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A Celebration of Raymond Smullyan
By Jason Rosenhouse
Dover Publications, Inc.Copyright © 2014 Jason Rosenhouse
All rights reserved.
I am one of the administrators at www.pianosociety.com, a website dedicated to hosting free classical piano music. People wishing to become a member of the site are asked to submit recordings of themselves playing piano, and then the board and other members evaluate the recordings to see if they are good enough. Raymond submitted his first recordings in March 2007. It was obvious upon first listening to them that his playing was certainly good enough, and we asked him to submit his biography and photo so we could add him as a member to the site. When I first read his bio, I was extremely impressed with his background. To learn that Raymond is not only a pianist, but also a mathematician, logician, philosopher, and magician was mind-boggling!
The website contains a forum where members submit recordings, and there are also several sub-forums where members chat about piano-related subjects. One of the sub-forums is just general in nature, where mostly anything goes. We tell jokes there and play games, mostly quizzes. I got to know Raymond more and more when he started posting in a certain thread that he started on the forum titled, "Puzzles, Jokes, Ancedotes, and Thoughts." First came the jokes—hundreds of them—mostly music-related, and everyone on the forum got a lot of laughs. Then Raymond began posting quizzes and puzzles for us to figure out. It became a competition to see which member would be the first to solve the puzzle. I know that I have never spent so much time trying to work out puzzles and quizzes until I met Raymond. It was a lot of fun; he really entertained everyone on the forum. And he's still doing it to this day!
In a short amount of time I learned that not only is Raymond the smartest person I've ever known, he is kind, funny, charming, and also a big flirt; something he wholeheartedly admits. He even nicknamed himself "the incorrigible one." I can say wholeheartedly that the website is better for having Raymond included as a member, and I personally feel very fortunate that I have gotten to know him.
Having recently returned to my schooldays hobby of composing chess problems, I was taken by surprise when my wife handed me a copy of Smullyan's book The Chess Mysteries of Sherlock Holmes. Browsing through this book introduced me to a rich variety of ideas in "Retrograde Analysis," the novelty of which is an inspiration to creative work. I have since discovered that over the years other composers have been similarly affected.
As a tribute to Smullyan, I offer the following problem:
White is to move and force checkmate in two moves.
This is a version of the problem featured in the chapter "You Really Can't You Know!" from the Sherlock Holmes book. Smullyan uses the storyline to motivate the demonstration that black cannot castle and to support the analysis with a restriction on the last move played. My version replaces this by posing the standard chess problem stipulation "Mate in 2." The construction reduces the number of white pieces, enhancing the problem's compliance with artistic standards of economy.
The solution is 1. Ke6. White threatens to give checkmate on the next move with 2. Qe7. In answer to black's defense Kd8, white replies with 2. Qf8. If black could castle there would be no mate, so to justify the solution it must be shown that castling is illegal (the convention in chess problems is to assume that a player can castle unless it can be shown by retrograde analysis that he cannot). The argument set forth below to show that either the black rook or king must have moved in the game leading to the diagram position closely follows the reasoning used by Smullyan.
Note that the white pawns have captured all six missing black pieces, while the black pawns have captured five of white's six missing pieces. In the diagram position it is white's move, so black played last, and we now ask what this move could have been.
If it was with the king or the rook, then black cannot now castle.
If it was the pawn capture fxg6, then the black king must have moved earlier in the game to allow the rook from h8 to escape from the back row and be captured by a white pawn. In this case as well, black can no longer castle.
If it was the pawn move a4-a3, then all five black pawn captures took place on white squares. It follows that white's dark squared bishop was not one of the pieces captured by the pawns. Therefore, black's pawns did capture all of the other missing white pieces including the white pawn from d2. This pawn could not have captured anything to move off the d-file, so in order to be available for capture it must have promoted on d8. When the promotion move d7-d8 was played, the black king could not have been standing in check on e8. It must have moved earlier, implying once again that black cannot now castle.
Finally, we come to the pawn on e5. This pawn could not have come from d6 or f6, since that would imply too many captures of white pieces. Nor could it have just come from e6, where it would have been checking the white king, or from e7, since that would mean that the black bishop on f8 could not have escaped to be captured by a white pawn. Having rejected all possible launch squares it is seen that this pawn did not play black's last move.
