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The chance of a lifetime
Interview Photography: Linda Cicero/Stanford News Service
When he ran away from home aged 14 to spend two years on the road as a magician’s assistant, Persi Diaconis had little idea that his fascination with magic would take him to Harvard University and beyond. Today he is not only one of the world’s top sleight-of-hand magicians but a professor of statistics at Stanford to boot. He has used his skills to debunk numerous instances of fraud and trickery, and proved that it takes seven shuffles to perfectly randomise a pack of cards. He tells Justin Mullins about his strange journey
The chance of a lifetime How did you become involved in magic?
When I was 5 I found a magic book and did a little show for my mother. I was the centre of attention and became hooked. When I was older, I was sitting in a cafeteria one day doing a trick where you deal the second card from a pack rather than the top card. A magician called Dai Vernon spotted me and saw some potential. One day he called, said he was going to Delaware the following day to do a show and asked if I wanted to go along as his assistant. I packed my bag and left. We travelled around for two years and I learned a great deal from him. I never went home again. How did your tricks end up being published?
As a teenager, I got to know Martin Gardner, the famous recreational mathematician. I showed him one of my mathematical magic tricks, and he published it in the column he had in Scientific American. I was very proud. He got me interested in the link between magic and mathematics. What is the link between magic and mathematics?
With practice, magicians can shuffle a pack of cards perfectly. They can cut the pack exactly in half and interweave the cards one after the
Profile Persi Diaconis is the Mary V. Sunseri professor of statistics and mathematics at Stanford University in California. In 1979 he was awarded a MacArthur Fellowship for showing exceptional promise of future creative work.
52 | NewScientist | 24 March 2007
070324_Op_Interview.indd 52
other. Suppose I have a pack with four aces on top and I shuffle it perfectly. The aces would then be every second card. If I shuffle it again, they would be every fourth card. If I was a crooked gambler and dealt four hands, I’d get the aces. Gamblers have been writing about what they can and can’t do with perfect shuffles for 300 years. There are two kinds of perfect shuffle. You can keep the original top card on top or place it second from top – those are called “out” and “in” shuffles. As a kid I learned a method for moving the top card to any other position in the pack. First express the position you want as a binary number and subtract 1. Then interpret the 1s and 0s in the number as in and out shuffles. If you carry out that sequence of in and out shuffles, the top card ends up where you want. That’s how I learned about binary numbers. Why are shuffles interesting mathematically?
If you out-shuffle a pack of cards eight times, the deck comes back to where it started. But it takes 52 in-shuffles to bring a deck back to the start – as many shuffles as there are cards in the deck. One interesting question is: are there larger decks, with say 104 cards, or some other number, where it also takes a deck-size number of out-shuffles to bring the deck back to the start? The answer is completely unknown. It’s linked to the Riemann hypothesis, one of the fanciest open problems in mathematics. That’s the kind of thing that makes the mathematician and magician in me rather happy.
Without a high-school education, was it hard to get involved in advanced mathematics?
When I was 24, I decided to enrol in night school at City College in New York. When I graduated, I applied to do statistics at Harvard. Martin Gardner wrote a letter for me saying: “Of the 10 best card tricks invented in the last two years, this kid invented two of them. And if he says he wants to do statistics, you should give him a chance.” One of the people on the Harvard committee, Fred Mosteller, was also a serious amateur magician and was influenced by Martin’s letter. That’s how I got in. What is statistics?
My favourite example of statistics is Carl Gauss’s role in the discovery of Ceres in 1801. At that time, people were sure there were only seven planets. But then an astronomer spotted Ceres and followed it for about 40 days. This was exciting stuff, in all the newspapers. Was there a new planet? Then he lost it in the sun. If you know the position and velocity of something orbiting the sun at one time, you should know where it is forever. But the observations were “noisy” because of poor-quality telescopes and errors in measuring Ceres’s position. Gauss took up the challenge. Within a year he had invented the statistical tools to handle noisy observations – the techniques of least-squares, Gaussian elimination and the Gaussian bell-shaped curve. Then he calculated where Ceres should be and told people where to point their telescopes. On the first clear night, they found it. It has ended up www.newscientist.com
16/3/07 5:13:52 pm
classed only as the largest asteroid, not a planet, though. A friend of mine says that statistics is the physics of data sets. For me, statistics is making human sense out of data from the world around us while facing up to the fact that our observations have noise in them. How did you become involved in the debunking of extrasensory perception?
