Advancing the understanding of spatial cognition by considering control

HolgerSchultheis(schulth@sfbtr8.uni-bremen.de)

SFB/TR8SpatialCognition,Universit¨atBremen,28334Bremen,Germany

Abstract

Theousabilitytoprocessspatialinformationiscrucialforvari-agingtasksbeenabstractasdiverseconcepts.as,navigation,planninglayouts,andman-inspentonunderstandingAccordingly,howspatialconsiderablecognitionisefforthas

virtuallythehumanmind.Theseendeavorshave,however,realizedsofarnamelycontrolnition.constitutescontrol.neglectedInoneathisimportantseriouscontributionaspectofspatialcognition,lackinunderstandingweshowthatspatialneglectingcognitiveMoreover,cognitionmodelsincludingweproposecontrolconceptionsforcomputationalcog-gratingtasks.Besidesconstitutingforfirsttwoapproachesparticulartospatialinte-allowcognitiongivingcontrolphenomenaamoreandspatialdetailedcognitionthesemodelspotentiallythancurrentlyaccountavailableoftherespectivetheories.

spatialControlinSpatialCognition

Theabilitytoprocessspatialinformation,reasonaboutspace,andcommunicateaboutitiscrucialinvariousdomainsofhu-manendeavor.Withoutthisabilitypeoplewouldnotbeableto,forinstance,navigatetheirenvironment,exchangeknowl-edgeaboutdangerousorattractiveplaces,planvacations,ex-ecutedirectedmovements,etc.Apartfromthesedomainsspatialcognitionhasfurthermorebeenshowntobeessen-tialformanagingabstractconcepts(e.g.,Torralbo,Santiago,&Lupianez,2006)andgainingscientificinsight(Machamer,Darden,&Carver,2000).Thus,spatialcognitionplaysanimportantroleinvirtuallyallhumanactivity.

Accordingtothisimportancetherehasbeenconsiderableefforttounravelhowspatialinformationisprocessedinthehumanmind.Forexample,abundantexperimentaldataex-istsonhumanperformanceintaskslikeperspectivetaking(e.g.,Avraamides&Kelly,2005),navigation(e.g.,Golledge,1995),andarchitecturaldesign(e.g.,Verstijnen,Leeuwen,Goldschmidt,Hamel,&Hennessey,1998).Suchdatahasusuallybeenanalyzedandinterpretedwithrespecttothetypesofrepresentationsand/oroperationsdefinedontheserepresentationsusedduringspatialcognition.Bytakingsuchafocusonrepresentationsand(corresponding)operations,re-searchers,sofar,mostly(seeAllen,1999,foranexception)seemtohaveneglectedathirdaspectessentialforunderstand-ingspatialcognition,namelycontrol.

Thenecessityfortakingcontrolintoaccountisnicelyex-hibitedbyworkdoneinthephilosophyofscience.Thereitisageneralobservationthatproperexplanationsofscien-tificphenomenaneedtoinclude—thoughsometimesnameddifferently—controlaspects.Forinstance,intermsofthemechanismsapproachtoscientificexplanationproposedby

Machameretal.(2000),tobeabletounderstandaphe-nomenonitisnotenoughtoconsideronlytheentitiesandactivitiesinvolvedinthescientificphenomenon.AsBechtel(2005)remarks,“Thesecret(...)istoorganizecomponentsappropriatelysothattheiroperationsareorchestratedtopro-ducesomethingbeyondwhatthecomponentscando.”Inad-ditiontoillustratingthatcontrolshouldbepartofaproperexplanatorydescription,Bechtel’sremarkhighlightsthefactthatcontrol(whichheterms“organize”,and“orchestrated”)mightinsomecasesevenbeanindispensableaspectforar-rivingatasatisfactoryexplanationofsomephenomenon.Consequently,neglectingcontrolintryingtounderstandspatialcognitionand,thus,anessentialpartofhumanbehav-ior,seemstobeinsufficient.Itisnotalonethe(typeof)rep-resentationsandtheirassociatedprocesseswhichconstitutethebasisforhumanspatialcognition,butalsohowtheserep-resentationsandoperationsareorganized.Tothebestofourknowledge,however,detailedaccountsofcontrolinspatialcognitionaremissingsofar.Thisisnottosaythatexistingmodelsofhumanspatialknowledgeprocessing(e.g.,Gun-zelmann,Anderson,&Douglas,2004;Barkowsky,2001)arerealizedwithoutinvolvingcontrolmechanisms.Anycompu-tationalmodelnecessarilyhassomeformofcontrolmech-anismsimplemented,becauseotherwiseitwouldnotleadtoreasonableresults.However,thesecontrolmechanismshavebeenrealizedmoreastheresultofthisnecessitythanastheresultofacarefulconsiderationofthespecificsofhu-mancontrolmechanismsintherespectivetasks.Putdiffer-ently,availablecontrolconceptionsareratherunelaborateby-productsofdevelopingmodelswhichmainlyfocusonrepre-sentationsandoperations.

