! How marking in dance constitutes thinking with the body I mean it is in between, it is somewhere between doing it and thinking it, itʼs just like thinking it with the body (professional dancer in interview about marking, 2009) In!dance,!there!is!a!practice!called!'marking'.!!When!dancers!mark,!they!execute!a! dance!phrase!in!a!simplified,!schematic!or!abstracted!form.!Based!on!our!interviews! with!professional!dancers!in!the!classical,!modern,!and!contemporary!traditions,!it!is! fair!to!assume!that!most!dancers!mark!in!the!normal!course!of!rehearsal!and! practice.!When!marking,!dancers!use!their!body@in@motion!to!represent!some!aspect! of!the!full@out!phrase!they!are!thinking!about.!Their!stated!reason!for!marking!is! that!it!saves!energy,!avoids!strenuous!movement!such!as!jumps,!and!sometimes!it! facilitates!review!of!specific!aspects!of!a!phrase,!such!as!tempo,!movement! sequence,!or!intention,!all!without!the!mental!and!physical!complexity!involved!in! creating!a!phrase!full@out.!!!It!facilitates!real@time!reflection.! In!figure!1,!a!specialized!form!of!marking,!called!'hand!marking',!is!shown.!!In!hand! marking,!the!timing!and!movement!of!the!fingers!represents!the!timing!and! movement!of!leg!movements.!!Most!marking!uses!more!parts!of!the!body!than!the! hands!alone,!and!the!movements!made!during!marking!are!closer!in!size!to!'full@out'! dance.!!! !! ! Figure 1. An Irish river dancer is caught in mid move. In 1b, the same move is marked using just the hands. River dancers typically mark steps and positions using one hand for the movement and the other for the floor. ! This!essay!is!an!inquiry!into!the!phenomenon!of!marking!and,!in!particular,!into! what!it!teaches!us!about!distributed!thinking!–!thinking!with!body!and!world.!!It!is! clear!that!dancers,!at!times,!use!their!body!as!a!way!to!sketch!movements,! sometimes!for!others,!sometimes!for!themselves,!and!sometimes!to!facilitate! coordination!in!duos!or!larger!groups.!!When!marking!is!used!as!a!tool!for! communication,!it!resembles!iconic!gesturing,!though!with!features!that!differentiate! it!from!classical!accounts!of!iconic!gesture.!!When!marking!is!used!to!facilitate! coordination!in!duos!or!trios,!it!provides!a!convenient!shareable!structure!for!joint! attention!and!negotiation.!!!It!grounds!speech!and!slows!down!activity!to!make!it! easier!for!participants!to!'work!things!out'.!!When!marking!is!used!behind!closed! 2! doors,!it!acts!as!a!tool!for!a!solo!dancer!to!explore!a!phrase!in!private,!and!the!way!it! functions!is!more!complex!and!diverse.!!It!is!a!mechanism.of.thought.!!Marking@for@ self!raises!fundamental!questions!about!the!role!of!bodily!movement!in!the!cognitive! economy!of!dancerly!thinking.!!I!will!discuss!all!three!forms!of!marking!here,!but! focus,!above!all,!on!the!private!form!–!marking@for@self.! The!practice!of!creating!a!simplified!version!of!a!process!–!a!personal.model!to!work! and!think!with!–!is!found!in!countless!activities!beyond!dance.!!Children!play!act!at! cooking,!keeping!house,!driving!a!car.!!They!walk!through!the!motions!of!working! with!utensils!and!artifacts!even!though!the!utensils!they!use!are!miniatures!or!toys.!! Often!they!operate!with!nothing!more!than!imaginary!artifacts,!moving!them!around! and!talking.!!They!do!this!together!in!social!play;!but!they!do!it!alone!too.!!Adults! who!play!tennis,!golf,!or!basketball,!also!can!be!seen!running!through!a!'practice'! swing!or!shot!for!themselves,!as!if!to!prepare!for!the!real!thing.!!Sometimes!they!do! this!with!the!appropriate!racket,!club,!or!ball!in!their!hands.!!But!sometimes!they!too! go!through!the!motions!–!as!dancers!or!children!do!–!without!any!artifact!at!all.!!In! all!cases,!the!action!performed!is!more!mock!than!real.!!There!is!no!ball!actually! stroked,!no!club!making!impact,!basketball!tossed,!or!actual!dance!phrase!being! performed.!!The!list!of!modeling!for!oneself!goes!on.!!Cellists!will!sometimes!practice! their!part!on!their!arm,!running!through!finger!positions!on!their!"right!forearm! held!upright!in!front!of!the!chest,!as!a!substitute!for!the!neck!of!the!cello"![Potter,! p109]!in!a!manner!reminiscent!of!an!Irish!river!dancer!hand!marking!a!jig.!!No! sound!merges.!Theatrical!performers,!too,!can!often!be!seen!muttering!their!lines,!or! executing!'practice'!moves!before!stepping!out!on!stage.!!It!is!a!standard!activity!in! theater!to!do!an!"Italian!run@through"!–!a!slang!phrase!for!saying!one's!lines!and! moving!about!the!stage!extra!fast!when!staging!a!play!to!clarify!the!timing!and! relative!positions!of!the!actors.!!All!these!cases!are!related!to!marking.!!In!the!case!of! staging,!the!process!is!identical!with!a!version!of!marking@for@others.!!The!common! element!throughout!is!that!people!seem!to!prefer!working!with!a!simplified!version! of!a!procedure!to!practicing!the!full@out!version.!! There!is!something!provocative!about!these!forms!of!partial!physical!simulation.!It! is!clear!how!marking!has!a!useful!function!when!its!purpose!is!social!and! communicative.!!When!marking@for@others!or!marking@for@coordination,!the! physical!movement!constitutes!a!material!object!for!joint!attention;!it!serves!as!a! shared!vehicle!of!thought!and!common!focus,!helping!everyone!to!'get!on!the!same! page'.!!But!when!a!dancer!is!marking!entirely!for!him!or!herself!what!function!does! it!serve?! ! Figure 2. Three ways of Practicing: regular full-out practice, partial simulation by making a smaller scale model of the full version and by using one's imagination to mentally simulate the full-out version or some aspect of it. 3! An!obvious!idea!is!that!marking@for@self!is!yet!another!form!of!practice.!!We! understand!why!people!rehearse!skills!in!their!full@out!version.!!They!are!practicing! in!the!standard!sense.!!The!closer!a!study!behavior!is!to!the!test!behavior!the!better! the!performance!when!tested![Lockhart!&!Craik!1990].!It!is!also!clear!that!running! through!future!performance!without!overt!action!–!purely!through!mental! simulation!–!can!also!improve!skills,!at!times.![Suinn!1984].!!!Mental!rehearsal!is,!by! now,!a!recognized!form!of!practice.![Meister!et!al!2004,!!Schoenberg!1987!]!!Is!there! also!a!middle!ground?!!If!there!are!both!inner!and!outer!versions!of!practice!might! there!not!also!be!an!intermediate!form!of!practicing,!one!that!is!not!completely! internal!simulation,!but!not!completely!external!production!either?!!! What!extra!might!this!mock!practice,!this!middle!ground,!confer?!Is!it!merely!an! extra!accompaniment!to!mental!simulation,!done!simply!because,!for!instance,!a! dancer!is!standing!when!mentally!simulating,!and!their!bodies!naturally!move!when! they!are!running!though!movements!in!their!head?!!Or!is!marking@for@self!done! intentionally!for!its!cognitive!benefits,!to!help!memory,!for!instance,!or!to!improve! critical!reflection?! From!interview,!we!were!told!that!marking!often!helps!memory,!much!like!singing!a! song!aloud!helps!someone!to!remember!the!lyrics,!or!reciting!part!of!a!speech!helps! an!actor!pick!up!their!part!midway!through.! ...!marking!is!rather!for!the!memory!than!for!the!movement,!it!doesn't!work!like!we! mark!some!of!the!movements!and!the!others!we!don't!do.!!It!is!just!the!matter!of!not! wasting!so!much!of!energy!if!you!are!not!sure!enough!what!you!have!to!do.!So!before! you!gonna!go!full!out!you!need!to!make!sure!exactly!what!the!choreography!is,!and! which!arm!goes!there,!which!leg!goes!first,!is!it!the!left!or!right,!the!grips,!just!to!kind! of!touch!each!other,!especially!for!the!duets.! !Just!make!sure!to!know!what!you!are! doing,! what! the! choreography! is,! and! then! you! can! go! full! out.! ! !! (dancer!A!in!interview)! It! is! a! retrace,! a! scrape! in! your! head.! ! You! could! learn! a! monologue,! a! 5! min! monologue,!but!!you!don't!have!to!do!it!fully,!you!can!just!sort!of!@!you!don't!have!to! say!it!you!can!just!go!over!it!in!your!head!to!be!able!to!know.!!So!in!movement!terms! I!can!know!that!the!arm!is!here,![dancer!gestures]!but!all!I!have!to!do!is!go!like!that! so!that!the!!...!I!am!just!setting!the!small!movements!to!trigger!the!pathway!that!has! already!been!already!placed,! you!know,! rather! than!having! to!do! the!whole! thing.! (dancer!N!in!interview)! For!some,!it!helps!reflection,!much!like!the!way!verbalizing!a!thought!aloud!helps!a! thinker!to!reflect!on!what!he!is!thinking,!or!the!way!summarizing!a!paragraph!may! help!an!author!to!rewrite!it.!!! ...! sometimes! even! when! you! know! something! it! is! good! to! mark! it! through! @! to! rework! it! in! your! brain,! to! make! another! idea! of! what! the! movement! is.!!! (dancer!M!in!interview)! ...!sometimes!it!is!good!to!come!back,!you!know!even!if!you!know!it!to!think!about!it,! again,!to!visualize!everything...sometimes!it!helps!a!lot..! !Like,!you!are!home!or!you! are! in! the! tube! for! one! hour! and! sometimes! we! catch! ourselves! doing! (subject! 4! gestures! and! makes! sound! to! show! how! he! thinks! and! marks)! because! you! are! thinking,!! ! ! ! ! ! (dancer!A!in!interview)! ! As!can!be!inferred!from!these!quotes,!my!bias!is!to!see!marking@for@self!as!having!a! direct!and!intentional!value.!!!Mock!practice!is!real!practice;!it!is!not!an! epiphenomenon!or!mere!accompaniment.!!It!is!intentional,!done!for!its!conscious! benefits.! This!question!of!function!does!not!arise!when!the!function!of!marking!is!social!and! communicative.!!When!marking@for@others!or!marking@for@coordination,!the! physical!movement!constitutes!an!object!of!joint!attention!and!serves!as!a!shared! vehicle!of!thought,!creating!a!common!referent!and!common!focus.!!It!helps!others! to!get!on!the!same!page.!!Can!we!be!equally!clear!about!the!function!marking–for@ self!serves?!!This!is!the!driving!question!behind!this!study.!!! The!paper!is!divided!into!three!parts:! 1. In!part!one,!I!describe!our!empirical!approach!to!the!phenomena!of!marking.!! The!data!presented!here!were!derived!from!a!major!effort!to!understand!the! creative!process!in!choreography.!!We!used!5@7!videocameras!to!tape!the! complete!creative!process!of!a!contemporary!dance!company!and! ethnographically!coded!hours!of!interview!and!terabytes!of!dance!footage.!! 