In the June 2008 Bulletin of the Saskatchewan Genealogical Society, an article by John Grenham was published bearing the above title.  Since answering the question posed in the title was the starting point of my genealogical exploration, I am borrowing some of his words  here.  He says:  "You have two parents, four grandparents, eight great-grandparents, sixteen great-great-grandparents, thirty-two great-great-greatgrandparents - the numbers tend to get a little blurry if you go much further..." but you get the idea.  

If you presume a conservative three generations in each century, around the year 1000, thirty generations ago, you should have over a billion ancestors.  My genealogical software has the capability of keeping track of these numbers, and since one of my ancestors was kind enough to track back one family line to the year 1000, I can attest to the billion figure.  If I put my name at the #1 position on the ancestry tree, and go back to my earliest ancestor on that line, his number, in the early 1000s on my computer is just under a billion.  That is, if all the lines of my ancestry were filled in, I would have roughly a billion direct ancestors in my data base.  

I don't, of course;  I have only something like 23,000 in my data base, and while they are all CONNECTIONS, they're not all direct ancestors;  many of them are people who married into my family lines.  

But still,  that billion figure for the year 1000 represents at least three times the entire population of the planet.

Back to Grenham:  "The calculation assumes that none of the couples over those thirty generations was in any way related.  If you marry your second cousin, your children will have only fourteen great-grandparents, not sixteen, twenty-eight great-great-greats instead of thirty-two.  At a stroke you will have removed more than 130 million of those notional ncestors a thousand years ago.  Marry your third cousin and you lose almost seventy million putative ancestors, and that still assumes that none of the intervening couples was related.  If just one set of grandparents in that third-cousin marriage were also third cousims, another four million ancestors vanish."

"In fact," says Grenham, "the chances are that almost all of your ancestors were related to each other in some way.  In the relatively settled rural areas of humanity until relatively recently, third or fourth cousin marriages were the norm, not the exception.  If you reverse the perspective the results are just as peculiar.  Pick any of your ancestors a thousand years ago.  Obviously he or she has had descendants in each of the intervening thirty generations, since you exist.  If more than child in each of those generations had children themselves, a very conservative assumption indeed, then you are only one of several hundred million descendants of that ancestor."

My data base does not, as noted above, contain several hundred million descendants of my ancestor born in the year 1037.  But my great-grandfather traced only ONE LINE of my many lines of ancestors.  It does not even contain all the descendants of my generation, and my children's and grandchildren's generations  - although I am working hard to acquire that information.  There is just TOO MUCH!  A fellow genealogy enthusiast, a second cousin in Cumbria, England, has told me that if it weren't for the fact that many of the family lines in England in the 19th and early 20th centuries were "without issue" he would have been unable to encompass the whole family in one tree.  That cousin does his genealogy work without benefit of computer...

Again, Grenham: "Thinking about ancestors on this scale might seem trivial, but it has some interesting implications.  The fact is that we are all a lot more related than we care to realize.  It should be less of a surprise to a genealogist than to a geneticist that 95% of all Europeans share the genes of seven women who loved 45,000 years ago.  Even those seven were probably second cousins."

Here Grenham is referring to Bryan Sykes' book, "The Seven Daughters of Eve," 2001, WW Norton and Company, London.  And this web site  -   can lead you to information on how to send in your DNA to determine which one of the seven sisters is your ancestress.  One of our Niebuhr kin has already done that.