第4章
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  Onthebasisofthishypothesis,theexplanationofthefactthatthenumbersofthefirstgroupcomeoutsomewhattoolargeisthat,inthecourseoftheexperiment,theexistenceofasavinginworkinthecaseofthederivedserieswasanticipated,andforthisreasonthelearningoftheseriestookplaceinvoluntarilywithasomewhatgreaterconcentrationofattention。

  Ontheotherhand,itmaybethat,inconsequenceoftheexcludedknowledge,therehasbeenatworkinthecaseofthenumbersofthesecondgroupadisturbingelementwhichhasmadethemsmaller。Here,tobesure,duringthelearningofthederivedseriesaverylivelycuriositydevelopedconcerningthecategoryoftransformationtowhichtheserieswhichhadjustbeenlearnedbelonged。Thatthismusthavehadadistracting,andthereforeretarding,influenceisprobablenotonlyinitselfbutalsothroughtheresultobtainedfromtheseriesderivedbypermutationofsyllables。Itwastobeexpectedthattheidentityofthesyllables,aswellasoftheinitialandendterms,wouldmakeitselffeltinthiscasebyasavingofwork,howeversmallthatsavingmightbe。Thelattereffectappears,itistrue,intheexperimentsofthefirstgroup。Withthoseofthesecondgroup,however,thereisnoticeable,insteadofthissavingofwork,aslightadditionalexpenditureoftime。This,ifitisnotmerelyaccidental,canscarcelybeexplainedotherwisethanthroughthedistractingcuriositymentioned。

  Itispossiblethatbothinfluenceswereatworksimultaneouslysothatthefirstexperimentsgaveresultswhichweresomewhattoohigh;andthesecond,resultsthatweresomewhattoolow。Itisallowable,underthishypothesis,toputthetwosetsoffigurestogethersothatthecontrastingerrorsmaycompensateeachother。Inthiswaytherewasfinallyobtainedoutofthe85doubleteststhefollowingtable。Section39。DiscussionofResultsIntheforegoingtableanespecialinterest,itseemstome,isconnectedwiththelast,andalsowiththenexttothelast,rowofnumbers。Whentherewascompleteidentityofallthesyllablesandtheinitialandendtermswereleftintheirplaces,theaveragesavingoftimefor17testsdealingwiththelearningofthederivedserieswassoslightthatitwashardlytobedetermined。Itfellwithinhalfofitsprobableerror。Thesyllableswere,therefore,inthemselves,outsideoftheirconnection,sofamiliartomethattheydidnotbecomenoticeablymorefamiliarafterbeingrepeated32times。Onthecontrarywhenarelatedserieswasrepeatedthesamenumberoftimes,eachsyllablebecamesofirmlyboundtothesyllablewhichfollowed8placesbeyondthat24hourslatertheinfluenceofthisconnectioncouldbedeterminedinnodoubtfulfashion。Itattainsavalue6timestheprobableerror。Itsexistence,therefore,mustbeconsideredtobefullyprovedalthoughnaturallywecannotbesosurethatitssizeisexactlywhatitwasfoundtobeintheexperiments。Althoughitsabsolutevalueissmall,yetitsinfluenceamountstoonetenthofthatoftheconnectionwhichbindseverymembertoitsimmediatesuccessor。Itissosignificant,andatthesametimethedecreaseintheafter-effectofconnectionswhichwereformedover2,3,7interveningmembersissogradualaone,thattheassertioncanbemade,amthesegroundsalone,thateventhetermswhichstandstillfurtherfromoneanothermayhavebeenboundtoeachothersubconsciouslybythreadsofnoticeablestrengthatthetimeofthelearningoftheseries。

  Iwillsummarisetheresultssofargiveninatheoreticalgeneralisation。

  Asaresultoftherepetitionofthesyllable-seriescertainconnectionsareestablishedbetweeneachmemberandallthosethatfollowit。Theseconnectionsarerevealedbythefactthatthesyllable-pairssoboundtogetherarerecalledtomindmoreeasilyandwiththeovercomingoflessfrictionthansimilarpairswhichhavenotbeenpreviouslyunited。Thestrengthoftheconnection,andthereforetheamountofworkwhichiseventuallysaved,isadecreasingfunctionofthetimeorofthenumberoftheinterveningmemberswhichseparatedthesyllablesinquestionfromoneanotherintheoriginalseries。Itisamaximumforimmediatelysuccessivemembers。Theprecisecharacterofthefunctionisunknownexceptthatitdecreasesatfirstquicklyandthengraduallyveryslowlywiththeincreasingdistanceoftheterms。