Inthiscontributionwewillshowthatexplicitlyconsider-ingcontrolinspatialcognitionisdirectlyrelevanttogainasatisfactoryunderstandingofspatialcognitionand,thus,theavailableapproachesareinsufficient.Furthermore,wewillproposeconceptionsfortwocomputationalmodelsincludingcontrolfortwospatialcognitiontasks.Sincecontrolhasbeenvirtuallyneglectedsofarinspatialcognitionresearch,thesemodelsarethefirsttointegrateaspectsofbothcognitivecon-trolandspatialcognition.Inaddition,themodelspotentiallyallowgivingmoredetailedaccountsofthemodeledspatialcognitionphenomenathanpreviouslyproposedtheoriesforthesephenomena.

Theremainderofthisarticleisstructuredasfollows:Inthenextsectionthephenomenaobservedinhumanimaginalperspectivetaking,existingexplanatoryapproachesforthistask,howconsideringcontrolmightimprovetheexplana-

torypowerofexistingapproaches,andfirststepstowardsacomputationalcognitivemodelforimaginalperspectivetak-ingwillbedetailed.Thesubsequentsectionwillcomprisethesameaspects,butforadifferentspatialcognitiontask,namelytheapprehensionofspatialterms.Finally,issuesforfutureworkwillbehighlightedintheconclusions.

ControlinImaginalPerspectiveTaking

AsRieser(19)remarks,planningandexecutingactionswhenmovingthroughanenvironmentrequiresjudgingspa-tialrelationsinthisenvironmentfromcertainlocationsand/ororientationsbeforethemovingbodyactuallyisatthecor-respondinglocations/orientations.Likewise,forexampletele-operatingavehicle,givingandunderstandingroutedi-rections,orconsideringwhetherchangingone’slocationwillimproveone’sviewonsomeaudio-visualdisplaymaycallforjudgingspatialrelationsfromcertainperspectiveswith-outmovingthebodyintothisperspective.Commontoallthesesituationsisthat(a)oneisinsidetheenvironmentforwhichthespatialrelationshavetobeidentifiedand(b)thesensoryinformationabouttheenvironmentavailableisjusttheegocentricvisualandauditoryimpression(i.e.,inpartic-ular,amap-likebird’seyeviewisnotavailable).Thetaskofjudgingspatialrelationsinsuchsituationsfromadiffer-entperspectivethanthebodilyonehasbeentermedimaginalperspectivetaking(IPTseeMay,2004).

Asillustratedbytheaboveexamples,IPTisessentialforeverydaylife.Thus,IPTmirrorstheimportanceofspatialcognitioningeneralforhumanbehavior(seeabove)and,ac-cordingly,inordertounderstandhowthisabilityisrealizedinthehumanmindnumerousexperimentshavebeenconducted.Thegeneralsetupofsuchexperimentsandtheirmainresultswillbedescribedinthenextsection.

