Hypothetical number of ancestors in 399 BC

[blarznik]

I was trying to get some idea of how many ancestors I had around the time of Socrates (399 BC is his death), so I tried coming up with a way to find it.

So I'll start at my birthday which is 1991. I'll pretend that my parents were both 30 when they had me; I'll also pretend every pair in history giving birth was 30 years old when giving birth.

I'll use intervals of 30 years going all way the way back to 399 BC from 1991, which is a 2390 year gap.

There are 79 intervals of thirty years that fit with in 2390 years gap.

So I came up with 2^79= 6.044*10^23
This can't be right?! This is basically Avogadro's number
I used 2^x to find the number of the ancestors at the time of 1781 (5 years after the declaration of independence) which at 7 generation was 128 people. And this seemed right.

I'm not adding the ancestors from previous intervals as I go along, each interval is just the number of people related to me at that particular time.

Am I doing anything wrong?
at birth...
# of present parents (1961)
2^1=2
# of grandparents (1931)
2^2=4
# of great grandparents (1901)
2^3=8...

 

[mathman]

Your arithmetic is OK. However, once you go back enough generations there is a lot of duplication. For example 10 generations back, there are over a thousand ancestors, but most likely nowhere near a thousand different people.

 

[pmsrw3]

Well, the number 2^79 is (about) correct, with one absolutely huge correction: those people are not all distinct. For instance, your mother's father's father's mother's ... father's mother may well have been the same person as your father's mother's mother's father's ... mother's mother. We are all distant cousins of each other -- we all have common ancestors.

 

[KingNothing]

Although 30 may be normal today, historically people usually had babies around 17-20.

 

[pmsrw3]

Although 30 may be normal today, historically people usually had babies around 17-20.

Historically people started to have babies around 17-20. 30 is not a bad guess for mean generation time.

 

[SteamKing]

You've calculated how many ancestors you had in 399 BC. Now suppose all 6 billion people on Earth now did the same calculation. The total number of ancestors in 399 BC would be roughly 2^79 * 2^32 = 2^111.

What happened to everybody?

 

[blarznik]

Good point. http://www.aisee.com/graph_of_the_month/inbred.gif
I guess it gets confusing when cousin or uncle/nephew relationships happen.