Anyone who studies their own roots and successfully manages to discover several generations of each of the family branches, finally realizes how problematic it is to clearly present the entire family tree, or the ancestors themselves. For with each generation of ancestors, it grows exponentially, so to say – in an avalanche. There is, however, a catch in this regard.
Indeed – as we wade into the past, with each generation we have to add more and more people to the ancestral chart. Everyone has two parents (even if they were unknown). That is why we have two parents, four grandparents, eight great-grandparents, etc. This growth follows an appropriate mathematical formula, which can be expressed by the statement that each successive generation of our ancestors contains as many people as the correspondingly greater power of the number 2. The generation of our parents consists of two people, so it is 21. The grandparent generation consists of four, which is expressed by the number 22. Great-grandparents are eight, which is the result of 23. So these numbers consistently double each time.
Meanwhile, it is assumed that there are three generations per one century on average – assuming that each subsequent one would be born every 30 years. We can say that there were 60 generations in the twenty centuries from the birth of Christ. If it was possible to establish information about our ancestors who lived 2,000 years ago and we would like to know how many lines in the family tree should be prepared for this one generation only, we would have to raise the number 2 to the 59th power. And that would give us a pyramidal number of over five hundred quadrillion (!) people (you would need 18 digits to write this number)… That’s what math says.
At the same time, there is probably no need to convince anyone that at the time when Octavian Augustus was the Roman emperor, there were not so many people on Earth and there could not be so many, because even the surface of our planet would not allow it (including the oceans! You can calculate it yourself). Regardless of whether one recognizes the origin of man from simpler forms of life through evolution, or from the biblical Adam and Eve – both assumptions indicate that “in the beginning” there were fewer of us and the population only grew with time.
These types of calculations can be the foremost entertainment for those who love math puzzles, but some genealogists may wonder where these conflicting conclusions come from? Of course, this problem was noticed, recognized and discussed a long time ago for example by the distinguished Polish historian and genealogist Włodzimierz Dworzaczek and many other researchers. Various terms are used for this phenomenon – pedigree collapse, ancestral loss, ancestor reduction, ancestral looping, ancestral identity, and more.
The explanation for this pedigree collapse is very simple – well, our ancestors were more or less related to each other, and thus, some of them had the same ancestors. And this is what leads to the so-called “loss” of ancestors – but only in our ancestors’ description, but in fact each of them always had two parents.
Perhaps quite a brutal, but a very clear example could be the family tree of a person coming from an incestuous relationship – such a person has two parents and instead of four grandparents, he has only two of them, because the parents would then be siblings. In this way, the paternal grandfather is identical to the maternal grandfather.
Genealogy in the 21st century may face a very serious challenge. Until now, no one could have had any doubt that each of the ancestors had two parents – a man and a woman. Today, however, the more and more transforming morality, as well as the advancement of technology in the field of genetics, biology of the human organism and reproduction, may lead to the fact that in the future it will not be so obvious to genealogists that each had two parents of different sex, or that a person was born as woman – she had to be buried as woman. Perhaps the pedigree collapse should be interpreted somewhat differently.