Professor of 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 . Accessed: 30/10/2014 13:17

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This content downloaded from 129.10.72.232 on Thu, 30 Oct 2014 13:17:17 PM All use subject to JSTOR Terms and Conditions DONALBERS

Professor of-Maaie

Mathematics

more more Persi Diaconis, professor ofmath just gets and random. That A Magical Beginning a ematics at Harvard, has just is not the way it works at all. It is ALBERS: At theage 14, you leftyour turned 50, but the energy and theorem that this phenomenon of the of next ten intact as City home and spent the of the 14-year old Persi who order of cards being you go intensity on What . . to years the road practicing magic. left high school to do magic full time from one, two, three shuffles. made you do that? for the next ten years of his life still being essentially random happens right at seven shuffles." DIACONIS: That's The burns brightly. simple. His work inmathematical statistics Diaconis is ranked among the top greatest magician in the a three "close in theworld. was aman named Dai Vernon. He called was so good that he was awarded up" magicians as $200,000 MacArthur Foundation Fel Close up magic is done tableside me up one day and said, "How would lowship, tax free and no strings at tached. The purpose of the awards, for are which applications neither solic ited or accepted, is to free creative so people from economic pressures they can do work that interests them. In spite of his mathematical achieve ments, Diaconis insists that he isbetter at magic, his first career, than he is at statistics.After ten years of doing magic on the road, he decided to trycollege. a At twenty-four,he enrolled as fresh man. Five years later he had earned his Ph.D. from Harvard. a Diaconis applies mathematics to wide range of real-world problems, claiming that "I can't relate to math ematics abstracdy. I need to have a real Dice! What is this mathematics or problem in order to think about it." Strange looking Persi, magic? a Not long ago he established major to on a How does like to on the road with me?" I result about card that is of opposed stage. much you go Professor Diaconis love His re and he "Meet me at importance to anyone who plays cards magic? said, "Great," said, and who would like assurance that the sponse is crystal clear: "If I could have theWest Side Highway two days from now cards in a deck are in random order. had a professorship inmagic, and ifthe at two o'clock." So with what money the itdoes I could and one Iwent Diaconis proved that a deck of cards world recognized magic way pick up suitcase, was a needs to be shuffled seven times in mathematics, I probably would be do on the road. It simply question of a order for the cards to be in random ing magic full-time and never would magnetic, brilliant expert in the field or statistics." on as a calls on a order. He says "You might think as you have done mathematics calling me, just guru was ex shuffle a deck more and more times it His background inmagic and statis disciple. I quite honored and to tics has also proved useful in exposing cited do it. to psychics, including Uri Geller. He is A: What did your parents say your co DON ALBERS is the editor ofMath Horizons currently working on books about leaving home topractice magic? as as DIACONIS: I didn't ask them. I well co-author of Mathematical People. incidences and mathematical magic. just

