Dear Cecil: Have you ever considered the puzzle of doubling ancestors? Everybody has two parents, four grandparents, eight great grandparents, and so on back through time, with the number of ancestors doubling in each generation. Go back 30 generations and the number of ancestors tops one billion. Eventually we arrive at a time when we have more ancestors than there could have been people in the world. How can this be? Common sense, not to mention the book of Genesis, suggests the human race started off with a handful of individuals whose numbers steadily increased. What are the implications of these two surging numerical tides, ancestors and descendants, butting head to head? Enclosed is a $10 check for the trouble of a personal reply. George M., Monrovia, California

Cecil replies:

You ask a question as cosmic as this one and you think a lousy sawbuck is going to cover it? Keep your money until you can fork over some real cash. The ancestor puzzle has its explanation in what one genealogist has called “pedigree collapse.” This occurs when relatives, usually cousins, marry, in effect narrowing the family tree. (Fortunately for the gene pool, most of the cousins are only distantly related.) When this happens you find that many of the “slots” in a given generation of your family tree are filled by duplicates.

Consider an extreme case. Mr. and Mrs. Nosepicker have two children, a girl and a boy. These two develop an unnatural yen for one another and marry. Six months later the girl gives birth to an eight-pound horseradish with a lisp. In theory, the horseradish has four grandparents. In reality, its maternal and paternal grandparents are identical. Two of the four grandparent slots are thus filled by duplicates — pedigree collapse with a vengeance. Only slightly less extreme is the case of Alfonso XIII of Spain (1886-1941). Because of inbreeding in the royal family, he had only ten great-great-grandparents instead of the expected 16.

If you go back far enough, however, pedigree collapse happens to everybody. Think of your personal family tree as a diamond-shaped array imposed on the ever-spreading fan of human generations. (I told you this was cosmic.) As you trace your pedigree back, the number of ancestors in each generation increases steadily up to a point, then slows, stops, and finally collapses. Go back far enough and no doubt you would find that you and all your ancestors were descended from the first human tribe in some remote Mesopotamian village. Or, if you like, from Adam and Eve in the Garden of Eden.

These simple facts have given rise to some remarkable displays of statistical pyrotechnics. Demographer Kenneth Wachtel estimates that the typical English child born in 1947 would have had around 60,000 theoretical ancestors at the time of the discovery of America. Of this number, 95 percent would have been different individuals and 5 percent duplicates. (Sounds like Invasion of the Body Snatchers, but you know what I mean.) Twenty generations back the kid would have 600,000 ancestors, one-third of which would be duplicates. At the time of the Black Death, he’d have had 3.5 million — 30 percent real, 70 percent duplicates. The maximum number of “real” ancestors occurs around 1200 AD — 2 million, some 80 percent of the population of England.

Pedigree collapse explains why it’s so easy for professional genealogists to trace your lineage back to royalty — go far enough back and you’re related to everybody. For that matter, you’re probably related to everybody alive today. Some geneticists believe that everybody on earth is at least 50th cousin to everybody else. For a fuller discussion of the above, see The Mountain of Names, by Alex Shoumatoff (1985).

Cecil Adams

Send questions to Cecil via cecil@straightdope.com.