# the amount of one person’s ancestors

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I googled the amount of people that lived on earth throughout its entire history, it’s roughly 108 billions. If I take 1 person and multiply by 2 for each generation of ancestors, at the 37th generation it already outnumbers that 108 billions. (it’s 137 billions). If we take 20 years for 1 generation, it’s only 740 years by the 37th generation.

How??

(I suck at math, I recounted it like 20 times, got that 137 billions at 37th, 38th and 39th generation, so forgive me if it’s not actually at 37th, but it’s still no more than 800 years back in history)

In: 1391

You’re assuming that everyone alive right now has different ancestors.

This is wrong because you and your sibling have the same parents. Your parents and their siblings have the same parents which means you have the same grandparents as your cousins. Follow it back enough and every ancestral line joins up eventually.

If everyone in history was an only child then your calculations would be correct, except for the fact that if that was the case then the population would decrease over time.

>I googled the amount of people that lived on earth throughout its entire history, it’s roughly 108 billions. If I take 1 person and multiply by 2 for each generation of ancestors, at the 37th generation it already outnumbers that 108 billions. (it’s 137 billions). If we take 20 years for 1 generation, it’s only 740 years by the 37th generation.

>How??

There’s only ever a limited amount of possible mates for any person at any point in time, no matter their geographic mobility. The further you go down (…up?) the tree the more of all those people will simply be **the same person**. I.e. your great-great-great-great-great-great-great-grandfather on your great-great-great-great-great-great-grandmother’s side will also be one of your great-great-great-great-great-great-great-*great*-grandfathers on your great-great-great-grandfather’s side and so on.

You’re assuming that all 137 billion of those ancestors are different people.

If your parents happened to be brother and sister, then you’d only have 2 grandparents instead of 4, because your parents shared both parents. That’s an extreme example, but if you researched your family tree far enough you would eventually start seeing ancestors who appear on both sides of a particular branch…4th cousins getting married, that sort of thing.

You assume that every one of your ancestors is only related to you in one way, that is an incorrect assumption.

A simple example is if your parent was siblings. Then there are only two instead of 4 people two generations back. The rest of the ancestor tree now gets halved.

Siblings having children is not common, it is just a simple example to show that the ancestor tree can collapse in size. Globally it is not uncommon that cousins to get married. Worldwide 10% of all marriages are between first or second cousins.

The more generation you go back the more likely it is that two persons that have children have a common ancestor. Do you know who your ancestors are 5 generations back? If your parents are from families that have lived in the same relativity small location for a long time I would say it is likely you find common ancestors not that far back.

There exists, in mathematics, something known as the “pigeonhole theorum” which simply states “if you have n available slots and more than n objects then by necessity there must be at least one slot which contains more than one object.”

In other words if I roll a 6 sided die 7 times, I have to have rolled at least one number at least twice.

So back to your question: for every generation back you go in your family tree (g) you have a number of ancestors 2^g at that generation level. So if 2^g is greater than the number of viable adults in the population than the pigeon hole theorun states that at least one person is at least two of your ancestors.