How many ancestors?

Perhaps in honor of the tax paying Americans and their math genuses...here's some arithmetic of my own.

I've started (arbitrarily, I admit) my counting of generations with my grandchildren as (1)
That makes my children generation (2)
And I would be (3)
My parent's generation (4)
My grandparent's generation (5)

Now to stop a moment and figure out how many of each generation are there for just me.  Each person has 2 parents,
so generation (4) has 2 for me
Generation (5) grandparents has 2 parents per person, or 4 for just me
Gen (6) great grandparents are 2 for each grandparent or 8 for me
(7) great great grandparents, 2 for each great grandparent or 16 for me
(8) great great great grandparents, 2 for each great great or 32 for me
(9) great great great great grandparents, 2 for each of last generation or 64 for me
(10) great great great great great grandparents, 2 for each of last generation or 128 for me.
(11) is a total of 256
(12) ancestors for just me would have to be 512
I actually have some ancestors in my (13) generation.  I sure don't know all of them...which would be 1,024 people.

Some of these people lived in Western Europe, and some were Native Americans, or from somewhere else entirely, and ended up meeting their mates and having a child.

And this is talking about just one generation at a time...all for just me.  So I'm pretty sure some cousins must have gotten together some of the time.  And not even known they were cousins, after all, if 1024 people were going to be parents of all these others, you'd better believe some would be related somehow.

If I knew who all those people were, I'd be amazed at all their life stories.  But the things I do know are:

• They all lived long enough to have at least one child

• Who also lived long enough to have at least one child

• There could be a total of all of those generations of parents which would be 2,046 parents that all once lived and gave me their genetic input.

• And I decided to stop counting, but we all know there were parents for the generation before the 13th...and so on.  Do you know how many parents there would have been in the 14th generation before me?  Answer: 4,092

This is where we begin to see that someplace along the line, ancestors merge all over the place.  At some point, multiplying times just 2 for each parent of each child, we will find the tribes of all humanity had just so many people  That's the fun thing about genetic tracing these days.  Some limited number of different lines can be defined by the genetic engineers.  Everyone is a descendent from these original limited lines.