IMPLICATIONS FROM MATHEMATICS.
*[Kannst du mir verzeihen?]
Too often, genealogists ignore their mathematics. We have seen recently how the number of ancestors grows very rapidly as we go back through the centuries. One of the implications of this is that the source of individual's gene pool is very large. We should be studying the broad field, not one specific path out of an uncountably large number. These individual lines count for very little in the large or total picture. In addition, an individual line extended over many generations, even though it appears to have names in each generation, is probably not correct.
To illustrate this last point, let us take the specific case of a lineage that purports to go back to Charlemagne. We have seen that there should be about forty-two generations in such a path. Let us ask what is the probability that each generation is correct.
First, we will note an observation. With the ease with which a paternity test can be made, some hospitals were proposing to test whether the paternity of each new born was correctly given in the paper work. The number of failures in confirming the father was so high that the hospitals saw that they had to abandon this effort. Too many people would be upset. (The failure rate was in the order of ten percent; e.g., the probability that the stated father was correct was 0.9.)
In the sequence back to Charlemagne, there are many reasons there might be an error. Confusion of names is one. False paternity is another. Recording errors and deliberate mistatements are other reasons. If we said that the probability that each step is correct is 0.97 (three times out of a hundred there is an error for some reason), then the probability that all of the steps are correct is the product of 0.97 times itself for 42 times. The answer is 0.28. In other words, there is only one chance out of four that the claim is true.
We are led to the conclusion from our recents studies that the probability that a "European" person today is a descendant of Charlemagne is very high. At the same time, the claim for a particular path back to Charlemagne is probably not true. We would do better to study the generalities and not the specifics. DNA studies are one way of doing that. They can give us percentages of earlier groupings which are present in an individual's DNA. And the DNA permits us to go much farther back in time than any study of specific lines can.
*[Can you forgive me?]
(27 Apr 07)
We gratefully acknowledge the work of John Blankenbaker who published over 2,500 Germanna History Notes via the Germanna-L@rootsweb.com email list from 1997 to 2008. We are equally thankful to George Durman (Sgt. George) for hosting the list and republishing the notes via rootsweb.com.