Charlemagne 742–814

Everyone is Descended From Charlemagne

[by Jack Lee]


Charlemagne 742–814

[Editor’ note– I stumbled across this fascinating article while researching Irish ancestors. Jack Lee has come up with an astounding revelation which most of us have thought of in reverse, as in– “So what if your 20th great-grandfather was the King of England’s personal bodyguard. Your gene pool has been greatly diluted since then.” This simply illustrates that we are all a lot more the same than we are different. ]

“As I was researching my Lee ancestral line back into the middle ages, I was excited to find that I am apparently a direct descendant of Charlemagne, the first Holy Roman Emperor. As I dug deeper, I found at least three separate lines of descent from him to me, and I saw more and more genealogical sites on the Web that claimed similar descent. This started me thinking about how likely it is that I, or anyone for that matter, might be descended from a particular person that far back. As a mathematician (though not by any means a probabilist), I figured I ought to be able to come up with at least a rough estimate of the probability. My conclusion, which was surprising (to me at least), is that

there is virtually no chance that anyone of European ancestry is not directly descended from Charlemagne.



“Here’s my reasoning. Charlemagne was approximately 40 generations back from the present day. Each person has 2 parents, 22 = 4 grandparents, 23 = 8 great-grandparents, … and 240, or approximately 1,000,000,000,000 (one trillion), 40th-generation ancestors, which means half a trillion male ancestors. Of course, since the entire male population of Europe at the time of Charlemagne was only about 15 million, these half trillion ancestors cannot all have been different men — obviously there has been a lot of cross-breeding, and many of our ancestral lines cross and re-cross, eventually ending up at the same person. Let’s assume that each of my 40th-generation male ancestors is a randomly-chosen man from eighth-century Europe (this is not really valid, but more on that below). Choosing any one such ancestor, say my father’s father’s … father’s father, the probability that that particular person is Charlemagne is one in 15 million. Pretty small. To put it another way, the probability that any particular ancestor was not Charlemagne is 1 – 1/15,000,000, or approximately 0.999999933

Do the Math

Do the Math

“But now consider the probability that none of my 40th-generation ancestors is Charlemagne. For that to happen, every one of my half trillion male ancestors has to not be Charlemagne, which would be an amazing coincidence. To see how amazing, let’s compute the probability. Assuming all of these various not-being-Charlemagne occurrences are independent of each other (more on this below), the laws of probability state that the probability of all these events occurring simultaneously is obtained by multiplying together their individual probabilities:

(0.999999933)·(0.999999933)·…·(0.999999933) = (0.999999933)500,000,000,000.



“This turns out to be an incredibly small number: about one chance in 1015,000. That’s a one with 15,000 zeroes after it, a number that’s too big even to display in a browser window. This is way more than the number of atoms in the universe (which is estimated to be about 1080). Therefore, if this analysis is even remotely close to correct, it’s virtually impossible that Charlemagne is not among my direct ancestors.

“Of course, there are a few sources of errors in this analysis, so there are various corrections one could make that might yield a more accurate estimate. Most obviously, one’s ancestors are not in fact randomly chosen people from eighth-century Europe. For example, anyone who had no children, or no grandchildren, cannot be an ancestor of someone living now. (Charlemagne has well-documented descendants down to the present day.) More generally, wealthy people survived at a far higher rate than the rest of the population, and so were much more likely to produce descendants – thus one’s ancestors are more likely to be found among the relatively small population of royalty and nobility, including Charlemagne. You might think of other, smaller, corrections, such as the fact that the probabilities of different ancestors being Charlemagne are not really independent: for example, if my father’s … father’s father was Charlemagne’s brother, then the probability that my father’s … mother’s father was Charlemagne himself is very small. And, of course, some of my ancestors came from outside of Europe. But I believe these effects cannot change the fact that the probability we’re talking about is so tiny as to be zero for all practical purposes.”

–Jack Lee

More Info:

  1. Charlemagne – Wikipedia, the free encyclopedia
  2. New Advent on Charlemagne
  3. Charlemagne — Articles, Video, Pictures and Facts
  4. Order of the Crown of Charlemagne In the United States of America
  5. Charlemagne (Holy Roman emperor) — Britannica Online
  6. BBC – History – Charlemagne
  7. Einhard: The Life of Charlemagne – Internet History Sourcebooks
  8. Charlemagne | The Economist
  9. Charlemagne | King of the Franks | Emperor of the Holy Roman Empire
  10. Middle Ages for Kids – Charlemagne
  11. News for Charlemagne
  12. François Hollande’s flawed vision for Europe
  1. The Mathematics Genealogy Project – Welcome!
  2. Potential Ancestors
  3. Redundancy in Ancestry
  4. The Mathematics Genealogy Project – Prolific Advisors
  5. Academic genealogy – Wikipedia, the free encyclopedia
  6. Unique Ancestors
  7. ‘Most Recent Common Ancestor’ Of All Living Humans
  8. The Mathematics Genealogy Project – YouTube
  9. The Royal We – Steve Olson – The Atlantic
  10. Marcotte Genealogy

About jayhack2012

I help you find actionable insight.
This entry was posted in Ancestry-Europe, Character Studies and tagged , , . Bookmark the permalink.

1 Response to Charlemagne 742–814

  1. Charlene B says:

    Re everyone being descended from Charlemagne, I am so glad I came across this post. I am not a mathematician nor do I have any background in statistics or genetics or anything remotely related to anything scientific. But soon after I joined I started wondering how many direct ancestors everyone has, for each generation going backwards.

    I was moved to do this because I got tired of people saying “my 5th-great-grandmother” rather than “one of my sixty-four 5th-great-grandmothers”. They even use that terminology on “Finding Your Roots” and “Who do you think you are?”

    My calculator only took me to 24th-great-grandparents, a total of 67,108,864 individuals. I knew it had statistical importance but I couldn’t explain it to people in a clear and concise way, because I couldn’t plug in any other numbers to show what I was trying to prove it meant.

    I just wanted to add two other concepts to the mix. I apologize if I am trying to compare the wrong concepts.

    #1 The chances of finding the link to royalty or famous people is much greater than finding the link to any of your other millions of ancestors from that same time period. They are the only ones who had books written about them and their descendants. Many of those books or portions of them have been re-printed or re-written or used as reference material during the past few centuries. Also, the gravestones of famous people and royalty are far more likely to still be standing and legible, than those of any other social class.

    #2 I think there is an additional theory that I hope makes sense. Even if someone doesn’t appear to be directly related to Charlemagne or his siblings, they very likely are directly descended from his grandparents, by way of a first cousin. Also likely part of nobility, also far more likely to survive to adulthood and have children who survived, just as you described in your article.

    Thank you for proving my point and then some,


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