implications of complexity research for command and cont:复杂性研究的指挥和控制的影响

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ImplicationsofComplexityResearchforCommandandControlM.I.BellFACT,29July2009 DisclaimersMostoftheseideasarenotoriginal;IwillnotacknowledgemysourcesIamresponsibleforanyerrors;feelfreetopointthemoutComplexitycanbecomplicated,evencomplexIgetnothingfromtheadmissioncharge;norefundswillbegiven2 BewareofHumptyDumpty“WhenIuseaword,”HumptyDumptysaid,inratherascornfultone,“itmeansjustwhatIchooseittomean–neithermorenorless.”“Thequestionis,”saidAlice,“whetheryoucanmakewordsmeansomanydifferentthings.”“Thequestionis,”saidHumptyDumpty,“whichistobemaster–that'sall.”CareisrequiredwhenusingeverydaywordsforspecializedpurposesThecommunityofinterestneedsclear,commondefinitionThegeneralpublicneedswarningstoavoidconfusion3 OutlineMotivationSometrivialquestions(notanswers)IntuitivecomplexityQuantifyingcomplexityFormalcomplexity:dynamicandarchitecturalDesignandcontrolofcomplexsystemsComplexityandC24 MotivationComplexityasabuzzword“Sixdegreesofseparation,”“butterflyeffect,”etc.haveenteredpopularcultureDozensofuniversitygroups,programs,seminars,andprojectsPioneers(e.g.,SantaFeInstitute)consideringmovingonComplexityasametaphor98of144papersinthe14thICCRTScontaintheword“complexity”ComplexityasamindsetAwarenessofchaos,“fattails,”“tippingpoints,”self-organizationComplexityasatoolboxFractalgeometry,nonlineardynamics,agent-basedsimulationComplexityasaparadigm“acceptedexamplesofactualscientificpractice…[that]providemodelsfromwhichspringparticularcoherenttraditionsofscientificresearch”–T.S.Kuhn,TheStructureofScientificRevolutions,19625 WhatisComplexity?Manyentities,manyinteractions,collectivebehaviorQualityorquantity?Definitionorcharacteristics?Emergence,self-organization,self-similarity,chaos,etc.Computationalcomplexity(ofaproblem)Resources(typicallytime)requiredtoobtainasolutionAlgorithmicinformationcontent(ofastring)LengthoftheshortestprogramthatwilloutputthestringStructuralcomplexitySelf-similarity,fractalgeometryDynamiccomplexityChaos,sensitivitytoinitialconditions,phasetransformations6 WhyareThingsComplex?ByselectionorbydesignSelectionNaturalorartificial(oftennot“survivalofthefittest”but“thesurvivorsarethefittest”)Preferentialgrowth(“therichgetricher”)DesignNonlinearityFeedbackcontrolOptimization7 WhyDoWeCare?Emergentbehavior(self-organization)Requisitevariety(control)Causality(prediction)Stability/instability(cascadingfailure)Unintendedconsequences8 IntuitiveComplexityDisorganizedcomplexity“aprobleminwhichthenumberofvariablesisverylarge,andoneinwhicheachofthemanyvariableshasabehaviorwhichisindividuallyerratic,orperhapstotallyunknown.However,…thesystemasawholepossessescertainorderlyandanalyzableaverageproperties”Organizedcomplexity“problemswhichinvolvedealingsimultaneouslywithasizablenumberoffactorswhichareinterrelatedintoanorganicwhole”–W.Weaver,AmericanScientist(1948)9 Complexityvs.OrderPHYSICSPressureTemperaturePhaseStatisticalAnalysisOrganized/DifferentiatedEntitiesSimpleEntitiesSystemsAnalysisECONOMICSGDPGrowthrate10 ‘‘Longrangedetailedweatherpredictionisthereforeimpossible,…theaccuracyofthispredictionissubjecttotheconditionthattheflightofagrasshopperinMontanamayturnastormasidefromPhiladelphiatoNewYork!’’–W.S.Franklin(1898)ButterflyEffect11 ArgumentforQuantification“Whenyoucanmeasurewhatyouarespeakingabout,andexpressitinnumbers,youknowsomethingaboutit;butwhenyoucannotmeasureit,whenyoucannotexpressitinnumbers,yourknowledgeisofameagerandunsatisfactorykind…”–WilliamThompson(LordKelvin),1824-1907Ifwecanquantifycomplexity,wecanDeterminewhetheronesystemismoreorlesscomplexthananotherDeterminewhetheracontrol(orC2)systemisoftheappropriatecomplexityforagivensituationTakeappropriatestepstocontrolcomplexity;e.g.,ReducethecomplexityofourenvironmentIncreasethecomplexityofanadversary’senvironment12 AlgorithmicInformationContentLengthoftheshortestpossibledescriptionofasystem(madeformalusingTuringmachineconcept)Pros:ConsistentwiththeideathatagoodtheorysimplifiesthedescriptionofphenomenaCons:Complexitymayseemtobeapropertyofourunderstandingofasystem,notofthesystemitselfThelengthofdescriptionmaydependonthevocabularyavailableRelativecomplexityoftwosystemsdependsonthedetailsoftheTuringmachineusedItisimpossibletoshowthatadescriptionistheshortestpossibleRandomsystemsaremaximallycomplex(counter-intuitive)13 