2/16/01

Mark
Shwartz, News Service (650) 723-9296;

mshwartz@stanford.edu

**Card tricks and mathematics: applying the
magician's trade to numerical dilemmas **

Instead of reaching for a pencil, Stanford
mathematician Persi Diaconis reaches for a pack
of cards.

"They are easier for my mind to think
about than sets of differential equations and
stuff like that," says Diaconis, who spent
10 years as a traveling magician. He explains
that cards can be used as simple mathematical
models to describe complex real-life systems.

Diaconis, the Mary V. Sunseri Professor of
Mathematics and Statistics at Stanford, will
perform a card trick at the annual meeting of the
American Association for the Advancement of
Science (AAAS) in San Francisco. His presentation
is part of symposium entitled, "Juggling,
Magic, Sport and Combinatorics," to be held
Friday, Feb. 16, at 9 a.m. PT. Thomas M. Cover,
the Kwoh-Ting Li Professor in the School of
Engineering and professor of statistics and
electrical engineering at Stanford, will speak in
the same session about the mathematical aspects
of sports.

During the AAAS meeting, Diaconis will explain
how he uses a magician's skill to solve
long-standing problems in physics, biology and
engineering. Lately he has been using cards to
work out problems in statistical mechanics a
branch of physics that uses statistics to predict
and explain how particles interact.

First, he spreads a deck of cards on a table.
Each card represents an individual atom, he says,
and each has a unique position relative to the
others. Also, every card appears either face-up
or facedown, which Diaconis equates to individual
atoms that can move either forward or backward.

He then starts shifting cards around and
flipping them over, just as atoms move and change
direction. His goal is to predict all the
different combinations possible for the entire
system the group of atoms or pack of cards.

"In my talk, I'll try to explain just
what arrangements are possible, as an
illustration of how a grown-up mathematician
could apply grown-up math ideas to a very
concrete problem," he says. "The card
trick helps because it's simple and neat enough
that I can do the math completely."

Of course, a small group of cards is a very
small sample compared to the number of atoms in
the world. But that is Diaconis's forte: applying
what he learns from a small, defined system to
the larger, complex reality. It's as if he is
looking at a small square of mesh screen in order
to learn something about the whole screen door.

"It's sort of like a magic trick,
really," says Diaconis. "You have these
particles bouncing around, obeying Newton's Laws,
and somehow, instead of having to clock how they
bounce around, we're able to say that if you know
one or two things about them, we can answer all
kinds of other questions about them."

During the AAAS symposium, Diaconis will
describe how he can apply his card trick to more
than atoms. For example, each card could
represent a protein, a drop of moving fluid or a
person carrying HIV.

Diaconis often chats with biochemists about
protein folding, listens to chemists puzzle over
fluid mechanics and helps computer scientists
design computers that play solitaire. "One
nice thing about statisticians and applied
mathematicians is that we get to talk to all
kinds of people if we want," he says. The
downside is that he usually ends up working in a
field he knows nothing about. "I often think
I get paid for my ability to tolerate feeling
stupid," he says.

Diaconis says that his magician's tricks can
be valuable tools for solving tangible scientific
dilemmas. But that may not be his ultimate
motivation. "I'm actually happy to just have
a good card trick," he says with a smile.

-30-

By Louisa Dalton