Too Few Men Existed for Me to Exist?

[ewlol]

This fails because of your assumption that every generation is consecutive. What about all the generations of people that never had kids, and then the ones that had many? I don't think you are correctly applying the historical population as a verification.

If my ancestor never have children, then I will not exist. I do exist, therefore my ancestor do have children. I think I do not need to worry about this issue.

That is a true and a fault of my previous wording. I think what I am trying to say is that you can't assume your number of ancestors to be equal to the world population for any given year...

[Ysh]

This fails because of your assumption that every generation is consecutive. What about all the generations of people that never had kids, and then the ones that had many? I don't think you are correctly applying the historical population as a verification.

If my ancestor never have children, then I will not exist. I do exist, therefore my ancestor do have children. I think I do not need to worry about this issue.

That is a true and a fault of my previous wording. I think what I am trying to say is that you can't assume your number of ancestors to be equal to the world population for any given year...

Yes, this is fundamentally the problem we face in this thread! My number of ancestor is not equal to world population. My number of ancestor is more than world population! How can it be?

[bolognaman]

I think your assumption of 32 years between generations stops being reasonably accurate in the early 19th century. If you're going back an additional 800 years, you should adjust this value. I'm not sure just how much it will change the final result, but it will surely make a difference. I think if it will take you close to year 0, you can safely assume your value to be within the error of the population estimation for that time.

Edit: I now realize that shortening the generation gap would make your number of ancestors grow faster. I really dunno

[Killshot47]

2^n assumes that nobody shares the same parents. You're basically saying that it's a binary tree, where generations is the depth of said tree. But a binary tree is exactly that, binary, so for each 1 you produce 2, which produces 4 which produces 8 and so on, but you could have 2 people produce 9 so 2 generations = 11, each of those 9 finds a mate and produces 9 more, which results in 81 children, each of them finds a mate and produces 9 more children which means we're now at 729 over 4 gens which would be 2^4 = 16 under 2^n, which doesn't match. You're right that every person has 2 parents, but there's plenty of people that have the same parents, 2^n falls apart there.

[Ysh]

2^n assumes that nobody shares the same parents. You're basically saying that it's a binary tree, where generations is the depth of said tree. But a binary tree is exactly that, binary, so for each 1 you produce 2, which produces 4 which produces 8 and so on, but you could have 2 people produce 9 so 2 generations = 11, each of those 9 finds a mate and produces 9 more, which results in 81 children, each of them finds a mate and produces 9 more children which means we're now at 729 over 4 gens which would be 2^4 = 16 under 2^n, which doesn't match. You're right that every person has 2 parents, but there's plenty of people that have the same parents, 2^n falls apart there.

Sharing parents is true I think. One tree can bear many fruits and things like this. Though I think this does not address problem. Even if I will have many sibling, I will still have 2 parent. Regardless of how many aunt and uncle I will have, each of my parent will still have 2 parent of their own. This is still 2^n when looking at ancestry of a single man. This parent sharing logic will however solve problem of how there can be more men than just me. After all, if there are not even enough men for me to exist, how can all 7b+ other men that are alive today exist? Clearly answer to this question is sharing of parent, but this unfortunately is not precise question bring up in original posting!

[Grog]

You're walking the tree from the branches, so towards the roots it needs to be smaller.

Say, for the sake of argument 2 parents have, on average, 4 children: Then it's n^2 towards us (from the past).
But you need to reverse it for the calculation you want to do (away from us to the past).

[Killshot47]

Yeah so under this function you have that say 64 people at 2^6. Well that's 64/2 32 sets of 2 to have kids, each of them has 1 kid, you now have people 32 possible people to make a kid, 32/2 is 16 sets of 2, each of them has a kid. This doesn't correlate to the population growth function which here is undefined. To know the common ancestors it takes to hold the population, you'd need to know the function f(x) of population growth. The number of common ancestors would be the inverse of that function. If population growth is 2^n, common ancestors would be some log function (log sub 2 of n? I don't remember)

Edit: Nah the log gets you the tree height n, but basically ancestors would be walking the population growth tree/function backwards.

[ewlol]

https://www.prb.org/howmanypeoplehaveeverlivedonearth/
I think this will be a more helpful statistic to ponder.

Your question is really thought provoking, however the logic of it seems grossly oversimplified. We are all coming down from one long chain of ancestors, otherwise we would never exist. It is true that there has never been a moment where humans ceased to exist since the origin of our species. How many people did it take to get me here?

Fossil record dates the origin of humans to 500,000+ years ago. Assuming a generational gap of 32 years, that means 15,625 generations have occurred. 2^15,625 is astronomical lol.

[stya]

The biggest problem here is that your mother and your father share ancestors, maybe not on first, second or third degree but the higher you go up the tree, the more likely it is.

Because the population was lower back then and the higher you go up the tree, the higher the number of ancestors you take into account. And when one single ancestor is shared in the tree, all his ancestor get automatically shared too, so it effectively cuts a branch of the tree.

I can really see it happen quickly in small villages and reduce dramatically your numbers... Towns/villages used to be very small in comparison to what we have these days.

[Hrenli]

Funny, I was thinking exactly the same thoughts a few months back. Clearly it just proves how related we all are. The binary tree of ancestors has to merge branches sooner or later otherwise we would had to start with infinite number of humans.