  Iftheabstractbutfamiliarconceptionsof’power,’’disposition,’

  besubstitutedfortheconcreteideasofsavinginworkandeasierreproduction,themattercanbestatedasfollows。Asaresultofthelearningofaserieseachmemberlassatendency,alatentdisposition,todrawafteritself,atitsownreturntoconsciousness,allthemembersoftheserieswhichfollowedit。Thesetendenciesareofvaryingstrength。Theyarethestrongestforthememberswhichimmediatelyfollow。Thesetendenciesareaccordinglyingeneralmosteasilydemonstrableinconsciousness。Theserieswillreturninitsoriginalformwithouttheinterventionofotherinfluenceswhiletheforcesdirectedtotheresuscitationoftheremainingmemberscanbeexplicitlydemonstratedonlybytheintroductionofotherconditions。

  Itisnaturallynotconceivablethatbyamerecapriceofnaturethevalidityoftheprinciplesdiscoveredshouldbelimitedexclusivelytothecharacterofthematerialinwhichtheywereobtained——i。e。,toseriesofnonsensesyllables。Theymaybeassumedtoholdinananalogouswayforeverykindofidea-seriesandforthepartsofanysuchseries。

  Itgoeswithoutsaying,whereverrelationsexistbetweentheseparateideas,otherthanthoseoftemporalsequenceandseparationbyintermediatemembers,theseforceswillcontroltheassociativeflow,notexclusively,butwithreferencetoallthemodificationsandcomplicationsintroducedbyrelationsofvariousaffinities,connection,meaning,andthelike。

  Atanyrate,itwillnotbedeniedthatthedoctrineofAssociationwouldgainthroughageneralvalidityoftheseresultsagenuineroundingoutand,sotosay,agreaterreasonableness。Thecustomaryformulation,\"ideasbecomeassociatediftheyareexperiencedsimultaneouslyorinimmediatesuccession,\"hassomethingirrationalaboutit。Iftheimmediacyofsuccessionistakenprecisely,theprinciplecontradictsthemostcommonexperiences。

  Ifitisnottakenexactly,thenitishardtostatewhatkindofsequenceisproperlymeantAtthesametimeitisnotclearwhyasequencenotquitedirectshouldhaveanadvantagewhichsuddenlydisappearsinthecaseofasequencestillmoreindirect。Aswenowknow,thedirectnessorindirect-nessofthesequenceiswithouteffectuponthegeneralnatureofwhathappensbetweenideaswhichsucceedeachother。Inbothcasesconnectionsareformedwhichonaccountoftheircompletesimilaritycanbedesignatedonlybythecommonterm,Association。Buttheseareofdifferentstrength。Asthesuccessionofunitedideasapproachesidealimmediacytheconnectingthreadsgrowstronger,andinproportionasitdepartsfromthisideal,thesethreadsgrowweaker。Theassociationsbetweenmoredistantterms,althoughactuallypresentanddemonstrableunderproperconditionshave,nevertheless,onaccountoftheirslightstrength,practicallynosignificance。Theassociationsbetweenadjacenttermsare,onthecontrary,ofrelativelygreatimportance,andwillmaketheirinfluenceabundantlyfelt。Ofcourse,iftheserieswereleftentirelytothemselvesandiftheywerealwaysproducedinpreciselythesameorder,foreachtermtherewouldappearonlyoneassociation,therelativelystrongest——namely,thatwiththeimmediatelysucceedingterm。Butseriesofideasareneverlefttothemselves。Therichandquicklychangingorderofeventsbringsthemintothemostmanifoldrelations。

  Theyreturnwiththeirmembersinthemostvariedcombinations。Andthen,undercertaincircumstances,thestrongeroftheselessstrongassociationsbetweenmoredistanttermsmustfindopportunitytoauthenticatetheirexistenceandtoenterintotheinnercourseofeventsinaneffectiveway。Itiseasytoseehowtheymustfavoramorerapidgrowth,aricherdifferentiation,andamany-sidedramificationoftheideaswhichcharacterisethecontrolledmentallife。Ofcoursetheyalsofavoragreatermanifoldness,andsoapparentlyagreaterarbitrarinessandirregularity,inmentalevents。

  BeforeIproceedfurther,Iwishtoaddafewwordsconcerningtheabovementioned(p。91[Section35])derivationoftheassociationofsuccessiveideasfromtheunitaryconsciousnessofaunitarysoul。Thereisacertaindangerinbringingtogetherapresentresultwithonefoundpreviously。

  Imentionedabove(p。47[beginningofChapterV])thatthenumberofsyllableswhichIcanrepeatwithouterrorafterasinglereadingisaboutseven。

  Onecan,withacertainjustification,lookuponthisnumberasameasureoftheideasofthissortwhichIcangraspinasingleunitaryconsciousact。Aswejustnowsaw,associationsareformedofnoticeablestrengthovermorethanseveninterveningmembers,thereforebetweenthebeginningandendofanine-syllableseries。Andonaccountofthesizeofthenumbersobtainedandthenatureoftheirgradation,itseemsprobablethat,evenwithalargernumberofsyllables,connectionswouldbeformedbetweentheirextremes。If,however,associationsarebuiltbetweenmemberstoofarseparatedtobeheldtogetherinasingleconsciousact,itisnolongerpossibletoexplainthepresenceofthoseassociationsonthebasisofthesimultaneouspresenceoftheunitedideasinconsciousness。