2. In!part!two,!I!explore!the!phenomena!in!detail.!!Marking,!as!mentioned,!comes!in! three!flavors:!!marking@for@others,!marking@for@coordination,!and!marking@for@ self.!!Each!is!described!and!analyzed.! 3. In!part!three,!I!take!up!the!question!of!why!marking@for@self!might!be!more! powerful!than!mental!simulation!by!itself.!!!There!are!several!possible!ways! recruiting!the!body!might!increase!the!power!of!thought.!!These!would!explain! what!'extra'!dancers!get!from!marking.!! My!conclusion,!overall,!is!that!a!body@in@motion!can!serve!as!a!dynamic!vehicle!of! thought!for!a!dancer,!much!like!trying!out!a!musical!phrase!on!a!piano!might!help!a! composer!think!compositionally.!!By!externalizing!a!form!their!author!is!able!to! entertain!thoughts!faster!and!more!deeply!than!otherwise!possible.!!Marking! provides!a!material!structure!that!supports!projecting!deeper,!enables!more! detailed!mental!simulation,!and!serves!to!facilitate!motor!learning.! Part One: Our Empirical Approach The!basis!for!this!study!was!initial!research!conducted!as!part!of!an!ongoing! collaboration!between!the!choreographer!Wayne!McGregor,!(hereafter!WM)!and!the! author,!on!the!topic!of!distributed!creative!cognition!and!choreographic!thought.!! WM!holds!the!position!of!resident!choreographer!at!the!Royal!Ballet!in!London.!!He! also!has!a!private!dance!company,!consisting!of!ten!extremely!talented!dancers!and! a!long@standing!expert!choreographic!assistant,!Odette!Hughes.!! 5! The! piece! we! observed! being! made,! and! which! forms! the! basis! for! the! data! and! analyses!presented!here,!was! created! in! two!periods:! a! three!week!episode!at! the! University!of!California,!San!Diego!(UCSD)!from!January!26th!to!February!15th!2009;! and!a!second!episode!in!London,!August!24th!2009!to!September!7th.!!Following!Sept.! 7th! there!were! intermittent!rehearsals!until! the!official!première,!a!month! later,!at! Sadler's! Wells! Theater,! on! October! 13th! 2009.! ! ! In! total,! there! were! 27! days! of! videographic! observation! and! interview,! spread! over! six! and! half! weeks! in! both! UCSD!and!London.! During!each!phase,!written!notes!were! taken! in! real@time.! !During! the! first!phase,! fifteen! students! took!notes;! during! the! second,! a! single! experienced!ethnographer! took! notes.! ! Both! phases! were! exhaustively! videotaped! using! five! high! definition! video! cameras! placed! on! the! walls,! and,! whenever! possible,! two! standard! video! cameras!were!placed!on!the!ceiling.! !The!whole!rehearsing!process,!11AM!to!5PM,! five! to! six! days! a! week! was! captured.! ! The! choreographer! was! interviewed! for! between!forty!and!sixty!minutes!on!digital!video!most!mornings!and!evenings.!!The! dancers! also! were! interviewed.! ! At! the! end! of! each! rehearsal,! four! dancers! were! selected!and!interviewed!in!groups!of!two,!for!thirty!minutes!each.!!Our!aim!with!the! dancers! was! to! have! them! reflect! on! specific! elements! of! the! rehearsal! that! day.!! Whenever!possible!we!had!them!describe!their!experience!during!the!day!and!then! show!us!through!movement!what!they!meant.!!By!requesting!physical!display!rather! than! speech! alone! we! sought! to! avoid! encouraging! the! dancers! to! theorize! and! speculate!unduly,!a!standard!risk!inherent!in!interviews.!! At! the! outset,! the! goal! of! our! research! was! to! understand! the! way! creativity! is! distributed!over!a!group.! !We!were!also! interested! in! the!nature!of! choreographic! thinking.! !We!had!prior!beliefs!about!distributed!creativity;!but!we!came!with! few! preconceptions! about! choreographic! thinking.! Our! hope! was! that! a! few! clear! phenomena! would! stand! out,! providing! the! basis! for! a! more! focused! study.! ! We! found! three! such! phenomena! related! to! choreographic! thinking:! marking,! sketching1,!and!riffing.2!!Only!marking!is!discussed!here.!! Our! research!method! combines! cognitive! ethnography!with! quantitative! analyses.!! Cognitive!ethnography!requires!acquiring!a!detailed!knowledge!of!a!community!of! practice,! and! then!using! that!knowledge! to! illuminate! specific!episodes!of!activity.! See! Williams! (2006).! ! To! acquire! knowledge! of! the! community! of! practice! we! interviewed! the! choreographer! as!well! as! the!dancers! repeatedly.! ! To!understand! specific!episodes!of!activity!as!they!arose,!we!videotaped!all!scheduled!interactions! between!choreographer!and!dancers!during!the!time!they!worked!together!over!six! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1 Sketching occurs whenever a dancer tries to imitate another dancer's performance in real-time. If the phrase is not yet known there are too many elements to be imitated at once, so dancers do their best to capture the essence of the phrase. This necessarily means 'sketching' the phrase in a coarse manner, though the focus of the dancer's sketch may be the dynamics or emotional force of a phrase, as much as the kinematic form of the phrase. 2 Riffing, is a term we invented ourselves, to refer to a practice by the choreographer in which he tries out phrases he has just seen his dancers performing. When riffing he seems to not only be appropriating those phrases by running them through his own body, but playing with them and altering them. Riffing was clearly a component of his creative process, reminiscent of musicians taking a theme and 'running' with it. 6! weeks.!!We!also!reviewed!all!notebooks,!and!used!our!interviews!as!an!opportunity! to! discuss! specific! moments! of! creative! activity.! ! Because! of! our! extensive! videotaping!and!post@analysis!of!the!footage!we!were!able!to!compare!marked!and! full@out!versions!of!phrases.!! To!code!the!video!we!used!ELAN!(see!figure!3),!a!free!software!system!developed!by! the! Max! Planck! Institute! for! Psycholinguistics,! designed! originally! for! studying! gesture! and! small@scale! interactions.! Systematic! audiovisual! analysis! depends! on! having! a! well@defined! vocabulary! of! coding! –! a! classification! of! activity! and! phenomena.! !We!developed!ours!by!reviewing!videos!individually!then!collectively! building! a! single! code! which! all! coders! practiced! using.! ! After! our! initial! analysis/coding! of! ongoing! activity,! we! discussed! 'special'! phenomena! such! as! marking! and! returned! to! the! video! data! to! code! for! these! as! well.! ! The! filmed! observations!and!interviews!allowed!us!to!create!an!informed!taxonomy!of!marking.! To!gather!more!data,!specific!to!marking,!we!requested!supplementary!interviews!to! probe!the!dancers'!own!views!on!marking.!These!were!undertaken!in!addition!to!the! normal!interviews!we!conducted!at!UCSD!and!in!the!first!days!in!London.!In!several! sessions,!we!had! the!dancers! come!before! the! camera!and!dance! full3out! a!phrase! they!knew!well!and!then!show!us!several!ways!they!might!mark!that!same!phrase.!! We!followed!this!up!with!questions!about!their!reasons!for!marking!one!way!versus! another.!!We!also!interviewed!them!in!a!less!structured!manner,!often!returning!to! the! question:! ! ! "When! do! you! mark,! and! how?"! which! led! to! multiple! follow! up! questions! and! nuances! of! speech,! as! well! as! spontaneous! performances! by! the! dancers.! The! videotaped! answers,!with! the! corresponding! gestures! and!markings,! were!transcribed!and!analyzed!in!detail!with!ELAN.! ! Figure 3. Snapshot of ELAN software used for analyzing marking. ! 7! After!sustained!review!of!our!footage!and!analysis!of!the!interviews,!it!became!clear! that!there!are!three!distinguishable!functions!of!marking.!These!were!first!reported! in!(Kirsh!2010b).!!They!are:!! 1. Marking3for3self:. dancers! use! their! body! to! encode! an! aspect! of! a! phrase! for! themselves.!They!are!not!concerned!with!communicating!their!phrase!to!anyone! (other! than! to! themselves).! ! Marking@for@self! may! be! for! reinforcing!memory,! reflecting! on! sequence,! or! for! personal! scrutiny! of! spatial! relations,! to! name! a! few.! ! These! last! functions! seem! related! to! activating! deeper! processing! about! movement,!about!working!things!out,!or!grasping!a!phrase!better.!!! 2. Marking3for3others:!dancers!use!their!bodies!to!encode!an!aspect!of!a!phrase!that! others! can! focus! attention! on.! ! For! example,! before! a! new! performance,! choreographer,!choreographic!assistant,!and!lighting!manager!review!all!phrases! on!stage.!!They!need!to!explore!the!visual!feel!of!putting!lights!in!one!position!or! another,!to!see!the!effect!of!shadows!and!illumination!on!dancers!and!set!as!the! dancers! move! about,! reach! up,! and! step! around! one! another.! ! To! support! exploration! of! these! issues! dancers! need! only! model! their! form! and! relative! positions.! !They!are!free!to!ignore!tempo,!emotional!valence,!and!dynamics.! !At! other!times,!the!choreographer!and!assistant!will!require!greater!resolution;! in! their!role!as!director!or!reflective!critic! they!seem!to!have!their!own!goals!and! agenda,!asking! the!dancer! to!show!specific!aspects!of!a!phrase.! !Again,!even! in! response!to!direct!comment,!dancers!will!perform!their!marked!phrase!with!less! energy!and!emotion!than!the!full@out!version.! 3. Marking3for3coordination:!here!two!or!more!dancers!run!through!a!phrase!as!a! tightly! coupled! team,! verifying! timing! and! grips! jointly! for! each! other.! The! function! of! the! different! bodies@in@motion! is! to! facilitate! team! coordination,! to! support!negotiation!of!positions,!and!to!enable!one!team!member!to!remind!the! other! of! constraints,! moves,! and! problematic! elements.! Marking@for@ coordination!also!creates!a!safer,!more!relaxed!space!in!which!partners!can!talk! about! aspects! of! a! phrase!while! they're!working! on! it.! ! In! full@out! practice,! or! when!they!are!showing!a!phrase!to!the!choreographer,!talk!has!little!place!unless! making!sound!is!part!of!the!dance!phrase!itself.!!Words!have!no!place!in!full@out! practice! because! dance! phrases! are! often! so! energetic! and! require! so! much! attention! –! at! least! the! phrases!we! observed! in! this! piece! –! that! there! is! little! headroom! left! for! discussion.! ! When! dancers! and! choreographer! do! talk,! accordingly,!we!found!that!it!is!usually!in!the!pauses!between!full@out!efforts,!or,! as!we!observed,!during!this!sort!of!joint!marking.!! Although! these! three! functions! are! logically! distinct,! we! found! that,! on! any! given! occasion,! a! single! marking! episode! might! serve! more! than! one! function.! ! For! instance,!marking! on! a! new! stage! lets! 