InvestigationofImaginalPerspectiveTaking

GrowinginterestinunderstandingIPThasresultedinanabundantnumberofexperiments(seee.g.,Avraamides&Kelly,2005;May,2004;Farrell&Robertson,1998;Easton&Sholl,1995;Presson&Montello,1994;Rieser,19).Al-thoughtheydifferwithrespecttotheprecisefactorstheyareinvestigating,thegeneraldesignisusuallythesameintheseexperiments.

AtypicalIPTexperimentconsistsoftwophases.Inthefirstphasesubjectsareplacedatacertainlocationwithacer-tainorientationinanenvironment.Besidestheparticipantsthereareanumberofobjectsintheenvironmentwhichsur-roundthesubject(seeFigure1;thelocationofthepersonisattheoriginofthetwoarrows,herorientationisindicatedbythesolidarrow).Theparticipantsaretoldtomemorizethelocationsoftheobjects.Afterthesubjectshavesufficientlylearnedthespatialarrangementthesecondphasebegins1.Inthesecondphasetheyareplacedinthesameenvironmentandusuallyatthesamelocationandorientationasinthefirstphase.Thistime,however,theyaredeprivedofanyvisualorauditoryinformation(e.g.,byblindfoldingandputtingonheadphones).Thesubjectsarethenaskedtojudgeanumberoforientationrelationsbetweenthemselvesandthesurround-ingobjects.Importantly,theyoftenhavetojudgethisrelation

1

readySometimesknowfromtheeverydayparticipantslife.Thearetestedfirstphaseinenvironmentsisobsoletethen.

theyal-182735Figure1:PrototypicalexperimentalarrangementusedinIPTstudies.

asiftheywouldbelocatedororienteddifferentlythantheyactuallyare.Forexample,consideringthesetupshowninFigure1thesubjectmightbeaskedtojudgetherelationofobject6toherselfasifshewouldbeorientedtoobject4(thepretendedorientationisindicatedbythedashedarrow).Themeasurescommonlyusedinsuchexperimentsarethetimesparticipantsneedtoindicateandtheaccuracy(determinedasdegreesofangulardeviation)withwhichtheycanindicatetheaskedfororientation.

Basedonthisgeneralframeworkseveralfactorshavebeenvariedintheparticularexperimentstoelucidatetherepresen-tationsandprocessesusedbyhumansduringIPT.Studiesdif-fer,forinstance,whether(a)theyuseirregularlyorregularlyarrangedobjects,(b)theytestinsmallscale(e.g.,aroom)orlargescaleenvironments(e.g.,acampus),(c)theytestinfa-miliarorunfamiliar(i.e.,newlylearned)environments,(d)avirtualorrealenvironmentisused,or(e)theparticipantshavetoindicatetheaskedfororientationverballyorbypointing.Regardlessofsuchspecifics,however,therearesomegeneralresultsoccurringundervirtuallyeveryexperimentalcondi-tion.First,judgingrelationsfromanimaginalperspectiveisharder,thatis,takesmoretimeandislessaccurate,thanjudg-ingrelationsfromtheactualperspective.Thisistrueforbothimaginalperspectivesresultingfromachangeinorientation(thesubjecthastoimaginefacinginadifferentdirectionthanheactuallyis)orachangeinlocation(thesubjecthastoimag-inebeinginadifferentlocationthanheactuallyis).Second,imaginalorientationchangesseemtobemoredifficultthanimaginallocationchanges.Third,thedeclineinperformanceobservedwithimaginalchangesinorientationislinearlypro-portionaltotheangulardifferencebetweentheactualandtheimaginalorientation.Somestudies,liketheonebyEastonandSholl(1995),alsopointataproportionalrelationbetweentheperformanceinimaginalchangeoflocationandthedis-tancebetweentheactualandtheimaginedlocation.Yet,thisrelationseemstoholdonlyundercertainenvironmental/ex-perimentalconditions(cf.May,2004;Rieser,19).

ExistingExplanations

Theprevalentexplanationfortheexperimentalresultsde-scribedintheprevioussectionhasbeenintermsofanalogicalrotationandtranslationprocesses(e.g.,Sholl,2001;Farrell&Robertson,1998).Simplyspeaking,thegeneralassumptionisthathumansareabletomentallyrotateand/ortranslate

themselvesintothepositionrequestedforthecurrenttaskandthencanjudgespatialrelationsfromthis(mentallytaken)po-sition.Togiveamoredetailedaccountonhowsuchmentalrotationofoneselfmightberealized,severaltypesofrepre-sentationstructuresandprocesseshavebeenproposed.

