Learning curve - Wikipedia

A learning curve is a graphical representation of the relationship between how proficient people are at a task and the amount of experience they have. Learningcurve FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch Relationshipbetweenproficiencyandexperience Forotheruses,seeLearningcurve(disambiguation). Anexampleofasubjectbecomingmoreproficientatataskastheyspendmoretimedoingit.Inthisexample,proficiencyincreasesrapidlyatfirstbutatlaterstagestherearediminishingreturns. Anexampleofwhatthecommon(yetconfusing)expression"steeplearningcurve"isreferringto.Thesubjectspendsagreatamountoftimebutdoesnotseeanincreaseinproficiencyatfirst. Alearningcurveisagraphicalrepresentationoftherelationshipbetweenhowproficientpeopleareatataskandtheamountofexperiencetheyhave.Proficiency(measuredontheverticalaxis)usuallyincreaseswithincreasedexperience(thehorizontalaxis),thatistosay,themoresomeone,groups,companiesorindustriesperformatask,thebettertheirperformanceatthetask.[1] Thecommonexpression"asteeplearningcurve"isamisnomersuggestingthatanactivityisdifficulttolearnandthatexpendingmucheffortdoesnotincreaseproficiencybymuch,althoughalearningcurvewithasteepstartactuallyrepresentsrapidprogress.[2][3]Infact,thegradientofthecurvehasnothingtodowiththeoveralldifficultyofanactivity,butexpressestheexpectedrateofchangeoflearningspeedovertime.Anactivitythatitiseasytolearnthebasicsof,butdifficultytogainproficiencyin,maybedescribedashaving"asteeplearningcurve". Learningcurvemayrefertoaspecifictaskorabodyofknowledge.HermannEbbinghausfirstdescribedthelearningcurvein1885inthefieldofthepsychologyoflearning,althoughthenamedidnotcomeintouseuntil1903.[4][5]In1936TheodorePaulWrightdescribedtheeffectoflearningonproductioncostsintheaircraftindustry.[6]Thisform,inwhichunitcostisplottedagainsttotalproduction,issometimescalledanexperiencecurve. Contents 1Inpsychology 2Ineconomics 3Examplesandmathematicalmodeling 4Inmachinelearning 5Broaderinterpretations 6Generallearninglimits 7Inculture 7.1"Steeplearningcurve" 7.2"Onasteeplearningcurve" 7.3Difficultycurvesinvideogames 8Seealso 9References 10Externallinks Inpsychology[edit] HermannEbbinghaus'testsinvolvedmemorizingseriesofnonsensesyllables,andrecordingthesuccessoveranumberoftrials.Thetranslationdoesnotusetheterm'learningcurve'—buthepresentsdiagramsoflearningagainsttrialnumber.Healsonotesthatthescorecandecrease,orevenoscillate.[4][3][7] Thefirstknownuseoftheterm'learningcurve'isfrom1903:"BryanandHarter(6)foundintheirstudyoftheacquisitionofthetelegraphiclanguagealearningcurvewhichhadtherapidriseatthebeginningfollowedbyaperiodofslowerlearning,andwasthusconvextotheverticalaxis."[5][3] PsychologistArthurBillsgaveamoredetaileddescriptionoflearningcurvesin1934.Healsodiscussedthepropertiesofdifferenttypesoflearningcurves,suchasnegativeacceleration,positiveacceleration,plateaus,andogivecurves.[8] Ineconomics[edit] In1936,TheodorePaulWrightdescribedtheeffectoflearningonproductioncostsintheaircraftindustryandproposedamathematicalmodelofthelearningcurve.[6] In1968BruceHendersonoftheBostonConsultingGroup(BCG)generalizedtheUnitCostmodelpioneeredbyWright,andspecificallyusedaPowerLaw,whichissometimescalledHenderson'sLaw.[9]Henamedthisparticularversiontheexperiencecurve.