  However,Irecognisethatthoseforwhomsuchaderivationisacherishedmatterarenotnecessarilyforcedbytheabovediscussiontoabandontheirconception。Sucharethosewhoconsidertheunitaryactsofaunitarysoulassomethingmoreoriginal,intelligible,transparentorbetterworthyofbeliefthanthesimplefactsofassociationdescribedabove,sothatthereductionofthelattertotheformerwouldbeanoteworthyachievement。

  Oneneedsbuttosaythat,inthecaseofanunfamiliarsequenceofsyllables,onlyaboutsevencanbegraspedinoneact,butthatwithfrequentrepetitionandgraduallyincreasingfamiliaritywiththeseriesthiscapacityofconsciousnessmaybeincreased。So,forexample,aseriesof16syllables,whichhavebeenthoroughlymemorised,maybepresentinasingleconsciousact。Accordinglythis\"explanation\"isfreelyavailable。Thoseforwhomitwasofvalueinthecaseofassociationbysimultaneityorimmediatesuccessioncanemployitfullyaswellforourcaseofindirectsequence。Andbecauseofthemodestrequirementswhichinpsychologyaresooftenimposeduponexplanations,thisviewwilldoubtlessforalongtimeservetomakedimthevisionandsopreventthefrankrecognitionofthisasoneofthemostwonderfulofallriddles,anditwillalsoactasahindranceinthesearchforitstrueunderstanding。Section40。ReverseAssociationsOfthemanyproblemswhichspringoutoftheresultspresentedIhavebeenableforthetimebeingtoinvestigateonlyafewandthesebymeansofonlyasmallnumberofexperiments。

  Asaresultofthefrequentrepetitionofaseries——a,b,c,d……——certainconnections——ab,ac,ad,bd,etc。——

  areformed。Theideaa,wheneverandhoweveritreturnstoconsciousness,hascertaintendenciesofdifferentstrengthtobringalsowithittoconsciousnesstheideasb,c,d。Arenowtheseconnectionsandtendenciesreciprocal?

  Thatis,ifatanytimecandnotaistheideabysomechancerevived,doesthishave,inadditiontothetendencytobringdandebackwithit,asimilartendencyinthereversedirectiontowardsbanda?Inotherwords:——Asaresultofthepreviouslearningofa,b,c。[sic]d,thesequencesa,b,c,a,c,e,aremoreeasilylearnedthananygroupingofequallengthofsyllablespreviouslyunknownsuchasp,q,r……Isthesamethingtrueofthesequencescba,andeca?Asaresultofmanifoldrepetitionofaseriesareassociationsalsoformedinthereverseorder?

  Theviewsofthepsychologistsseemtobedivergentuponthispoint。

  Onesidecallattentiontotheundoubtedfactthatinspiteofcompletemasteryof,say,theGreekalphabetapersonisnotatallinapositiontorepeatitreadilybackwardsifhehasnotspeciallystudiedandpracticeditinthisform。

  Theothersidemakeextensiveuseofreverseassociations,asofsomethingquiteintelligible,intheirexplanationoftheoriginofvoluntaryandpurposivemovements。Accordingtothemthemovementsofthechildareatfirstinvoluntaryandaccidental。Withcertaincombinationsofthese,intenselypleasurablefeelingsresult。Inthecaseofmovementsasoffeelings,memorytracesremainwhich,byrepetitionoftheoccurrences,arealwaysmorecloselyassociatedwitheachother。Ifthisconnectionhasattainedacertainstrength,themereideaoftheagreeablefeelingleadsbackwardstotheideaofthemovementwhicharousedit;thencomestheactualmovementandwithitalsotheactualsensedfeeling。

  TheconceptionofHerbart,whichwelearnedtoknowabove(p。94[Section35]),holdsthemiddlecoursebetweenthesetwoviews。Theideac,whichappearsinthecourseofaseries,fuseswiththeideasbanda,whichhaveprecededitandwhichareyetpresentalthoughbecomingdim。Ifcislateronreproduced,itbringsbandawithitbutdimmed,notfullyuninhibitedorclearlyconscious。Withthesuddenarousalofamemberoutofthemidstofaserieswesurveythatwhichpreceded\"atonceingradedclearness\";butneverdoesithappenthattheseriesrunsoffinreverseorder。Tothememberwhichspringsupinconsciousnesstheresucceedindueorderandincompleteconsciousnessthosetermswhichfolloweditintheoriginalseries。

  ForthepurposeoftestingtheactualrelationsIcarriedoutanexperimententirelysimilartothepreviouslydescribedinvestigations。Outofgroupseachcomposedofsix16-syllableseriesarrangedbychancenewgroupswerederivedeitherthroughmerereversalofthesequenceorbythatplustheskippingofanintermediatesyllable。Thenthetwosetsofgroupswerelearnedbyheart,thederivedform24hourslaterthantheoriginal。

