modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... ·...
TRANSCRIPT
![Page 1: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/1.jpg)
1
Modelingoftechnologicalperformancetrendsusingdesigntheory
SubarnaBasnet
MassachusettsInstituteofTechnology,DepartmentofMechanicalEngineering,77MassachusettsAve,Cambridge,Massachusetts02139
ChristopherL.Magee
MassachusettsInstituteofTechnology,InstituteforData,Systems,andSociety,77MassachusettsAve,Cambridge,Massachusetts02139
Abstract
Functionaltechnicalperformanceusuallyfollowsanexponentialdependenceontimebuttherateofchange(theexponent)variesgreatlyamongtechnologicaldomains.Thispaperpresentsasimplemodelthatprovidesanexplanatoryfoundationforthesephenomenabasedupontheinventivedesignprocess.Themodelassumesthatinvention‐novelandusefuldesign‐arisesthroughprobabilisticanalogicaltransfersthatcombineexistingknowledgebycombiningexistingindividualoperationalideastoarriveatnewindividualoperatingideas.Thecontinuingproductionofindividualoperatingideasreliesuponinjectionofnewbasicindividualoperatingideasthatoccursthroughcouplingofscienceandtechnologysimulations.Theindividualoperationalideasthatresultfromthisprocessarethenmodeledasbeingassimilatedincomponentsofartifactscharacteristicofatechnologicaldomain.Accordingtothemodel,twoeffects(differencesininteractionsamongcomponentsfordifferentdomainsanddifferencesinscalinglawsfordifferentdomains)accountforthedifferencesfoundinimprovementratesamongdomainswhereastheanalogicaltransferprocessisthesourceoftheexponentialbehavior.Themodelissupportedbyanumberofknownempiricalfacts:furtherempiricalresearchissuggestedtoindependentlyassessfurtherpredictionsmadebythemodel.Keywords:Modeling,design,combinatorialInvention,technologicalperformance
![Page 2: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/2.jpg)
2
Nomenclature and terminology QJ=intensiveperformanceofartifactswithinatechnologicaldomain,Jt=timeIOI=individualoperatingideasPIOI=probabilityofcombinationofanytwoIOIIOI0=basicIOI‐IOIthatfirstintroduceanaturalphenomenonintheOperationsregimeIOIC=cumulativenumberofIOIintheOperationsregimeIOIL=maximumnumberofpossibleIOIinOperationsregimeattimetIOISC=IOICsuccessfullyintegratedintoadomainartifactK=annualrateofincreaseinIOIcintheOperationsregimeKJ=annualrate(whentimeisinyears)ofperformanceimprovementmeasuredbytheslopeofaplotoflnQJvs.timefi=fitnessinUnderstandingregimeforascientificfieldiFU=cumulativefitnessofUnderstandingregimedJ=interactionparameteroftechnologicaldomainJdefinedasinteractiveout‐linksfromatypicalcomponenttoothercomponentsinartifactsindomainJsJ=designparameteraffectingtheperformanceofanartifactindomainJAJ=exponentofdesignparameterinpowerlawfordomainJ,relatingperformanceandthedesignparameter
1. Introduction Inventionsaretheoutputsofthedesignprocesswhentheyreachsufficientnoveltyandutilitytoratethatterm:theyareabasicbuildingblockoftechnologicalprogressandthefundamentalunitofthispaper.Inourformulation,technologicaldomainsconsistofdesignedartifactsthatutilizeaspecifiedbodyofknowledgetoachieveaspecificgenericfunction(Mageeet.al.2014).Thus,technologicaldomainsinvolvealargenumberofinter‐relatedinventionsasevensingleartifactscanembodymultipleinventions.Arthur(2006)usedtheterm“technologies”todescribesomethingthatbridgesinventionsandtechnologicaldomains;accordingtoArthur,theseuse“effects”toachievesome“purpose”.Thus,onecanalsosaythateachartifactisamaterialrealizationofitsdesignthatintentionallyembodiestheeffects.Thispaperbringstogetherthreebodiesofresearchthatdonotusuallyinteract.Thefirstisthedesignresearchfield,particularlyitscognitivescientificinsightsonthedesignprocess.Thesecondisthetechnologicalchangefieldwheremostresearchershavebeeneconomistsorbusinessscholars.Thethirdareaisquantitativemodelingofperformanceofartifacts.Theobjectiveoftheworkreportedhereistouseunderstandingofthedesignandinventionprocesstomodelperformance‐howwellaspecificdesignedartifactachievesitsintendedfunctionorpurpose.Inparticular,weexamineperformancetrends‐thetimedependenceofperformanceasrealizedinaseriesofimproveddesignsofartifactsthatarise
![Page 3: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/3.jpg)
3
overtime.Wedosoinanattempttodevelopanexplanatoryandquantitativepredictivemodelforwhyperformanceimprovesexponentiallyovermultipledesignswithwidelyvaryingratesamongtechnologicaldomains,rangingfrom3to65%annuallyfordomainscharacterizedsofar.Ourresearchquestioniswhetheraquantitativepredictivemodelbaseduponfoundationsandinsightsaboutthedesignprocessleadstoresultsconsistentwiththisexponentialbehaviorandwhethersuchamodelhelpsexplainandpossiblypredictthevariationintherateofimprovement.Wefirstdiscusssomerelevantliteratureineachofthethreeintersectingfields.
2 Background
2.1 Design, invention and cognitive psychology literature Whatconnectionsbetweentechnologicalchangeanddesignresearchcanbeinferredfromtheexistingliterature?Businessscholarsandeconomistsoftenviewtechnicalchangeasoccurringinsideablackbox,andhaveusuallyavoidedexaminingdesignactivitiesthatarethesourceoftechnologicalchange.AnimportantrecentpublicationthatbeginstobuildabridgebetweenaspectsofdesignresearchandtheeconomicsoftechnologicalchangeisthepaperbyBaldwinandClark(2006).Theseauthors(andLuoetal.2014)pointspecificallytoacentralrolefordesigninachievingeconomicvalue.Inadditiontoeconomicperspectives,anotherviewthatsomewhatignoresdesignisthelinearmodelaccreditedtoVannevarBush(Bush,1945),whichconsiderstechnologicalchangeoccurringthroughapplicationofscience.Asacounterview,inhisseminalbook,TheSciencesoftheArtificial,HerbertSimon(1969,1996)wasthefirsttohighlightthatdesignisanactivitystandingonitsownright,likenaturalsciences,andhasitsownsetoflogic,concepts,andprinciples.Whiletheprimarygoalofnaturalscienceistoproducepredictiveexplanationsofnaturalphenomena,theprimarygoalofdesignistocreateartifacts.Thedesignactivityiscentraltocreationandimprovementofartifactsinalltechnologicaldomainsandinvolvescognitiveactivitiessuchastheuseofknowledge,reasoning,andunderstanding.Theseindisputablecognitiveactivitieshavebeennotedbymanyscholarswhohavestudiedinventionanddesign(Simon1969,Dasgupta1996,GeroandKannengiesser(2004),HatchuelandWeil2009).Inthecontextofrealizinghigherperformancefromsubsequentgenerationsofartifacts,theroleofinvention,asoneoutcomeofthedesignprocess,isacriticalonesinceimprovementinperformanceofartifactsmuststronglyreflecttheinventions.AsVincenti(1990,pg.230)putsit,inventiveactivityisasourceofnewoperationalprinciples,andnormalconfigurationsthatunderliefuturenormalorradicaldesigns.Theoperationalprinciples(Polyani1962,Vincenti1990)ofanartifactdescribehowitscomponentsfulfilltheirspecialfunctionsincombiningtoanoveralloperationtoachievethefunctionoftheartifact.ModelsfoundusefulindescribingthecreativedesignprocessincludetheGeneploremodel(Finke,WardandSmith1996),topologicalstructures(BrahaandReich2003),FBStheory(GeroandKannengiesser2004),CKtheory(HatchuelandWeil2009),infuseddesign(Shaietal.2009),analyticalproductdesign(Frischknechtetal.2009),andothermodelingapproaches.Althoughalloftheseframeworksinclude–tosomedegree‐thekeyideaof
![Page 4: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/4.jpg)
4
combiningexistingideas(forexample,intheformofconceptualsynthesis,andblendingofmentalmodelsdescribedindiscussionoftheGeneploremodel),theframeworkfoundmosthelpfulinourmodelingofperformancechangesresultingfromacumulativedesignprocessisanalogicaltransfer.AlthoughthisideacanbetracedasbeginningwithPolya(1945)orearlier,theframeworkremainsanactiveareaindesignresearch(Clementetal.1994,HolyoakandThagard1995,Goel1997,GentnerandMarkman1997,LeclerqandHeylighen2002,DahlandMoreau2002,ChristensenandSchunn2007,Linseyetal.2008,Tsengetal.2008,Linseyetal.2012,Fuetal.2013).Scholarsofanalogicaltransfer(GentnerandMarkman1997,Holyoaketal.1995andWeisberg2006)explainanalogicaltransferasinvolvingtheuseofconceptualknowledgefromafamiliardomain(base)andapplyingittocreateknowledgeinadomainwithsimilarstructure(target):analogicaltransferexploitspastknowledgeinboththebaseandtargetdomains.Theanalogiesutilizedcanbelocal,regionalorremote,dependingonsurfaceandstructuralsimilaritiesbetweenobjectsinvolvedinthebaseandtargetdomains.WeisbergdiscussestheexampleoftheWrightbrothersusingseveralanalogicaltransferstofirstrecognizeandsolvetheproblemofflightcontrol.First,theyviewedflyingasbeingsimilartobikinginwhichtheriderhastobeactivelyinvolvedincontrollingthebike,anapplicationofregionalanalogy.Interestingly,manyothersattemptingtodesignartifactsforflyingdidnotaccessthisregionalanalogyandthusdidnotevenidentifythekeycontrolproblem.Second,theWrightbrothersstudiedbirdstoseehowtheycontrolledthemselvesduringflight,andlearnedthattheyadjustedtheirpositionabouttherollingaxisusingtheirwingtips.Fromthisinsight,theyhadtheideaofusingsimilarmovingsurfaces,anotherinstanceofusingregionalanalogy.Lastly,theydevelopedtheideaofwarpingthewings,demonstratedbyusingatwistedcardboardbox,toactlikevanesofwindmillstomaketheairplaneroll.Theuseofthreeanalogicaltransfersincombinationtoseeandsolvetheflightcontrolproblemisaclearcaseofanalogicaltransferbutthereisalsoevidence(citedearlierinthisparagraph)ofmuchwiderapplicability.Therearemoreabstractversionsofcombinatorialanalogicaltransferthathavebeenproposedinthewiderliterature.BasedonanextensivehistoricalstudyofmechanicalinventionsanddrawinginsightsfromGestaltpsychology,Usher(1954)proposedacumulativesynthesisapproachforcreationofinventions.Thenotionofbisociation(Koestler1964,Dasgupta1996)developsthecumulativesynthesisapproachfurtherandsaysthatanewinventiveideaisideatedcombiningdisparateideas.Morerecently,Fleming(2001)andArthur(2006)haverespectivelyusedthesamecombinatorialnotionsofinventioninstudyingtechnologicalchange.Otherresearchinthetechnologicalchangeliteraturealsodiscussesarelatedconceptthatisusuallycalled“spillover”.Rosenberg(1982)showedthatsuchtechnologicalspillovergreatlyimpactedthequantityandqualityoftechnologicalchangeintheUnitedStatesinthe20thcentury–aresultsupportedbyNelsonandWinter(1982)andRuttan(2001).Indeed,arecentpaperbyNemetandJohnson(2012)statesthat“oneofthemostfundamentalconceptsininnovationtheoryisthatimportantinventionsinvolvethetransferofknowledgefromonetechnicalareatoanother”.Wenotethatthesedescriptionsdonotalwaysmakeacleardistinctionregardingwhetherthetransferisoccurringattheidealevelorattheartifactlevel.Theyaresilentregardinghowandfromwheredesignersorinventorsgettheirdisparateideastocombineandregardingdetailsaboutthecomplexitiesoftransferandcombination.
![Page 5: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/5.jpg)
5
Analogicaltransferofideasasabroadmechanismandexpertiseasthefoundationofideas(Weisberg,2006)providesadequatespecificityformodelingscienceandinventioninthispaper.Weisbergcontendsthatanalogicaltransferisutilizedingenerationofbothscientificandtechnologicalknowledge.Existingknowledgeprovidesthefoundationalbasisforanalogicaltransfertooccur.Asimilarargumenthasbeenappliedtothemoreabstractnotionofcombinations.Usherdescribesacumulativesynthesisapproach‐afourstepsocialprocess(perceptionoftheproblem,settingthestage,theactofinsight,criticalrevision)‐whichbringstogetherinventivestructurestocreatenewinventions.Ruttan(1959),hasarguedthatUsher’sformulationprovidesa“theoryofthesocialprocessesbywhich‘newthings’comeintoexistencethatisbroadenoughtoencompassthewholerangeofactivitiescharacterizedbythetermsscience,invention,andinnovation”.ModelsofbothUnderstandingandOperationsregimeinourpaper(definedinthenextparagraph)utilizetheabstractionthatknowledgeiscreatedbyprobabilistically1combiningexistingknowledgemadeavailablebyanalogicaltransfer.Vincenti(1990),andMokyr(2002)taketheviewthatscientificandtechnologicalknowledgecanbeclassifiedintodescriptive(Understanding)andprescriptive(Operations)knowledge2regimes.TheUnderstandingregimecanbeseenasabodyof‘what’knowledgeandincludesscientificprinciplesandexplanations,naturalregularities,materialsproperties,andphysicalconstants.Aunitofunderstandingisfalsifiable(Popper1959)andenablesexplanationandpredictionaboutspecificphenomena,includingbehaviorofartifacts.TheOperationsregime,ontheotherhand,canbeviewedasabodyof‘designknowledge’,whichsuggestshowtoleveragenatural‘effects’(Arthur,2006,Vincenti,1990))toachieveatechnologicaladvantageorpurpose.Itincludes,operatingprinciples,designmethods,experimentalmethods,andtools(Dasgupta1996,Vincenti1990).Basedonthisdistinction,understandingenablesgenerationofoperationalknowledge,whichultimatelycontributestowardsdesignofsomeartifact.However,operationsisnotentirelybaseduponexistingunderstandingandinfactinnovationsinknow‐howcanandoftendooccurbeforeanyunderstandingofrelatednaturaleffectsisavailable.AnimportantaspectofdesignandinventionisthecooperativeinteractionbetweenUnderstandingandOperationsregimes(Musson,1972,MussonandRobinson1989).Usingahistoricalperspective,Mokyr(2002)hascarefullyobservedthatasynergisticexchangebetweenthetwohasbeenoccurring,whereeachenablestheother.ThecontributionofUnderstandingtoOperationsiswellknown:itprovidesprinciples,andregularitiesofnaturaleffects,includingnewones,intheformofpredictiveequations,anddescriptive1Atapointintime,notallpossiblecombinationsofexistingknowledgeleadtonewknowledge.2Weusetheterms“Understanding”and“Operations”,sinceeachonebringsmoreclaritytothenatureofunderlyingactivity.Understandingreferstoconceptualinsightthatisgeneratedaboutanobjectorenvironment,whereasOperationsreferstotheideaofactingonanobjectorenvironmenttogetsomedesiredeffect,aswellasexperimentalmethodsincludedintheterm‘science’.