Sholl(2000),forexample,hassuggestedthatthehumanIPTabilityreliesonasetofseparateallo-andego-centricrepresentationstructures.Theformermainlyrepresentstheobject-to-objectrelationsoftheobjectsintheenvironment.Thelatterconstitutesaviewpoint-dependentself-centeredco-ordinatesystemwhichissuperimposed/basedontheallo-centricrepresentation.Thisego-centriccoordinatesystemcanbeviewedassomekindoffilterormediatorbetweentheallo-centricrepresentationandtheego-centricrepresentationofspace:Bysuperimposingtheego-centriccoordinatesys-temovertheallo-centricrepresentationtheobject-to-objectrelationscanbetransformedintoself-referencedcoordinates(e.g.,someobjectisinfrontofoneself).

Normallythisego-centricrepresentationcoincideswiththeactualbodilypositionintheenvironment,thatis,objectsintheenvironmentwhichareinfrontofone’sbodywillberep-resentedasbeinginfrontofoneself.Importantly,however,Sholl(2000)assumesthatitisalsopossibletodissociatetheego-centriccoordinatesystemfromthebodilyposition.Indoingso,humansareabletotransformtheallo-centricallyrepresentedspatialinformationintoanego-centricrepresen-tationassumingapositionand/ororientationofoneselfwhichisdifferentfromthebodilyheldposition.AccordingtoShollitispreciselythisabilitytodissociatetheself-centeredcoordinatesystemfromthebodywhichallowsIPT.Whenaskedtojudgetherelationbetweenanobjectasifoneselfwouldhaveapositionand/ororientationwhichdiffersfromthebodilyone,humansneedonlyrotateand/ortranslatetheirego-centeredcoordinatesystemtotherequestedposi-tionandcanthenreadoffthespatialrelationbetweenthem-selvesandthetargetobject.Yet,rotatingandtranslatingtheego-centriccoordinatesystemisnotwithoutcost.SimilartotheconceptionofthementalrotationofobjectsproposedbyShepardandMetzler(1971),itisassumedthatmentallyrotat-ing/translatingtheself-referencesystemisanalogtorotating/translatingone’sbody.Thisimpliesthatthetimeneededtotakeanimaginalperspectiveisproportionaltotheangulardisparitybetweenactualandimaginedperspectiveorthedis-tancebetweenactualandimaginedpositionforrotationandtranslation,respectively.

Theseimplicationsaresupportedregardingrotations,wherethetimeneededtotaketheimaginalperspectivegrowsproportionallywithincreasingdisparity(seeabove).Yet,theempiricalevidenceregardingtranslationsisambiguous.Onlysomeofthestudiesinvestigatingtranslations(e.g.,Easton&Sholl,1995)havefoundarelationbetweendistanceandmen-taltranslationtimes,whileotherexperimentscouldnotrepli-catethisfinding(e.g.,Rieser,19).

AstheworkbyMay(2004)(seealsoMay,2000,1996)suggeststheseambiguousresultsregardingtranslationtasksstemfromamisconceptionofanalogicaltransformationthe-oriesofIPT.Insteadofpositingthatpeoplementallyrotateortranslatethemselves,heassumesthattheperformancepat-ternsobservedinIPTstudiesarebetterexplainedbyconflictsbetweenincompatibleactionvectors.Moreprecisely,inhis