ComputationalComplexityThenumberofoperations(typicallymultiplications)neededtosolveaproblemPros:Acomplexproblemtakeslonger(ormoreresources)tosolvethanasimpleoneThedifficultyofacomplexproblemgrowsrapidlywithitssizen:Problemsthatcanbesolvedintimeproportionaltonkare“polynomialtime”problemsProblemsthatcanbesolvedintimeproportionaltoenorn!are“exponentialtime”problemsCons:Thereisnoalgorithmfordetermininghowhardaproblemis!14 FormalComplexityDynamic(process)CorrespondsroughlytocomputationalcomplexityOriginatedinnon-lineardynamicsArchitectural(structural)CorrespondsroughlytoalgorithmicinformationcontentOriginatedincommunicationtheory15 MandelbrotSetAcomplexnumbercisamemberofthesetifstartingwithz0=0,zn+1=zn2+cisboundedB.Mandelbrot,ca.197816 EscapeProblemsMandelbrotsetAcomplexnumbercisamemberofthesetifstartingwithz0=0,zn+1=zn2+cisboundedInotherwords,cisnotamemberifzn+1escapesSinaibilliardY.Sanai,ca.1963MadeintoanescapeproblembyBleheretal.(1988)17 SinaiBilliardx00x105x10618 PredictionHorizonDiscontinuityinboundaryconditions(aswellasnon-linearity)cancausedivergenttrajectoriesSimilarinitialconditionsproducesimilartrajectoriesforalimitedtime19 DifferentialGamesModelingconflictinadynamicalsystem(e.g.,pursuit-evasion)Eachplayer(twoormore)hasastate-dependentutilityfunctionthatheseekstomaximizeEachplayerhasasetofcontrolvariablesthatinfluencethestateofthesystemWhatarethebeststrategies?Whatarethepossibleoutcomes?Example:homicidalchauffeurproblem(R.Isaacs,1951)The“pedestrian”isslowbuthighlymaneuverableThe“vehicle”ismuchfasterbutfarlessmaneuverableUnderwhatinitialconditions(ifany)canthepedestrianavoidbeingrunoverindefinitely?Somegames(complexones?)generatestate-spacestructureswithfractalgeometry20 ControlSystemsControllerSystemSensor+–ModelGoalControllerSystemOpenLoopClosedLoop21 Aircraft(N=6,Nc=3,4)andautomobiles(N=3,Nc=2)arenon-holonomicNostablecontrolsettingsarepossible;noteverypathcanbefollowedEverypossiblepathcanbeapproximatedControlTheoryDegreesoffreedom(sixforanaircraft)(x,y,z)=coordinatesofcenterofmass(,,)=yaw,pitch,rollHolonomicityNdegreesoffreedomNccontrollabledegreesoffreedomSystemisHolonomicifNc=NNon-holonomicifNcN22 RequisiteVarietyandStabilityRequisitevariety(Ashby,1958)TocontrolasystemwithNccontrollabledegreesoffreedomthecontrolsystemitselfmusthaveatleastNcdegreesoffreedomGivenrequisitevarietyinthecontrolsystemforaholonomicsystem,stabilityispossibleLyapunovstability:pathsthatstartnearanequilibriumpointxestaynearxeforeverAsymptoticstability:pathsthatstartnearxeconvergetoxeExponentialstability:theconvergenceisasfastaspossible(Lyapunovexponent)23 Internet200124 Scale-FreeNetworkRandom–A.Barabási,etal.(2000)k=degree(numberofconnectionsPowerlaw(=-1.94)PreferentialgrowthandattachmentDiameter(max.distancebetweennodes)vs.fractiondeletedFailure=randomnodedeletedAttack=high-degreenodedeletedE=random,SF=scale-freeWorld-WideWebFailureandAttackTolerance25 FatTails26 CellularAutomataNumber ofliveneighborsAction<2Die2Donothing3Becomealive>3DieGameofLife–J.Conway(1970)27 EmergenceEmergentobjectsbelongtoahigherlevelofrepresentationthanindividualcellsortheirbehaviorrulesLevels(GameofLife):CellsandrulesObjects(blinkers,gliders,blocks,beehives,etc.)Interactionsofobjects(attraction/repulsion,annihilation,etc.)Architecturesofobjects(guns,puffers,rakes,etc.)MultiscaleRepresentation(Y.Bar-Yam):eachlevelofrepresentationhasitsown:Scale:numberofentitiesorcomponentsVariety:numberofpossibleactionsorstatesFundamentalquestionsHowisbehaviorateachleveldetermined?Canconstraintsorbehaviorsathigherlevelsinfluencelowerones?Isthere“downwardcausation”?Canwedesignfordesiredbehaviors?28 Gosper’s“GliderGun”29 DesignandControlSystemscanbecomecomplexeitherbecauseorinspiteofdesignrulesSimplicityisgenerallyagoal,butitcompeteswithothergoals:efficiency,robustness,versatility,etc.Systemsgenerallyevolvetowardgreatercomplexity,notless30 FunctionalDecompositionTraditionalengineeringpracticeHierarchicalstructureIndependentmodulesSystem/subsystemorsystem(family)ofsystems31 Commonality32 Reuse33 BigBallofMud“ABIGBALLOFMUDishaphazardlystructured,sprawling,sloppy,duct-tapeandbailingwire,spaghetticodejungle…Thesesystemsshowunmistakablesignsofunregulatedgrowth,andrepeated,expedientrepair.”“…acomplexsystemmaybeanaccuratereflectionofourimmatureunderstandingofacomplexproblem.Theclassofsystemsthatwecanbuildatallmaybelargerthantheclassofsystemswecanbuildelegantly,atleastatfirst.”–B.FooteandJ.Yoder,inPatternLanguagesofProgramDesign4(2000)34 HighlyOptimizedTolerance(HOT)“Ourfocusisonsystemswhichareoptimized,eitherthroughnaturalselectionorengineeringdesign,toproviderobustperformancedespiteuncertainenvironments.Wesuggestthatpowerlawsinthesesystemsareduetotradeoffsbetweenyield,costofresources,andtolerancetorisks.Thesetradeoffsleadtohighlyoptimizeddesignsthatallowforoccasionallargeevents.”