![Page 6: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/6.jpg)
6
facts,suchasmaterialproperties.FlemingandSorenson(2004)provideevidencethatunderstandinghelpsinventorsbyprovidingarichermaptosearchforoperatingideas,whichcanbecombinedtogether.Understandingalsoprovidesinsightaboutwherenewtechnologicalopportunitiesmaybefound(Klevoricetal.1995).Beyondthesecontributions,thereisthemoregeneralview,discussedintheinitialparagraphofthissection,thatnewoperationalideascanbederivedfromnewunderstanding.Whatislessdiscussedisthemulti‐facetedcontributionsofOperationstotheUnderstandingregime.Inhispaper,Sealingwaxandstring,deSollaPrice(1983),aphysicist,andhistorianofscience,highlightedthatinstruments(anoutputoftheOperationsregime)wereadominantforceinenablingscientificrevolutions.Hestates:“changesinparadigmthataccompanygreatandrevolutionarychanges(inscience)werecausedmoreoftenbyapplicationoftechnologytoscience,ratherthanchangesfrom‘puttingonanewthinkingcap’“.Operationsprovidetoolsandinstrumentstomakemeasurements,andtomakenewdiscoveries.Inhisbook,TheScientist:AHistoryofScienceToldThroughtheLivesofitsGreatestInventors,Gribbin(2002),aBritishastrophysicist,andsciencewriter,hasdescribedhowtheabilitytogrindeyeglasslensesmadeitpossibletomakebettertelescopes,andhencepavedthewayforastronomerstomakenewdiscoveries.Neworimprovedobservationaltechniquesarestillamajordriverofprogressinscience.Gribbinhasaptlysummarizedtheenablingexchangebetweenthetworegimes:“newscientificideasleading…toimprovedtechnologyandnewtechnologyprovidingscientistswiththemeanstotestnewideastogreaterandgreateraccuracy”.Additionally,theOperationsregimeprovidesnewproblemsfortheUnderstandingregimetostudy,andhasledtobirthofnewfieldsinUnderstanding(Hunt2010).Basedupontheseinsightsandwithourfocusonexplainingperformanceimprovementarisingfromcontinuingstreamsofinventions,ourmodeltreatsmutualexchangebetweenUnderstandingandOperations.Indesignofartifacts,Simon(1962)introducedthenotionofinteractionsinhisessayonthecomplexityofartifacts.Whenadesignofanartifactischangedfromonestatetoanother(withdifferencesbetweenthetwostatesasdefinedbymultipleattributes,sayD1,D2,andD3)bytakingsomeactions(say,A1,A2,andA3),inmanycases,anyspecificactiontakenmayaffectmorethanoneattribute,thuspotentiallymanifestingasinteractionsoftheattributes.Thesamenotionofinteraction/conflictsiscapturedbytheconceptofcouplingoffunctionalrequirements(Suh2001),ordependenciesbetweencharacteristics(Weber2003),whichcanoccurwhentwoormorefunctionalrequirementsareinfluencedbyadesignparameter.Theoreticallyitseemsidealtohaveonedesignparametercontrollingonefunctionalrequirementtoachieveafullydecomposable(modular)design(Suh2001,BaldwinandClark2000).However,Whitney(1996,2004)hasarguedthat,inreality,howdecomposableadesignofanartifactcanbedependsonthephysicsinvolvedoradditionalconstraints,suchaspermissiblemass.Thesearereflectedascomponent‐to‐component,andcomponent‐to‐systeminteractions,orasaneedtohavemulti‐functionalcomponents.Consequently,Whitneyargues,complexelectro‐mechanical‐optical(CEMO)systems,primarilydesignedtocarrypower,cannotbemadeasdecomposableasVLSIsystemsprimarilydesignedtotransmitandtransforminformation.Forexample,inenergyapplications,theimpedanceoftransmittingandreceivingelementshastobematchedformaximumpowertransfer,thusmakingthetwoelementscoupled.Further,CEMOsystemstypicallyneedtohavemulti‐functionalcomponentsinordertokeeptheartifactsize
![Page 7: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/7.jpg)
7
reasonable,creatingcouplingofattributesatthecomponentlevel.AnothertypeofinteractionWhitneyhasidentifiedarethesideeffects,suchaswasteheatincomputers,andcorrosionofelectrodesinbatteries‐thatoccurinartifacts,whichinsomeelectro‐mechanicalsystemscanconsumesignificantportionofthedesigneffortfortheirmitigation.Thepresence,andthustheresolution,ofthesedifferentinteractionscausesignificantdelay,consumesignificantengineeringresourcesandpotentiallystopapplicationsofsomeconcepts,thusmakingthelevelofinteractionsofatechnologicaldomainapotentiallystrongfactorinfluencingitsrateofimprovement.BaseduponWhitney’swork,theeffectofinteractionsonratesofimprovementwassuggestedqualitativelybyKohandMagee(2008)andaquantitativemodeloftheeffectwasdevelopedbyMcNerneyetal.(2011)–seesection2.3.Theinfluenceofdesignparametersonartifactperformanceisanessentialpartofdesignknowledge.Manytechnologicaldomainshavecomplexmathematicalequationsrelatingsomeaspectsofperformancewithdesignparameters.Indeed,theso‐calledengineeringscienceliteraturehassuchequationsformanyaspectsaffectingthedesignofartifactsofperhapsalltechnologicaldomains.Simplerrelationshipsconcerningthegeometricalscaleofartifactsarealsoavailableandgenerallygiveperformancemetricsasafunctionofadesignvariableraisedtoapower.Useofpower‐lawrelationshipscanbefoundin:1)Sahal(1985)whostudiedscalinginthreedifferentsetsofartifacts‐airplanes,tractors,andcomputers;and2)BelaGold(1974)whodemonstratedthatdoublingthesizeofablastfurnacereducestheircostbyabout40%.Theconstantpercentchangeperdoublinginsizeresultsfromthepowerlaw(assumedbyGold)betweenperformance/costandgeometricalvariablessuchasvolume.
2.2 Technological change literature Whatdescriptivemodelsandtheorieshelpusunderstandwhytechnologiesimproveandhowtheimprovementpatternsarestructured?Schumpeter(1934)introducedtheideathatentrepreneurs,whoseprimaryroleistoprovideimprovedproductsandservicesthroughinnovation,driveeconomicprogress.Theseinnovations,whichSchumpeterdescribesasindustrialmutations,displacecompetingproductsandservicesfromtheeconomy.However,they,too,aredisplacedbyhigherperforminginnovationsthatfollow,thusperpetuatingthecycleofcreativedestruction.BuildinguponSchumpeter’snotion,Solow(1956)recognizedandincorporatedtechnologicalchangeasthekeyelementinhisquantitativeexplanatorytheoryofeconomicgrowth.Thebasicconclusionthattechnologicalchangeisthefoundationofsustainedeconomicgrowthhasstoodthetestoftime.Latertheoristsofeconomicgrowth(Arrow1962,Romer1990,Acemoglou2002)haveattemptedtodealwiththemorecomplexproblemofembeddingtechnologicalchangewithintheeconomy(endogenoustodifferentdegrees).Althoughthelatertheoriesareimportant,theissuesareoutsidethescopeofthispaperandwillnotbecoveredhere.Arelatedquestionofdemand‐pullandtechnology‐pushdoeshavemorerelevance. Whatdrivestechnologicalinnovation?Someearlyexplanationsemphasizedpuredemandpush(CarterandWilliams(1957,1959),Bakeretal.1967,MyersandMarquis1969,Langrishetal.1972,Utterback1974)wheretheneedsoftheeconomyatagiventime
![Page 8: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/8.jpg)
8
dictatetechnologicaldirection.MoweryandRosenberg(1979)reanalyzedthedataandmethodologyinthisearlyworkandarrivedatastrongroleforscience/technologypush(thediscoveriesofscientistsandinventorsprimarilydeterminetechnologicaldirection).Takingabalancedview,Dosi(1982)arguedthatbothmarket‐pull(customerneedsandpotentialforprofitability)andtechnology‐push(intheformofpromisingnewtechnology,andtheunderpinningprocedures)areequallyimportantforbeingsourcesofinnovation.TushmanandAnderson(1986)discussdiscontinuitiesashavinglargesocio‐technicaleffectsandnotethatsuchdiscontinuitiesareanessentialelementoftechnologicalchange.Inanotherhighlyreferencedpaper,HendersonandClark(1990)emphasizetheimportanceofarchitecturalchangeofartifacts‐asopposedtocomponentchange‐havinglargeeffectsonthefirm‐levelimpactofchange.Christensen(1996),ontheotherhand,viewstechnologicalchangeoccurringasaseriesofdisruptiveproductinnovationsthatstartinanichemarketcateringtodifferentfunctionalrequirements,butthenrapidlyimprovetowardstherequirementsofmainstreamperformance.Thedisruptivetechnologysurpassesthematuremarketleaders(byachievingthenecessaryperformanceinsmaller,cheaperartifacts),anddisplacesthem.Alloftheconceptsoftechnologicalchangedescribedintheprecedingparagraphs‐atleastimplicitly‐dependuponrelativeratesofchangeofperformance.Thisisthefocusofourmodelingeffortsowewillnowbrieflyreviewconceptsrelatedtotrendsinperformanceofdesignedartifacts,andwhatpatternstheyhavefollowed.Wefirstreviewtwoestablishedframeworks–generalizationsofWright’searlyresearch,andMoore’sLaw‐fordescribingtrendsintechnologicalperformance.In1936TheodorePaulWright(1936)inhisseminalpaper“FactorsaffectingtheCostofAirplanes”forthefirsttimeintroducedtheideaofmeasuringtechnologicalprogressofartifacts.Fromhisempiricalstudyofairplanemanufacturing,hedemonstratedthatlaborcostortotalcostofspecificairplanedesignsdecreasedasapowerlawagainsttheircumulativeproduction.Thisrelationshipisexpressedas: C=C0P‐w (1) WhereC0,andCareunitcostofthefirst,andsubsequentairplanesrespectively,andwherePandwarecumulativeproductionanditsexponentthatrelatesittounitcost.Wrightexplainsthatlaborcostreductionsarerealizedasshopfloorpersonnelgainexperiencewiththemanufacturingprocesses,andmaterialusageandhaveaccesstobetterproductiontools.SinceWright’swork,thisapproachhasbeenusedtostudyproductionofairplanesandshipsduringWorldWarII,andextendedtoprivateenterprises(Yelle,2007).ItshouldbenotedthatWrightdidnotlookatimprovementduetonewdesigns,insteadheonlyconsideredimprovedmanufacturingofafixeddesign.GordonMoore(1965)presentedthesecondapproach‐usingtimeastheindependentvariableandinvestigatingaseriesofnewlydesignedartifacts‐inhisseminalpaperthatdescribesimprovementofintegratedcircuits.Heobservedthatthenumberoftransistorsonadiewasdoublingroughlyevery18months(modifiedto2yearsin1975).This
![Page 9: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/9.jpg)
9
exponentialrelationshipbetweenthenumberoftransistorsonadieandtime,famouslyknown3asMoore’sLaw,canbemathematicallyexpressedas: QJ(t)=QJ(t0)exp{KJ(t‐t0)} (2)
WhereQJ(t0)andQJ(t)arethenumberoftransistorsperdie(ameasureofperformance)attimet0andtimet,andKJistherateofimprovement(annualiftimeisinyears).Forintegratedcircuits,theexponentialrelationshiphasheldbroadlytrueforfivedecades.Others(Girifalco1991,Nordhaus1996,KohandMagee(2006,2008)andLeinhard2008)utilizedthistemporalapproachtostudyperformanceofdifferenttechnologies,andhavedemonstratedthatmanytechnologiesexhibitexponentialbehaviorwithtime.Morerecently,Mageeetal.(2014)extendedthestudyto73differentperformancemetricsin28differenttechnologydomains.Theperformancecurveshavecontinuedtodemonstrateexponentialbehavior,althoughannualratesvarywidelyacrossdomains.WenotethatMooreandallotherswhousedhisframeworkbasicallycomparedtheperformanceofdifferentdesignsovertimedifferentiatingtheWrightandMooreframeworks.However,itisalsopossibletousetheWrightframeworkfordifferentdesignsbutonlyiftheamountproducedincreasesexponentiallywithtime(Sahal,1979,Nagyetal.2013,Mageeetal2014).Inordertoclarifyforreadersthenatureofempiricalperformancedata,wepresentperformancedatafortwosampledomains,magneticresonanceimaging(MRI)andelectricmotors(Fig.1a),andasummaryofimprovementratesfor28domains(Fig.1bfromMageeetal.2014).Theexponentialtrendforeachdomaincanbedescribedbyequation(2),whereQJ(t)andQJ(t0)aretheintensiveperformanceofanartifactindomainJattimetandt0,andKJistheannualrateofimprovementofthedomaininquestion.
3ThisdesignationwasgiventotherelationshipbyCalTechprofessorCarverMead.
![Page 10: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/10.jpg)
10
Fig. 1a: Exponential growth of performance in sample domains – Electric motor and Magnetic resonance imaging (MRI). Adapted from Magee et al. 2014 with permission.
KJ(%)
Fig. 1b: Annual rate of performance improvement, KJ, for 28 domains. Adapted from Magee et al. 2014with permission.