In conclusion, it has been shown that for all possible last moves by black either the black rook or king have moved and therefore castling is illegal.
I greatly appreciate having this opportunity to express my gratitude to Raymond Smullyan for the treasures I have discovered in his books.
I first met Raymond Smullyan when I took his course in Mathematical Logic at Princeton in 1959. I had previously taken a rigorous logic course in the Philosophy Department, taught by Hilary Putnam, so I felt well-prepared for the Math Department's logic course. In fact, I probably felt the course would be a breeze, involving very little effort on my part to get an A grade. I did in fact get an A, but I worked very hard in the course because it was so interesting! Ray was developing his "Analytic Tableaux" system for doing first-order logic (see the essay by J. Michael Dunn). It was an intuitive and elegant formulation based on an earlier system developed by E.W. Beth. But whereas Beth used two separate tableaux, Smullyan got away with just one. It was beautiful. I had never before been in a math class where new mathematics was being created before my eyes. It was intoxicating.
After college, I decided to pursue a PhD in mathematics, specializing in logic. I first went to Cornell but wasn't happy there; I missed the feeling of being a part of the creative process that I'd had when in Ray's logic class. So I left Cornell and went to Yeshiva University, where Ray and Martin Davis had recently taken up residence in a newly created graduate program. I took Ray's Set Theory course, as did Melvin Fitting, and again that feeling of excitement returned, and I earned my PhD with Ray as my thesis advisor. It was at this time that Ray started his first puzzle book, What is the Name of this Book?, and he gave it to me to read in manuscript form. I passed it on to my ten-year-old daughter Lenore, and she loved it. She even made a few corrections, as I recall, and later told me that she was very proud of me because I knew the author. Probably it influenced her choice of career—she has taken up the family business and is a mathematician at Tufts University.
Whatever Ray does, be it mathematics, puzzles, music, or magic, is characterized by beauty and elegance. Also, it is always very entertaining. In fact, Ray is the ultimate entertainer; he will always have something new to delight you!
I am very grateful to have been his student and friend these many years.
We would go visit Raymond Smullyan, who had been my father's PhD advisor, and his wife, Blanche, in their home in the Catskills, about once a year, starting when I was about nine years old, and continuing through when I was in high school. These visits all blur together, so I don't remember what happened which year, but I clearly remember Ray, and Blanche, and those large, wonderful, beautiful collie dogs that lived with them.
When one is nine, one begins to wonder a little about her parents, and what they do, and what their place is in the world. Clearly my father was pretty special, because we were invited to visit Ray Smullyan, who seemed like he could have popped out of a storybook. In fact, he looked just like Rip Van Winkle, who had also "lived" in the Catskill Mountains.
My family would drive up from New York City: me, my mother, my father, and my younger sister Minda. We usually stayed two or three nights with them each visit. The first visit I remember clearly: Ray shared with me some of the puzzles that would later become part of What is the Name of This Book?, testing them out, he said, to make sure they would work. He was really pleased I liked them so much, and he sent a full typewritten copy of the manuscript home with me. I went through it eagerly in the following months, and I got all the way through the Insane Vampires, but the Gödel Islands were a bit beyond me at that age. (When I took a college Logic class in high school, I finally understood and appreciated the final chapters.) I made some observations in pencil in the manuscript about the wording of some of the problems and solutions, which were sent off to him by my parents, and Ray seemed very pleased. When the book was about to be published, he telephoned my parents to make sure he had spelled my name right and gotten my age right (I had since turned 10), because he was going to thank me in the acknowledgments.
Later visits pretty much followed the same pattern—Ray would share puns or magic tricks with my sister and me, and then he would show us some of the material from the next book he was writing. He introduced me to retrograde chess puzzles when he was working on his book of them. The talk turned to philosophy when he was writing The Tao is Silent, and I remember him and Blanche telling us the "Whichever way the Wind Blows" story. When my dad started talking formal logic with Ray, or the conversation turned too adult or over my head, I'd go out to the backyard and join my little sister in stroking the big and beautiful dogs in the sun; my favorite was Peekaboo, the mother dog.
Our visits were never complete without music. Always, Blanche would play piano for us, and she was a wonderful and skilled classical pianist. Ray, who was also a fine pianist, would often go to the piano and play, or improvise, as well. Sometimes my sister and I would bring our violins and play for them, accompanied by Blanche on the piano.