[10][11] ResearchbyBCGinthe1970sobservedexperiencecurveeffectsforvariousindustriesthatrangedfrom10to25percent.[12] Theeconomiclearningofproductivityandefficiencygenerallyfollowsthesamekindsofexperiencecurvesandhaveinterestingsecondaryeffects.Efficiencyandproductivityimprovementcanbeconsideredaswholeorganizationorindustryoreconomylearningprocesses,aswellasforindividuals.Thegeneralpatternisoffirstspeedingupandthenslowingdown,asthepracticallyachievablelevelofmethodologyimprovementisreached.Theeffectofreducinglocaleffortandresourceusebylearningimprovedmethodsoftenhastheoppositelatenteffectonthenextlargerscalesystem,byfacilitatingitsexpansion,oreconomicgrowth,asdiscussedintheJevonsparadoxinthe1880sandupdatedintheKhazzoom-BrookesPostulateinthe1980s. Acomprehensiveunderstandingoftheapplicationoflearningcurveonmanagerialeconomicswouldprovideplentyofbenefitsonstrategiclevel.Peoplecouldpredicttheappropriatetimingoftheintroductionsfornewproductsandofferingcompetitivepricingdecisions,decidinginvestmentlevelsbystimulateinnovationsonproductsandtheselectionoforganizationaldesignstructures.[13] BalachanderandSrinivasanusedtostudyadurableproductanditspricingstrategyontheprinciplesofthelearningcurve.Basedontheconceptsthatthegrowingexperienceinproducingandsellingaproductwouldcausethedeclineofunitproductioncost,theyfoundthepotentialbestintroductorypriceforthisproduct.[14]Asfortheproblemsofproductionmanagementunderthelimitationofscarceresources,Liao[15]observedthatwithoutincludingtheeffectsofthelearningcurveonlaborhoursandmachineshours,peoplemightmakeincorrectmanagerialdecisions.DemeesterandQi[16]usedthelearningcurvetostudythetransitionbetweentheoldproducts’eliminatingandnewproducts’introduction.Theirresultsindicatedthattheoptimalswitchingtimeisdeterminedbythecharacteristicsofproductandprocess,marketfactors,andthefeaturesoflearningcurveonthisproduction.Konstantaras,Skouri,andJaber[17]appliedthelearningcurveondemandforecastingandtheeconomicorderquantity.Theyfoundthatthebuyersobeytoalearningcurve,andthisresultisusefulfordecision-makingoninventorymanagement. Examplesandmathematicalmodeling[edit] Alearningcurveisaplotofproxymeasuresforimpliedlearning(proficiencyorprogressiontowardalimit)withexperience. Thehorizontalaxisrepresentsexperienceeitherdirectlyastime(clocktime,orthetimespentontheactivity),orcanberelatedtotime(anumberoftrials,orthetotalnumberofunitsproduced). Theverticalaxisisameasurerepresenting'learning'or'proficiency'orotherproxyfor"efficiency"or"productivity".Itcaneitherbeincreasing(forexample,thescoreinatest),ordecreasing(thetimetocompleteatest). Fortheperformanceofonepersoninaseriesoftrialsthecurvecanbeerratic,withproficiencyincreasing,decreasingorlevelingoutinaplateau. Whentheresultsofalargenumberofindividualtrialsareaveragedthenasmoothcurveresults,whichcanoftenbedescribedwithamathematicalfunction. S-curveorsigmoidfunction Exponentialgrowth Exponentialriseorfalltoalimit Powerlaw Severalmainfunctionshavebeenused:[18][19][20] TheS-CurveorSigmoidfunctionistheidealizedgeneralformofalllearningcurves,withslowlyaccumulatingsmallstepsatfirstfollowedbylargerstepsandthensuccessivelysmalleroneslater,asthelearningactivityreachesitslimit.Thatidealizesthenormalprogressionfromdiscoveryofsomethingtolearnaboutfollowedtothelimitoflearningaboutit.Theothershapesoflearningcurves(4,5&6)showsegmentsofS-curveswithouttheirfullextents.Inthiscasetheimprovementofproficiencystartsslowly,thenincreasesrapidly,andfinallylevelsoff. Exponentialgrowth;theproficiencycanincreasewithoutlimit,asinExponentialgrowth