I got hooked on it through Martin Gardner. Somebody had sent a book into Scientific American about “psychic” photography. The claim was that a guy called Ted Serios could take a Polaroid picture and it would have some image produced just by his thoughts on it – a plane flying through the picture or a
“I became interested in the link between magic and mathematics” www.newscientist.com
070324_Op_Interview.indd 53
Cro-Magnon man, say. Martin paid me and some technical photographers to go and watch this guy. I caught him sneaking a little marble with a photograph on it into a tube in front of the camera. It was a trick. Are you still debunking these days?
Yes, I still get calls. There are many ways that bad science happens – one is outright fraud and trickery like Serios, another is bad statistics. An example of bad statistics is a book called The Bible Code, which has sold 3 million copies. It’s by a bunch of mathematicians and rabbis who claim that you can use the book of Genesis and arithmetic progressions to predict the future. It is quite a complicated piece of mathematics, but the proof of it was basically statistical. It goes something like this: you take some phrase like “Persi Diaconis” and find the shortest progression in Genesis that spells it out. You can find anything, I promise you. Then you take some phrase that is
related to the first phrase, like “shuffling cards”, and you find the shortest progression that contains that. The book claims that these progressions are physically closer together than they would be by chance. They had some way of trying to quantify this that was just crazy. But you had to be a professional statistician to know. How are you still involved in magic?
I write magic tricks for friends. Maybe one of them will be doing a trade show for a steel company and will call asking whether I can invent a trick with tin cans. I still subscribe to magic journals. Magic is a community that I am part of. I am writing a book called Mathematics and Magic Tricks that is almost finished and might be done in a year. So right at the moment I’m doing a fair amount more magic than I normally do. I’m also teaching a course on mathematics and magic so I perform for the kids a little bit and do my perfect shuffles. ● 24 March 2007 | NewScientist | 53
16/3/07 5:14:15 pm
When he ran away from home aged 14 to spend two years on the road as a magician’s assistant, Persi Diaconis had little idea that his fascination with magic would take him to Harvard University and beyond. Today he is not only one of the world’s top sleight-of-hand magicians but a professor of statistics at Stanford to boot. He has used his skills to debunk numerous instances of fraud and trickery, and proved that it takes seven shuffles to perfectly randomise a pack of cards. He tells Justin Mullins about his strange journey
The chance of a lifetime How did you become involved in magic?
When I was 5 I found a magic book and did a little show for my mother. I was the centre of attention and became hooked. When I was older, I was sitting in a cafeteria one day doing a trick where you deal the second card from a pack rather than the top card. A magician called Dai Vernon spotted me and saw some potential. One day he called, said he was going to Delaware the following day to do a show and asked if I wanted to go along as his assistant. I packed my bag and left. We travelled around for two years and I learned a great deal from him. I never went home again. How did your tricks end up being published?
As a teenager, I got to know Martin Gardner, the famous recreational mathematician. I showed him one of my mathematical magic tricks, and he published it in the column he had in Scientific American. I was very proud. He got me interested in the link between magic and mathematics. What is the link between magic and mathematics?
With practice, magicians can shuffle a pack of cards perfectly. They can cut the pack exactly in half and interweave the cards one after the
Profile Persi Diaconis is the Mary V. Sunseri professor of statistics and mathematics at Stanford University in California. In 1979 he was awarded a MacArthur Fellowship for showing exceptional promise of future creative work.
52 | NewScientist | 24 March 2007
070324_Op_Interview.indd 52
other. Suppose I have a pack with four aces on top and I shuffle it perfectly. The aces would then be every second card. If I shuffle it again, they would be every fourth card. If I was a crooked gambler and dealt four hands, I’d get the aces. Gamblers have been writing about what they can and can’t do with perfect shuffles for 300 years. There are two kinds of perfect shuffle. You can keep the original top card on top or place it second from top – those are called “out” and “in” shuffles. As a kid I learned a method for moving the top card to any other position in the pack. First express the position you want as a binary number and subtract 1. Then interpret the 1s and 0s in the number as in and out shuffles. If you carry out that sequence of in and out shuffles, the top card ends up where you want. That’s how I learned about binary numbers. Why are shuffles interesting mathematically?
