April 3, 2004
Puzzles + Math = Magic
TLANTA — In a room off the Japanese-style entryway of a house here, a small mahogany coffee cup is firmly attached to a polished wooden saucer. A wooden spoon sits on the plate. So do two white sugar cubes, also made of wood. But can the cup be lifted off the saucer? It seems locked in place. There are no obvious joints, no hidden pieces that can be turned.
"The trick," says Mark Setteducati, a magician based in New York, "is to think of it as a real cup." That is the approach used by Akio Kamei, a Japanese puzzle-maker, who sculptures fine woods into shopping bags, envelopes, books and dice. In each, hidden internal carvings and intricate joints hold the object together. But the key is to consider the nature of the object being portrayed — that cup, for example; only then will the puzzle reveal its secrets.
And what is the first thing done when faced with a cup and sugar cubes? One puts the cubes into the cup and stirs. That is precisely what works. The cubes sit on the flat surface of cup's wooden liquid and seem drawn to particular spots near the rim. And the cup is released from the saucer's locked grasp.
Followers of Mr. Kamei's work are used to such wit (see the Kamei entries at http://www.johnrausch.com/PuzzleWorld), but in this house even the professional puzzle makers, magicians and mathematicians seem to walk around the rooms slack jawed, gazing at walls of display cases of antique puzzles, bingo sets, dexterity tricks, impossible objects. Forget ships in bottles — how did the inventor Harry Eng get a tennis ball, two sneakers, a deck of cards, a pack of cigarettes and a dictionary into a narrow necked-jug that seems locked from the inside?
And is the house itself not a source of wonder? Just outside is a Japanese rock garden and waterfall, landscaped by Takeo Uesugi using boulders from Tennessee; nearby, a humidity-controlled garage houses a collection of more than 1,200 dictionaries from before 1800.
It is the home of Tom Rodgers, an Atlanta investor and businessman. Under his stewardship and partial sponsorship, devotees of mathematics, magic and games come for three days every two years from as far as Japan and England. They meet each other in Mr. Rodgers's house and in a hotel's conference halls, sharing their analyses and inventions, paying tribute to the man who inspired them all: the one-time columnist for Scientific American, Martin Gardner.
Mr. Gardner, 89 and living in Oklahoma, attended only the first two Gatherings for Gardner, as these meetings are called, and missed the sixth, from March 26 to March 28, as well. But as a writer who redefined the nature of recreational mathematics, and inspired many hundreds of careers, he remains its guiding spirit.
From the start of his "Mathematical Games" column in 1956 until he retired in 1991, Mr. Gardner must have discussed the work of at least half of the 180 or so people in attendance. Now younger generations are joining in, making this the largest gathering yet. Mr. Rodgers arranges the program with the guidance of Mr. Setteducati and the mathematician Elwyn Berlekamp.
Some are professionals at play, others have professions that actually are play. Mr. Setteducati, for example, has patented toys (he has even patented a book, "The Magic Show," that doesn't just contain magic tricks; it seems to perform them). Another puzzle creator, Ivan Moscovich, designed a science museum in Tel Aviv in 1964 that inspired the interactive play of the Exploratorium in San Francisco and other recent science museums.
At the St. Regis Hotel in Atlanta, brief talks are offered about subjects ranging from the technical to the magical: Fibonacci numbers, rope tricks, the history of dice, the prospect of multiple universes. A British businessman, Adrian Fisher, describes his design of the world's largest hedge maze, made of jasmine bushes, now growing in Yunnan, China (www.mazemaker.com). Two speakers, Kay Caskey and Laurie Young, proselytize for the therapeutic powers of juggling (http://www.nytimes.com/2004/04/03/arts/www.laughways.com) and teach sedentary puzzlers how to toss scarves.
At the evening magic shows, a Swedish magician, Lennart Green — a retired physician now spoken of with awe in his new profession — adopts a bleary-eyed, clumsy persona, seeming to make mistake after mistake, but instantly pulls card by card out of a deck, writing an audience member's phone number, or fans out a well-shuffled deck neatly ordered into separate suits.
The play also had its serious side. Matthew T. Keennon, a designer for Aerovironment Inc., recently returned from Iraq where his company's spy planes are in use. One of the company's flying machines, the "Microbat RC Ornithopter," he says, boasts a 9-inch wingspan, a 25-minute power supply and a weight of just 14 grams: its wings flap.
But aside from the influence of Mr. Gardner, which is bound to recede over time, what is the common ground for these participants and their puzzles? Mr. Berlekamp, a professor of mathematics at the University of California at Berkeley readily acknowledges that "most mathematicians would consider this on the P.R. side of mathematics; most magicians would consider it on the mathematical side of magic."
Yet it is also much more. Arthur Ganson (http://www.arthurganson.com/), who shows a film clip of a wiry contraption, whose sole function is to make a wishbone seem to walk. Meanwhile, Tyler MacCready, the son of Aerovironment's founder, demonstrates a toy glider so light and sensitive it can be steered and kept aloft using nothing more than the faint breeze created by hands held a few inches below its surface, inspiring an auditorium saturated with inventors to burst into applause.
In the case of Mr. Ganson's machine, the wonder is at how complicated a mechanism was required to do something so apparently simple, in Mr. MacCready's at how simple a solution was needed to accomplish something usually so complicated.
In both, though, the wonder is how something is done. Magicians are also inventors, but spur astonishment not at how something is done — though that is always the question asked — but that it is done at all.
At one performance, the magician Jamy Ian Swiss asked an audience member to come onstage and close her eyes. He promised he would pass a wire hanger through her body without her feeling it. But he let the audience see precisely how the trick was done. The audience laughed at the trick's obviousness, but she, having seen nothing, was amazed. "Now which of you," the magician asked, "has had the better experience?"
The mathematician and puzzler dissent, of course, insisting that the best experience is in knowing. The goal is not illusion, but disillusion. See the coffee cup as a mechanism with magnets, show the palmed cards, explain why certain series of numbers act in a certain way.
The truth, they believe, is its own magic. At one magic show, a mathematician, Arthur T. Benjamin, able to perform stunningly fast calculations in his head, took a four-digit number, asked calculator-wielding guests to multiply it by any three-digit numbers they wished. They were then asked to read off all but one digit of the result in any order. In each case, he guessed the remaining digit. Astonishing as magic, but even more astonishing as puzzle — the method has a simple mathematical explanation (which can be sought, for those interested, in the properties of numbers divisible by 9 — which the original number was).
Not all solutions are easy or even possible, of course. But the mathematician, the magician, the inventor and the puzzler, for all their different attitudes, are always at play in this shape-shifting world, believing that if something is well understood, like Mr. Kamei's cup, perhaps, its secrets can be revealed, or manipulated, or applied. The task may always end up far easier, or far harder, than it looks.
As the mathematician Peter Winkler said in one talk: "No matter how simple something is, there's room for it to be too hard to do."