None of the waitresses at therestaurant where Thelma had workedknew what had happened to her. Sheleft her job six months before, and theyhadnt heard from her since.

No Thelma OKeefe was in the Tulsaphone book. I drove back to Normanfeeling sad and frustrated. Should I hirea detective? The Norman yellow bookhad a long list of investigators andtwo detective agencies.

I was planning to call one of theagencies when my telephone rang. Itwas Thelma!

I heard you were asking about me,she said.

Yes. How did you get my phonenumber?

Its on the Internet. How are strings?

Not so good. It didnt predict darkmatter. It didnt predict dark energy. Iteven failed to pass one of my tests.Lots of stringers are starting to havedoubts, including me.

If we meet again, said Thelma, donttell me about it.

Further ReadingTwo recent books attacking string/Mtheory as pseudoscience are Not EvenWrong, by mathematician Peter Woit(Basic Books, 2006), and The Troublewith Physics, by Lee Smolin (MarinerBooks, 2007). See Chapter 18, IsString Theory in Trouble? in my book,The Jinn from Hyperspace (PrometheusBooks, 2008).

Editor's note: A provocative andwidely discussed article in which string theory is used to suggest thatgravity is not a fundamental force, butis rather a consequence of entropy, isErik Verlinde's On the Origin of Gravity and the Laws of Newton(2010), which can be found athttp://arxiv.org/abs/1001.0785.

DOI: 10.4169/194762110X525557

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Bruce Torrence

Gathering for Gardner

Photographs courtesy of Bruce Torrence

Its a chaotic scene in the lobby of theRitz-Carlton. Theres a dental con-vention getting under way, and astravel-weary orthodontic professionalstrickle into the packed room, theyencounter a bewildering display. Everytabletop holds a collection of fascinat-ing objectspuzzles of every imagina-ble shape and designaround whichmagicians, mathematicians, and puzzlemasters gather to discuss their latestinventions. The conversations areanimated, and there is a tangiblefeeling that something important isunfolding. And indeed there is:unbeknownst to the dentists, the ninthGathering for Gardner has just begun.

Atlanta has been host to this unlikelyconvention of tinkerers and freethinkers for almost two decades. Theyassemble to pay homage to MartinGardner, the prolific and magnetic

author whose interests spanned theseemingly disparate disciplines ofmathematics, puzzles, magic, and thespirited debunking of pseudoscience.This invitation-only affair attracts lumi-naries in all of these fields, and despitetheir obvious differences, there is a fer-tile and dynamic common ground anda deep mutual respect among theparticipants.

What Has Tuesday Got to Do with It?The organization of the conference issimple: there is one grand conferenceroom with a single stage. Speakers givebrief presentations in turn and areawarded a dollar coin for each minutethat they finish ahead of their allottedtimean innovative and surprisinglyinexpensive management tactic. Onlyone speaker really cashed in: GaryFoshee, a mechanical puzzle collector

the week and that births are independ-ent of one another. With these assump-tions in hand, the puzzle succumbseasily 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 likelyscenarios for a single birth. Foshee hastwo children, and with no other infor-mation, it follows that there are 142 =196 equally likely poss bilities for twochildren. But at least one of his childrenis a (boy, Tuesday), and some simplecounting reveals that just 27 of the 196outcomes satisfy this criterion. To seethis, simply note that there are 14cases where the Tuesday boy is thefirst born, and 14 where he is the sec-ond born, and subtract the single casethat was counted twice. Among these27 equally likely poss bilities, how manyinclude two boys? Exactly 13thereare seven with (boy, Tuesday) as thefirst child, and seven with (boy, Tues-day) as the second child, from whichwe subtract the one we counted twice.Hence, the answer to Foshees riddle is13/27, close to, but not exactly, 1/2.

Of course, the riddle leads naturally toa host of other questions. Does one isa boy born on a Tuesday mean thatthe other was not born on a Tuesday? Idont read it this way. After all, thequestion makes clear that there is aposs bility that the second child is aboy, so why shouldnt the child beallowed to arrive on a Tuesday also?More glaring is the counterintuitivenature of the result itself. Why shouldsomething like the day of the weekaffect the outcome? In thinking aboutthis, its important to understand thathad the day of the week not beenmentioned, the answer would be 1/3,not 1/2, for only one of the threeequally likely gender scenarios BB, BG,GB yields two boys. Its all aboutcounting the possible outcomes. If youare still wondering what Tuesday has todo with it, you may wish to consult theFurther Reading section at the end ofthe article.

illusion and perception, and on and on.The topics bounced so completely fromone idea to the next that the effect wasboth intoxicating and refreshing. Spon-taneous discussion arose in and out ofthe conference room. What doesTuesday have to do with it?