'choreography'! and! 'lighting'! scrutinize! the! bodies@in@motion!to!note!stage!positions,!changes!in!light!and!shade,!and!the!overall! feel! of! the! interaction! with! the! set.! ! The! primary! function! of! marking! here! is! marking@for@others.3! ! Yet,! in! addition! to! this! marking@for@others! function,! the! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 3 It is worth noting that the context imposes slightly different goals for the dancers than when they markfor-others to remind the choreographer of some aspect of a phrase. These differences in types of marking8! dancers! also! learn! something! useful! about! the! look! and! feel! of! dancing! on! a! particular!stage.! !They,! too,!need! to!be! familiarized!with!deviations! from!standard! spatial! relations! and! lighting.! ! This! is! a! big! reason! dance! companies! require! a! complete!run!through!before!each!performance.!!One!act!of!marking,!here,!serves!a! dual!function:!simultaneously!as!marking@for@others!and!marking@for@self.!!! On! occasion,! the! same! act! of! marking! can! even! serve! all! three! functions.! ! For! instance,! if! dancers! mark! duets! or! trios! and! they! run! through! grips! and! mutual! positioning!on!a!new!stage,!they!may!create!a!situation!where!there!is!marking@for@ coordination,! marking@for@others,! and! marking@for@self,! though! admittedly! this! situation! is!unlikely! to!occur.! !The! logic! is! that,! as!before,! the! choreographic! team! has!the!opportunity!to!observe!lighting!and!angles,!each!dancer!personally!benefits! from!reviewing!timing!and!coordination!for!themselves,!and!joint!marking!occurs!as! well!because!each!dancer!needs!the!physical!presence!of!their!duet!or!trio!partners! to!experience!the!full!feel!of!coordination.! Part Two: The Phenomena in Detail Despite!their!important!functional!differences,!all!three!forms!of!marking!differ!from! dancing!full@out!in!much!the!same!ways,!though!often!in!different!degrees.!!We!can! distinguish! five! such! dimensions:! all! are! ways! marking! falls! short! of! full@out! execution!whatever!its!form!and!function.!!! Requiring) less) energy) and) displaying) fewer) dynamics! is! perhaps! the! most! universal!difference!between!marking!a!phrase!and!dancing!it!full!out,!regardless!of! function.!!Executing!dance!phrases!over!the!course!of!a!day!is!fatiguing,!and!in!many! circumstances,!unnecessary.! !For! instance,!when!working!with!others! in!a!duet!or! trio,! many! of! the! key! decisions! of! relative! position! must! be! solved! through! negotiation! and! coordinated! testing.! !Movements!must! be! slowed!down,! tried! out! and! talked!about.! !By!marking! together! two!dancers! can!help!each!other! to! recall! grips! and! positions.! ! In! marking@for@others,! the! key! elements! to! be! externally! reviewed!may!be!spatial!rather!than!dynamical,!shape!rather!than!speed!of!motion.!! Choreographers! typically! do! not! review! phrases! in! marked! form.! ! They! prefer! viewing!movements! full@out! (from! interview!with!WM).! But!when! they! do! accept! marked!versions,!it!is!invariably!because!they!do!not!want!to!overtax!their!dancers.! Lastly,! in!marking@for@self,!a!dancer's!reason!for!marking!ranges!from!marking!the! run!up! to! a!phrase! to! situate!him!or!herself,! to! set! the! conception!of! the!phrase's! structural! shape!before!practicing! the!problematic! step!over!and!over;! to! create!a! convenient!synoptic!version!for!reflection;!or!simply!to!practice!some!aspect!of!the! phrase!that!can!be!rehearsed!without!all! the!simultaneous!elements!of!the!phrase.!!! Whatever!the!reason,!though,!by!marking!a!dancer!saves!energy.! Variability)of)size:!Marking!also!comes!in!a!continuum!of!sizes,!from!the!very!small! to! full! size! (but! less! energetically).!Whatever! type! of!marking!we! observed! –! for@ others,! self,! or! coordination! –!we! found! huge! variance! in!marking! size.! ! In! 'small! marking',!the!amount!of!movement!is!minimal;!the!marking!movements!tend!to!be! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! for-others can be captured in a more refined taxonomy that identifies species of marking-for-others. 9! in! the! upper! body! (hands! and! head! mainly),! and! the! objective,! in! general,! is! to! review!the!steps,!the!relationship!between!simultaneous!movements,!such!as!when! an!arm!and!leg!move!in!parallel,!and!occasionally!to!attend!to!timing.!!See!figure!4a! and!4b.!!In!extreme!cases,!such!as!Irish!river!dancing!–!a!form!of!step!dancing!where! the!arms!are!kept!still!during!the!full@out!performance,!see!figure!1!–!marking!may! be! done! exclusively!with! two! fingers! of! one! hand! tapping! on! the! knuckles! of! the! other! hand! to! mark! foot! rhythm,! position,! and!movement.! ! It! is! hard! to! imagine! finger! marking! used! for! anything! other! than! marking@for@self,! though! in! river! dancing!two!dancers!might!synchronize!timing!by!hand!marking!together.!!In!larger! marking,! especially! when! the! objective! is! to! show! the! floor! space! required! by! a! movement,!or!to!show!off!the!structure!of!a!phrase!to!someone!else,!the!movements! may! be! full! size,! showing! the! spatial! extent! of! the! move,! but! with! less! intent,! emotion,!or!energy!than!the!real!movement!(figure!4c).!!! The! bottom! line:! reduced! size! is! a! clear! indicator! of! marking,! and! the! easiest! to! identify! when! coding! for!marking! in! video.! ! But! it! is! not! required.! ! Marking! size! varies!depending!on!whether!it!is!for@self!and!determined!entirely!by!a!solo!dancer,! or! whether! it! is! negotiated! between! dancer! and! choreographer,! or! dancer! and! partner.! If! marking! is! full@sized! then! other! factors,! such! as! speed,! emotion,! and! dynamics,!must!be!used!to!differentiate!it!from!dancing!full!out.!! ! !!!!!! ! ! Figures 4a, 4b, 4c. The images here show the contrast between small and larger marking. In 4a, the male dancer is remembering a step, and using his hand to small mark it. In 4b, the female dancer is showing how she marks a pirouette. She is using a formal gesture for a pirouette that she learned as a ballet dancer. Her marking is small and conventional. In 4c, a second female dancer is marking a phrase using movements that are of comparable size to those in the full phrase. They preserve the form but not the dynamics of her fullout. Substitutability:!It!is!common!during!marking!to!use!a!movement!in!one!body!part! to!represent!a!movement!in!another.!!Hand!movements!regularly!stand!in!for!leg! movements;!head!tilts!or!head!turns!often!represent!a!torso!turn!or!a!whole!body! turn.!!When!legs!are!moved!in!parallel,!one!leg!may!easily!stand!in!for!two.!This!is! shown!in!figures!4a!and!4b.!!See!figure!5!for!a!standing!version,!where!a!dancer! marks!a!leg!movement!with!his!hands.!!See!also!marking!an!Irish!river!dance,!as! seen!in!figure!1,!where!fingers!stand!in!for!legs.!!!The!substitution!of!one!leg!for!two! is!one!way!marking!differs!from!iconic!gesturing,!where!rarely!if!ever!will!there!be!a! collapse!of!elements!in!a!manner!that!distorts!their!appearance.!![reference]! 10! . ! ! ! ! ! ! ! ! ! Conventional) gestures:! In! ballet! and! other! formalized! dance! forms,! dancers! are! taught! to! use! specific! gestures! as! ways! of! marking! certain! moves.! ! These! are! a! conventionalized! form! of! small! markings.! ! For! instance,! as! seen! in! figure! 6,! the! female!dancer!marks! for! the! interviewer!with!her!hand! to! show! that,! at! a! certain! point!in!the!phrase,!a!pas.de.bourrée!is!required.!!When!marking@for@self!her!gesture! would! be! unaccompanied! by! speech.! ! This! one! small! gesture! refers! to! a! complex! sequence! of! full!moves!well! known!by!ballet! dancers.! !When!marking@for@self,!we! observed!that!dancers!who!do!not!rely!on!a!ballet!vocabulary!still!mark!in!a!way!that! is! reminiscent!of!ballet!marking;!but!each!dancer!has!personal! idiosyncrasies! that! violate! convention.! ! In! figure!4a,! for! instance,! a!dancer!with!deep! training! in!both! modern!and!ballet!represents!a!leg!movement!with!his!arms.!!His!marking!appears! to!be!a!hybrid:!part!conventional,!and!part!personal!gesture.!!The!point,!again,!is!that! in! most! marking! by! professional! dancers! there! is! an! element! of! conventionality! whether!they!are!marking!for!themselves,!for@others,!or!for@coordination.!!Honoring! convention,!at!least!in!part,!is!not!required!for!marking!to!be!meaningful,!but!among! our!sample!of!dancers,!it!is!what!we!observed.. Aspectival:! Marking! typically! represents! an! aspect! of! the! full! phrase,! with! some! forms!of!marking!focusing!solely!on!tempo,!others!focusing!on!sequence,!still!others! focusing!on!spatial!position.! !For! instance,!when!dancers!mark! for! space! they!will! keep!the!scale!of!the!full!phrase,!but!other!aspects!will!be!ignored!or!only!partially! represented.!!Even!when!they!cover!the!same!space!as!dancing!full!out,!or!they!move! in!a!complete!manner,!covering!a! full!arc!with!their!arms!or!a! full!movement!with! their!legs,!their!movements!are!less!expressive,!requiring!less!energy!and!containing! fewer!dynamics.!!At!other!times,!just!the!movement!of!the!upper!body!or!the!torso! orientation!may! be!marked! and! the!movement! of! a! leg! or! arm! is! left! completely! unmarked.! ! As! they! reported! in! interview,! reduced! form! is! often! the! outcome! of! attending! to! only! certain! aspects! of! the! phrase.! ! Indeed,! because! marking! is! by! ! ! ! Figure(5.! !A!dancer!marks!a!leg!movement! with!his!hands!in!his!own!personal!manner! that! is! a! hybrid! of! conventional! ballet! marking!and!personal!choice.!! Figure(6.!!A!dancer!from!a!strong!ballet! tradition!offers!a!conventional!small! marking!with!her!hands.! 