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Professor of Magic Mathematics Author(s): DON ALBERS and Persi Diaconis Source:
Professor of Magic Mathematics
Author(s): DON ALBERS and Persi Diaconis
Source: Math Horizons, Vol. 2, No. 3 (February 1995), pp. 11-15
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/25678003 .
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DONALBERS
Professor
of-Maaie
Mathematics
Persi
Diaconis, professor ofmath
has just
ematics at Harvard,
turned 50, but the energy and
intensity of the 14-year old Persi who
left high school to do magic full time
for the next ten years of his life still
burns brightly.
statistics
His work inmathematical
was so good that he was awarded a
Fel
$200,000 MacArthur Foundation
no
tax
and
free
strings at
lowship,
more and more random. That
just gets
is not the way itworks at all. It is a
of the
theorem that this phenomenon
order of cards being intact as you go
from
one,
two,
three
shuffles.
being essentially random happens
at
seven
. . to
right
shuffles."
is ranked among the top
Diaconis
three "close up" magicians in theworld.
is done tableside as
Close up magic
A Magical Beginning
ALBERS: At theage of 14, you leftyour
New York City home and spent thenext ten
years on the road practicing magic. What
made you do that?
DIACONIS:
That's
simple. The
in the United States
greatest magician
was aman named Dai Vernon. He called
me up one day and said, "How would
tached. The purpose of the awards, for
are neither solic
which applications
is to free creative
ited or accepted,
from economic pressures so
people
can
do work that interests them.
they
In spite of his mathematical
achieve
insists that he isbetter
ments, Diaconis
at magic, his first career, than he is at
statistics.After ten years of doing magic
on the road, he decided to trycollege.
At twenty-four,he enrolled as a fresh
man. Five years later he had earned his
Ph.D.
from
Harvard.
to a
Diaconis
applies mathematics
wide range of real-world problems,
claiming that "I can't relate to math
ematics abstracdy. I need to have a real
Strange lookingDice! What is thisPersi, mathematics ormagic?
problem in order to think about it."
Not long ago he established a major
result about card shuffling that is of
you like to go on the road with me?" I
opposed to on a stage. How much does
at
re
"Meet me
His
and he said,
love
Professor
Diaconis
to
cards
who
said,
"Great,"
magic?
anyone
plays
importance
two
from
"If
I
the
West
Side
could
have
is
clear:
and who would like assurance that the
days
sponse
Highway
crystal
had a professorship inmagic, and ifthe now at twoo'clock." So with what money
cards in a deck are in random order.
I could pick up and one suitcase, Iwent
world recognized magic theway itdoes
Diaconis
proved that a deck of cards
on the road. Itwas simply a question of
I probably would be do
needs to be shuffled seven times in mathematics,
a magnetic, brilliant expert in the field
order for the cards to be in random
ing magic full-time and never would
a
or statistics."
mathematics
have
done
order. He says "You might think as you
calling on me, just as guru calls on a
was
and ex
I
honored
inmagic and statis
His background
shuffle a deck more and more times it
disciple.
quite
cited to do it.
tics has also proved useful in exposing
A: What did your parents say to your
psychics, including Uri Geller. He is
co
on
about
books
DON ALBERS is the editor ofMath Horizons
leaving home topractice magic?
currently working
I didn't ask them. I just
DIACONIS:
mathematical
as well as co-author
incidences
and
of Mathematical
People.
magic.
1995 11
MathHorizonsFebruary
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lefthome. My parents were upset atmy
leaving, but somehow they found out
that Iwas okay. For a long time Iwas the
black sheep of the family. Only when I
started graduate school at Harvard did
my family begin to think that I wasn't
terrible.
A: So they
felt verybad about your going
to
off practice magic.
Sure they did, I was
DIACONIS:
being groomed to be a virtuoso musi
cian. Iwent toJulliard from the ages of
5 to 14. After school and on weekends
I played the violin. All of my family
members
[mother, father, sister, and
are
brother]
professional musicians.
They thought Iwas going to become a
violinist and having me desert music
to
for magic was not very appealing
them. I think they have come to accept
it all now. They never came to accept
themagic, even though Iwas good at it.