“ThecharacteristicfeaturesofHOTsystemsinclude:(1)highefficiency,performance,androbustnesstodesigned-foruncertainties;(2)hypersensitivitytodesignflawsandunanticipatedperturbations;(3)nongeneric,specialized,structuredconfigurations;and(4)powerlaws.”–J.M.CarlsonandJ.Doyle,PhysicalReview(1999)35 ComplexityandC2Complexsystemsanalysisisnot(yet)arevolutionarynewparadigmWecanusethecomplexitymindsetandtoolboxtore-visitandre-assessC2problemsSpeedofcommandandtheOODAloopComplexendeavorsTheDIME/PMESIIconstructWickedproblemsTheC2ApproachSpaceOptimizationRareeventsEmergenceandcausality36 SpeedofCommand/ControlABControl:“Correctforcrosswinds”ABCommand:“FlyfromAtoBCABCommand:“DiverttoC37 OODALoopvs.ControlLoopObserveChoosegoalOrientSenseerrorDecideFindcorrectionActCorrectTraditionally:commandishuman,controltechnologicalModerncontroltheorydescribeshighlycomplexbehaviorsPotentialforapplicationtocommandproblems38 ComplexEndeavorsComplexendeavorshaveoneormoreofthefollowingcharacteristics:Thenumberanddiversityofparticipantsissuchthat:Therearemultipleinterdependent“chainsofcommand”TheobjectivefunctionsoftheparticipantsconflictwithoneanotherortheircomponentshavesignificantlydifferentweightsTheparticipants’perceptionsofthesituationdifferinimportantwaysTheeffectsspacespansmultipledomainsandthereisAlackofunderstandingofnetworkedcauseandeffectrelationshipsAninabilitytopredicteffectsthatarelikelytoarisefromalternativecoursesofaction–D.AlbertsandR.Hayes,Planning:ComplexEndeavors(2007)InterpretationasdifferentialgamesUtilityfunctionsofcoalitions(Uc=utilityfunctionofthecoalition,Ui=utilityfunctionofmemberi)Tightcoalition:UcisafixedfunctionoftheindividualUiLoosecoalition:UcisafunctionoftheindividualUithatdependsonthestateofthesystem,allowinggain/lossofcommitment,subversion,defection,etc.39 DIME/PMESIIFormalismStatevariables:Political,Military,Economic,Social,Information,InfrastructureControlvariables(interventions):Diplomatic,Information,Military,EconomicQuestions:DoesDIMEhaverequisitevarietytocontrolPMESII?Whathappenswhenthegameistwo-sided?many-sided?40 CompetitionPMESIIPMESIIDIMEDIMERecentstudy(AT&L/N81)indicatesthatavailablemodelsdonotcaptureessentialfeaturesTheprocessbywhichPMESIIstategeneratesDIMEinterventionsTheadversaryresponseandresultingfeedbackloops41 The“InvisibleHand”AdamSmith:marketforcesprovideclosed-loopcontroloftheeconomyModerneconomists:areyoukidding?Noreasontoassume:RequisitevarietyincontrolvariablesStablesolutionsorattractorsinstatespaceApplicationofgametheory:“Rationalactor”assumptionlimitschoicesofutilityfunctionsLimitedabilitytodealwithcoalitionsSimilarissuesinotherPMESIIvariables42 WickedProblemsThereisnodefinitiveformulationofawickedproblemWickedproblemshavenostoppingruleSolutionstowickedproblemsarenottrue-or-false,butgood-or-badThereisnoimmediateandnoultimatetestofasolutiontoawickedproblemEverysolutiontoawickedproblemisa"one-shotoperation";becausethereisnoopportunitytolearnbytrial-and-error,everyattemptcountssignificantlyWickedproblemsdonothaveanenumerable(oranexhaustivelydescribable)setofpotentialsolutions,noristhereawell-describedsetofpermissibleoperationsthatmaybeincorporatedintotheplanEverywickedproblemisessentiallyuniqueEverywickedproblemcanbeconsideredtobeasymptomofanotherproblemTheexistenceofadiscrepancyrepresentingawickedproblemcanbeexplainedinnumerousways.Thechoiceofexplanationdeterminesthenatureoftheproblem'sresolutionTheplannerhasnorighttobewrong–H.RittelandM.Webber,PolicySciences(1973)43 NoEvolutionThereisnodefinitiveformulationofawickedproblemWickedproblemshavenostoppingruleSolutionstowickedproblemsarenottrue-or-false,butgood-or-badThereisnoimmediateandnoultimatetestofasolutiontoawickedproblemEverysolutiontoawickedproblemisa"one-shotoperation";becausethereisnoopportunitytolearnbytrial-and-error,everyattemptcountssignificantlyWickedproblemsdonothaveanenumerable(oranexhaustivelydescribable)setofpotentialsolutions,noristhereawell-describedsetofpermissibleoperationsthatmaybeincorporatedintotheplanEverywickedproblemisessentiallyuniqueEverywickedproblemcanbeconsideredtobeasymptomofanotherproblemTheexistenceofadiscrepancyrepresentingawickedproblemcanbeexplainedinnumerousways.Thechoiceofexplanationdeterminesthenatureoftheproblem'sresolutionTheplannerhasnorighttobewrong44 