Elec. MotorRate = 3.1 %R² = 0.9657
MRI
Rate = 21.3 %R² = 0.8561
1.E‐05
1.E‐04
1.E‐03
1.E‐02
1.E‐01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+00
1.E+01
1.E+02
1.E+03
1880 1910 1940 1970 2000 2030 2060
MRI (resolution/tim
e)
Electric motor (W
att/liter)
Electric Motor MRI
![Page 11: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/11.jpg)
11
Arecentpaper(BensonandMagee,2015a)hasempiricallyinvestigatedthevariationoftheimprovementratesinthese28domains.Theworkhasimportantrelationshipstothecurrentworksowedescribeittonotetherelationshipsbuttoalsoclarifythefundamentaldifferences.BensonandMageefoundstrongcorrelationsbetweenspecificmeta‐characteristicsofthepatentsinthe28domains4andtheimprovementrateinthedomains.Theseauthorsfoundthatpatentmeta‐characteristicsreflectingtheimportance(citationsperpatentbyotherpatents),recency(ageofpatentsinadomain)andimmediacy(theaverageovertimeoftheusageofcurrentnewknowledgeinthedomain)areallcorrelatedwiththeimprovementrate.Theyfoundaparticularlystrongcorrelation(r=0.76,p=2.1x10‐6)withametricthatcombinesimmediacyandimportance(theaveragenumberofcitationsthatpatentsinthedomainreceiveintheirfirstthreeyears).Thefindings(andassociatedmultipleregressions)arerobustovertimeandwithdomainselectionandareofpracticalimportanceinpredictingtechnologicalprogressindomainswhereperformancedataisnotavailable(BensonandMagee,2015).Nonetheless,theconceptualbasisforthefindingsisobservedattributesoftheinventiveoutputfromatechnologicalfield(importance,recencyandimmediacyofapatentset)andnottheprocessofinvention,designknowledgeorothertechnicalaspectsofdesignedartifactsinthedomain.Theaimoftheworkreportedinthepresentpaperistodevelopamodelthatyieldsinsightsaboutthepaceofchangewithoutrecoursetoconceptsbaseduponobservationoftheoutputovertime.Iffullysuccessful,wewouldbeabletojudgethepotentialforchangebasedonlyuponthenatureofthedesignknowledgeandwemightevenbeabletofindnewapproachesthatmightachievetechnologicalgoalsatmorerapidimprovementrates.
2.3 Literature on quantitative modeling of technological change Whatresearchhasattemptedtomodelthetechnologicalperformancetrendsthatwejustdiscussed?Muth(1986)andAuerswaldetal.(2000)havedevelopedmodelstoexplainWright’sresultsbyintroducingthenotionofsearchfortechnologicalpossibilities.Eachpaperassumesthatrandomsearch,akeyelementoftechnologicalproblemsolving,forabettertechniqueismadewithinafixedpopulationofpossibilities.Consideringacaseofasinglemanufacturingprocess,Muth(1986)developedamodeltocapturetheideaofsubstitutingmanufacturingsequenceswithbetterones.Hearguesthatshoppersonnelimprovetheprocessbylearningthroughexperienceandmakingrandomsearchfornewtechniques,whichenableimprovementofprocessesleadingtocostreductions.Muthdemonstratedthatthenotionoffixedpossibilitieseasilyleadstofewerandfewerimprovementsthatcanberealizedandhearguesthatthedata(forfixeddesigns)showsalevelingoffandeventualstoppageasthemodelsuggests.BuildingonMuth’sideaofrandomsearchwithinasetoffixeddesignpossibilities,Auerswaldetal.modeledamulti‐processsystem,inwhichdifferentprocessescanbecombinedtocreatediverserecipes,andforthefirsttimeintroducedthenotionofinteractionsbyallowingadjoiningprocessestoaffecteachother’scost.
4Thepatentsarefoundbyanewtechnique‐BensonandMagee2015b
![Page 12: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/12.jpg)
12
FollowingsimilarreasoningasMuthandAuerswaldetal.,McNerneyetal.(2011)havedevelopedastochasticmodeltoexplainhowthecostreductionofamulti‐componentsystemisinfluencedbycomponentinteractions,whichtheyrefertoasconnectivitybetweencomponents.McNerneyetal.operationalizedthenotionofinteractionsasout‐linksrepresentinginfluenceofacomponentonothercomponents.Whenaspecificcomponentinadomainartifactchangesbyintroducinganewoperationalidea,thechangeaffectsthedesignofallthecomponentsitinfluences.Iftheperformanceoftheartifact(influencingandinfluencedcomponents)asawholeimproves,thenMcNerneyetal.considertheinteractionstoberesolvedandtheoperatingideaisconsideredsuccessful.TheMcNerneyetal.paperdemonstratesthatartifactswithmoreinteractionsimprovemoreslowlythanartifactswithlessinteractions.Usingagent‐basedmodeling,Axtelletal.(2013)havedevelopedacompetitivemicro‐economicmodeloftechnologicalinnovationutilizingthenotionoftechnologicalfitness.AlthoughtheydonotdiscussorciteMoore’slaworhiswork,theyhavedemonstratedthatcumulativetechnologicalfitnessofallagentsincreasesexponentiallyovertime.ThisisdifferentfromotherresearcherswhohavepredominantlybeenfocusedonWright’sframework.Consistently,Axtelletal.considernewdesignsandnotjustprocessoptimization.Usingasimulationapproach,ArthurandPolak(2006)havemodeledhownewgenerationsofartifactsarisebycombiningcurrentlyavailableartifacts.Theartifactsconsideredareelectroniclogicgates.Newdesigns(combinations)aremorecomplexlogicgatesthatcanthenalsobecombinedintoevenmorecomplexlogicgates.Intheirmodel,ArthurandPolakspecifyseveraldesigngoalstowardstowhichthelogicgatesevolve.Theyhavedemonstratedthatdesignswithhigherlevelsofcomplexitycannotbeattainedwithoutrealizingdesignconfigurationswithintermediatelevelsofcomplexity,andnewdesignswithhigherfunctionalitysubstituteforcurrentdesignswithinferiorfunctionality.Thismodelismuchricherthanothermodelsinrepresentingtheartifactpartofthedesignprocess;however,itdoesnotconsiderperformanceimprovement,asdotheothermodels.Itisalsolimitedtodevelopingpre‐specifiedartifactsandisthusaspecificprocess;consequently,itisnotopen‐endedorgeneralwhicharecharacteristicsnecessaryformodelingperformancetrendsforgeneraltechnologicaldomains.Althoughsomearemoreexplicitthanothers,onefeaturecommontoallthesemodelsisthatallutilizethenotionofbuildingupontheperformance(intheformofcost)ordesignsofthepast,akeyfeatureofcumulativeprocessesincludedinthemodelpresentedhere.Ontheotherhand,theydonotconsidertwoaspectswebelieveusefulinansweringourresearchquestion.First,noneofthemdiscussesorincludestheinfluentialroleplayedbyexchangebetweenscienceandtechnology.Inthispaper,wetreatthedesignprocessandtheexchangebetweenscienceandtechnologyasimportantelementsforunderstandingthechangeinperformanceovertimethatinturnisessentialtounderstandingtechnologicalchange.Second,noneconsiderthedesignprocessoroperatingprinciplesandinsteadlookatcombinationsattheartifactlevelinsteadofcombinationofideas.
![Page 13: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/13.jpg)
13
3. Overview of the model
3.1 Conceptual basis of model Thedesiredoutputfromtheconstructedmodelareperformanceimprovementrates.Toagreewithknownempiricalresults,performanceshouldincreaseexponentiallywithtime.Weutilizetwosetsofmechanismsfromdesigntoconstructtheoverallmodel.Thefirstset,whichgivesrisetoexponentialtrends,includesgrowthofknowledge‐understandingandoperations‐usingcombinatorialanalogicaltransferaidedwithmutualexchangebetweenthetwo.Thesecondset,whichgivesrisetovariationinimprovementrates,includescomponentinteractionsandscalingofdesignvariables.Sincethegoalofthemodelistodevelopanexplanatoryandquantitativepredictivemodel,whilemodelingthesemechanismswehave,wherenecessary,simplified(removeddetails)andutilizedabstractiontokeepthemodeltractable.TheoverallarchitectureofthemodelisshowninFigure2.BasedontheworkofVincenti(1990)andMokyr(2002)thatwediscussedearlier,weclassifyscientificandtechnicalknowledgeintoUnderstandingandOperationsregimes.WefurthersplittheOperationsregimeintoideaandartifactsub‐regimeswherenon‐physicalrepresentationofartifactsareintheideasub‐regime.Theideasub‐regime,representedasanideaspool,consistsofindividualoperatingideas(IOI).TheIOI(individualoperatingidea)conceptisanabstractionandgeneralizestheideaofoperatingprincipleintroducedbyPolyani(1962)andincludesanyideas,includingoperatingprinciples,inventionclaims,designstructures,componentintegrationtricks,tradesecretsandotherdesignknowledgethatleadtoperformanceimprovementofartifacts.AnIOIisdifferentthanaunitofunderstanding(UOU)whichincludesscientificprinciples,andfactualinformation.Anexampleofaunitofunderstanding(UOU)istheprincipleoftotalinternalreflection,whichdescribeshowabeamoflightundergoesreflectioninsideadensemedium,whentheangleofincidenceisaboveacriticalvalue(seeFig.3).Thisprincipleaccuratelydescribesanaturaleffect,butitdoesnotprescribehowwecanuseittotransmitinformation.Ontheotherhand,apairofparallelsurfaces(orafiber)enclosingadensemediumandutilizingtheprincipleoftotalinternalreflectionprovidesamechanism–anoperatingprinciple‐tomakearayoflighttraveldownthelengthofthemedium(seeFig.3).SuchamechanismisanexampleofanIOI.Unlikeartifacts,whichbelongtoaspecifictechnologicaldomain,wemodelIOIintheideas(IOI)poolasbeingnon‐domainspecificandavailabletoalltechnologicaldomains.Forinstance,theoperatingprincipleoftotalinternalreflectionisutilizedinfiberoptictelecommunications,fluorescentmicroscopy,andfingerprinting,verydistincttechnologicaldomains.Intheideasub‐regime,designers/inventorssourceexistingideas(IOI)usinganalogicaltransferandcombinethemprobabilisticallytocreatenewideas(IOI).OncenewIOIaresuccessfullycreatedthroughprobabilisticcombination,theybecomepartoftheIOIpool,thusenlargingthenumberofideas(IOI)inthepoolforcombination.Itisimportanttoclarifythatmodelconsiderscombinationsattheideaslevelrathercombinationofcomponents,withtheformerbeingfundamentalandallowingcombinationofideasfromdifferentfieldsusinganalogicaltransfer.
![Page 14: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/14.jpg)
14
Fig.2:ModelofexchangebetweenUnderstandingandOperationsregimesandmodulationofIOIassimilationbyinteraction(dJ)andscaling(AJ)parametersofdomainJ.Exampleofunitofunderstanding(UOU)
Exampleofincrementaloperatingidea(IOI)
Principleoftotalinternalreflection
Totalinternalreflectionbetweenparallelsurfacesenclosingdensemedium:mechanismtomakelighttravellongitudinally(fiberoptics)
Fig.3Examplesofunitofunderstanding(UOU)andincrementaloperatingidea(IOI)
Understanding
regime
IOIpoolIOI C,K
Operationsregime
DomainJ
Interactions
Perf.ScalingAJ
Interactions
QJKJ
FU dJ
Artifact
![Page 15: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/15.jpg)
15
WemodelgrowthintheexplanatoryreachoftheUnderstandingregimebysimulatingasimilarcombinatorialanalogicaltransferprocess.TheUnderstandingregimeisconceptualizedtoconsistofunitsofunderstanding(UOU).Theunitsofunderstanding(UOU)fromdifferentfieldswithintheunderstandingregimeparticipatetocreateanewunitofunderstanding(UOU)thatpotentially(probabilistically)hasagreaterlevelofexplanatoryandpredictivepower.FollowingthetreatmentinAxtelletal.(2013),wemodeltheexplanatoryandpredictivepowerofafieldofUnderstandingasafitnessparameter,fi.IfthenewUOUhasagreaterfitnessvalue,itreplacestheUOUwiththesmallestfitnessvalue.Sinceourprimaryfocusisonperformance‐theoutputoftheOperationsregime,wesimulatetheUnderstandingregimeonlyatthishigherabstractionlevel.Althoughbothregimes–UnderstandingandOperations–evolveindependently,theycannotdosoindefinitely.WemodelthedeSollaPriceandGribbininsightsbyhavingeachregimeactasa“barrier‐breaker”fortheotherregime.Wheneachregimehitsabarrier,theothercaneventuallyaidinbreakingthebarrier:infusionofunderstandingenablescreationofimportantIOIintheOperationsregime;andinfusionofnewoperationaltoolsenablenewdiscoveriesintheUnderstandingregime.Theperformancesoftheartifactsintechnologicaldomainsareimprovedbyaseriesofdesigns/inventions(IOI)overtime.IOIenabledesignerstochangespecificcomponentsinthedomainartifactleadingtoapotentialimprovement.FollowingMcNerneyetal.’streatment,theIOIinquestionisassimilatedonlyiftheperformanceoftheartifactoverallimproves.Another,andfinal,factorthatwemodelisscaling,apropertyinherentinthephysicsofthedesignoftheartifact.5,6ThesuccessfullyassimilatedIOI,whichwerefertoasIOIS,effectimprovementofthedomainartifactbyenablingfavorablechangeofarelevantdesignparameter.Thedesignparameterisincreasedordecreasedsuchthatitleadstoimprovedperformance7.Scalingreferstohowchangeinadesignparameterrelatestorelativechangeintheperformanceofanartifact.Theformulationweuseinthemodelisthatrelativeperformancechangeisrelatedtodesignparametersraisedtosomepower,inotherwordsscaled.Ascoveredinsection2.1,thisisthemostwidelyusedfunctionalrelationshipwithdecentempiricalsupportandtheoreticaljustificationinsomecases(Barenblatt1996).
5Recallthattheperformanceweconsiderinthispaperisintensive,e.g.,energydensity,w/cm3.6Inrelationstoartifactssuchassoftware,physicsreferstothemathematicsbehindthesoftware.7Taguchi(1992)notedthatsomephenomenatendtoworkbetterwhencarriedoutatasmallerscale(“smallerisbetter”),whileotherarebetteratlargerscale(“largerisbetter”).Integratedcircuits,forexample,performbetterasdimensionsarereduced,sincesmallerdimensionsleadtoshorterdelays,andhigherdensityoftransistors,bothofwhichcontributetowardsimprovedcomputationpervolumeorcost.
