on

PAPER

Perceptionandunderstandingofeffectsofgravityandinertiaonobjectmotion

In-KyeongKim1andElizabethS.Spelke2

1.2.

LaSierraUniversity,USA

MassachusettsInstituteofTechnology,USA

Abstract

Experimentsusingapreferentiallookingmethod,aperceptualjudgmentmethod,andapredictivejudgmentmethodinvestigatedthedevelopment,from7monthsto6yearsofage,ofsensitivitytotheeffectsofgravityandinertiaoninanimateobjectmotion.Theexperimentsfocusedonasituationinwhichaballrolledoffaflatsurfaceandeithercontinuedinlinearmotion(contrarytogravity),turnedabruptlyandmoveddownward(contrarytoinertia),orunderwentnatural,parabolicmotion.Whenchildrenviewedthethreefullyvisiblemotions,boththepreferentiallookingmethodandtheperceptualjudgmentmethodprovidedevidencethatsensitivitytoinertiadevelopedbetween7monthsand2years,andthatsensitivitytogravitybegantodevelopafter3years.Whenchildrenpredictedthefuturelocationoftheobjectwithoutviewingthemotions,thepredictivejudgmentmethodprovidedevidencethatsensitivitytogravityhaddevelopedby2years,whereassensitivitytoinertiabegantodeveloponlyat5±6years.Thesefindingssuggestthatknowledgeofobjectmotiondevelopsslowlyoverchildhood,inapiecemealfashion.Moreover,thesamesystemofknowledgeappearstobetappedbothinpreferentiallookingtasksandinjudgmenttaskswhenchildrenviewfullyvisibleevents,butadifferentsystemmayunderliechildren'sinferencesaboutunseenobjectmotions.

Humanadultsaresensitivetoavarietyofeffectsofgravityandinertiaonthemotionsofobjects.Inparticular,ahand-heldobjectthatisreleasedinmid-airlooksnaturalonlyifitbeginstomovedownward,anobjectthatfallsfreelylooksnaturalonlyifitundergoesappropriateacceleration(Shanon,1976),andanobjectthatrollsoffaclifflooksnaturalonlyifitmovesdownwardonaparabolicpath(Kaiser,Proffitt&McCloskey,1985).

Whataretheoriginsofthissensitivity?Gravityandinertiahaveconstrainedthemotionsofobjectsthrough-outthehistoryoftheearth,andhumansandotheranimalshaveevolvedavarietyofsensoryandmotormechanismsthattakeaccountoftheireffects(Howard,1982;Schone,1984).Itisthereforepossiblethathumanshavealsoevolvedperceptualandcognitivemechanismsthataresensitivetoeffectsofgravityandinertia.Alternatively,humanadultshavealifetimeofexperi-enceobservingobjects,andtheymayhavelearnedaboutnaturalobjectmotions.Onegoalofthepresentresearchistoinvestigatethesecontrastingpossibilitiesthroughstudiesofinfantsandchildren.

Despitetheirsensitivitytothenaturalnessofper-ceivedphysicalevents,adultsarepronetoerroriftheymustinferthepathoraccelerationofamovingobjectthatishidden(Shanon,1976;McCloskey,1983).Moreover,adultsoftengivemistakenexplanationsforthemotionsofobjectsandmakeerroneouspredictionsaboutfutureobjectmotions(e.g.Piaget,1976;Clement,1982).Theseobservationssuggestthatthetacitconcep-tionsunderlyingadults'perceptionofobjectmotionaredistinctfromtheexplicitconceptionsthatunderlietheirpredictions,judgmentsandexplanations.

Whataretheoriginsofthegapbetweenimplicitandexplicitknowledgeofobjectmotion?Studiesofschool-agedchildrenprovideevidencethattheexplicitknowl-edgeguidingjudgmentsaboutobjectmotionsometimesdiffersfromtheimplicitknowledgeguidingactionsonobjectsinchildrenasyoungas5years.Indeed,thesamechildmayactsoastopropelanobjectcorrectly,and

Addressforcorrespondence:ElizabethS.Spelke,E10-246,DepartmentofBrainandCognitiveSciences,MIT,Cambridge,MA02139,USA.#BlackwellPublishersLtd.1999,108CowleyRoad,OxfordOX41JF,UKand350MainStreet,Malden,MA02148,USA.

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340In-KyeongKimandElizabethS.Spelke

thenreporterroneouslyontheconditionsthatguidedheractions(Piaget,1976;Krist,Fieberg&Wilkening,1993).

Somepreviousresearchwithinfantsalsosuggestsadiscrepancybetweentheknowledgethatguidesactionsonvisibleobjectsandtheknowledgethatguidesinferencesabouthiddenobjects.Wheninfantsreachforacontinuouslyvisiblemovingobject,theirreachesare`predictive'i.e.aimedaheadoftheobject'scurrentlyvisibleposition,andguidedbyinertia(vonHofsten,Vishton,Spelke,Rosander&Feng,1998).Incontrast,wheninfantsviewanobjectthatmovesbehindanoccluder,theirlookingpreferencesbetweeneventsinwhichtheobjectreappearsatdifferentpositionssuggestsnosensitivitytoinertia(Spelke,Katz,Purcell,Ehrlich&Breinlinger,1994).Thesefindingssuggestthatthegapbetweenactionandjudgmentextendsbacktoinfancy,buttheyarenotdecisivefortworeasons.First,itisunclearwhetherpreferentiallookingtaskstapthesamekindofknowledgeastheverbaljudgmenttasksgiventoadults(seeBertenthal,1996,andSpelke,Breinlinger,Macomber&Jacobson,1992,fordiscus-sion).Second,thestudiesassessinginfants'predictivereachingforfullyvisibleobjectsusedsomewhatdifferenteventsandpresentationconditionsthanthoseassessinginfants'preferentiallookingatpartlyoccludedobjects,andsotheycannotbecompareddirectly.Asecondgoalofthepresentresearchistoexplorethepossibledivergencebetweenpreferentiallookingmethodsandverbaljudgmentmethods,aswellasthepossibledivergencebetweenperceptionsofandjudgmentsaboutconstraintsonobjectmotion,throughsystematiccomparisonsoftheearlydevelopmentofsensitivitytoobjectmotionacrossdifferentkindsoftasks.

Athirdgoalofthisresearchistoinvestigatethenatureofhumanknowledgeofgravityandinertia.Diverseconceptionsofobjectmotionhavebeenexpressedinthehistoryofscience(Duhem,1954;Kuhn,1970,1977)andbycontemporarysciencestudents(Champagne,Klopher&Anderson,1980;Clement,1982).Inthehistoryofphysics,theoriesofforce,accelerationandvelocityhavebeensubjecttocontinuousinnovation.Aristotelians,impetustheorists,andclassicalandrelativisticphysicistshaveoffereddifferentexplanationsforobjectmotionanddifferentdescriptionsofhowobjectsmoveunderparticularconditions.Studiesofcontemporarycollegestudentshavebeeninterpretedbysomeinvestigatorsassuggest-ingthatstudentsreasonintuitivelyasimpetustheoristsdid(McCloskey,1983).Otherinvestigators,however,haveproposedthatstudents'reasoningisbasedonpiecemealknowledgeratherthanonanygeneralconceptionsofobjectmotion(diSessa,1983).

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Thepresentresearchaimstoshedlightonthisissuebyinvestigatingthedevelopmentofsensitivitytoeffectsofgravityandinertiaonthepathofmotionofanobjectthatmovesoffasupportingsurface,andbycomparingchildren'sperformanceinthissituationtotheirperformanceinasituationstudiedpreviously,inwhichanobjectmovedonaninclined,supportingsurfacewitheitherappropriateorinappropriateaccel-eration(Kim&Spelke,1992).Ifasingleconceptionofgravityunderliesinfants'reactionstomovingobjectsinbothsituations,theninfantsshouldbecomesensitivetothenaturalpathofmotionforanunsupportedobjectatthesameageatwhichtheywerefoundtobecomesensitivetothenaturalaccelerationofapartiallysupportedobject:between5and7monthsofage(Kim&Spelke,1992).Ifpiecemealknowledgeunderlieshumans'commonsenseunderstandingofeffectsofgravityandinertia,incontrast,thenunderstandingmayemergeatdifferenttimesinthesedifferentsituations.

Thisresearchfocusedonthedevelopmentofsensi-tivitytogravityandinertiainonesituation.Ifaballrollsdownarampandthenoffitsedge,itcontinuestomoveforwardwhilealsomovingdownwardatasteadilyacceleratingspeed.Theforwardanddownwardmotionscombinetoformaparabolicpath.Experiments1±5investigated7-month-oldinfants'sensitivitytothiseffectofgravityandinertiainfullyvisibleevents,usingKimandSpelke's(1992)preferentiallookingmethod.Thefindingsofalltheseexperimentswerenegative,providingevidencethatthesensitivitytogravityandinertiashowninKimandSpelke'sstudiesreflectedlimited,piecemealknowledgeofobjects.Experiments6±8nextinvestigatedsensitivitytothesameeventsat2yearsofage,providingevidenceforemergingsensitivitytoinertiabutnotgravity.Experiments9±12investi-gatedhowthissensitivitydevelopsin3-to6-year-oldchildren,bothwiththepreferentiallookingmethodandwithaverbaljudgmentmethodassessingchildren'sperceptionofthenaturalnessofobservedobjectmotions.Thetwomethodsprovidedevidenceforthesamedevelopmentalchangesinsensitivitytoinertiaandgravity,suggestingslowpiecemealdevelopmentofasinglesystemofperceptualknowledge.Finally,Experi-ment13investigatedthedevelopmentofsensitivitytoinertiaandgravity,in2-to6-year-oldchildren,bymeansofadifferentverbaljudgmenttaskassessingchildren'spredictionsaboutthefuturepositionofanobjectwhosemotiontheyhavenotseen.Thislastexperimentprovidedevidenceforadifferentdevelop-mentalsequence,suggestingthatthedivergencebetweenperceptionandjudgmentfoundinadultsbeginsearlyindevelopment.

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Perceivingandunderstandingobjectmotion341

Sensitivitytogravityandinertiain7-month-oldinfants

Overview

Experiments1±5werebasedonthemethodsandfindingsofKimandSpelke(1992).InKimandSpelke'sexperiments,separategroupsof5-and7-month-oldinfantswerehabituatedtotwodifferenteventsinwhichaballrolleddownwardorupwardonarampwithappropriateacceleration,speedingupasitmoveddownwardorslowingdownasitmovedupward.Theninfantsweretestedwitheventsinwhichtherampwasinclinedintheoppositedirectionandtheballrolledwithaccelerationwhichwaseithernovelbutappropriateorfamiliarbutinappropriate.At5months,infantslookedlongeratthenovel,appropriateaccelerationpattern,suggestingthattheydiscriminatedthetwomotionsbutwerenotsensitivetotheinappropriatenessofupwardacceleratingordownwarddeceleratingmotioninthissituation.At7months,incontrast,infantslookedlongeratthefamiliarbutnowinappropriateaccelera-tionpattern,providingevidenceforsensitivitytotheeffectofgravityinthissituation.Between5and7months,infantsappearedtobegintoimplicitlyexpectadownwardlymovingobjecttoaccelerateandanupwardlymovingobjecttodecelerate.

Thepresentexperimentswereundertakentoinvesti-gatethegeneralityof7-month-oldinfants'sensitivitytotheeffectsofgravityonamovingobject.WeusedthemethodandstimuliofKimandSpelke(1992),withonechange.Insteadoftestinginfantswithaballrollingonafullrampwithtwodifferentpatternsofacceleration,eachofthepresentstudiestestedinfantswithaballrollingonatruncatedrampandthencontinuingontwodifferentpaths.If7-month-oldinfantshavedevelopedageneralsensitivitytogravity,thentheymightexpectgravitytoinfluencethepathaswellastheaccelerationofobjectmotion.Ifinfants'sensitivitytogravityismorepiecemeal,incontrast,theninfantsmightfailtoexpectgravitytoinfluenceanobject'spathofmotion.