conceptiontheego-centricpointingdirectiondefinedbytheactualbodypositionandorientationinterfereswiththere-quested(imaginal)pointingpositionandthushampersjudg-ingspatialrelationsfromtheimaginalperspective.Mayas-sumesthattheconflictissomuchmoreseverethegreatertheangulardifferencebetweentheactualandtheimagineddirec-tionis.Severalthingsarenoteworthywithrespecttothisac-count.First,theconflictisassumedtooccuratthelevelofac-tionselection.Second,thedifficultyofimaginaltranslationsshoulddependonlyonthediscrepancyofpointingdirectionsbetweenactualandimaginalperspectiveandnotonthedis-tancebetweenactualandimaginedposition—aclaimwhichhasbeensupportedbytheexperimentsofMay(2004).Third,May’sconceptioncanalsoeasilyaccountfortheproportion-allyincreasingdifficultyofimaginalrotationswithincreas-ingrotationangle,sincetheangulardisparitybetweenactualandimaginedpointingdirectionincreaseswithrotationalan-gle.Consequently,thisconflicttheorydoesnotonlyreconcilecontradictoryexperimentalresults,butalsogivesamorepar-simoniousaccountforIPT.Thus,May’stheoryseemstobesuperiortotheanalogicaltransformationapproaches.

Nevertheless,oncloserinspectionofthetheory,twothingsbecomeapparent.Forone,May’sconceptionisstillfarfromconstitutingasatisfactoryexplanationofhumanIPT.BesidespositingthatconflictsunderlietheperformancedeficitsinIPTthetheorydoesnotprovidemuchdetailoncomplementaryaspectsnecessarytogiveafullaccountofhumanIPT.Inad-dition,controlseemstobecrucialforexplainingthehumanbehaviorinIPTtasks.

InthenextsectionwewillelaboratewhyandhowcontrolisessentialforexplainingIPT.Doingthiswillnotonlysub-stantiateandcorroborateourinitialclaimoftheimportanceofconsideringcontrolinspatialcognition,butatthesametimeresultinafirstconceptionforacomputationalmodelofIPT.

IncludingControl

TheimportanceofcontrolforexplainingIPTbecomesclearwhenconsideringresearchontaskswitching.Taskswitch-ing(seeMonsell,2003,foranoverview)referstotheabilityofhumanstochangethetaskcurrentlyworkedonandstillperformtheinvolvedtasksquiteaccuratelyevenifthestim-uliandmotorresponsesinvolvedinthetasksarequitesim-ilarorevenidentical(calledbivalentstimuliandresponses).Sincetaskswitchingrequirestheorganizedreconfigurationofmentalresources,itisgenerallyassumedthatsuccessfultaskswitchingheavilyinvolvesthecontrolfacultiesofthehumanmind.Duetothisrelationtaskswitchinghasbeenstudiedextensively(e.g.,Allport,Styles,&Hsieh,1994)togaininsightintohumancontrolmechanisms.Inthelightofthecurrentdiscussionthefollowingthreeresultswhichhaveemergedfromthestudiesareofmajorimportance:

•Taskexecutionisslowerandmoreerrorpronejustafterataskswitch.Thisdecrementintaskperformanceafterswitchingiscalledswitchcost.

•Switchcostcanbereducediftheparticipantsareallowedtoprepareforachangeintasksbeforeperformingthe(justchangedto)task.

•Preparationforaswitchdoesnoteliminateswitchcostcompletely.Thishasbeeninterpretedsuchthatacompleteswitchoftaskscanonlybeexecutedafterthestimulitobeprocessedinthescopeofthetaskhavebeenpresented.Inthelightofthesethreeeffectsreconsiderationoftypi-calIPTtasksasdescribedaboverevealsseveralsimilaritiesofIPTtotaskswitching.Toseethisassume(a)thatthecaseinwhichtheimaginedperspectivecoincideswiththebod-ilyperspectivecorrespondstotheconditionwherethetaskisnotswitchedand(b)thatthecaseinwhichactualandimag-inedperspectivedonotcoincidecorrespondstotheconditionwherethetaskhastobeswitched.Giventhesecorrespon-dencesthesimilaritiesbetweenIPTandtaskswitchingarethefollowing:First,IPTusesbivalentstimuliandresponses,becauseboththestimuli(i.e.,thetargetobjects)andthere-sponses(indicatingthedirectiontothetargetobject)areusedforallperspectives.Second,takinganimaginedperspec-tive(astaskswitching)iscostly.Third,asshownbySohnandCarlson(2003)thecostsfortakinganimaginedperspec-tivescanbereducedbyasuitablepreparationtime.Fourth,preparationtimedoesnotcompletelyabolishthecostfortak-inganimaginedperspective(May,2004;Sohn&Carlson,2003;Sholl,2001).Importantly,astheexperimentsby(May,2004)exhibittherequestedperspectivecanonlybetakencompletelyafterthestimulusforthetask(namelythetargetobject)hasbeenpresented.

