Descendants

[FUZZY]

Very few people bother to determine what an amazing potential for overpopulation they have. Let us consider yours. If you and your wife have a meager two children, it would seem you are not adding much to the world. But let's suppose that in 5 years each of your children has two children. In another 25 years, each grandchild has two kids. In another 25 years, each great-grandchild has two offspring-and so on for a thousand years. How many descendants would you have?

[Thalia]

In terms of overpopulation, let's start with one couple. They have two children. If they were the only family in the world, they'd have to have the children together. So instead of doubling, the next generation would still only have two people. Two people are giving birth to two people. Later generations repeat. Assuming each couple has one boy and girl. Eventually the older generations will die so while the population would increase at first, you'd eventually hit a limit. Maybe 3 or 4 generations. Obviously there's more than one couple in the world but I would think each generation would have the same number as the previous. To increase the population after 3 or 4 generations, someone needs to have more than two children.

[bonanova]

First thought

Spoiler

2^(1000/25) = 2⁴⁰.  About 1.1 trillion>

Edit: Well, that's the number born in the 40^th generation.
Adding all the generations gives double that amount.

 

[telesphorelalancette]

If they have two with someone else's two they won't increase the population. Houuuuuuu, burn!

[bonanova]

3 hours ago, telesphorelalancette said:

If they have two with someone else's two they won't increase the population. Houuuuuuu, burn!

Doesn't each birth increase the population? What if, miraculously, no one will die?

But the question does not hinge on when/whether people will die.
The question asks: how many descendants will you have?

[bonanova]

"... for a thousand years. How many descendants would you have?"

But we're not enumerating the world's population. We're quantifying the part of it that comprises your descendants. Two children, four grandchildren, ...

[Buddyboy3000]

@FUZZY Does the 1000 years start after your children has two children, or from when the question starts?

[FUZZY]

3 hours ago, Buddyboy3000 said:

@FUZZY Does the 1000 years start after your children has two children, or from when the question starts?

from when the question starts.

[Thalia]

On 10/16/2016 at 9:33 PM, bonanova said:

"... for a thousand years. How many descendants would you have?"

But we're not enumerating the world's population. We're quantifying the part of it that comprises your descendants. Two children, four grandchildren, ...

I was addressing the first line about the potential for overpopulation. Not the question itself. 

[bonanova]

I get that. I thought it was strange that the question was introduced with an "overpopulation" flavor. (Maybe it was just a red herring.) My comment badly implied that yours wasn't responsive to the question; I meant to opine that the introduction wasn't all that germane.

There are a couple of "paradoxes" when one considers family trees and such. For example we all have two parents, four grandparents, eight GGPs, sixteen GGGPs, and so on. So how is an exponentially increasing heritage as we go back in time consistent with a growing population going forward? Was there an original, parenting "couple" N generations back? If so, how could they singly play all the roles of my 2^N progenitors at that time? And, if two kids/family going forward gives a stable population, how can it also produce an exponential personal progeny?

I found Mitochondrial Eve an interesting read.

[Thalia]

A while back, I made a family tree. Several generations back, I found a single person in more than one person's line. It might have been an error. 2^N ancestors in a generation assumes no one had children with their sibling, cousin, or otherwise related person. Apparently, in my tree, someone married a relative. The same assumption is made for 2^N descendants.

Interesting wiki page. Never heard of that before.

Edited October 22, 2016 by Thalia

[bonanova]

Yeah, that's it. I have an online tree now (ancestry.com) with a few thousand names. I get inquiries and "matches" almost daily from people who descended from an uncle's sister-in-law of an 8th-generaltion direct ancestor. Soon you realize how interconnected the human family is. The gene pool is constantly being stirred. Even if you could map the whole thing you'd need a lot of color coding to discern in individual's tree. We'd all be different colors simultaneously, and a lot of "branches" would be tied into knots. (Rednecks all... )

[FUZZY]

On ‎10‎/‎12‎/‎2016 at 3:55 PM, bonanova said:

First thought

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2^(1000/25) = 2⁴⁰.  About 1.1 trillion>

Edit: Well, that's the number born in the 40^th generation.
Adding all the generations gives double that amount.

The first gen (children) are 5 yrs from now as per the question. So, the 25 yrs interval starts from the 2nd gen (grandkids). 1000 yrs from now .....would not it be from 1st gen onwards . Hmm...   how 2^40 ? would not it be < 2^40? Not that it would make a lot of difference, it would still be in trillions, of course! Jus bein' curious .........that's all.