Enumerating our forebears bears fruit, whether or not Liz marries Prince Rainier
From time to time here I have confessed my illiteracy in numbers, knowing that illiteracy was not quite the right word.
Now I know what to call myself.
Writing in Newsweek on “Orders of Magnitude,” the Temple University mathematics professor John Allen Paulos notes that an inability to grasp large numbers is innumeracy; ergo, a person thus disabled is an innumerate.
“This disability is so widespread,” he says, “that it can lead to bad politics, poor personal decisions (and) even a susceptibility to pseudoscience.”
He points out that if people understood the laws of probability they would be less inclined to believe in psychics, who profess to predict the future.
“That some unlikely event will come to pass is likely; that a particular one will is not. The pronouncements of psychics or astrologers are sufficiently vague so that the probability that some predictions will occur is very high. It is the particular incidents that are seldom true. Yet the overwhelming majority of incorrect predictions are conveniently forgotten and the correct ones are greatly magnified by publicity. Without a feel for number and chance, people can easily be misled.”
Although the National Enquirer has not asked me for an interview, my counterpredictions of psychic predictions made in that and similar checkout-counter newspapers have been perfect over the past few years.
Lavinia D. Hobart of Marina del Rey writes that she saved the counterpredictions I made on Oct. 4, 1985, and notes that every one of them was correct.
Among the predictions I counterpredicted were these: Liz Taylor will marry Prince Rainier; Frank Sinatra and several other celebrities will be trapped in the Monaco palace, but Princess Caroline will lead them to safety; “Dallas” star Patrick Duffy will be shot in real life as he attempts to foil a bank holdup in Los Angeles (actually, and unfortunately, Duffy’s parents were shot in real life by a holdup man in Montana); the Air Force will admit it has a UFO hidden in the desert; Monaco’s Prince Albert will have a sizzling romance with 50-year-old Brigitte Bardot.
“None of these were on target,” Hobart points out, “but you scored 100% on your predictions.”
Recently I have tried to cope here with the magnitude of a billion and a trillion, and the amount of interest that would accrue from $1 lent at 6% interest compounded from the beginning of the Christian era. (It would be $1,809,041 plus 42 zeroes.)
With important concepts like those to worry about, I don’t know why I should bother with the problem of how many ancestors we have, but since George O. Morrison of Monrovia posed the question, I can’t get it out of my mind.
Morrison is puzzled by the apparent paradox in the fact that as we go back in time our forebears double every generation. Thus, we each have two parents, four grandparents, eight great-grandparents and 16 great-great-grandparents.
He has worked it out mathematically back through 30 generations and found that the total of direct ancestors each of us would have had then is 1,073,741,824.
Figuring three generations per century, 30 generations would take us back 1,000 years, to the 10th Century. Morrison is right in suspecting that the world didn’t even have that many people in 986. According to the Encyclopedia Britannica, the world population in AD 1000 was only 340 million.
Then how, he wonders, can each of us have more than 1 billion direct ancestors?
I suspect it has something to do with intermarriage. When a generation reaches the number of 16, cousins begin to intermarry, and the pool of grandparents is reduced.
What happens when we take the generations back to the beginning of the species?
If we believe the fundamentalists, and accept the theory that Adam and Eve were our sole progenitors, then of course our number of ancestors somehow has to dwindle down to two in 6,000 years. (According to the Archbishop James Ussher, creation occurred in 4004 BC.)
How did Adam and Eve give rise to the family of man? We are told that they had three sons, Cain, Abel and Seth, and that later Adam had both sons and daughters, presumably by Eve. Cain slew Abel in a jealous rage; Abel apparently had no offspring.
Genesis tells us that “Cain knew his wife,” and she bore him a son; that son begot a son, and that son begot a son, and so on down through five generations to Lamech, whose second wife, Zilah, bore him a son and, at last, a daughter--the first in Cain’s line.
Yet there always seemed to be women waiting in the wings to bear more sons to Cain and his progeny. (Seth also had a son by one of those nameless wives.)
What I want to know is where did Cain’s wife come from, and all the others?
Could she have been one of Adam and Eve’s daughters? If so, we are all indeed the children of incest.
But of course Genesis is mythical symbolism. It cannot be taken literally.
If, on the other hand, the evolutionists are right, and man arose on the plains and valleys of Africa, not in Eden, and we are descended from a common ancestor with gorillas and chimpanzees, then, Morrison asks: “What are the implications of these two surging numerical tides butting head to head? Has my mathematics gone astray? Am I asking the right questions? Am I completely off the beam?”
I wouldn’t know. I’m an innumerate.