MathHorizons February 1995 11

This content downloaded from 129.10.72.232 on Thu, 30 Oct 2014 13:17:17 PM All use subject to JSTOR Terms and Conditions lefthome. were at is an saw My parents upset my accomplished magician.) He DIACONIS: During the first few but out was a a leaving, somehow they found that I troubled kid and took years Iwas in very good company. Iwas that Iwas For a time Iwas the tome. He me to okay. long liking told call him if being shepherded around by Dai black of the when I I to a sheep family. Only had any questions. So I used call Vernon, brilliant man, themagician's started graduate school at Harvard did him and talk about magic, and he got magician and the best inventor of subtle to me my family begin think that I wasn't interested inworking on mathemati sleight of hand magic of the century. terrible. cal tricks warm to me because he would He taught magic: we talked magic A: So bad about that. theyfelt very your going morning, noon, and night. Since he off topractice magic. A: Did you know thatMartin Gardner was sort of old, and since I could do the was was a DIACONIS: Sure they did, I big name? sleight of hand verywell, when he would to a being groomed be virtuoso musi DIACONIS: Sure. I knew who the give magic lessons, he would have me went to cian. I Julliard from the ages of other magicians respected, who was demonstrate tricks, and then he would 5 to 14. After school on famous and who was not so famous. He and weekends explain them. So my experience was I All was a played the violin. of my family obviously very special guy, the vaguely structured and very colorful? on members [mother, father, sister, and kind of guy who could go and on a lotmore colorful than I choose to put are brother] professional musicians. about things and remain interesting into any interview. I met all kinds of I was to a never They thought going become and be pompous, just kind and interesting street people, was often violinist me and having desert music instructive. He also was genuinely de broke, hitchhiked, and so forth. was for magic not very appealing to I leftVernon when I was about 16 them. I think come to was on own. they have accept and my He went on to now. never came to it all They accept Hollywood to found what isnow known the even was at magic, though I good it. as theMagic Castle, which is a fabulous I was better at than I am at a magic what magic club, private, wonderful magic I do now. place where movie stars hang out. I A: How did you get intomagic? decided I didn't want to do that and DIACONIS: When I was five on years would stay my own. So I stayed in I found old, the book 400 Tricks You Chicago, lived in a theatrical hotel, and Can Do Howard Thurston. I it by picked played club dates, usually for $50 a and out that I a up figured could do few night. I did pretty well thatway. I even tricks. I soon did a little at magic show tually drifted back toNew York, doing mother's I re my day camp. clearly magic and pursuing it as an academic member that I was the center show. of discipline, inventing tricks, giving les attention. Iwasn't horrible on apparently, sons, and collecting old books magic, and a I sent magic became hobby. inmy which I still do. Itwas just my life. I did dimes formail-order catalogs on magic, itwith all my energy. and for I would my birthday ask for A: Magic veryoften has card tricksasso tricks as When I to presents. got public ciated with it and perhaps card playing. school Imet other kids were who magi Were you playing cards at the same time? cians and I the I joined Magic Club. DIACONIS: No, not at the begin a ProfessorDiaconis posed infront of one ofhis threwmyself into itwith real fury.All Much later somehow I a in hisHarvard ning. got copy the that I didn't into favorite paintings office. energy put doing of Feller's famous book on probability, homework or else anything connected and I got interested in probability that with school I into On a new on a put magic. many lighted if I showed him twist way. Iwould cut school and out at trick days hang that he might know. He didn't try A: How did that happen ? the magic store until closing time. to put someone down because itwas a DIACONIS: It was due to another A: Who would assemble at the magic trivial twist on something. When I friend of mine, Charles Radin, who is a store? a new showed him little idea, he would mathematical physicist at the Univer DIACONIS: Older and a note once a magicians make of it.Every in while sityof Texas, He was in college on the other kids were who interested inmagic. he would put something of mine into straight and narrow while I was still In was a there big, lively his "Mathematical Games" column in doing magic. We had been kids to I was I magic community. When 12, Scientific American magazine and that gether in school. One day he went to met at the cafeteria was a me. great thing for Barnes and Noble Bookstore to buy a where used to out. He magicians hang book and Iwent along for the ride. He was the kindest, nicest man, and he On theRoad said Feller was the best, most interest took time out to me some show lovely, ing book on probability, and I started little tricks that I could do. (Gardner, A: You went on the road at age 14. What to look at it. It looked as if itwas filled in addition to a were being great writer, also thoseyears like? with real-world problems and interest

12 MathHorizons February 1995

This content downloaded from 129.10.72.232 on Thu, 30 Oct 2014 13:17:17 PM All use subject to JSTOR Terms and Conditions " Diaconis illustratesa point. He claims that "inventinga magic trickand inventinga theoremare verysimilar activities...

ing insights, and so I said, "I'm going to said Harvard didn' taccept any students invented in the last five years, this guy buy it."He said, "You won't be able to from City College, even the really good Diaconis invented two of them, and he read it," I said, "Oh, I can do anything ones. So, I decided not to apply in is interested in doing statistics. He re like that." Well, in fact, I couldn't; I mathematics. Instead I applied in sta ally could change theworld. Why don't tried pretty hard to read Volume 1 of tistics; itwas the only statistics depart you give him a try?"Fred later told me Feller, and it's one of the big reasons I ment I applied to.At the time, I didn't that I would not have been admitted if 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 try it for six Statisticsis the Physics of Numbers DIACONIS: I started at City College months and see if I liked it. I did like it, me at night. They wouldn't take during they liked me, and I stayed on to finish A: You have spent most of your profes the day because I was something of a a Ph.D. sional lifeworking in statistics. What is strange person, so I went for a couple Because ofmy strange background I statistics toyou ? of years at night taking one or two probably wouldn't have gotten into DIACONIS: Statistics, somehow, is courses. I discovered that I liked col Harvard had itnot been for the inter the physics of numbers. Numbers seem lege, and I decided to tryfor a degree. vention of Martin Gardner. I was talk to arise in the world in an orderly I finished up in two and a half years. It ing to Martin a lot during that time, fashion. When we examine the world, was a short time after I started college asking his advice as towhere to go, and the same regularities seem to appear that I dropped magic as a vocation. he was, of course, professing to know again and again. Inmore formal terms, nothing about mathematics. I said I statistics ismaking inferences from data. Martin Gardner and Graduate was thinking of applying to theHarvard It is the mathematics associated with School statistics department, and he said that the application of probability theory to he had a friend there named Fred real-world problems, and deciding A: How did you end up atHarvard? Mosteller. Now Fred Mosteller isa great which probability measure is actually I from in in DIACONIS: graduated City statistician, who his youth had governing. College inJanuary, and decided to start vented some very good magic tricks. A: Do you think of statistics as part of graduate school inmid-year. It turned There is, for example, a trick called the mathematics? out that some places, including Mosteller Spelling Trick, which is still DIACONIS: Yes. It ispart of applied Harvard, did accept mid-year applica being used today. Martin wrote a letter mathematics. There is something about tions. Harvard's mathematics in "Dear inferences depart which he said something like, making that goes beyond ment hadn't taken anyone from City Fred. I am not a mathematician, but of mathematics. Inmathematics you must College in 20 years. All of my teachers the ten best card tricks that have been have something that is correct and