ExponentialriseorfalltoaLimit;proficiencycanexponentiallyapproachalimitinamannersimilartothatinwhichacapacitorchargesordischarges(exponentialdecay)througharesistor.Theincreaseinskillorretentionofinformationmayincreaserapidlytoitsmaximumrateduringtheinitialattempts,andthengraduallylevelsout,meaningthatthesubject'sskilldoesnotimprovemuchwitheachlaterrepetition,withlessnewknowledgegainedovertime. Powerlaw;similarinappearancetoanexponentialdecayfunction,andisalmostalwaysusedforadecreasingperformancemetric,suchascost.Italsohasthepropertythatifplottedasthelogarithmofproficiencyagainstthelogarithmofexperiencetheresultisastraightline,anditisoftenpresentedthatway. ThespecificcaseofaplotofUnitCostversusTotalProductionwithapowerlawwasnamedtheexperiencecurve:themathematicalfunctionissometimescalledHenderson'sLaw.Thisformoflearningcurveisusedextensivelyinindustryforcostprojections.[21] Inmachinelearning[edit] Furtherinformation:Learningcurve(machinelearning) Plotsrelatingperformancetoexperiencearewidelyusedinmachinelearning.Performanceistheerrorrateoraccuracyofthelearningsystem,whileexperiencemaybethenumberoftrainingexamplesusedforlearningorthenumberofiterationsusedinoptimizingthesystemmodelparameters.[22]Themachinelearningcurveisusefulformanypurposesincludingcomparingdifferentalgorithms,[23]choosingmodelparametersduringdesign,[24]adjustingoptimizationtoimproveconvergence,anddeterminingtheamountofdatausedfortraining.[25] Broaderinterpretations[edit] Initiallyintroducedineducationalandbehavioralpsychology,thetermhasacquiredabroaderinterpretationovertime,andexpressionssuchas"experiencecurve","improvementcurve","costimprovementcurve","progresscurve","progressfunction","startupcurve",and"efficiencycurve"areoftenusedinterchangeably.Ineconomicsthesubjectisratesof"development",asdevelopmentreferstoawholesystemlearningprocesswithvaryingratesofprogression.Generallyspeakingalllearningdisplaysincrementalchangeovertime,butdescribesan"S"curvewhichhasdifferentappearancesdependingonthetimescaleofobservation.Ithasnowalsobecomeassociatedwiththeevolutionarytheoryofpunctuatedequilibriumandotherkindsofrevolutionarychangeincomplexsystemsgenerally,relatingtoinnovation,organizationalbehaviorandthemanagementofgrouplearning,amongotherfields.[26]Theseprocessesofrapidlyemergingnewformappeartotakeplacebycomplexlearningwithinthesystemsthemselves,whichwhenobservable,displaycurvesofchangingratesthataccelerateanddecelerate. Generallearninglimits[edit] Learningcurves,alsocalledexperiencecurves],relatetothemuchbroadersubjectofnaturallimitsforresourcesandtechnologiesingeneral.Suchlimitsgenerallypresentthemselvesasincreasingcomplicationsthatslowthelearningofhowtodothingsmoreefficiently,likethewell-knownlimitsofperfectinganyprocessorproductortoperfectingmeasurements.