11! definition! incomplete! it! is! hard! to! conceptualize! it! as! anything! but! an! abstraction! along! one! or! more! dimensions.! ! Only! some! aspects! of! the! full! out! version! are! preserved!in!its!marked!form,!though!these!may!vary!with!function!and!occasion.!! These!elements!can!always!be!found!in!marking.!!They!are!of!particular!interest! because!they!show!how!a!motor!program!defining!a!full!phrase!can!be!reduced,! altered!and!truncated!while!still!being!of!value!to!a!dancer.!!I!explore!why!this!might! be!so!in!later!sections.!I!now!turn!to!how!the!primary!types!of!marking!differ.!! Marking-for-others Marking@for@others!rarely!increases!personal!insight!or!enhances!recall;!it!is!meant! to!show!another!person!some!facet!of!a!movement!–!its!range,!shape,!formal! structure,!its!sequence!or!rhythm.!!Sometimes,!it!is!performed!to!remind!the! choreographer!of!some!element!of!a!phrase;!or!it!may!help!him!to!think!through!a! passage!by!acting!as!a!light!run@through!on!analogy!with!'an!Italian!run@through'!in! theater.!!In!such!cases,!the!function!of!marking@for@others!is!to!support!dancer@ choreographer!dialogue,!or!to!provide!the!choreographer!himself!with!an!abstracted! structure!to!reflect!on.!!It!never!seems!produced!to!facilitate!deeper!processing!by! the!dancer!personally.!!! In!the!company!we!studied!there!were!strict!rules!or!conventions!about!how!to! mark!'properly'!when!marking!for!the!choreographer!or!his!assistant.!!Movements! were!supposed!to!be!'complete';!they!were!to!cover!most!of!the!space!and!form!of! the!full@out!phrase.!!Dynamics!and!tempo!could!be!altered,!but!the!end!points!of! each!movement!were!supposed!to!be!clearly!marked.!!Sometimes,!the!approximate! tempo!was!to!be!preserved!as!well!as!spatial!extent.!!During!interviews!with!the! company!each!dancer!was!asked!if!the!way!they!marked!for!the!choreographer!or! his!assistant!was!the!same!as!the!way!they!marked!for!themselves.!!To!a!person!they! replied!that!the!two!were!different,!that!the!norms!they!were!held!to!were!strict,! and!that!marking!was!to!be!far!more!complete!than!when!marking@for@self.!!Despite! these!formal!requirements,!however,!movements!were!rarely!energetic!or! dynamically!correct.!!The!one!sure!element!we!observed!always!missing!in!marking@ for@others!was!emotional!intensity.!!! 12! ! Figure!7.!!!Five!dancers!are!marking!for!the!choreographer,!WM,!and!his!assistant,!OH!at!the! end!of!a!session.!!Another!is!stretching.!!As!WM!and!OH!watch,!they!also!discuss!elements!of! what! they!are!seeing.! !OH!has!set!very!strict!norms!for!marking.! !Movements!must!retain! their!form!and!extent,!despite!low!energy.!! Marking-for-coordination In!marking@for@coordination!the!focus!is!on!directing!the!joint!attention!of!two!or! three!dancers!to!structural!elements!of!a!phrase,!such!as!grips,!timing,!relative! position,!tempo,!sequence,!and!body!orientation.!!Typically!all!dancers!have!a!good! idea!of!their!phrase!before!they!mark@for@coordination,!but!there!remain!fine!details! of!who!does!what,!when,!and!where!that!need!to!be!sorted!out.!!And,!of!course,!the! act!of!marking!makes!distributed!memory!possible;!two!or!more!people!can!cue,! remind!and!prompt!each!other!in!ways!that!help!each!to!recall!his/her!part.! For!example,!in!the!sequence!of!images!8a@g!below,!a!gestural,!body,!and! conversational!dialogue!takes!place!between!two!dancers!as!they!work!out!how! they!should!execute!their!duet.!!The!dancers!have!been!tasked!to!create!a!sequence! of!movements!–!a!score!–!whose!parts!are!shared!among!them,!though!at!times!both! may!perform!the!same!elements.!!On!the!first!day!of!making!this!phrase,!they! worked!for!an!hour!to!create!new!movements.!!Shown!is!an!83!second!snippet!taken! on!the!second!day.!!They!are!40!minutes!into!the!one@hour!session!allocated!to! consolidating!the!phrase.!!The!two!dancers!are!marking!their!parts,!at!times!for! themselves!to!help!them!remember!their!own!movements,!but!primarily!they!are! marking!to!facilitate!coordination.!Until!now!they!have!been!!marking!for! coordination!unproblematically.!!This!stops!because!P!is!confused!over!the! movement!sequence!and!timing!and!this!leads!to!a!breakdown!in!position!and!over! timing.!P!is!not!in!the!right!position!to!start!at!A's!shoulder!and!run!his!hand!down! A's!arm!to!the!elbow.!!P's!arm!and!torso!must!be!oriented!to!let!him!move!from! shoulder!to!elbow!behind!his!back.!!A!is!partly!in!the!way!and!P's!body!orientation!is! wrong.!!The!timing!issue!concerns!whether!P!should!begin!to!reach!around!for!A's! elbow!while!A!is!still!putting!his!hand!near!P's!left!hip.!!The!problem,!they!discover,! 13! is!that!A!must!lower!his!shoulders!more!and!stay!in!that!bent!position!longer,!P's! feet!should!be!more!parallel!to!A's,!and!then!P!must!wait!for!A!to!finish!his!grip.!It! takes!them!a!little!more!than!a!minute!of!marking@for@coordination!to!jointly!recall! the!timing,!and!also!to!figure!out!how!to!adjust!their!foot,!hand!and!hip!positions.!! Thes!sequence!shows!how!they!resolve!their!confusion,!mixing!talk,!gesture,!and! most!importantly!large!marking.4.!In!about!60!seconds!A!and!P!were!able!to!sort!out! a!difficult!sequence!of!grips!and!positions.! A(and(P(Duet(3(Steps(1,(2,(3(&(4( ! ! ! ! ! !!!!!!Step(1!00:03!!!!!!!Step(2!00:10!!!!!!!Step(3!00:11!!!!!Step(3!00:14!!!!Step(3!00:!15! Figure(8a.!!!20!second!segment.!In!this!first!segment,!P!and!A!are!marking!the!first! attempt!of!steps!1,!2,!3!and!4!of!their!annotation!phrase.!!They!get!stuck!at!3.!At!10s.! they! try! the! second! and! third! steps! in! quick! succession.! ! Because! step! 2! is! incorrectly! executed! they! get! stuck! when! trying! to! do! step! 3.! P! makes! multiples! attempts! to! transition! from!2!to!3,! tucking!his!arm!under!A's!arm,!crossing! it!over! afterwards,! but! both! A! and! P's! positions! are! wrong.! ! Feet! and! hip! positions! are! wrong;! so!P! cannot! rotate!his! torso!and!complete!his! step,!nor! reach! for! the! right! grips!on!A's!body.!! ))))) ! ((((((Step(1!00:21!!!!!!!!!Step(2!00:!22!!!!!!!!!Step(3!00:25!!!!!Step(3!00:!29!!!!Step(3!00:34! Figure(8b.! ! !15!second!segment!At!21s,! they! try!a!second!attempt!at! steps!1,!2,!3.!! This!time,!step!2!includes!the!grip!on!A's! left!shoulder!that!will!be!part!of!the!final! phrase;!P's!feet!position!are!improved;!but!P's!hip!is!still!off,!and!A!is!not!bent!over! low!enough!to!make!it!possible!for!P!to!twist!as!he!must.!The!breakdown!emerges! again!in!the!transition!from!2,!where!P!must!grip!A's!left!shoulder),!to!step!3,!where! P!'s!hand!must!slide!from!A's!right!shoulder!to!his!elbow.!! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 4 This collection of images also shows distributed memory, since both dancers are working jointly to remember the phrase. 14! )))))19)second)segment) ! !!!!!!!!!!!!!!!!!!!!!!!Step(1!00:36!!!!!!Step(2!00:39!!!!Step(2!00:43!!!!!!Step(2!00:!46! ! ! (((((((( ( ( ( (Step(3!00:49!!!!!!Step(3!00:52! Figure( 8c.! ! ! 19! second! segment! P! ! &! A! are! again!marking! the! same! sequence! of! steps,!now!for!the!third!time.!They!get!stuck!again!in!step!2.!!At!39s,!we!see!how!P's! foot! position,! P's! arms! and! A's! torso! angle! are! wrong.! ! At! 43s,! still! in! step! 2,! P! gestures!a!small!'no'!with!his!head,!he!cannot!get!into!3.!!!At!49s,!we!see!P!still!trying! to!get!into!3,!griping!A's!right!shoulder!correctly,!but!then!tucking!his!arm!under!A's,! instead!of!descending!to!A's!elbow.!P!is!confused,!and!A!doesn't!adequately!lower!his! head.!! ! .....Three!00:56!!!!!!!!!One,)Two!00:58!!!!!!!!!!!!!!Step(1!1:00!!!!!!!!!Step(1!1:01! Figure(8d.! ! !5second!segment!At!56s,!A!corrects!P!saying!No,!Three!!(Laughs),!and! they!both!stop!marking.!At!57s!P!gestures!two!with!his!fingers,!and!says!So!its!one,! two?!!At!58s!A!says!yes,!while!P!is!still!gesturing.!P!starts!marking!for!coordination! with! step! 1! again! at! 1:00,! while! P! is! still! marking! for! memory! from! step! 1.! P! is! marking! for! self! in! an! exploratory! manner! in! order! to! figure! out! the! moves! and! timing.!!He!seems!confused.!At!01:01!A!asks!P!Should!I!go,!should!I!follow!you!after! One?.!Paolo!stops!and!turns!to!A.! 15! . ! !!!!!!Step)2!01:02!!!!!!!!!!!One!01:03!!!!!!!!Two!01:03!!!!!!!!!!!)Three!01:05!!!!!!!!!!One!01:04! Figure(8e.! ! !13!second!segment!At!1:02,!A!marks!the!grip!for!step!2!with!a!specific! transformation,!a!translation!of!his!waist!in!90!degrees!@!with!his!right!arm.!At!1:03,! A!suggests:!And!we!go!from!two!to!three.!P!agrees,!and!marks!for!himself!up!until! 1:05,!saying!aloud!the!numbers:!One,!Two,!Three,!One!which!refer!to!the!steps.! !At! 1:04!A!nods!in!agreement.!!The!problem!has!been!resolved.!! ! !!!!!!!!!!!!!!!!Step)1!01:05! Step(2!01:10!!!!!!!!)))))))))))Step)3)!01:11! ! !!!!!!!!!!!!!!!!!!!!!)Step)3!01:13!!!!!!!!!!!!!!!!!!Step)3!!01:15! !!!!!!!!!!!!Step)3!!01:16! Figure(8f.! ! !11!second!segment!At!1:05,!A!marks!step!One!for!coordination!for!the! fourth!time,!while!P!is!in!the!first!position!marking!for!self.!!They!both!say!out!loud! One!! !At!01:10!A!&!P!mark!for!coordination!step!2,.and!say!aloud!Two!.. .At. .1:11,!P! says!Three.!He!repeats!until!00:17!the!marking!for!the!step!4!times,!while!A!stays!in! the!correct!position!from!2.!! ! 