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This content downloaded from 129.10.72.232 on Thu, 30 Oct 2014 13:17:17 PM All use subject to JSTOR Terms and Conditions beautiful, and that is enough to qualify set of mathematical tools, and often magic and my interest in statistics come as mathematics. In It's a clear ex statistics, however, the question has been asked several together. marvelous, there is the question of trying to decide times, and eventually the question ample of a nice applied math problem. what is true in the world, and that is drives you on to understand the set of Any respectable proof of parapsychol somehow going beyond any formal tools, and then for me the game isn't ogy by the standards of today is statisti set to system. finished until the of tools yields the cal in nature, and therefore in order me more answer. This can take There are a to Nothing pleases than be years. be good investigator you have know ing able to take some mathematical questions I have worked on for 30 years. about statistics. One of the big prob a idea and apply it to solve problem. Until I get the right answer, I don't lems for investigators me to is But the bottom line for has be stop. that sometimes theywork with people or that I actually get an answer to the who cheat, deliberately subcon case or problem. In the of the card shuf The Artof FindingReal sciously, both. fling, how many times do I have to Problems My involvement began when Scien shuffle a deck of cards? The answer is tificAmerican reviewed a book that con A: How do real seven for real shuffles of a deck with youfind problems? tained a report of a psychic in Denver fifty-twocards. Without the number DIACONIS: That's probably what who purported tomake psychic photo seven at the end, all of the underlying I'm best at. What makes somebody a graphs with his mind. Investigators mathematical ideas would bring their Polaroid wouldn't mean as much cameras and a snap pic to me. ture of this guy's head, and A: The group theoryis more usually they would get a beautifulfor you as a result. picture of his head; but DIACONIS: Abso once in awhile the photo lutely! I can't relate to graphs would look some mathematics abstractly. I thing like a fork, or a bi a in or need real problem plane, Cro-Magnon order to think about it, Man or something like but given a real problem that. Martin Gardner ar I'll learn anything it takes ranged for me to go to to get a solution. I have Denver to investigate him; taken at least thirty for and while I was there I mal courses in very fancy caught him cheating un theoretical math, and I got questionably. A's and wrote good final Over the years I have never Laurent the Toulouse has been several so papers, and it just Professor Saloff-Coste,right, of University of investigated Diaconis' main collaborator the several Here we see them meant anything. It didn't for past years. called psychics, as a kind a markov chains, and where tohave stick at all; that's some discussing problem offinite perhaps of hobby and also as a dinner. thing about me. source of interesting prob Ph.D. thesis involved a con mathematician is a bal lems. I it s also a service to the My very good applied guess crete problem, namely the crazy first ance between finding an interesting scientific community. It's hard for or an a digit phenomenon. If you look on the real-world problem and finding in dinary scientists to do good job at front page of The New York Times, and teresting real-world problem which re debunking psychics. We may all feel observe all of the numbers which ap lates to beautiful mathematics. In my that it is baloney, but it's very hard to pear there, how many of them do you case, I browse an awful lot, sit in on determine why. thinkwill begin with one? Some people courses, and read a lot of mathematics. think about a ninth. It turns out em As a result, I have a rather superficial Debunking pirically thatmore numbers begin with knowledge of very wide areas of math A: is ithard scientists todebunk one, and in fact it isa very exact propor ematics. Also, I am reasonably good at Why for tion of numbers that seem to begin talking to people and finding out what psychics? with one; it is .301. Now that's an em ails them problemwise. DIACONIS: It's because most people pirical fact, and it's sort of surprising. It (a) don't know the tricks, and (b) don't comes up in all kinds of real data. Ifyou Psychicsand ESP have the statistical background. It is open a book of tables, and look at all of very easy for the tricks to be concealed A: How did become involved with the numbers on the page, about 30% you in poor statistics. A combination of (a) and ESP research ? of them begin with one. Why should psychics and (b) can be devastating. You can be a that be? It's always been that way for DIACONIS: ESP is a nice example terrific physicist or mathematician, me. There is some question and some of an area where my background in but if you don't have experience in

