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Gathering for Gardner Knew What Had Happened to Her None of the waitresses at the restaurant where Thelma had worked Gathering for Gardner knew what had happened to her. She Bruce Torrence left her job six months before, and they hadn’t heard from her since. No Thelma O’Keefe was in the Tulsa phone book. I drove back to Norman feeling sad and frustrated. Should I hire a detective? The Norman yellow book had a long list of “investigators” and two detective agencies. I was planning to call one of the agencies when my telephone rang. It was Thelma! “I heard you were asking about me,” she said. “Yes. How did you get my phone number?” “It’s on the Internet. How are strings?” “Not so good. It didn’t predict dark matter. It didn’t predict dark energy. It even failed to pass one of my tests. Lots of stringers are starting to have doubts, including me.” “If we meet again,” said Thelma, “don’t Photographs courtesy of Bruce Torrence tell me about it.” t’s a chaotic scene in the lobby of the author whose interests spanned the Further Reading Ritz-Carlton. There’s a dental con- seemingly disparate disciplines of vention getting under way, and as mathematics, puzzles, magic, and the Two recent books attacking string/M I travel-weary orthodontic professionals spirited debunking of pseudoscience. theory as pseudoscience are Not Even trickle into the packed room, they This invitation-only affair attracts lumi- Wrong, by mathematician Peter Woit encounter a bewildering display. Every naries in all of these fields, and despite (Basic Books, 2006), and The Trouble tabletop holds a collection of fascinat- their obvious differences, there is a fer- with Physics, by Lee Smolin (Mariner ing objects—puzzles of every imagina- tile and dynamic common ground and Books, 2007). See Chapter 18, “Is ble shape and design—around which a deep mutual respect among the String Theory in Trouble?” in my book, magicians, mathematicians, and puzzle participants. The Jinn from Hyperspace (Prometheus masters gather to discuss their latest Books, 2008). inventions. The conversations are What Has Tuesday animated, and there is a tangible Editor's note: A provocative and Got to Do with It? feeling that something important is widely discussed article in which The organization of the conference is unfolding. And indeed there is: string theory is used to suggest that simple: there is one grand conference unbeknownst to the dentists, the ninth gravity is not a fundamental force, but room with a single stage. Speakers give Gathering for Gardner has just begun. is rather a consequence of entropy, is brief presentations in turn and are Erik Verlinde's “On the Origin of awarded a dollar coin for each minute Atlanta has been host to this unlikely Gravity and the Laws of Newton” that they finish ahead of their allotted convention of tinkerers and free (2010), which can be found at time—an innovative and surprisingly thinkers for almost two decades. They http://arxiv.org/abs/1001.0785. inexpensive management tactic. Only assemble to pay homage to Martin one speaker really cashed in: Gary DOI: 10.4169/194762110X525557 Gardner, the prolific and magnetic Foshee, a mechanical puzzle collector SEPTEMBER 2010 • MATH HORIZONS • WWW.MAA.ORG/MATHHORIZONS 9 the week and that births are independ- ent of one another. With these assump- tions in hand, the puzzle succumbs easily to elementary probability theory. If one denotes a single birth by a two- tuple such as (boy, Tuesday) or (girl, Sunday), then there are 14 equally likely scenarios for a single birth. Foshee has two children, and with no other infor- mation, it follows that there are 142 = 196 equally likely poss bilities for two children. But at least one of his children is a (boy, Tuesday), and some simple counting reveals that just 27 of the 196 outcomes satisfy this criterion. To see this, simply note that there are 14 cases where the Tuesday boy is the first born, and 14 where he is the sec- ond born, and subtract the single case that was counted twice. Among these 27 equally likely poss bilities, how many include two boys? Exactly 13—there are seven with (boy, Tuesday) as the first child, and seven with (boy, Tues- day) as the second child, from which we subtract the one we counted twice. Hence, the answer to Foshee’s riddle is 13/27, close to, but not exactly, 1/2. Of course, the riddle leads naturally to a host of other questions. Does “one is a boy born on a Tuesday” mean that the other was not born on a Tuesday? I and designer, faced the audience and illusion and perception, and on and on. don’t read it this way. After all, the spoke slowly, “I have two children. One The topics bounced so completely from question makes clear that there is a is a boy born on a Tuesday. What is the one idea to the next that the effect was poss bility that the second child is a probability I have two boys?” After a both intoxicating and refreshing. Spon- boy, so why shouldn’t the child be pause, he continued. “The first thing taneous discussion arose in and out of allowed to arrive on a Tuesday also? you think is ‘What has Tuesday got to the conference room. “What does More glaring is the counterintuitive do with it?’ Well, it has everything to do Tuesday have to do with it?” nature of the result itself. Why should with it.” And with that, he stepped something like the day of the week down (and collected a hefty stack of Foshee’s puzzle proved a perfect affect the outcome? In thinking about coins from the organizers). catalyst for discussion, and it is both this, it’s important to understand that fun and instructive to reason through it. had the day of the week not been Other talks focused on space-filling One first has to make a few assump- mentioned, the answer would be 1/3, curves and genome folding, origami tions, and most of the people I spoke not 1/2, for only one of the three mazes, Lewis Carroll’s mathematics, with agreed that it’s best to keep it equally likely gender scenarios BB, BG, dancing tessellations, psychological simple. Let’s assume that there are no GB yields two boys. It’s all about explanations for children’s magic multiple births, and that any single birth counting the possible outcomes. If you theory, the history of Rubik’s cube, the is equally likely to be a boy or a girl. are still wondering what Tuesday has to relation between computer hacking and Assume further that births are uniformly do with it, you may wish to consult the invention, self-replicating machines, distributed among the seven days of Further Reading section at the end of the article. 10 SEPTEMBER 2010 • MATH HORIZONS • WWW.MAA.ORG/MATHHORIZONS Just as Foshee’s riddle yields to listener reads those words as it plays. Abstract Structures elementary probability theory, the Cinematic scenes in which actors Another highlight of the gathering was vast majority of questions and puzzles changed costumes out of frame and an afternoon dedicated to socializing posed at the gathering can be returned in their new garb went and sculpture building. Attendees were approached using basic principles. unnoticed by the entire audience (until invited to participate in the construction Each question has some clever twist, we were prompted to look for the and installation of several mathematical and of course this is the hallmark of a change in a second showing). sculptures at the home of Tom good brainteaser. Not all yield so easily, Performance artists and magicians also Rodgers, one of the main organizers of however. Bill Gosper, discoverer of the took to the stage and presented the event. On the lighter side, literally, “glider gun” in Conway’s game of life stunning illusions with amazing skill. Vi Hart led a group that created and considered by many to be the Attendees were treated to close-up geometric balloon art. At the other founder of the hacker community, magic after hours by some of the best extreme, Chaim Goodman-Strauss proudly shared his “Dozenegger” in the business. The net effect was one collaborated on a weighty steel puzzle. This is a physical puzzle in of fascination with a subtly disturbing sculpture that suggested a space-filling which twelve circles, each a different aftertaste. Everyone came away with a curve packed neatly into a cube. Other size meticulously laser-cut from a sheet similar feeling: how is it that we can be sculptures were created using materials of acrylic, must be snuggly packed (but deceived so easily? Seeing and such as aluminum, wood, bamboo, and not forced) into a larger elliptical cavity. believing will never again be the same. plastic. Under the direction of their (You can find it on his website—see the designers—George Hart, Carlo Séquin, Further Reading section.) Akio Hizume, Rinus Roelofs, among others—it was a tour de force of master Magic and illusion played a big part in craftsmen at the top of their game. The the proceedings. Individual presenta- collaborative enterprise also tions in this area fell squarely in the field emphasized to the pure mathemati- of cognitive psychology, highlighting cians among us some of the practical peculiarities in human perception. A difficulties that arise when an abstract cube with a corner removed can be idea is realized as a solid structure. interpreted at least three ways (a large Every sculpture presented unique cube with a smaller cube cut out of it; a challenges, and their successful large cube with a smaller cube jutting resolution led to a deep sense of out from it; and a large three-sided fulfillment as the day came to a close.
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