AsinKimandSpelke(1992),theinfantsinExperiments1±5firstwerehabituatedtoanobjectundergoingnaturalmotioninastraightline.Indifferentexperiments,theobjecteithermovedlaterallyonaslantedorhorizontalplanarsurface,oritwasreleasedinmid-airandfellvertically.Afterhabituation,infantsweretestedwitheventsinwhichtheobjectrolledoffaslantedorhorizontalcliffandeitherunderwentnaturalmotiononaparabolicpathorunderwentunnaturalmotion.InExperiments1±4,theunnaturalmotionconsistedofacontinuationoftheobject'sprevious,linearpathofmotion:apaththatisinconsistentwith

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theeffectsofgravityonanobjectinfreefall.InExperiment5,theunnaturalmotionconsistedofanabruptturnastheobjectrolledoffthesurface,followedbyvertical,downwardmotion:apaththatisincon-sistentwiththeeffectsofinertia.Lookingtimestothetesteventswerecompared,ontheassumptionthatinfantswhoweresensitivetothenaturalnessoftheobject'sparabolicmotionwouldlooklongeratthetestdisplayswithunnaturalmotion.Experiment1

Infantswerehabituatedtoavideotapedeventinwhichaballrolledonaslantedrampwithconstant,naturalacceleration.Thentheyweretestedwitheventsinwhichtherighthalfoftherampwasremoved,theballrolleddownandofftheramp,andtheballcontinuedeitheronaparabolicpath(novelbutnatural)oronastraightlineasduringhabituation(familiarbutinconsistentwithgravity).Ifinfantsaresensitivetotheeffectofgravityontheunsupportedball'smotion,theywilllooklongeratthetesteventpresentingthelinearmotion.Method

SubjectsParticipantsweresixmaleandsixfemaleinfantsranginginagefrom6months15daysto7months15days(M󰂈6months28days).Threeadditionalinfantswereeliminatedfromtheexperimentbecauseofexperimentererror(one),distractionbyasibling(one),ordistractionbyaparent(one).DisplaysTheexperimentusedtwointroductorydis-plays,onehabituationdisplay,andtwotestdisplays,allvideotapedincoloronaVHScassettesystem(seeFigures1(a)and3).Attheinfant'sdistance(60cmfromthecenterofthescreen),theballsubtended2.5󰀎,anditmovedatanaveragespeedof20󰀎as.Forthehabituationdisplay,agreen,planar,supportingsurfacewasslanted15󰀎downwardsfromlefttoright.Ayellowstyrofoamballdecoratedwithbluesparkleswasintroducedbyahandatthefarleft,upperendoftheinclinedramp,wasplacedontherampandreleased,androlleddowntherampandoffthescreen.Theballrolledfor1.3s;theentireeventlasted4.5sandoccurredrepeatedly.Beforethehabituationsequence,therewasoneintroductorydisplay,inwhichanexperimentertappedonthesurfaceoftheramptobeusedforthehabituationtrial.

Forthetestevents,therampwascutinhalf,andthecoloroftherampwaschangedtoredtoelicitinfants'attentiontothechange.Inoneofthetestevents,theball

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342In-KyeongKimandElizabethS.Spelke

Figure1SchematicdepictionoftheeventsusedforExperiments1À12.

wasreleasedasbefore,rolleddownthetruncatedramp,andthenfellfromtheedgeoftheramponaparabolicpath(natural).Intheothertestevent,theballwasreleasedandthenrolledstraightacrossthescreenasifitwasstillbeingsupportedbyacompleteramp(unnatur-al).Itactuallyrolledonapairoffishingwires,whichwerenotvisibleonthevideoimage.Forthetestevents,theballmovedfor1.3s,eachcompleteeventlasted6s,andtheeventsagainoccurredrepeatedly.Beforethetesttrials,therewasanintroductorydisplayshowinganexperimenterwhotappedonthesurfaceofthetruncated

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rampandwavedherhandtoshowtherewasnothingbutemptyspacetotherightoftheramp.

Twelveadultsnaivetothepurposeofthepresentstudiesratedthenaturalnessofthehabituationandtesteventsinthisexperiment.Foreachevent,themotionoftheballwasrepeatedthreetimes.Theeventswereshownincounterbalancedorderacrosssubjects,withinalargersetofeightdisplays.Afterthepresentationofanevent,asubjectwasaskedtoratewhetherthemotionappearednaturalorunnaturalonascalefrom1(verynatural)to5(veryunnatural).

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Perceivingandunderstandingobjectmotion343

Figure2showstheaverageratingsforthethreeevents.Allsubjectsratedthehabituationevent(Fig-ure2(b))andtheparabolictestevent(Figure2(c))asverynatural,andallsubjectsratedthestraighttestevent(Figure2(g))asveryunnatural.Theratingsforeachoftheseeventsdifferedsignificantlyfromtheneutralratingof3:respectivevaluesfort(22)󰂈23.0,11.73and9.75;allp`0.001.

DesignEachinfantwaspresentedwiththesamehabituationdisplayfollowedbythesametwotestdisplaysinalternation.Halftheinfantsofeachsexwerepresentedfirstwiththelineartestdisplay;theremaininginfantswerepresentedfirstwiththeparabolictestdisplay.

ProcedureInfantsfirstwerepresentedwiththeintro-ductorydisplaywiththefullrampforabout10s.Thehabituationsequenceimmediatelyfollowed.Afterthelasthabituationtrial,infantswerepresentedwiththeintroductorydisplaywiththehalframpforabout10s,andthenthetestsequencefollowed.Duringthetestsequence,infantswerepresentedwiththetwotestdisplaysinalternationforatotalofsixtrials.Inter-observeragreementaveraged0.93.Results

MeanlookingtimesforthehabituationandtesttrialsareshowninFigure3.Log-transformedlookingtimesweresubjectedtoa2(Testorder)by3(Testtrialpair)by2(Testevent:straightvsparabolic)analysisof

variance(ANOVA).TherewasasignificanteffectofTestorder,F(1,10)󰂈10.87,p`0.01:infantslookedlongeratthetestsequencewhentheparabolictesteventwaspresentedfirst.ThiseffectwascomplicatedbyaTestorderbyTesteventinteraction,F(1,10)󰂈25.33,p`0.01,andaTesttrialpairbyTesteventinteraction,F(2,20)󰂈3.51,p`0.05:infantslookedlongeratwhichevertesteventwaspresentedfirst,andtheylookedlongeratthestraighteventinthefirsttrialpairandattheparaboliceventinthethirdpair.However,therewasnomaineffectofTestevent,F(1,10)󰂈2.32,p󰂈0.16.Discussion

Afterfamiliarizationwithaneventinwhichaballrolleddownwardonaninclinedplane,7-month-oldinfantsshowednopreferencebetweenthestraightandpara-bolictestevents.Thus,theexperimentprovidesnoevidencethatinfantsperceivedthecorrectparabolicmotionasmorenatural.

Itispossible,however,thatthepresenttestwastoostringent.Likethenaturaltestevent,theunnaturaltesteventinthepresentexperimentpresentedamotionthatwasbothdownwardandforward:thus,bothtestmotionswereconsistentwithaspectsofinertiaandgravity.Infantsmighthaveperceivedbothoftheseeventsasmorenaturalthananeventinwhichanunsupportedobjectunderwentnodownwardmotion.Itispossible,therefore,thattheinfantsunderstoodthattheobjectshouldmoveforwardanddownward,butfailedtoappreciatethattheforwardanddownwardmotionsshouldcombinetoformaparabolicpath.

Figure2Adults'judgmentsofthenaturalnessofeachoftheeventspresentedtoinfantsandchildreninExperiments1À12(standarddeviationsinparentheses).

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344In-KyeongKimandElizabethS.Spelke

Figure3MeanlookingtimesduringthelastsixhabituationtrialsandthesixtesttrialsbytheinfantsinExperiment1.

Accordingly,Experiment2presentedinfantswithanunnaturaleventinwhichanunsupportedobjectunder-wentnodownwardmotionatall,inordertoinvestigatewhetherinfantsexpectmotiondownwardratherthanhorizontalmotionthroughtheair.Experiment2

Experiment2wasidenticaltoExperiment1exceptforthehorizontalinclinationofthesurfaceinthehabitua-tionandtestevents.Seven-month-oldinfantswerehabituatedtoavideotapedeventinwhichaballrolledonahorizontalsurfaceatanatural,nearlyconstantvelocity.Then,forthetestevents,thesurfacewascutinhalf,theballwassetinmotiononthesurface,andafterrollingoffthesurfaceiteitherfollowedaparabolicpath(unfamiliarbutnatural)orrolledstraightacrossthescreen(familiarbutinconsistentwithgravity).Ifinfantsappreciatedthattheobjectshouldmovedownwardafterlosingitssupport,thentheywereexpectedtolooklongeratthetesteventwiththelinearmotion.Method

ThemethodwasthesameasinExperiment1exceptasfollows.Participantswereeightinfants,fourmalesandfourfemales,ranginginagefrom6months15daysto7months15days(M󰂈7months0days).Noinfantfailedtocompletetheexperiment.

ThedisplaysaredepictedschematicallyinFigures1(b)and4.Forthehabituationdisplay,agreenhorizontalplanecoveringthebottomhalfofthescreenwasused.Aballwastappedbyahandatthefarleftendoftheplane,andtheballrolledataconstantvelocityacrossandoffthescreen.Theballrolledfor1.1s,andoneentireeventlasted3.7s.Forthetestdisplays,aredtruncatedplanecoveringthebottomleftquadrantofthescreenwasused,theballwastappedasbefore,andit

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eitherrolledofftheplaneonaparabolicpath(natural)orfollowedthesamelineartrajectoryacrossthescreenasduringhabituation(unnatural).Inbothtestevents,theballmovedfor1sandoneentireeventlasted3.7s.Exceptfortheinclinationoftheplane,thetappingoftheball,andthedurationoftheevents,alltheeventswerethesameasinExperiment1.

ThehabituationandtesteventswerepresentedtoadultswhoratedtheirnaturalnessalongwiththeeventsfromExperiment1(seeFigure2).Thehabituationevent(Figure2(d))andtheparabolictestevent(Figure2(e))wereratedasverynaturalbyadults,whereasthestraighttestevent(Figure2(h))wasratedasveryunnatural.Alltheratingsdifferedfromtheneutralvalueof3:respectivevaluesoft(22)󰂈7.71,9.95and23.0;allp`0.001.

Inter-observeragreementaveraged0.94.Results

MeanlookingtimesforthehabituationandtesttrialsareshowninFigure4.ThedatawereanalyzedasinExperiment1.TheANOVAyieldednosignificanteffects.Inparticular,therewasnomaineffectofTestevent,F(1,6)`1.Discussion

Afterfamiliarizationwithaneventinwhichaballrolledonaflatplane,7-month-oldinfantslookedequallyattheparaboliceventandstraightevent.Theexperimentthereforeprovidesnoevidencethat7-month-oldinfantsexpectanunsupported,movingobjecttomovedown-wardonaparabolicpathratherthanhorizontallythroughtheair.

ThepresentfindingspresentaninterestingcontrastwiththeresearchofKimandSpelke(1992).BecauseExperiments1and2usedthesamemethodasthe

Figure4MeanlookingtimesduringthelastsixhabituationtrialsandthesixtesttrialsbytheinfantsinExperiment2.

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Perceivingandunderstandingobjectmotion345

experimentsofKimandSpelke(1992),infants'failuretolooklongerattheeventswithlinearmotionsuggeststhatinfants'sensitivitytothenoveltyofobjectmotionsthatviolateeffectsofgravityandinertiadependsonpiecemealknowledgeratherthanonsensitivitytogeneralphysicalconstraintsonobjects.Nevertheless,thereisoneproceduraldifferencebetweenthesetwosetsofexperimentsthatcomplicatestheircomparison:Inthepresentexperiments,theobjectwasreleasedbyahandandthenrolledoff-screen,whereasinKimandSpelke's(1992)experimentstheobjectwasreleasedbyahandandthencaught,attheoppositesideofthescreen,byasecondhand.Itispossiblethateventsinwhichanobjectcomesvisiblytoreston-screenareeasierforinfantstounderstandthanareeventsinwhichanobjectmovescompletelyfromview.Experiment3wasconductedtotestthispossibilityandtoprovideamoredirectcomparisonbetweenthepresentexperimentsandthoseofKimandSpelke(1992).Experiment3

Experiment3presentedthesameeventsasExperiment2,withoneexception:afterthehandreleasedtheballontheleftsideofthescreenandtheballrolledrightwardacrossthescreen,asecondhandcaughtitontherightsideofthescreen.Thespatialandtemporalcharacter-isticsoftheseeventswereassimilaraspossibletothoseofKimandSpelke(1992),inwhichaballrolledonafullrampinclinedeitherdownwardorupward.AsinExperiment2,however,theballrolledonafull,horizontalrampduringthehabituationsequenceandrolledonatruncatedrampduringthetest,oneitheralinearoraparabolicpath.Method

ThemethodwasthesameasinExperiments1and2exceptasfollows.Participantswereeightinfants,threemalesandfivefemales,ranginginagefrom6months15daysto7months15days(M󰂈7months2days).Oneadditionalinfantwaseliminatedbecauseofexperimen-talerror.

