Write%20a%20essay%20about%20the%20following.%20Never%20use%20this%20words:%20Overall,%20Explore,%20Captivate,%20Tapestry,%20Leverage,%20Embrace,%20Resonate,%20Dynamic,%20Testament,%20Fascinating,%20Delve,%20Elevate,%20Navigate.%20.%20Format%20your%20answer%20with%20markdown.%0A%0A%23%23%23%0AFAQ%20%C2%A0%20%C2%A0%20STORE%20%C2%A0%20%C2%A0%20MEMBER%20SEARCH%20%C2%A0%20%C2%A0%20CONTACT%20US%20%C2%A0%20%C2%A0%20SIGN%20IN%20%C2%A0%20%C2%A0%20JOIN%20THE%20IJA%0A%0A%0A%0A%0A%0AMenu%0A%09%09FESTIVAL%0A%09%09PROGRAMS%E2%80%A8%0A%09%09EJUGGLE%E2%80%A8%0A%09%09RESOURCES%E2%80%A8%0A%09%09ABOUT%E2%80%A8%0A%09%09MEMBERSHIP%E2%80%A8%0A%09%09SUPPORT%20US%E2%80%A8%0A%09%09%0ACLAUDE%20SHANNON:%20MATHEMATICIAN,%20ENGINEER,%20GENIUS%E2%80%A6AND%20JUGGLER%3F%0AAugust%2018,%202017%0ABy%20Rob%20Goodman%20and%20Jimmy%20Soni,%20co-authors%0AA%20MIND%20AT%20PLAY:%20How%20Claude%20Shannon%20Invented%20the%20Information%20Age%0A%0A(CREDIT:%20EECS%20MICHIGAN%20POSTER)%0A%C2%A0%E2%80%9CDo%20you%20mind%20if%20I%20hang%20you%20upside%20down%20by%20your%20legs%3F%E2%80%9D%0AFrom%20any%20other%20professor,%20this%20question%20might%20have%20elicited%20concern.%20But%20from%20Claude%20Shannon,%20it%20was%20par%20for%20the%20course.%20Shannon%20had%20in%20mind%20an%20elaborate%20experiment:%20combining%20two%20forms%20of%20juggling%E2%80%94bounce%20and%20toss%E2%80%94by%20suspending%20a%20juggler%20by%20his%20feet.%0AToss%20juggling%20is%20the%20airborne%20form%20of%20the%20art%20most%20familiar%20to%20us.%20Bounce%20juggling,%20on%20the%20other%20hand,%20consists%20in%20keeping%20objects%20in%20motion%20by%20hitting%20them%20against%20the%20ground%20in%20a%20pattern,%20a%20motion%20akin%20to%20the%20beating%20of%20hand%20drums.%20As%20generations%20of%20jugglers%20have%20discovered%20in%20the%20early%20stages%20of%20mastering%20their%20craft,%20bouncing%20items%20against%20the%20ground%20requires%20far%20less%20energy%20than%20tossing%20them%20in%20the%20air;%20in%20a%20bounce%20juggle,%20the%20balls%20arrive%20at%20the%20hand%20at%20the%20very%20top%20of%20their%20arc,%20the%20slowest%20speed%20they%E2%80%99ll%20have%20during%20the%20entire%20sequence.%20But%20even%20though%20the%20bounce%20juggler%20has%20the%20advantage%20of%20catching%20a%20ball%20at%20the%20nadir%20of%20its%20speed,%20conventional%20juggling%20of%20the%20tossing-and-catching%20kind%20is%20a%20more%20fluid%20motion,%20one%20that%20comes%20more%20naturally%20to%20us%20and%20affords%20the%20juggler%20more%20control%20than%20the%20percussive%20effort%20of%20bounce%20juggling.%0AShannon%20wondered:%20Was%20it%20possible%20to%20marry%20the%20physics%20of%20these%20two%20styles%3F%20Could%20you%20capture,%20in%20one%20motion,%20the%20fluidity%20of%20toss%20juggling%20and%20the%20efficiency%20of%20bounce%20juggling%3F%20In%20practical%20terms:%20If%20you%20were%20dangling%20by%20your%20feet,%20could%20you%20toss%20balls%20in%20the%20air,%20let%20gravity%20do%20the%20work%20of%20bringing%20the%20balls%20down%20to%20earth,%20and%20then%20catch%20them%20again%3F%20Both%20the%20inquiry%20and%20the%20method%20were%20vintage%20Shannon:%20whimsical,%20indifferent%20to%20practicalities,%20and%20originating%20in%20an%20activity%20that%20typical%20professors%20might%20have%20dubbed%20unserious,%20but%20which%20Shannon,%20a%20tenured%20member%20of%20the%20MIT%20faculty,%20found%20amusing%20enough%20to%20merit%20scholarly%20time%20and%20attention.%0AThat%E2%80%99s%20how%20Arthur%20Lewbel,%20an%20MIT%20student,%20found%20himself%20suspended%20by%20his%20feet%20in%20the%20middle%20of%20Shannon%E2%80%99s%20living%20room.%20The%20balls%20went%20up%E2%80%A6and%20dropped%20unceremoniously%20to%20the%20ground.%20%E2%80%9CAs%20a%20physical%20experiment,%20it%20was%20a%20complete%20failure,%E2%80%9D%20remembered%20Lewbel.