The mathematical study of genealogy indicates that everyone in the
                   world is descended from Nefertiti and Confucius, and everyone of
                      European ancestry is descended from Muhammad and
                                   Charlemagne 
                                        
                                   by Steve Olson 
                                        
                                      ..... 
                                        
                     A  few years ago the Genealogical Office in Dublin moved from a
                       back room of the Heraldic Museum up the street to the
                       National Library. The old office wasn't big enough for all the
                       people stopping by to track down their Irish ancestors, and
                  even the new, much larger office is often crowded. Because of its
                  history of oppression and Catholic fecundity, Ireland has been a
                  remarkably productive exporter of people. The population of the
                  island has never exceeded 10 million, but more than 70 million people
                  worldwide claim Irish ancestry. On warm summer days, as tourists
                  throng nearby Trinity College and Dublin Castle, the line of visitors
                  waiting to consult one of the office's professional genealogists can
                  stretch out the door.

                  I suspect that many people have had a fling with genealogy somewhat
                  like mine. In my office I have a file containing the scattered lines of
                  Olsons and Taylors, Richmans and Sigginses (my Irish ancestors),
                  that I gathered several years ago in a paroxysm of family-mindedness.
                  For the most part my ancestors were a steady stream of farmers,
                  ministers, and malcontents. Yet a few of the Old World lines hint at
                  something grander—they include a couple of knights, and even a
                  baron. I've never taken the trouble to find out, but I bet with a little
                  work I could achieve that nirvana of genealogical research,
                  demonstrated descent from a royal family.

                  Earlier this year I went to Dublin to learn more about the Irish side of
                  my family and to talk about genealogy with Mark Humphrys, a young
                  computer scientist at Dublin City University. Humphrys has dark hair,
                  deep-blue eyes, heavily freckled arms, and a pasty complexion. He
                  became interested in genealogy as a teenager, after hearing romantic
                  stories about his ancestors' roles in rebellions against the English. But
                  when he tried to trace his family further into the past, the trail ran cold.
                  The Penal Laws imposed by England in the early eighteenth century
                  forbade Irish Catholics from buying land or joining professions, which
                  meant that very few permanent records of their existence were
                  generated. "Irish people of Catholic descent are almost completely cut
                  off from the past," Humphrys told me, as we sat in his office
                  overlooking a busy construction site. (Dublin City University, which
                  specializes in information technology and the life sciences, is growing
                  as rapidly as the northern Dublin suburb in which it is located.) "The
                  great irony about Ireland is that even though we have this long, rich
                  history, almost no person of Irish-Catholic descent can directly
                  connect to that history."

                  While a graduate student at Cambridge University, Humphrys fell in
                  love with and married an Englishwoman, and investigating her
                  genealogy proved more fruitful. Her family knew that they were
                  descended from an illegitimate son of the tenth Earl of Pembroke.
                  After just a couple of hours in the Cambridge library, Humphrys
                  showed that the Earl of Pembroke was a direct descendant of
                  Edward III, making Humphrys's wife the King's great-granddaughter
                  twenty generations removed. Humphrys began to gather other
                  genealogical tidbits related to English royalty. Many of the famous
                  Irish rebels he'd learned about in school turned out to have ancestors
                  who had married into prominent Protestant families, which meant they
                  were descended from English royalty. The majority of American
                  presidents were also of royal descent, as were many of the
                  well-known families of Europe.

                  Humphrys began to notice something odd. Whenever a reliable family
                  tree was available, almost anyone of European ancestry turned out to
                  be descended from English royalty—even such unlikely people as
                  Hermann Göring and Daniel Boone. Humphrys began to think that
                  such descent was the rule rather than the exception in the Western
                  world, even if relatively few people had the documents to
                  demonstrate it.

                  Humphrys compiled his family genealogies first on paper and then
                  using computers. He did much of his work on royal genealogies in the
                  mid-1990s, when the World Wide Web was just coming into general
                  use. He began to put his findings on Web pages, with hyperlinks
                  connecting various lines of descent. Suddenly dense networks of
                  ancestry jumped out at him. "I'd known these descents were
                  interconnected, but I'd never known how much," he told me. "You
                  can't see the connections reading the printed genealogies, because it's
                  so hard to jump from tree to tree. The problem is that genealogies
                  aren't two-dimensional, so any attempt to put them on paper is more
                  or less doomed from the start. They aren't three-dimensional, either,
                  or you could make a structure. They have hundreds of dimensions."

