I need help to figure out a math equation.

I have been thinking about who started the human chain reaction. Who started to populate the world. And i wanted to start out by trying to figure out my own chain of existence first. But how??

I have come to a huge problem. I thought that the easiest way was to just do it mathematically, but that wasn't as easy as i thought. I just wanted to change names with numbers.

Here is how i started.

Mom + Dad = me

It takes 4 people to create Mom and dad. Because Mom and Dad also have parents.

It takes 8 people to create the 4 who created mom and dad.

It takes 16 people to create the 8 .

And it takes 32 people to create the 16.

And 64 to create the 32.

And 128 to create the 64.

As you see the numbers only get higher and higher. And if i keep on going it will never end.

How can i figure out who the first link is in my chain of existence?


I know there are certain things i can leave out.

1. People who died without producing a offspring.

2. People who are sterilised and can't produce a offspring.

3. Brothers and sisters.

But how or where do i start to divide the equation by 2 so i end up with the first link?




[edit on 27.06.08 by spy66]

You should divide it every average generation. For instance, every 40-60 years you should kill off that generation, as that was the average life expectancy for the past few thousand years so every generation or so. Also you must factor in plagues, wars, and mass deaths every so often to account for population dropoffs. Then maybe you might start arriving at some interesting numbers. Also, many children over time have been born illegitamately, so factor that in too. Moreover, tracking back bloodlines will yeild many sources coming back to many differing reigions. Also, perhaps starting this equation solely from the bottom is erroneous. If you start with the assumption that ensuing generations came from a small limitied population perhaps you should work the equation from both ends as to meet in the middle. Hope this helps some how.

[edit on 10-6-2009 by dashen]

reply to post by spy66


Starting from the year you were born go backwards in time.......Every generation or group of parents , would be an average lifespan and mix that with the average age people have kids and you could come up with an approxamite date maybe.

Combine that time with the population humans were supposed to be at and maybe we could start to be on to something.

Great question and topic though... Has got me stumped...

Originally posted by dashen
You should divide it every average generation. For instance, every 40-60 years you should kill off that generation, as that was the average life expectancy for the past few thousand years so every generation or so. Also you must factor in plagues, wars, and mass deaths every so often to account for population dropoffs. Then maybe you might start arriving at some interesting numbers. Also, many children over time have been born illegitamately, so factor that in too. Moreover, tracking back bloodlines will yeild many sources coming back to many differing reigions. Also, perhaps starting this equation solely from the bottom is erroneous. If you start with the assumption that ensuing generations came from a small limitied population perhaps you should work the equation from both ends as to meet in the middle. Hope this helps some how.

[edit on 10-6-2009 by dashen]

Well the problem is: It doesn't matter how many i kill of as long as they have made a Kid.

A kid still has to have two parents even if they died in a war or by disease.
It takes two to make a kid.

The only way i can divide down the equation is if a lot of the kids where made from incest.

This problem also concerns you and your link. You will face the same problem as i do if you think about it

reply to post by spy66


That's why i think that there is reason to start with a hypothetical minimum of original points at the top of the equation, and you at the bottom and work your way to the middle. Logically it should look like a bell curve over time. And yes, you should very well expect much incest going back, that is how thing get back to normal after population dropoffs happen. And I do not mean proper incest, but first cousins reproducing will make a larger dent in the equation than you think.

[edit on 10-6-2009 by dashen]

Originally posted by dashen
reply to post by spy66

 

That's why i think that there is reason to start with a hypothetical minimum of original points at the top of the equation, and you at the bottom and work your way to the middle. Logically it should look like a bell curve over time. And yes, you should very well expect much incest going back, that is how thing get back to normal after population dropoffs happen. And I do not mean proper incest, but first cousins reproducing will make a larger dent in the equation than you think.

[edit on 10-6-2009 by dashen]

I see your point, and i have thought a lot about it.
But i was hoping to do it 100% accurate without using a hypothetical minimum of original points.

I could just start out with 2 hypothetically. But then it only becomes a hypothetical equation. Because it will add up no matter what as long as i am create. But why can't it be done from my end. Why do i have to start at the top to get the equation to go up.

If it can be done from the top i should be able to add it all up from the bottom and end up with at least 2.







[edit on 27.06.08 by spy66]

reply to post by spy66


There is a multitude of factors omitted here that make your initial assumptions poor in calculating with any degree of accuracy.

I will not even get into the trouble of mentioning the first couple one that sprung into my mind since it very soon become chaotic and its almost impossible to render a mathematical formula that represents reality/history.

However statistics which is a science by its own right may give you a hand of help when considering this more thoroughly.

Another hand of help i would suggest is using the knowledge of the human genome through the knowledge of DNA as a tool. I have read an article on DNA and all the past of our history it unfolds to us.