14 Math HorizonsFebruary 1995

This content downloaded from 129.10.72.232 on Thu, 30 Oct 2014 13:17:17 PM All use subject to JSTOR Terms and Conditions running experiments with human sub you have a problem that you're trying A Professorshipin Magic jects and with cueing, etc., you may to solve with constraints. In mathemat A: did you leave as an occu have a very tough time. Having the ics, it's the limitations of a reasoned Why magic ? experience often makes itvery obvious argument with the tools you have avail pation what's wrong, and when you point out able, and with magic it's to use your DIACONIS: I left the performing the trick or statistical fallacy to some tools and sleight of hand to bring about part of it. Show business is very differ body else, they say aha. It's hard for a certain effect without the audience ent from being a creative magician. In people to spot it on their own. knowing what you're doing. The intel fact, the reason I left it is because you A: The public's interest, inESP, astrol lectual process of solving problems in can't be too creative. There is tremen ogy, and numerology is very high.How do the two areas is almost the same. When dous pressure to do the same 17-minute you explain theirfondness for it? you're inventing a trick, it's always pos act: itworks and it gets laughs. I can a reac an on DIACONIS: It is basic human sible to have elephant walk stage, remember very clearly changing the tion towonder at something surprising and while the elephant is in front of closing trick of my act, a trick with such as an unusual coincidence. That butterflies. I took the butterfly trick seems to be a hard-wired reaction in out to do something else. After my people. Perhaps it iswired in there for performance, my agent rushed up to protection. I think it isunquestionable me backstage, and said I couldn't take that we have a mecha the trick out of act. He pattern-detecting A , butterfly my nism that works and is alerted and said, "That's what I book you on." At delighted by surprising coincidences. L that point, Iwondered if Iwas going to When I was a performer, I learned end up doing the same seventeen min that it ismuch easier to entertain people utes for the next twenty years? that tricks are real can be done as a aca by pretending your Magic very magic, than to do wonderful tricks and demic and creative discipline; it's very just present them as tricks. People, if similar to doing mathematics, except you let them, are quite willing to be for the fact that the world treats you lieve the most outlandish things, and more seriously ifyou're a mathemati the fact that you can do a little sleight of cian. If you say that you're a professor hand and actually make something at Harvard, people treat you respect happen in addition to creating a spell fully. If you say that you invent magic of wonder makes itall themore believ tricks, they don't want to introduce able. Large proportions of our under A you to their dog. graduates believe that parapsychology A: When you were doing magic, you said a V is demonstrated fact. thatyou werefollowing thewind. Are you I read very thoroughly for ten years stillfollowing thewind? all of the refereed, serious parapsy DIACONIS: When I was young and chology literature. There isnot a single, doing magic, if I heard that an Eskimo repeatable experiment in that litera had a new way of dealing a second card ture. Most people don't seem to know using snowshoes, I'd be off toAlaska. I that. spent ten years doing that, traveling The business card the A: Do you still do music? of professional magi around the world, chasing down the cian, Persi Warren (Diaconis), who home DIACONIS: I don't do music any left exclusive, interesting secrets of magic. at age and more, but I still do magic, The way I do fourteen performedprofessionally Since then I've worked in number the next ten for years. magic is very similar tomathematics. I theory, classical mathematical statistics, do it seriously as an academic disci you, sneak something under your coat, philosophy of statistics, psychology of pline. I study itshistory. I invent tricks, but that's not a good trick. Similarly vision and pure group theory. What and I write material for other magi with mathematical proof, it is always happens now is that if I hear about a cians. Imeet with them, do tricks occa possible to bring out the big guns, but beautiful problem, and if that means an sionally and practice. That's activity then you lose elegance, or your conclu learning some beautiful math machine, that is not very different from math sions aren't very different from your then, boy, I'm off in a second to learn ematics forme. I subscribe to 20 magic hypotheses, and it's not a very interest the secrets of the new machine. I'm just journals. You might say I do magic as a ing theorem. following the mathematical wind. I hobby, but for me it's quite close to One difference between magic and Diaconis is in the south France the math. mathematics is the competition.The of for year, following themathematical winds ofdifferential Inventing a magic trick and invent competition in mathematics is a lot geometryand finite group theory.At thehalf a theorem are very similar activities stiffer than in ing magic. centurymark, he claims tobe getting slightly less in the sense. In both see. following subjects applied in his outlook. We'll

MathHorizons February 1995 15

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