Iwas better at magic than I am at what
I do now.
is an accomplished magician.) He saw
DIACONIS:
the first few
During
was
that I was a troubled kid and took a
I
in
years
very good company. Iwas
me.
to
me
to
He
told
call
if
him
around
liking
being
shepherded
by Dai
I had any questions. So I used to call Vernon, a brilliant man, the
magician's
him and talk about magic, and he got magician and the best inventor of subtle
me interested inworking on mathemati
sleight of hand magic of the century.
cal tricks because he would warm to He taught me magic: we talked
magic
that.
morning, noon, and night. Since he
A: Did you know thatMartin Gardner was sort of old, and since I could do the
was a big name?
sleight of hand verywell, when he would
Sure. I knew who the give magic lessons, he would have me
DIACONIS:
other magicians
demonstrate tricks, and then he would
respected, who was
famous
and who was not so famous.
He
explain them. So my experience was
was obviously a very special guy, the
vaguely structured and very colorful?
a lotmore colorful than I choose to put
kind of guy who could go on and on
about things and remain interesting
into any interview. I met all kinds of
and never be pompous, just kind and
interesting street people, was often
instructive. He also was genuinely de
broke, hitchhiked, and so forth.
I leftVernon when I was about 16
and
store?
DIACONIS:
Older magicians
and
other kids who were interested inmagic.
In New York City there was a big, lively
I was 12, I
magic community. When
met Martin Gardner at the cafeteria
where magicians used to hang out. He
was the kindest, nicest man, and he
took time out to show me some lovely,
little tricks that I could do. (Gardner,
in addition to being a great writer, also
my
own.
He
went
on
to
night. I did pretty well thatway. I even
tually drifted back toNew York, doing
magic and pursuing it as an academic
discipline, inventing tricks, giving les
sons, and collecting old books on magic,
which I still do. Itwas just my life. I did
itwith all my energy.
A: Magic veryoftenhas card tricksasso
my mother's day camp. I clearly re
member that show. Iwas the center of
attention. Iwasn't horrible apparently,
and magic became a hobby. I sent inmy
dimes formail-order catalogs on magic,
with school I put intomagic. On many
days Iwould cut school and hang out at
the magic store until closing time.
A: Who would assemble at themagic
on
Hollywood to found what isnow known
as theMagic Castle, which is a fabulous
magic club, a private, wonderful magic
place where movie stars hang out. I
I didn't want to do that and
decided
would stay on my own. So I stayed in
Chicago, lived in a theatrical hotel, and
played club dates, usually for $50 a
A: How did you get intomagic?
DIACONIS:
I was five years
When
I
found
the
book
400 Tricks You
old,
Can Do byHoward Thurston. I picked it
up and figured out that I could do a few
tricks. I soon did a littlemagic show at
and for my birthday I would ask for
tricks as presents. When I got to public
school Imet other kids who were magi
cians and I joined the Magic Club. I
threwmyself into itwith a real fury.All
the energy that I didn't put into doing
homework or anything else connected
was
ProfessorDiaconis posed infront of one ofhis
favorite paintings in hisHarvard office.
lighted ifI showed him a new twiston a
trick that he might know. He didn't try
to put someone down because itwas a
trivial twist on something. When
I
showed him a new little idea, he would
make a note of it.Every once in a while
he would put something of mine into
his "Mathematical Games" column in
and that
Scientific American magazine
was a great thing forme.
On theRoad
A: You went on the road at age 14. What
were thoseyears like?
ciated with it and perhaps card playing.
Were you playing cards at the same time?
DIACONIS:
No, not at the begin
ning. Much later somehow I got a copy
of Feller's famous book on probability,
and I got interested in probability
that
way.
A: How did that happen ?
It was due to another
DIACONIS:
friend ofmine, Charles Radin, who is a
mathematical
physicist at the Univer
was in college on the
of
He
Texas,
sity
straight and narrow while I was still
doing magic. We had been kids to
gether in school. One day he went to
Barnes and Noble Bookstore to buy a
book and Iwent along for the ride. He
said Feller was the best, most interest
ing book on probability, and I started
to look at it. It looked as if itwas filled
with real-world problems
12 MathHorizonsFebruary
1995
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and interest
Diaconis
illustratesa point. He claims that "inventinga magic trickand inventinga theoremare verysimilar activities...
