The fun of genealogy rests with discovering interesting ancestors, including nobility. Everyone loves to discover a Duke or an Earl in the family tree. However, an important question is: just how many ancestors are in your tree?
A great site called 'Number of Ancestors in a Given Tree' looks at the math of genealogy. The mathematical equation is 2n = x, where n is the number of generations back and x ia the number of persons in that generation (grandparents). (Each generation is 20 years).
Therefore, in the first generation, a person has 2 ancestors, called parents; In generation 2, 4 ancestors or grandparents. Following the equation a person has 8 great grandparents in generation 3 (23 = 8).
The number increases exponentially quickly. A person has 256 6th great-grandparents in generation 8, 1024 8th great-grandparents in Gen-10, and 1,048,567 18th great-grandparents in Gen-20. A person has 2,097,151 cumulative grandparents in Gen-20. Clearly someone of those million or so great-grandparents is likely 'famous'.
The numbers increase out of control quickly: over 2 million 19th great-grandparents in Gen 21, over 4 million 20th great-grandparents in Gen 22, and in Gen-25 (750 years) you have over 33 million grandparents. A person is likely to have some stinkers too by then. If you started in 1950, that would mean in 1200, roughly 8% of persons living on earth were your great-grandparents (33 million great-GPs/ 400 million population of the earth)
For instance, if you trace back one of our trees (or maybe both) through Joseph Loomis, one can get to Edward III King of England Plantagenet. That's right the 19th great-grandfather of GRG, some 21 generations back was King Edward the IIIrd. He and 2,097,151 other 19th great-grandparents. How is that for name dropping?