![Page 16: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/16.jpg)
16
3.2 Mathematical summary Aperformance(intensive)metricofadomain,labeledQJ,isafunctionofasetofdesignparameters(s1,s2,s3)ofadomainartifactandtimebutforsimplicityhereweconsideronlyasingleparameter(s).ThedesignparameterischangedbyIOIs(successfullyassimilatedIOIintodomainartifacts),whichinturnareassimilatedfromIOIC(numberofaccumulatedoperatingideasintheIOIpoolshowninFigure2).IOICisafunctionoftime.Equationsdescribingthesenestedvariablesinlogarithmicformare: lnQJ=f1(lns);lns=f2(lnIOISC);lnIOISC=f3(lnIOIC);lnIOIC=f4(t) (3) Assumingthatthefunctionsarecontinuousandalldependenceisthroughthenamedvariables,thechainruleisappliedandyields dlnQJ/dt=dlnQJ/dlns∙dlns/dlnIOISC∙dlnIOISC/dlnIOIC∙dlnIOIC/dt (4) Thefirsttermontherighthandsiderepresentsrelativeimpactofdesignvariablechangeonperformancechange,whichwillbeshowninsection4.5tobeequaltothescalingparameter(AJ)whenQJfollowsapowerlawins:dlnQJ/dlns=AJ.Thesecondtermisthe‘smaller‐is‐better/larger‐is‐better’factor,andcapturesthenotionwhetheradesignvariablehastobeincreasedordecreasedinordertoimproveperformance.Wecapturethisdependenceusinganabstractionandequatedlns/dlnIOIsc=+/‐1. Thus,equation(4)becomes
dlnQJ/dt=AJ∙(±1)∙dlnIOISC/dlnIOIC∙dlnIOIC/dt
(5)
Thethirdtermontherightofequation(5)represents‘difficultyofimplementingideas’inspecificdomains,andthusrelatesthedomainspecificsuccessfulIOISCtotheIOICinthepool:wewillshowinsection4.4‐followingMcNerneyetal.‐thatdlnIOISC/dlnIOIC=1/dJ,wheredJistheinteractionparameterintroducedbyMcNerneyetal.Finally,thefourthtermrepresentstherateofideaproduction.K=dlnIOIC/dtisarrivedatbyasimulationofcombinatorialanalogicaltransferwhichispresentedinthefirst(following)sectionoftheresults.
4. Results
4.1 Overall IOI simulation Asnotedinsection3.1,wemodeltheIOIasresultingfromcombiningknowledgefrompriorIOIbyprobabilisticanalogicaltransfer.Fig4aschematicallyrepresentscombinationofIOI,inwhichspecificIOIaandbcombinetocreateIOIdwithaprobability,PIOI.Ifthiscombinationattemptsucceeds,thenewlycreatedIOIdthenisaddedtothepoolofIOI(Fig4b).Insubsequenttimesteps,IOIdcanattempttocombinewithanotherspecificIOIinthepool,suchasIOIc,toprobabilisticallycreateamoreadvancedIOIe.Ascombinationadvances,thecumulativenumberofindividualoperatingideas,IOICgrows.WefurthermakethedistinctionbetweenderivedIOIandbasicIOI,whichwelabelasIOI0.IOI0are
![Page 17: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/17.jpg)
17
fundamentalIOI,whichfirstintroduceanaturaleffectintoanoperationalprincipletoachievesomepurpose.Theexample(describedinsection3.1)ofapairofcloseparallelsurfaces(orafiber)enclosingadensemediumandutilizingprincipleoftotalinternalreflectiontotransmitabeamoflightlongitudinallycanbeviewedasanexampleofanIOI0.Incontrast,derivedIOI,justasthetermsuggests,areobtainedthroughcombinationoftwoIOI0,orbetweenanIOI0andaderivedIOIorbetweentwoderivedIOI.Inthissense,IOIa,b,andcinthefigurerepresentIOI0andIOIdande,derivedIOI.
Inonerunofthesimulation,westartwiththeinitialnumberofbasicindividualoperatingideas,IOI0.Ateachtimestep,themaximumnumberofcombinationsweallowtobecreatedisequaltohalfthenumberoftotalIOIavailable.Theintentionistoalloweachoperatingideatocombinewithanotheroperatingideaoncepertimesteponaverage.Figure5showsresultsfromasimulationrunstartingwith10basicIOIandaprobabilityofcombination,PIOI,equalto0.25.Figures5aand5bwithtimestepsontheX‐axisandthecumulativenumberofoperatingideas,IOIContheY‐axisshowthatthecumulativenumberofoperatingideas,IOIC,growsexponentiallywithtimeatanimprovementrate(K)of0.116.
Forthissimplifiedcase,therateofgrowthofIOI,K,canbemathematicallyshowntobeequaltoln(1+PIOI/2),=0.118whichcanbeeasilyderivedasfollows:
Atinatimestept,numberofIOInewlycreated=PIOI∙IOIC(t)/2 (6)
Fig.4:Combinationofindividualoperatingideasa)basicandderivedIOIb)accumulationofIOIthroughfeedback
a+b d
PIOI
IOIpool BasicIOI:a,b,cDerivedIOI:d,e
![Page 18: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/18.jpg)
18
IOIC IOIC
Fig.5:GrowthofIOICovertime:initialIOI0=10,probabilityofcombination,PIOI=0.25:(a)linearY‐axis(b)logarithmicY‐axis.
IOIC(t+1)=IOIC(t)+PIOI∙IOIC(t)/2=IOIC(t)∙(1+PIOI/2) (7)
RatioofIOICbetweenconsecutivetimesteps,r=IOIC(t+1)/IOIC(t)=(1+PIOI/2) (8)
Then,ingeneral,IOIc(t)canbewrittenintermsofaninitialIOI0andratio,randtimestep,t;theexpressioncanbestatedinanexponentialform.
IOIC(t)=IOI0rt=IOI0exp{lnr∙t}=IOI0∙exp{ln(1+PIOI/2)∙t}=IOI0∙exp{k∙t} (9)
Where,therateofgrowthofIOIC(t),
K=ln(1+PIOI/2) (10)
ForverysmallvaluesofPIOI,
K≈PIOI/2 (11)
Thesimulationresultstothispointassumethatindefinitelylargenumbersofoperatingideas,IOI,canbecreatedoutoffewbasicIOI.ThisisbecausethemodelassumesthatthesameoperatingideascanberepeatedlyusedtocreatenewIOIwithoutlimit.(Forexample,recombining(a,b)witha,thenwithbwouldgivenewoperatingIOI(((a,b),a),b)andeventuallyanarbitrarilylargenumberofa,bpairs.IndefinitemultipleusesofthesamebasicideatocreateinnumerableIOIdoesnotappeartoberealistic.Inordertobetterreflectthisintuition,weintroduceaconstraintthatanyderivedIOIcanutilizeanIOI0onlyonce.TheconstraintoperationalizesthenotionthatcountingrepetitioususeofbasicIOIasnewdesignsthatpotentiallyimproveperformanceisunrealistic.Accordingtothis
0
200
400
600
800
0 20 40
IOI0 = 10
1.E+00
1.E+01
1.E+02
1.E+03
0 20 40
IOI0 = 10
![Page 19: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/19.jpg)
19
constraint,derivedIOI((a,b),c)inFigure4wouldbeallowed,butnot((a,b),b).Employingthisconstraint,thesimulationyieldstheresultsinFig.6a,asemi‐loggraph,showingthecumulativenumberofIOIinitiallygrowingexponentiallywithtime.However,lateronthecurvebendsoverandhitsalimit,demonstratingthatallcombinationpossibilitieshavebeenusedup,andthepoolofoperatingideasstagnateswhichisalsoshownonthelinearplot(Figure6b)resemblingawell‐known“Scurve”.
IOIC
a)
IOIC
b)
Fig.6:GrowthofcumulativeIOIC(t)afterimplementingtheconstraintthatIOI0canbeusedonlyoncebyanyspecificderivedIOIs;a)semi‐logplotandb)linearplot.
Themaximumnumberofcombinationpossibilities,whichisafunctionofIOI0inthepool,definesthelimit.Thislimit,ormaximumnumberofcombinationpossibilities,isgivenbyasimplecombinatoricsequation(Cameron1995):
2 1 (12)
Equation12entailsthatthelimitincreasesrapidlyasIOI0increases,duetoitsgeometricdependenceonIOI0.Forexample,forIOI0equalto5,10,15,and20thecorrespondinglimitsare31,1023(Figure6),32767,and1,048575combinationpossibilities.
AnaturalquestionthatarisesfromthisresultiswhatmightdeterminetheIOI0overtime?WepostulatearoleforUnderstandinginthisregardandwefirstbrieflylookathowUnderstandingevolvesovertime.
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
0 20 40 60 80
IOI0 = 10
0
200
400
600
800
1000
1200
0 20 40 60 80
IOI0 = 10
![Page 20: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/20.jpg)
20
4.2Combinatoric simulations for Understanding regime JustliketheOperationsregime,wemodeltheUnderstandingregimetoalsogrowthroughaprobabilisticanalogicaltransferprocess,inwhichunitsofunderstandingcombinetocreatenewunitsofunderstanding.Inthismodel,weenvisionthattheUnderstandingregimeiscomposedofmanyfields,witheachfieldhavinganexplanatoryreach.UsingatreatmentsimilartotheoneusedbyAxtelletal.(2013),theexplanatoryreachofafieldmaybeviewedasafitnessvalueofthetheoreticalunderstandingofthatfield,whichwedenotewithfi.FollowingAxtelletal.,whenunitsfromtwofieldswithfitnessvalues,f1andf2,combine,thefitnessoftheresultingunitisrandomlychosenfromatriangulardistributionwiththebaseorX‐axisdenotingthefitnessvaluesrangingfrom0tof1+f2,andtheapexrepresentingthemaximumvalueoftheprobabilitydistributionfunction,givenby2/(f1+f2).SeeFig7a.Iftheresultingfitnessofthenewunderstandingunitishigherthanthefitnessofeitherofthetwocombiningunits,thenewunderstandingunitreplacestheunitwhosefitnessisthesmallestamongthethree.WeassumethecumulativefitnessoftheUnderstandingregime(FU)asawholetobeequaltothesumoftheindividualfitnessvalueofeachfield.Oursimulationassumes10fieldswithstartingfitnessvaluesrangingfrom0to1,whicharerandomlyassigned.Consequently,theaveragecumulativefitness(FU)valueisinitially5.Asthesimulationproceeds,fitnessvaluesofthe10fieldsgrowindependently,andasaresult,thecumulativefitnessoftheUnderstandingregimegrows.Fig.7bshowsresultsfromasimulationrunexhibitingroughlyexponentialgrowthofcumulativefitnessovertime.Thus,asimplemodelforgrowthoftheUnderstandingregimeisalsoexponential.However,aswiththeOperationsregime,unlimitedgrowthbysimplecombinationofscientifictheoriesisnotrealistic.TheUnderstandingregimealsocannotprogressbysimplecombinationofexistingunderstandingbutinsteadexperiencesalimitthatweenvisionasdependinguponavailabilityofoperational(technological)toolsavailablefortestingscientifichypothesesandfordiscoveringneweffects.Weexpressthisdependencethroughanequationwhichexpressesthemaximumcumulativefitnessatanytime,maxFU(t),assimplyproportionaltotheIOIexistingatthattime:maxFU(t)=ZF∙IOIC(t) (13)WhereIOICthusrepresentsanapproximationfortheeffectivenessofavailableoperationaltools,andZFisaconstantofproportionality.ThisequationcapturestheconceptfirstsuggestedbyPricethattheextent(orscope)ofexplanatoryreachoftheUnderstandingregimeisdependentuponwhatexperimentaltoolsareavailableforscientistsandresearchers.Italsorecognizesinthetermsofourmodelthatthesetoolsareessentiallyoperationalartifacts.
![Page 21: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/21.jpg)
21
a)
b)
Fig. 7: a) Triangular distribution of possible fitness values that can be assumed by a new unit of understanding b) Growth of FU (cumulative fitness of Understanding regime) over time.
4.3 Exchanges between Understanding and Operations regimes Asdiscussedinsection3.1,priorqualitativeworkindicatesthattheinteractionofUnderstandingandOperationsisprobablybestmodeledbyassumingmutualbeneficialinteraction.Inourmodel,wecapturethisenablingexchangefromtheUnderstandingtotheOperationsregimeusingasimplemathematicalcriterion:FU(t)/FU(t_prev)≥cutoff_ratio(R) (14)Where,FU(t)andFU(t_prev)representcumulativefitnessvaluesattimesteptandthemostrecenttimestep,t_prev,atwhichaIOI0hadbeenintroduced.ThiscriterionstatesthatwhencumulativefitnessoftheUnderstandingregimegrowsbysomemultiple(R)fromthetimewhenthelastIOI0wasinvented,understandinghasimprovedenoughtogenerateanewIOI0,whichbecomesavailableforcombinationswithallexistingIOI.Thethresholdratio,R,determinesthefrequencyatwhichIOI0arecreated.
WenowshowresultsfromasimulationincludingtheexchangeandlimitsonIOI0.Inthesimulation,westudyhowsynergisticexchangefromUnderstandinginfluencestherateofgrowthofIOIintheOperationsregime,includingescapefromstagnation.Wefocusparticularlyontwovariables,namely,theinitialnumberofIOI0intheOperationsregime
a b c
0
FU
![Page 22: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/22.jpg)
22
andthethresholdratioRforcreationofnewIOI0.Otherpertinentvariablesaretheprobabilityofcombination,PIOI,thenumberofattemptspertimestepandthenumberoftimestepsperyearandarenotvariedinthissetofresults.Forthissimulationstudy,Table(1)presentstheparametervaluesforIOI0(column3)andthethresholdratiosofcumulativefitness(column4)thatareused.Asanexample,5B3RstartswithIOI0of5andanewIOI0iscreatedwhencumulativefitnessgrowsbyafactorof3.BoththeinitialnumberofIOI0andthethresholdratiosofcumulativefitnessaresetat3differentvalues,givingatotalsetof9parametercombinations.Forall9runs,theprobabilityforcombinationiskeptconstantat0.25,andweassumeoneattemptperyearlytimestep.