%20Some%20physical%20limits%20even%20perfect%20math%20can%E2%80%99t%20crack;%20and%20in%20this%20case,%20even%20the%20great%20Claude%20Shannon%20couldn%E2%80%99t%20overcome%20the%20most%20obvious%20problem%20with%20the%20experiment%E2%80%99s%20design:%20How%20well%20does%20anyone%20do%20anything%20upside%20down%3F%0A***%0ALewbel%20had%20become%20accustomed%20to%20inquiries%20of%20the%20may-I-hang-you-upside-down%20variety.%20He%20was%20the%20founder%20of%20the%20MIT%20Juggling%20Club%20and%20first%20met%20Shannon%20when%20the%20famous%20information%20theorist%20casually%20dropped%20by%20the%20club%E2%80%99s%20meeting%20unannounced.%20Shannon%20was%20there%20for%20the%20same%20reason%20that%20parents%20the%20world%20over%20find%20themselves%20in%20rooms%20not%20necessarily%20of%20their%20choosing:%20his%20daughter,%20Peggy,%20wanted%20him%20to%20go.%20She%E2%80%99d%20read%20about%20the%20club%20in%20the%20Boston%20Globe,%20and%20while%20it%20probably%20required%20minimal%20arm-twisting%20to%20get%20her%20unicycling,%20tinkering%20father%20to%20attend,%20the%20initial%20interest%20in%20the%20Juggling%20Club%20was%20Peggy%E2%80%99s.%0A%E2%80%9CHe%20just%20showed%20up,%20and%20didn%E2%80%99t%20tell%20anyone%20who%20he%20was.%20There%20were%20a%20bunch%20of%20jugglers%20standing%20outside%20practicing%20and%20he%20just%20walked%20up%20and%20said,%20%E2%80%98Can%20I%20measure%20your%20juggling%3F%E2%80%99%E2%80%9D%20remembered%20Lewbel.%20%E2%80%9CThat%20was%20the%20first%20thing%20he%20said%20to%20us,%20and%20it%20was%20something%20no%20one%20had%20ever%20asked%20us%20before.%E2%80%9D%20Lewbel%20and%20the%20other%20jugglers%20agreed%20to%20be%20measured,%20and%20Shannon%20and%20Lewbel%20developed%20a%20fast%20friendship.%0ADrop-ins%20from%20star%20faculty%20of%20Shannon%E2%80%99s%20stature%20weren%E2%80%99t%20unusual.%20As%20Lewbel%20tells%20it,%20%E2%80%9COne%20nice%20thing%20about%20juggling%20at%20MIT%20is%20that%20you%20never%20know%20who%20will%20show%20up.%20For%20example,%20one%20day%20Doc%20Edgerton,%20inventor%20of%20the%20strobe%20light,%20stopped%20by%20the%20juggling%20club%20and%20asked%20if%20he%20could%20photograph%20some%20of%20us%20juggling%20under%20strobe%20lights.%E2%80%9D%20What%20was%20unusual%20was%20a%20return%20visit.%20But%20return%20Shannon%20did,%20repeatedly,%20even%20hosting%20the%20club%20at%20his%20Winchester%20home%20when%20they%20needed%20space%20for%20pizza-and-movie%20night.%20%E2%80%9CThe%20Juggling%20Club%20and%20the%20jugglers%20enchanted%20us,%E2%80%9D%20remembered%20Peggy%20Shannon.%0A(CREDIT:%20COURTESY%20OF%20THE%20SHANNON%20FAMILY)%0AShannon%20had%20dabbled%20in%20juggling%20for%20decades.%20As%20a%20boy,%20he%20had%20imagined%20himself%20a%20fairground%20performer.%20At%20Bell%20Labs,%20the%20stories%20of%20his%20achievements%20in%20information%20theory%20were%20almost%20always%20accompanied%20by%20tales%20of%20his%20juggling%20while%20riding%20a%20unicycle%20in%20the%20Labs%E2%80%99%20narrow%20halls.%20At%20home%20in%20Winchester,%20there%20were%20ample%20objects%20stashed%20in%20the%20playroom%20to%20toss%20and%20catch.%20By%20that%20point,%20Shannon%20had%20developed%20his%20talents%20as%20an%20amateur%20juggler%20far%20past%20the%20point%20of%20mere%20amusement:%20he%20was%20said%20to%20be%20able%20to%20juggle%20four%20balls,%20which,%20as%20anyone%20who%20has%20tried%20to%20juggle%20knows,%20is%20a%20worthy%20achievement.%0ARonald%20Graham,%20a%20fellow%20mathematician-juggler,%20attributed%20some%20of%20his%20success%20to%20a%20trick%20borrowed%20from%20Galileo.%20%E2%80%9CWhen%20Galileo%20wanted%20to%20slow%20gravity%20down,%20he%20just%20tilted%20a%20table%E2%80%9D%20and%20let%20a%20ball%20roll%20from%20one%20end%20to%20the%20other,%20said%20Graham.%20%E2%80%9CImagine%20a%20big%20table,%20and%20then%20as%20you%20tilt%20the%20table,%20you%20get%20closer%20to%201%20g.%E2%80%9D%20By%20sliding%20pucks%20up%20a%20tilted%20air%20hockey%20table,%20Shannon%20was%20able%20to%20study%20their%20patterns,%20and%20refine%20his%20juggling%20technique,%20in%20a%20kind%20of%20slow%20motion.