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The day I finished this book I ran across an article purporting to say that we are all directly related to Charlemagne. Mr. Lee thesis cannot be true because even he admittedly states that the formula does not take into account factors that would influence a proper answer. Here is a portion of what he has to relate:


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Thanks for posting. I'm not a mathematician, so that may be the reason I'm not following this line of thought well enough Johnny; and I also cannot work out who the Mr Lee you refer to is  but maybe I haven't looked at this aspect for so long that I'm forgetting a reference that I posted? :( Let me take a stab at engaging you though. You say =In my opinion, this mathematical formulation is nonsensical or a nonsequitur for all practicality. It is an insult to genealogist who has patiently traced direct bloodlines. We may all be related to Charlemagne as we are related to each other but not in a direct line. But to say we are all directly related to Charlemagne is wishful thinking. The line from Charlemagne in the 8th Century means the calculation is based on one person being Charlemagne and 14,999,999 are not Charlemagne. It assumes that the 15 or so million males and females, living at the time, other than Charlemagne did not exist. They did not produce, or did or did not contribute to the holes in the probability theory. Now the number of probably descendants is not just one trillion but 15 million trillion. How can this be? An utterly mind boggling and confusing figure. More importantly it is not a valid figure for researching ancestors.= >It doesn’t assume the 15 million others don’t exist at all. I think it assumes that we are equally likely to be descended from each of them (whose lines are still going today) – if we know we have European ancestry.


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=None of the probability formula takes into account wartime deaths, couples who do not produce, disease or the birth and death rates. These three factors alone could nullify all probability calculations.= >I think they do take attrition into account, simply because the figure is worked backwards from the surviving descendants living today. If you are alive today, the number of 30th great grandparents you could have is 4 thousand million; which so far exceeds the Europeans alive at the time as to make it highly probable that you are descended on at least one line from all of those whose descent lines survived into the 21st Century (ie Virtually impossible that you aren't.) More recently, genetics has confirmed what statistics suggested: http://www.nbcnews.com/science/sciencenews/alleuropeansarerelat.... 

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=I choose to look only at people who can prove that they have a direct line to Charlemagne based on lineal research, not probability. So much for the defeatist attempt to neutralize the elitists= >I suspect that this is the crux of your objection to the statistical point that the European descendant alive today who is not descended from Charlemagene is far more unique than the one who is. Well then Geni is a great place for you, because the genealogical paper trail is what it tracks. (Assuming the paper trail is falsifiable! :)) So everyone who has posted here has the paper trail to ‘prove’ their connection to Charlemagne. The point the statistical articles referenced on his profile are making is not intended to diminish that achievement so much as to make you aware that it is nothing special to be descended from Charlemagene; what is special is being able to track how you are. 

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Charlemagne, Emperor of the West is Ulf Ingvar Göte Martinsson's 30th great grandfather!


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Johnny, if you're interested in this subject and you like math you might like Joseph Chang's 1999 paper "Recent Common Ancestors of All PresentDay Individuals". http://www.stat.yale.edu/~jtc5/papers/CommonAncestors/AAP_99_Common... As far as I know, this was the seminal article that created the meme we are all descended from Charlemagne. There have been other articles that extend and clarify his thinking. As Sharon says, if there were only 15 million people in Europe in the time of Charlemagne and you have 4 thousand million (4 trillion in American numbers) ancestors in that generation, the odds are astronomical that you are descended from every person in Europe who has living descendants. You are approaching the problem in a different way, by calculating the probability that a specific person alive in Charlemagne's generation has living descendants. I agree, that method can't give a reliable answer because so many lines have died out. BTW, people use a lot of different numbers to represent the number of ancestors alive in the time of Charlemagne. You can easily calculate your own preferred number by taking 2 to the power of the number of generations. If 30 generations, then 2 to the 30th power, or 1,073,741,824. If 35 generations, then 2 to the 35th power, or 34,359,738,368. Google will do the math for you. Just type in "2 to the 30th power". I think you already know this, but I'm pointing it out for other people who might not. 

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I've always thought a better criticism of this model would be that it doesn't adequately take into account the problem that marriage is not random. It ignores both class and geography. People tend to marry at or near their own social class, and they tend to marry someone from a neighboring farm or village. I've had a chance to pose this question to some of the experts. Their answer is that class and geography slow the initial rate of diffusion, but don't change the result. Certainly, during the first few generations Charlemagne's descendants were primarily royals and nobles. But, with royal bastards, and foreign marriages, and military defeats, and all the other things that make history interesting, his descendants began to spread into the general population. Three hundred years after Charlemagne, all European kings and substantial numbers of their nobles were descended from him. In countries like England and Scotland that had greater social mobility the spread would have been faster. In countries like Germany that were more socially rigid the spread would have been slower. But in all cases, the spread kept going. 4 trillion is a huge number to argue against. You'd be thinking that nowhere in all those people did anyone move into the area or marry just a little outside their class. I'm not sure I accept this answer entirely. Probably it's right and I'm just stubborn, but my experience has been that it's relatively common for British people to find descents from Charlemagne and relatively uncommon for German people. And my gut says that even if everyone has at least one line to Charlemagne most people's ancestry is going to be a bit more concentrated in the class and area their proven ancestors came from. 

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Several people have pointed out that DNA studies are tending to confirm the mathematical model, so this 2013 paper "The Geography of Recent Genetic Ancestry across Europe" is worth reading. http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.p... He accepts the mathematical model. "1,000 years is about 33 generations, and 2(33)≈10(10) is far larger than the size of the European population, so long as populations have mixed sufficiently, by 1,000 years ago everyone (who left descendants) would be an ancestor of every presentday European." I've been trying to think of a way to summarize the paper in plain language, but I don't think I can improve on this quote from the Abstract: "We find that a pair of modern Europeans living in neighboring populations share around 2–12 genetic common ancestors from the last 1,500 years, and upwards of 100 genetic ancestors from the previous 1,000 years. These numbers drop off exponentially with geographic distance, but since these genetic ancestors are a tiny fraction of common genealogical ancestors, individuals from opposite ends of Europe are still expected to share millions of common genealogical ancestors over the last 1,000 years." In other words, the DNA shows that people across Europe have common genetic ancestors. The number of common ancestors is higher for neighboring populations, and lower for distant populations. The authors give an example "we estimate that someone from Hungary shares on average about five genetic common ancestors with someone from the United Kingdom between 18 and 50 generations ago." There are many other interesting examples. But (follow the math), "we would conservatively estimate that for every genetic common ancestor there are tens of millions of genealogical common ancestors. Most of these ancestors must be genealogical common ancestors many times over, but these must still represent at least thousands of distinct individuals." So, what we see in the DNA is consistent with the mathematical model that says, "most people alive today in Europe share nearly the same set of (European, and possibly worldwide) ancestors from only 1,000 years ago". 