thus you have 4 grandparents. (Still with me so far?) Thus the number of ancestors you have doubles with every generation. 2 parents, 4 grandparents, 8 great grandparents, 16 great great grandparents, etc.

Now let's assume that a new generation is born every 25 years (this is a good estimate plus it helps make the math easier). So over the course of 1,000 years that would equal 40 generations (1,000/25= 40)

Now comes the hard part (and the mind boggling part). If we double the number of ancestors with every generation and if we go back 1,000 years, the number of direct ancestors everyone of us had is 1,099,511,627,776 ! (2n40= 1,099,511,627,776) That comes out to over 1 trillion ancestors! And that is only going back 1,000 years.

Currently (2010), the US Census Bureau estimates the worlds population at approximately 6.887 billion (6,887,000,000). So how is it possible to have over one trillion ancestors a thousand years ago when the current world population is around 6-7 billion? There is only one possible explanation I can come up with and that is that individuals have to fit into your family tree in more than one place... and many times over!