%20The%20pucks%E2%80%99%20paths%20%E2%80%9Cwere%20not%20parabolas,%20just%20pointy,%20and%20you%20could%20practice%20doing%20that.%E2%80%9D%0APart%20of%20juggling%E2%80%99s%20appeal%20to%20Shannon%20might%20have%20been%20the%20fact%20that%20it%20didn%E2%80%99t%20come%20easily.%20For%20all%20his%20mathematical%20and%20mechanical%20gifts,%20%E2%80%9Cit%20was%20something%20he%20simply%20could%20not%20master,%20making%20it%20all%20the%20more%20tantalizing,%E2%80%9D%20wrote%20Jon%20Gertner.%20%E2%80%9CShannon%20would%20often%20lament%20that%20he%20had%20small%20hands,%20and%20thus%20had%20great%20difficulty%20making%20the%20jump%20from%20four%20balls%20to%20five%E2%80%94a%20demarcation,%20some%20might%20argue,%20between%20a%20good%20juggler%20and%20a%20great%20juggler.%E2%80%9D%20Here,%20at%20least,%20Shannon%20was%20destined%20to%20be%20merely%20good.%0A***%0ATo%20some,%20juggling%20lacks%20the%20nobility%20of%20mathematical%20pastimes%20like%20chess%20or%20music.%20And%20yet%20the%20tradition%20of%20mathematician-jugglers%20is%20an%20ancient%20and%20distinguished%20one.%20As%20best%20as%20we%20can%20tell,%20that%20tradition%20began%20in%20the%20tenth%20century%20CE%20in%20an%20open-air%20market%20in%20Baghdad.%20It%20was%20there%20that%20Abu%20Sahl%20al-%20Quhi,%20later%20one%20of%20the%20great%20Muslim%20astronomers,%20got%20his%20start%20in%20life%20juggling.%20A%20few%20years%20later,%20Al-Quhi%20became%20a%20kind%20of%20court%20mathematician%20for%20the%20local%20emir,%20who,%20fascinated%20by%20planetary%20motion,%20built%20an%20observatory%20in%20the%20garden%20of%20his%20palace%20and%20put%20Al-Quhi%20in%20charge.%20The%20appointment%20bore%20some%20fine%20mathematical%20fruit:%20Al-Quhi%20invented%20an%20adjustable%20geometrical%20compass,%20likely%20the%20world%E2%80%99s%20first,%20and%20led%20the%20revival%20among%20Muslim%20geometers%20of%20the%20study%20of%20the%20Greek%20thinkers%20Archimedes%20and%20Apollonius.%0AFrom%20juggling%20in%20a%20market%20to%20measuring%20the%20courses%20of%20planets:%20what%20they%20had%20in%20common,%20what%20drew%20Al-Quhi%20and%20so%20many%20of%20future%20number-crunching%20jugglers,%20was%20the%20patterns%20of%20parabolas%20and%20arcs,%20equations%20played%20out%20over%20open%20space.%20As%20Graham%20observed,%20%E2%80%9Cmathematics%20is%20often%20described%20as%20the%20science%20of%20patterns.%20Juggling%20can%20be%20thought%20of%20as%20the%20art%20of%20controlling%20patterns%20in%20time%20and%20space.%E2%80%9D%20So%20it%E2%80%99s%20no%20surprise%20that%20generations%20of%20mathematicians%20could%20be%20found%20on%20university%20quads,%20tossing%20things%20in%20the%20air%20and%20catching%20them.%20Burkard%20Polster,%20author%20of%20The%20Mathematics%20of%20Juggling,%20writes,%20%E2%80%9Cnext%20time%20you%20see%20some%20jugglers%20practicing%20in%20a%20park,%20ask%20them%20whether%20they%20like%20mathematics.%20Chances%20are,%20they%20do.%20.%20.%20.%20Most%20younger%20mathematicians,%20physicists,%20computer%20scientists,%20engineers,%20etc.%20will%20at%20least%20have%20given%20juggling%20three%20balls%20a%20go%20at%20some%20point%20in%20their%20lives.%E2%80%9D%0ASo%20what%20drew%20Shannon%20to%20the%20study%20of%20juggling%3F%20%E2%80%9CHe%20liked%20peculiar%20motions%E2%80%A6I%20think%20what%20he%20liked%20about%20juggling%20was%20that%20it%20was%20a%20peculiar%20physical%20motion,%E2%80%9D%20noted%20Lewbel.%20It%20was%20in%20the%20early%201970s%20that%20these%20peculiarities%20finally%20tugged%20enough%20to%20provoke%20him%20to%20write%20a%20mathematical%20paper%20on%20the%20topic.%0AJuggling,%20observed%20Lewbel,%20%E2%80%9Cis%20complex%20enough%20to%20have%20interesting%20properties%20and%20simple%20enough%20to%20allow%20the%20modeling%20of%20these%20properties.