  Iftheschemefortheoriginalformiswrittenasfollows:I(1)I(2)1(3)……I(15)I(16),thenthecorrespondingderivedseriesisthusdesignated:Inthecaseofmerereversalofthesyllablesequence;I(16)I(15)I(14)……I(2)I(1),[sic]

  Inthecaseofreversalplusskippingofanintermediatesyllable,I(16)I(14)I(12)……I(4)I(2)I(15)I1(13)……I(3)I(1)。

  ForthefirstkindofderivationIhavecarriedouttenexperiments;

  forthesecond,onlyfour。

  Theresultsareasfollows:

  Inrelationtothetimeoflearningtheoriginalseriesthesavingamountsto124percent。

  Inrelationtothetimeoflearningtheoriginalseriesthesavingamountedto~percent。

  Asaresultofthelearningofaseriescertainconnectionsofthemembersarethereforeactuallyformedinareverseaswellasinaforwarddirection。

  Theseconnectionsarerevealedinthisway,thatserieswhichareformedoutofmembersthusconnectedaremoreeasilylearnedthansimilarseries,whoseindividualmembersarejustasfamiliarbutwhichhavenotbeenpreviouslyconnected。Thestrengthofthepredispositionsthuscreatedwasagainadecreasingfunctionofthedistanceofthemembersfromeachotherintheoriginalseries。Itwas,however,considerablylessforthereverseconnectionsthanfortheforwardones,thedistancesbeingequal。Withanapproximatelyequalnumberofrepetitionsoftheseriesthememberimmediatelyprecedingagivenmemberwasnotmuchmorecloselyassociatedwithitthanthesecondonefollowingit;thesecondpreceding——sofarasmaybedeterminedonthebasisofthesefewresearches——scarcelyasfirmlyasthethirdfollowing。

  Ifonecouldassumeamoregeneralvalidityforthisrelationfoundherefirstinconnectionwithsyllableseries,themutuallyopposedexperiencesjustmentionedwould,Ibelieve,becomethoroughlyintelligible。Whereaseriesconsistsofonlytwomembers——asinthecaseoftheconnectionbetweenasimpleideaofmovementandthatofanagreeablefeeling——then,bymeansoffrequentrepetitiontheendtermwillacquiresostrongatendencytocallupafteritselftheinitialtermthatthelatterwillactuallyappear。Forthebringingupofthetermfirstprecedingitistheonlythingforwhich,asaresultofthemanyrepetitions,thesecondtermhasacquiredapredisposition。But,nomatterhowmanyrepetitionstheremaybeinthecaseofalongseries,itwillneverhappenonthearousalofamiddletermthattheserieswillreappearinareverseorder。For,howevereasilytheimmediatelyprecedingtermmayconnectitselfwiththeoneforthemomentaroused,theimmediatelysucceedingtermwillappearmoreeasilybyfar,andsowillwinthevictory,providedotherinfluencesdonotintervene。

  NomatterhowthoroughlyapersonmayhavelearnedtheGreekalphabet,hewillneverbeinaconditiontorepeatitbackwardswithoutfurthertraining。Butifhechancestosetoutpurposelytolearnitbackwards,hewillprobablyaccomplishthisinnoticeablyshortertimethanwasthecaseinthepreviouslearninginthecustomaryorder。Theobjectionisnotinpointthatapoemorspeechwhichhasbeencommittedtoheartisnotnecessarilylearnedmorequicklybackwardsthanitwasoriginallyforwards。

  Forwiththelearninginreversedirectionthenumerousthreadsofinnerconnectiononwhichrapidlearningofmeaningfulmaterialingeneraldependswillbebroughttonothing。Section41。TheDependenceofAssociationsofIndirectSequenceupontheNumberofRepetitionsTheconnectionsetupasaresultofmanyrepetitionsbetweentheimmediatelysucceedingmembersofanidea-orsyllable-seriesisafunctionofthenumberofrepetitions。AsaresultoftheinvestigationsofChapterVI,whichwerepurposelydirectedtothediscoveryofthisrelation,anapproximateproportionality,withintolerablywidelimits,hasbeenmadeoutbetweenthenumberofrepetitionsandthestrengthoftheconnectionsestablishedbythem。Thelatterwasmeasured,preciselyasintheinvestigationsofthepresentchapter,bytheamountofworksavedinrelearningtheconnectedseriesafter24hours。

