Stanford's Persi Diaconis, one of the world's great mathematicians, left home at 14 to live as a traveling magician. His talk on April 19 will reveal the math behind magic.

# The math behind the curtain

A talk by 'Magic Man' Persi Diaconis reveals the mathematics behind magic tricks-and its more serious applications

By Deane Morrison

April 14, 2006

A career as a mathematician didn't seem to be in the cards for young Persi Diaconis. As a child, he studied violin at Juilliard, but he left home at 14 to begin a life as an itinerant magician. Still in his teens, he landed in a shady Caribbean gambling house, where he tried to find ways to keep himself and other traveling magicians from getting fleeced. For that, he needed mathematics. The next thing he knew, he was studying math at City College of New York and then, at age 26, heading to Harvard for graduate school in statistics. On Wednesday, April 19, Diaconis--now recognized as one of the world's great mathematicians--will reveal some of the amazing mathematical underpinnings to magic, using performable tricks that can even fool magicians. His free talk, sponsored by the University's Institute for Mathematics and its Applications (IMA), will begin at 7 p.m. in 125 Willey Hall, 225 19th Ave. S., Minneapolis. But the math behind magic has its serious side, too. Diaconis, a professor at Stanford University, will perform several card tricks and show how the mathematics of such feats applies to situations like breaking and entering, robot vision, cryptography, random number generation, and DNA sequence analysis. Take, for example, a door that can only be unlocked by punching the correct three-digit code, entered via punch pads numbered one through five. "When I was at Harvard, one of the rest rooms had a lock like that," says Diaconis. "One Saturday night, I went there and found I'd forgotten the three numbers." There were 125 possible combinations, and he had no way to breeze through them. But, he says, thieves made short work of such a lock at the Baltimore Hilton by using mathematics. "When you punch in numbers, the machine remembers the last three you entered," Diaconis explains. "So if you punch 1, 2, and 3, and it doesn't open, and then you punch 4, the machine treats it as 2,3, and 4. Then if you punch 5, it registers as 3, 4, and 5, and so on. That means that after you've entered three numbers you can punch just one number for each new try, but in what order? There is a mathematical way to find the sequence to punch that will run through all the possible combinations without repeating." "He is one of the world's most original thinkers in statistics and mathematics," says Doug Arnold, director of IMA, of Diaconis. "He is also one of the greatest expositors and communicators in those subjects." Diaconis is no stranger to the IMA, having already visited the institute for scientific work. His lecture meshes well with the mission of IMA, which is to bring mathematics to bear on all sorts of real-world problems, from scheduling airlines to beefing up computer security. Last year, the National Science Foundation recognized its contributions with a $19.5 million grant. Nor is Diaconis' lecture the first time the IMA has been associated with a fun topic. In the realm of magic, no problem is too hard for Diaconis to tackle. He is well known for finding that it takes seven shuffles to randomize a deck of cards and that if a deck is shuffled eight times in just the right way, the cards will return to their original order. And coin tossing, that paragon of fairness, turns out not to be entirely random. After observing numerous half-dollar flips, Diaconis found that it landed on the same side as it started about 51 percent of the time. But if you balance a penny or nickel on edge and spin it, it will land tails up almost 80 percent of the time. Diaconis is also a prominent debunker of tricks by psychics and scam artists. Among his colleagues, Diaconis is known for his willingness to talk about some of the difficulties of mathematics. One example is his effort to find out whether shaved dice, thrown over and over by a team of graduate students, would land in a nonrandom manner. Using specially manufactured shaved dice and a specially constructed craps table, he uncovered a mathematical truth: that finding a bias in the way the dice landed would require so many throws that human counting error would mask any bias.