%E2%80%9D%20But%20for%20all%20of%20its%20mathematical%20richness,%20when%20Shannon%20first%20began%20his%20work%20on%20the%20topic,%20he%20was%20starting%20from%20scratch:%20the%20field%20had%20no%20body%20of%20written%20work.%0AThe%20first%20important%20scientific%20work%20on%20the%20topic%20was%20in%20the%20field%20of%20psychology.%20In%201903,%20Edgar%20James%20Swift%20published%20a%20paper%20in%20the%20American%20Journal%20of%20Psychology%20that%20studied%20the%20time%20it%20took%20to%20learn%20how%20to%20juggle,%20as%20an%20examination%20of%20the%20most%20effective%20ways%20to%20teach%20neurosensory%20skills.%20The%20nature%20of%20juggling%20itself%20seems%20to%20have%20been%20something%20of%20an%20afterthought.%20The%20insight%20Swift%20was%20after%20wasn%E2%80%99t%20%E2%80%9CHow%20does%20a%20juggler%20learn%20his%20craft%3F%E2%80%9D%20so%20much%20as%20%E2%80%9CHow%20can%20a%20human%20being%20learn%20any%20craft%3F%E2%80%9D%20Following%20in%20his%20footsteps,%20psychologists%20continued%20to%20use%20juggling%20as%20a%20research%20tool%20into%20the%20mid-twentieth%20century.%20But%20where%20psychologists%20had%20found%20juggling%20useful%20in%20their%20research,%20mathematicians%20had%20been%20reluctant%20to%20use%20a%20favorite%20pastime%20as%20a%20source%20of%20data%20and%20experiments.%20Until%20Shannon%20arrived%20on%20the%20scene,%20no%20papers%20had%20explored%20the%20math%20of%20juggling.%0AHow%20could%20that%20be%3F%20How%20had%20millennia%E2%80%99s%20worth%20of%20mathematicians%C2%A0tried%20their%20hands%20at%20juggling%20but%20published%20no%20mathematical%20results%20on%20the%20topic%3F%20In%20some%20ways,%20it%E2%80%99s%20not%20hard%20to%20understand.%20Mathematics%20was%20then,%20as%20now,%20a%20fiercely%20competitive%20discipline,%20and%20while%20card%20games,%20puzzles,%20juggling,%20and%20other%20such%20entertainments%20may%20have%20been%20amusing%20mathematical%20hobbies,%20no%20serious,%20ambitious%20mathematician%20would%20have%20mistaken%20a%20circus%20routine%20for%20a%20topic%20deserving%20sustained%20research%20or%20publication.%20No%20one,%20that%20is,%20until%20Claude%20Shannon.%20Unmoved%20by%20material%20concerns,%20freed%20of%20the%20need%20to%20burnish%20his%20reputation,%20and%20driven%20by%20curiosity%20for%20curiosity%E2%80%99s%20sake,%20he%20could%20throw%20himself%20headlong%20into%20the%20study%20of%20juggling%20without%20any%20of%20the%20misgivings%20his%20colleagues%20might%20feel%20about%20doing%20the%20same.%0A***%0AIn%20the%20context%20of%20Shannon%E2%80%99s%20other%20work,%20the%20juggling%20paper%20is%20unremarkable.%20It%20didn%E2%80%99t%20inaugurate%20a%20new%20field%20of%20study,%20and%20it%20didn%E2%80%99t%20bring%20him%20international%20acclaim.%20Shannon%20neither%20published%20it%20nor%20entirely%20finished%20it.%20Though%20Shannon%20was%20perhaps%20the%20first%20scientist%20to%20study%20juggling%20with%20mathematical%20rigor,%20the%20paper%E2%80%99s%20striking%20feature%20isn%E2%80%99t%20its%20originality%20or%20the%20quality%20of%20its%20mathematics,%20but%20rather%20what%20it%20reveals%20about%20its%20author%E2%80%99s%20wide-ranging%20reading%20and%20research.%20If%20information%20theory,%20genetics,%20and%20switching%20proved%20the%20depth%20of%20Shannon%E2%80%99s%20thinking,%20juggling%20displayed%20his%20dexterity.%20It%20is%20a%20testament,%20as%20well,%20to%20%C2%A0Shannon%E2%80%99s%20belief%20that%20just%20about%20anything%20could%20be%20the%20object%20of%20serious%20mathematical%20analysis.%0AShannon%20opens%20the%20paper%20with%20a%20dialogue%20from%20Lord%20Valentine%E2%80%99s%20Castle,%20Robert%20Silverberg%E2%80%99s%20science%20fiction%20novel%20set%20on%20the%20distant%20planet%20of%20Majipoor.