  Ifnow,asaresultofrepetitions,connectionsarealsosetupbetweenmembersofaserieswhicharenotimmediatelysuccessive,thestrengthofthelatterisnaturallyalsoinsomewaydependentuponthenumberofrepetitions。Thequestionarisesinwhatformthedifferentdependenceoccursinthiscase。Doesaproportionalityexistherealso?Ifthenumberofrepetitionsismadegreater,willthethreadsofseparatestrength,whichbindtogetherallthemembersofaserieslearnedbyheart,increaseinstrengthinthesameproportion?Oristhenatureandrateoftheirincreaseinstrengthadifferentoneasisthecasewiththestrengthofthethreadsthemselves?Onthebasisofourpresentknowledgeneithertheonenortheotherofthesepossibilitiescanbedeclaredself-evidentTofacilitateaninsightintotheactualconditionsIhaveinstitutedafewpreliminaryexperimentsinthefollowingway。Sixaeriesof16syllableseachwereimpresseduponthememorybya16-or64-foldattentiverepetition。

  After24hoursanequalnumberofderivedseriesofthesamelength,whichhadbeenobtainedfromthosealreadylearnedbyskippingoneintermediatesyllable,werelearnedbyhearttothefirstrepetition。Inordertomaketheinvestigationsusefulinotherways,theserieswerederivedinthiscasebyamethodsomewhatdifferentfromthatdescribedabove(p。97[Section36])。Thelattermethoddiffersfromtheformerinthatheretheodd-numberedsyllablesoftheoriginalserieswerenotfollowedbytheeven-numberedsyllablesofthesameseries。Butalltheodd-numberedsyllablesoftwooriginalserieswereunitedtoformanew16-syllableseries。Thentheeven-numberedsyllablesofthesameoriginalserieswereunitedtoformasecondnewseries。Theschemeofthederivedserieswasthereforenot,asabove,I(1)I(3)I(5)……I(15)I(2)I(4)……I(16)II(1)II(3)II(5)……II(15)II(2)II(4)……II(16)

  butratherI(1)I(3)I(5)……I(15)II(1)I(3)……I(15)I(2)I(4)I(6)……I(16)II(2)II(4)……II(16)

  Theeffectofthederivationuponthelearningofthederivedseries,cannot,asitseems,beessentiallyaffectedthroughthisslightchange。

  Here,asintheabovedescribedmethodofderivation,thesyllableswhichduringthefirstlearninghadbeenseparatedfromeachotherbyaninterveningsyllablewerelearned24hourslaterinimmediatesuccession。

  ForeachnumberofrepetitionsusedinlearningImade8doubletests,whichgavethefollowingresults:

  Numberofrepetitionsemployedfortheimpressionofeachoftheoriginalseries:

  1664Numberofsecondsrequiredforlearningthesixderivedseriesafter24

  hours(includingtherecital):

  11781157

  1216982

  12161198

  9501148

  1358995

  10191017

  11911183

  12301198

  ——————————————-

  Average11701109

  Probableerror3022Onaccountofthesmallnumberofexperimentstheresultingaveragesare,unfortunately,notveryexact;butthegeneralcharacteroftheresultswouldremainthesameevenifweconsideredthevaluefalsewithinthewholerangeoftheprobableerror。Thischaracterbecomesapparentuponcomparisonwiththevaluesgivenabove(p。56[middleofChapter6])forlearningbyheartsix16-syllableserieswhichhadnotpreviouslybeenlearned。Thistookplacein1,270seconds。Aftertheoriginalserieshadbeenrepeated16times,thederivedserieswaslearnedwithasavingofabout100seconds;afterrepetition64times,withalikesavingof161

  seconds。Quadruplingtherepetitionsresultedinincreasingthesavingonlyalittlemorethanhalfasmuchagain。Theincreaseinstrengthoftheassociationsreachingoveranintermediatememberwasinnowiseproportionaltothenumberofrepetitions,forthecasesstudied,notevenwithinthelimitsforwhichthiswasnoticeablythecaseforassociationsfromonemembertoitsimmediatesuccessor。Onthecontrarytheeffectoftherepetitionsinthecaseofassociationsofindirectsequencedecreasedconsiderablysoonerandmorequicklythaninthecaseofthoseofdirectsequence。

  Thereisverycloseagreementbetweenthepairofvaluesjustfoundandthenumbergivenabove(p。99,I[Section37])——theprocedurebeing,ashere,withouttheexclusionofknowledge——forthelearningofderivedserieswhichthedaybeforehadbeenlearnedintheiroriginalformtothepointoffirstpossiblereproduction。Thisnumber,itistrue,wasobtainedundersomewhatdifferentconditions。Inthefirstplace,notalwayswerethesamenumberofrepetitionsemployedforlearning,buteachtimeasmanyaswererequiredforthefirstpossiblereproduction——i。e。,notexactly,butontheaverage,32。Moreover,thenatureofthederivationofthesenseswassomewhatdifferent,aswasstatedabove。Butthesedifferenceshavelittleweightinthecaseofnumberswhichotherwisecouldhavelittleclaimtoexactness。Iadducethereforethisvalueforcomparison,andinadditionthenumbersgiveinChapterVIfortheinfluenceofrepetitionsontherelearningofthesameuntransformedseries。Herethenisthetable。

