Powers of Two, or What I Think About Before I Go to Bed

This is the sort of thing I wonder about at night before I go to sleep. Some nights these things actually prevent me from sleeping. Like this one: consider the fact that, in order for you to be born, you had to have two parents, who also had to have two parents, and so on. Given that my grandparents were born in the early part of the 20th century, let’s say that there are about three generations in a family per century. So, since the year 1, about 60 generations (3 generations times 20 centuries).

So the math goes like this: 2 parents, 4 grandparents, 8 great-grandparents, 16 great-great-grandparents and so on to the 60th power.

2 to the 60th power = 1,152,921,504,606,846,976.

So 2,000 years ago I would have had about 1 quintillion great60 grandparents? That can’t be right. Somebody tell me why my math is faulty. My brain hurts.

4 thoughts on “Powers of Two, or What I Think About Before I Go to Bed”

  1. Sounds about right to me, except I think the number might be much higher – 3 generations per century is quite conservative. That means that people are having children at an average age of about 33 years old, when I think anytime pre-20th century would be more like half that.

    Ah, the beauty of exponential growth…

  2. Oh yeah, these are definitely conservative numbers. But the trick is, I’ve realized, that most of those 1 quintillion people are the same people. Yes I have 1 quintillion great60 grandparents but several billion or so are probably the same people. Still my brain hurts.

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