%20It%E2%80%99s%20a%20chronicle%20of%20the%20adventures%20of%20an%20itinerant%20juggler%20named%20Valentine,%20who,%20as%20it%20happens,%20is%20actually%20a%20king%20whose%20throne%20and%20title%20have%20been%20taken%20from%20him:%0A%E2%80%9CDo%20you%20think%20juggling%E2%80%99s%20a%20mere%20trick%3F%E2%80%9D%20the%20little%20man%20asked,%20sounding%20wounded.%20%E2%80%9CAn%20amusement%20for%20the%20gapers%3F%20A%20means%20of%E2%80%A8picking%20up%20a%20crown%20or%20two%20at%20a%20provincial%20carnival%3F%20It%20is%20all%20those%20things,%20yes,%20but%20first%20it%20is%20a%20way%20of%20life,%20friend,%20a%20creed,%20a%20species%20of%20worship.%E2%80%9D%0A%E2%80%9CAnd%20a%20kind%20of%20poetry,%E2%80%9D%20said%20Carabella.%0ASleet%20nodded.%20%E2%80%9CYes,%20that%20too.%20And%20a%20mathematics.%20It%20teaches%20calmness,%20control,%20balance,%20a%20sense%20of%20the%20placement%20of%20things%20and%20the%20underlying%20structure%20of%20motion.%20There%20is%20a%20silent%20music%20to%20it.%20Above%20all%20there%20is%20a%20discipline.%20Do%20I%20sound%20pretentious%3F%E2%80%9D%0AFor%20Shannon,%20it%20was%20important%20that%20people%20reading%20this%20paper%20%E2%80%9Ctry%20not%20to%20forget%20the%20poetry,%20the%20comedy%20and%20the%20music%20of%20juggling%20for%20the%20Carabellas%20and%20Margaritas%20future%20and%20present.%E2%80%9D%20We%20can%20sense%20something%20of%20Shannon%E2%80%99s%20self-consciousness%20in%20the%20next%20sentence,%20when%20he%20interrupts%20this%20train%20of%20thought%20and%20cribs%20Sleet%20to%20ask%20the%20reader,%20%E2%80%9CDoes%20this%20sound%20pretentious%3F%E2%80%9D%0AIf%20it%20did,%20Shannon%20knew%20it.%20It%20might%20explain%20why%20his%20next%20paragraphs%20seek%20to%20soften%20the%20lofty-sounding%20beginnings%20of%20the%20paper%20by%20grounding%20the%20reader%20in%20the%20history%20of%20juggling.%20In%20the%20span%20of%20roughly%20two%20pages,%20he%20travels%20over%204,000%20years%20and%20covers%20a%E2%80%A8considerable%20range%20of%20popular%20and%20cultural%20nods%20to%20juggling.%20The%20paper%E2%80%99s%20historical%20tour%20opens%20in%20early%20Egypt,%20circa%201900%20BCE,%20in%20tombs%20with%20juggling%20scenes%20etched%20into%20the%20walls,%20four%20women%20each%20tossing%20three%20balls%20apiece.%20From%20there%20it%E2%80%99s%20off%20to%20the%E2%80%A8Polynesian%20island%20of%20Tonga,%20with%20the%20sailor-%20adventurer%20Captain%20James%20Cook%20and%20scientist%20Georg%20Forster.%20The%20year%20was%201774,%20and%20Forster%20observed,%20in%20A%20Voyage%20Round%20the%20World,%20that%20the%20Tongans%20had%20a%20flair%20for%20keeping%20multiple%20objects%20suspended%20in%20the%20air%20in%20sequence.%20Shannon%20quotes%20Forster%E2%80%99s%20observation%20of%20one%20girl%20who,%20%E2%80%9Clively%20and%20easy%20in%20all%20her%20actions,%20played%20with%20five%20gourds,%20of%20the%20size%20of%20small%20apples,%20perfectly%20globular.%20She%20threw%20them%20up%20into%20the%20air%20one%20after%20another%20continually,%20and%20never%20failed%20to%20catch%20them%20all%20with%20great%20dexterity,%20at%20least%20for%20a%20quarter%20of%20an%20hour.%E2%80%9D%0AFrom%20there%20it%20was%20back%20to%20dry%20land%20and%20400%20BCE,%20to%20Xenophon%E2%80%99s%20The%20Banquet%20and%20an%20audience%20with%20Socrates,%20who,%20upon%20seeing%20a%20young%20woman%20juggle%20twelve%20hoops%20in%20the%20air,%20is%20moved%20to%20observe,%20%E2%80%9CThis%20girl%E2%80%99s%20feat,%20gentlemen,%20is%20only%20one%20of%20many%20proofs%20that%20woman%E2%80%99s%20nature%20is%20really%20not%20a%20whit%20inferior%20to%20man%E2%80%99s,%20except%20in%20its%20lack%20of%20judgment%20and%20physical%20strength.%20So%20if%20any%20one%20of%20you%20has%20a%20wife,%20let%20him%20confidently%20set%20about%20teaching%20her%20whatever%20he%20would%20like%20to%20have%20her%20know.%E2%80%9D%20For%20Shannon,%20Socrates%E2%80%99s%20comment%20is%20interesting%20on%20two%20levels.%20For%20one%20thing,%20if%20the%20girl%20in%20this%20scene%20did%20in%20fact%20juggle%20twelve%20hoops,%20she%20would%20hold%20the%20world%20record%20for%20the%20most%20objects%20juggled%20at%20a%20single%20time.