  Icallattentionagaintothefactthatthenumbersgivenaboveareinpartratherinexactandthattheyweregainedunderverylimitedconditions。

  However,itisallowabletosketchsummarilyandwithhypotheticalelaborationtheviewwhichtheseresultsmakeappeartobethemostprobableexplanationofanimportantgroupofinnerprocessesandwhichfillspleasinglyandcompletelyahithertoemptyplaceinourknowledge。

  Withtheimprintingandinternalfixationofanidea-seriesthroughitsmanifoldrepetition,innerconnections,associations,arewovenbetweenalltheseparatemembersoftheseries。Thenatureoftheseissuchthatseriesmadeoutofmembersthusassociatedarepickedupandreproducedmoreeasily,withlessresistancetobeovercome,thansimilarseriesmadeupofmembersnotpreviouslyassociated。Theirnaturecanalsobestatedinthisway,thateachmemberoftheserieshasthedefinitetendencyonitsownreturntoconsciousnesstobringbackotherswithit。Theseconnections,ortendencies,areofdifferentstrengthfromseveraldifferentpointsofview。Forthemoredistantmembersoftheoriginalseriestheyareweakerthanforthenearer;forspecificdistancesbackwardstheyareweakerthanforthesamedistancesforward。Thestrengthofalltheconnectionsincreasesasthenumberofrepetitionsincreases。Buttheoriginallystrongerthreadsbetweenthenearermembersarestrengthenedconsiderablymorequicklythantheweakeroneswhichconnectthemoredistantterms。Themore,therefore,thenumberofrepetitionsincreases,thestronger,bothabsolutelyandrelatively,becometheconnectionsbetweenimmediatelysuccessiveterms。

  Tothesamedegreethemoreexclusiveanddominantbecomesthetendencyofeachtermatitsownreturnintoconsciousnesstodrawafteritselfthattermwhichhadalwaysimmediatelyfolloweditduringtherepetitions。Section42。IndirectStrengtheningofAssociationsIconcludewiththementionofanoteworthyfactwhichappearedincidentallyinconnectionwiththeinvestigationsmentionedintheprecedingparagraphs。

  Onaccountoftheuncertaintyofthenumericalresultswhichcomeintoconsideration,Icancallattentiontoitonlywithgreatreserve。Icannot,how-ever,passitbyaltogetherbecauseitisprobableinitself,andbecause,withfurtherconfirmation,itwillthrowacharacteristiclightoninnerprocesseswhichareactuallypresentbutwhichremainunconscious。Itwillalsorevealtherelativeindependenceoftheseprocessesfromconsciousaccompaniments,asIhaveshownabove(§24)。

  Thederivationofthetransformedseriesinthecaseofthelastmentionedinvestigationswasaccomplished,ashasbeenstated,inthefollowingway。

  Outoftwo16-syllableseriesselectedbychance,firstalltheodd-numberedsyllableswerecombinedtoformanewseriesandthenalltheeven-numberedtoformasecondserieswhichfollowedinimmediatesuccession。Inthecaseofagroupconsistingofsixseriesofthissort,therefore,thederivedseriesIIcontainednothingbutsyllableswhichinthefirstprocessofmemorisinghadfollowedimmediatelyuponthecorrespondingmembersofseriesI。ThederivedseriesIVboreasimilarrelationtoseriesIII,andseriesVItoseriesV。Thefollowingphenomenonappeared,whichisthepeculiarrelationtowhichIwishtocallattention。LesstimewasrequiredforlearningbyheartseriesII,IV,VIontheaveragethanforseriesI,III,V,althoughinalltheothergroupsofseries,whetheroriginalorderived,theconversewasthecase。

  Iadducesomenumericaldatainevidenceofthisrelation。

  Fromalltheexperimentswithsixseriesof16syllableswhichwerelearnedtothepointofthefirstrecital,tenimmediatelysuccessiveexperimentsarechosenbychancefortwodifferenttime-periods。ThetimesforcommittingtomemoryseriesI,III,Varecombinedincalculation,asarealsothoseforseriesII,IV,VI。

  ThesumofseriesII,IVandVI,foundbyaveragingthetenexperiments,ishereinbothcases,ascanreadilybeseen,considerablygreaterthanthesumofseriesI,III,V。Thedifferencesare,tobesure,ofverydifferentamountsfortheseparateexperiments,andinonecasetheyhaveapronouncednegativevalue;butthesefluctuationsarerepresentedinthelargeprobableerrorofthedifferencesoftheaverages;and,inspiteofthesizeoftheseerrors,thepositivecharacterofthedifferencesmaybeconsideredasfairlycertain。

  Inallotherinvestigatedcasesthefollowingresultappears:therearelargefluctuationsofthedifferencesintheindividualexperiments,butacombinationoftheseveralexperimentsshowsadecisivepredominanceforseriesII,IV,VIalthoughthesurplusissmallerthaninthecaseofthetwoexperimentsinquestion。Thusinthecaseofitearliertestsinwhichserieswerelearnedbyheartwhichhadbeenderivedbyskippingoneintermediatesyllableandwhichhadbeenlearnedthedaybeforeintheoriginalformtheresultswere(p。99,I[Section37]):