ThedisplaysaredepictedschematicallyinFigure5.Forthehabituationevent,aballwastappedbyahandattheleftendoftheplane,wascaughtbyasecondhandattherightendoftheplane,washeldbriefly,andthencarriedoffthescreen.Foreachtestevent,theballwastappedandthenwascaughtbyasecondhandatthefinalposition(parabolicorstraight-acrosspath),heldbriefly,andthencarriedoffthescreen.Forallthreeevents,theballmovedfor1.2s,andoneentireevent

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Figure5MeanlookingtimesduringthelastsixhabituationtrialsandthesixtesttrialsbytheinfantsinExperiment3.

lasted5s.Alleventsoccurredrepeatedly.Inter-observeragreementaveraged0.96.Results

MeanlookingtimesforthehabituationandtesttrialsareshowninFigure5.TheANOVAshowedonlyasignificanteffectofTesttrialpair,F(2,12)󰂈10.20,p`0.005:lookingtimedeclinedoversuccessivepairsoftesttrials.TherewasnomaineffectofTestevent,F(1,6)󰂈1.88,pb0.2.

AsecondANOVAwiththeadditionalbetween-subjectsfactorofExperimentcomparedthetesttriallookingpatternsinExperiments2and3.ThisanalysisshowedagaintheeffectofTesttrialpair,F(2,24)󰂈11.91,p`0.001,butnoothersignificanteffects.Inparticular,therewasnointeractionofExperimentandTestevent,F(1,12)󰂈1.67,pb0.2.Discussion

Afterhabituationtoaneventinwhichaballrolledonaflatplane,7-month-oldinfantsshowednopreferencebetweenthestraightandparabolictestevents.Longerexposuretotheball'sfinalpositiondidnotenhanceinfants'sensitivitytothenaturalnessofitspathofmotion.

Inthreeexperiments,therefore,7-month-oldinfantsshowednopreferencebetweenanaturaleventinwhichanobjectrolledoffasurfaceandunderwentparabolicmotionandanunnaturaleventinwhichtheobjectcontinuedinlinearmotion.Theresultsprovidenoevidencethat7-month-oldinfantsexpectanobjectthatrollsoffaclifftomovedownward,relativetothestraight-acrosspath,inaccordwiththeeffectsofgravityonobjectmotion.

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346In-KyeongKimandElizabethS.Spelke

ThepresentresultscontrastwiththoseofKimandSpelke(1992),whousedverysimilareventsandthesamemethodasExperiment3.Although7-month-oldinfantsappeartoexpect,onsomelevel,thatanobjectwillacceleratewhenitmovesdownwardanddeceleratewhenitmovesupwardonaninclinedplane,theydonotappeartoexpectthatanobjectwillbegintomoveonaparabolicpathwhenitmovesoffaplaneandbeginstofallfreely.

Nevertheless,itispossiblethatinfantsindeedexpectanobjecttomovedownwardwhenitlosesitssupport,butthatExperiments1±3failedtorevealthisexpecta-tionbecausetheypresentedinfantswithtoostringentatestofsensitivitytoeffectsofgravity.Theseexperimentspittedthesuperficialfamiliarityofthetesteventsagainsttheirphysicalnaturalness,becausethemotionofthehabituationeventwasthesameasthatoftheunnaturaltestevent.Itispossible,therefore,thatinfantsrespondedbothtothenaturalnessandtothesuperficialfamiliarityofobjectmotion.NotethatthispossibilitycannotexplainthedifferencebetweenthepresentexperimentsandthoseofKimandSpelke(1992),whichalsopittedthesuperficialfamiliarityoftesteventsagainsttheirphysicalplausibility.Nevertheless,thenextexperimenttestedinfants'sensitivitytogravityfurtherbyinvestigatinginfants'reactionstohorizontalandparabolicmotionsafterhabituationtoaneventinwhichanobjectappearedinfreefall,suchthatthetwotestmotionswerebothnovel.Experiment4

Seven-month-oldinfantswerehabituatedtoavideo-tapedeventinwhichaballunderwentavertical,free-fallmotion.Then,forthetestevent,aballrolledonaplaneandcontinuedtofollowaparabolicpath(natural)orastraightpath(inconsistentwithgravity).Method

ThemethodwasthesameasinExperiment1exceptasfollows.Participantswere12infants,sixmalesandsixfemales,ranginginagefrom6months15daysto7months15days(M󰂈7months3days).Twoadditionalinfantswereeliminatedbecauseoffussiness.

ThedisplaysaredepictedschematicallyinFigures1(c)and6.Forthehabituationdisplay,therewasagreenrectangular-shaped,truncatedramp,whichcov-eredtheleftbottomquarterofthescreen.Ahandheldaballattherightsideoftheramp,andreleasedit.Theballunderwentafreefallanddisappearedoffthescreen.Theballfellfor0.43s,andoneentireeventlasted3.7s.Thiseventwasratedasverynaturalbyadults,arating

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thatdifferedfromtheneutralvalueof3,t(22)󰂈11.73,p`0.001(Figure2(a)).ThetestdisplayswerethesameasinExperiment2.Inter-observeragreementaveraged0.95.Results

MeanlookingtimesforthehabituationandtesttrialsareshowninFigure6.Althoughtheinfantstendedtolooklongeratthetesteventwiththestraightpath,thistendencywasnotsignificant,F(1,10)󰂈2.63,p󰂈0.13.TheonlysignificanteffectintheanalysiswasamaineffectofTesttrialpair,F(2,20)󰂈5.96,p`0.01:lookingtimedeclinedonsuccessivepairsoftesttrials.Discussion

Afterhabituationtoaneventinwhichaballunderwentafree-fallmotion,7-month-oldinfantsshowednosignificantpreferenceforthestraightovertheparabolictestevents.LikeExperiments1±3,therefore,Experi-ment4providesnoevidencethat7-month-oldinfantsaresensitivetothenatural,parabolicpathofmotionofanobjectthatrollsoffasupportingsurface.

Insummary,fourexperimentsfailedtoprovideevidencethat7-month-oldinfantsaresensitivetotheeffectofgravityonthemotionofanobjectthatrollsoffasupportingsurface.Itispossible,however,thatinfantsaresensitivetoadifferentaspectofthemotionofsuchanobject:Theymayimplicitlyappreciatethattheobject'smotionissubjecttoinertia.Accordingly,thenextexperimentinvestigated7-month-oldinfants'sensi-tivitytotheeffectsofinertiaonobjectmotioninthesamesituationasExperiment1.

Figure6MeanlookingtimesduringthelastsixhabituationtrialsandthesixtesttrialsbytheinfantsinExperiment4.

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Perceivingandunderstandingobjectmotion347

Experiment5

Seven-month-oldinfantswerehabituatedtoavideo-tapedeventinwhichaballrolledonaslantedrampataconstantacceleration.Then,forthetestevents,therampwascutinhalfasbefore,theballrolleddownandofftheramp,andthentheballeithercontinuedonaparabolicpath(natural)orturnedandmovedstraightdownward(inconsistentwithinertia).Ifinfantsaresensitivetotheeffectsofinertiainthissituation,theywilllooklongeratthestraight-downtesteventbecausetheballabruptlyceasestomoveforwardafterleavingtheramp.Method

ThemethodwasthesameasinExperiment1exceptasfollows.Participantswere12infants,sevenmalesandfivefemales,ranginginagefrom6months15daysto7months15days(M󰂈6months29days).Noinfantfailedtocompletetheexperiment.

ThedisplaysaredepictedschematicallyinFigures1(d)and7.ThefamiliarizationeventandthenaturaltesteventwerethesameasinExperiment1.Fortheunnaturaltestevent,theballrolledontherampuntilitreacheditsedge,andthenitmadeasuddenturnandmovedstraightdownward.Thiseventwasmadethroughthevideoediting,bycombiningasegmentinwhichtheballrolleddownontherampwithasegmentinwhichitunderwentastraight-downfree-fallmotion.Theballmovedfor1.3s,andacompleteeventlasted6s.Thiseventwasratedasveryunnaturalbyadults,aratingthatdifferedfromtheneutralvalueof3,t(22)󰂈23.0,p`0.001(Figure2(f)).Inter-observeragreementaveraged0.95.Results

MeanlookingtimesforthehabituationandtesttrialsareshowninFigure7.ThedatawereanalyzedasinExperiment1andshowednosignificanteffects.Inparticular,therewasnomaineffectofTestevent,F(1,10)`1.Discussion

Afterfamiliarizationwithaneventinwhichaballrolleddownwardonaninclinedplane,7-month-oldinfantslookedequallyattheparaboliceventandstraight-downevent.Eventhoughtheinfantsinthisexperimentwerehabituatedtoaneventpresentingadifferentpathofmotionthaneitherofthetestevents,infantsdidnotrespondtothestraight-downmotionasunnaturalorunexpected,relativetotheparabolicmotion.The

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Figure7MeanlookingtimesduringthelastsixhabituationtrialsandthesixtesttrialsbytheinfantsinExperiment5.

experimentthereforeprovidesnoevidencethat7-month-oldinfantsaresensitivetotheeffectsofinertiaonthemotionofaballthatrollsoffacliff.Discussionofthestudiesof7-month-oldinfantsAfterhabituationtothenatural,linearmotionofanobjectrollingonaplanarsurface,7-month-oldinfantswerepresentedwiththesameobjectundergoingthesamemotiononatruncatedsurface,rollingoffthesurface,andcontinuingeitheronanaturalparabolicpathoronapathinconsistentwithgravity(continuedlinearmotion)orinertia(abruptturningdownward).Theinfantsdidnotrespondtoeitherthelinearortheabruptlyturningpathofmotionasunexpectedorunnatural,relativetothenatural,parabolicpathofmotion.Theexperimentsthereforeprovidenoevidencethatinfantsaresensitivetothenaturalnessofthecorrectparabolicmotioninthissituation.

Thisconclusionmightbequestionedonthreegrounds.First,itisbasedentirelyonnegativefindings,butnegativefindingscouldresultfromtheuseofaninsensitivemethodorinadequatedisplays.Inthepresentcase,however,themethodisthesameasthatofKimandSpelke(1992),whichyieldedpositivefindingswithinfantsinthesamesubjectpopulation.Thedisplays,moreover,areverysimilartothoseofKimandSpelke(1992)andevokedclearjudgmentsofnaturalnessaunnaturalnessfromadults(seeFigure2).Althoughonecanneverconcludethatchildrenlackagivenability,thepresentfindingssuggeststronglythatinfantswhoviewaballrollingonaninclinedplanearemoresensitivetotheeffectsofgravityandinertiaontheobject'saccelerationthantotheeffectsofgravityandinertiaontheobject'spathofmotion.

Second,ourexperimentsmightbecriticizedbecausetheyonlytestedinfants'reactionstothreepathsoffallingmotion,whereasthereareinfinitelymany

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348In-KyeongKimandElizabethS.Spelke

possiblepathsanobjectcouldfollow,andthecorrectparabolicpathwouldbedifferentdependingontheinitialforceandotherfactors.Itispossible,therefore,thatinfantshadanexpectationaboutthemotionoftheobjectbutthatwefailedtotestthisexpectationbecausewepresentednotesteventsthatcorrespondedtoit.Webelieve,however,thatthemotionspresentedduringthehabituationtrialsofExperiments1±3and5renderthispossibilityunlikely.InExperiments1and5,wespecifiedforinfantstheinitialaccelerationoftheobjectbyusingthesameslantedplaneinthehabituationandtestevents,andinExperiments2and3wespecifiedtheinitialforcewithwhichtheobjectwashitonthehorizontalplanebyhittingtheobjectwiththesameforceduringhabituationandtest.Alltheexperimentsthereforegaveinfantstheopportunitytopickuptherelevantinformationabouttheobject'svelocityandaccelerationduringthehabituationtrials.Althoughitispossiblethatinfantshadaspecific,erroneousexpecta-tionaboutthemotionoftheobjectthatfailedtocorrespondtoanyofthetestevents,thispossibilityappearsunlikely,becausesuchanexpectationwouldfailtoaccordbothwiththenaturalmotionsofobjectsandwiththeactualmotionsinfantsviewedduringthehabituationperiod.