GiventhiscorrespondencebetweentaskswitchingandIPTaswellasthefactthattaskswitchingisgenerallyassumedtorelyoncontrolmechanismsimpliesthatconsideringcon-troliscrucialforunderstandinghumanIPTbehavior.More-over,itallowsdrawingonalreadyexistingresultsfromtaskswitchingresearchwhendevelopingaccountsofIPTpro-cesses.Meiran(2000),forinstance,proposedacomputa-tionalmodeloftaskswitchingwhichisabletoexplainseveraloftheempiricallyobservedeffects.Interestingly,inrepro-ducingtheeffectsthemodelexplainstaskswitchingdifficul-tiesasmainlyarisingfromaresponseconflictbetweentheresponsefortheprevioustaskandtheresponseforthecur-rent(i.e.,justswitchedto)task.Transferredtotheperspec-tiveswitchingdomainthismeansthatIPTdifficultiesmainlyarisefromtheconflictbetweentheresponsewhentheimag-inedandthebodilyperspectivearealike(“noswitch”)andtheresponsewhenthetwoperspectivesarenotalike(“switch”).NotonlydoesthiscorrespondnicelytoMay’soriginalcon-ception,butalsoastudybyWang(2004)hasrecentlysup-portedthisidea.Itisbecauseofthiscorrespondenceregard-ingthelocusofconflictthattheapproachofMeiran(2000)seemsespeciallysuitedasastartingpointfordevelopingacontrolmodelofIPT.

Ofcourse,itisnotpossibletoimportthemodelofMeiran(2000)one-to-oneintotheIPTdomain.Forexample,therepresentationformatforstimuliandresponsesneedstobemodifiedtoaccountfortheparticularitiesoftheIPTtask.Furthermore,itisnotimmediatelyclearwhetherresponserepetitioneffects(i.e.,theincreasedperformanceduringtaskswitchingiftheresponseisthesameintwosubsequenttri-als)and,thus,thecorrespondingmodelbehavioralsoholdsforIPT.Nevertheless,mainpartsofMeiran’smodellikethetaskdependent—anddynamicallychanging—weightingofthetasksetsandthecomputationsusedtoselectthefinalre-

sponseseemwellsuitedtomodelIPT.Asaresult,thepre-sentedanalysisofIPTshowstherelevanceofcontrolforun-derstandingIPT.Whatismore,theanalysisleadstoafirstdetailedconceptionofacomputationalmodelforIPT2.

ControlinSpatialTermApprehension

Anotherhighlyresearchedareaofhumanspatialcognitionishowpeopleuselanguagetocommunicateaboutspatialsit-uations.Althoughtheuseoflanguageinspatialcognitionhasmanymorefacets(e.g.,Tversky&Lee,1998;Levin-son,1996),wewillconcentrateontheapprehensionofspatialtermssuchas“above”,“right”,etc.Moreprecisely,wewillfocusonthecomputationalframeworkforspatialtermusedevelopedbyLoganandcolleagues(see,e.g.,Carlson&Lo-gan,2001;Logan&Sadler,1996).Althoughsuchafocusmightseemrestrictivegiventhemultitudeofapproachestospatialtermapprehension,forthiscontributionsuchfocusingseemsnecessary/expedientforatleastthreereasons.First,duetospacelimitationsitisnotpossibletodiscussmorethanoneapproachanditsrelationtocontrol.Second,theconsid-eredcomputationalframeworkhasbeenproventobeavalu-ableframeworkforanalyzingandaccountingforempiricaldata.Third,theframeworkparticularlynicelyallowspointingouttherelevanceofcontrolforunderstandingtheprocessesinvolvedinspatialtermapprehension.