[27]Thesepracticalexperiencesmatchthepredictionsofthesecondlawofthermodynamicsforthelimitsofwastereductiongenerally.Approachinglimitsofperfectingthingstoeliminatewastemeetsgeometricallyincreasingefforttomakeprogress,andprovidesanenvironmentalmeasureofallfactorsseenandunseenchangingthelearningexperience.Perfectingthingsbecomesevermoredifficultdespiteincreasingeffortdespitecontinuingpositive,ifeverdiminishing,results.Thesamekindofslowingprogressduetocomplicationsinlearningalsoappearsinthelimitsofusefultechnologiesandofprofitablemarketsapplyingtoproductlifecyclemanagementandsoftwaredevelopmentcycles).Remainingmarketsegmentsorremainingpotentialefficienciesorefficienciesarefoundinsuccessivelylessconvenientforms. Efficiencyanddevelopmentcurvestypicallyfollowatwo-phaseprocessoffirstbiggerstepscorrespondingtofindingthingseasier,followedbysmallerstepsoffindingthingsmoredifficult.Itreflectsburstsoflearningfollowingbreakthroughsthatmakelearningeasierfollowedbymeetingconstraintsthatmakelearningeverharder,perhapstowardapointofcessation. NaturalLimitsOneofthekeystudiesintheareaconcernsdiminishingreturnsoninvestmentsgenerally,eitherphysicalorfinancial,pointingtowholesystemlimitsforresourcedevelopmentorotherefforts.ThemoststudiedofthesemaybeEnergyReturnonEnergyInvestedorEROEI,discussedatlengthinanEncyclopediaoftheEartharticleandinanOilDrumarticleandseriesalsoreferredtoasHubertcurves.Theenergyneededtoproduceenergyisameasureofourdifficultyinlearninghowtomakeremainingenergyresourcesusefulinrelationtotheeffortexpended.Energyreturnsonenergyinvestedhavebeenincontinualdeclineforsometime,causedbynaturalresourcelimitsandincreasinginvestment.Energyisbothnature'sandourownprincipalresourceformakingthingshappen.Thepointofdiminishingreturnsiswhenincreasinginvestmentmakestheresourcemoreexpensive.Asnaturallimitsareapproached,easilyusedsourcesareexhaustedandoneswithmorecomplicationsneedtobeusedinstead.AsanenvironmentalsignalpersistentlydiminishingEROIindicatesanapproachofwholesystemlimitsinourabilitytomakethingshappen. UsefulNaturalLimitsEROEImeasuresthereturnoninvestedeffortasaratioofR/Iorlearningprogress.TheinverseI/Rmeasureslearningdifficulty.ThesimpledifferenceisthatifRapproacheszeroR/Iwilltoo,butI/Rwillapproachinfinity.Whencomplicationsemergetolimitlearningprogressthelimitofusefulreturns,uR,isapproachedandR-uRapproacheszero.ThedifficultyofusefullearningI/(R-uR)approachesinfinityasincreasinglydifficulttasksmaketheeffortunproductive.Thatpointisapproachedasaverticalasymptote,ataparticularpointintime,thatcanbedelayedonlybyunsustainableeffort.Itdefinesapointatwhichenoughinvestmenthasbeenmadeandthetaskisdone,usuallyplannedtobethesameaswhenthetaskiscomplete.Forunplannedtasksitmaybeeitherforeseenordiscoveredbysurprise.Theusefulnessmeasure,uR,isaffectedbythecomplexityofenvironmentalresponsesthatcanonlybemeasuredwhentheyoccurunlesstheyareforeseen. Inculture[edit] "Steeplearningcurve"[edit] Theexpression"steeplearningcurve"isusedwithoppositemeanings.Mostsources,includingtheOxfordEnglishDictionary,theAmericanHeritageDictionaryoftheEnglishLanguage,andMerriam-Webster’sCollegiateDictionary,definealearningcurveastherateatwhichskillisacquired,soasteepincreasewouldmeanaquickincrementofskill.[2][28] However,thetermisoftenusedincommonEnglishwiththemeaningofadifficultinitiallearningprocess.[3][28] Arguably,thecommonEnglishuseisduetometaphoricalinterpretationofthecurveasahilltoclimb.