%20On%20this%20fact%20Shannon%20is%20willing%20to%20give%20Xenophon%20and%20Socrates%20the%20benefit%20of%20the%20doubt:%20%E2%80%9CWho%20could%20ask%20for%20better%20witnesses%20than%20the%20great%20philosopher%20Socrates%20and%20the%20famous%20historian%20Xenophon%3F%20Surely%20they%20could%20both%20count%20to%20twelve%20and%20were%20careful%20observers.%E2%80%9D%0ABut%20that%E2%80%99s%20Shannon%E2%80%99s%20only%20concession;%20Socrates%E2%80%99s%20chauvinism%20doesn%E2%80%99t%20sit%20well.%20Mustering%20as%20much%20antagonism%20as%20we%20might%20imagine%20Shannon%20capable%20of,%20he%20dismisses%20Socrates%E2%80%99s%20blinkered%20view%20of%20a%20woman%E2%80%99s%20capacities.%20%E2%80%9CIt%20is%20amusing%20to%20note%20how%20Socrates,%20departing%20from%20his%20famous%20method%20of%20teaching%20by%20question,%20makes%20a%20definite%20statement%20and%20immediately%20suffers%20from%20foot-in-mouth%20disease.%20Had%20he%20but%20put%20his%20period%20nine%20words%20before%20the%20end%20he%20could%20have%20been%20the%20prescient%20prophet%20of%20the%20women%E2%80%99s%20equality%20movement.%E2%80%9D%20Later%20in%20the%20paper,%20Shannon%20makes%20the%20case%20for%20female%20jugglers%20more%20explicit.%20Two%20he%20singles%20out%20for%20special%20mention:%20Lottie%20Brunn,%20the%20%E2%80%9Cworld%E2%80%99s%20fastest%20female%20juggler%E2%80%9D%20and%20a%20fixture%20on%20the%201920s%20European%20theater%20circuit;%20and%20Trixie%20Firschke,%20the%20%E2%80%9Cfirst%20lady%20of%20juggling,%E2%80%9D%20a%20German%20child%20star%20born%20to%20a%20Budapest%20circus%20family.%0ASo,%20beginning%20in%20ancient%20Egypt%20and%20passing%20through%20the%20medieval%20minstrel%E2%80%99s%20hybrid%20of%20%E2%80%9Cjuggling,%20magic,%20and%20comedy,%E2%80%9D%20Shannon%20ends%20in%20the%20world%20of%20twentieth-century%20variety%20shows.%20Their%20leading%20lights%E2%80%94%20including%20W.%20C.%20Fields%E2%80%94inspired%20a%20generation%20of%20girls%20and%20boys,%20including%20the%20young%20Claude%20Shannon,%20to%20terrify%20their%20parents%20with%20talk%20of%20running%20away%20to%20join%20the%20circus.%0AThe%20history%20lesson%20concluded,%20it%20was%20on%20to%20a%20more%20serious%20inquiry:%20how%20to%20understand%20the%20psyche%20of%20a%20juggler%20and%20the%20practice%20of%20juggling%3F%20Specifically,%20how%20does%20one%20make%20sense%20of%20a%20practice%20that%20requires%20precision%20but%20is%20also%20the%20stuff%20of%20comedy%3F%20A%20gymnast%E2%80%99s%20fault%20elicits%20pity,%20a%20kind%20of%20disappointment%20shared%20by%20performer%20and%20audience;%20a%20juggler,%20failing%20to%20catch%20a%20club,%20is%20just%20as%20likely%20to%20be%20met%20with%20laughter.%20How%20do%20jugglers%20deal%20with%20this%3F%0A%E2%80%9CJugglers%20are%20surely%20the%20most%20vulnerable%20of%20all%20entertainers,%E2%80%9D%20Shannon%20writes,%20walking%20up%20again%20to%20the%20edge%20of%20autobiography.%20Indeed,%20most%20serious%20jugglers%20are%20forced%20to%20develop%20a%20range%20of%20mind%20games%20and%20public%20feints%20to%20deal%20with%20the%20anguish%20of%20%E2%80%9Cthe%20missed%20catch%20or%20the%20dropped%20club.%E2%80%9D%20Their%20coping%20strategies%20vary%20with%20skill%20level:%20lesser%20jugglers%20paper%20over%20their%20failures%20with%20comedy%20and%20props;%20the%20experts%20make%20their%20failures%20appear%20as%20intentional%20as%20their%20successes.%0ABut%20this%20vulnerability%20is%20precisely%20why,%20Shannon%20notes,%20juggling%E2%80%99s%20ranks%20can%20be%20roughly%20divided%20into%20two%20camps:%20performance%20jugglers%20and%20technical%20jugglers.%20Technicians%20are%20in%20a%20numbers%20game,%20an%20arms%20race%20of%20objects%20juggled.%20The%20more%20objects%20in%20the%20air,%20the%20bigger%20the%20bragging%20rights.