Table1:Simulationstudy:ParametervaluesofIOI0 andR (thresholdratiosofcumulativefitnessofUnderstanding)forthestudy.Results:KistheslopefittingthesimulationresultstoanexponentialwithR2forthefit(alsoshown).Otherparameters,suchasprobabilityofcombination,PIOI=0.25,arekeptconstant. Simulation
RunInitialIOI0
ThresholdratioR
Simulationavg.K(±2stddev)8
R2 K =ln(1+PIOI/2)
1 5B1.5R 5 1.5 0.123(±0.011) 0.998 0.1182 5B3R 5 3.0 0.055(±0.019) 0.959 0.1183 5B5R 5 5.0 0.039(±0.007) 0.943 0.1184 10B1.5R 10 1.5 0.122(±0.011) 0.997 0.1185 10B3R 10 3.0 0.115(±0.007) 0.998 0.1186 10B5R 10 5.0 0.117(±0.007) 0.983 0.1187 20B1.5R 20 1.5 0.116 (±0.007) 0.998 0.1188 20B3R 20 3.0 0.116(±0.009) 0.998 0.1189 20B5R 20 5.0 0.119(±0.016) 0.998 0.118
8Thestandarddeviationwasestimatedfromsevenrepetitionsforeachsimulationrun.
![Page 23: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/23.jpg)
23
Fig. 8: Growth of IOIc; initial IOI0 and R (cumulative fitness ratio) for each run are shown in the legend
for each run; e.g., 10B5R represents 10 IOI0 and fitness ratio of 5.
ThesimulationresultsinFig.8showsthetemporalgrowthofIOICintheOperationsregimefortheninerunsshowninTable1.Runs5B3Rand5B5Rclearlystandout:theyhaveabumpygrowthsincetheyencounterperiodsofstagnationmultipletimes,astheyevolve.Moreover,theireffectiveratesofgrowtharemeager,standingonlyat0.055and0.04,whichismuchlowerthan0.118,therategivenbyEquation10{ln(1+PIOI/2)}.Columns5,6,and7listtheK,R2,andKcalculatedusingln(1+PIOI/2)respectively.Thesmalldeviations
1
10
100
1000
10000
0 20 40 60 80 100 120 140 160 180
IOIC
Time
5B1.5R 5B3R 5B5R
10B1.5R 10B3R 10B5R
20B1.5R 20B3R 20B5R
![Page 24: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/24.jpg)
24
fromequation10foundfortheother7runsarewithinthe2‐sigmaestimatedfrommultiplesimulationrepetitionsforeachrun.Both5B3Rand5B5RstartwithlowinitialIOI0of5andhavehighercumulativefitnessthresholdratios(R)forinfusionofnewIOI0.LowinitialIOI0impliesthattheOperationsregimehasalownumberofcombinatorialpossibilitiesofIOItostartwith.Additionally,sincenewIOI0arenotcomingfastenoughtopushthefrontierofcombinatorialpossibilitiesofIOIfarenough,theOperationsregimequicklyexhauststhepossibilitiesandagainstagnates.Run5B5Rstagnatesforlongerperiodscomparedto5B3Rsinceithasahigherthresholdratio(R)forinfusionofanewIOI0andthusslowerprogress.TheOperationsregimecannotescapethestagnationuntilanotherIOI0iscreatedwithinfusionofnewunderstanding.Itisclearfromthecurvesthatthispatternrepeatsitselftimeaftertime.Othersimulationruns,exceptrun10B5Rgrowexponentiallyandsmoothlyandtheirratesareconsistentwiththetheoreticalvaluecalculatedusingln(1+PIOI/2),0.1178.ThesecurveshaveeitherhighenoughIOI0tostartwithorfastinfusionofIOI0,orboth.Run5B1.5R,forexample,startswithalownumberofIOI0buthasfastinfusionofIOI0,sincethethresholdratioRisonly1.5.Ontheotherhand,run20B5RhasslowinfusionofIOI0(highR),butstartswithhighinitialIOI0.Theserunsdonotexhibitstagnationfortworeasons.ThefirstreasonisthatthefrontierofcombinatorialpossibilitiesforsomerunsisveryfarfromthenumberofrealizedIOIatagiventimestep.Forexample,run20B5Rhasoveramillionpossibilitieswhenitstartswith20IOI0.ThesecondreasonisthatthefrontierofthecombinatorialpossibilitieskeepsonmovingfurtherawayasIOIcincreases.Run5B1.5R,forexample,startswith5IOI0,andyetitneverexperiencesstagnationduetofastinfusionofIOI0(lowR)thatpushthefrontierofcombinatorialpossibilities.ThegrowthofIOICisalsofreeofstagnationforruns(e.g.,suchasRun10B3R)withmediumnumberofinitialIOI0andmediumrateofinfusionofIOI0(mediumR).Thisistruebecausebothfactorsincombinationensurethatfrontierofcombinatorialpossibilitiesisfarenoughtostartwith,andthefrontiercontinuestomoverapidlyenoughwithtime.Run10B5Rexhibitssomewhatunusualbehavior.Althoughitgrowssmoothlyatthebeginningforquitesometime,itexperiencesstagnationlateron.Thisisbecausethefrontierofcombinatorialpossibilitiesisfarenoughawaytosustainsteadygrowthearlyon.Later,theOperationsregimeexhauststhecombinatorialpossibilitiesbeforenewIOI0arrive.However,onceanewIOI0arrives,itjumpstartsagainbutitbrieflyhaltsateachnewlimitdemonstratingthevalueoffrequentinterchangebetweenUnderstandingandOperationsinthissimulation9.9ThesimulationsarebaseduponinfusionofIOI0dependinguponaratio(R)ofgrowthincumulativeunderstanding,butsimilarresultsarefoundwithassumingamodelofdifferenceinFU.
![Page 25: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/25.jpg)
25
WehaveseenthatacombinatorialprocesscombinedwithsynergisticexchangebetweenUnderstandingandOperationsleadstoanexponentiallygrowingpoolofoperatingideas,IOIC.Thisgrowthisdescribedbyanexponentialfunction:
exp (15A)
(15B)Where,K=theeffectiverateofgrowthofIOIC,IOI0(t0)=thenumberofinitialbasicIOI,t=time,t0=initialtime.Ouroverallmodel(Section3,Figure2)envisagesthatthisexponentiallygrowingpoolofoperatingideas,IOIC,providesthesourcefortheexponentialgrowthofperformanceoftechnologicaldomains.HowdoesthisexponentialgrowthofIOICresultinperformanceimprovementandwhataccountsforthevariationinratesofperformanceimprovementacrosstechnologicaldomains?
4.4 Modeling interaction differences among domains Asexplainedinsection3,twofactorspotentiallyresponsibleformodulatingtheexponentialgrowthofoperatingideasastheyareintegratedintotechnologicaldomainsarethedomaininteractionsandscalingofrelevantdesignvariables.WeconsiderdomaininteractionsfirstfollowingtheworkofMcNerneyetal.(2011)whomodeledhowinteractionsinprocessesaffectunitcost.WebuildontheirmathematicaltreatmenttoanalyzetheeffectofinteractionsbetweencomponentsuponintegratinganIOIintoanartifactinadomain,whichinturnimprovestheartifact’sperformance.Figure9ashowsasimplifiedschematicofanartifactinatechnologicaldomainthathasthreecomponents(1,2,3)withinteractionbeingdepictedbyout‐goingarrows,representinginfluence,fromacomponenttoothercomponents,includingitself.Theoutgoingarrowsarereferredtoasout‐links.Thenumberofout‐links,d,fromacomponentprovidesameasureofitsinteractionlevel,andhasvalueof1orgreaterasMcNerneyetal.assumeeachcomponentatleastaffectsitself.Forsimplicity,Figure9ashowseachcomponentwithtwoout‐links,toitselfandtoanothercomponent.Werepresentaninstanceofanattemptbeingmadetoimprovetheperformanceofcomponent2byanIOIbeinginserted.Sincecomponent2interactswithitselfandanothercomponent,theperformanceoftheinteractingcomponentisalsochangedbytheinsertionbutinafashiondescribedprobabilistically.Theperformanceimprovementattemptisaccepted,onlyiftheperformanceoftheartifactasawholeimproves.Ifthatdoesoccur,wefollowMcNerneyetal.andconsidertheinteractionsbeingsuccessfullyresolvedtoimprovetheperformance.Forasimplifiedartifactwithdnumberofout‐linksforeachcomponent(d=2inFig.9a),McNerneyet.al.’streatment(2011)forunitcostresultsinthefollowingrelationship:dC/dm=‐B∙Cd+1 (16)
![Page 26: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/26.jpg)
26
Where,C=unitcostnormalizedwithrespecttoinitialcost10,m=numberofattempts,d=numberofout‐links,B=constantThisequationstatesthatthelevelofinteractioninherentinthedomainartifactinfluencestherateofunitcostreduction.Weadaptthisequationforouranalysisinthefollowingmanner.WeinterpretthenumberofattemptsasIOIcsincethenumberofIOIdeterminestheattempts(ateachattemptanIOIisbeingintroducedintoanartifacttomakeadesignchange).Secondly,costreductionisinverselyrelatedtoperformanceimprovement,suchasinatypicalmetrickWh/$.11WiththeseextensionsofMcNerneyetal.equation16canbere‐writtenas:d(Q)/dIOIc=B∙Q‐(d‐1) (17)Where,Q=performance
a)
b)
Fig. 9: Interactions in an artifact; a) illustration of interactions as out‐links b) sample space of probabilities for unit cost .
SinceasshowninEquations4and5,successfullyresolvedoperatingideasinadomain,IOISC,arethesourceforitsperformanceimprovement,wereplaceperformanceQofadomainwithIOISC.AnIOIisconsideredasuccessfulattemptiftheinteractionresolution
10Thenormalizedunitcostis1orlesssoincreasesindinequation16resultinlessimprovementperattempt.11Theconceptcanbefurthergeneralizedtoincludeperformancemetricswhichinvolveotherresourceconstraintssuchasvolume,mass,andtime,insteadofcost(e.g.,kWh/m3).
n=3;d=2n=#ofcomponentsd=out‐links(interactions)
d C
(1,1)
1 2
3
IOI
C1+C2 = C1(t) + C2(t) = C
C1
C
C0
C2
![Page 27: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/27.jpg)
27
leadstonetperformanceimprovementoftheartifact,andthecountofsuccessfulIOIisdenotedbyIOISC.Themodifiedequationshownbelowstatesthattheinteractionlevel,d,hasaretardingeffectonthegrowthofIOISCinadomain.d(IOISc)/dIOIc=B∙IOISc‐(d‐1) (18)Wesolvethedifferentialequationbyseparatingthevariables(IOISContheleftandIOIContheright),andintegratingbothsidesusingdummyvariables,andexpressIOISCexplicitly.Theintegrationlimitsare:a)fortherightside,0toIOIC,b)fortheleftside,1toIOISC.Theresultis:
∙ ∙ 1 / (19)SinceBanddareclosetounity,andIOIc>>1,wecanignore1inthebrackets.Sinceourgoalistodetermine{dlnIOISC/dlnIOIC},wetakethenaturallogofbothsidesanddifferentiateitwithrespecttolnIOIC,resultinginthefollowingexpressionwhichwillbesubstitutedintoequation5insection4.6:dlnIOIsc/dlnIOIc=1/dJ (20)
4.5 Performance models ‐ scaling of design variables Ourresearchquestionisconcernedwithintensivetechnologicalperformanceofdomainartifacts.Theintensivetechnologicalperformancerepresentsaninnateperformancecharacteristicofanartifact.Weoperationalizethenotionofintensiveperformancebydividingdesirableartifactoutputswithresourceconstraints(e.g.,mass,volume,time,cost).Anintensiveperformancemetricforbatteriesisenergydensity,kWh/m3.Wenowconsiderthreeexamplesofrelationshipsbetweenintensiveperformanceanddesignvariables.
4.5.1 Selected examples Wefirstconsiderblastfurnacesusedinthemanufacturingofsteelasrepresentativeofreactionvesselsofvariouskinds.Widelyusedperformanceattributesforablastfurnacearecapacityandcost,wherecostcanbeconsideredtheresourceconstraint.So,anintensiveperformancemetriccanbedefinedascapacity(outputperhourordaytypically)perunitcost.Thecapacityofareactionvesselisproportionaltoitsvolumewhileitscostisprimarilyproportionaltosurfacearea(Lipseyetal.2005).Thefollowingdimensionalanalysisshowsthatfollowingthesesimplisticassumptions,intensiveperformanceofareactionvesselislinearlyproportionaltosize,s.QRV=capacity/costofreactionvessel=s3/s2=s1 (21)Gold(1974)hasempiricallyshownthatthecostofablastfurnacegoesupby60percentwhenthecapacityisdoubled.IntensiveperformanceQRVusingthisempiricalfindinggoesupby1.25(=2/1.6)whens3doubles,andthussgoesupby1.26(=2.333)closelyagreeingwiththesimplyderivedequation21.
![Page 28: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/28.jpg)
28
Asecondexampleweconsiderisspecificpoweroutputfrominternalcombustion(andotherheat)engines.Poweroutput(kW)isproportionaltovolumeoccupiedbythecombustionchamberminustheheatlossfromtheengine,whichinturnisproportionaltotheengine’ssurfacearea.Thepower,then,is:power=As3–Bs2;B/A<1 (22)WhereAandBareconstantsforpowergenerationandheatlossrespectively.QIC=specificpowerαpower/volumeofengine;thusspecificpoweris=(As3–Bs2)/s3=A–B/s (23)Equation23indicatesthat,similartoreactionvessels,specificpoweroutputofICenginesincreaseswithsizesobothare“largerisbetter”artifacts”.ForsmallvaluesofB/As,specificpowerincreasesapproximatelylinearlywiths.Forlargervaluesofs,theincreaseislessthanlinearins.Asafinalexample,weconsiderinformationtechnologies,whoseperformanceimprovementranksamongstthehighest.Severalmoderninformationtechnologiesdependuponintegratedcircuit(IC)chips.ElectroniccomputershavebeenimprovingperformancebyreducingthefeaturesizesoftransistorsinICchipsformicroprocessors.Thenumberofcomputationspersecondperunitvolume,anintensivemeasureofperformance,dependsuponfrequencyandthenumberoftransistorsinaunitvolume.Frequencyisinverselyproportionaltothelineardimensionofafeature,s,andthenumberoftransistorsperunitareaisinverselyproportionaltoareaofthefeature.Thus,Computationpersecpercc=1/s∙1/s2=s‐3 (24)Thedimensionalanalysisindicatesthatcomputationspersecondincreasesrapidlyforadecreaseinalineardimensionofafeature.Thisisduetothecubic(orhigher)12dependenceofcomputationspersecondonfeaturesize.Thenegativesigncapturesthefactthatreductionofthedesignvariableincreasesperformance–smallerisbetterforthisartifact.