16! ! )))))))))))))))))Step)3!01:17!!!!!!!!!)Step)4!!!!01:20!!!!!!!Step)3)01:21!!!!!!!!!Step)4!!!01:22! Figure(8g.!!!5!second!segment!At!1:17.P!seems!to!have!problems!to!transition!from! 3!to!4.!A!failed!attempt!because!of!working!arms!and!grips!is!rectified!in!01:22,!after! repeating!step!3!for!the!5th!time!in!this!final!attempt.!! The!image!sequence!shows!that!slowing!down!a!phrase!and!working!on!parts!in! semi@isolation!is!a!natural!way!to!study!and!reflect!on!key!aspects,!while!sharing! awareness!about!what!has!to!be!done!together.!!In!this!respect,!marking!resembles! practicing.aspects!of!a!move,!whether!in!music,!sports,!or!art.!!In!most!fields,! mastering!technique!involves!using!practice!time!to!focus!on!the!difficult!parts.!! Marking,!as!I!have!defined!the!term,!is!almost!always!present!in!such!cases,!though! not!always!for!long.!!A!solo!violinist!may!slow!down!a!phrase!to!concentrate!on!a! particular!transition!or!technical!element,!then!speed!up!or!add!more!feeling!once! core!technical!elements!are!understood!and!mostly!memorized!.!!The!difference! between!a!solo!violinist's!actions!when!marking@for@self!and!two!or!more!dancers'! marking@for@coordination!is!that!when!individuals!mark!together!they!must! coordinate!their!marking!to!ensure!focus!is!on!their!mutual!problem.!!This!is!found! in!musical!duets!and!ensembles!too.!!Together,!the!participants,!alter!tempo,! slowing!and!telling!each!other!things!that!lead!to!better!performance.!!This!means! that!unlike!marking@for@self,!where!marking!is!under!one!person's!exclusive!control,! during!marking@for@coordination!people!there!must!be!agreement!on!pace,! resolution,!detail!and!focus.!!! To!sum!up!so!far,!in!marking3for3others!and!marking3for3coordination!there!is!an! obvious!point!to!marking:!to!provide!a!vehicle,!an!anchor![Hutchins!2005,!Kirsh! 2009],!or!a!material!structure![Alac!&!Hutchins!2004,!Kirsh!2010b]!that!can!serve!as! a!common!reference!for!all!parties.!Marking!as!a!body@in@motion,!in!these!shared! contexts,!is!a!public!structure!that!can!be!used!to!focus!and!manage!joint!attention.!! It!facilitates!discourse!because!it!is!easier!to!stop,!identify,!and!isolate!attributes!of!a! phrase.!!In!the!case!of!marking@for@coordination,!it!provides!a!shared!structure!for! two!or!more!dancers!to!feel!and!ratify.!!One!dancer!will!apply!a!grip,!for!instance,!the! other!will!accept!it,!then!both!enter!a!state!of!common!knowledge!where!A!knows! that!B!knows!that!both!know!the!grip!has!been!accepted.!!All!this!can!be!done! without!dancing!full@out,!as!long!as!the!target!structure!is!sufficiently!well!marked! that!both!parties!know!they!are!thinking!about!the!same!full@out!structure.!!!By!no! means!is!achieving!this!common!knowledge!trivial.!!But!joint!memory,!coordinated! execution!in!the!marking!phase!and!later!in!the!full@out!version,!as!well!as!the!final! 17! ratification!by!the!choreographer,!seems!to!insure!that!the!proper!phrase!is! mastered.!! Marking-for-self In!marking@for@self,!the!function!marking!serves!is!less!evident!than!when!marking! is!for@others,!or!when!marking!is!for@coordination.!!For!this!reason!it!is!both! provocative!and!potentially!of!special!interest.!!We!cannot!assume!that!during! marking@for@self!dancers!are!just!practicing,!because!as!stated!before,!there!are! many!reasons!a!dancer!may!decide!to!mark@for@self:!to!situate!themselves!in!a! phrase,!to!review!the!phrase!synoptically,!to!focus!on!a!particular!aspect!of!the! phrase,!such!as!foot!or!arm!movements!or!step!sequence.!Even!when!the!function!of! marking@for@self!is!known,!there!remains!the!puzzle!of!why!anyone!should!bother!to! mark!–!to!move!their!body!–!instead!of!standing!quietly!and!just!mentally!simulating! themselves!dancing!their!phrase.!In!mental!simulation,!dancers!can!slow!down!a! phrase!too.!!They!can!situate!themselves,!or!fixate!on!aspects!and!look!for! imperfection,!possibly!just!as!easily,!and!certainly!with!less!physical!energy.!!What! cognitive!extra!does!marking!give!them?!!Why!do!they!mark@for@themselves?!! Sports!advertising!is!replete!with!reasons!to!mark!and!practice!in!slow!motion,!and! therefore!to!buy!videos!of!slow!motion!golf!swings,!tennis!strokes,!archery,!etc..!!As! one!website!put!it:! Why!is!the!slow!motion!golf!swing!the!best!way!to!practice!your!golf!swing?!! The!reason! is!simple!enough!–!a!golf!swing!done! in!slow!motion!helps!you! see!if!you!are!doing!it!correctly!for!maximum!effect.!!Golf!is!a!highly!technical! game! that! involves! learning! a! lot! of! details! to! make! the! perfect! grip,! the! perfect!swing!and!so!forth.! If!you!make!your!practice!golf!swings!at!regular!speed,!you!will!not!be!able! to!see!if!you!are!doing!it!correctly,!as!in!holding!the!golf!club!in!the!right!way,! pivoting!your!body!just!so,!and!swinging!the!club!at!the!right!angle!and!with! the!right!force.! When! you! practice! with! slow!motion! golf! swings,! you! will! be! able! to! see! what! you! are! doing! clearly.! ! Thus,! when! you! catch! yourself! making! a! mistake,! you! can! just! stop! at! mid@swing! and! correct! your! mistake! immediately.!![http://golfswingtips.grovetech.com/slow@motion@golf@swing/]! Unless!a!slow!motion!swing!is!fundamentally!different!in!form!than!a!full@pace! swing,!the!commentary!provides!a!prima!facie!reason!for!slowing!movements!down! during!practice.!!Dancers!might!benefit!from!slowing!things!down!when!practicing,! or!when!reflecting!on!form,!if.there.is.a.clear.exemplar.of.the.proper.way.the.phrase. should.be.performed.!!But!these!reasons!fail!to!explain!why!one!might!mark!if!there! is!no!external!norm.!Even!more!importantly,!they!do!not!explain!why!one!might! mark!in!a!'different'!way!than!the!normative!full@out!phrase.!The!point!of!using!a! video!that!slows!down!a!movement!is!that!the!practiced!movement!resembles!the! 'referent'!movement!shown!in!a!slowed!down!or!stepwise!form.!!A!coach!could!look! at!both!and!point!out!discrepancies.!!In!marking@for@self,!however,!the!way!a!dancer! 18! marks!may!be!such!that!no!third!party!can!tell!whether!the!phrase!being!marked!is! correct.!!Too!much!is!going!on!in!the!head.!!!!! The!problem!can!be!restated!like!this.!!When!dancers!mark@for@self!they!are!free!to! mark!in!their!own!idiosyncratic!manner!and!for!their!own!personal!reasons.!!! Whereas!there!are!conventions!when!a!dancer!is!marking@for@others!and!there!is! the!need!for!joint!agreement!when!dancers!are!marking@for@coordination,!there!are! no!public!constraints!on!how!someone!may!mark@for@self.!!!This!means!that!when! dancers!mark@for@self!they!may!mark!in!ways!that!are!understood!only!by! themselves.!!They!are!the!sole!beings!who!know!how!to!interpret!those!markings! correctly.!!It!is!a!very!private!act.!!! This!makes!marking!much!like!an!externalized!version!of!mental!simulation,!which! too!is!private.!!!Both!mental!simulation!and!marking!require!dancers!to!have!a!clear! idea!of!their!full@out!phrase!–!or!at!least!a!good!approximation!of!it.!Dancers!rarely,! if! ever,! mark! a! phrase! they! have! not! already! seen! full@out.! ! On! the! odd! occasion! when!they!have!not!already!seen!a!phrase!correctly!executed,!they!at!least!know!the! success!conditions!of!the!component!parts!and!how!they!are!to!be!assembled.!!The! choreographer!in!showing!them,!or!making!on!them,![Kirsh!et!al.!2009],!established! what!he!expected.! !And,! if! the!phrase!was! the!product!of!a! task!assigned! to! them,! rather!than!being!the!outcome!of!the!choreographer's!direct!involvement!in!shaping! movement,! then!the!requirements!of! the! task!will!be!sufficiently!explicit! that!each! dancer!should!know!what!is!expected.!!!So!why!mark?!!What!more!can!the!physical! manifestation!of!a!movement!add!to! the!target!already! 'mentally!grasped'! through! imagination?! !How!can!marking!ever!be!more!powerful!than!inner!visualization!or! imagination!alone?!! Part Three: How can marking be more powerful than mental simulation? There!are!several!ways!recruiting!the!body!might!augment!the!power!of!dancerly! thought!and!attention,!ways!that!marking!manages!to!deliver!cognitive!benefits!that! surpass!those!from!mental!simulation!alone.!! Let!us!start!with!some!intuitive!distinctions.!!Dancers!in!interview!mentioned! marking!for!different!reasons:!to!help!them!recall,!to!help!them!memorize,!and!to! help!them!explore!the!overall!shape!of!a!phrase.!!!!For!our!purposes,!recall!differs! from!memorizing!in!that!a!phrase!to!be!recalled,!presumably,!is!already!in!body!or! 'muscle!memory'!whereas!a!phrase!still!to!be!memorized!has!been!practiced!but!is! not!yet!fixated!in!motor!memory.!!The!notion!of!body!or!muscle!memory,!so!popular! in!dance5!and!sports6!literature!is!typically!understood!as!a!form!of!motor!learning! that!involves!automatizing!or!consolidating!a!motor!procedure!through!repetition.!7! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 5 Solway, Diane. "How the body (and mind) learns a dance". New York Times, May 28, 2007. 6 Taras V. Kochno. "Muscle Memory and Motor Learning In Golf". Sports Medicine & Rehabilitation, International. Sept 10th, 2010. http://www.drkochno.com/muscle_memory.htm 7 Krakauer,J.W., & Shadmehr, R. (2006). Consolidation of motor memory. Trends in Neurosciences, 29: 19! Exploration!of!a!phrase,!by!contrast,!is!less!about!memorizing!or!recalling!than! about!understanding!the!structural!and!intentional!elements!of!a!dance!movement.!!! it!is!good!to!mark!it!through!@!to!rework!it!in!your!brain,!to!make!another!idea!of! what!the!movement!is.!!! ! ! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(dancer!M!in!interview)! This!requires!conceptualizing!aspects!of!it.!!!As!before,!a!dancer!will!have!seen!and! practiced!a!phrase,!but!unlike!memorizing,!where!the!goal!is!to!lock!in!an!already! mastered!phrase,!in!exploration!the!phrase!has!not!yet!been!fully!mastered!and!the! goal!of!marking!is!to!improve!understanding!of!the!shape,!dynamics!or!intention!of! the!phrase.!!When!they!are!marking!for!exploration,!dancers!behave!as!if!they!have! norms!concerning!the!phrase's!form,!perhaps!because!they!recall!instructions!given! by!the!choreographer,!or!because!they!have!seen!others!perform!the!phrase!well.8!! As!they!mark,!they!seem!to!be!asking!themselves,!'am!I!meeting!the!norms?'!!This! might!equally!be!done!through!mental!simulation,!but!the!question!asked!here!is! whether!by!marking,!dancers!are!in!a!better!position!to!explore!the!phrase.!! I!will!not!discuss!our!observations!of!marking!for!recall!or!for!memorization,!despite! their!relevance!to!research!in!motor!learning.!!I!think!these!observations!constitute! a!valuable!type!of!support!for!contemporary!theories!of!hierarchical!motor! programs,!especially!those!that!explain!how!a!motor!program,!normally!executed! through!the!legs,!can!be!rerouted!and!adapted!so!that!it!is!executed!