  Sumofseries(II,IV,VI)minusSumofseries(I,III,V)=33(P。E。m=23)~

  Withsixlatertestsofthesamesort(p。103,I[Section37]):

  Sumof(II,IV,VI)minusSumof(I,III,V)=42(P。E。m=

  29)。

  Withtenexperimentswithserieswhichhadbeenrepeatedthedaybefore16timeseach(p。55[beginningofChapter6]):

  Sumof(II,IV,VI)minusSumof(I,III,V)=17(P。E。m=21),etc。

  Onaccountofthelargenessoftheprobableerrorasingleoneofthelastgivenfigureswouldhavelittlesignificance。Bymeansoftheircorrespondenceastothenatureofthedifferencetheygaininprobability,andthephenomenonbecomesquiteintelligibleinlightoftheresultsofSection18。There,andwithespecialdearnessinthecaseof16-syllableseries,itwasshownthatthelearningoftheindividualseriesoccurredintheformoffairlyregularoscillations。Thesewereofsuchasortthatarelativelyslowlylearnedseriesfollowedonelearnedrelativelymorequicklyandviceversa(p。43[endofChapter4],Fig。3)。Sinceinthecaseofeachexperimentthefirstserieswaslearnedontheaveragethemostquicklyandthesecondthemostslowly,bythecombinationofseriesI,III,VtheaverageminimaareunitedandofseriesII,IV,VItheaveragemaxima。Thedifference,S(II,IV,VI)minus(I,III,V)is,therefore,ingeneralpositive。

  Accordinglyitmustbesurprisingthatinthecaseofboththegroupsoftestsmentionedintheprecedingparagraphs,thisdifferenceisonthecontraryofanegativesign。

  Thefluctuationsofthenumbersfortheseparateexperimentsarealsointhiscaseverygreat。However,itisevidentonthefirstglanceandwithoutfurthercomparisonthatastrongdisplacementofthedifferencestothenegativesidehastakenplace。Thisfactisalsoexpressedbytheaverages。Incontrastwithpreviousresults,theseriesII,IV,VIwerelearnedinsomewhatshortertimethanseriesI,III,V。

  Thatthisexceptionrestsonmerechanceispossiblebutnotveryprobable。

  Theprobableerrors,althoughlarge,arenotlargeenoughtoindicatethis。

  Iwouldsoonerfearthatitwasacaseofdisturbanceoftheresultsthroughtheoft-mentionedsourceoferror,anticipationoftheoutcome(p。27ff。[ChapterIII]andp。101[Section37])。DuringtheprogressoftheexperimentIbelievedwithincreasingcertaintythatIcouldforeseethesmallerexpenditureoftimeforthelearningofseriesII,IV,VI,anditwasonlybecauseIthoughtsomethingofthissortthatIchangedthemethodofderivationofthetransformedseries。Icannot,therefore,excludethepossibilitythat,merelyonthebasisofthishiddenpresuppositionandinamanneraltogetherunrevealedtoconsciousness,agreaterconcentrationofattentionwaspresentinlearningseriesII,IV,VIthaninlearningseriesI,III,V。However,thisassumptionisnottobetakenpositivelyasthecorrectone。Theassumptionthatthewholeofthedifferencefoundistobetracedbacktotheinfluenceofthissourceoferrorwouldinvolvetheascriptionofaprettylargefunctiontoaninvoluntaryandcompletelyunconsciousaccommodationofattentionduetoasecretexpectation。

  Thereremains,accordingly,acertainprobabilityforthethirdpossibility,namely,thatthecontrastingcharacteroftheaveragedifferenceshasinpartatleastanobjectivebasis,thatthemorerapidlearningofthederivedseries,II,IV,VI,wasinpartduetotheirmannerofderivation。

  Theproperwayinwhichtothinkofthiscausationwouldbecomedearonlybytheintroductionofphysiologicalconceptionswhichmustfirstbeconstructedoratleastremodelled。Ifuseismadeofthelanguageofpsychology,then,asinthecaseofallunconsciousprocesses,expressioncanbeonlyfigurativeandinexact。

  Asaresultofthelearningbyheartofaseriesintheoriginalformtheseparatesyllables,wemustsay,retainfairlystrongtendenciesupontheirownreturntoconsciousnesstobringafterthemthesyllableswhichimmediatelysucceededthem。If,therefore,thesyllables1,3,5,etc。,returntoconsciousness,thesyllables2,4,6,etc。,haveatendencyalsotoappear。Thistendencyisnotstrongenoughtobringaboutasaconsciouslyperceivableeventtheactualappearanceof2,4,6。Thelatterareinevidenceonlyinacertaininnerconditionofexcitability;somethingtakesplaceinthemwhichwouldnothaveoccurredif1,3,5hadnotbeenrepeated。