%20Shannon%20references%20one%20of%20the%20world%E2%80%99s%20great%20technicians,%20Enrico%20Rastelli,%20about%20whom%20Vanity%20Fair%20would%20say%20in%20eulogy:%20%E2%80%9CIn%20his%20twenty%20years%E2%80%99%20devotion%20to%20his%20craft%20this%20son%20of%20Italy%20elevated%20it,%20for%20probably%20the%20first%20time,%20to%20what%20was%20unmistakably%20an%20art.%E2%80%9D%20Rastelli,%20Shannon%20noted,%20was%20able%20to%20keep%20ten%20balls%20in%20the%20air%20simultaneously.%20Shannon%20also%20remarks%20that%20Rastelli%20%E2%80%9Ccould%20do%20a%20one-armed%20handstand%20while%20juggling%20three%20balls%20in%20the%20other%20hand%20and%20rotating%20a%20cylinder%20with%20his%20feet.%E2%80%9D%0A(CREDIT:%20EUGENE%20DAUB.%20THIS%20WAS%20ONE%20OF%20THE%20EARLY%20MOCK-UPS%20OF%20THE%20SHANNON%20STATUE)%0ARastelli%20and%20his%20breed%20of%20technical%20juggler%20held%20the%20most%20interest%20for%20Shannon,%20and%20mathematicians%20since.%20Call%20it%20seriousness%20of%20purpose,%20or%20the%20possibility%20of%20organizing%20by%20numbers%20and%20implicit%20for-%20mulas%20the%20quest%20to%20manage%20an%20ever-increasing%20number%20of%20objects.%20For%20the%20mathematician,%20performance%20juggling,%20enjoyable%20though%20it%20might%20be%20to%20watch,%20possesses%20none%20of%20these%20qualities.%20The%20joy%20of%20the%20crowd,%20the%20thrill%20of%20the%20motion,%20the%20comedy%20of%20the%20effort%E2%80%94all%20of%20these%20are%20amusing%20but%20ultimately%20uninteresting%20to%20a%20mind%20trained%20in%20math.%20The%20paper%E2%80%99s%20journey%20begins%20here:%20in%20the%20challenge%20of%20increasing%20the%20number%20of%20objects%20juggled%20while%20still%20maintaining%20precision,%20the%20intersection%20of%20mathematics%20and%20movement.%0A***%0AIt%20shouldn%E2%80%99t%20come%20as%20any%20particular%20surprise%20that%20Shannon,%20whose%20love%20of%20juggling%20was%20surpassed%20only%20by%20his%20love%20of%20music,%20opens%20the%20mathematical%20section%20of%20the%20paper%20with%20a%20reference%20to%20jazz%E2%80%94in%20particular,%20to%20the%20drummer%20Gene%20Krupa,%20who%20said%20that%20%E2%80%9Cthe%20cross%20rhythm%20of%203%20against%202%20is%20one%20of%20the%20most%20seductive%20known.%E2%80%9D%20For%20Shannon,%20the%20pattern%20of%20three%20against%20two%20is%20a%20useful%20analogue%20for%20an%20introduction%20to%20the%20mathematics%20of%20juggling.%20It%E2%80%99s%20the%20pattern%20by%20which%20most%20people%20first%20learn%20to%20juggle:%20three%20balls%20in%20two%20hands.%0APick%20apart%20the%20motions%20of%20a%20juggler%20and%20what%20emerges%20are%20a%20series%20of%20predictable%20parabolas.%20One%20ball%20tossed%20in%20the%20air%20produces%20one%20arc;%20multiple%20balls,%20multiple%20arcs.%20All%20that%E2%80%99s%20left%20is%20to%20combine%20them%20into%20a%20consistent%20pattern,%20set%20to%20a%20rhythm.%20This%20was%20how%20Shannon%20approached%20the%20problem%20of%20juggling%E2%80%94not%20only%20as%20an%20exercise%20in%20coordination,%20but%20as%20an%20algebraic%20formula.%20His%20juggling%20theorem%20stated%20the%20following:%0A(F%20+%20D)%20H%20%3D%20(V%20+%20D)%20N%E2%80%A8%0AF%20%3D%20how%20long%20a%20ball%20stays%20in%20the%20air%0AD%20%3D%20how%20long%20a%20ball%20is%20held%20in%20a%20hand%0AH%20%3D%20number%20of%20hands%E2%80%A8%0AV%20%3D%20how%20long%20a%20hand%20is%20empty%E2%80%A8%0AN%20%3D%20number%20of%20balls%20being%20juggled%0AShannon%E2%80%99s%20theorem%20tracks%20time%20continuously.%20As%20Lewbel%20put%20it,%20%E2%80%9CThe%20way%20the%20juggler%20achieves%20the%20rhythm%20in%20Shannon%E2%80%99s%20theorem%20is%20by%20trading%20off%20time%20in%20a%20continuous%20way;%20the%20more%20time%20one%20ball%20spends%20in%20the%20air%20relative%20to%20the%20time%20it%20spends%20in%20your%20hand,%20the%20more%20time%20you%20have%20to%20deal%20with%20the%20other%20balls,%20and%20so%20the%20more%20balls%20you%20can%20juggle.%20Shannon%E2%80%99s%20theorem%20makes%20this%20trade%20off%20in%20times%20precise.