4.5.2 Generalization of scaling of design variables Thethreeexampleswehavepresentedillustratethenotionthatintensiveperformanceimprovedbydifferentdegreesdependinghowthedesignvariablesarescaled.Inthefirsttwocases,a10percentincreaseinadesignvariablewillimproveperformanceby10percentorless.However,inthecaseofcomputations,forthesame10percentchangeindesignvariable(featuresize),theperformancewouldimprovebyover33percent.Thisdependenceismodeledasapower‐law13:
12Iftheverticaldimensionalsodecreasesovertimeasthefeaturesizedecreases,ahigherpower‐perhapsapproaching4‐wouldapply.13Theengineexampledemonstratesthatthisisanapproximationinmanycases.
![Page 29: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/29.jpg)
29
(25) lnQJ=AJlns (26)
dlnQJ/dlns=AJ (27)
Where,AJisthescalingfactorfordomainJ,sisthedesignvariable.
4.6 Bringing all elements together WenowbringtheresultsforrateofIOISCgrowthandinfluenceofinteractionandscalingtogether.Forthereader’sconvenience,wereproduceequation4here,andsubstitutetheresultsforthefourfactors: dlnQJ/dt=dlnQJ/dlns∙dlns/dlnIOISC∙dlnIOISC/dlnIOIC∙dlnIOIC/dt (4)Substitutingtheresultsfromequations27,20,and15Bforthefirst,thirdandfourthterms,±1forthesecondterm,andthenrearranging,weget:
dln
∓1 1
(28)
Equation28representstheoverallmodeloftheannualrateofimprovementfordomainJ.Accordingtothisequation,KJ,theannualrateofimprovementofdomainJdependsuponK,theexponentialrateatwhichtheIOICpoolincreasesinsize.Kisthenmodulatedbydomainspecificparameters,dJ(interaction)inverselyandAJ(scaling)proportionallytoresultinadomainspecificrateof improvementKJ.TheminussignisconvertedintopositiveonebynegativesignofAJ(forthosecaseswheresmallerisbetter).OneobservationtonoteisthatAJand dJ are constants for a given domain, thus resulting in a time invariant rate (or asimpleexponential)foradomain.
5. Discussion
Thegoalofthispaperwastodevelopamathematicalmodelthatutilizesmechanismsinthedesign/inventionprocesstoexaminethenatureoftechnologicalperformanceimprovementtrends.TheexplorationhasutilizedsimulationtogaininsightintoacombinatorialprocessbaseduponanalogicaltransferandUnderstanding/Operationsexchangeandquantitativelymodeledinteractionsandscaling.Inthissection,wefirstbrieflyreviewtheconsistenciesofthemodelwithempiricalresults(andwhatisknownabouttechnologicalchange).Allempiricalresultsweareawareofarefoundtosupportthemodel.Wethenconsidertheasyetuntestedpredictionsfromthemodelaswellastheassumptionsmadeinthemodel.Accordingtothemodel,theexponentialnatureofperformanceimprovementforalltechnologicaldomainsarisesintheidearealmoftheoperationalknowledgeregime,where
![Page 30: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/30.jpg)
30
newinventiveideasarecreatedusingcombinatorialanalogicaltransferofexistingideas,which,inturn,becomethebuildingblocksforfutureinventiveideas.Weemphasizethatthecombinationsmodeledareoccurringattheidealevel,althoughcombinationscanalsotakeplacebetweencomponents.Asnotedinsection3.1,wemakethisdistinctionastheformerismuchmorepervasiveandallowscombinationofideasfromdifferentfields;however,itislikelythatsomeideascannotbecombinedandthisistreatedprobabilisticallysincemanycombinationattemptsfail.ThemodeldemonstratesthisincessantcumulativecombinatorialaspectofknowledgeinboththeUnderstandingandtheOperationsregimesmanifestsasexponentialtrends.ThecombinatorialmodelissimplebutitleadsnaturallytotheexponentialbehaviorwithtimethathasonlybeenobtainedpreviouslybyAxtelletal.inamodelthatwentbeyondperformancetodiffusionoverasetofagents.Sincesuchexponentialbehaviorwithtimeisoneofthemostwidelynotedbehaviorsoftechnicalperformance(Moore1965,KohandMagee2006,2008,Nagyetal.2013,Mageeet.a.2014),thecombinatoricmodelenactinganalogicaltransferthatwasdevelopedinthecurrentpaperisclearlysupportedbywhatisknownempiricallyaboutperformancetrendswithtime.TheOperationsandtheUnderstandingregimescanimproveindependentlyinthemodelbutnotindefinitely.HowlongtheOperationsregimecanimprovedependsinthemodeluponthesizeofthetechnologicalpossibilityspace,whichaccordingtothemodelisdependentonthenumberofbasicIOI,fundamentaloperationalprinciples,existing.TheUnderstandingregimecanalsoexperiencestagnation,butthishappenswhentheoperationaltoolsthatscientistsandresearchersusefordiscoveryandtestinghypothesesarenotadequate.TheOperationsregimecomestoitsrescuebyprovidingtheseoperationaltoolsinformofempiricalmethods,toolsandinstruments(increasednumbersofindividualoperatingideas),whichgreatlyenhancesthescientistsabilitytodiscoverandtest,andthusfurtherpushthelimitsofunderstandinginthemannersuggestedbyPrice(1983),Gribbin(2002)andinthefollowingquotefromToynbee(1962).
Physical Science and Industrialism may be conceived as a pair of dancers both of whom know their steps and have an ear for the rhythm of the music. If the partner who has been leading chooses to change parts and to follow instead there is perhaps no reason to expect that he will dance less correctly than before.
Inthissense,theOperationsregimeandtheUnderstandingregimeareliketwoindependentneighborswhointeractformutualbenefit.Inthemodel,theirfrequencyofinteractionhoweverinfluencestheireffectiverateofgrowth.Ourmodelisaspecificrealizationthatachievesthismutualinteractionthathaspreviouslybeenwidelynotedfromdeepqualitativeresearch.TheresultsinFigure8aresummarizedasasurfaceplotinFigure10.K,theeffectiverateofgrowthofIOICwasdeterminedbytheinitialIOI0,andthefrequencyofinteraction(α1/lnR).Theformerdeterminedtheenvelopeoftechnologicalpossibilityspace.WhenIOI0arehigh,theeffectiverateofgrowthKisclosetothetheoreticalcombinatorialratedeterminedbyEquation10{ln(1+PIOI/2)},irrespectiveofwhethertherewasfrequentexchange.However,whentheIOI0arelow,thelimitishitrepeatedly,translatinginto
![Page 31: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/31.jpg)
31
haltingandareducedeffectiverateofgrowth.ThevalueofKinthiscasewasdeterminedbythefrequencyofenablingexchangefromtheUnderstandingregime,withhigherfrequency(lowR)leadingtohighereffectiverate.Withsufficientlyhighfrequency,evenwithlowinitialIOI0,theeffectiverateKeventuallyapproachesthetheoreticalrate.
![Page 32: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/32.jpg)
32
Fig.10:VariationofKasafunctionofinitialIOI0andR.LowerRreferstohigherfrequencyofinteractionwiththeUnderstandingregime.Detailedhistoricalstudiesoftechnologicalchange(Mokyr2002)notecenturiesofslow,haltingprogressthateventuallybecomesmuchmorerapidandsustainedstartinginthelate18thcenturyintheUK.Aninterestingconsistencyoftheseobservationswithourmodelisseensinceourmodelattributesthetransitiontosustainedhigherimprovementratetothecombinatorialgrowthofindividualideasthatareabletoreinforceoneanotherbytheanalogicaltransfermechanism.ThatourmodelpartiallyaccomplishesthisthroughthesynergisticexchangebetweenUnderstandingandOperationsisalsoconsistentwiththedetailedhistoricalstudiesasinterpretedbymanyobservers(Schofield1963,Musson1972,RosenbergandBirdzell1986,MussonandRobinson1989,Mokyr2002,Lipseyetal.2005).TheKJvaluesfoundempiricallyvarybyapproximatelyafactorof22(from0.03to0.65accordingtoMageeetal.(2014).Equation28statesthatannualimprovementrateforadomainisdeterminedbytheproductofKtimesthescalingparameter,AJ,andthereciprocaloftheinteractionparameter,dJ.Accordingtothisresult,thelasttwoparametersproducethevariationofimprovementratesacrossdomains.Duringtheembodimentprocess,interactionsprevalentinthedomainartifactsinfluencehowmanyinventiveideascanbeabsorbed.ThepercentincreaseinsuccessfullyabsorbedideasbyadomainartifactisinverselyproportionaltotheaverageinteractionparameterofthedomaindJ.By
5
10
150
0.04
0.08
0.12
0.16
1.5
3
5
K
R
0.12‐0.16
0.08‐0.12
0.04‐0.08
0‐0.04
![Page 33: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/33.jpg)
33
definition,theminimumvalueofdis1andthemaximummightbehigherbutavalueof6appearsreasonable.Theotherfactorthatispredictedtodifferentiatedomainsisperformancescaling.Inventiveideasaffectartifactperformancebymodifyingthedesignparametersindomainartifacts.ThemodelindicatesthattherelativeimprovementofperformanceforagivennumberofabsorbednewoperatingideasisgovernedbythescalingparameterAJ.Theexamplespresentedinsection4.5illustratedthatthevalueofAJcanvaryacrossdomains.Inparticular,fortheICdomain(wheresmallerisbetter),AJisapparently3to4timeslargerthanfortypicallarger‐is‐betterdomainssuchascombustionengines.Thus,therangeofKJempiricallyobservedispotentiallyexplainablebychangesindJandAJ,butmuchmoreempiricalworkisneededtofullysupportthesequantitativeimplicationsofEquation28aswillbediscussedfurtherbelow.TheempiricalfindingsofBensonandMagee(2015a)alsosupportthemodel.Inparticular,theyfoundnocorrelationofratesindomainswitheffortinadomain(measuredbynumberofpatentsorpatentingrate)orwiththeamountofoutsideknowledgeusedbyadomain(thisisverylargeforalldomains).Theyinterpretedtheirfindingsbya“risingseametaphor”thatrepresentsallinventionsandscientificoutputbeingequallyavailabletoalldomainsbutthatfundamentalsinthedomainsdeterminetherateofperformanceimprovement.OveralleffortinUnderstanding(science)andinventionincreasetheratesinalldomainsbutthedifferencesamongratesofimprovementareduetodifferencesinfundamentalcharacteristicsamongthedomains.Themodelinthispaperidentifiesinteractionsandscalingastwosuchfundamentalsandequation28isspecificaboutthevariationexpectedduetothesetwofundamentalcharacteristics.Thus,ourmodelissupportedbywhatisknownempiricallyincludingexponentialdependenceofperformanceontime;slow,haltingprogressintheearlystagesoftechnologicaldevelopment;aroleforscienceinenablingtechnologicalperformanceimprovement;therangeofvariationinperformanceimprovementacrossdomains;andtheimportanceofdomainfundamentalstovariationinperformance.However,towhatextentdoesitachievetheideallevelofunderstandingmentionedinsection2whendiscussingtherelatedBensonandMageeresearch?Itis‐asdesired‐baseduponwhatisknownaboutthedesign/inventiveprocessanddoesnotrelyuponcharacteristicsonlydeterminedbyobservationofoutputinadomain.Moreover,itprovidesexplanationsofexistingempiricalresultsnotmadebypriormodels.However,doesitmakeanynewpredictions;doitsassumptionsappearreasonable;andwhatnewavenuesofdesignresearch,ifany,doesitopenupforfurtherexploration?Weconsidertheseissuesintheremainderofthediscussion.TherearethreenewpredictionsmadebythemodelasinstantiatedinEquation28.Theseare:1)thatthenoiseinestimatingKJshouldvarywithKJlinearlyratherthanforexamplebeindependentofKJ;2)thatperformanceimprovementcomparisonsacrossdomainsvaryas1/dJwheredistheinteractionparameter;and3)thatperformanceimprovementacrossdomainsvaryasAJ.ThefirstpredictionfollowsfromthefactthatthemodelascribesallvariationintheprocesstotheprobabilisticanalogicaltransferprocessthatcreatesIOIandthusanynoisegeneratedintheprocessisamplifiedbythesamefactorsthatdetermineKJ(namely1/dJandAJ.).Veryrecentworkappearstoconfirmthefirstprediction.Inacareful
![Page 34: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/34.jpg)
34
studyoftheobservednoiseinawidevarietyofdomains,FarmerandLafondhavefindthatthevariationinKJisproportionaltoKJofferingempiricalsupporttotheformofEquation28.ThisispotentiallyanimportantconfirmationofapredictionofthemodelbutthecarefulworkbyFarmerandLafondhaspotentialdatalimitations(detailedintheirpaper)andfurtherworkofthiskindishighlydesirable.Prediction2isthatcomponentinteractions(dJ),whichcharacterizethedomains,influenceimprovementratebymodulatingtheimplementationofIOIinthedomainartifacts.ThispredictioncanbetestedbystudyoftheperformanceimprovementratesoveravarietyofdomainswhereanindependentassessmentofdJismade.Theauthorshaveperformedsuchatestusingpatentdata(BasnetandMagee2016)andtheresults,whichdemonstratepositivecorrelationbetweenimprovementrates(KJ)andinteractionparameter(dJ),offersupportfortheanalysisofMcNerneyetal.thatweuseinourmodel.Prediction3isthatrelativeimprovementamongdomainsvariesproportionallytothescalingparameterforthedomaindesignparameters,aconsequenceofperformancefollowingapowerlawwiththedesignparameters.Ifscalinglawswerefound(orderived)foravarietyofdomainswhoserateofprogressisknown,prediction3canalsobetested.Inthispaper,weshowedthatthefactorAisatleast3timeslargerforIntegratedcircuitsthanforcombustionengines.WhilethisprovidespreliminarysupportforthemodelsinceIntegratedcircuitsimproveabout7timesfasterthancombustionengines(Mageeetal,2014),twopointsdonotachievearigoroustest.Onewouldneedtohavereliablescalingfactorsforatleast10domainswithvaryingKJtodeterminewhetherthispartofthemodelisempiricallysupported.Afundamentalaspectoftheoverallmodelisthatitdifferentiatesbetweentheidea/knowledgeandartifactaspectsofdesignandinvention.Suchdecompositionisanessentialstepinarrivingatourkeyresult(equation28throughequation5).Itisnotclearthatthisassumptionistestablesoitmustremainanunverifiedassumptionordefinitionbutwedonotethatitappearstoaccordwithrealityinthatinventors/designersspendsignificantamountoftimeworkingwithideasandrepresentationsofartifacts,forexampleintheformofsketchesanddrawings,wellbeforetheybuildartifacts.Othershavenotedthehigherleverageofanalogicaltransferbetweenideasasopposedtodesignedartifacts(Weisberg2006).Apotentiallyimportantandnon‐obviousassumptionmadeinthemodelisthatinventiveeffortincreasesasthecumulativenumberofindividualoperatingideas‐IOIC‐increases.ThisassumptionisintroducedwhenweassumethateveryexistingIOIundergoesacombinationattemptineachtimestep.AsIOICincreases,thismeansthatmoreinventionsareattemptedineachsuccessivetimestep.ThisassumptioniscriticaltoobtainingtheexponentialtimedependenceforIOICandthusforQbecausethegrowthofIOICwouldbechokedoffifinventiveattemptsdidnotincreaseovertime.Althougharigoroustestofthisassumptionissuggestedforfurtherwork,wedonotesupportfortheassumptionintheexponentialgrowthofpatentsovertime(Younetal.2014,PackalenandBhattachayra,2015)14.ApproximatesupportisalsogivenbytheroughlyexponentialgrowthofR&D
14Bothofthesepapersshowmorerapidexponentialincreasesbefore1870andslowerbutstillexponentialincreasesovertimefrom1870tothepresentinthenumberofUSpatents.
