If there is a large number of people and each picks his or her own initial secret number and generates a new one from the old one in accordance with the procedure above, all of them will eventually have the same secret number and thereafter the numbers will move in lockstep.
Consider now a holy book with the compelling property that no matter what word from the early part of the book is chosen, the following procedure always leads to the same climactic and especially sacred word.
Begin with whatever word you like; count the letters in it; say this number is X; proceed forward X words to another word; count the letters in it; say this number is Y; proceed forward Y words to another word; count the letters in it; say this number is Z; keep on doing this until the climactic and especially sacred word -- say "God" or "heaven" -- is reached. (The letter count of each word plays the role of the numbered cards.)
It's not too hard to imagine frenzied checking of this procedure using word after word from the early part of the holy book and the increasing certainty among some that divine inspiration is the only explanation for the fact that the procedure always ends on the sacred word. If the generating rule were more complicated than the simple one above, the effect would be even more mysterious.
The reader can experiment with his own examples or check out the August 1998, issue of Scientific American, where puzzlemeister Martin Gardner, who graciously blurbed my book, came up with an elegant illustration of its proposal for a religious hoax.
Martin Kruskal, I should note, was innocent of perpetrating any hoaxes. He was simply a very fine applied mathematician.
In any case, Happy April Fool's Day to Hoaxers and Fools alike.
John Allen Paulos, a professor of mathematics at Temple University, has written such best-sellers as "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNEWS.com appears the first weekend of every month.