"
said Harvard didn' taccept any students
invented in the last five years, this guy
ing insights, and so I said, "I'm going to
even
to
it."
He
"You
won't
be
able
from
the
Diaconis
invented two of them, and he
said,
City College,
really good
buy
ones. So, I decided not to apply in
is interested in doing statistics. He re
read it," I said, "Oh, I can do anything
in fact, I couldn't; I mathematics.
like that." Well,
Instead I applied in sta
ally could change theworld. Why don't
1 of
tried pretty hard to read Volume
tistics; itwas the only statistics depart
you give him a try?"Fred later told me
that Iwould not have been admitted if
Feller, and it's one of the big reasons I ment I applied to.At the time, I didn't
went to college, for I realized that I very much care about statistics, but I
ithad not been for that letter.
needed some tools in order to read it. thought it would be fun to go to
A: What college?
Harvard. I thought Iwould tryitfor six Statisticsisthe
PhysicsofNumbers
I started at City College
months and see ifI liked it. I did like it,
DIACONIS:
at night. They wouldn't takeme during
A: You have spent most of your profes
they liked me, and I stayed on to finish
a Ph.D.
the day because I was something of a
sional lifeworking in statistics.What is
Because ofmy strange background I
statistics toyou ?
strange person, so I went for a couple
DIACONIS:
of years at night taking one or two probably wouldn't
have gotten into
Statistics, somehow, is
courses. I discovered that I liked col
Harvard had itnot been for the inter
the physics of numbers. Numbers seem
to arise in the world in an orderly
vention of Martin Gardner. I was talk
lege, and I decided to tryfor a degree.
I finished up in two and a half years. It
was a short time after I started college
that I dropped magic as a vocation.
Martin Gardner and Graduate
School
ing to Martin a lot during that time,
asking his advice as towhere to go, and
he was, of course, professing to know
I said I
nothing about mathematics.
was thinking of applying to theHarvard
statistics department, and he said that
he had a friend there named Fred
A: How did you end up atHarvard?
Mosteller. Now Fred Mosteller isa great
I graduated from City
DIACONIS:
statistician, who in his youth had in
some very good magic tricks.
to
start
in
and
decided
vented
January,
College
in
It
school
turned
There
is, for example, a trick called the
graduate
mid-year.
out that some places,
Mosteller
including
Spelling Trick, which is still
did
used
Harvard,
accept mid-year applica
being
today. Martin wrote a letter
in
tions. Harvard's
mathematics
which
he
said something like, "Dear
depart
ment hadn't taken anyone from City
Fred. I am not a mathematician,
but of
College
in 20 years. All of my teachers
the ten best card tricks that have been
fashion. When we examine the world,
the same regularities seem to appear
again and again. Inmore formal terms,
statistics ismaking inferences from data.
It is the mathematics
associated with
the application of probability theory to
and deciding
real-world problems,
is actually
which probability measure
governing.
A: Do you think of statistics as part of
mathematics?
DIACONIS:
Yes. It ispart of applied
mathematics. There is something about
inferences that goes beyond
making
Inmathematics you must
mathematics.
have something that is correct and
MathHorizonsFebruary
1995 13
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beautiful, and that is enough
to qualify
as mathematics.
however,
In
statistics,
set of mathematical
tools, and often
the question has been asked several
the question
times, and eventually
drives you on to understand the set of
tools, and then forme the game isn't
there is the question of trying to decide
what is true in the world, and that is
somehow going beyond any formal
system.
finished until the set of tools yields the
me more
than be
Nothing pleases
ing able to take some mathematical
idea and apply it to solve a problem.
But the bottom line for me has to be
that I actually get an answer to the
case of the card shuf
problem. In the
fling, how many times do I have to
shuffle a deck of cards? The answer is
seven for real shuffles of a deck with
answer.
mean
can
take
years.
There
are
questions I have worked on for 30 years.
Until I get the right answer, I don't
the number
fifty-twocards. Without
seven at the end, all of the underlying
mathematical
ideas
wouldn't
This
stop.
TheArtof FindingReal
Problems
A: How do youfind real problems?
