Friday, July 10, 2009

MATHEMATICS AND GENEALOGY


In this planet, we, the human beings are more related of what we think. A mathematical explanation of this affirmation will take us to understand it, though the numbers initially could be a little deceitful.
We all necessarily have 2 parents. And 4 grandparents. And 8 great-grandfathers. And 16 great-great-grand-fathers. If we follow up to the sixth generation, we descend from 32 persons. In the seventh one, of 64. In the eighth one, of 128. In the ninth one, of 256. In the tenth one, of 512. In the eleventh one, of 1024. In the twelfth one, of 2048. And so on, until we find (oh!) in this exponential progression that in the generation N º 18 we descend from 131.072 persons. Hitherto, everything is possible. But if we continue forward, in the generation n º 32 - only 800 years ago – we should descend from 2 billion persons. And here the question comes: how can this be possible if, in the year 1200, there were no these inhabitants in the world, but only approximately 350 millions?
Steve Olson, author of “Mapping Human History ", together with Douglas Rhode, a neurobiologist of the MIT, and computer scientist, developed in 2004 interesting results on this question.
The response is a necessary consequence: in order that this has to happen (and it does) the ancestors have to repeat themselves between generations. For example: the same ancestor may be our forefather on the part of mother in the generation 32 and on the part of father in 31, etc. A simple equation illuminates these figures: 2 billions divided 350 millions, is 5.714. This means that, 800 years ago, our ancestors are repeated in our genealogical trees more than 5.000 times. If to 6 billion today inhabitants the ancestors repeat themselves 5.700 times, it is highly possible that 800 years ago almost we all have common ancestors. If we continue backward in the time, and there are less and less available people to put in the family trees and more branches of 6500 million family trees of the people living today, it’s mathematically inevitable that in some point, will be someone who appears at least once in everybody’s tree. And continuing backward, there will come a time in which every person of the Earth is an ancestor of all of us, until, certainly, someone is the common ancestor of everyone.
In this calculation will be necessary to deduce those who died without leaving descent, and the lines of interrupted lineage.
Inversely, any person that, 800 years ago has emigrated from a continent to other one might be the ancestor of more than 2 billion individuals, nowadays.
Surprising, isn’t it?
Therefore, because of this, it’s necessary to have some care about the ideas on different races, ethnics and the prejudices that all of that transports: all the human beings are more siblings of what we believe!
. “No matter the languages we speak or the color of our skin, we share ancestors who planted rice on the banks of the Yangtze, who first domesticated horses on the steppes of the Ukraine, who hunted giant sloths in the forests of North and South America, and who labored to build the Great Pyramid of Gizeh,” says Steve Olson in an article of Nature.

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