![Page 35: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/35.jpg)
35
spendingovertime(NSF,2014)andbytheroughlyexponentialgrowthofgraduateengineersglobally15overtime(NSF,2014)ThemodelassumesasimpleexchangebetweenUnderstanding(largelyscience)andOperations(largelytechnology)asdescribedbyEquations13and14.Thedetailsofthismechanismarenottestablebutinouropinionnotcriticalbecauseotherformalisms(basedupondifferencesratherthanratiosandbaseduponcountofunitsofunderstandingratherthanourchoiceofexplanatoryreach)leadtoresultscloselysimilartothosereportedhere.Therefore,thisassumptionremainsunverifiedbutisnotcriticaltoourconclusions.Similarly,theinitialvalueofIOI0choseninthesimulation(andtheexchangefrequencywithUnderstanding(α1/lnR))isessentialtoourfindingofhaltingslowgrowththatcantransitiontosustainedandmorerapidgrowth.Althoughthisfindingisconsistentwithdetailedobservationasnotedaboveandtheinitialnumberofusefulideasmustbesmall,thereisnoindependentmeansofassessingIOI0.Moreover,wehavemadeanumberofassumptionsinparametervaluestoconstructasimpleandoperationalsimulation.Thevaluesforparametersinthesimulation,suchasPIOI,numberoftimesteps,numberofscientificfields,R,fitnessvaluesarechosentokeepthecomputationalcostreasonable,withoutsacrificingtheessentialaspects.Simulationsshowthatresultsarerobusttodifferentcombinationsofparametervalueswithrespecttoexponentialtrendsandvariationinrates.Therefore,thesechoicesandsimplificationsdonotundercuttheexplanatoryorpredictivecapabilitiesofthemodelbutdolimitthepotentialfornon‐calibratedcalculationof,forexample,theimprovementrateforadomainsinceKisonlyapproximatelyknown.Tomakethemodeltractable,wehavemadenumberofsimplifyingabstractions,introducingseveralotherlimitationstothemodel.Sincethemodelisnotagent‐based,itdoesnotdistinguishbetweenorganizationsnorbetweeninventors.Sinceourgoalistoexplainthepatternsatthedomainlevel,weconsiderthedomainasoneentity.Forthisreason,variationsamongorganizationsoramonginventorswithinadomainarenottakenintoaccount,andhencethemodelisnotusefultounderstandorganizationalorindividualinventoreffectivenessinitscurrentformandanysystematicdifferencesamonginventorcapabilityacrossdomainsisignored.Second,onceIOIarecreatedbyanyinventor,themodelassumestheyareinstantlyavailableforcombinatorialanalogicaltransferacrossthepoolunderlyingalldomains.Thus,themodeldoesnottakeintoaccounttimedelaythatcanresultdueto,forexample,geography,secrecyandgovernmentalregulations,andhenceisnotusefulforstudyingsuchfactors’influenceintechnologicalchange.Third,themodelassumesthat2pre‐existingideasaresufficient(probabilistically)tocreateanotherideawhereasinventionsalsoresultfrombringingmorethan2pre‐existingideastogether.However,addingsuchcomplicationstothemodelandsimulationdoesnotchangethefundamentalfindingssincethecreationofnewideaswouldstillincreaseasthenumberofpre‐existingideasincreaseaslongaswestillassumeanincreasinginventioneffort.Fourth,althoughconceptuallythenotionoffitnessofscientificfieldsmakessense,howthe
15OthersupportingevidenceisalsopossibletoseeintheNSFmaterialathttp://www.nsf.gov/statistics/seind14/index.cfm/overview/c0s1.htm#s2
![Page 36: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/36.jpg)
36
fitnesscanbemeasured,andwhomeasuresitforascientificfieldarecontested,especiallyforrapidlygrowingfields.ThisanalysisofthepredictionspointsoutthatsomekeyaspectsofEquation28havethepotentialtobeempiricallytestedandthusareclearfutureresearchactivitiessuggestedbythemodel.Amongthesefutureresearchactivities,oneimportantissuetodiscussistheextensionspossibletodesignresearchpotentiallyopenedupbythecurrentwork.Themodelinthispaperexplicitlyconsidersdesignchangesinsucceedingartifactsinaseriestobethecentralelementintechnologicalchangeovertime.Thus,itaddstothefewotherpapers(BaldwinandClark2006,Luoetal.2014)thathaveconnectedthesetwolargefieldsofresearch‐technologicalchangeanddesigntheory.Thispaperinparticularconnectsdesignconceptuallyandquantitativelytochangesinperformanceovertime.Sincethereissignificantdataofthistype(Moore,1965,Girifalco1991,Nordhaus1996,KohandMagee(2006,2008)andLeinhard2008),thispaperpointsthewayforfurtherquantitativecomparisonsofmodelsbasedupondesigntheorywithdata.Anotherlineofresearchthatthismodelsuggestsismoreexplicitconsiderationofinteractionsandscalingaspartofdesigntheories.Thecurrentmodelexploressimplemodelsforbothofthesethatarecapableofpredictingdifferencesintimedependenceofperformanceindifferingdomains.Designofartifactscouldconceptuallybechangedsothatthepotentialforimprovementwithongoingredesignisenhancedpossiblythroughreducedinteractionsormoreintensivescalingrelationships.Thus,thecurrentpapersuggeststhepotentialimportanceoffurtherresearchonspecificdifferencesindesignapproacheswithdifferentscalinglawsandwithdifferentlevelofinteractions.
6. Concluding remarks Themodelandsimulationsoftheimprovementsinperformanceduetoaseriesofinventions(newdesigns)overtimepresentedinthisworkarebaseduponasimpleversionofanalogicaltransferasacombinatorialprocessamongpre‐existingoperational/inventiveideas.Themodelissupportedbyanumberofempiricallyknownaspectsoftechnologicalchangeincluding:1. Thetransitionfromslow,hesitanttechnologicalchangetomoresustainedtechnological
progressastechnologicalideasaccumulate;2. Arolefortheemergenceofthescientificprocessinstimulatingthetransitioninpoint1;3. Theexponentialincreaseofperformancewithtime(generalizedMoore’sLaw)seen
quitewidelyempirically;4. Thatstochasticnoiseintheslopesofthelogperformancevs.timecurvesis
proportionaltotheslope;5. Thelevelofeffortindomainsisnotimportantintherateofprogress.
Themodelalsoindicatesthat:6. Therateofperformanceincreaseinatechnologicaldomainisatleastpartly(and
possiblylargely)duetofundamentaltechnicalreasons(componentinteractionsand
![Page 37: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/37.jpg)
37
scalingofdesignvariables),ratherthancontextualreasons(suchasinvestmentinR&D,scientificandengineeringtalent,ororganizationalaspects).
Numerousmodelingassumptionsweremadeindevelopingthemodelbutonlysomeofthesearecriticaltotheconclusionsjustlisted.Furtherspecificresearchissuggestedtomovesomecriticalassumptionsintothetestablecategory,andtoconsiderinteractionsandscalingparametersinnewdesignapproaches.Thesearediscussedinthepaperparticularlyfortheassumptionsunderlyingpoint6above.Thetestsinvolvedetailedstudiesoftheinteractionandscalingparametersinavarietyofdomains.Allofthisfutureresearchcouldsupportorleadtomodificationofpoint6.
Acknowledgement
TheauthorsaregratefultotheInternationalDesignCenterofMITandtheSingaporeUniversityofTechnologyandDesign(SUTD)foritsgeneroussupportofthisresearch.WewouldalsoliketothankDr.JamesMcNerneyforhelpfuldiscussionaboutartifactinteractions.WewanttoalsoacknowledgevaluableinputonanearlierversionofthispaperbyDr.JamesMcNerneyandDr.Daniel.E.Whitney.
![Page 38: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/38.jpg)
38
Reference
Acemoglu, D. (2002). Directed Technical Change. TheReviewofEconomicStudies, 69(4),781–809.http://doi.org/10.2307/1556722
Arrow, K. J. (1962). The economic implications of learning by doing’. The Review ofEconomicStudies,29(3).
Arthur, W. B. (2007). The structure of invention. Research Policy, 36(2), 274–287.http://doi.org/10.1016/j.respol.2006.11.005
Arthur,W.B.,&Polak,W. (2006). TheEvolution of Technologywith a Simple ComputerModel.Complexity,11(5),23–31.http://doi.org/10.1002/cplx
Auerswald, P., Kau, S., Lobo, H., & Shell, K. (2000). The production recipes approach tomodeling technological innovation : An application to learning by doing. JournalofEconomicDynamics&Control,24,389–450.
Axtell, R. L., Casstevens, R., Hendrey, M., Kennedy, W., & Litsch, W. (2013). CompetitiveInnovation and theEmergence ofTechnologicalEpochsClassification : Social SciencesShort title : Competitive Innovation Author contributions : Retrieved fromhttp://www.css.gmu.edu/~axtell/Rob/Research/Pages/Technology_files/TechEpochs.pdf
Baker,N.R.,Siegman J.,R.A.H. (1967).TheEffectsofPerceivedNeedsandMeanson theGeneration of Ideas for Industrial Research and Development Projects. IEEETransactionsonEngineeringManagement,(December).
Baldwin,C.Y.,&Clark,K.B.(2006).Between“Knowledge”and“TheEconomy”:TheNotesontheScientificStudyofDesigns.InB.Kahin&D.Foray(Eds.),AdvancingKnowledgeandTheKnowledgeEconomy(pp.298–328).Cambridge,MA:TheMITPress.
Baldwin,CarlissY.,Clark,K.B. (2000).DesignRules:ThePowerofModularity. Cambridge,MA:MITPress.
Barenblatt, G. I. (1996). Scaling,Self‐similarity,andIntermediateAsymptotics:DimensionalAnalysis and Intermediate Asymptotics. New York, New York, USA: CambridgeUniversityPress.
Basnet, S., & Magee, C. L. (2016). Dependence of technological improvement on artifactinteractions.Retrievedfromhttp://arxiv.org/abs/1601.02677
Benson, C. L., & Magee, C. L. (2015a). Quantitative Determination of TechnologicalImprovement from Patent Data. PloS One, (April).http://doi.org/DOI:10.1371/journal.pone.0121635April15,2015
Benson,C.L.,&Magee,C.L.(2015b).Technologystructuralimplicationsfromtheextensionof a patent search method. Scientometrics, 102(3), 1965–1985.http://doi.org/10.1007/s11192‐014‐1493‐2
Braha, D., & Reich, Y. (2003). Topological structures for modeling engineering designprocesses. Research in Engineering Design, 14(4), 185–199.http://doi.org/10.1007/s00163‐003‐0035‐3
Cameron, P. J. (1995). Combinatorics:Topics,Techniques,Algorithms (1st ed.). New York,
![Page 39: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/39.jpg)
39
NewYork,USA:CambridgeUniversityPress.
Carter, C.F. andWilliams, B.R. (1959). Carter,C.F.andWilliams,B.R.,1959. Investment inInnovation.(London:OxfordUniversityPress.
Carter, C.F.,Williams,B. R. (1957). IndustryandTechnicalProgress:FactorsGoverningtheSpeedofApplicationofSciencetoIndustry.London:OxfordUniversityPress.
Christensen, B. T., & Schunn, C. D. (2007). The relationship of analogical distance toanalogicalfunctionandpreinventivestructure:thecaseofengineeringdesign.Memory&Cognition,35(1),29–38.http://doi.org/10.3758/BF03195939
Christensen, C.M.,&Bower, J. L. (1996). CustomerPower, Strategic Investment, and theFailure of Leading Firms. Strategic Management Journal, 17(3), 197–218.http://doi.org/10.1002/(SICI)1097‐0266(199603)17:3<197::AID‐SMJ804>3.0.CO;2‐U
Clement,C.a,Mawby,R.,&Giles,D.E.(1994).TheEffectsofManifestRelationalSimilarityon Analog Retrieval. Journal of Memory and Language.http://doi.org/10.1006/jmla.1994.1019
Dahl,D.W.,&Moreau,P. (2002).The InfluenceandValueofAnalogicalThinkingDuringNewProductIdeation.JournalofMarketingResearch,39(1),47–60.
Dasgupta,S.(1996).CreativityandTechnology.OxfordUniversityPress.
deSollaPrice,D.J.(1986).Sealingwaxandstring.InLittleScience,BigScienceandbeyond.NewYork,NewYork,USA:ColumbiaUniversityPress.