NoDesignThereisnodefinitiveformulationofawickedproblemWickedproblemshavenostoppingruleSolutionstowickedproblemsarenottrue-or-false,butgood-or-badThereisnoimmediateandnoultimatetestofasolutiontoawickedproblemEverysolutiontoawickedproblemisa"one-shotoperation";becausethereisnoopportunitytolearnbytrial-and-error,everyattemptcountssignificantlyWickedproblemsdonothaveanenumerable(oranexhaustivelydescribable)setofpotentialsolutions,noristhereawell-describedsetofpermissibleoperationsthatmaybeincorporatedintotheplanEverywickedproblemisessentiallyuniqueEverywickedproblemcanbeconsideredtobeasymptomofanotherproblemTheexistenceofadiscrepancyrepresentingawickedproblemcanbeexplainedinnumerousways.Thechoiceofexplanationdeterminesthenatureoftheproblem'sresolutionTheplannerhasnorighttobewrong45 ComplexityThereisnodefinitiveformulationofawickedproblemWickedproblemshavenostoppingruleSolutionstowickedproblemsarenottrue-or-false,butgood-or-badThereisnoimmediateandnoultimatetestofasolutiontoawickedproblemEverysolutiontoawickedproblemisa"one-shotoperation";becausethereisnoopportunitytolearnbytrial-and-error,everyattemptcountssignificantlyWickedproblemsdonothaveanenumerable(oranexhaustivelydescribable)setofpotentialsolutions,noristhereawell-describedsetofpermissibleoperationsthatmaybeincorporatedintotheplanEverywickedproblemisessentiallyuniqueEverywickedproblemcanbeconsideredtobeasymptomofanotherproblemTheexistenceofadiscrepancyrepresentingawickedproblemcanbeexplainedinnumerousways.Thechoiceofexplanationdeterminesthenatureoftheproblem'sresolutionTheplannerhasnorighttobewrong46 Wicked,Complex,orIll-Posed“Inrealitytheproblemsarenotsomuch‘wicked’ascomplex.”–E.SmithandM.Clemente,14thICCRTS(2009)“Wicked”problemsarebestdescribedasdifferentialgamesMultipleparticipantscompetetomaximizetheirindividualutilityfunctionsMostsocialpolicyproblems(whendescribedasgames)probablyarecomplex,butformalanalysisisjuststartinginbiologyandeconomicsTheRittel-Webberdescriptionreflectsamisguidedattemptbythe“planner”todefineasingleutilityfunction(i.e.,createasingle,tightcoalition)“Wickedness”isnotapropertyofthesystembutofhowwehavedefinedtheproblem47 C2ApproachSpaceThreedimensions(D.AlbertsandR.Hayes,2007):PatternsofinteractionDistributionofinformationDistributionofdecisionrightsIncidentresponsemodel(M.Bell,14thICCRTS)Assumptions(decentralizedC2)Decisionrights:widelydistributedInformation:widelydistributedInteraction:highlylimitedResults(agent-basedsimulation)Effective“edge”organizationsdonothavetobenearthehighendofallthreedimensionsSelf-organizationcanoccurwithverysimplebehaviorrulesSelf-organizationcanbecounter-productiveIterativerefinementoftherulesetneededtoexcludebadcases48 OptimizationOptimizationoflarge,non-linearsystemsisalmostalwayscomputationallyhard(exponentialtime)HeuristicapproacheswillsometimesgivegoodapproximatesolutionsRobustnessisanissueDemonstratingstability(tosmallperturbations)maybecomputationallyhardComplexsystemsoftenhave“brittle”optimaTheprobabilityoflargeperturbationsmaybegreatlyincreasedbynon-lineardynamicsExtremeoptimization(HOT)altersthedistributionofpropertiesorbehaviors(fattails)49 RareEventsNotasrareaswemightexpectScale-free(self-similar)structuresyieldpower-lawdistributionsProbabilitiescanbemanyordersofmagnitudegreaterthanpredictedbythenormaldistributionDistributionsmaynotbestable(linearcombinationsofindependenteventsdonothavethesamedistributionastheevents)JointprobabilitiesmaynotbeproductsofindividualeventprobabilitiesIncreasedprobabilityofrareeventsequences(cascadingfailures)50 CausalityComplexityresearchdealswithcausal(deterministic)systemsOppositeofcausalisrandom(notcomplex)Complexitycan:MakeitdifficulttodiscovercausalrelationshipsLimitprediction51 UnintendedConsequencesWhenwesaythatanoutcome(oraside-effect)is“unintended,”dowemerelymeanthatitisunanticipated?Ifwecouldanticipate(predict)suchanoutcomeoreffect,woulditnecessarilybecomeintended?Doesethicalorlegalresponsibilityfollow?Canblamebeassignedwithoutevidenceofpredictability?52 ConclusionsComplexityresearchhasdeeprootsinseveraltraditionalscientificdisciplinesIthasadvancedthestate-of-theartinthesefieldsandpromotedcross-pollinationamongthemIthasbeenamajorenablerinthedevelopmentofnewsub-disciplines(e.g.,socialnetworkanalysis,non-lineardynamics)Ithasnot(yet)yieldedarevolutionarynewparadigmforscientificresearchItofferssignificantpotentialbenefitsinC2researchThemindsetandtoolboxcanbeexploitedtoadvanceORandC2researchmethodologyDiscoveriesinotherdisciplinescanbetranslatedintousefulinsightsorpartialsolutionstoC2problemsItdoesnotinvalidateanypreviousworkorchallengethegoalsofC2research53 QuestionsorComments?54