That's probably what
DIACONIS:
I'm best at. What makes somebody a
magic and my interest in statistics come
together.
statistics. One of the big prob
lems for parapsychology
investigators
is that sometimes theywork with people
or subcon
who cheat, deliberately
or
both.
sciously,
My involvement began when Scien
American reviewed a book that con
tific
tained a report of a psychic in Denver
who purported tomake psychic photo
graphs with his mind.
Investigators
would bring their Polaroid
cameras
A: The group theoryismore
beautifulfor you as a result.
DIACONIS:
Abso
to
I
can't
relate
lutely!
anything. It didn't
stick at all; that's some
thing about me.
plane,
Man
that.
Ph.D.
thesis
a
snap
pic
or
or
Cro-Magnon
something
Martin
like
ar
Gardner
ranged for me to go to
Denver to investigate him;
and while I was there I
caught him cheating un
ProfessorLaurent Saloff-Coste,right,of theUniversity ofToulouse has been
Diaconis'
main
collaborator
for
the past
several
years. Here
we
see them
discussing a problem offinite markov chains, and perhaps where tohave
dinner.
a
con
is a bal
very
good applied mathematician
ance
an
the
first
between
crazy
namely
finding
interesting
If you look on the
real-world problem and finding an in
digit phenomenon.
front page of The New York Times, and
teresting real-world problem which re
In my
observe all of the numbers which ap
lates to beautiful mathematics.
case, I browse an awful lot, sit in on
pear there, how many of them do you
thinkwill begin with one? Some people
and read a lot of mathematics.
courses,
As a result, I have a rather superficial
think about a ninth. It turns out em
knowledge of verywide areas of math
pirically thatmore numbers begin with
ematics. Also, I am reasonably good at
one, and in fact it isa very exact propor
My
and
ture of thisguy's head, and
usually they would get a
picture of his head; but
once in awhile the photo
graphs would look some
thing like a fork, or a bi
to me.
meant
ex
clear
about
as much
mathematics
abstractly. I
in
need a real problem
order to think about it,
but given a real problem
I'll learn anything it takes
to get a solution. I have
taken at least thirty for
mal courses in very fancy
theoretical math, and I got
A's and wrote good final
papers, and it just never
a marvelous,
It's
ample of a nice applied math problem.
Any respectable proof of parapsychol
ogy by the standards of today is statisti
cal in nature, and therefore in order to
be a good investigator you have to know
involved
crete problem,
tion of numbers that seem to begin
with one; it is .301. Now that's an em
pirical fact, and it's sort of surprising. It
comes up in all kinds of real data. Ifyou
open a book of tables, and look at all of
the numbers on the page, about 30%
of them begin with one. Why should
that be? It's always been that way for
me. There is some question and some
talking to people and finding out what
ails them problemwise.
Psychicsand ESP
A: How did you become involved with
psychics and ESP research ?
ESP is a nice example
DIACONIS:
in
of an area where my background
lems.
questionably.
Over the years I have
so
several
investigated
called psychics, as a kind
of hobby and also as a
source of interesting prob
I guess
it s also
a
service
to
the
scientific community. It's hard for or
dinary scientists to do a good job at
debunking psychics. We may all feel
that it is baloney, but it's very hard to
determine why.
Debunking
A: Why is ithardfor scientists todebunk
psychics?
DIACONIS:
It's because most people
(a) don't know the tricks, and (b) don't
have the statistical background.
It is
very easy for the tricks to be concealed
in poor statistics.A combination of (a)
and (b) can be devastating. You can be
a terrific physicist or mathematician,
but
if you don't
14 MathHorizonsFebruary
1995
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have
experience
in
running experiments with human sub
jects and with cueing, etc., you may
the
have a very tough time. Having
often
makes
it
obvious
very
experience
what's wrong, and when you point out
the trick or statistical fallacy to some
body else, they say aha. It's hard for
people to spot iton their own.
A: The public's interest,inESP, astrol
ogy, and numerology is very high.How do
you explain their
fondness for it?