Basedonanumberofexperimentsthecomputationalframeworkproposesthatapprehendingspatialtermscom-prisesatleast(a)spatiallyindexing(i.e.,identifying)therel-evantobjects,(b)imposingaframeofreference(FoR)ononeoftheobjects,and(c)basedonthisFoRdeterminetherelationbetweenthetwoobjects.Toillustratethisaccount,considerthefollowingexample:Youareaskedtoverifytheassertion“Theflyisabovethetable”givenadepictioncon-tainingaflyandatable(seeFigure2).AccordingtoLogan’saccount,toverifythestatementyoufirstneedtofindthetableandtheflyinthedepiction.Onceyoufoundthemyounowneedtojudgetherelationbetweenthem.Todothis,LoganandSadler(1996)posit,yousuperimposeaFoRontheta-ble(indicatedwithdashedarrowsinFigure2).TheFoRissuperimposedonthetable,becausetheflyhastobelocatedwithrespect/referencetothetable.Furthermore,FoRsareassumedtobecoordinatesystem-likerepresentationswhichcanbeanchoredinobjectsandwhichstructurethespaceonwhichtheyareimposed.Thus,byimposingareferenceframeonthetablethespacesurroundingthetableisstructuredandobjectspopulatingthissurroundingspacecanbeassignedaspatialrelationwithrespecttothetable.InthescopeoftheexamplethismeansthatonceyouhaveimposedtheFoRonthetableyoucandeterminethespatialrelationoftheflytothetableand,asaresult,verifythegivenstatement.

Giventhisconceptiontheneedforandimportanceofcon-trolforunderstandingtheuseofspatialtermsstemsfromthefactthattherearesituationsinwhichmorethanone(type

2

tion,AtfirstsightmannsinceHiatt,Trafton,itmayseemHarrison,thatthisandisSchultznotafirstdetailedconcep-perspectiveetal.(2004)inspiredtaking.haveYet,already(2004)andGunzel-theformerproposedseemscomputationalmodelsofmodel(e.g.,atechnicaltasksolutionthanacognitivetomodelbemoreandtheacognitivelylatterdoesavailable).

amap-likewhichviewdiffersoftheregardingenvironmentimportantiscontinuouslyaspectsfromvisuallyIPTaboveleftrightbelowFigure2:Anexamplesituationforassigning/verifyingspa-tialterms.

of)FoRcanbesuperimposedonthereferenceobject.Con-sideringagaintheaboveexampleatleastthreeFoRs—whichcorrespondtothethreeFoRsproposedbyLevinson(1996)—couldbeemployedtoverifytheassertion:First,onecouldusetheintrinsicreferenceframeofthetablewheretheabove-belowaxisrunsparalleltothelegsofthetable.Second,onecouldalsousearelativeFoRwheretheabove-belowaxisco-incideswiththespine.Finally,athirdalternativewouldbetouseanabsolutereferenceframe.InanabsoluteFoRtheabove-belowaxiscoincideswithgravityorcardinaldirec-tions.Asaresult,ifseveralFoRsarepotentiallyavailable,theselectionofoneoftheFoRsbecomesanessentialaspectoftheapprehensionofspatialterms.Inparticular,asCarl-son(1999)hasshown(seealsoCarlson-Radvansky&Irwin,1994;Carlson-Radvansky&Jiang,1998)thisselectionex-hibitsthefollowingproperties:

•Whenusingspatialpropositions,initially,severalFoRsareactivatedsimultaneously.

•TheactivationofthedifferentFoRsisautomaticinthesensethatpeopledonotseemtobeabletodeliberatelyavoidactivationofseparateFoRs.