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《implications of complexity research for command and cont:复杂性研究的指挥和控制的影响》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库

ImplicationsofComplexityResearchforCommandandControlM.I.BellFACT,29July2009 DisclaimersMostoftheseideasarenotoriginal;IwillnotacknowledgemysourcesIamresponsibleforanyerrors;feelfreetopointthemoutComplexitycanbecomplicated,evencomplexIgetnothingfromtheadmissioncharge;norefundswillbegiven2 BewareofHumptyDumpty“WhenIuseaword,”HumptyDumptysaid,inratherascornfultone,“itmeansjustwhatIchooseittomean–neithermorenorless.”“Thequestionis,”saidAlice,“whetheryoucanmakewordsmeansomanydifferentthings.”“Thequestionis,”saidHumptyDumpty,“whichistobemaster–that'sall.”CareisrequiredwhenusingeverydaywordsforspecializedpurposesThecommunityofinterestneedsclear,commondefinitionThegeneralpublicneedswarningstoavoidconfusion3 OutlineMotivationSometrivialquestions(notanswers)IntuitivecomplexityQuantifyingcomplexityFormalcomplexity:dynamicandarchitecturalDesignandcontrolofcomplexsystemsComplexityandC24 MotivationComplexityasabuzzword“Sixdegreesofseparation,”“butterflyeffect,”etc.haveenteredpopularcultureDozensofuniversitygroups,programs,seminars,andprojectsPioneers(e.g.,SantaFeInstitute)consideringmovingonComplexityasametaphor98of144papersinthe14thICCRTScontaintheword“complexity”ComplexityasamindsetAwarenessofchaos,“fattails,”“tippingpoints,”self-organizationComplexityasatoolboxFractalgeometry,nonlineardynamics,agent-basedsimulationComplexityasaparadigm“acceptedexamplesofactualscientificpractice…[that]providemodelsfromwhichspringparticularcoherenttraditionsofscientificresearch”–T.S.Kuhn,TheStructureofScientificRevolutions,19625 WhatisComplexity?Manyentities,manyinteractions,collectivebehaviorQualityorquantity?Definitionorcharacteristics?Emergence,self-organization,self-similarity,chaos,etc.Computationalcomplexity(ofaproblem)Resources(typicallytime)requiredtoobtainasolutionAlgorithmicinformationcontent(ofastring)LengthoftheshortestprogramthatwilloutputthestringStructuralcomplexitySelf-similarity,fractalgeometryDynamiccomplexityChaos,sensitivitytoinitialconditions,phasetransformations6 WhyareThingsComplex?ByselectionorbydesignSelectionNaturalorartificial(oftennot“survivalofthefittest”but“thesurvivorsarethefittest”)Preferentialgrowth(“therichgetricher”)DesignNonlinearityFeedbackcontrolOptimization7 WhyDoWeCare?Emergentbehavior(self-organization)Requisitevariety(control)Causality(prediction)Stability/instability(cascadingfailure)Unintendedconsequences8 IntuitiveComplexityDisorganizedcomplexity“aprobleminwhichthenumberofvariablesisverylarge,andoneinwhicheachofthemanyvariableshasabehaviorwhichisindividuallyerratic,orperhapstotallyunknown.However,…thesystemasawholepossessescertainorderlyandanalyzableaverageproperties”Organizedcomplexity“problemswhichinvolvedealingsimultaneouslywithasizablenumberoffactorswhichareinterrelatedintoanorganicwhole”–W.Weaver,AmericanScientist(1948)9 Complexityvs.OrderPHYSICSPressureTemperaturePhaseStatisticalAnalysisOrganized/DifferentiatedEntitiesSimpleEntitiesSystemsAnalysisECONOMICSGDPGrowthrate10 ‘‘Longrangedetailedweatherpredictionisthereforeimpossible,…theaccuracyofthispredictionissubjecttotheconditionthattheflightofagrasshopperinMontanamayturnastormasidefromPhiladelphiatoNewYork!’’–W.S.Franklin(1898)ButterflyEffect11 ArgumentforQuantification“Whenyoucanmeasurewhatyouarespeakingabout,andexpressitinnumbers,youknowsomethingaboutit;butwhenyoucannotmeasureit,whenyoucannotexpressitinnumbers,yourknowledgeisofameagerandunsatisfactorykind…”–WilliamThompson(LordKelvin),1824-1907Ifwecanquantifycomplexity,wecanDeterminewhetheronesystemismoreorlesscomplexthananotherDeterminewhetheracontrol(orC2)systemisoftheappropriatecomplexityforagivensituationTakeappropriatestepstocontrolcomplexity;e.g.,ReducethecomplexityofourenvironmentIncreasethecomplexityofanadversary’senvironment12 AlgorithmicInformationContentLengthoftheshortestpossibledescriptionofasystem(madeformalusingTuringmachineconcept)Pros:ConsistentwiththeideathatagoodtheorysimplifiesthedescriptionofphenomenaCons:Complexitymayseemtobeapropertyofourunderstandingofasystem,notofthesystemitselfThelengthofdescriptionmaydependonthevocabularyavailableRelativecomplexityoftwosystemsdependsonthedetailsoftheTuringmachineusedItisimpossibletoshowthatadescriptionistheshortestpossibleRandomsystemsaremaximallycomplex(counter-intuitive)13 