It isa basic human reac
DIACONIS:
to
at
tion wonder
something surprising
such
as
an
unusual
coincidence.
you have a problem
to solve
with
that you're
constraints.
trying
In mathemat
ics, it's the limitations of a reasoned
argument with the tools you have avail
able, and with magic it's to use your
tools and sleight of hand tobring about
a certain effect without the audience
knowing what you're doing. The intel
lectual process of solving problems in
the two areas is almost the same. When
you're inventing a trick, it's always pos
sible to have an elephant walk on stage,
and while the elephant is in front of
That
seems
to be a hard-wired reaction in
people. Perhaps it iswired in there for
protection. I think it isunquestionable
that we
nism
have
a
pattern-detecting
that works
and
and
hobby, but for me
it's quite
close
to
math.
Inventing a magic trick and invent
ing a theorem are very similar activities
in the following sense. In both subjects
be
too
I left the performing
business is very differ
a creative magician.
In
I left it is because you
creative.
is tremen
There
dous pressure todo the same 17-minute
act: itworks and it gets laughs. I can
remember very clearly changing the
closing trick of my act, a trick with
butterflies. I took the butterfly trick
out to do something else. After my
performance, my agent rushed up to
me backstage, and said I couldn't take
the butterfly trick out of my act. He
can
be
done
as
a
very
aca
demic and creative discipline; it's very
similar to doing mathematics,
except
for the fact that the world treats you
more seriously ifyou're a mathemati
cian. If you say that you're a professor
at Harvard,
A
V
in that litera
seem to know
pline. I study itshistory. I invent tricks,
and I write material for other magi
cians. Imeet with them, do tricks occa
sionally and practice. That's an activity
that is not very different from math
ematics forme. I subscribe to 20 magic
journals. You might say I do magic as a
can't
Magic
graduates believe that parapsychology
is a demonstrated fact.
I read very thoroughly for ten years
all of the refereed, serious parapsy
chology literature. There isnot a single,
A: Do you still do music?
I don't do music any
DIACONIS:
more, but I stilldo magic, The way I do
I
magic is very similar tomathematics.
do it seriously as an academic disci
DIACONIS:
part of it. Show
ent from being
fact, the reason
utes for the next twenty years?
lieve the most outlandish things, and
the fact that you can do a little sleight of
hand and actually make
something
happen in addition to creating a spell
of wonder makes itall themore believ
able. Large proportions of our under
that.
A: Why did you leavemagic as an occu
pation ?
said, "That's what I book you on." At
if Iwas going to
that point, Iwondered
same
seventeen min
end up doing the
L
delighted by surprising coincidences.
I was a performer, I learned
When
that it ismuch easier to entertain people
by pretending that your tricks are real
magic, than to do wonderful tricks and
just present them as tricks. People, if
you let them, are quite willing to be
repeatable experiment
ture. Most people don't
,
A
mecha
is alerted
A ProfessorshipinMagic
The business card of theprofessional magi
cian,PersiWarren (Diaconis), who lefthome
at age fourteen and performedprofessionally
for
the next
ten years.
you, sneak something under your coat,
but that's not a good trick. Similarly
with mathematical
proof, it is always
to
out
the big guns, but
possible
bring
then you lose elegance, or your conclu
sions aren't very different from your
hypotheses, and it's not a very interest
ing theorem.
One difference between magic and
is the competition.The
mathematics
in
is a lot
mathematics
competition
stiffer than inmagic.
people treat you respect
fully. If you say that you invent magic
tricks, they don't want to introduce
you to their dog.
A: When you were doing magic, you said
thatyou werefollowing thewind. Are you
stillfollowing thewind?
DIACONIS:
When Iwas young and
doing magic, ifI heard that an Eskimo
had a new way of dealing a second card
using snowshoes, I'd be off toAlaska. I
spent ten years doing that, traveling
around the world, chasing down the
exclusive, interesting secrets of magic.
in number
then I've worked
theory, classical mathematical statistics,
philosophy of statistics, psychology of
vision and pure group theory. What
happens now is that if I hear about a
Since
beautiful problem, and if that means
learning some beautiful math machine,
then, boy, I'm off in a second to learn
the secrets of the new machine. I'm just
following the mathematical wind. I
Diaconis
is in the south ofFrance
for
the year,
following themathematicalwinds ofdifferential
At thehalf
geometryand finite group theory.
mark, he claims tobegettingslightlyless
century
applied
in his outlook. We'll
see.
MathHorizonsFebruary
1995 15
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