As Blanche got older (Ray never seemed to change), instead of her serving us lunch at the house, we would go to one of the little restaurants in town for a pancake brunch. Ray was a local celebrity—everyone knew him—and he would never stay at our table for long. Instead, he would go from table to table, particularly if there were children, and pull coins out of their ears, or perform other small feats of closeup magic.
Each year, it seemed, another book would follow, and Ray would sign a copy for us. I worked through many more puzzles, although usually from the book after it was published; I never again read a full manuscript.
I went on to major in math at Yale, and then I got my PhD in applied math at MIT. Whenever someone would ask me to suggest a good book for a teenager gifted in math, I would always recommend Raymond's What is the Name of this Book? or The Lady or the Tiger. I went on to faculty positions, first at Johns Hopkins University in Baltimore, and then at Tufts University in the Boston area. In both places, I frequently taught the core Discrete Mathematics class that is required of all computer science majors, and I always (to this day) incorporated some of Smullyan's puzzles. My favorites are Portia's caskets, the Lady and the Tiger, Knights and Knaves, or Alice in the Forest of Forgetfulness. My daughters recently turned nine, and I have just had the joy of sharing What is the Name of this Book? with them. My signed copy has been consulted so many times that it is in tatters, but they have been trying to take care of it. So Raymond Smullyan has had an enormous impact on me: personally, on my teaching, and with my family.
We lived near Hartford, Connecticut, during the years 1956 to 1959. The philosopher Hilary Putnam and his family joined us there during the summers of 1958 and 1959 so he and I could work together. Raymond came to visit Hilary one day and that's how we met. The three of us were having lunch at a restaurant in Hartford when Raymond took a paper napkin from the table, crumpled it into a ball, placed it in my open palm, and asked me to make a fist. Warning me that what he was about to do was highly illegal, he picked up the salt shaker and liberally salted my hand. When I opened it, the napkin had been transformed into a crumpled dollar bill.
Some years later, Ray and I were colleagues at the new Graduate School of Science at Yeshiva University. With Ray's wife Blanche, my wife Virginia, and our sons Harold (9) and Nathan (7), we traveled together in Europe. In 1962, on our way to the upcoming International Congress of Mathematicians in Stockholm, the six of us drove north together to Scotland. In fine form, Raymond, affecting an English accent, bemoaned the loss of India, exclaiming, "Things haven't been the same since we lost India." When we were viewing spectacular scenery, Raymond's refrain was always: "This is very beautiful, but not as beautiful as Tannersville" (Raymond lived in Tannersville, which is a village in the Catskill Mountains about an hour's drive from Manhattan). When we arrived in Scotland, he wanted to tell us what was important about being in Scotland, repeating over and over again, "The main thing when you're in Scotland is ..." But we never were to find out what this main thing was. This tease was mainly directed at our boys.
Later that summer we toured Greece together, driving around the Peloponneses in two VW beetles. Raymond had developed an appreciation for the subtle differences between the olives of the various locales. We could stop to rest at a village, seat ourselves at a café, and Raymond would order "elyes," the Greek word for olives being one of the very few he had learned. Crossing the Peloponneses on the then largely unpaved road to Andritsina, there were many absolutely spectacular mountain vistas. Raymond's response was always the same: "Very beautiful, but not as beautiful as Tannersville."
As the summer heat increased, like so many Greeks, we left the mainland for the islands. At that long ago time the wonderful island of Mykonos had no airport, and local people and visitors could meet in easy friendship. I remember well one evening when we and some local people were seated around a table in a café on the waterfront and Raymond commenced to do magic. Now, the local people were unaware of the remarkable effects that could be achieved by a professional using misdirection. As far as they were concerned, magic was magic, and since leaving childhood behind, they didn't believe in magic. And yet here it was being performed before their eyes. Raymond had never before had such an overwhelming effect on an audience.
I'm sure that other contributors to this book will discuss some of Raymond's contributions to mathematical logic. What I would like to emphasize about his work is that Raymond always sought the simplest and most elegant formulations and that he always found them.
Excerpted from FOUR LIVES by Jason Rosenhouse. Copyright © 2014 Jason Rosenhouse. Excerpted by permission of Dover Publications, Inc..
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