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Math / Geneaology Question

 
 
dupre
 
Reply Mon 27 Aug, 2007 10:09 am
Hi.

If

Quote:
Anatomically modern humans appear in the fossil record in Africa about 130,000 years ago.
Quote:


And, if

Each generation averages 25 years for a birthing (I know that's a stretch, but anyway ...)

And, of course,

Each person has two parents, who each have two parents, etc. ... (probably another stretch, with incest and all, but anyway ...)

How many direct ancestors would any given person have?

Thanks. It's not for a class, just something I've always wondered and can't figure out on my own.

Thanks, again!
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dupre
 
  1  
Reply Mon 27 Aug, 2007 10:11 am
Re: Math / Geneaology Question
Hi.

If

Quote:
Anatomically modern humans appear in the fossil record in Africa about 130,000 years ago.


And, if

Each generation averages 25 years for a birthing (I know that's a stretch, but anyway ...)

And, of course, if

Each person has two parents, who each have two parents, etc. ... (probably another stretch, with incest and all, but anyway ...)

How many direct ancestors would any given person have?

Thanks. It's not for a class, just something I've always wondered and can't figure out on my own.

Thanks, again!
0 Replies
 
Quincy
 
  1  
Reply Mon 27 Aug, 2007 11:47 am
2^(130 000/25).
0 Replies
 
dupre
 
  1  
Reply Mon 27 Aug, 2007 11:57 am
is 2^, two squared?

Sorry, I'm not at all good with math.

Thanks.
0 Replies
 
dupre
 
  1  
Reply Mon 27 Aug, 2007 12:03 pm
I'm getting a different answer on another forum:

Quote:
In the 1st generation before you you had 2 ancestors
in the 2nd generation before you you had 2x2 ancestors

in the nth generation before you you had 2^n ancestors

(ignoring that these overlap and so double count to an appalling extent)

Each generation is 25 years, so 130000 years is 5200 generations, so the number of ancestors is:



Um back in a sec . . .
0 Replies
 
dupre
 
  1  
Reply Mon 27 Aug, 2007 12:04 pm
Here's the link:

http://www.mathhelpforum.com/math-help/miscellaneous/18104-geneaology-ancestor-question.html#post66345
0 Replies
 
Quincy
 
  1  
Reply Mon 27 Aug, 2007 12:52 pm
Ok, given what you have stated, those are the only assumptions, that is all we are going to go by, then:

On average each generation is 25yrs, and humanity has been around 130 000yrs, so there have been 130 000/25 generations, right?

Then as this man says:

Quote:
In the 1st generation before you you had 2 ancestors
in the 2nd generation before you you had 2x2 ancestors

in the nth generation before you you had 2^n ancestors


So, after 130 000/25 generations, there are

2^(130 000/25) ancestors.
0 Replies
 
dupre
 
  1  
Reply Mon 27 Aug, 2007 01:01 pm
Thanks, quincy.

Is there a real number for that?

Any chance you could share it?

These guys at the math forum are hung up on plagues and such.

I guess they think that because there were plagues, my ancestors weren't able to procreate and I do not exist.

?????????

Of course, this is a huge approximation.

WishI could be specific, but no one kept records back then, right?

Geez!

Would think that would be obvious. . . .


???
0 Replies
 
Quincy
 
  1  
Reply Mon 27 Aug, 2007 03:02 pm
Using the calculator that comes with Windows (Start=>Accesories=>Calculator.), we get the exact result:

2.2697e+1565

Which is quite certainly more people than has ever walked this earth.
0 Replies
 
dupre
 
  1  
Reply Mon 27 Aug, 2007 03:14 pm
Hi, Quincy.

Got the reasonable answer here.

Forms of incest, overlapping. There's no way there were distinct parents for each person:

http://www.sosmath.com/CBB/viewtopic.php?p=144000#144000

Thanks, Quincy.

Are you really in Africa?

That is so darn interesting!

I'm in Texas.

Wish I could get out and see the world.

How lucky you are!
0 Replies
 
Quincy
 
  1  
Reply Tue 28 Aug, 2007 02:07 pm
dupre wrote:
Hi, Quincy.

Got the reasonable answer here.

Forms of incest, overlapping. There's no way there were distinct parents for each person:

http://www.sosmath.com/CBB/viewtopic.php?p=144000#144000


Hmm, yes, a more reasonable answer would be obtained if you think that the overwhelming number of people in the history of mankind have had numerous children, the ancestors of whom survived n generations, which would significantly reduce the number of ancestors.