ComputationalComplexityThenumberofoperations(typicallymultiplications)neededtosolveaproblemPros:Acomplexproblemtakeslonger(ormoreresources)tosolvethanasimpleoneThedifficultyofacomplexproblemgrowsrapidlywithitssizen:Problemsthatcanbesolvedintimeproportionaltonkare“polynomialtime”problemsProblemsthatcanbesolvedintimeproportionaltoenorn!are“exponentialtime”problemsCons:Thereisnoalgorithmfordetermininghowhardaproblemis!14 FormalComplexityDynamic(process)CorrespondsroughlytocomputationalcomplexityOriginatedinnon-lineardynamicsArchitectural(structural)CorrespondsroughlytoalgorithmicinformationcontentOriginatedincommunicationtheory15 MandelbrotSetAcomplexnumbercisamemberofthesetifstartingwithz0=0,zn+1=zn2+cisboundedB.Mandelbrot,ca.197816 EscapeProblemsMandelbrotsetAcomplexnumbercisamemberofthesetifstartingwithz0=0,zn+1=zn2+cisboundedInotherwords,cisnotamemberifzn+1escapesSinaibilliardY.Sanai,ca.1963MadeintoanescapeproblembyBleheretal.(1988)17 SinaiBilliardx00x105x10618 PredictionHorizonDiscontinuityinboundaryconditions(aswellasnon-linearity)cancausedivergenttrajectoriesSimilarinitialconditionsproducesimilartrajectoriesforalimitedtime19 DifferentialGamesModelingconflictinadynamicalsystem(e.g.,pursuit-evasion)Eachplayer(twoormore)hasastate-dependentutilityfunctionthatheseekstomaximizeEachplayerhasasetofcontrolvariablesthatinfluencethestateofthesystemWhatarethebeststrategies?Whatarethepossibleoutcomes?Example:homicidalchauffeurproblem(R.Isaacs,1951)The“pedestrian”isslowbuthighlymaneuverableThe“vehicle”ismuchfasterbutfarlessmaneuverableUnderwhatinitialconditions(ifany)canthepedestrianavoidbeingrunoverindefinitely?Somegames(complexones?)generatestate-spacestructureswithfractalgeometry20 ControlSystemsControllerSystemSensor+–ModelGoalControllerSystemOpenLoopClosedLoop21 Aircraft(N=6,Nc=3,4)andautomobiles(N=3,Nc=2)arenon-holonomicNostablecontrolsettingsarepossible;noteverypathcanbefollowedEverypossiblepathcanbeapproximatedControlTheoryDegreesoffreedom(sixforanaircraft)(x,y,z)=coordinatesofcenterofmass(,,)=yaw,pitch,rollHolonomicityNdegreesoffreedomNccontrollabledegreesoffreedomSystemisHolonomicifNc=NNon-holonomicifNcN22 RequisiteVarietyandStabilityRequisitevariety(Ashby,1958)TocontrolasystemwithNccontrollabledegreesoffreedomthecontrolsystemitselfmusthaveatleastNcdegreesoffreedomGivenrequisitevarietyinthecontrolsystemforaholonomicsystem,stabilityispossibleLyapunovstability:pathsthatstartnearanequilibriumpointxestaynearxeforeverAsymptoticstability:pathsthatstartnearxeconvergetoxeExponentialstability:theconvergenceisasfastaspossible(Lyapunovexponent)23 Internet200124 Scale-FreeNetworkRandom–A.Barabási,etal.(2000)k=degree(numberofconnectionsPowerlaw(=-1.94)PreferentialgrowthandattachmentDiameter(max.distancebetweennodes)vs.fractiondeletedFailure=randomnodedeletedAttack=high-degreenodedeletedE=random,SF=scale-freeWorld-WideWebFailureandAttackTolerance25 FatTails26 CellularAutomataNumber ofliveneighborsAction<2Die2Donothing3Becomealive>3DieGameofLife–J.Conway(1970)27 EmergenceEmergentobjectsbelongtoahigherlevelofrepresentationthanindividualcellsortheirbehaviorrulesLevels(GameofLife):CellsandrulesObjects(blinkers,gliders,blocks,beehives,etc.)Interactionsofobjects(attraction/repulsion,annihilation,etc.)Architecturesofobjects(guns,puffers,rakes,etc.)MultiscaleRepresentation(Y.Bar-Yam):eachlevelofrepresentationhasitsown:Scale:numberofentitiesorcomponentsVariety:numberofpossibleactionsorstatesFundamentalquestionsHowisbehaviorateachleveldetermined?Canconstraintsorbehaviorsathigherlevelsinfluencelowerones?Isthere“downwardcausation”?Canwedesignfordesiredbehaviors?28 Gosper’s“GliderGun”29 DesignandControlSystemscanbecomecomplexeitherbecauseorinspiteofdesignrulesSimplicityisgenerallyagoal,butitcompeteswithothergoals:efficiency,robustness,versatility,etc.Systemsgenerallyevolvetowardgreatercomplexity,notless30 FunctionalDecompositionTraditionalengineeringpracticeHierarchicalstructureIndependentmodulesSystem/subsystemorsystem(family)ofsystems31 Commonality32 Reuse33 BigBallofMud“ABIGBALLOFMUDishaphazardlystructured,sprawling,sloppy,duct-tapeandbailingwire,spaghetticodejungle…Thesesystemsshowunmistakablesignsofunregulatedgrowth,andrepeated,expedientrepair.”“…acomplexsystemmaybeanaccuratereflectionofourimmatureunderstandingofacomplexproblem.Theclassofsystemsthatwecanbuildatallmaybelargerthantheclassofsystemswecanbuildelegantly,atleastatfirst.”–B.FooteandJ.Yoder,inPatternLanguagesofProgramDesign4(2000)34 HighlyOptimizedTolerance(HOT)“Ourfocusisonsystemswhichareoptimized,eitherthroughnaturalselectionorengineeringdesign,toproviderobustperformancedespiteuncertainenvironments.Wesuggestthatpowerlawsinthesesystemsareduetotradeoffsbetweenyield,costofresources,andtolerancetorisks.Thesetradeoffsleadtohighlyoptimizeddesignsthatallowforoccasionallargeevents.”