If you out-shuffle a pack of cards eight times, the deck comes back to where it started. But it takes 52 in-shuffles to bring a deck back to the start – as many shuffles as there are cards in the deck. One interesting question is: are there larger decks, with say 104 cards, or some other number, where it also takes a deck-size number of out-shuffles to bring the deck back to the start? The answer is completely unknown. It’s linked to the Riemann hypothesis, one of the fanciest open problems in mathematics. That’s the kind of thing that makes the mathematician and magician in me rather happy.
Without a high-school education, was it hard to get involved in advanced mathematics?
When I was 24, I decided to enrol in night school at City College in New York. When I graduated, I applied to do statistics at Harvard. Martin Gardner wrote a letter for me saying: “Of the 10 best card tricks invented in the last two years, this kid invented two of them. And if he says he wants to do statistics, you should give him a chance.” One of the people on the Harvard committee, Fred Mosteller, was also a serious amateur magician and was influenced by Martin’s letter. That’s how I got in. What is statistics?
My favourite example of statistics is Carl Gauss’s role in the discovery of Ceres in 1801. At that time, people were sure there were only seven planets. But then an astronomer spotted Ceres and followed it for about 40 days. This was exciting stuff, in all the newspapers. Was there a new planet? Then he lost it in the sun. If you know the position and velocity of something orbiting the sun at one time, you should know where it is forever. But the observations were “noisy” because of poor-quality telescopes and errors in measuring Ceres’s position. Gauss took up the challenge. Within a year he had invented the statistical tools to handle noisy observations – the techniques of least-squares, Gaussian elimination and the Gaussian bell-shaped curve. Then he calculated where Ceres should be and told people where to point their telescopes. On the first clear night, they found it. It has ended up www.newscientist.com
16/3/07 5:13:52 pm
classed only as the largest asteroid, not a planet, though. A friend of mine says that statistics is the physics of data sets. For me, statistics is making human sense out of data from the world around us while facing up to the fact that our observations have noise in them. How did you become involved in the debunking of extrasensory perception?
I got hooked on it through Martin Gardner. Somebody had sent a book into Scientific American about “psychic” photography. The claim was that a guy called Ted Serios could take a Polaroid picture and it would have some image produced just by his thoughts on it – a plane flying through the picture or a
“I became interested in the link between magic and mathematics” www.newscientist.com
070324_Op_Interview.indd 53
Cro-Magnon man, say. Martin paid me and some technical photographers to go and watch this guy. I caught him sneaking a little marble with a photograph on it into a tube in front of the camera. It was a trick. Are you still debunking these days?
Yes, I still get calls. There are many ways that bad science happens – one is outright fraud and trickery like Serios, another is bad statistics. An example of bad statistics is a book called The Bible Code, which has sold 3 million copies. It’s by a bunch of mathematicians and rabbis who claim that you can use the book of Genesis and arithmetic progressions to predict the future. It is quite a complicated piece of mathematics, but the proof of it was basically statistical. It goes something like this: you take some phrase like “Persi Diaconis” and find the shortest progression in Genesis that spells it out. You can find anything, I promise you. Then you take some phrase that is
related to the first phrase, like “shuffling cards”, and you find the shortest progression that contains that. The book claims that these progressions are physically closer together than they would be by chance. They had some way of trying to quantify this that was just crazy. But you had to be a professional statistician to know. How are you still involved in magic?
I write magic tricks for friends. Maybe one of them will be doing a trade show for a steel company and will call asking whether I can invent a trick with tin cans. I still subscribe to magic journals. Magic is a community that I am part of. I am writing a book called Mathematics and Magic Tricks that is almost finished and might be done in a year. So right at the moment I’m doing a fair amount more magic than I normally do. I’m also teaching a course on mathematics and magic so I perform for the kids a little bit and do my perfect shuffles. ● 24 March 2007 | NewScientist | 53
16/3/07 5:14:15 pm