quick math question

[cdn2wheeler]

I need some help with a small mathematics equation. I'm numerically-challenged so bear with me here.

I'm trying to calculate the number of descendants going back to 1 A.D. The way I figure it, a generation is 25 years. Since this is 2007, there have been just over 80 generations between 1 A.D. and now.

Each generation required two people to procreate. Three generations would be 2 to the power of 3 (2 x 2 x 2) = 8 people. So, if I want to calculate the number of descendants, from parents, grandparents, great-grandparents and so forth back to 1 A.D., so I simply use 2 to the power of 80? That number comes up as stupidly large... like, 12 to the power of 23 people. Doesn't seem to make sense.

What am I missing?

[Brutha]

You count specific people multiple times. One of your Great-Great-Great-Grandfathers on the side of your mother could also be a Great-Great-Great-Grandfather one the side of your dad.

[dalang]

Originally Posted by cdn2wheeler

What am I missing?

Nothing, really. 2^80 is the number of descendants in the 80th generation if you assume that everyone has 2 children (although it's a bit unclear why you came up with this number based on the fact that you need 2 people for procreation) and everyone has a partner from outside the population. The total number of descendants is even bigger: 2^81-1.

Nothing wrong with this number, although this is probably not a realistic model of what really happened.

For illustration, have a look at binary trees (f.e. 3 generations):
height = number of generations = 3
number of nodes = total number of descendants 2^4 -1 = 15
number of leaves = current generation = 2^3 = 8

It's probably next to impossible to create a model that could be called realistic for this, but that's a topic for anthropologists. Wars and diseases had a big impact, I guess. Brutha's comment is also valid.

[ChefSalad]

Believe it or not, it's been established that you are the descendant of every on earth at 1 AD. The question then is the global population at that time.

[Brutha]

Believe it or not, it's been established that you are the descendant of every on earth at 1 AD. The question then is the global population at that time.

It isn't really completly clear. I would for example doubt that the majority of Innuit are the ancestors of every one who lived in Australia 2000 years ago.
There is quite a lot of guesswork involed when you talk about people from different cultures.

[DarkSociologist]

Every one of your ancestors has had at least one descendant that you can be certain of having (otherwise you wouldn't exist). So to calculate the minimum number of descendants, you would subtract that person's generation from 80. For example, if you wanted to find out the total number of descendants that your ancestor from 1AD had, then it would be 80-1 or 79, since he is the first generation.

On the other hand, if you want to know how many ancestors that you have (assuming that each one is unique and follow the 25 years/generation pattern), then the equation becomes more complex. I'm not sure how to write sigma notation here, so I'm going to use java as an example:

the equation would be (where x is the number of generations you want to count):

for(i=1;i<=x;i++)
{
ancestors = ancestors + Math.pow(2,i);
}

This adds the number of ancestors from each generation:
Parents: 2 - total 2
Grandparents: 4 - total 6 (4+2)
Great-Grandparents: 8 - total 14 (8+4+2)
and so on

Assuming there are 79 generations between you and your ancestors from 1AD, then you have 1.2089258196146292 x 10^24 unique ancestors, which is a lot. Due to the high cohesiveness of individuals in a society, I would guess that after the 3rd generation up, you are probably going to see a high rate of relatedness between your ancestors of the same generation.

[openeyes]

Originally Posted by cdn2wheeler

I need some help with a small mathematics equation. I'm numerically-challenged so bear with me here.

I'm trying to calculate the number of descendants going back to 1 A.D.?

You might enjoy this:

How Many People Have Ever Lived on Earth? - Population Reference Bureau

[Addict]

You count specific people multiple times. One of your Great-Great-Great-Grandfathers on the side of your mother could also be a Great-Great-Great-Grandfather one the side of your dad.

I'm pretty sure this is your answer. 2^80 would be the right answer for the number of ancestors 80 generations removed from you assuming every person in a generation isn't related to each other. And this obviously can't be true. With this restriction, it's pretty damn difficult to make a good estimate.

Nothing, really. 2^80 is the number of descendants in the 80th generation if you assume that everyone has 2 children (although it's a bit unclear why you came up with this number based on the fact that you need 2 people for procreation) and everyone has a partner from outside the population. The total number of descendants is even bigger: 2^81-1.

I'm thinking that cdn2wheeler meant his ancestors. Descendants doesn't really describe what we're trying to figure out since we're counting backwards. That would explain the "2 children" assumption. Instead, cdn2wheeler assumed "2 parents" for each ancestor. You're right about the total number being 2^81-1 though.

Believe it or not, it's been established that you are the descendant of every on earth at 1 AD. The question then is the global population at that time.

I'm fairly certain this is downright impossible, since it's believed humans migrated to the Americas about 12,000 years ago.