                  Much of Humphrys's genealogical research now appears on his Web
                  page Royal Descents of Famous People. Sitting in his office, I asked
                  him to show me how it works. He clicked on the name Walt Disney.
                  Up popped a genealogy done by Brigitte Gastel Lloyd (Humphrys
                  links to the work of others whenever possible) showing the
                  twenty-two generations separating Disney from Edward I. Humphrys
                  pointed at the screen. "Here we have a sir, so this woman is the
                  daughter of a knight. Maybe this woman will marry nobility, but
                  there's a limited pool of nobility, so eventually someone here is going
                  to marry someone who's just wealthy. Then one of their children
                  could marry someone who doesn't have that much money. In ten
                  generations you can easily get from princess to peasant."

                      he idea that virtually anyone with a European ancestor
                      descends from English royalty seems bizarre, but it accords
                      perfectly with some recent research done by Joseph Chang, a
                      statistician at Yale University. The mathematics of our ancestry
                  is exceedingly complex, because the number of our ancestors
                  increases exponentially, not linearly. These numbers are manageable
                  in the first few generations—two parents, four grandparents, eight
                  great-grandparents, sixteen great-great-grandparents—but they
                  quickly spiral out of control. Go back forty generations, or about a
                  thousand years, and each of us theoretically has more than a trillion
                  direct ancestors—a figure that far exceeds the total number of human
                  beings who have ever lived.

                  In a 1999 paper titled "Recent Common Ancestors of All
                  Present-Day Individuals," Chang showed how to reconcile the
                  potentially huge number of our ancestors with the quantities of people
                  who actually lived in the past. His model is a mathematical proof that
                  relies on such abstractions as Poisson distributions and Markov
                  chains, but it can readily be applied to the real world. Under the
                  conditions laid out in his paper, the most recent common ancestor of
                  every European today (except for recent immigrants to the Continent)
                  was someone who lived in Europe in the surprisingly recent
                  past—only about 600 years ago. In other words, all Europeans alive
                  today have among their ancestors the same man or woman who lived
                  around 1400. Before that date, according to Chang's model, the
                  number of ancestors common to all Europeans today increased, until,
                  about a thousand years ago, a peculiar situation prevailed: 20 percent
                  of the adult Europeans alive in 1000 would turn out to be the
                  ancestors of no one living today (that is, they had no children or all
                  their descendants eventually died childless); each of the remaining 80
                  percent would turn out to be a direct ancestor of every European
                  living today.

                  Chang's model incorporates one crucial assumption: random mating in
                  the part of the world under consideration. For example, every person
                  in Europe would have to have an equal chance of marrying every
                  other European of the opposite sex. As Chang acknowledges in his
                  paper, random mating clearly does not occur in reality; an Englishman
                  is much likelier to marry a woman from England than a woman from
                  Italy, and a princess is much likelier to marry a prince than a pauper.
                  These departures from randomness must push back somewhat the
                  date of Europeans' most recent common ancestor.

                  But Humphrys's Web page suggests that over many generations
                  mating patterns may be much more random than expected. Social
                  mobility accounts for part of the mixing—what Voltaire called the
                  slippered feet going down the stairs as the hobnailed boots ascend
                  them. At the same time, revolutions overturn established orders,
                  countries invade and colonize other countries, and people sometimes
                  choose mates from far away rather than from next door. Even the
                  world's most isolated peoples—Pacific islanders, for
                  example—continually exchange potential mates with neighboring
                  groups.

                  This constant churning of people makes it possible to apply Chang's
                  analysis to the world as a whole. For example, almost everyone in the
                  New World must be descended from English royalty—even people
                  of predominantly African or Native American ancestry, because of
                  the long history of intermarriage in the Americas. Similarly, everyone
                  of European ancestry must descend from Muhammad. The line of
                  descent for which records exist is through the daughter of the Emir of
                  Seville, who is reported to have converted from Islam to Catholicism
                  in about 1200. But many other, unrecorded descents must also exist.

                  Chang's model has even more dramatic implications. Because people
                  are always migrating from continent to continent, networks of descent
                  quickly interconnect. This means that the most recent common
                  ancestor of all six billion people on earth today probably lived just a
                  couple of thousand years ago. And not long before that the majority
                  of the people on the planet were the direct ancestors of everyone
                  alive today. Confucius, Nefertiti, and just about any other ancient
                  historical figure who was even moderately prolific must today be
                  counted among everyone's ancestors.

                  Toward the end of our conversation Humphrys pointed out something
                  I hadn't considered. The same process works going forward in time;
                  in essence every one of us who has children and whose line does not
                  go extinct is suspended at the center of an immense genetic hourglass.
                  Just as we are descended from most of the people alive on the planet
                  a few thousand years ago, several thousand years hence each of us
                  will be an ancestor of the entire human race—or of no one at all.

                  The dense interconnectedness of the human family might seem to take
                  some of the thrill out of genealogical research. Sure, I was able to
                  show in the Genealogical Office that my Siggins ancestors are
                  descended from the fourteenth-century Syggens of County Wexford;
                  but I'm also descended from most of the other people who lived in
                  Ireland in the fourteenth century. Humphrys took issue with my
                  disillusionment. It's true that everyone's roots go back to the same
                  family tree, he said. But each path to our common past is different,
                  and reconstructing that path, using whatever records are available, is
                  its own reward. "You can ask whether everyone in the Western world
                  is descended from Charlemagne, and the answer is yes, we're all
                  descended from Charlemagne. But can you prove it? That's the game
                  of genealogy."