“ThecharacteristicfeaturesofHOTsystemsinclude:(1)highefficiency,performance,androbustnesstodesigned-foruncertainties;(2)hypersensitivitytodesignflawsandunanticipatedperturbations;(3)nongeneric,specialized,structuredconfigurations;and(4)powerlaws.”–J.M.CarlsonandJ.Doyle,PhysicalReview(1999)35 ComplexityandC2Complexsystemsanalysisisnot(yet)arevolutionarynewparadigmWecanusethecomplexitymindsetandtoolboxtore-visitandre-assessC2problemsSpeedofcommandandtheOODAloopComplexendeavorsTheDIME/PMESIIconstructWickedproblemsTheC2ApproachSpaceOptimizationRareeventsEmergenceandcausality36 SpeedofCommand/ControlABControl:“Correctforcrosswinds”ABCommand:“FlyfromAtoBCABCommand:“DiverttoC37 OODALoopvs.ControlLoopObserveChoosegoalOrientSenseerrorDecideFindcorrectionActCorrectTraditionally:commandishuman,controltechnologicalModerncontroltheorydescribeshighlycomplexbehaviorsPotentialforapplicationtocommandproblems38 ComplexEndeavorsComplexendeavorshaveoneormoreofthefollowingcharacteristics:Thenumberanddiversityofparticipantsissuchthat:Therearemultipleinterdependent“chainsofcommand”TheobjectivefunctionsoftheparticipantsconflictwithoneanotherortheircomponentshavesignificantlydifferentweightsTheparticipants’perceptionsofthesituationdifferinimportantwaysTheeffectsspacespansmultipledomainsandthereisAlackofunderstandingofnetworkedcauseandeffectrelationshipsAninabilitytopredicteffectsthatarelikelytoarisefromalternativecoursesofaction–D.AlbertsandR.Hayes,Planning:ComplexEndeavors(2007)InterpretationasdifferentialgamesUtilityfunctionsofcoalitions(Uc=utilityfunctionofthecoalition,Ui=utilityfunctionofmemberi)Tightcoalition:UcisafixedfunctionoftheindividualUiLoosecoalition:UcisafunctionoftheindividualUithatdependsonthestateofthesystem,allowinggain/lossofcommitment,subversion,defection,etc.39 DIME/PMESIIFormalismStatevariables:Political,Military,Economic,Social,Information,InfrastructureControlvariables(interventions):Diplomatic,Information,Military,EconomicQuestions:DoesDIMEhaverequisitevarietytocontrolPMESII?Whathappenswhenthegameistwo-sided?many-sided?40 CompetitionPMESIIPMESIIDIMEDIMERecentstudy(AT&L/N81)indicatesthatavailablemodelsdonotcaptureessentialfeaturesTheprocessbywhichPMESIIstategeneratesDIMEinterventionsTheadversaryresponseandresultingfeedbackloops41 The“InvisibleHand”AdamSmith:marketforcesprovideclosed-loopcontroloftheeconomyModerneconomists:areyoukidding?Noreasontoassume:RequisitevarietyincontrolvariablesStablesolutionsorattractorsinstatespaceApplicationofgametheory:“Rationalactor”assumptionlimitschoicesofutilityfunctionsLimitedabilitytodealwithcoalitionsSimilarissuesinotherPMESIIvariables42 WickedProblemsThereisnodefinitiveformulationofawickedproblemWickedproblemshavenostoppingruleSolutionstowickedproblemsarenottrue-or-false,butgood-or-badThereisnoimmediateandnoultimatetestofasolutiontoawickedproblemEverysolutiontoawickedproblemisa"one-shotoperation";becausethereisnoopportunitytolearnbytrial-and-error,everyattemptcountssignificantlyWickedproblemsdonothaveanenumerable(oranexhaustivelydescribable)setofpotentialsolutions,noristhereawell-describedsetofpermissibleoperationsthatmaybeincorporatedintotheplanEverywickedproblemisessentiallyuniqueEverywickedproblemcanbeconsideredtobeasymptomofanotherproblemTheexistenceofadiscrepancyrepresentingawickedproblemcanbeexplainedinnumerousways.Thechoiceofexplanationdeterminesthenatureoftheproblem'sresolutionTheplannerhasnorighttobewrong–H.RittelandM.Webber,PolicySciences(1973)43 NoEvolutionThereisnodefinitiveformulationofawickedproblemWickedproblemshavenostoppingruleSolutionstowickedproblemsarenottrue-or-false,butgood-or-badThereisnoimmediateandnoultimatetestofasolutiontoawickedproblemEverysolutiontoawickedproblemisa"one-shotoperation";becausethereisnoopportunitytolearnbytrial-and-error,everyattemptcountssignificantlyWickedproblemsdonothaveanenumerable(oranexhaustivelydescribable)setofpotentialsolutions,noristhereawell-describedsetofpermissibleoperationsthatmaybeincorporatedintotheplanEverywickedproblemisessentiallyuniqueEverywickedproblemcanbeconsideredtobeasymptomofanotherproblemTheexistenceofadiscrepancyrepresentingawickedproblemcanbeexplainedinnumerousways.Thechoiceofexplanationdeterminesthenatureoftheproblem'sresolutionTheplannerhasnorighttobewrong44 