(Asteeperhillisinitiallyhard,whileagentleslopeislessstrainful,thoughsometimesrathertedious.Accordingly,theshapeofthecurve(hill)maynotindicatethetotalamountofworkrequired.Instead,itcanbeunderstoodasamatterofpreferencerelatedtoambition,personalityandlearningstyle.) Shortandlonglearningcurves ProductAhaslowerfunctionalityandashortlearningcurve.ProductBhasgreaterfunctionalitybuttakeslongertolearn Theterm'learningcurve'withmeaningsof'easy'and'difficult'canbedescribedwithadjectiveslike'short'and'long'ratherthansteepand'shallow'.[2]Iftwoproductshavesimilarfunctionalitythentheonewitha"steep"curveisprobablybetter,becauseitcanbelearnedinashortertime.Ontheotherhand,iftwoproductshavedifferentfunctionality,thenonewithashortcurve(ashorttimetolearn)andlimitedfunctionalitymaynotbeasgoodasonewithalongcurve(alongtimetolearn)andgreaterfunctionality. Forexample,theWindowsprogramNotepadisextremelysimpletolearn,butofferslittleafterthis.AttheotherextremeistheUNIXterminaleditorviorVim,whichisdifficulttolearn,butoffersawidearrayoffeaturesaftertheuserhaslearnedhowtouseit.[29] "Onasteeplearningcurve"[edit] BenZimmerdiscussestheuseoftheterm"onasteeplearningcurve"inDowntonAbbey,atelevisionseriessetintheearly20thcentury,concentratingmainlyonwhetheruseofthetermisananachronism."MatthewCrawley,thepresumptiveheirofDowntonAbbeyandnowtheco-owneroftheestate,says,'I'vebeenonasteeplearningcurvesincearrivingatDownton.'BythishemeansthathehashadadifficulttimelearningthewaysofDownton,butpeopledidnotstarttalkingthatwayuntilthe1970s."[3][30] Zimmeralsocommentsthatthepopularuseofsteepasdifficultisareversalofthetechnicalmeaning.Heidentifiesthefirstuseofsteeplearningcurveas1973,andthearduousinterpretationas1978. Difficultycurvesinvideogames[edit] Theideaoflearningcurvesisoftentranslatedintovideogamegameplayasa"difficultycurve",whichdescribedhowhardthegamemaygetastheplayerprogressesthroughthegameandrequiringtheplayertoeitherbecomemoreproficientwiththegame,gainbetterunderstandingofthegame'smechanics,and/orspendtime"grinding"toimprovehisorhercharacters.Establishingtherightdifficultycurveispartofachievingthegamebalancewithinatitle.Aswithlearningcurvesineducationalsettings,difficultycurvescanhavemultitudesofshapes,andgamesmayfrequentlyprovidevariouslevelsofdifficultythatchangetheshapeofthiscurverelativetoitsdefaulttomakethegameharderoreasier.[31][32]Optimallythedifficultyofavideogameincreasesincorrespondencewithplayersability.Gamesmustneitherbetoochallengingnortooundemandingnortoofortuitous.[33]Theplayerswillcontinueplayingaslongasagameisperceivedtobewinnable.Thisisthereforereferredtoastheillusionofwinnability.Togenerateanillusionofwinnabilitygamescaninclude,internalvalue(asenseofmovingtowardsagoalandbeingrewardedforit)drivenbyconflictwhichcanbegeneratedbyanantagonisticenvironmentandstorydrivensuspenseintheformofworldbuilding.Thelatterisnotpivotaltoprogressinginagame.[34]Gamedesignersmayalsomakechangesingameplayby,forinstance,limitingresources.Oneperspectiveisthatifplayersarenottrickedtobelievethatthevideogameworldisreal-iftheworlddoesnotfeelvibrant-thenthereisnopointincreatingthegame.