(in!rough!and! analogous!form)!through!the!arms.!!In!our!discussion!earlier,!it!was!noted!that!a! phrase!may!be!marked!in!various!sizes,!it!may!focus!on!an!aspect!of!the!full!phrase,! and!arms!and!legs!may!be!intersubstituted.!!To!have!a!motor!program!that!can!be! run!in!so!flexible!a!manner!puts!heavy!constraints!on!motor!learning!and!rehearsal.!!! My!focus,!here,!instead,!is!on!how!marking@for@self!facilitates!exploring!a!phrase! more!than!mentally!simulation.!!To!presage!what!follows:!the!answer,!in!brief,!is! that!creating!an!external!structure!connected!to!a!thought!–!whether!that!external! structure!be!a!marked!dance!form,!a!pencil!sketch,!a!gesture,!or!an!uttered!linguistic! structure!–!is!part!of!an!interactive!strategy!of!bootstrapping!thought![Kirsh!09,! 10a,b].!It!works!by!providing!an!understructure,!or!material!anchor![Hutchins,!05],! for!mental!projection.!!When!there!is!something!aptly!structured!outside!we!are!able! to!hang!more!mental!imagery,!or!more!complex!propositions,!on!it!than!we!could! without!it.!!Marking!a!phrase,!therefore,!serves!to!empower!dancerly!thought! because!it!provides!the!scaffold!to!mentally!project!more!detailed!structure!than! could!otherwise!be!held!in!mind.!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 58-64. 8 Celnik, P., Classen, J., Cohen, G.L., Duque, J., Mazzocchio, R., Sawaki, L., Stephan, K., & Ungerleider, L. (2005). Formation of a Motor Memory by Action Observation. The Journal of Neuroscience, 25(41), 9339-9346 20! The argument from externalization Here! is! one! reason! to! work! with! external! versions! of! thought:! through! externalization,! dancers! are! able! to! attend! more! effectively! to! difficult! aspects! of! their!movement!than!by!mentally!simulating!that!movement!alone.!!Attention!works! differently!on!the!outside!than!the!inside.!!Physical!structures!have!more!details!to! cue!off!of!and!monitor!than!internal!ones.! !They!generate!more!elements!to!attend! to,! more! opportunities! to! be! surprised.! ! Because! one! cannot! literally!monitor! a! mental! rehearsal,! creation! of! an! external! model! of! a! dance! phrase! permits! monitoring!its!execution.9! To! appreciate! the! cognitive! extras! that! physical! simulation! offers,! we! first! must! understand!the!power!of!mental!rehearsal.!!Try!this!little!experiment.!!Mentally!say! the!following!tongue!twister!several!times!quickly.!! Stitsky's(textile(center.((((Stitsky's(textile(center.((((Stitsky's(textile(center( Don't! just! read! it! quickly.! ! Say! it! internally.! ! As! experts! at! speaking,! we! have! a! powerful! capacity! to! mentally! rehearse! sentences.! ! Close! your! eyes! and! say! it! internally!again.!!Now!say!it!out!loud!in!quick!sequence.! A! few! things! should!be! apparent.! ! First,! it! is! possible! to!have!difficulty! saying! the! phrase! internally,! though! how! much! trouble! depends! on! the! vividness! of! inner! speech!and!the!number!of!times!you!say!the!phrase!internally.!!Fluent!readers!often! gloss!over!words,!understanding! them,!without!stumbling!on!speech!complexities.!! At!high!reading!speeds,!vision!is!paramount!and!auditory!imagery!is!low,![Pintner!R.! (1913)]! and! readers! do! not! really! formulate! sounds,! or! formulate! them! very! completely,!as!they!read.![ibid]!!If!you!are!like!me!as!your!reading!speed!approaches! speaking! speed,! the! sound! structure! of! sentences! becomes!more! fully! resolved! in! inner!speech,!and! if! there! is!going!to!be!any!articulation!trouble,! it!starts! to!show.!! This! is! the! case! when! you! explicitly! say! a! tongue! twister! in! inner! speech.!! [Oppenheim! 2008]! Say! the! sentence! quickly! in! your! outer! voice! and! if! you! have! trouble! saying! the! sentence! aloud!you! should! find!you!also!have! trouble! saying! it! internally.! ! The! reverse! is! also! true:! trouble! saying! a! sentence! internally! predicts! trouble!externally.! Based! on! this! experience,! it! might! seem! that! mental! rehearsal! resembles! overt! performance.! ! If! you! are! going! to! stumble! outside! then! likely,( you! will! stumble! inside.! ! Accordingly,! it! may! also! confer! most! of! the! benefits! of! overt! practice:! practicing! on! the! inside! often! yields! improved! performance! outside.! [Decety! 96,! Meister!2004]! Nonetheless,! there! is! still! an! important!difference!between! saying! things! out! loud! and!saying! them! internally.! !This! is!my!second!observation.!The! tongue!and!other! physiological!parts!used! in!speech!have!a!physical!dynamics! that!are!not!perfectly! simulated! internally.! ! Each! overt! speech! performance! encounters! physiological! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 9 Slezak, P., 1995. The 'philosophical' case against visual imagery. In: Slezak, P., Caelli, T. and Clark, R. (Eds.) Perspectives on Cognitive Science: Theories, Experiments and Foundations. Ablex, Norwood, NJ, pp. 237–271. 21! parameters!not!duplicated!in!mental!rehearsal,!such!as!how!wet!or!dry!the!mouth!is,! and! some! higher! order! effects! of! movement! and! muscle! control,! such! as! the! interactions! between! jaw,! tongue,! mouth,! and! vocal! chords.! ! [McGuire! PK,! et! al.!! (1996)].! ! Mental! simulation! does! not! improve! performance! when! these! factors! matter!significantly.!! Now,! try! a! second! experiment! concerning! mental! simulation.! ! Do! a! mental! walkthrough!of!getting!dressed!in!the!morning.!!Choose!a!level!of!detail!that!involves! imagining!each!piece!of!clothing,!where!it!is!found!in!your!room,!and!where!you!will! put! it! on.! ! In! the! mental! simulation! literature,! this! is! called! simulation! for! preparation.![Markman!et!al,!2009]! Here's!my!version.! !To! speed!up!my!morning! ritual,! I! lie! in!bed!a!moment! longer,! thinking! through! exactly!what! I! am!going! to!wear,!where! I! am!going! to! find! each! piece! of! clothing,! and! then! I! briefly! see!myself! putting! each! one! on.! ! By! informal! measures,!this!substantially!increases!the!speed!of!my!morning!rituals,!especially!if!I! include! in! my! mental! simulation,! the! sequencing! of! shower,! drying! off,! shaving,! tooth!brushing,!and!the!rest.!! Yet,! the! world! still! surprises! me.! ! This! is! the! third! observation.! ! As! good! as! my! mental!simulations!may!be,!there!are!invariably!aspects!of!the!way!things!really!are! that!I!did!not!anticipate.!!!Maybe!my!mentally!selected!socks!are!not!there,!or!buried! amidst!others.!!So!now,!there!is!an!extra!step!I!did!not!rehearse:!searching.!!Maybe! my!pant!pockets!contain!things!I!have!to!remove,!or!there!are!socks!in!the!legs!that! should!have!been!placed! in!the! laundry!bin.! ! If! I!were!to! 'dance'!around!the!room,! marking!my! later! performance,! I'd! see! these! extra! steps,! I'd! know!more! perfectly! how!things!are!this!morning,!and!not!rely!on!default!assumptions.!! What!does! this! tell!us?! !That! there!are! limits! to! the! realism!of!mental! simulation?!! Certainly.! !That!doing! in! the!world! is! still!more! fine@grained!and! informative! than! doing!in!the!mind?!!Yes.!!But!even!more,!it!points!to!the!value!of!physical!simulation! for!structuring!attention.!!Physical!simulation!involves!letting!the!outside!go!its!own! way!and! then!periodically! conceptualizing!what! is!happening.! ! ! It! adds! something! extra.! ! At! first,! this! extra!might! seem! to! be! the! outcome! of! simple!monitoring! @! a! reality!check!that!comes!from!observation.!! !But,!in!addition!to!updating!our!world! knowledge,!the!process!of!doing!in!the!world!invites!reconceptualizing!the!observed! events.! The!opportunity!to!reconceptualize!things!is!something!mental!simulation!does!not! offer.!!It!is!a!major!reason!'externalizing'!what!is!in!mind!is!a!more!powerful!strategy! than!working!with!things!in!the!mind!alone.!10!!For!instance,!given!a!physical!object,! such!as!a!chair,!and!a!mental!image!of!the!same!chair,!our!perceptual!system!will!be! far!more! active! in! the!way! it!probes! the! external! chair! than! the!way! our! imagery! system!will! probe! a!mental! image! of! that! chair.! ! There! is!more! to! be! discovered! when!a! structure! is! external! than!when! it! is! internal.! ! It!has!greater! causal!depth.!! Thus,! when! we! look! at! a! scene,! the! patterns,! or! figures! we! see! initially! may! be! replaced! over! time! by! different! patterns! or! figures,! as! our! eyes! follow! cues! and! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 10 Kirsh [2010a] discusses eight ways externalizing helps thinking. 22! notice!details!as!they!move!over!the!external!structures.!!This!is!especially!evident!in! figures! that! are! ambiguous! and! whose! interpretation! typically! reverses! after! a! minute!or!two.!!See!figure!9.! 9a 9b 9c Figure 9. Fig 9a is a classical ambiguous image of a saxophonist and a woman's face. Can you see both? Fig 9b is a Necker cube. The ambiguous figure in 9c is harder to reverse. After an initial period of 'interpretation lock', people normally toggle between the different interpretations of images like these. Not so when these figures are recreated in mental images. They don't toggle. Whereas the perceptual system interacts with external cues and attributes to actively look for consistent interpretations, often leading to change and surprise; the mental imagery system creates and sustains an object under an intention. It doesn't 'look' at the internal image, it creates it. ! The!lesson!to!derive!from!ambiguous!figures!and!from!scenes!that!take!time!to!'fully'! discern!is!that!what!is!discoverable!through!perception!is!not!always!discoverable!in! mental! imagery!of!the!same!structure.! ! [Chambers!&!Reisberg!1985]! !Studies!have! repeatedly! shown! that! when! mentally! imaging! a! reversible! object,! even! one! as! simple! as! a! Necker! cube,! see! figure! 9b,! the! interpretation! a! subject! starts! with! remains!the!sole! interpretation! long!after!the!figure!would!toggle! if!observed!with! open!eyes.! !It!is!as!if!mental!imagery,!and!by!extension!mental!rehearsal!or!mental! simulation,! cannot! escape! its! own! 'intentional! envelope'.! ! A! mental! image! is! sustained!by!a!conception!of!the!thing!or!process!to!be!conjured.! !Thus!a!subject's! own!idea!of!the!target!object!is!the!driving!force!determining!what!the!object!seems! to!be.!!In!principle,!this!conceptualization!could!change.!!But,!as!an!empirical!matter! it!does!not.!!The!mental!object!has!no!autonomy!from!the!subject.!!!It!is!sustained!by! the!subject!and!has!no!reality!independent!of!the!subject.! When!there!is!a!real!object!present,!however,!the!intentional!envelope!