%E2%80%9D%20(He%20also%20pointed%20out%20the%20irony,%20given%20the%20rest%20of%20Shannon%E2%80%99s%20digital%20innovations,%20that%20the%20juggling%20theorem%E2%80%99s%20measurement%20of%20continuous%20time%20makes%20it%20analog.)%20Each%20side%20of%20the%20equation%20tracks%20a%20different%20part%20of%20the%20act%20of%20juggling:%20the%20left%20side%20tracks%20the%20pattern%20of%20the%20balls,%20and%20the%20right%20side%20tracks%20the%20pattern%20of%20the%20hands.%20Because,%20as%20Lewbel%20put%20it,%20%E2%80%9Cthe%20amount%20of%20time%20balls%20spend%20being%20juggled%20is%20the%20same%20as%20the%20time%20the%20hands%20spend%20juggling%20them,%E2%80%9D%20the%20equality%20is%20maintained.%0A***%0AShannon%E2%80%99s%20work%20on%20juggling%20might%20have%20ended%20here;%20already%20he%20had%20lent%20the%20study%20of%20juggling%20considerable%20legitimacy,%20and%20given%20a%20generation%20of%20mathematician-jugglers%20the%20ability%20to%20combine%20their%20two%20passions%20without%20fear%20of%20embarrassment.%20But%20a%20paper%20was,%20in%20this%20case,%20insufficient.%20In%201983,%20as%20he%20had%20so%20often%20before,%20Shannon%20brought%20the%20work%20from%20the%20world%20of%20theory%20into%20the%20realm%20of%20mechanics:%20he%20set%20out%20to%20build%20his%20own%20juggling%20robot.%0A%E2%80%9CIt%20all%20started%20when%20Betty%20brought%20home%20a%20little%20four-inch%20clown,%20doing%20a%20five%20ball%20shower,%20from%20the%20cake%20decorating%20store%20($1.98).%20I%20was%20both%20amused%20and%20bemused%E2%80%94amused%20as%20a%20long-time%20amateur%20juggler%20who%20even%20as%20a%20boy%20wished%20to%20run%20away%20and%20join%20the%20circus,%20but%20be-%20mused%20by%20the%20unlikely%20shower%20pattern%20and%20the%20plastic%20connections%20between%20the%20balls,%E2%80%9D%20Shannon%20wrote.%0A%0AThe%20cake-store%20clown%20only%20appeared%20to%20juggle%E2%80%94but%20Shannon%E2%80%99s%20robot%20actually%20did.%20Assembled%20from%20his%20Erector%20Set,%20the%20finished%20product%20was%20able%20to%20handle%20three%20balls.%20The%20balls%20bounce%20off%20a%20tom-tom%20drum,%20and%20the%20robot%20moves%20its%20paddle%20arms%20in%20a%20rocking%20motion,%20%E2%80%9Ceach%20side%20making%20a%20catch%20when%20it%20rocks%20down%20and%20a%20toss%20when%20it%20rocks%20up.%E2%80%9D%20Though%20Shannon%20never%20completed%20the%20bounce-juggling%20robot%E2%80%99s%20counterpart%E2%80%94a%20robot%20that%20could%20authentically%20toss%20juggle%E2%80%94he%20still%20built%20his%20own%20set%20of%20clowns%20that%20put%20on%20a%20convincing%20imitation.%0AAnd%20there%20was%20one%20way,%20he%20noted%20with%20pride,%20in%20which%20they%20outclassed%20any%20human:%20%E2%80%9CThe%20greatest%20numbers%20jugglers%20of%20all%20time%20cannot%20sustain%20their%20record%20patterns%20for%20more%20than%20a%20few%20minutes,%20but%20my%20little%20clowns%20juggle%20all%20night%20and%20never%20drop%20a%20prop!%E2%80%9D%0A%0A(CREDIT:%20JUGGLE.ORG)%0A(CREDIT:%20JUGGLE.ORG)%0AGUEST%20CONTRIBUTOR%0A%0AYou%20can%20contribute%20to%20the%20eZine,%20too!%20Just%20email%20us%20at%20the%20link%20in%20the%20Contact%20Us%20section%20at%20the%20top%20of%20the%20page...%0ALEAVE%20A%20REPLY%0A%0AYou%20must%20be%20logged%20in%20to%20post%20a%20comment.%0AABOUT%20IJA%0ACreated%20in%201947,%20the%20IJA%20has%20grown%20to%20be%20a%20primary%20resource%20for%20jugglers%20around%20the%20globe.%20The%20IJA%20is%20a%20501(c)(3)%20non-profit%20organization,%20with%20the%20mission%20to%20render%20assistance%20to%20fellow%20jugglers.%0ABUSINESS%0ABusiness%0ABoard%20and%20Officers%0ANominations%20%26%20Election%20Rules%0AFinancials%0ABoard%20Minutes%0ARoles%20%26%20Responsibilities%0ABylaws%0A%0ALogin%20with%20Your%20Membership%0A%C2%A9%202023%20INTERNATIONAL%20JUGGLERS'%20ASSOCIATION,%20INC.%0A%0A%0A%0A%0A%09%09FAQ%0AToggle%20the%20Widgetbar%0A%0A%0A%23%23%23