•FinalselectionofoneoftherivalingFoRsseemstobere-alizedbyinhibitingtheother(notselected)FoRs.ThispatternofpropertiesoftheprocessesinvolvedintheselectionofFoRsstronglysuggeststherelevanceofcontroltotheuseofspatialterms,sinceitparallelsobservationsintasksusuallyassumedtolargelyinvolvecontrolmechanisms.TheStrooptask,forinstance,hasbeenshown(see,e.g.,Co-hen&Huston,1994)toexhibitnearlyidenticalpatternsofpropertiesasthoseoutlinedabove:Representationsforwordmeaningandwordcolorareactivatedsimultaneously;acti-vationofwordmeaningcannotdeliberatelybeavoided;andfinalselectionofoneoftherepresentationsisrealizedbyin-hibitingtheother.FollowingasimilarargumentasinthecaseofIPTthisshowsthatconsideringcontroliscrucialtoobtainacompleteandsatisfactoryunderstandingoftheuseofspa-tialterms.Whatismore,thiscorrespondencealsoopensuppossibleapproachesfordevelopingadetailedaccountofonecrucialaspectofhumanspatialtermapprehension.

Duetothenatureoftheselectionprocesswinner-takes-allnetworks(i.e.,networksinwhichthenodesinhibiteachotherandactivatethemselvesthroughreflexiveconnections,cf.Hagan,Demuth,&Beale,1996)seemtobeespeciallysuitedforrealizingadetailedaccountoftheinvolvedcon-trolmechanisms(seeSchultheis,underreview,foramorethoroughargumentregardingtheappropriatenessofwinner-takes-allnetworks).AswithIPTthisfirstconceptionofacomputationalaccountwillprobablyneedtobeadaptedtothespecificsoftheuseofspatialterms.Nevertheless,eventhisfirstconceptionofadaptingexistingcomputationalprin-ciplesconstitutesamoredetailedexplanationofthemecha-nismsinvolvedintheselectionofFoRsduringspatialtermapprehensionthanthosecurrentlyavailable.

Conclusions

Previousresearchinspatialcognitionhasmainlyconcen-tratedonidentifyingrepresentationsandprocessesbutvir-tuallyneglectedcontrol.Inthisarticleitisshownthatratherthaninvestigatingspatialcognitioninisolationfromcontrolthesetwoaspectsofhumancognitionneedtobeconsideredtogether.Acloseanalysisoftwowellresearchedspatialcog-nitiontasks,namelyimaginalperspectivetakingandappre-hensionofspatialterms,revealedthatinbothtaskscontrolprocessescanbeassumedtoplayanimportantrole.Asaresult,tryingtounderstandhumanspatialcognitionwithoutconsideringcontrolseemstobeunreasonable.

Inresponsetotheseobservationsweconceptualizedtwocomputationalmodelsforthetwospatialcognitiontasks.Im-portantly,thesetwomodelstakeintoaccountcontrolaspectsandthusrealizefirstdetailedaccountsintegratingcontrolandspatialcognition.Besidesbeingintegratedthetwoproposedmodelsalsopotentiallyallowamorethoroughexplanationofhumanperformanceinbothspatialcognitiontasksthanpre-vioustheories.

Onemajorissueforfutureworkistofurtherinvestigatetowhatextentthecontrolmechanismsforparticularspatialtasksdifferfromeachother.Judgingfromtheaboveanalysisitwouldseemthatthecontrolmechanismsinvolvedinspa-tialcognitionmightdifferconsiderablyfordifferentspatialtasks.Yet,itseemsprematuretotakeadefinitedecisiononthisquestionatthemoment—furtherinvestigationswillhavetoshowwhetherthecontrolmechanismsinthedifferenttasksaredistinctorcanbereconciledwitheachotherormaybere-ducedtoacommonbasis.Inexploringthisissues,weplanto(a)refinethetwoproposedmodels,(b)extendthegeneralideasexhibitedbythemodelstootherareasofspatialcogni-tion,and(c)identifyfurthercontrolprincipleswhichmightbeimportantforunderstandingspatialcognition.

Acknowledgments

InthispaperworkdoneintheprojectR1-[ImageSpace]oftheTransregionalCollaborativeResearchCenterSFB/TR8Spa-tialCognitionispresented.FundingbytheGermanResearchFoundation(DFG)isgratefullyacknowledged.

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