–!the!manner! of! perceiving! and! conceiving! a! scene! –! is! partly! driven! by! the! way! the! subject! actively! probes! or! interacts! with! the! object! as! well! as! the! subject's! active! conceptualization.!!When!there!is!an!external!object!it!can!'talk!back'.! !Accordingly,! as! perceptual! attention! moves! to! different! parts! of! the! object,! new! cues! and! attributes! come! into! focus.! ! The! resulting! interactive! dynamic,! when! applied! to! 23! vision,!has!been!called!by!Noe!'enactive'!vision.!![Noe!2004,!See!also!Hurley!1998]!!In! enactive! perception,! both! agent! and!world! are! in! active! dialogue:! what! one! see's! depends! in! part! on! where! and! how! one! looks,! and! where! and! how! one! looks! depends!on!what! there! is! to! see,! on!one's!motivations,! tasks,! skills,! and! activities.!! This!can!easily!lead!a!subject!to!look!at!an! 'unchanging'!object!and!see!things!in!it,! even!see!it!in!a!new!way.!!That!is,!the!interactive!dynamic!of!perception!can!cause!a! subject!to!reconceptualize!the!overall!structure!and!identity!of!a!scene.!! The! obvious! implication! for! marking! is! that! by! externalizing! their! movements,! dancers! are! able! to! create! an!object! of!perception! that! can!be! conceptualized!and! reconceptualized!in!ways!that!go!beyond!mental!simulation.!!They!can!harness!their! movement,!and!their!attentional!system,!for!further!cognitive!ends:!trying!out!forms! that! can! be! seen! in! new!ways,! then! exploring! those! new!ways! in! further!ways! of! moving.!!!! Perhaps!the!best!analogy!of!this!interactive!dynamic!is!graphical!sketching.!!Suppose! a! graphic! artist! is! given! a! simple! object! –! a! pair! of! scissors! –! then! provided!with! paper!and!cardboard!and!asked!to!make!a! few!cuts.!After!a!minute,! the!scissors! is! removed! and! the! artist! asked! to! make! an! illustration! of! the! scissors.! ! In! making! concrete!his!mental!image!of!the!scissors,!questions!arise!for!the!artist!about!details! of!the!scissors.!!How!much!of!the!whole!length!is!blade!and!how!much!handle?!!How! thick!is!the!blade?!!What!is!the!shape!of!the!finger!holes?! !By!having!the!chance!to! interact!with! a! slowly! evolving! pencil! sketch,! one! that! can! be! constructed,! erased! and!redone,!the!artist!has!a!chance!to!recreate!the!scissors!with!attention!to!details! that!before!may!have!gone!unnoticed.! !He! can! reconceptualize!parts! interactively.!! Creating! the! pencil! sketch! forces! an! interactive! level! of! engagement! with! his! memory!of!what!he!saw!that!cannot!be!matched!by!pure!imagination.!!The!external! artifacts!and!representation!help!him!to!interactively!explore!his!visual!memory!of! what! he! saw,! and! perhaps! more;! the! interaction! may! even! force! a! greater! integration! of! knowledge! about! scissors,! leading! him! to! infer! details! he! never! noticed,!attributes!that!must!be!there.!! This! interactive! strategy! of! recalling! an! image,! realizing! it! physically,! conceptualizing!what! is! now! external,! and! then! reconsidering!whether! that! is! the! best! conceptualization,! is! a! powerful!mechanism! of! thought.! ! In! dance! as!well! as! most! thoughtful! activity,! it! can! lead! to! new! conceptualizations! and! to! new! things! being!noticed.!!!! It!depends!on!a!second!process!–!projection!–!to!which!I!now!turn.! How Projection adds power to externalization I! have! been! arguing! that! physical! simulation! –! specifically! marking! a! phrase! –! provides! the! material! basis! for! triggering! attention! and! reflection,! making! reconceptualization!possible.!!It!supports!interactive!thinking.!!!This!a!key!process!in! using!marking! to! help! explore! and! rethink! a! dance! phrase.! ! It! is! easy! to! see! how! interactivity!might!help!explain!how!a!subject!can!learn!from!full@out!practice.!!But! isn't! it! necessary! that! the! target! of! interactive! inquiry!be! close! to! the! 'real'! thing?!! How!can!small!or!incomplete!movements!facilitate!rethinking!a!phrase?!!! 24! My! conjecture! is! that! a! movement! need! only! be! as! complete! as! is! necessary! to! support!!mentally!projecting.additional.structure.!!Marking,!even!small!marking,!can! provide!the!material!basis!for!this!sort!of!projection.!!When!dancers!mark!they!use! their!bodily!movement!to!'anchor'!projections!of!how!their!target!movement!ought! to!look!and!feel.!!Because!this!anchor!is!external,!they!can!distribute!the!complexity! of! mentally! simulating! ways! of! performing! a! phrase.! ! They! can! use! the! external! structure! as! a! scaffold! or! support,! much! the! way! a! designer! when! sketching! his! current! idea! can! use! a! simple! curve! to! both! encode! current! thoughts! and! as! a! support! to!prompt!new!ways!of! thinking.! !A!sketch!constitutes! the!external!object! for! interactive! inquiry,! and! it! doesn't! matter! that! it! is! incomplete! because! it's! function! is! to! stimulate! further! projection.! ! By! analogy,! marking,! even! small! marking,! ought! to! permit! a! more! interactive! engagement! of! full@out! moves! than! mental! simulation!unaided!by!external! support!because! it! constitutes! the!external! thing!that!a!dancer!needs!to!monitor,!probe!and!rethink.!!Bodily!movement!acts!as!a! scaffold!that!supports!better!mental!rehearsal!and!mental!exploration.! To!expand!this!idea!it!is!necessary!to!define!our!terms.!!! In!the!phenomenology!of!perceptual!experience,!a!distinction!can!be!drawn!between! perception,!projection,!and!imagination.!! Perception:!When!we!perceive!an!object,!our!experience! is! that!we!are!seeing! an! object! that! really! is! there;!we! feel! it! is! external! to! us,! it! is! the. independent. cause!of!our!perception,!and!our!experience!is,!in!some!sense,!involuntary.!!! Projection:! When! we! project! onto! an! object,! we! experience! ourselves! intentionally!augmenting!the!object;!we!feel!that!there!is!both!the!external!thing! causing!part!of!our!experience!and,!in!addition,!there!is!an!extra!element!caused. or!partially.caused!by!us.!!Part!of!our!experience!is!under!our!control.! Imagination:!When!we!imagine!an!object,!we!feel!as!if!we!are!the!sole.cause!of! our! imagined! experience.! !We!know!our! image! is! internal,! that! it! is! generated! and!sustained!by!us,!and!that! there!need!be!nothing!external! that! is!present!at! the!moment.!! Projection! lives! somewhere! between! perception! and! imagination.! ! See! figure! 10.!! Projection!has!an!imagination!component!because!the!projected!element!is!conjured! by!the!subject!–!the!subject!augments!the!external!structure.!!But!equally,!projection! has! a! purely! perceptual! component! because! the! projected! element! is! somehow! superimposed! or! anchored! on! what! is! perceptually! present! and! so! must! make! contact!with!the!external!structure.!!! ! Figure 10. The difference between perception, projection and imagination can be 25! understood as the difference between playing tic tac toe when you can see all moves written on a board (perception), vs. playing the game where all you can see is the board grid with nothing marked on it (projection), vs. playing with a blank page in front of one or blindfolded (imagination). Kirsh [2009] found that projection helps weak imagers in a 3 by 3 game and both weak and strong visualizers in 4 by 4 games. ! Projection! needs! a! physical! basis! because! by! definition! it! is! adding! intentional! content!to!what!is!already!there.!!The!simplest!way!to!think!of!projection!is!to!treat! it! as! the! psychological! equivalent! of! augmented! reality.! ! This! involves! engaging! some!part!of!visual!experience11,!though!just!where!in!the!chain!of!visual!processing! this! intentional!augmentation!occurs! is!not!yet!clear.! !Presumably,!projection!does! not! add! to! early! perception,! because! that! would! require! subjects! to! insert! conceptualized!content!into!a!pre@conceptual!process.!!Present!day!theory!holds!that! early!vision!is!involuntary,!and!'cognitively!impenetrable'.!![Pylyshyn!1999].!!So,!we! do!not!have!intentional!access!to!early!vision.![ibid,!Pylyshyn!2002].!!Nonetheless,!at! some!point,!perceptual!experience! is! sufficiently!conceptualized! that!a! subject! can! intentionally! choose! a! part! of! the! visual! scene! to! augment.! ! Conceptualization,! of! some! sort,! is! required! because! a! subject! must! anchor! his! or! her! projection! in! something!they!recognize.!!! We! found! support! for! this! idea! in! an! experiment! we! ran! recently! [Kirsh! 2009].!! Subjects! were! taught! to! play! the! game! of! tic@tac@toe! by! identifying! their! chosen! move!by!calling!out!its!cell!number!(which!they!were!trained!to!learn).!!There!were! two! main! conditions:! projection! and! imagination.! ! See! figure! 8.! ! There! was! no! condition!equivalent! to!perception!because!performance! is! invariably!better!when! the!entire!state!of!the!board!is!visible,!and!cognitive!strategies!can!be!perceptually! driven! in!ways! that!are!difficult! in!mental! simulation.! ! So!having! such!a! condition! would!be!uninformative.! !To!account! for!differences! in! imagery!ability!all! subjects! were!given!a!VVIQ2!imagery!test.! Our!results!were!surprising.!!We!expected!everyone!to!benefit!from!a!visible!tic@tac@ toe!grid,!but!this!was!not!what!we!found.!!Only!weak!visualizers!benefited,!and!even! so,!their!benefits!only!trended!to!significance!in!the!pilot!experiment!we!ran.!When! we! increased! the!problem!complexity!by! increasing! the!game! to! a!4!by!4!board!–! where! winning! requires! getting! four! in! a! row! rather! than! three! –! we! found! that! weak! visualizers! clearly! benefited! from! the! grid;! their! projection!was! statistically! better! than! imagination.! ! Strong! visualizers! trended! toward! improvement! and!we! predict!with!more!subjects!they!too!would!have!performed!significantly!better.!!The! inference! we! drew! was! that! people! make! use! of! external! structure! to! project! possibilities!when!they!have!difficulty!visualizing!those!possibilities.!!Augmenting!a! