This month's Who's Counting briefly examines three very different stories in the news. The first concerns Dan Brown's "The Da Vinci Code" and the movie of the same name. The novel is based on the premise that Jesus married and had children, and that a direct descendant of his is alive today.
Probability theory tells us, however, that if Jesus had any children, his biological line would almost certainly have either died out after relatively few generations, or else would have grown exponentially so that many millions of people alive today would be direct descendants of Jesus.
Of course, this is not a special trait of Jesus' descendants. If Julius Caesar's children and their descendants had not died out, then many millions of people alive today could claim themselves Caesar's descendants. The same can be said of the evil Caligula and of countless anonymous people living 2000 years ago. It is not impossible to have just a few descendants after 2000 years, but the likelihood is less than minuscule.
The research behind these conclusions, growing out of a subdiscipline of probability theory known as branching theory, is part of the work of Joseph Chang, a Yale statistician, and Steve Olson, author of "Mapping Human History: Genes, Race, and Our Common Origins."
Going back another millennium, we can state something even more astonishing. If anyone alive in 1000 B.C. has any present day descendants, then we would all be among them. That is, we are descended from all the Europeans, Asians, Africans and others who lived 3,000 years ago and have descendants living today.
Consider the implications for future generations. If you have children and if your biological line doesn't die out, then every human being on earth 2,000 or 3,000 years from now would be your direct descendant.
Getting back to "The Da Vinci Code," we can conclude that if the heroine of the book were indeed descended from Jesus, then she would share that status with many millions if not billions of other people as well. This makes the book's plot even harder to swallow, but then probability was never much of a match for fiction or Hollywood.
Announcing Project Safe Childhood last month, Attorney General Alberto Gonzales cited a frightening figure: "It has been estimated that, at any given time, 50,000 predators are on the Internet prowling for children." The only problem with this statistic is that it seems to have been made up out of whole cloth.
The phrase "at any given time" may be Gonzales' own bit of hyperbole, but his office cited media outlets that have focused on pedophiles and used the 50,000 statistic. Some involved with the shows in turn cited law enforcement agents for the figure, and now the attorney general cites the media.
Jason McClure, a writer on legal affairs, recalls that in the 1980s, 50,000 was the number of people killed annually by satanic cults as well as the number of children kidnapped annually by strangers. Both of these numbers later proved baseless and absurdly high but perhaps derived some of their initial appeal from the roundness of the figure and its middling nature, neither too small nor too large.
In any case, this is another instance of a common phenomenon: A number gains a certain currency when commentator A pulls it out of ... the air and is then cited by B as the number's source; B is cited by C as the number's source; C is cited by D; and so on, until someone in the loop is cited by A, and few ever check to see if the number has any validity. Still, for a while at least, "everyone knows" it's true.
Home Run Records and Prime Numbers
Thirty-two years ago, Hank Aaron hit his 715th home run and surpassed Babe Ruth's record of 714, a feat that Barry Bonds accomplished just last month. Reams of newsprint have been devoted to various aspects of these record-breakings but not well known is that Aaron's breaking of the record stimulated a spate of mathematical papers about what has come to be known as Ruth-Aaron pairs.
If we break 714 into its prime number factors, we find that 714 = 2 x 3 x 7 x 17. Likewise 715 = 5 x 11 x 13. Adding the prime factors of 714 and 715, we find that they have the same sum. That is, 2 + 3 + 5 + 17 = 29, and 5 + 11 + 13 = 29. Consecutive numbers like 714 and 715 whose prime factors add up to the same number have come to be called Ruth-Aaron pairs.
Interestingly, if we multiply 714 (which equals 2 x 3 x 7 x 17) by 715 (which equals = 5 x 11 x 13), we find that 714 x 715 = 2 x 3 x 5 x 7 x 11 x 13 x 17. So we have the product of the two consecutive whole numbers, 714 and 715, that is equal to the product of the first seven prime numbers: 2 x 3 x 5 x 7 x 11 x 13 x 17.
In any case, as is their wont, mathematicians tried to find out how common these properties were among pairs of consecutive numbers and whether there were arbitrarily large examples of such pairs. (No one knows yet.) Even Paul Erdos, the famous peripatetic mathematician wrote about Ruth-Aaron pairs (or Ruth-Aaron-Bonds pairs) and proved a crucial theorem about them.
Having grown up in Milwaukee, where Aaron played for years for the Braves (before the team moved to Atlanta), I can't help but hope that "Hammering Hank's" record of 755 home runs stands, even though the latter number (755 = 5 x 151) seems to be rather mathematically undistinguished.
Professor of mathematics at Temple University, John Allen Paulos is the author of best-selling books including "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.