Third,theseexperimentscontainnobaselinemeasuresofpreferenceforparabolic,linear,andabruptlyturningmotions,independentofthephysicalplausibilityoftheseevents.Itispossible,therefore,thatinfantshadanintrinsicpreferenceforparabolicmotion,andthatthispreferenceoffsettheirnoveltyreactionstotheunnaturaltestevents.Thispossibilityrevealsaninherentlimitationofexperimentsusingthepreferentiallookingmethodtotestforinfants'sensitivitytothenaturalnessofdifferentpathsofobjectmotion.Itisnotpossibletotestforstimuluspreferencesamongdifferentpathsofmotionindependentofthephysicalplausibilityofthosepathsofmotion.Forexample,onecouldpresentinfantswithanobjectthatunderwentlinear,parabolic,andabruptlyturningmotionwhilerollingonasingle,continuoushorizontalsurface.Onsuchasurface,however,thelinearmotionwouldbenaturalandtheothermotionswouldbeunnatural.Becausethereisnosituationinwhichlinear,turning,andparabolicmotionsareequallynatural,nopurebaselineconditionscanberunintheseexperiments.

Althoughwecannotconductmeaningfulbaselineconditionsforthepresentexperiments,aconsiderationofinfants'visualpreferencesinother,relatedexperi-mentsforwhichbaselinemeasuresarepossiblecastsdoubtonthethesisthatinfantsaresensitivetothenaturalnessofparabolicmotionbutthattheirsensitivityismaskedbyabaselinepreferenceforthatmotion.In

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theexperimentsbyKimandSpelke(1992),forexample,infantswerefoundtohaveageneralpreferenceforacceleratingobjectmotionoverdeceleratingobjectmotion.Nevertheless,thispreferencedidnotpreventtheiralsoexhibitingarobustpreferenceforadecelerat-ingmotionthatwasnaturalandinconsistentwiththedownwardforceofgravity,relativetoanacceleratingordeceleratingmotionthatwasnatural.InexperimentsbyGergely,Nadasdy,CsibraandBiro(1995),infantswerepresentedwithtestdisplaysinvolvingonelinearmotionandonecurvedmotion,asinthepresentstudies.Becausetheinvestigators'focuswasonanimate,goal-directedmotions,theywereabletocreateconditionsinwhichboththelinearandthecurvedmotionswerenatural,aswellasconditionsinwhichonemotionwasnaturalandtheotherwasnot.Infantsshowedarobustvisualpreferencefortheunnaturalmotions,suggestingthatanybaselinepreferenceforcurvilinearmotionwasoutweighedbyinfants'reactionstothenaturalnessorunnaturalnessofevents.Althoughwecannotbecertainthatthepresentsituationisfreeofbaselinepreferences,webelieveitisnoteworthythatfiveexperiments,usingamethodthathasproducedclearpositivefindingsinotherstudies(Kim&Spelke,1992),allfailedtoprovideevidencethat7-month-oldinfantsaresensitivetothenatural,parabolicpathofmotionofanobjectthatrollsoffasupportingsurface.Eithersuchsensitivityisabsent,oritistooweaktooverridean(unknown)intrinsicpreferenceforparabolicmotion.Ineithercase,comparisonofthepresentfindingswiththoseofKimandSpelke(1992)suggeststhatsensitivitytoobjectmotiondevelopsinapiecemealfashionininfancy.

Inviewofthenegativefindingswith7-month-oldinfantsandthelimitationsofthepreferentiallookingmethodforprobingthosefindingsfurther,theremain-ingexperimentsinvestigated2-to6-year-oldchildren'sperceptionandreasoningaboutthepathofafallingobject.Preference-for-noveltytestsarestillpossiblewitholderchildren,andtheywereconductedat2and3yearsofage.Inaddition,3-to6-year-oldchildren'sjudgmentsaboutthesamevisibleobjectmotionswereelicitedtoprovideinformationabouttheirexplicitconceptionsofobjectmotionandtoallowtestsforadiscrepancybetweenperceptionandjudgment.

Sensitivitytogravityandinertiain2-year-oldchildren

Overview

Two-year-oldchildrenweretestedwiththeeventspresentedinExperiments1±5,usingavariationofthe

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Perceivingandunderstandingobjectmotion349

preferentiallookingmethodfromthoseexperiments,tailoredtothisage.Experiment6usedtheeventsofExperiment1andinvestigatedwhether2-year-oldchildrenimplicitlyappreciatethatanobjectthatrollsoffaninclinedsupportingsurfaceshouldincreaseitsdownwardmotionandfollowaparabolicpath.BecausethefindingsofExperiment6werenegative,Experiment7usedtheeventsofExperiment2andinvestigatedwhethersuchchildrenimplicitlyappreciatethatanobjectthatrollsoffahorizontalsupportingsurfaceshouldbegintomovedownward,inaccordwithgravity.Finally,Experiment8usedtheeventsofExperiment5andinvestigatedwhether2-year-oldchildrenimplicitlyappreciatethatanobjectthatrollsoffasupportingsurfaceshouldcontinueinsomeforwardmotion,inaccordwithinertia.Experiment6

Experiment6wasareplication,withmodifications,ofExperiment1.Twoseparategroupsof2-year-oldchildrenwerefamiliarized,onthreetrials,eitherwithaneventinwhichaballrolledonafullinclinedplanewithanacceleratingmotion,asinExperiment1,orwithaneventinwhichaballwasreleasedbesideatruncatedplaneandunderwentaverticalfree-fallmotion,asinExperiment4.ThenalltheinfantsweretestedwiththetwotesteventsofExperiment1,inwhichtheballrolledoffthetruncatedplaneandcontinuedtomoveeitheronaparabolicpath(natural)oronastraightpath(inconsistentwithgravity).Asintheexperimentswithinfants,lookingtimestothetestdisplaysweremeasuredandcomparedtodeterminewhetherthechildrentendedtolooklongerattheunnaturaltestmotion.Method

ThemethodwasthesameasinExperiment1exceptasfollows.

SubjectsParticipantswere13maleandthreefemalechildrenranginginagefrom2years1monthto2years11months(M󰂈2years6months).Twoadditionalchildrenweretestedandeliminatedfromtheexperimentbecauseofexperimentererror(one)orparentalinter-ference(one).

DisplaysanddesignHalfthechildrenwerefamiliarizedwiththehabituationdisplayofExperiment1andhalfwiththehabituationdisplayofExperiment4.AllthechildrenweretestedwiththetestdisplaysofExperiment1,withhalfthechildrenineachfamiliarizationconditionviewingtheunnaturaltestdisplayfirst.Prior

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tofamiliarizationandtest,childrenviewedtheappro-priateintroductorydisplaysfromExperiments1and4.ProcedureBeforestartingtheexperiment,theexperi-mentersplayedwiththechildtofamiliarizehimorherwiththenewenvironment.After5to10minutesofplay,heorshewentfortheexperimentwithaparent.Thechildwasseatedonaboosterseatwithhisorhereyes30inchesfromthesameTVscreenusedwithinfants.Theparentwasaskedtostandbehindthechildsothatheorshefeltsecurebutwasaskednottotalkorlookatthedisplay.

Asintheexperimentswithinfants,childrenwerepresentedwithavideotapedintroductorydisplayforabout10s.Thentheywereshownthreetrialsofthefamiliarizationdisplay.(Threetrialswereusedratherthanafullhabituationsequencebecause2-year-oldchildrenappearedtobecomeboredwiththeeventsmorequicklythaninfants.)Thenthechildrenwereshownthesecondintroductorydisplay,andfinallytheyweretestedwithparabolicandstraighttesteventsasinthestudieswithinfants.

Inter-observeragreementaveraged0.92.Results

MeanlookingtimesforthefamiliarizationandtesttrialsareshowninFigure8.Log-transformedlookingtimesweresubjectedtoa2(Familiarizationcondition)by2(Testorder)by3(Testtrialpair)by2(Testevent:parabolicvsstraight)ANOVA.TheanalysisrevealedmaineffectsofFamiliarizationcondition,F(1,12)󰂈6.44,p`0.05,andTesttrialpair,F(1,12)󰂈26.19,p`0.001:childreninthefree-fallfamiliarizationconditionlookedsignificantlylongerduringthetestsequencethanthoseinthestraight-acrosscondition,andallchildrentendedtolooklongestonthefirstpairoftesttrials.TherewasnoeffectofTestevent,F(1,12)`1:childrenlookedequallyattheeventsthatwereconsistentversusinconsistentwithgravity.Aseparateanalysiswithfree-fallfamiliarizationconditiongrouponlyagainrevealednoeffectofTestevent,F(1,7)`1.Discussion

Like7-month-oldinfants,the2-year-oldchildrenwhowerepresentedwithaballthatrolledoffacliffshowednopreferenceforanunnatural,linearmotionoveranatural,parabolicmotion.Theexperimentthereforeprovidesnoevidencethatthechildrenweresensitivetotheeffectofgravityinthissituation.Thenextexperimentaccordinglytestedwhether2-year-oldchil-

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350In-KyeongKimandElizabethS.Spelke

Method

ThemethodwasthesameasExperiment6,exceptasfollows.Participantswere15maleandninefemalechildrenranginginagefrom1year9monthsto2years10months(M󰂈2years3months).Threeadditionalchildrenfailedtocompletetheexperimentbecauseoflackofinterest(one)orparentalinterference(two).DisplayswerethesameasExperiments2and4.Results

LookingtimesduringthefamiliarizationandtesttrialsarepresentedinFigure9andwereanalyzedasinExperiment6.Therewasnosignificantdifferencebetweenthetwofamiliarizationgroups,F(1,22)`1.TheonlysignificantfindingintheanalysiswasamaineffectofTestorder,F(1,20)󰂈29.75,p`0.001:lookingtimedeclinedoversuccessivepairsoftesttrials.Inparticular,therewasnoeffectofTestevent,

Figure8Meanlookingtimesduringthelastthree

familiarizationtrialsandthesixtesttrialsbythe2-year-oldchildreninExperiment6.

drenaresensitivetogravityinthesimplersituationofExperiment2,inwhichanobjectrollsoffahorizontalcliffandeithercontinuesinhorizontalmotionorbeginstomovedownward.

Experiment7

Experiment7wasareplicationofExperiments2and4witholderchildren.Separategroupsof2-year-oldchildrenwerefamiliarizedwithaneventinwhichaballeitherrolledonaflatplane,undergoingfullyhorizontalmotion,orfellthroughtheairtothesideofatruncatedplane,undergoingvertical,free-fallmotion.Thenallthechildrenweretestedwitheventsinwhichtheballrolledofftheflat,truncatedplaneandcontinuedeitheronaparabolicpath(natural)oronalinear,horizontalpath(unnatural).If2-year-oldchildrenexpectanobjecttobegintomovedownwardwhenitlosesitssupport,thenthechildrenshouldhavelookedlongerattheunnaturallineartestevent.

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Figure9Meanlookingtimesduringthelastthree

familiarizationtrialsandthesixtesttrialsbythe2-year-oldchildreninExperiment7.

