Teaching The Tricks Of the Trade

While most professors try to teach their students a few tricks of the trade, Persi W. Diaconis has built his entire career around teaching tricks.

Diaconis, Leverett professor of mathematics, is a world-class sleight of hand artist and a master card player who uses his tricks to teach mathematical concepts, such as probability.

In a graduate seminar on "Topics in Mathematical Statistics," Diaconis uses a simple card game called "Say Red" to illustrate a complex mathematical theorem.

In the card game, he turns over one card at a time from the top of a randomly shuffled deck. Students must guess whether the card will be red--if it is, they win a dollar. If it's black, they lose one.

The only condition, he says, is that students must say red at least once during the game.

The game raises the question of whether the student has any advantage in guessing the color.

"[It would seem] if the first card is black you'd have some advantage [by saying red], but there's nothing you can do other than making it perfectly fair," Diaconis says, explaining that the probability a card will be red is always 50 percent.

Diaconis, 50, says his interest in things mathematical began at an early age.

"I've always been fascinated by magic tricks--there are some terrible little tricks and good tricks too," he says, adding that many card tricks can be understood by the rules of mathematics. "Even today if I have a math problem and I can translate it into the language of cards, I can solve it."

The translation of mathematical formulae into concrete objects assists Diaconis in his investigations.

Displaying a mechanical mystery bolted to the top of a bookshelf in his Science Center office, Diaconis explains that the machine eliminates the chance element in coin tossing.

"I think that coin tossing isn't random, it's physics," he says. "You can show that a very slight change in how you flip it makes for the difference between heads and tails."

A few sample tosses reveal something amiss in the machine built by the physics lab. The coin, which is supposed to come up heads every time, repeatedly turns tails.

"Last time I did it, I got 50 out of 50," Diaconis shrugs, leaving the physics problem for later contemplation.

Diaconis has spent his lifetime studying the interrelation of mathematics, probability and randomness.

An expert on the mathematics of coincidence, he received his Ph.D. from Harvard in 1974.

After teaching at Stanford University, he returned to Harvard in 1987 and now teaches Mathematics 191: "Mathematical Probability" and works with graduate students.

In addition to working on mathematic texts and journal articles, Diaconis has given a number of lectures to lay-persons not versed in the language of mathematics.

In 1992 and 1993 he gave lectures as part of the University's lecure series on "research for non-specialists," including a talk on coincidences and on the search for randomness.

Celebrated in the field of mathematics, he was also mentioned in a 1993 article in The New Yorker, which called him one of the "pure amateurs in the best sense."

Despite his expert knowledge of card tricks and games, Diaconis says he never plays competitively because winning makes him unpopular.

"And if I lose they say, 'He's not so good,'" he adds.