[35][36] Seealso[edit] Forgettingcurve Learningspeed Laborproductivity Learning-by-doing(economics) Populationgrowth Trialanderror References[edit] ^Compare:"LearningCurve".BusinessDictionary.Archivedfromtheoriginalon14August2020.Retrieved8December2018.Graphicalrepresentationofthecommonsenseprinciplethatmoreonedoessomethingthebetteronegetsatit.Learningcurveshowstherateofimprovementinperformingataskasafunctionoftime,ortherateofchangeinaveragecost(inhoursormoney)asafunctionofcumulativeoutput. ^abcReichenbach,DanielJ.;Tackett,ADarrel;Harris,James;Camacho,Diego;Graviss,EdwardA.;Dewan,Brendan;Vavra,Ashley;Stiles,Anquonette;Fisher,WilliamE.;Brunicardi,FCharles;Sweeney,JohnF.(2006)."LaparoscopicColonResectionEarlyintheLearningCurve".AnnalsofSurgery.243(6):730–737.doi:10.1097/01.sla.0000220039.26524.fa.PMC 1570580.PMID 16772776.,seethe"Discussions"section,Dr.Smith'sremarkabouttheusageoftheterm"steeplearningcurve":"First,semantics.Asteeplearningcurveisonewhereyougainproficiencyoverashortnumberoftrials.Thatmeansthecurveissteep.Ithinksemanticallywearereallytalkingaboutaprolongedorlonglearningcurve.Iknowitisasubtledistinction,butIcan'tmisstheopportunitytomakethatpoint." ^abcdeZimmer,Ben(February8,2013)A"SteepLearningCurve"for"DowntonAbbey".visualthesaurus.com ^abEbbinghaus,Hermann(1913).Memory:AContributiontoExperimentalPsychology.AnnalsofNeurosciences.Vol. 20.TeachersCollege,ColumbiaUniversity.pp. 155–6.doi:10.5214/ans.0972.7531.200408.ISBN 978-0-7222-2928-6.PMC 4117135.PMID 25206041. ^abHall,GranvilleStanley;Titchener,EdwardBradford;Dallenbach,KarlM.(1903).TheAmericanJournalofPsychology.Vol. 14.UniversityofIllinoisPress. ^abWright,T.P.(1936)."FactorsAffectingtheCostofAirplanes"(PDF).JournaloftheAeronauticalSciences.3(4):122–128.doi:10.2514/8.155. ^"ClassicsintheHistoryofPsychology–IntroductiontoEbbinghaus(1885/1913)byR.H.Wozniak".psychclassics.yorku.ca. ^Bills,A.G.(1934).Generalexperimentalpsychology.LongmansPsychologySeries.pp.192–215.NewYork:Longmans,GreenandCo. ^"WhatisHenderson'sLaw?".Henderson'sLaw.Retrieved2020-06-02. ^ Henderson,Bruce(1968-01-01)TheExperienceCurve.BostonConsultingGroup ^Grant,RobertM.(2004),Contemporarystrategyanalysis,U.S.,UK,Australia,Germany:Blackwellpublishing,ISBN 1-4051-1999-3 ^Hax,ArnoldoC.;Majluf,NicolasS.(October1982),"Competitivecostdynamics:theexperiencecurve",Interfaces,12(5):50–61,doi:10.1287/inte.12.5.50 ^Abernathy,W.J.;Wayne,K.(1974),"Limitsofthelearningcurve",HarvardBusinessReview,52(5):109–119 ^Balacahnder,S.;Srinivasan,K.(1998),"Modifyingcustomerexpectationsofpricedecreasesforadurableproduct",ManagerialScience,44(6):776–786 ^Liao,W.M.(1979),"Effectsoflearningonresourceallocationdecisions",DecisionSciences,10(1):116–125 ^Demeester,L.L.;Qi,M.(2005),"Managinglearningresourcesforconsecutiveproductgenerations",InternationalJournalofProductionEconomics,95(2):265–283 ^Konstantaras,I.;Skouri,K.;Jaber,M.Y.(2012),"Inventorymodelsforimperfectqualityitemswithshortagesandlearningininspection",AppliedMathematicalModelling,36(11):5334–5343 ^Newell,A.(1980)Mechanismsofskillacquisitionandthelawofpractice.UniversityofSouthernCalifornia ^Ritter,F.E.,&Schooler,L.J.(2002)"Thelearningcurve".InInternationalEncyclopediaoftheSocialandBehavioralSciences,pp.8602–8605.Amsterdam:Pergamon.ISBN 9780080430768 ^Leibowitz,Nathaniel;Baum,Barak;Enden,Giora;Karniel,Amir(2010)."Theexponentiallearningequationasafunctionofsuccessfultrialsresultsinsigmoidperformance"(PDF).JournalofMathematicalPsychology.54(3):338–340.doi:10.1016/j.jmp.2010.01.006. ^"LearningCurveBasics"(PDF).Archivedfromtheoriginal(PDF)on2013-07-18.Retrieved2013-03-17.U.S.DepartmentofDefenseManualNumber5000.2-M,mandatestheuseoflearningcurvesforcostingofdefenseprograms(variablecostsofproduction) ^Sammut,Claude(2011).Webb,GeoffreyI.