It is time to grade the homework. Joy came up with a hypothetical problem which I may not understand fully. Her suggested answer is in the ball park, in that her answer is greater than 0% and less than 100%. So far, good.
Her problem was this. She and a cousin both go back to two brothers who married two sisters at the fourth great-grandparent level. The gene pool in total would be at the level one more generation than this. So by the time we get back to then, they each would have 128 pairs of ancestors.
Let's work this out in detail. Joy and her cousin each have one set of parents, two sets of grandparents, four sets of great-grandparents, eight sets of g-g-grandparents, sixteen sets of g-g-g-grandparents, thirty-two sets of g-g-g-g-grandparents. This is the level at which two brothers married two sisters. To get to the common gene pool we need to go one more level at which there are 64 sets of g-g-g-g-g-grandparents. From this total set, two of the sets are in common, namely the parents of the brothers and the parents of the sisters. So the degree of relatedness is 2/64. Just to round this off in an easy to remember number, it is 3% of the genes in the two people today could have a common source. Probably the answer will not be exactly this because there is an element of randomness, but by the law of large numbers it should not deviate much from this.
The problem that Joy proposed went back several generations and the number of ancestors doubles at each generation. The number grows fast. (It is called exponential growth.)
Let us think about another situation together. What is the degree of relatedness between first cousins once removed? We found that first cousins shared 50% of the gene pool. Second cousins, if worked out, would share 25% of the gene pool. First cousins once removed could be expected to be somewhere between these two values. I believe the correct answer is 37.5%.
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Different subject. I had an email from Tivolt Zoltan in Hungary. It amazes me what communication has become with the Internet. It also shows the need for Euro-English to help us communicate.
Tivolt Zoltan had noticed that we had discussed the Tivolt name here. Before you think the idea (Hungarian origins) is crazy, remember that the eastern border of Austria and the western border of Hungary join. Some of our people are known to have come from Austria. Maybe some came from Hungary.
Tivolts live in southwest Hungary today, especially in the small village called Porrog. Maybe we will have another village to visit.
(12 Sep 02)
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.