Dosi, G. (1982). Technological paradigms and technological trajectories. ResearchPolicy,11(3),147–162.http://doi.org/10.1016/0048‐7333(82)90016‐6
Farmer,J.D.,&Lafond,F.(2015).Howpredictableistechnologicalprogress ?Retrievedfromhttp://arxiv.org/abs/1502.05274
Fehrenbacker,K. (2012).WecanthankMoore’sLawfor theVCcleantechbust.Retrievedfrom http://gigaom.com/2012/02/01/we‐can‐thank‐moores‐law‐for‐the‐vc‐cleantech‐bust/
Finke, R. A.,Ward, T. B., & Smith, S.M. (1996).CreativeCognition:Theory,Research,andApplications.Cambridge,MA:MITPress.
Fleming,L.(2001).RecombinantUncertaintyinTechnologicalSearch.ManagementScience,47(1),117–132.http://doi.org/10.1287/mnsc.47.1.117.10671
Fleming, L., & Sorenson, O. (2004). Science as a map in technological search. StrategicManagementJournal,25(89),909–928.http://doi.org/10.1002/smj.384
Frischknecht, B., Gonzalez, R., Papalambros, P. Y., & Reid, T. (2009). A design scienceapproachtoanalyticalproductdesign.InternationalConferenceonEngineeringDesign,DesignSociety,PaloAlto,CA,(August),35–46.
Fu,K.,Chan,J.,Cagan,J.,Kotovsky,K.,Schunn,C.,&Wood,K.(2013).TheMeaningof“Near”and “Far”:The Impact of StructuringDesignDatabases and theEffect ofDistanceofAnalogy on Design Output. Journal of Mechanical Design, 135(2), 021007.http://doi.org/10.1115/1.4023158
Gentner, D., & Markman, A. B. (1997). Structure mapping in analogy and similarity.
![Page 40: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/40.jpg)
40
AmericanPsychologist,52(1),45–56.
Gero, J. S., & Kannengiesser, U. (2004). The situated function‐behaviour‐structureframework. Design Studies, 25(4), 373–391.http://doi.org/10.1016/j.destud.2003.10.010
Girifalco. (1991). Dynamics of Technological Change. New York, New York, USA: VanNostrandReinhold.
Goel,A.K.(1997).Design,analogy,andcreativity.IEEEExpert,12(3).
Gold,B.,The,S.,Economics, I.,&Sep,N.(1974).EvaluatingScaleEconomies :TheCaseofJapaneseBlastFurnaces.TheJournalofIndustrialEconomics,23(1),1–18.
Gribbin, J. (2002).TheScientists:AHistoryofScienceToldThroughtheLivesofItsGreatestInventors.NewYork,NewYork,USA:RandomHouse.
Hatchuel, A.,&Weil, B. (2009). C‐Kdesign theory:An advanced formulation.ResearchinEngineeringDesign,19(4),181–192.http://doi.org/10.1007/s00163‐008‐0043‐4
Henderson,R.M.,&Clark,K.B. (1990).Architectural Innovation :TheReconfigurationofExistingProductTech‐nologies and theFailureofEstablishedFirms.AdministrativeScienceQuarterly,35(1),9–30.
Holyoak, K. J., & Thagard, P. R. (1995). Mental Leaps: Analogy in Creative Thought.Cambridge,MA:MITPress.
Hunt, B. J. (2010). PursuingPower and Light. Baltimore, MD: Johns Hopkins UniversityPress.
Klevorick, A. K., Levin, R. C., Nelson, R. R., & Winter, S. G. (1995). On the sources andsignificance of interindustry differences in technological opportunities. ResearchPolicy,24(2),185–205.http://doi.org/10.1016/0048‐7333(93)00762‐I
Koestler,A.(1964).TheActofCreation.London:Hutchinson&Co.
Koh,H.,&Magee,C.L.(2006).Afunctionalapproachforstudyingtechnologicalprogress:Application to information technology. TechnologicalForecastingandSocialChange,73(9),1061–1083.http://doi.org/10.1016/j.techfore.2006.06.001
Koh,H.,&Magee,C.L.(2008a).Afunctionalapproachforstudyingtechnologicalprogress :Extension to energy technology☆. TechnologicalForecastingandSocialChange, 75,735–758.http://doi.org/10.1016/j.techfore.2007.05.007
Koh,H.,&Magee,C.L.(2008b).Afunctionalapproachforstudyingtechnologicalprogress:Extension to energy technology. TechnologicalForecastingandSocialChange, 75(6),735–758.http://doi.org/10.1016/j.techfore.2007.05.007
LangrishJ.,GibbonsM.,EvansW.G.,Jevons,F.R.(1972).WealthfromKnowledge:AStudyofInnovationinIndustry.NewYork,NewYork,USA:Halsted/JohnWiley.
Leclercq, P., & Heylighen, A. (2002). Analogies Per Hour. In J. S. Gero (Ed.), ArtificialIntelligenceinDesign’02(pp.285–303).Dordrecht:KluwarAcademicPublishers.
Lienhard, J. H. (2008). How Invention Begins: Echoes of Old Voices in the Rise of NewMachines.NewYork,NewYork,USA:TheOxfordUniversityPress,UK.
![Page 41: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/41.jpg)
41
Linsey, J. S., Markman, A. B., & Wood, K. L. (2012). Design by Analogy: A Study of theWordTree Method for Problem Re‐Representation. Journal of Mechanical Design,134(4).
Linsey,J.S.,Wood,K.L.,&Markman,A.B.(2008).Modalityandrepresentationinanalogy.ArtificialIntelligence forEngineeringDesign,AnalysisandManufacturing, 22, 85–100.http://doi.org/10.1017/S0890060408000061
Lipsey, Richard G., Carlaw, Kenneth I., Bekar, C. T. (2006). Economic Transformations:GeneralPurposeTechnologiesandLongTermEconomicGrowth.NewYork,NewYork,USA:TheOxfordUniversityPress.
Luo, J.,Olechowski,A.L.,&Magee,C.L.(2014).Technology‐baseddesignandsustainableeconomic growth. Technovation, 34(11), 663–677.http://doi.org/10.1016/j.technovation.2012.06.005
Magee,C.L.,Basnet,S.,Funk, J.L.,&Benosn,C.L. (2014).Quantitativeempiricaltrendsintechnical performance (No. ESD‐WP‐2014‐22). Cambridge, MA. Retrieved fromhttp://esd.mit.edu/WPS/2014/esd‐wp‐2014‐22.pdf
McNerney,J.,Farmer,J.D.,Redner,S.,&Trancik,J.E.(2011).Roleofdesigncomplexityintechnology improvement. PNAS, 108(38), 9008–9013.http://doi.org/10.1073/pnas.1017298108/‐/DCSupplemental.www.pnas.org/cgi/doi/10.1073/pnas.1017298108
Meyers,S.,Marquis,D..(1969).SuccessfulIndustrialinnovation.Washington,D.C.:NationalScienceFoundation.
Mokyr, J. (2002). The Gifts of Athena: Historical Origins of the Knowledge Economy.Princeton:PrincetonUniversityPress.
Moore, G. E. (1965). Cramming more components onto integrated circuits. Electronics,38(8),1–4.
Mowery,D.,&Rosenberg,N. (1979).The influenceofmarketdemandupon innovation:acritical review of some recent empirical studies. Research Policy, 8(2), 102–153.http://doi.org/10.1016/0048‐7333(79)90019‐2
Musson,A.E.(1972).Science,technologyandeconomicgrowthintheeighteenthcentury.(A.E.Musson,Ed.)(1sted.).Routledge.
Musson, A. E., & Robinson, E. (1989). ScienceandTechnologyintheIndustrialRevolution.GordonandBreachSciencePublishers.
Muth, J.F. (1986).SearchTheoryand theManufacturingProgressFunction.ManagementScience,32(8),948–962.http://doi.org/10.1287/mnsc.32.8.948
Nagy, B., Farmer, J. D., Bui, Q. M., & Trancik, J. E. (2013). Statistical basis for predictingtechnological progress. PloS One, 8(2), e52669.http://doi.org/10.1371/journal.pone.0052669
Nelson, Richard R., Winter, S. G. (1982). An Evolutionary Theory of Economic Change.Cambridge,MA:HarvardUniversityPress.
Nemet,G.,Johnson,E.(2012).Doimportantinventionsbenefitfromknowledgeoriginating
![Page 42: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/42.jpg)
42
inothertechnologicaldomains?ResearchPolicy,41(1).
Nordhaus,W. D. (1996). Do Real‐Output and Real‐WageMeasures Capture Reality? TheHistory of Lighting Suggests Not. In The Economics of New Goods (pp. 27–70).Retrievedfromhttp://www.nber.org/chapters/c6064.pdf
Polanyi, M. (1962). PersonalKnowledge:Towards aPost‐CriticalPhilosophy. Chicago, IL:UniversityofChicagoPress.
Polya,G.(1945).HowtoSolveIt:ANewAspectofMathematicalMethod(1sted.).Princeton,NJ:PrincetonUniversityPress.
Popper,K.(1959).LogicofScientificDiscovery(1sted.).Hutchinson&Co.
Romer,P.M.(1990).EndogenousTechnologicalChange.JournalofPoliticalEconomy,98(5).
Rosenberg, N. (1982). Inside theBlackBox:Technology andEconomics. Cambridge, MA:CambridgeUniversityPress.
Rosenberg, N., & Birdzell, L. E., J. (1986). How the West Grew Rich: The EconomicTransformationoftheIndustrialWorld.US:BasicBooks.
Ruttan,V.W.(1959).UsherandSchumpeteronInvention,Innovation,andTechnologicalChangeAuthor ( s ): VernonW .RuttanReviewedwork ( s ): Publishedby :OxfordUniversityPress.TheQuarterleyJournalofEconomics,73(4),596–606.
Ruttan, V. W. (2001). Technology, Growth, and Development: An Induced InnovationPerspective.NewYork,NewYork,USA:OxfordUniversityPress.
Sahal, D. (1979). A Theory of Progress Functions. AIIE Transactions, 11(1), 23–29.Retrieved fromhttp://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:A+I+I+E+Transactions#8
Sahal,D.(1985).Technologicalguidepostsandinnovationavenues.ResearchPolicy,14(2),61–82.http://doi.org/10.1016/0048‐7333(85)90015‐0
Schofield,R.(1963).TheLunarSocietyofBirmingham:ASocialHistoryofProvincialScienceandIndustryinEighteenth‐CenturyEngland.Clarendon.
Schumpeter, J. A. (1934).TheTheoryofEconomicDevelopment. Cambridge, MA: HarvardUniversityPress.
Shai,O.,Reich,Y.,&Rubin,D.(2009).Creativeconceptualdesign:Extendingthescopebyinfused design. CAD Computer Aided Design, 41(3), 117–135.http://doi.org/10.1016/j.cad.2007.11.004
Simon, H. A. (1962). The Architecture of Complexity. Proceedings of the AmericanPhilosophicalSociety,26(6),467–482.http://doi.org/10.1016/S0016‐0032(38)92229‐X
Simon,H.A.(1969).TheSciencesoftheArtificial(1sted.).Cambridge,MA:TheMITPress.
Simon,H.A.(1996).TheSciencesoftheArtificial(3rded.).Cambridge,MA:TheMITPress.
Solow, R. M. (1956). A Contribution to the Theory of Economic Growth. TheQuarterlyJournalofEconomics,70(1),65–94.http://doi.org/10.2307/1884513
![Page 43: Modeling of technological performance trends design theoryweb.mit.edu/cmagee/www/documents/46... · Massachusetts Institute of Technology, Institute for Data, Systems, and Society,](https://reader034.vdocuments.mx/reader034/viewer/2022051811/60209bed04a0625d32636cb2/html5/thumbnails/43.jpg)
43
Suh, N. P. (2001).AxiomaticDesign:AdvancesandApplications (1st ed.). New York, NewYork,USA:TheOxfordUniversityPress,UK.
Taguchi, G. (1992). Taguchi on Robust Technology Development: Bringing QualityEngineeringUpstream.AsmePressSeries.
Toynbee,A. J. (1962). Introduction:TheGenesesofCivilizations. InAStudyofHistory,12Vol.NewYork,NewYork,USA.
Tseng, I., Moss, J., Cagan, J., & Kotovsky, K. (2008). The role of timing and analogicalsimilarity in thestimulationof ideageneration indesign.DesignStudies,29(3),203–221.http://doi.org/10.1016/j.destud.2008.01.003
Tushman,M. L.,&Anderson, P. (1986). TechnologicalDiscontinuities andOrganizationalEnvironmentslifecycles.AdministrativeScienceQuarterly,31,439–465.
Usher,A.P.(1954).AHistoryofMechanicalInventions(1sted.).NewYork,NewYork,USA:BeaconPress,BeaconHill,MA.
Utterback,J.M.(1974).Innovationinindustryandthediffusionoftechnology.Science(NewYork,N.Y.),183(4125),620–626.http://doi.org/10.1126/science.183.4125.620
Vincenti, W. (1990).WhatEngineersKnow,andHowTheyKnow It. Baltimore, MD: JohnHopkinsUniversityPress.
Weber, C., & Deubel, T. (2003). NEW THEORY‐BASED CONCEPTS FOR PDM AND PLMProperty‐DrivenDevelopment/Design(PDD),1–10.
Weisberg,R.W.(2006).Creativity.InCreativity(1sted.,pp.153–2007).Hoboken,NJ:JohnWiley&Sons,Inc.
Whitney,D.E.(1996).WhyMechanicalDesignWillNeverbeLikeVLSIdesign.ResearchinEngineeringDesign,8,125–138.
Whitney, D. E. (2004). Physical limits to modularity. InMITEngineeringSystemDivisionInternal Symposium. Retrieved fromhttps://esd.mit.edu/symposium/pdfs/papers/whitney.pdf
Wright,T.P.(1936).FactorsAffectingtheCostofAirplanes. JournalofAero.Science,122–138.
Yelle, L. E. (2007). The learning curve: historical review and comprehensive survey.DecisionSciences.
Youn,H.,Bettencourt,L.M.a.,Strumsky,D.,&Lobo,J.(2014).InventionasaCombinatorialProcess: Evidence from U.S. Patents. Physics Society, June, 1–22. Retrieved fromhttp://arxiv.org/abs/1406.2938v1