# Exponential growth using multiplication

• January 17th, 2013, 02:12 AM
leohopkins
Exponential growth using multiplication
Hi guys,

I'm finding something difficult to understand and perhaps someone could tell me the logic behind this.

I have two parents, each one of my parents have two parents and so forth, so.

I have 2 parents
I have 4 grand parents
I have 8 great grand parents
I have 16 great great grand parents
and 32 great great great grand parents ........

With this exponential growth, if I carry on to just 37 generations of humans, it turns out that I should have just over 63 Billion great great (37 times...) grand parents. How can this be possible as I'm pretty sure that there have been far more than 37 generations of humans, but at no time have there ever been 63 Billion people living on the planet at the same time as a single generation.

Can someone explain this?

thanks,
• January 17th, 2013, 03:15 AM
tk421
Quote:

Originally Posted by leohopkins
With this exponential growth, if I carry on to just 37 generations of humans, it turns out that I should have just over 63 Billion great great (37 times...) grand parents. How can this be possible as I'm pretty sure that there have been far more than 37 generations of humans, but at no time have there ever been 63 Billion people living on the planet at the same time as a single generation.

Can someone explain this?

Distant (and sometimes not all that distant) relations often marry. So your calculation effectively double-counts (and triple-counts, and quadruple-...) sets of great...grandparents.

Marriages generally occur between people of a similar geographical region, making it highly likely that there are not that many degrees of separation between them. Stated another way, there are many shared ancestors, so your binary tree model doesn't reflect reality.
• January 17th, 2013, 03:34 AM
river_rat
Yep, we are all the product of extended family incest.
• January 17th, 2013, 03:48 AM
leohopkins
Thanks guys, this makes a bit more sense.
• January 17th, 2013, 05:11 AM
John Galt
Of course, one consequence of the calculation you have made is that beyond a certain point in time we are all pretty much related to everyone else. I claim I am a descendant of Alexander the Great and Julius Ceasar, but so are you.
• January 17th, 2013, 06:55 AM
river_rat
I think our most recent common ancestor lived longer ago then JC though JG?

Oh, to bring this back to mathematics, what we have here is that our pedigree tree is not a tree but at some point becomes an acyclic (unless things got really hinky in your family in the past) directed graph.
• January 17th, 2013, 08:40 AM
Strange
Quote:

Originally Posted by river_rat
I think our most recent common ancestor lived longer ago then JC though JG?

For the entire human population, it is estimated to be between 5,000 and 15,000 years ago (Identical ancestors point - Wikipedia, the free encyclopedia). For a smaller population, it will be more recent.
• January 17th, 2013, 09:22 AM
John Galt
Quote:

Originally Posted by river_rat
I think our most recent common ancestor lived longer ago then JC though JG?

Using as my source a dimly remembered BBC documentary, I think you only have to go back as far as 1200AD. I'll see if I can dig something concrete up.
• January 17th, 2013, 10:00 AM
Strange
This came up on a BBC radio program (*) the other day when someone asked if there was any evidence that Jesus was a descendant of King David. It turned out that 1,000 years later, pretty much all of The Big J's peers in the holy land would have been descendants of The Big D.

(*) More or Less: BBC News - Family trees: Tracing the world's ancestor
• January 20th, 2013, 12:25 PM
eaglepass
<IMG border=0 alt="" src="http://www.thescienceforum.com/images/icons/icon1.png"> January 17th, 2013, <FONT color=#88aace>03:12 AM</FONT>
<DIV style="MARGIN-LEFT: 40px">Hi guys,<BR><BR>I'm finding something difficult to understand and perhaps someone could tell me the logic behind this.<BR><BR>I have two parents, each one of my parents have two parents and so forth, so.<BR><BR>I have 2 parents<BR>I have 4 grand parents<BR>I have 8 great grand parents<BR>I have 16 great great grand parents<BR>and 32 great great great grand parents ........<BR><BR>With this exponential growth, if I carry on to just 37 generations of humans, it turns out that I should have just over 63 Billion great great (37 times...) grand parents. How can this be possible as I'm pretty sure that there have been far more than 37 generations of humans, but at no time have there ever been 63 Billion people living on the planet at the same time as a single generation.<BR><BR>Can someone explain this?<BR>thanks, <BR><BR>Hi leohopkins...I hope you are doing okay. Your observation got my attention when you mention the math invoved in it. However, I would like to share some observations that I have come accross along this topic in my lifetime.<BR><BR>There are some factors that, in my opinion, should be considered when it comes to the <U><STRONG>number of persons living on planet earth at the same time</STRONG></U>. The first and most important one is the death rate vs. the birth rate. Another factor that might have an effect on the amount of population <U><STRONG>(related to an amount of grandparents)</STRONG></U> is possible <U><STRONG>"infidelity"</STRONG></U> of two kinds: the man fathering children with more than one wife and the wife having children from more than one man. And, ofcourse, the divorce rate which has a similar effect on the infidelity factor. Another factor that may have some effect on this topic is incest. These are just a few of the factors that may affect the total number of grandparents living on planet earth at the same time. The same parent may have been counted more than once!<BR>MY QUOTE: "IN ORDER TO THINK OUT THE BOX, ONE MUST FIRST STEP OUT OF THE BOX!"<BR>eaglepass</DIV>
• January 20th, 2013, 02:53 PM
Dywyddyr
Quote:

Originally Posted by eaglepass
I hope you are doing okay. Your observation got my attention when you mention the math invoved in it.

It's a pity it didn't get your attention as far as logic is concerned.

Quote:

The first and most important one is the death rate vs. the birth rate.
And how would the death rate affect the general fact that each person has two parents? Even if both died - one after conception, the other after giving birth they must have been alive at the same time to manage conception.

Quote:

Another factor that might have an effect on the amount of population (related to an amount of grandparents) is possible "infidelity" of two kinds: the man fathering children with more than one wife and the wife having children from more than one man. And, ofcourse, the divorce rate which has a similar effect on the infidelity factor.
And much the same here: unless BOTH partners in a couple are alive it's not possible to "commit" infidelty. And, historically, divorce was harder to achieve.

Quote:

Another factor that may have some effect on this topic is incest. These are just a few of the factors that may affect the total number of grandparents living on planet earth at the same time. The same parent may have been counted more than once!
Right, because the incidence of incest is massively going to alter the general figure. How much incest would have to be committed to change that figure by even one order of magnitude?

Quote:

MY QUOTE: "IN ORDER TO THINK OUT THE BOX, ONE MUST FIRST STEP OUT OF THE BOX!"
Perhaps you should change your motto to "In order to think out of the box one must first learn how to think".
• January 20th, 2013, 07:30 PM
Write4U
Quote:

Originally Posted by leohopkins
Thanks guys, this makes a bit more sense.

This may help.

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