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Perceivingandunderstandingobjectmotion351

F(1,20)`1:childrenshowednolookingpreferencefortheunnaturalevent.Discussion

Two-year-oldchildrenshowednoreliablelookingpreferencesbetweeneventsinwhichaballrolledoffahorizontalcliffandcontinuedinnaturalparabolicmotionorunnaturallinearmotion.Theirlookingpatterns,likethoseofthe7-month-oldinfantsinExperiments2±4,thereforeprovidenoevidencethat2-year-oldchildrenaresensitivetothiseffectofgravityonobjectmotion.Thenextexperimentinvestigatedwhether2-year-oldchildrenaresensitivetotheeffectofinertiaonobjectmotioninthissituation.Experiment8

Experiment8wasareplicationofExperiment5witholderchildren.Separategroupsof2-year-oldchildrenfirstwerefamiliarizedwitheventsinwhichanobjectrolledonaninclinedplaneorfellthroughtheair,asinExperiment6,andthenweretestedwitheventsinwhichtheobjectrolledoffatruncatedinclinedplaneandeithercontinuedonaparabolicpath(natural)orturnedabruptlyandmovedonastraight-downpath(incon-sistentwithinertia).If2-year-oldchildrenaresensitivetoinertia,theyshouldlooklongerattheunnaturalevent.Iftheyfailtounderstandthiseffect,theyshouldlookequallyatthetwotestevents.Method

Participantswere12maleand12femalechildrenranginginagefrom1year11monthsto2years8months(M󰂈2years3months).Threeadditionalchildrenwereeliminatedfromtheexperimentbecauseofparentalinterference(two)orotherdistractions(one).FamiliarizationdisplayswerethesameasinExperiment6,testdisplayswerethesameasinExperiment5,andtheprocedurewasthesameasinExperiments6and7.Inter-observeragreementaveraged0.92.Results

MeanlookingtimesforthefamiliarizationandtesttrialsareshowninFigure10.Log-transformedlookingtimeswereanalyzedasinExperiments6and7andrevealedasignificanteffectofTestevent,F(1,20)󰂈19.76,p`0.001:2-year-oldchildrenlookedreliablylongeratthestraight-downeventthanattheparabolicevent.Childrenexhibitedasignificantpreferenceforthe

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straight-downeventbothafterfamiliarizationwiththefree-fallmotion,F(1,10)󰂈10.51,p`0.05,andafterfamiliarizationwiththestraight-acrossmotion,F(1,10)󰂈9.25,p`0.05.TheonlyothersignificanteffectwasamaineffectofTesttrialpair,F(1,20)󰂈17.17,p`0.005:lookingtimedeclinedoverthetestsequence.Discussion

Afterfamiliarizationwitheitherslantedlinearorfree-fallmotion,2-year-oldchildrenlookedlongeratatesteventinwhichtheballrolledoffacliff,abruptlyturned,andcontinuedonastraight-downpaththanataneventinwhichitrolledoffthecliffandcontinuedinparabolicmotion.Despitethesuperficialfamiliaritytothestraight-downeventfortheinfantsfamiliarizedtofree-fallmotion,childrenrespondedtothestraight-downeventasmorenovelorunexpected.Theyseemedtoperceivetheparaboliceventasmorefamiliarorexpected

Figure10Meanlookingtimesduringthelastthree

familiarizationtrialsandthesixtesttrialsbythe2-year-oldchildreninExperiment8.

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352In-KyeongKimandElizabethS.Spelke

thantheabruptlyturningeventinwhichtheobjectbegantomovestraightdownward.

Thisexperimentprovidesevidencethatinfantsaresensitivetooneeffectofinertiaonthemotionofanobjectthatrollsoffasupportingsurface:theobjectshouldcontinueinforwardmotionofsomekindandnotturnabruptlydownward.TogetherwithExperiment5,thestudiessuggestthatthissensitivitydevelopsbetween7monthsand2yearsofage.ThissuggestionisconsistentwiththefindingsofSpelkeetal.(1994),usingapreferentiallookingmethodwithpartlyoccludeddisplays,whofoundthatsensitivitytotheeffectofinertiaonthemotionofanobjectonahorizontalplanebeginstodeveloponlyafter6monthsofageandisnotcompleteat12months.Itcontrastswiththefindingsofexperimentsusingapredictivereachingmethod,however:By6months,infantsaimtheirreachingforafullyvisible,movingobject,atpositionsthatareconsistentwiththecontinuedforwardmotionoftheobject(vonHofstenetal.,1998).Sensitivitytoinertiaappearstodevelopslowly,andperhapsinatask-specificmanner.

Discussionofthestudiesof2-year-oldchildren

Experiments6,7and8provideevidencethat2-year-oldchildrenhavedevelopedsomeknowledgeaboutthebehaviorofanobjectthatrollsoffasupportingsurfaceandcontinuesmovinginfreefall,buttheysuggestthatthechildren'sknowledgeisnotcomplete.Althoughsuchanobjectisexpectedtocontinueinsomeforwardmotion,bothnaturalparabolicmotionandunnaturallinearmotionappeartobeequallyacceptabletothechildren.Thesefindingsunderscorethegradual,piece-mealnatureofchildren'sdevelopingknowledgeofconstraintsonobjectmotion.

ThepositivefindingsofExperiment8contrastwiththenegativefindingsofKaiseretal.(1985),usingolderchildrenandadifferentmethod.Childrenaged412to12yearswereaskedtopredictthetrajectoryofaballrolledofftheedgeofatableandthatofaballdroppedfromamovingmodeltrain.Mostpreschoolandkindergartenchildrenjudgedthattheballwouldfallstraightdown.Thiserroneousjudgmentcontrastswith2-year-oldchildren'ssuccessfulperformanceinExperiment8,suggestingadivergencebetweenchildren'sperceptionandjudgments.Nevertheless,theexperimentsbyKaiseretal.(1985)differedfromExperiment8inanumberofrespects,includingtheageofthesubjectsandspecificfeaturesofthedisplays.Inthenextexperiments,wecomparechildren'sperceptionsandjudgmentsmoredirectly,usingthesamedisplaysforbothtasks.

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ThenegativefindingsofExperiments6and7contrastwiththefindingsfromourinitialstudywithadults,whoviewedthesameeventspresentedtochildrenandjudgedtheirnaturalness.Becauseadultsfindthecontinuedlinearmotiontobeunnatural(Figure2),thenegativefindingswith2-year-oldchildrensuggestthatknowledgeofobjectmotioncontinuestodevelopafter2yearsofage.Nevertheless,thestudywithadultsusedadifferentmeasurethanExperiments6±8(verbaljudgmentratherthanpreferentiallooking),complicatingthecomparisonacrossstudies.Experiments9±13addressthisproblem.Finally,thenegativefindingsofExperiments6and7contrastwiththefindingsofexperimentsbyHood(1995),investigating2-to4-year-oldchildren'ssensitiv-itytogravityineventsinwhichaballtraveleddownwardthroughacurvedtube.Hoodpresentedchildrenwitheventsinwhichaballwasdroppedintoacurved,opaquetube.Askedwheretheballlanded,childrenpointedreliablytoapositiondirectlybelowitspointofrelease,suggestingsensitivitytotheeffectofgravityontheobject'smotion.Children'sperformanceinHood'sexperiment,likeinfants'successfulperfor-manceintheexperimentsofKimandSpelke(1992)andothers,furthersuggeststhatsensitivitytogravitydevelopsinapiecemealfashion.Nevertheless,theexperimentsbyHooduseddifferentdisplaysandadifferentmeasurethanthepresentstudies,makingcomparisonsacrossthestudiesproblematic.Thenextexperimentsinvestigatethecontinueddevelopmentofsensitivitytoconstraintsonobjectmotionusingthesamesetofperceptionandjudgmenttaskswithchildrenaged3±6years.

Perceptionandjudgmentsabouteffectsofgravityandinertiain2-to6-year-oldchildren

Thefinalexperimentsexplorethetask-specific,piece-mealnatureofchildren'sknowledgemoredirectly,inolderchildren.Threedifferenttaskswereusedtotest3-to6-year-oldchildren'ssensitivitytotheeffectsofgravityandinertiaonthemotionofanobjectthatrollsoffacliff.InExperiments9,10,11and12,childrenwerepresentedwiththevideotapedeventsfromthepreviousexperiments,theyparticipatedinthesamepreferentiallookingexperimentsasdidthe2-year-oldchildreninExperiments6±8,andtheywerealsoasked,attheendofthestudy,whicheventspresentedmotionthatwas`silly'.InExperiment13,childreninfiveagegroups,from2yearsto6years,werepresentedwitharealballandthree-dimensionaltruncatedcliffandwereaskedtopredictwheretheballwouldlandafterrollingoffthecliff.

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Perceivingandunderstandingobjectmotion353

Experiment9

Experiment9investigatedwhether3-to4-year-oldchildrenimplicitlyappreciatethataballmovingdown-wardonaslantedsurfaceshouldincreaseitsdownwardmotionifitmovesoffthesurface.TheexperimentusedthesamemethodasExperiment6,withoneinnovation:attheendofthepreferentiallookingexperiment,childrenwereshowneachofthetesteventsforonefinal,briefviewingandwereaskedwhicheventpresentedmotionthatwasunnatural.Method

ThemethodwasthesameasinExperiment6exceptasfollows.Participantswerefivefemaleand11malechildrenranginginagefrom3years1monthto4years10months(M󰂈3years9months).Threeadditionalchildrenfailedtocompletetheexperimentbecauseofexperimentererror.Childrenwerepresentedwiththesamefamiliarizationandtestevents(straight-acrossandparabolicmotions)asinExperiment6,followingexactlythesamelookingtimeprocedureasforthatexperiment.Afterviewingthetesteventsonsixtrials,theywereshowneachtestdisplayforonefinaltimeandwereaskedwhichwas`okay'andwhichwas`silly'.Results

MeanlookingtimesforthetesttrialsareshowninFigure11.Log-transformedlookingtimeswereana-lyzedasinExperiments6±8andrevealedonlyamaineffectofTesttrialpair,F(1,12)󰂈8.97,p`0.05,indicatingthatlookingtimedeclinedovertheseriesoftesttrials.TherewasnoeffectofTestevent,F(1,12)`1.

Onthejudgmenttask,eightchildrensaidtheunnaturaleventwassilly,andeightchildrensaidthatthenaturaleventwassilly;binomialpb0.4.Thosewhosaidtheunnaturaleventwassillywerenomorelikelytoshowavisualpreferencefortheunnaturaleventthanthosewhosaidthenaturaleventwassilly(respectively,fourandfiveoftheeightchildrengivingeachjudgmentlookedlongerattheunnaturalevent).Discussion

Experiment9providednoevidencethat3-to4-year-oldchildrenimplicitlyexpectanobjectmovingdownwardonaslantedsurfacetoincreaseitsdownwardmotionwhenitmovesoffthesurface.Neitherthelookingtimemethodnorthejudgmentmethodprovidedevidenceforanyconsistentreactiontotheimpossible,lineartestevent.Like7-and24-month-oldinfants,3-year-oldchildrenthereforeshownosignsofsensitivitytothiseffectofgravityonobjectmotion.Accordingly,thenextexperimentinvestigatedwhether3-to4-year-oldchil-drenimplicitlyexpectahorizontallymovingobjecttobeginmovingdownwardwhenitlosesitssupport.Experiment10

ThenextexperimentusedthemethodofExperiment9withtheeventsofExperiments2,4and7,eventsinwhichanobjectrolledoffahorizontalsurfaceandeitherbegantomovedownwardonaparabolicpath(natural)orcontinuedinhorizontalmotion(contrarytogravity).Method

Participantswereeightmaleandsixfemalechildrenranginginagefrom3years1monthto4years10months(M󰂈3years8months).Nosubjectwaseliminatedfromthesample.ThemethodwasthesameasExperiment9.Results

MeanlookingtimesforthetesttrialsareshowninFigure12andwereanalyzedasinExperiment9.TheanalysisrevealedamaineffectofTesttrialpair,F(1,10)󰂈40.95,p`0.001,indicatingthatchildrenlookedlongerontheearliertesttrials,butnoeffectofTestevent,F(1,10)󰂈1.81,pb0.2.

Onthejudgmentmeasure,eightchildrensaidtheunnatural(straight-across)eventwassilly,foursaidthenaturaleventwassilly,onesaidthatneithereventwassilly,andonerefusedtoanswerthequestion.Althoughtheseresponsestendedtogointhecorrectdirection,

Figure11Meanlookingtimesduringthesixtesttrialsbythe3-to4-year-oldchildreninExperiment9.

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354In-KyeongKimandElizabethS.Spelke

months(M󰂈5years9months).Oneadditionalparticipantwaseliminatedbecauseofexperimentererror.Results

MeanlookingtimesforthetesttrialsareshowninFigure13andwereanalyzedasinExperiment9.TheanalysisrevealedasignificanteffectofTesttrialpair,F(1,11)󰂈16.37,p`0.005:lookingtimedeclinedovertheseriesoftesttrials.Inaddition,therewasamarginallysignificanteffectofTestevent,F(1,11)󰂈3.37,p󰂈0.09:childrentendedtolooklongerattheunnaturallinearmotion.

Onthejudgmentmeasure,11childrensaidthattheunnaturaleventwassilly,andfoursaidthenaturaleventwassilly.Thisdifferencewasmarginallysignifi-cant;p`0.06,binomialtest.