Quote:
Thanks, Quincy.

Are you really in Africa?

That is so darn interesting!

I'm in Texas.

Wish I could get out and see the world.

How lucky you are!


Well, there is the good ad the bad of Africa; thankfully I experience mostly the good. I hope by "seeing the world" you mean the good and the bad.
0 Replies
 
dupre
 
  1  
Reply Tue 28 Aug, 2007 02:27 pm
I see what you are saying, but even if One Person had multiple siblings, it would in now way affect that One Person's number of ancestors.

And, even if that One Person's great-grandmother, and even, great-great-grandmother and so forth had siblings, it would in no way affect the number of direct ancestors that One, Individual, Person had.
0 Replies
 
Quincy
 
  1  
Reply Tue 28 Aug, 2007 02:31 pm
If you are trying to calculate the minimum number of people originally required to get the present population, then it would make big difference.
0 Replies
 
engineer
 
  1  
Reply Tue 28 Aug, 2007 02:38 pm
dupre wrote:
I see what you are saying, but even if One Person had multiple siblings, it would in now way affect that One Person's number of ancestors.

And, even if that One Person's great-grandmother, and even, great-great-grandmother and so forth had siblings, it would in no way affect the number of direct ancestors that One, Individual, Person had.


One person can be your ancestor numerous times. NOTE: After a few generations, this is not incest. Think of a village of 200 people in some past period where the population has been stable for 200 years and there are few newcomers. Everyone is related to everyone else several generations back, so if you marry someone from town, you will have many common ancestors. Your children will not have 2x the number of ancestors you had because both you and your spouse had ancestors in common.
0 Replies
 
dupre
 
  1  
Reply Tue 28 Aug, 2007 03:01 pm
Quote:
If you are trying to calculate the minimum number of people originally required to get the present population, then it would make big difference.


I think that's where some of the confusion is.

I am not trying to calculate the minimum number of people orginally required to get the present population.

I am trying to calculate how many direct ancestors One Person might have, back through to 5200 generations.

I have two parents.

Four grandparents.

Eight great-grandparents.

Sixteen great-grandparents.

Thirty-two great-great-grandparents.

And so forth.

Add them all up after 5200 generations back.
0 Replies
 
dupre
 
  1  
Reply Tue 28 Aug, 2007 03:30 pm
engineer,

Well said.

Thank you.
0 Replies
 
username
 
  1  
Reply Tue 28 Aug, 2007 04:09 pm
The generally accepted figure now, I think, is somewhere between 160,000 and 200,000 years, not just 130K, but anyway figuring with 130K, it's:

It's 2x2x2x2.... 5200 times, or 2 to the 5200th power. I haven't used logarithm tables in a fair number of years now, but I think this converts to roughly 10 to the 1560th power, that is ten followed by 1560 zeroes--which is a pretty large number. Considering there are around 6 billion people on earth today, which only equals 6 times ten to the 9th, and we know there were nothing like 10 to the 1560 people on earth 130K years ago, (and in fact there was a population crunch somewhere around 100K years ago, and fewer than 10,000 people are the ancestors of everybody alive today), it's pretty obvious that our ancestors were a really randy bunch, and pretty much everybody has done it with everybody else time and again.
0 Replies
 
dupre
 
  1  
Reply Tue 28 Aug, 2007 04:11 pm
username,

Randy, indeed!
0 Replies
 
akaMechsmith
 
  1  
Reply Sat 1 Sep, 2007 05:21 pm
When looking for your number of ancestors one has to keep in mind that every time someone mates with a cousin no matter how far removed is would cut the number of ancestors in the preceding generation for the progeny by half.

Since within a few hundred years back the chances of mating with a cousin of some sort improve considerably it makes it kind of hard to figure.

You are very likely to have some people ancestral to you on both sides.
How would you count them? In 10 (American Revolution) generations you will have 2048 ancestors. In 20-- 2,097,152. A million males and a million females.
There is a pretty good chance that any one of one group "knew" any one of the other :wink:

It works like this in epidemicology also. In the 70s there were numerous articles on how the AIDS epidemic would infect us all by 2005. Didn't happen Exclamation
0 Replies
 
spendius
 
  1  
Reply Sat 1 Sep, 2007 05:43 pm
Bestway to see how proximate it is to oneself is to realise the Jesus is about 70 odd rumpie-pumpies back and Homer just over twice that. 600 for the cave painters depending on which carbon dating machine you have faith in.
0 Replies
 
 

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