Foshees puzzle proved a perfectcatalyst for discussion, and it is bothfun and instructive to reason through it.One first has to make a few assump-tions, and most of the people I spokewith agreed that its best to keep itsimple. Lets assume that there are nomultiple births, and that any single birthis equally likely to be a boy or a girl.Assume further that births are uniformlydistributed among the seven days of

and designer, faced the audience andspoke slowly, I have two children. Oneis a boy born on a Tuesday. What is theprobability I have two boys? After apause, he continued. The first thingyou think is What has Tuesday got todo with it? Well, it has everything to dowith it. And with that, he steppeddown (and collected a hefty stack ofcoins from the organizers).

Other talks focused on space-fillingcurves and genome folding, origamimazes, Lewis Carrolls mathematics,dancing tessellations, psychologicalexplanations for childrens magictheory, the history of Rubiks cube, therelation between computer hacking andinvention, self-replicating machines,

10 SEPTEMBER 2010 MATH HORIZONS WWW.MAA.ORG/MATHHORIZONS

Just as Foshees riddle yields toelementary probability theory, the vast majority of questions and puzzlesposed at the gathering can beapproached using basic principles.Each question has some clever twist,and of course this is the hallmark of agood brainteaser. Not all yield so easily,however. Bill Gosper, discoverer of theglider gun in Conways game of lifeand considered by many to be thefounder of the hacker community,proudly shared his Dozeneggerpuzzle. This is a physical puzzle inwhich twelve circles, each a differentsize meticulously laser-cut from a sheetof acrylic, must be snuggly packed (butnot forced) into a larger elliptical cavity.(You can find it on his websitesee theFurther Reading section.)

Magic and illusion played a big part inthe proceedings. Individual presenta-tions in this area fell squarely in the fieldof cognitive psychology, highlightingpeculiarities in human perception. Acube with a corner removed can beinterpreted at least three ways (a largecube with a smaller cube cut out of it; alarge cube with a smaller cube juttingout from it; and a large three-sidedroom with a cube sitting in its backcorner). Verses of Led ZepplinsStairway to Heaven, playedbackwards can be made to say prettymuch whatever you want provided the

listener reads those words as it plays.Cinematic scenes in which actorschanged costumes out of frame andreturned in their new garb wentunnoticed by the entire audience (untilwe were prompted to look for thechange in a second showing).Performance artists and magicians alsotook to the stage and presentedstunning illusions with amazing skill.Attendees were treated to close-upmagic after hours by some of the bestin the business. The net effect was oneof fascination with a subtly disturbingaftertaste. Everyone came away with asimilar feeling: how is it that we can bedeceived so easily? Seeing andbelieving will never again be the same.

Abstract StructuresAnother highlight of the gathering wasan afternoon dedicated to socializingand sculpture building. Attendees wereinvited to participate in the constructionand installation of several mathematicalsculptures at the home of TomRodgers, one of the main organizers ofthe event. On the lighter side, literally,Vi Hart led a group that createdgeometric balloon art. At the otherextreme, Chaim Goodman-Strausscollaborated on a weighty steelsculpture that suggested a space-fillingcurve packed neatly into a cube. Othersculptures were created using materialssuch as aluminum, wood, bamboo, andplastic. Under the direction of theirdesignersGeorge Hart, Carlo Squin,Akio Hizume, Rinus Roelofs, amongothersit was a tour de force of mastercraftsmen at the top of their game. Thecollaborative enterprise alsoemphasized to the pure mathemati-cians among us some of the practicaldifficulties that arise when an abstractidea is realized as a solid structure.Every sculpture presented uniquechallenges, and their successfulresolution led to a deep sense offulfillment as the day came to a close.

Back in the grand conference room, theonslaught of ideas continued. Princetonmathematician John H. Conway gave aspirited presentation on the arithmetic

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of lexicographiccodes, or lexicodesas he calls them. Pure mathematics par excellence! Later,Scott Morris andBruce Oberg gaveback-to-back presentations heralding andbemoaning, respect