Afurther2(Age)by2(Habituationcondition)by2(Testorder)by3(Trialpair)by2(Testevent)analysiscomparedthelookingtimesofthe5-to6-year-oldchildreninExperiment11withtothoseofthe3-to4-year-oldchildreninExperiment10.TheresultsshowedamaineffectofTestevent,F(1,21)󰂈4.56,p`0.05:childrenlookedlongerattheunnaturalevent.TherewasalsoamaineffectofTrialpair,F(1,21)󰂈45.85,pb0.001,andaninteractionofTesteventbyTestorder,F(1,21)󰂈4.86,p`0.05.Botheffectsreflectedthedeclineinlookingovertheseriesoftesttrials.TherewasnointeractionofAgebyTestevent,F(1,21)`1.Five-to6-year-oldchildren'slookingtimesforthenaturalandunnaturaleventswerenotsignificantlydifferentfromthoseof3-to4-year-oldchildren.

Figure12Meanlookingtimesduringthesixtesttrialsbythe3-to4-year-oldchildreninExperiment10.

theydidnotdiffersignificantly;p󰂈0.19,binomialtest.Judgmentsandpreferentiallookingpatternsagainshowednosystematicrelation:longerlookingattheunnaturaltesteventwasshownbyfiveoftheeightchildrenwhosaidtheunnaturaleventwassillyandbythreeofthefourchildrenwhosaidthenaturaleventwassilly.Discussion

LikeExperiment9,Experiment10providesnoclearevidencethat3-to4-year-oldchildrenreacttotheperceptiblemotionofanobjectasmoreunnaturaliftheobjectcontinuesinlinearmotionafterleavingasupportingsurface,relativetonaturalparabolicmotion.Nevertheless,Experiment10showedatrendinthecorrectdirectiononthejudgmentmeasure,suggestingthatsensitivitytotheeffectsofgravitymaybedevelopingoverthisagerange.Experiment11thereforetested5-and6-year-oldchildreninthesamesituationasExperiment9.Experiment11

Experiment11investigatedwhether5-to6-year-oldchildrenimplicitlyappreciatethatanobjectthatrollsoffaslantedcliffshouldincreaseitsdownwardmotion.Method

TheexperimentusedthesamemethodasExperiment9.Participantswereninemaleandsixfemalechildrenranginginagefrom5years0monthsto6years11

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Figure13Meanlookingtimesduringthesixtesttrialsbythe5-to6-year-oldchildreninExperiment11.

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Afinalanalysiscomparedthejudgmentsofthe5-to6-year-oldchildreninExperiment11withthoseofthe3-to4-year-oldchildreninExperiment10.Overall,19childreninthetwostudiesjudgedthattheunnaturaleventwassillywhereaseightjudgedthatthenaturaleventwassilly±asignificantdifference,p`0.02,binomialtest.Judgmentsatthetwoagesdidnotdiffer,pb0.20,Fisherexacttest.Discussion

ThefindingsofExperiment11,togetherwiththoseofExperiments1±10,suggestthatsensitivitytothenaturalparabolictrajectoryoftheballbeginstodevelopbetween3and6yearsofage.Five-to6-year-oldchildrentendedtojudgethattheunnaturallinearmotionwassillierthanthenaturalparabolicmotion,andtheytendedtolooklongerattheunnaturaltestevent.Althoughneithertendencywasstrongenoughtoreachsignificancewithinthissample,bothtendenciesweresignificantwhenthedatafromthe5-to6-year-oldchildrenwerecombinedwiththoseofthe3-to4-year-oldchildreninExperiment10,whoweretestedwiththesameevents.Incontrast,7-month-oldinfantsand2-year-oldchildrenshowednosensitivitytotheeffectsofgravityintheseeventswhentheyweretestedwiththepreferentiallookingmethod.Thesefindingssuggestthatsensitivitytooneeffectofgravityisemergingbetween2and6yearsofage,with3±4yearsasatimeoftransition.

Nevertheless,thissuggestionmustbequalifiedbytwoquestionsaboutthepresentmethods.First,concerningthejudgmenttask,dochildrenshowgraduallyemergingreactionstotheviolationofgravitybecausetheirsensitivitytotherelevanteffectsofgravityemergesslowlyorbecausethejudgmenttaskitselfonlyslowlybecomesasensitivemeasureofchildren'sknowledge?Perhapsthe3-to6-year-oldchildreninthepresentstudieshadhighlyconsistentreactionsofsurprisetotheunnaturaltestevent,buttheirresponseswerenothighlyconsistentwithineachagegroupbecausechildrendidnotunderstandourquestionsaboutthenaturalnessofobjectmotionorfailedtocommunicatetheiranswerseffectively.Second,concerningthelookingtimemethod,whydidchildrennotshowmorerobustsensitivitytotheeffectsofgravityintheirlookingtimes?Doestheweaknessofthelookingpreferenceswithineachofthetwoagegroupsstemfromtheweaknessofchildren'ssensitivitytogravity,orfromlimitstoourpreferentiallookingmethodattheseages?

Experiment12wasundertaken,inpart,toaddressboththesequestions.InExperiment12,3-to4-year-oldchildrenwerepresentedwiththeeventsofExperiments5

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and8,eventsinwhichanobject'smotioneitherwasnaturalorfailedtoaccordwithinertia.AsinExperi-ments8±10,lookingtimesweremeasuredtothenaturalandunnaturalevents.AsinExperiments9±11,judg-mentsaboutthenaturalnessofobjectmotionwereelicitedaswell.Becausethe2-year-oldchildreninExperiment8hadshownrobustreactionstotheimpossibletestevent,wereasonedthat3-and4-year-oldchildrenalsowouldbesensitivetothisevent.Theirreactionsonthepreferentiallookingandjudgmenttasksthereforecouldserveasameasureoftheeffectivenessofthetasks.Ifthejudgmentmethodisrelativelyinsensitiveattheageswehavetested,then3-to4-year-oldchildrenshouldfailtoshowsensitivitytoinertiabythejudgmentmethod.Ifthepreferentiallookingmethodislesseffectiveatolderthanatyoungerages,becauseolderchildrenarelessengagedbytheeventsandthereforeshowconsistentlookingpatterns,then3-to4-year-oldchildrenshouldfailtoshowsensitivitytoinertiabythepreferentiallookingmethod.Incontrast,ifagivenmethodisappropriateatthisage,then3-to4-year-oldchildren,liketheyoungerchildreninExperiment8,shouldgiveevidenceofsensitivitytoinertiawhentestedbythatmethod.

Experiment12Method

Experiment12usedtheeventsofExperiment8andthemethodofExperiments9±11.Participantsweresevenmaleandeightfemalechildrenranginginagefrom3years0monthsto4years10months(M󰂈3years11months).Nofurthersubjectsweretestedandeliminated.

Results

MeanlookingtimesforthetesttrialsareshowninFigure14andwereanalyzedasinthepreviousexperiments.Theanalysisrevealednosignificanteffects:inparticular,noeffectofTestevent,F`1.Onthejudgmenttest,tenchildrensaidtheunnatural(straight-down)eventwassilly,threesaidthenaturaleventwassilly,andtworefusedtoanswer.Analysisofthosechildrengivinganswersrevealedareliabledifferenceinchildren'sjudgmentsforthetwoevents,p`0.05,binomialtest.Longerlookingattheunnaturaleventwasshownbyfiveofthetenchildrenwhosaidtheunnaturaleventwassillyandbyoneofthethreechildrenwhosaidthenaturaleventwassilly.

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356In-KyeongKimandElizabethS.Spelke

Figure14Meanlookingtimesduringthesixtesttrialsbythe3-to4-year-oldchildreninExperiment12.

Discussion

The3-to4-year-oldchildreninthisexperimentlookedequallyataneventinwhichanobjectthatrolledoffacliffcontinuedinnaturalparabolicmotionandaneventinwhichtheobjectchangeditsmotionabruptlyandfellstraightdownward,contrarytoinertia.Incontrast,thechildrenreliablyjudgedthatthefirsteventwas`okay'andthesecondeventwas`silly'.Thechildrenthereforeshowedsensitivitytoinertiabythejudgmentmeasurebutnotbythepreferentiallookingmeasure.

Concerningthepreferentiallookingmeasure,thepresentfindingscontrastwiththoseofExperiment8:2-year-oldchildren,testedwiththesamepreferentiallookingmethodandevents,lookedreliablylongeratthetesteventthatwasinconsistentwithinertia.Itisunlikelythatthisagedifferencereflectsanydeclinewithageinsensitivitytoinertia,bothbecausesuchadeclinewouldbeinherentlyimplausible,givenchildren'sexperiencewithnaturallymovingobjects,andbecausetheolderchildrenshowedcontinuedsensitivitytoinertiabythejudgmentmeasure.Weconcludethatthepresentversionofthepreferentiallookingmethod,usedwiththepresentdisplays,islesssensitiveattheolderage.Olderchildren'sincreasedrestlessnessandimpatiencewiththesimplerepeatedeventsofthisstudyprobablyaccountforthisagedifference.

ThepresentfindingscastlightonthefindingsfromthepreferentiallookingmethodinExperiments10and11.Asagroup,the3-to6-year-oldchildreninthoseexperimentsjudgedsignificantlythatthelineartesteventwaslessnaturalthantheparabolicevent,andthechildrenshowedconsistentlookingpreferencesbetweentheevents,butneithertendencywasstrong.Giventhe

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presentevidencethatthepreferentiallookingmethodislesssensitiveatolderages,theweakfindingsfromthatmethodinExperiments10and11probablystemfromlimitsonthepresentpreferentiallookingmethodratherthanfromlimitson5-to6-year-oldchildren'ssensitivitytogravity.

Thepresentfindingsalsocastlightonthegradualdevelopmentofsensitivitytogravitysuggestedbychildren'sjudgmentsinExperiments10and11.Althoughthe3-to6-year-oldchildrentogethershowedsignificantjudgmentsinaccordwithgravity,theirjudgmentsalsowerenotconsistentenoughtobesignificantateitheragealone.Wenotedpreviouslythatthisfinding,byitself,couldreflecteithertheslowdevelopmentofsensitivitytogravityoranincrease,withage,inthesensitivityofthejudgmenttask.Inthepresentexperiment,however,3-to4-year-oldchildrengaveconsistentjudgmentsaboutthenaturalnessofobjectmotioninrelationtoinertia,castingsomedoubtonthelatterpossibility.Weconcludethatsensitivitytotheeffectofgravityonthemotionofanobjectthatrollsoffacliffincreasesgraduallyoverthepreschoolyears.Finally,thepresentfindingssupporttheprincipalconclusionsfromExperiments1±8:children'ssensitivitytotheeffectsofgravityandinertiaonamovingobjectthatlosesitssupportdevelopslowly,withsensitivitytoinertiaprecedingsensitivitytogravity.InExperiments6±8,2-year-oldchildrentestedwiththepreferentiallookingmethodlookedlongeratanunnaturaleventinwhichanobjectabruptlyturnedafterrollingoffacliff,contrarytoinertia,buttheylookednolongeratanunnaturaleventinwhichtheobjectcontinuedinlinearmotion,contrarytogravity.InExperiments9,10and12,3-to4-year-oldchildrentestedwiththejudgmentmethodshowedsensitivitytotheunnaturalnessoftheabruptturningoftheobject,contrarytoinertia,butasagrouptheydidnotshowconsistentreactionstotheunnaturalnessofthecontinuedlinearmotionoftheobject,contrarytogravity.Thecommonpatternsoffindingsacrossthesestudiessuggestthatboththepreferentiallookingmethodandthejudgmentmethodtapacommonsystemofknowledgeofobjectmotion.Bothmethods,however,assesschildren'sreactionstofullyvisibleobjectmotions.Doesthesamesystemofknowledgeguidechildren'spredictionsorinferencesaboutobjectmotionsthatarenotdirectlyvisible?Experiment13

Thefinalexperimentinvestigated3-to5-year-oldchildren'sunderstandingofobjectmotionusingadifferentjudgmenttask,focusingontheirpredictionsaboutthefuturemotionofanobject.Childrenwere

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presentedwitharealthree-dimensionalslantedrampwiththeshapeofthetruncatedrampinthetesteventsofExperiments1and6±8.Ahand-heldballwasplacedatthehighendoftheramp,whereitwasreleasedandallowedtorolldowntheramp,butitwascaughtattheendoftherampandsounderwentnofreefall.Childrenwereaskedwheretheballwouldlandifitwerenotcaughtandinsteadrolledofftheramp.