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 11 In 1910 Perky performed a set of experiments in which subjects fixated on a screen while visualizing objects, such as a tomato. Simultaneously, a faint patch of color, of an appropriate size and shape, and just above the normal threshold of visibility, was back projected onto the screen. The subjects thought the projected images were in fact the product of their own imagination. ! 26! scene! enables! them! to! perform! better! than! relying! on! their! imagination! alone! without!the!help!of!an!external!scaffold.!! What! does! this! tell! us! about!marking?! !Nothing! directly.!We! cannot! reliably! infer! from!this!experiment!that!by!creating!an!external!scaffold,!dancers!should!be!able!to! hold!in!mind!structures!of!greater!complexity!than!would!otherwise!be!possible!by! mental! simulation! without! external! support.! ! The! lesson! of! tic@tac@toe! is! only! suggestive!in!the!dance!domain!because!it!directly!applies!only!to!those!cases!where! it! is! hard! for! subjects! to! visualize!possibilities.! !Dancers!may!have!no!difficulty! in! visualizing!or!mentally!simulating!their!dance!phrases.!!! On! the! other! hand,! if! better! performance! in! tic@tac@toe! occurs! in! the! projection! condition! because! subjects! can! use! an! interactive! strategy! in! that! condition,! then! marking!may!facilitate!dancerly!cognition!because!it!provides!an!external!structure! to!interact!with.!!Dancers!can!use!their!bodies@in@motion!as!sketch@like!structures!to! interactively!elaborate!their!conception!of!their!phrase.! !Marking,! in!that!case,!will! act! like! a! graphic! artist's! sketch,! the! difference! is! that! in! dance,! movement! is! ephemeral!while! in! sketching!an! illustration! is!persistent!and!supports!a!different! set! of! interactive! strategies.! ! This! might! lend! support! to! the! claim! that! marking! enables!dancers!to!keep!in!mind!structures!of!greater!complexity.!! The! second! point! is! that! by! creating! an! external! structure! that! can! be! actively! probed! and! interactively! conceptualized,!marking! partially! explains! how! a! dancer! can!improve!full@out!performance!through!error@driven!motor!learning.!!One!of!the! larger!challenges!in!understanding!motor!learning!today!is!to!explain!how!a!subject! can! create! an! error! signal! that! marks! the! difference! between! a! normative! 'description'!of!the!target!movement!and!actual!movement.!!Subjects!must!be!able!to! tell!the!respects!in!which!their!performance!falls!short!of!the!ideal,!and!then!use!a! measure!of! that! 'error'! to!modify! the!underlying!motor!program!so! that!generates! behavior!closer!to!the!ideal.! !On!standard!accounts,!this!motor!program!is!updated! by!back@propagating!the!error!signal!to!improve!motor!output!next!time.![Jordan!&! Rumelhart!1992,!Wolpert!et!al,!1995]!!The!driving!question,!though,!is!where!does! that!error!signal!come!from?!!! In! dance,! the!normative!model! of! a! phrase!must! be! constructed! from! the! original! learning!context.!!Either!a!choreographer!will!have!shown!or!shaped!a!phrase,!or!the! dancer!himself!has!created!it.!!In!either!case,!there!are!observational!components!of! the! phrase! –! what! it! looks! like! visually! when! well! executed! –! and! there! are! conceptual! ideas! associated!with!what! is! involved! in! performing! the! phrase!well.! For!instance,!a!dancer!may!have!created!a!move!by!enacting!what!it!is!like!to!climb! out! of! a! barrel.! ! Research! done! to! date! on! how! explicit! thoughts! shape! motor! behavior!falls!under!the!theory!of!hierarchical!motor!learning.![Botvinick,!2008]!!It! is! in! an! early! stage! of! development.! ! The! effect! of! observation! on! movement,! meanwhile,!has!been!discussed!in!the!mirror!neuron!literature.![Stefan!et!al,!2005].! It,!too,!is!in!an!early!stage!of!development.!!The!relevance!of!both!approaches!is!that! they!offer!an!account!of!how!a!normative!model!can!drive!motor!learning.!!! 27! But! there! is! a! wrinkle.! ! In! order! to! extract! an! error! measure! the! activation! of! a! normative!model!must! not! draw! down! on! the! resources! needed!when! practicing! full,! or!marking,! or!mentally! simulating.! ! Else! it! will! not! be! possible! to! create! an! error!signal!or!the!quality!of!the!signal!will!decline.!! !It!is!here!that!marking!shows! its! superiority! to!mental! simulation.! !For,!presumably,! to!note! that!a!given!mental! simulation!of!a!phrase!is!incorrect!a!dancer!must!simultaneously!create!an!image!of! the!ideal!and!compare!it!with!the!actual!imagery!of!movement.!!In![reference!]!it!was! shown! that! it! is! hard! if! not! impossible! to! simultaneously! hold! different! mental! images.!!!It!is!here!that!marking!shows!its!value.!!If!a!dancer!can!offload!most!of!the! cost! of! imagining! a! phrase! by! 'leaning! on'! the! external! form! created! by!marking,! then!there!are!more!internal!resources!available!for!comparing!the!projection!of!the! phrase!with! the! image! of! the! normative! phrase.! ! The! result! is! that! a! better! error! measure! can! be! generated.! ! This!means! that!marking! behaves! as! an! element! in! a! distributed! representation! of! a! phrase,! and! the! cognitive! cost! of! distributed! representations!is!lower!than!comparable!representations!generated!and!sustained! internally.!! Conclusion Marking!is!part!of!the!practice!of!dance:!it!is!a!component!of!the!creative!process,! prevalent!during!the!rehearsal!process,!involved!during!practice!and!reflection,!and! common!when!people!are!nervous!and!waiting!in!the!wings.!!Processes!analogous!to! marking!are!found!in!most!activities!requiring!physical!technique,!such!as!sports! and!musical!performance.!!!The!general!phenomenon!is!remarkably!prevalent!and! yet!little!studied.!! I!discussed!three!types!of!marking:!marking@for@others,!marking@for@coordination! and!marking@for@self.!!They!are!distinguished!by!their!function.!!Marking@for@others! is!a!method!of!showing!one's!dance!phrases!to!another!in!a!manner!that!is! sufficiently!clear,!despite!being!less!energetic!and!less!emotional,!that!the!form!of! the!phrase!can!be!clearly!seen!and!the!remainder!of!the!phrase!can!be!inferred.!!It!is! usually!performed!for!the!choreographer!or!his!assistant.!!In!dance!companies,!there! are!often!norms!for!marking@for@others.!!! Marking@for@coordination!is!a!method!of!working!with!a!duet!or!trio!partner!to!work! through!grips,!positions,!and!timing.!!Dancers!go!through!the!motions!of!their!part,! and!they!practice,!jointly!recall,!discuss,!and!negotiate.!!Often!they!slow!down!the! phrase!they!are!marking.!!! In!marking@for@self,!dancers!use!their!body@in@motion!to!represent!for!themselves! some!aspect!of!a!'full@out'!phrase.!!It!is!a!method!of!practice!and!personal!reflection,! though!it!too!covers!diverse!phenomena,!such!as!running!through!a!phrase!to!reach! the!part!needing!practice,!slowing!the!phrase!down,!and!so!on.!!! I! have! argued! that! marking@for@self! is! an! example! of! interactive! cognition! –! an! extremely!prevalent!activity.!!People!often!think!by!means!of!an!interactive!strategy! of!creating!external!structure,!then!projecting!meaning!onto!that!structure,!and!then! creating! additional! external! structure.! Projection! is! another!way! of! saying!mental! 28! augmentation.!!It!is!the!extra!we!'see'!in!a!scene!when!we!look!into!possible!futures,! into!the!effects!of!actions!we!envision!ourselves!doing.! Noe![op!cit]!has!called!this!anticipation!of!the!future,!which!he!sees!as!an!essential! component!of!vision,!to!be!enactive!perception.!!Projection!differs!from!perception,!! even!in!this!enactive!sense,!however,!in!that!it!allows!envisioning!actions!that!might! change! the! thing! perceived,! such! as! reshaping! or! elongating! a! movement,! or! penciling! in!a!mark!on!an! illustration,!or!an!X!on!a!perceived! tic! tac! toe!board.! In! perception,! our! anticipated! actions! do! not! change! the! thing! perceived.! Projection,! nonetheless,! shares! with! enactive! perception,! the! assumption! of! an! active! agent! making! sense! of! the! world! through! continuous! engagement:! an! agent! sees! the! world,!anticipates!how!it!might!be!changed,!then!changes!the!world.!!!!!This!ongoing! cycle,!I!contend,!let's!dancers!and!people,!in!general,!outperform!themselves.!!They! harness!the!outside!to!bootstrap!thought!to!new!heights.!!!And!because!marking!can! be!fast,!it!constitutes!a!suitable!vehicle!of!thought.!!! ( Acknowledgements:! ! Many! people! have! helped! in! this! project:! Dr! Dafne! Muntanyola! worked! extensively! on! ethnographic! analyses! of! the! dance! data,! and! extracted! the! marking@for@coordination! images! that! comprised! the! example! used! here.!!!She!gave!helpful!comments!throughout.!!Twenty@five!students!in!my!class!on! Creative!Cognition!in!Dance!during!the!winter!of!2009!worked!tireless!to!code!video! and! transcribe! interviews.! Wayne! McGregor! has! always! been! encouraging! and! immensely! generous!with! his! time! and! views;! and! the! dancers! in! Random!Dance! happily! gave! us! interviews! despite! their! fatigue! at! the! end! of! each! day,! Scott! delaHunta! the! director! of! Random! Research! brokered! the! research! project! and! constantly! challenged! us! intellectually.! Thanks! to! the! Committee! on! Academic! Research,! UCSD! for! a! seed! grant! to! cover! expenses.! ! ! And! finally,! thanks! to! an! anonymous!reviewer!of!this!article!for!his!or!her!excellent!and!helpful!advice.!!! References Alac,! M.! &! Hutchins,! E.! (2004).! I! See!What! You! Are! Saying:! Action! as! Cognition! in! FMRI!! Brain!Mapping!Practice.!Journal!Of!Cognition!And!Culture,!4,3:!629@661.!! ! Botvinick,!M.!M.!(2008).!Hierarchical!models!of!behavior!and!prefrontal!function.!Trends!in! Cognitive!Sciences,!12,.!201@20! Carver,!R.!P.!(1992).!Reliability!and!Validity!of!the!Speed!of!Thinking!Test,!Educational!and! 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