My guess is getting to study what the DNA has to offer in finding the answer you are seeking. I think it will complement your requirements if it does not fulfill them all together!

Take care !

There are infinite possibilities to you question. I don't believe this can be solved with math alone. There are to many factors you have to consider as well as a definent answer to when man was first on the earth. If you are a science believing person then you start with the first single celled organism that started our race. If you are a bible believing man then you can only go back to adam and eve. Also you have to take into consideration of when exactly where we call humans. We're we humans from the single celled organism or perhaps were weren't consider human till the time of the caveman. I do not believe this can be solved because of all the possibilities you have to choose from.

reply to post by spy66


You cannot begin tracking progenetors from the bottom solely, because the number would increase exponentially, defying known fact. Starting from a hypothetical number and rectifying it in the middle will help you balance and check the equation and help account for certain problems that arise in this sort of calculation.

Originally posted by GEORGETHEGREEK
reply to post by spy66

 

There is a multitude of factors omitted here that make your initial assumptions poor in calculating with any degree of accuracy.

I will not even get into the trouble of mentioning the first couple one that sprung into my mind since it very soon become chaotic and its almost impossible to render a mathematical formula that represents reality/history.

However statistics which is a science by its own right may give you a hand of help when considering this more thoroughly.

Another hand of help i would suggest is using the knowledge of the human genome through the knowledge of DNA as a tool. I have read an article on DNA and all the past of our history it unfolds to us.

My guess is getting to study what the DNA has to offer in finding the answer you are seeking. I think it will complement your requirements if it does not fulfill them all together!

Take care !

Well even if i study DNA i can never complete the whole link. Because non of us share the same DNA even within the family.

I could probably trace the tracks back to the 32 that was needed to create the 16. But i doubt it?

Now i am talking about things i have no clue about. But i know it takes two to tangle to create a kid.

Do you honestly think i can trace my DNA back to the original two.

If so we should share the same DNA.

I think what you are asking for is

2 ^ N

If we go back 8 generations,

2 ^ 8 = 256

If we go back 50, it's

2 ^ 50 = 1125899906842624

Of course there are many other things to take into account, so this 2 ^ 50 number looks way out of whack, as you say, issues like inbreeded, deaths, multiple children and so on all take place.

But that is at least what you appear to be hinting towards wanting in your post.

2 ^ 1 = 2
2 ^ 2 = 4
2 ^ 3 = 8
2 ^ 4 = 16
etc


[edit on 10-6-2009 by jimminycricket]

Originally posted by jimminycricket
Well, just a simple look at it, would be..

You need 2 people to make you..
They needed 2 to make each of them...
and so on, so it's a

2 ^ N issue

If we go back 8 generations,

2 ^ 8 = 256

If we go back 50, it's

2 ^ 50 = 1125899906842624

Of course there are many other things to take into account, as you say, like inbreeded, deaths, multiple children and so on, but if we say 50 generations at average age 25 of giving birth, that's only 1250 years...

I rushed a little on the math here, excuse me if I'm not quite spot on, but I think what you are asking for is the

2 ^ N

part.

Yes you are onto something. But how do i get N to disappear so i end up with the first link.

Life span have no meaning as long as they have made kids before they die. Because i am right here
It doesn't matter if they die after they have made the babies. Because their kid and some other kid kept the chain going by making their own kid.
Brother and sister dont matter unless they are the next link in my chain. But that's going to be a hard one to trace or put into the equation accurately?

But even if i have one incest case in my chain. Their parents need 4 to make them and so on.




[edit on 27.06.08 by spy66]

Sorry, I edited my post a few times to try and make it clearer, I'm not very good at explaining math.

basically, you substitute N for your number of generations, and you can use a calculator to work it out, most calculators will have a button, usually marked as x ^ y, power, or exponent.

Originally posted by jimminycricket
Sorry, I edited my post a few times to try and make it clearer, I'm not very good at explaining math.

basically, you substitute N for your number of generations, and you can use a calculator to work it out, most calculators will have a button, usually marked as x ^ y, power, or exponent.

I have tried that but the equation wont end. Not on my calculator. Because i don't know where the generation begins.

I also tried this by switching DNA with random numbers. But the equation only expands. It doesn't get smaller at all.

I don't think this one can be debunked at all. I have tried a few of the tips in here but they dont make the equation end up at a beginning. I only get more numbers to work with.

I can do a example with DNA by using numbers.

Lets say my DNA is: 1

The equation the easy way becomes like this:

Mom (1) + Dad (1) = 1 (me)

But since mom and dad both give of matter and energy to create me i can make a new equation.

0.5 + 0.5 = 1 (me)

It really doesn't matter what numbers you use as long as i am made.

And you don't escape the fact that you have to create 4 more equations to have your parents. And 8 more to have their parents.