NoDesignThereisnodefinitiveformulationofawickedproblemWickedproblemshavenostoppingruleSolutionstowickedproblemsarenottrue-or-false,butgood-or-badThereisnoimmediateandnoultimatetestofasolutiontoawickedproblemEverysolutiontoawickedproblemisa"one-shotoperation";becausethereisnoopportunitytolearnbytrial-and-error,everyattemptcountssignificantlyWickedproblemsdonothaveanenumerable(oranexhaustivelydescribable)setofpotentialsolutions,noristhereawell-describedsetofpermissibleoperationsthatmaybeincorporatedintotheplanEverywickedproblemisessentiallyuniqueEverywickedproblemcanbeconsideredtobeasymptomofanotherproblemTheexistenceofadiscrepancyrepresentingawickedproblemcanbeexplainedinnumerousways.Thechoiceofexplanationdeterminesthenatureoftheproblem'sresolutionTheplannerhasnorighttobewrong45 ComplexityThereisnodefinitiveformulationofawickedproblemWickedproblemshavenostoppingruleSolutionstowickedproblemsarenottrue-or-false,butgood-or-badThereisnoimmediateandnoultimatetestofasolutiontoawickedproblemEverysolutiontoawickedproblemisa"one-shotoperation";becausethereisnoopportunitytolearnbytrial-and-error,everyattemptcountssignificantlyWickedproblemsdonothaveanenumerable(oranexhaustivelydescribable)setofpotentialsolutions,noristhereawell-describedsetofpermissibleoperationsthatmaybeincorporatedintotheplanEverywickedproblemisessentiallyuniqueEverywickedproblemcanbeconsideredtobeasymptomofanotherproblemTheexistenceofadiscrepancyrepresentingawickedproblemcanbeexplainedinnumerousways.Thechoiceofexplanationdeterminesthenatureoftheproblem'sresolutionTheplannerhasnorighttobewrong46 Wicked,Complex,orIll-Posed“Inrealitytheproblemsarenotsomuch‘wicked’ascomplex.”–E.SmithandM.Clemente,14thICCRTS(2009)“Wicked”problemsarebestdescribedasdifferentialgamesMultipleparticipantscompetetomaximizetheirindividualutilityfunctionsMostsocialpolicyproblems(whendescribedasgames)probablyarecomplex,butformalanalysisisjuststartinginbiologyandeconomicsTheRittel-Webberdescriptionreflectsamisguidedattemptbythe“planner”todefineasingleutilityfunction(i.e.,createasingle,tightcoalition)“Wickedness”isnotapropertyofthesystembutofhowwehavedefinedtheproblem47 C2ApproachSpaceThreedimensions(D.AlbertsandR.Hayes,2007):PatternsofinteractionDistributionofinformationDistributionofdecisionrightsIncidentresponsemodel(M.Bell,14thICCRTS)Assumptions(decentralizedC2)Decisionrights:widelydistributedInformation:widelydistributedInteraction:highlylimitedResults(agent-basedsimulation)Effective“edge”organizationsdonothavetobenearthehighendofallthreedimensionsSelf-organizationcanoccurwithverysimplebehaviorrulesSelf-organizationcanbecounter-productiveIterativerefinementoftherulesetneededtoexcludebadcases48 OptimizationOptimizationoflarge,non-linearsystemsisalmostalwayscomputationallyhard(exponentialtime)HeuristicapproacheswillsometimesgivegoodapproximatesolutionsRobustnessisanissueDemonstratingstability(tosmallperturbations)maybecomputationallyhardComplexsystemsoftenhave“brittle”optimaTheprobabilityoflargeperturbationsmaybegreatlyincreasedbynon-lineardynamicsExtremeoptimization(HOT)altersthedistributionofpropertiesorbehaviors(fattails)49 RareEventsNotasrareaswemightexpectScale-free(self-similar)structuresyieldpower-lawdistributionsProbabilitiescanbemanyordersofmagnitudegreaterthanpredictedbythenormaldistributionDistributionsmaynotbestable(linearcombinationsofindependenteventsdonothavethesamedistributionastheevents)JointprobabilitiesmaynotbeproductsofindividualeventprobabilitiesIncreasedprobabilityofrareeventsequences(cascadingfailures)50 CausalityComplexityresearchdealswithcausal(deterministic)systemsOppositeofcausalisrandom(notcomplex)Complexitycan:MakeitdifficulttodiscovercausalrelationshipsLimitprediction51 UnintendedConsequencesWhenwesaythatanoutcome(oraside-effect)is“unintended,”dowemerelymeanthatitisunanticipated?Ifwecouldanticipate(predict)suchanoutcomeoreffect,woulditnecessarilybecomeintended?Doesethicalorlegalresponsibilityfollow?Canblamebeassignedwithoutevidenceofpredictability?52 ConclusionsComplexityresearchhasdeeprootsinseveraltraditionalscientificdisciplinesIthasadvancedthestate-of-theartinthesefieldsandpromotedcross-pollinationamongthemIthasbeenamajorenablerinthedevelopmentofnewsub-disciplines(e.g.,socialnetworkanalysis,non-lineardynamics)Ithasnot(yet)yieldedarevolutionarynewparadigmforscientificresearchItofferssignificantpotentialbenefitsinC2researchThemindsetandtoolboxcanbeexploitedtoadvanceORandC2researchmethodologyDiscoveriesinotherdisciplinescanbetranslatedintousefulinsightsorpartialsolutionstoC2problemsItdoesnotinvalidateanypreviousworkorchallengethegoalsofC2research53 QuestionsorComments?54

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