Magic tricks are inextricably linked to statistics and mathematical models, according to Persi Diaconis in his public lecture, “Mathematics and Magic,” delivered Wednesday night in Cubberley Auditorium.

 

“Mathematics and Magic” is part of a series organized by the Mathematics Department and is intended for individuals with backgrounds in any level of math.

 

“A few members of the faculty got together, along with the chairman, and came up with an idea to make mathematics more accessible to Stanford and the community in general,” said Pat Cahill, the administrative associate for the Mathematics Department.

 

Diaconis’s talk coincides with the recent release of his book, “Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks,” which was co-written with mathematician Ron Graham.

 

Diaconis began his lecture with an interactive magic trick. Before the show began, each audience member selected four cards. After telling the audience members to remember their bottom cards, Diaconis led the audience through a series of seemingly random cutting. At the end of the trick, every audience member finished with his or her bottom card in the opposite direction of the other three cards.

 

“We’ve just done a tiny piece of mathematics,” Diaconis said, who then used combinatorics, a branch of math concerning finite structures, number theory and an overhead projector to explain the phenomenon.

 

Diaconis performed another trick in which he allowed five members of the audience to each choose cards, and then accurately guessed which card each person was holding.

 

A few theories that were presented during the lecture included graph theory and the de Bruijn sequence, a complex cyclic sequence. Diaconis emphasized the history behind the theories.

 

Diaconis discussed the application of complicated math theorems in everyday life. He stated that de Bruijn sequences are used by telephone companies as well as for DNA sequencing and signal processing. Diaconis added that a two-dimensional de Bruijn system gave rise to the dot-positioning system that digital pens currently use.

 

“Using the powers of two, which expand extremely rapidly, the pen not only knows where it is on the page, but also what page [it is on] in a book and what book it is in,” Diaconis said.

 

Diaconis first became interested in the relationship between mathematics and magic as a young child. After performing as a street magician, Diaconis wanted to explore the theory behind the magic that he was doing.

 

“Math and magic may seem like two unrelated topics, but further exploration of magic creates mathematical theories, and mathematical theories, in turn, can [create] new magic tricks,” he said.