I think what may be melting your brain and why your equation looks out of wack because it doesn't take into account how each branch of your tree can interlink.

For example, all the links from me, if taken in isolation can look like a massive number that makes no sence. However if we look at where my links overlap with yours, then look at how our links overlap with someone elses, you start to see that the numbers being talked about are all shared.

At a certian point in your links every family line connects. This is why the ultimate number would end up being the same for everyone.

[edit on 11/6/2009 by balrathamir]

Someone posted a similar question here: Population Numbers: Something is not right here.

Here is what I have learned about this problem:

Ancestors from different lines are not necessarily unique as pairing of relatives could allow for less than the upper bound of 2^(n-1) ancestors in the nth generation (assuming the first generation is oneself); for example, the ratio could be 510:1 in the 10th generation if there are two cousins in the 8th generation. This is known as pedigree collapse [1].

As a previous poster has mentioned, a way to visualize this is to follow two lines on a family tree; going back far enough these lines will intersect at a common ancestor. These intersections cause a divergence from the geometric progression 2^(n-1) and eventually the tree collapses to an identical ancestors point which for the current world population has been estimated to be between 5,000 and 15,000 years ago [2,3] with a population between < 1 million and 25 million [4,5].

Here is a recursive procedure to calculate the number of ancestors in the nth generation:

numAncestors(descendant, n)
if descendant.visited == true return 0
descendant.visited = true
if n == 1 return 1
return numAncestors(descendant->mother, n-1) + numAncestors(descendant->father, n-1)

As seen in this procedure, common ancestors result in some parents not being counted for a given generation i.e. pedigree collapse. If the theory of evolutionary common descent is correct then for large enough n (which depends on the variable rate of pedigree collapse) the tree collapses to the last universal ancestor or to an ancestral gene pool [6].

Originally posted by tmk81
Someone posted a similar question here: Population Numbers: Something is not right here.

Here is what I have learned about this problem:

Ancestors from different lines are not necessarily unique as pairing of relatives could allow for less than the upper bound of 2^(n-1) ancestors in the nth generation (assuming the first generation is oneself); for example, the ratio could be 510:1 in the 10th generation if there are two cousins in the 8th generation. This is known as pedigree collapse [1].

As a previous poster has mentioned, a way to visualize this is to follow two lines on a family tree; going back far enough these lines will intersect at a common ancestor. These intersections cause a divergence from the geometric progression 2^(n-1) and eventually the tree collapses to an identical ancestors point which for the current world population has been estimated to be between 5,000 and 15,000 years ago [2,3] with a population between < 1 million and 25 million [4,5].

Here is a recursive procedure to calculate the number of ancestors in the nth generation:

numAncestors(descendant, n)
if descendant.visited == true return 0
descendant.visited = true
if n == 1 return 1
return numAncestors(descendant->mother, n-1) + numAncestors(descendant->father, n-1)

As seen in this procedure, common ancestors result in some parents not being counted for a given generation i.e. pedigree collapse. If the theory of evolutionary common descent is correct then for large enough n (which depends on the variable rate of pedigree collapse) the tree collapses to the last universal ancestor or to an ancestral gene pool [6].

I have now used your equation but still i have to make a impossible assumptions with the equation (N) to get it to go up.

Because i cant use the nr "1" in my equation. Because it takes 2 to make a copy. And 4 to create the 2 and so on.

To give you a different picture of this: Lets say i get married and have kids. And my kids have kids with others. They have kids and so on.
I get a pyramid that expands out wards with other peramids from me and my wife down through our kids. But if i look up towards my parents the pyramid also expands but you have to flip the perami this time. And it will go on infinite with other peramids. Try it!

Its like i am the core existence of all pyramids. You see i cant use your equation to figure out the beginning of my chain. It will only end logically with my parents because they created me. If i go beyond my parents the assumption only gets bigger. And the equation gets more inaccurate.



I also would like to show you how i have done this but i don't know how i can get my images onto this site?






[edit on 27.06.08 by spy66]

reply to post by spy66


You would need a definite starting point or the equation would be infinite, which human existence is not. I would read some genealogy sites about the latest theories and finds regarding a 'Eve' of the human race. From there you can start, also I would use some computer program as the arithmetic will get extremely complex as the numbers increase, also a TI-83 calculator is good for help with equations and such. You might try putting it into a log rhythm format or something like that.

You left out imbreding...not trying to be funny here.

But sometimes there doesn't need 4 people to make your parents. If they are brother and sister...it only took 2 people to make your parents. Yah..it might seem sick to all of us...but it happens. And then it also happens with cousins, 2nd cousins, etc. Go back far enough and most of us are related...right?

So take cousins that have a child for instance. The child's line would go something like 1(child)