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Görgényi-paradox

The Görgényi-paradox is about a contradiction between a simple mathematic operation of exponentation and the commonly accepted idea of lineage and the perceptible growth of population on Earth. It states if every person have two parents and they also have two parents and so on ad infinitum, in relatively short time we can reach incredibly high numbers of ancestors needed to live one person today.

Contents

Presentation
The Görgényi-Paradox, or paradox of lienage, is a variation of the wheat and chessboard problem about geometric progression. It says since everybody has two parents and the two parents also have two parents and so on, the number of one person’s ancestors is equal with $$2^n$$, where $$n$$ is the number of a given generation. For example, if we say one generation from birth to give new life is an average 25 years than one thousand years is equal with 40 generations therefore the number of ancestors of every person today was 2 on the 40th power in 1014 A.D. It is the incredibly big number of 1 099 511 627 776, which is a nonsense.

History
The Görgényi-Paradox was formulated by Tamás Görgényi, Hungarian writer in 1992. His original intention was to prove falseness of every racist ideology by proving every single living person of today comes from the same ancestors. But it turned out the paradox is more interesting from other view points. He haven't published it because the theorem can be regarded as a simple logic fact recognizeable by anybody.

False attempts of solution
Most people can’t understand this paradox at first because it is just the opposite of the reality, nevertheless it is a valid contradiction between mathematics and facts. To help to see the problem let’s imagine a tower built from blocks. Every cube is supported by two blocks, but in that case every block also can hold two blocks, except on the sides, so it is an arithmetic progression. If the tower contains 40 stories the number of blocks in the bottom line will be only 40. But it is impossible to build a tower by the rules of geometric progression. If you understood you have 8 grand-grandparents and every one of them had 8 grand-grandparents also, and so on, you could see the $$2^n$$ leads to nonsensical numbers. The first attempt to solve the problem usually is the assumed fact of incest. But that is not just unrealistic to assume in one thousand years before us the incest was generally accepted but it's missing the point. The conception of every person requires the fusion of 2 gametes in a valid intercourse with insemination. The number of "valid coitions" in the 40th generation requires 1451.1 sexual intercourse in every second for 12 years on end. (The sexual maturity requires 12 years at least. 12 years contains 378 846 720 seconds. If we half the number of ancestors we get the number of "valid coitions", which is 549 755 813 888. Now we must divide it with the number of seconds.)

Evolution Theory
The problem is valid not just with humans but every living being with sexual reproduction. If we take insects, or amphibians, in which case the longevity of a generation is only a few year, we must suppose 1000 years before us existed so many individual insect or amphibian to produce the next generations that nobody could count them. And if we think on evolution and try to see hundreds million years the requested number of the ancestors of one lizard today is inexpressibly high. It means the theory of evolution must face the problem of its first rule: the species evolved by generation to generation.

Genealogy
In genealogy only the unilinear descent, or family tree research, and genetic disorder are the commonly accepted areas of interest. Generally they're going back only to six generations, and where they serch previous ancestors, for example in royal families, they are loking only on male-line, excluding the majority of the females.