Ifsubjectshadjudgedwithoutconstraintwheretheobjectwouldland,thenthepresenttaskwoulddifferfromthepreviousonesintwogeneralrespects:itwouldassesspredictionsaboutmotionsthechildhadnotseenratherthanreactionstoperceivedmotions,anditwouldpresentthechildwithamuchlargernumberofresponseoptions(essentiallyaninfinitenumber,becausetheballcouldlandanywhere).Becausewewishedtofocusonthefirstdifference,weattemptedtomaketheresponseoptionsavailabletochildreninExperiment13moresimilartothoseavailabletochildreninExperiments9±12.Accordingly,childrenwereshownjustthreeloca-tionswheretheballcouldland,eachcorrespondingtooneofthethreemotionstestedinthepreviousexperiments.Childrenweretoldtheballwouldlandinoneofthesethreepositionsandwereaskedtochoosethecorrectone.Method

SubjectsParticipantswere(a)twomaleandsixfemalechildrenranginginagefrom2years1monthto2years11months(mean2years7months),(b)fivemaleandthreefemalechildrenranginginagefrom3years3monthsto3years11months(mean3years6months),(c)twomaleandsixfemalechildrenfrom4years3monthsto4years11months(mean4years7months),(d)threemaleandfivefemalechildrenfrom5yearsto5years11months(mean5years3months),and(e)fourmaleandfourfemalechildrenfrom6years2monthsto6years11months(mean6years6months).

DisplaysFigure15depictsthedisplayusedinthisexperiment.Arampofredfoamboard(41cmwideÂ66.5cmhigh)slantedby15󰀎wasattachedbywhiteinvertedL-shapedfoamboard(49cmwideand61cmhigh).InthatL-shape,threeholes(10cmindiameter)weremadeonthefinalpositionofthestraight,parabolic,orstraight-downpath:thedistancesbetweentheedgeoftherampandthecentersoftheholeswere5cm,30cmand55cm(45cminheight),respectively.ProcedureAchildwasseatedinfrontofthedisplayandwasshowntheredrampandthethreeholesinthe

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Figure15SchematicdepictionoftheapparatususedforExperiment13.

L-shape.AyellowNerfball(6cmindiameter)wasplacedatthelefttopoftheramp;itwasreleasedbytheexperimenter'srighthandandcaughtattherightendoftherampbytheexperimenter'slefthand.Thechildwaspresentedthissameeventfourtimes.Thenthechildwasaskedtopointtowhichholetheballwouldlandinafterrollingofftheedgeoftheramp.Hisorheranswerwasrecorded.Results

Figure16presentsthepercentageofparticipantsofeachagegroupwhogaveeachofthethreeanswers.Eightoutofeightchildrentestedat2,3and4yearschosethestraight-downposition:eachbinomialp`0.001.At5years,fourchildrenchosethestraight-downposition,threechosetheparabolicposition,andonechosethestraight-acrossposition,binomialpb0.20.At6years,sevenchildrenchosethecorrect,parabolicpositionandonechosethestraight-downposition,binomialp`0.005.Comparisonsacrossthedifferentagesre-vealedasignificantchangebetween4and5years,12(2)󰂈5.3,p`0.05,andbetween4and6years,12(1)󰂈12.44,p`0.005,butnotbetween5and6years,12(2)󰂈4.4,p󰂈0.11.Discussion

The2-,3-and4-year-oldchildrenconsistentlyjudgedthattheballwouldlandinthestraight-downhole,asiftheyexpectedtheobjecttomovestraightdownward.Althoughthisexpectationshowssomesensitivitytogravity,itshowsnosensitivitytoinertia:theyoungerchildrendidnotjudgethattheobjectwouldcontinuemovingforwardasitfell.Incontrast,the6-year-old

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358In-KyeongKimandElizabethS.Spelke

Figure16Percentageofchildrenjudgingthattheballwouldlandinthecorrectparaboliclocation,thestraight-downlocation(contrarytoinertia)orthestraight-acrosslocation(contrarytogravity)ateachagefrom2to6years.

childrenconsistentlyjudgedthattheballwouldlandintheparabolichole,asiftheyexpectedtheobjecttomovebothforwardanddownward.Fiveyearsappearstobeatransitionalagebetweentheyoungerandolderpattern.ThepresentexperimentreplicatesthefindingofKaiseretal.(1985)thatyoungchildrentendtopredictthatanobjectthatmovesoffasupportwillbegintomovestraightdownward,contrarytoinertia.Inthepresentstudy,however,childrengavecorrectpredic-tions,inaccordwithinertia,atayoungeragethaninKaiseretal.'s(1985)study,wheremanychildrencontinuedtomakestraight-downpredictionswellintotheearlyschoolyears.Proceduraldifferencesbetweentheseexperimentsmayaccountfortheirdifferentfindings.First,wepresentedchildrenwithafreelymovingobjectthatwascaughtbyahandbeforerollingoffacliff,whereasKaiseretal.presentedaballthatrolledinsideaclearplastictubeandstoppedattheendofthetubebecausetheendwasblocked.Children'sjudgmentsaboutobjectmotionmaybelessaccurateinthelattersituation(seeHood,1995).Second,weconstrainedchildren'spredictionstothreelocationsbypresentingthreefixedindentationsthataballcouldenterandaskingthemtochoosetheonewheretheballwouldland.Incontrast,Kaiseretal.(1985)presenteda

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movablecupandaskedchildrentoplacethecupattheplacewheretheyjudgedtheballwouldland.Ourtaskmayhavefacilitatedchildren'sjudgmentsbothbycallingtheirattentiontothecorrectparaboliclocationandbylimitingtheirchoices.

Thepresentexperimenthastwolimitations.First,becausetheexperimentdoesnotassesschildren'spredictionabouttheexactlandingpointoftheobjectbutonlytheirchoiceamongthreecandidatelocations,itisnotasensitivemeasureofbiasinchildren'sjudgments.Itispossible,forexample,thattheolderchildrenwouldhaveunderestimatedtheobject'slandingpositionifgivenalessconstrainedtask(seeKristetal.,1993).Nevertheless,children'sanswersrevealedclearconsistencywithinfourofthefiveagesandacleardevelopmentalchangeacrosstheages.Theconsistencyofchildren'sanswerssuggeststhatthequestionsweresimpleenoughforeventheyoungestchildrentounderstand,allowingcomparisonsofchildren'spercep-tionsandinferencesaboutobjectmotionatagesasyoungas2±3years.

Amoreseriouslimitationofthisexperimentisthatitdidnotfocusontheobject'spathofmotionbutonlyonitsfinalposition.Forthisreason,children'schoiceoftheparabolicholedoesnotnecessarilyimplythattheyexpectedtheobjecttomoveonaparabolicpath:theymighthaveexpectedittofollowadifferentpathtothisfinalposition.Wecannotconclude,therefore,that6-year-oldchildrenexpectedtheobjecttoundergoparabolicmotion.Nevertheless,wecaninferfromtheirjudgmentsthatthe6-year-oldchildrenhadcometoappreciatethattheobjectshouldmovebothforwardanddownward,insomemanner,afterrollingoffthecliff.

DiscussionofExperiments9À13

Experiments9±13investigatedchildren'sdevelopingsensitivitytoeffectsofgravityandinertiaonthemotionofaballthatrollsoffasupport,bymeansoftwonewmethods:aperceptualjudgmentmethodinwhichchildrenreportwhetheragivenvisiblemotionlooksnormalor`silly',andapredictivejudgmenttaskinwhichtheballandsupportarepresentedbutmotionoffthesupportisneverseen,andchildrenareaskedtopredictwheretheballwouldlandifitrolledoffthesupport.Childrengiventheperceptualjudgmenttaskalsoweretestedwiththepreferentiallookingmethod,bothtoensurethattheirexposuretotheeventswascomparabletothatofthechildreninthepreviousexperimentsandtoallowcomparisonoftheresultsobtainedwithdifferentmethods.Unfortunately,thefindingsoftheseexperimentscastdoubtonthe

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usefulnessofthepreferentiallookingmethodwithchildrenabove3yearsofage,atleastforthepresentdisplays.The3-to4-year-oldchildreninExperiment12showednoreliablelookingpreferencebetweenthenaturalmotionandthemotioninconsistentwithinertia,contrarybothtotheirjudgmentsaboutthenaturalnessoftheseeventsandtothelookingpreferencesofthe2-year-oldchildreninExperiment8.Incontrast,bothjudgmentmethodsgaveconsistentandinterpretablefindingsacrossalltheagestested:from3to6yearsfortheperceptualjudgmenttaskandfrom2to6yearsforthepredictivejudgmenttask.Wefocusonthesefindings.

Bytheperceptualjudgmenttask,childrenshowedclearsensitivitytoinertiaattheyoungestagetested.At3to4years,theyjudgedreliablythatthenaturalparabolicmotionwasnormalwhereastheunnaturalmotioninwhichtheobjectabruptlyturneddownwardwasnot.ThesefindingsaccordwiththefindingsofExperiment8usingthepreferentiallookingmethod.Theysuggestthatsensitivitytoinertiaiswellestablishedinyoungchildren,whenthechildrenviewfullyvisibleevents.

Inaddition,theperceptualjudgmenttaskprovidesevidencethatsensitivitytogravitydevelopsslowlyfrom2to6years.Whenchildrenwerepresentedwithaballthatrolledoffaslantedrampandcontinuedineithernaturalparabolicmotionorunnaturallinearmotion,theytendedtojudgereliablythattheparabolicmotionwasmorenaturalbothat3±4yearsandat5±6years,butthistendencywasnotsignificantat3±4years,marginallysignificantat5±6years,andsignificantonlywhenthetwoageswerecombined.Becausethejudgmenttaskgivesreliablefindingsattheyoungeragewhenitisusedtoassesschildren'ssensitivitytoinertia(Experiment12),theweakerfindingsobtainedwhenitisusedtoassesssensitivitytogravitydonotplausiblystemfromlimitstothemethoditself.Instead,3±4yearsappearstobeatransitionalperiodforthedevelopmentofsensitivitytogravityinthepresentsituation.Likethefindingsofthepreferentiallookingexperiments,thesefindingssuggestthatsensitivitytoinertiadevelopsbeforesensitivitytogravityforthepresenteventsandthatsensitivitytogravitydevelopsslowly,inapiecemealfashion.

Thefindingsofthepredictivejudgmenttaskdifferedfromthoseofboththepreferentiallookingexperimentsandtheperceptualjudgmenttaskinsomestrikingrespects.First,theyoungestchildrentendedtorespondmerelyatchanceonthetaskspresentingfullyvisiblemotion(Experiments1±7and9),butyoungchildrenunanimouslygavethewrongresponseonthepredictivejudgmenttask.Thisfindingsuggeststhatchildrenwere

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notsimplyconfusedoruncertain,butrathermiscon-ceivedtheobject'smotiononthepredictivejudgmenttask.Second,children'sresponsesatallagesshowedsensitivitytogravity.At2,3and4yearsofage,childrenunanimouslypredictedthattheobjectwouldmovestraightdownward,inaccordwithgravitybutcontrarytoinertia.Atnoagedidchildrentendtojudgethattheobjectwouldcontinueinlinearmotion,despitethefactthathalfthechildreninExperiment9reported,whenpresentedwiththismotion,thatlinearmotionlookedmorenaturalthanthecorrectparabolicmotion.Third,children'spredictionsshowedsensitivitytoinertiaonlyattheoldestagetested±6years±with5yearsappearingtobeatransitionalagebetweenapureresponsetogravityandaresponsetogravityandinertia.Whereassensitivitytoinertiadevelopedbeforesensitiv-itytogravityontheperceptualjudgmenttask,thereversepatternwasobtainedonthepredictivejudgmenttask.

Thecontrastingdevelopmentalpatternsobservedonthetwojudgmenttasksprovideevidencefora`doubledissociation',overdevelopment,inchildren'sperfor-mance.Thesepatternscannotbeexplainedbyproposingthatonetaskissimplymoresensitivethantheotherorthatknowledgeofonephysicalconstraintissimplystrongerthanknowledgeoftheotherconstraint.Rather,theperceptualjudgmenttaskappearstobeamoresensitivemeasureofknowledgeofinertia,whereasthepredictivejudgmenttaskappearstobeamoresensitivemeasureofknowledgeofgravity.WeconsiderthepossiblesignificanceofthisdoubledissociationintheGeneraldiscussion.