  Theybehavelikeaforgottennamewhichoneattemptstorecollect。

  Thisisnotconsciouslypresent;onthecontrary,itisbeingsought。Inacertainway,however,itisundeniablypresent。Itisonthewaytoconsciousness,asonemightsay。Forifideasofallsortswerecalledupwhichstoodinconnectionwiththeearlierexperiencedname,apersoncouldusuallytellwhethertheyagreedwiththeonenowsoughtforbutnotyetfound,ornot。Asaresultofthefrequentrepetitionofthesyllables1,3,5

  previouslyconnectedwiththesyllables2,4,6,thelatterwereplacedinasimilarslightlypronouncedconditionofexcitation,lyingbetweenconsciousappearanceontheonesideandsimplenon-appearanceontheother。

  Andthisexcitationhas,asitnowappearsfromourtests,aresultaltogethersimilartothatofactualreturntoconsciousness。Innerconnectionsareestablishedbetweensuccessivelyandinternallyarousedsyllablesjustasbetweensyllablessuccessivelyraisedtoconsciousness,exceptthattheformerarenaturallyoflessstrength。Secretthreadsarespunwhichbindtogethertheseries2,4,6,notyetarousedtoconsciousness,andpreparethewayforitsconsciousappearance。Suchthreadsexistedalreadyingreaterstrengthasaresultofthelearningoftheoriginalseries;

  thepresenteffectisthatofstrengtheningsomewhatconnectionsalreadymade。Andthatisnothingelsethanwhatwasfoundabove:iftwosyllable-combinations——1,3,5……and2,4,6……——arefrequentlyassociatedinconsciousness(thelearningoftheoriginalseries)thenthesubsequentlearningofthesecondcombination(derivedseriesII,IV,VI)soonafterthelearningofthefirst(derivedseriesI,III,V)hasconsiderablylessresistancetoovercomethanthelatter。Acertainstrengtheningofassociationstakesplace,notonlydirectly,throughconsciousrepetitionoftheassociatedmembers,butalsoindirectlythroughtheconsciousrepetitionofothermemberswithwhichthefirsthadbeenfrequentlyconnected。

  Thiswayofviewingthematterisaconsequenceoftheassumption(whichbecamenecessaryabove,p。109[Section39])oftheformationofassociativeconnectionsovermoreinterveningmembersthancouldbecomprehendedinoneclearlyconsciousact。Theseconnectionswouldbeveryfruitfulintheexplanationofmanysurprisingphenomenaofmemoryandrecollection,butonaccountoftheuncertaintyoftheirexperientialbasisIrefrainforthepresentfrompursuingthemfurther。

  Footnotes[1]Herbart,Lehrb。z。Psychol。,Sect。29。Asimilar\"pleasing\"view,ashecallsit,wasdevelopedbyLotze,Metaphysik(1879)

  p。527,withthemodificationthatheattemptstoeliminatethenotionofvaryingstrengthoftheideas,whichviewherejects。Inaccordancewiththeviewmentionedfirstabove,heseestherealreasonforafaithfulreproductionofaseriesofideasinthefactthatassociationismadeonlyfromonelinktothefollowinglink。Accordingly,heteaches,inhisLecturesonPsychology(p。22),\"Anytwoideas,regardlessofcontent,areassociatedwhentheyareproducedeithersimultaneouslyorinimmediatesuccession——i。e。,withoutaninterveninglink。Anduponthiscanbebasedwithoutfurtherartificethespecialeasewithwhichwereproduceaseriesofideasintheirproperorderbutnotoutofthatorder。By\"furtherartifice\"heseemstomeanHerbart’sattemptatanarrangement[2]Ihaveomittedtopresentafewtestswithseriesof16syllableseachfromwhichthisnumberwasobtained,becausetheresultsofthesixthchaptersufficientlycoverthispoint。There(p。55[beginningofChapterVI]),wesawthatsixseriesof16syllableseach,eachseriesbeingrepeated32times,couldbememorisedafter24hoursinanaverageof863seconds。32repetitionsare,onanaverage,justnecessarytobringaboutthefirstpossiblereproductionofseriesof16syllableseach。Consideringthecloseproportionwhichexistsbetweenthenumberofrepetitionsonagivendayandthesavingofworkonthenext,itcannotmuchmatterwhethertheserieswererepeated,each32times,orwerememorisedeachtothefirstpossiblereproduction。Sincethelatterrequiresabout1,270seconds,theworkofrepetitiononthefollowingdayamounts,asstatedabove,toabouttwothirdsofthistime。Therelativesavingwhen16-syllableseriesarerelearnedafter24hours,is,therefore,scarcelydifferentfromthatfoundforseriesof12and13syllables(chaptersVIIandVIII),whileitgraduallyincreasesforstillgreaterlengthofseries。

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