A little math can to do anything, from magic to religion. Today we'll look at how a simple trick was used in everything from a regular stage illusionist routine to a game that seemed to uncannily channel divine intervention when reading the Bible. All it takes is the ability to count.
In 1998, Martin Gardner decided to get a little controversial in his regular column in Scientific American. He asked people to go pick up a certain version of the Bible and turn to a specific passage. He then gave them a seemingly random choice — if they followed a certain sequence of steps, they would always finish at the word "God."
He asked readers to start at a certain point and choose any word from the first to the tenth. They were then to count the letters in that word. If the word had three letters, they were to go forward three spots. If it had two, they would advance two. When they got to the new word, they would count the letters in it, and go forward that amount of words, They'd repeat and repeat the sequence until they got to the word that was too long, and too near the end, to allow them to go another step. No matter what initial word they chose, they would end that particular book at the word "God."
The game was meant lightheartedly, and the Bible was chosen merely because it was a book likely to be in many homes and nearly all hotel rooms. No one purported this to be mystical. But the trick is used in a semi-mystic setting. Stage magicians have used it as proof of their psychic powers.
It was originated by Martin Kruskal, a physicist and mathematician. The Kruskal Count, as it's widely known, is simple. A deck is shuffled and laid out in rows by the audience member. The audience member picks a card at random in the first row, sees the number on it, and skips that number of cards forward in the deck, then repeats the process. Face cards count as five, and aces count as one.
The process is repeated, and at last the audience member looks at the final card (after which there are too few cars to do any more steps). The magician can turn their back or screen the cards from their view until the audience member is done. The audience member then is instructed to think about their card, and boom — the magician knows the card! In reality, the magician, while making a certain amount of fuss to stall, has done the same thing as the audience member and picked a card in the top row and then followed the same pattern. Here's a quick demonstration of a game.
Both the Bible trick and the card trick use the same concept. They're creating a chain of steps. The chain might start at a random point, but words are only so long, and the cards only count so high. If, no matter where you start, you make stops every three to nine letters (or cards) eventually you are going to land on the same word as someone following another chain. Since the word that you're currently on determines where you go next, once you and another person have landed on the same word, you're both following the same chain from then on. A sufficiently long passage, or string of cards, and everyone will eventually meet up.
The longer the passage or the string of cards, the more certain it is that, no matter where you start, you'll meet up with everyone else eventually. A two-deck card trick has a 95% chance of ending on the same card, no matter which card is initially chosen. By the same token, if you let the game run the length of the Bible, you could probably tell people to pick any word from the first ninety percent of the Bible and be assured of them ending on the same word.