(ed.).EncyclopediaofMachineLearning(1st ed.).Springer.p. 578.ISBN 978-0-387-30768-8. ^Madhavan,P.G.(1997)."ANewRecurrentNeuralNetworkLearningAlgorithmforTimeSeriesPrediction"(PDF).JournalofIntelligentSystems.p. 113,Fig.3. ^Singh,Anmol(2021)."Machinelearningforastronomywithscikitlearning".LearningCurveMyPersonalTutor.{{citeweb}}:CS1maint:url-status(link) ^Meek,Christopher;Thiesson,Bo;Heckerman,David(Summer2002)."TheLearning-CurveSamplingMethodAppliedtoModel-BasedClustering"(PDF).JournalofMachineLearningResearch.2(3):397. ^Gersick,ConnieJG(1991)."RevolutionaryChangeTheories:AMultilevelExplorationofthePunctuatedEquilibriumParadigm".TheAcademyofManagementReview.16(1):10–36.doi:10.5465/amr.1991.4278988.JSTOR 258605. ^Petley,BrianW.(1988)."TowardstheLimitsofPrecisionandAccuracyinMeasurement".PhysicsinaTechnologicalWorld(88):291.Bibcode:1988ptw..conf..291P. ^ab"Steeplearningcurves".2009-07-16. ^Curves,apparentlyfromRowe,Steve(17November2004)CodeEditorLearningCurves.msdn.com ^Zimmer,Ben(February13,2012)"DowntonAbbey"anachronisms:beyondnitpickery,upenn.edu,alsoCommentbyJOliver :SeasonThree,episode5 ^Larsen,JimmyMarcus(May24,2010)."DifficultyCurves".Gamasutra.RetrievedFebruary3,2020. ^Aponte,Maria-Virginia;Levieux,Guillaume;Natkin,Stéphane(2009)."ScalingtheLevelofDifficultyinSinglePlayerVideoGames"(PDF).InNatkin,S.;Dupire,J.(eds.).LectureNotesinComputerScience.InternationalConferenceonEntertainmentComputing2009.Vol. 5709.Berlin:Springer.doi:10.1007/978-3-642-04052-8_3.RetrievedFebruary3,2020. ^Ruggill,JuddEthan;McAllister,KenS.(11May2011)."Work".GamingMatters:Art,Science,Magic,andtheComputerGameMedium.UniversityofAlabamaPress.p. 89.ISBN 978-0-8173-1737-9. ^Wolf,Mark,J.P.(12May2020).World-BuildersonWorld-Building:AnExplorationofSubcreation.Taylor&Francis.p. 67.ISBN 978-0-429-51601-6. ^VanEck,Richard(31May2010)."FeedforwardasanEssentialActivePrinciple".GamingandCognition:TheoriesandPracticefromtheLearningSciences:TheoriesandPracticefromtheLearningSciences.IGIGlobal.pp. 112–115.ISBN 978-1-61520-718-3. ^Holmes,Dylan(2012)."TheRiseofCutscenes".AMindForeverVoyaging:AHistoryofStorytellinginVideoGames.DylanHolmes.p. 83.ISBN 978-1-4800-0575-4. Externallinks[edit] Learningcurve Retrievedfrom"https://en.wikipedia.org/w/index.php?title=Learning_curve&oldid=1090321290" Categories:LearningCognitivescienceCurvesHiddencategories:CS1maint:url-statusArticleswithshortdescriptionShortdescriptionisdifferentfromWikidataPagesusingtheGraphextension Navigationmenu Personaltools NotloggedinTalkContributionsCreateaccountLogin Namespaces ArticleTalk English Views ReadEditViewhistory More Search Navigation MainpageContentsCurrenteventsRandomarticleAboutWikipediaContactusDonate Contribute HelpLearntoeditCommunityportalRecentchangesUploadfile Tools WhatlinkshereRelatedchangesUploadfileSpecialpagesPermanentlinkPageinformationCitethispageWikidataitem Print/export DownloadasPDFPrintableversion Languages AfrikaansالعربيةAzərbaycancaБългарскиCatalàDeutschΕλληνικάEspañolEuskaraفارسیFrançais한국어BahasaIndonesiaItalianoעבריתქართულიNederlands日本語PortuguêsРусскийSvenskaУкраїнська粵語中文 Editlinks