ThefindingsfromthepredictivejudgmenttaskcomplementthoseofKaiseretal.(1985),Hood(1995)andKristetal.(1993).LikethechildreninHood's(1995)experimentandliketheyoungestchildreninKaiseretal.'sexperiments,the2-to5-year-oldchildreninExperiment13tendedtopredictthattheballwouldfallstraightdownwardafterlosingitssupport.LikethechildreninKristetal.'s(1993)experiments,thesechildrenshowedadiscrepancybetweentheirpredictivejudgmentsaboutwheretheballwouldlandandothermeasuresoftheirknowledge(perceptualjudgmentsinourexperiments,predictiveactionsinKristetal.'sexperiments).

Finally,thefindingsofthepredictivejudgmenttaskcomplementHood'sfindingsconcerningchildren'sjudgmentsaboutobjectmotionsinrelationtogravityandsolidity(1994;Hood,Uller&Carey,1996).Hoodpresented2-to4-year-oldchildrenwithadisplaystudiedbySpelkeetal.(1992)withinfants,inwhichaballwasdroppedbehindascreenandeitherlandedonthefirstsurfaceinitspath(consistentwithsolidityandgravity)

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360In-KyeongKimandElizabethS.Spelke

orlandedonthesecondsurfaceinitspath(inconsistentwithsolidity).LikethechildreninExperiment13,thechildreninHood'sexperimentfirstwereshowntheentiredisplayandthenwereaskedtojudgetheball'smotionwithoutseeingitdirectly.IncontrasttoExperiment13,however,childrenwerenotaskedtopredicttheball'sfuturemotionbutratherwereaskedtoinferitshiddenmotion:aftertheballwasdroppedbehindthescreen,childrenpointedtothepositiontheyjudgedittooccupy.Children'sjudgmentswerecon-sistentwithgravity,asinthepresentexperiments.Interestingly,theirjudgmentswerenotconsistentwithsolidity,incontrasttopreviousfindingswithinfantsusingadifferenttaskinwhichtheobject'sinitialmotionpathandfinalpositionwerevisible.Likethepresentstudies,Hood'sfindingsprovideevidenceforadissocia-tionbetweenperceptionandjudgmentat2yearsofage.

Generaldiscussion

Thepresentresearchbeganwiththreequestions.First,whataretheoriginsofknowledgeofeffectsofgravityandinertiaonobjectmotion:doesthisknowledgebeginearlyininfancyordoesitdevelopmoreslowly?Second,howdoesthisknowledgegrow:dochildrenatsomeagegainageneralunderstandingofgravityandinertia±anunderstandingthatallowsthemtomakesenseofobjectmotionindiversesituations±ordotheygraduallyacquiremorepiecemealknowledgeofhowparticularkindsofobjectsmoveunderparticularkindsofcircumstances?Third,whataretheoriginsofthegap,foundinadults,betweenouroftenaccurateperceptualsensitivitytoconstraintsonobjectmotion,ononehand,andouroftenerroneousexplicitjudgmentsaboutobjectmotion,ontheother?

Concerningthefirsttwoquestions,thepresentexperimentsprovideevidencethatsensitivitytotheeffectsofgravityandinertiaonobjectmotiondevelopsslowlyandinapiecemealfashion.Althoughthe7-month-oldinfantsinKimandSpelke's(1992)experi-mentsperceivedthemotionofaballonaninclinedplaneasmorefamiliarornaturaliftheballrolleddowntheplanewithincreasingspeedoruptheplanewithdecreasingspeed,relativetomotiondownwardorupwardwiththeopposite(unnatural)patternofacceleration,thefindingsofExperiments1±5caststrongdoubtonthepossibilitythatthissuccessreflectsanygeneralunderstandingoftheeffectsofgravityandinertia.InExperiments1±5,7-month-oldinfantswerepresentedwitheventsthatdifferedfromthoseofKimandSpelke(1992)injustonesignificantrespect:duringthetesttrials,theballrolleddownwardonatruncated

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ratherthanafullplane.Ifinfantsweresensitivetothegeneral,combinedeffectsofgravityandinertia,theyshouldhaveperceivedtheball'smotion,onleavingtheplane,asmorenaturalorfamiliarifitfollowedaparabolicpath.Contrarytothisprediction,infantsshowednodifferentialreactionstoparabolic,linearorabruptlyturningmotionsoftheball.Thesefindingssuggestthatinfants'successfulperformanceinKimandSpelke's(1992)experimentsdependedonlocal,re-strictedknowledgeaboutobjectmotion.

ThefindingsofExperiments6±12providefurtherevidenceforthegradual,piecemealdevelopmentofsensitivitytotheeffectsofgravityandinertia.When2-year-oldchildrenwerepresentedwiththesameeventsastheinfantsinExperiments1±5,theyreactedtotheparabolicmotionasmorefamiliarornaturalthantheabruptlyturningmotionbutnotasmorenaturalthanthecontinuedlinearmotion.Thesefindings,whichshowsensitivitytotheeffectofinertiabutnotgravityonthecontinuedmotionoftheball,suggestthatthechildrenwerepartiallybutnotcompletelysensitivetotheappropriatemotionoftheballafteritrolledoffitssupport.Finally,whenchildrenaged3±4and5±6yearswerepresentedwiththeseevents,theyreactedtotheparabolicmotionasmorefamiliarornaturalthaneitheroftheothertwomotions,butthesefindingswerereliableonlywhenthetwoagegroupswerecombined.Sensitivitytotheeffectsofgravityandinertiaonthemotionofafullyvisibleballthatrollsoffitssupportthereforeappearstodevelopslowlyoverthefirstsixyears.

Concerningthethirdquestion,thefindingsofthepresentexperimentssupporttwosuggestionsabouttheoriginsandnatureofthegapbetweenperceptionsofandjudgmentsaboutobjectmotion.First,thisgapdoesnotappeartoemergewiththedevelopmentofexpertisefromaninitiallyunitaryandcoherentsystemofknowl-edgeofobjectmotion,butratherappearstobepresentfromtheearliestpointindevelopmentatwhichthisknowledgeismanifest.Attheearliestageatwhichchildrenbegantoshowsensitivitytoconstraintsonthemotionoftheballafteritleftthecliff±2years±theyalreadyshowedqualitativelydifferentpatternsofsensitivitytothemotionindifferenttaskcontexts.Whenpresentedwithfullyvisiblemotions,2-year-oldchildrenshowedsensitivitytoinertia(Experiment8)butnotgravity(Experiments6and7).Whenpresentedwiththesametypeofcliffdisplaywithnovisiblemotionandaskedtojudgewheretherollingballwouldland,2-year-oldchildrenshowedsensitivitytogravitybutnotinertia(Experiment13).Thedivergencebetweenperceptionandjudgmentfoundinadultsandolderchildrenthereforehasrootsearlyindevelopment.

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Second,thegapfoundwithinfantsdoesnotappeartoreflectadivergencebetweenimplicitandexplicitknowl-edge,butratheragapbetweentheknowledgethatguidesperceptionofseenmotionsversusinferencesaboutunseenmotions.ThetwotasksusedinExperiment13bothassessedchildren'sexplicitjudgmentsaboutobjectmotion,yettheygavedivergentfindings,withtheperceptualjudgmenttaskrevealingmoreprecocioussensitivitytoinertiaandthepredictivejudgmenttaskrevealingmoreprecocioussensitivitytogravity.More-over,thefindingsoftheperceptualjudgmenttaskconvergedwiththoseofthepreferentiallookingtaskusedinExperiments1±8,withbothtasksprovidingevidenceformoreprecocioussensitivitytoinertia.

Otherresearchsupportsthesesuggestions.Studiesofhumaninfants,assessingtheirsensitivitytothephysicalconstraintsofinertiaandcontinuity(objectsmoveonconnectedpaths),revealeddiscrepantfindingsintwodifferenttaskcontexts.Wheninfantswerepresentedwithobjectsthatmovedfromviewinpreferentiallookingexperiments,theirreactionstothereappearanceoftheobjectsprovidedevidenceforsensitivitytocontinuitybutnotinertia(Spelkeetal.,1994;Spelke,Kestenbaum,Simons&Wein,1996).Incontrast,wheninfantswerepresentedwithfullyvisibleobjectsinpredictivereachingexperiments,theiraimingfortheobjectsprovidedevidenceforsensitivitytoinertiabutnotcontinuity(vonHofsten,1980;vonHofstenetal.,1998).Recentexperimentssuggest,however,thatthecriticaldifferencebetweentheseexperimentsconcernednottheresponsemeasure(lookingversusreaching)butthepresenceversusabsenceofocclusion(Munakata,1997;vonHofsten,Feng&Spelke,submitted;seealsoHoodetal.,1996).Differentsystemsofknowledgemayguideinfants'reactionstofullyvisibleobjectmotions,ononehand,andtheirextrapolationsofpartlyoccludedobjectmotions,ontheother.

Studiesofhumanadultswithneurologicaldisordersaccordwiththesuggestion,fromthepresentstudies,thatpreferentiallookingexperimentstapthesamesystemofknowledgeasexplicitjudgmenttasks.Squireandcolleagues(e.g.McKee&Squire,1993;McDo-nough,Mandler,McKee&Squire,1995)testedamnesicadultsbothwithstandardtestsofexplicitmemoryandwithseveraltestsofmemorygiventoinfants,includingadelayedimitationtestandapreferentiallookingtest.Patientswhoshowedanimpairmentonthestandardexplicitmemorytestsalsowereimpairedonthedelayedimitationandpreferentiallookingtests.Thesefindingsprovideconvergingevidencethatnoveltyreactionsinpreferentiallookingexperimentsareguidedbythesamesystemofknowledgeasexplicitjudgmentsoffamiliarityandnovelty.

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Perhapsthemostinterestingfindingtoemergefromtheseexperimentsconcernsthe`doubledissociation'betweensensitivitytoinertiaandsensitivitytogravityrevealedbytheperceptualandthepredictivejudgmenttasks.Instudiesofneurologicalpatients,someinvestiga-torshavevieweddoubledissociationsasevidencefortwodistinctcognitivesystems,eachofwhichcanbeselectivelyimpairedbyneurologicaldamage(e.g.Shallice,1988).Otherinvestigatorshavesuggestedthatthesedissociationsmayreflectdifferentcomponentsofasinglecognitivesystem(seeMcCarthy&Warrington,1990,andCar-amazza&Shelton,1998,fordiscussion).Oneitherinterpretation,however,wemaydrawtwolessonsfromthepresentfindings.First,children'sdevelopingknowl-edgeofobjectmotionisnotasimple,unitarywhole:agivenaspectofknowledgemayrevealitselfononetaskandnotonanothertask,evenwhenneithertaskissimplyeasierormoresensitivethantheother.Onethereforecannotconclude,onthebasisofasingletask,thatachildofagivenageeither`has'or`lacks'someaspectofmatureknowledge.Second,andmorepositively,children'sdevelopingknowledgeofobjectmotionrevealsitselfinabroadarrayoftasksandcontexts.Thepresentexperi-mentshavefocusedonthreesuchtasksandcontexts:preferentiallookingatfullyvisibleobjectmotions,judgmentsaboutthenaturalnessoffullyvisibleobjectmotions,andjudgmentsaboutthefuturepositionofanobjectthatundergoesamotionthatisnotseen.Otherexperimentshavefocusedonothertasksandcontexts,includingpredictivereachingforvisibleoroccludedobjects(vonHofstenetal.,1998;submitted),preferentiallookingatpartlyoccludedmotions(e.g.Spelkeetal.,1994,1996),actingtopropelanobject(Kristetal.,1993)andreportingwhereanoccludedfallingobjecthaslanded(e.g.Hood,1995).Exploringthedevelopmentofphysicalknowledgeineachofthesetaskcontextsshouldprovidecognitivepsychologistswitharichterrainforexploringtheemergenceandnatureofknowledgeofthephysicalworld.

Acknowledgements

WethankAbbyFriedman,KirstenCondryandEvelynPoeyforassistance,andFrankKeil,CarolKrumhanslandBarbaraFinlayforadvice.TheworkwassupportedbyagrantfromNIHtoESS(R37-HD23103).

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