6d - Sandberg - Statistics of the lifespan of complex ...

StatisticsofthelifespanofcomplexsystemsOr:istheresenescence?

AndersSandbergFutureofHumanityInstitute

OxfordMartinSchoolUniversityofOxford

RobertMcCall,ThePrologueandthePromise(1983)

Myinterest:howlong-termcanprojectsbe?

• Arethereany“physical”lawsthatpreventsocietiesfromexistingindefinitely?

Thelifecycleofcivilizations

ThomasCole(1834)TheSavageState

Thelifecycleofcivilizations

ThomasCole(1834)TheArcadianorPastoralState

Thelifecycleofcivilizations

ThomasCole(1836)TheConsummationofEmpire

Thelifecycleofcivilizations

ThomasCole(1836)Destruction

Thelifecycleofcivilizations

ThomasCole(1836)Desolation

Wecareaboutcivilization-likecomplexsocialorganisations

• Theycanallowthegrowthofhumancapitalandwellbeing• Economiesofscale• Long-termprojects• Existentialriskreduction?

• Theirfallinducessignificantlossesofwellbeing,knowledge,populationandmaynowinduceexistentialrisks.

PieterBruegeltheElder:TheTowerofBabel(c.1563)

Macrohistorical theoriesofcivilizationlongevity• Cyclictheories(ibnKhaldun,Vico,Turchin)• Decadence(Gibbons)• Organicageing(Mommsen,Spengler)• Entropy(Adams,Georgescu-Roegen)• Spiritualdecline/internalpowerfailure(Toynbee)• Unsustainablecomplexity(Tainter)• Risingenergycosts(Homer-Dixon,Rifkin,Garrett)• Environmentaldegradation(Diamond)• Outsideinvasion• Disasters,environmentalshifts(Diamond)

Increasingriskovertime

Istheregrowingrisk?

• Let’stestwithhistoricaldata!• Nullmodel:constantrisk.

• Survivalcurve:exponentialdeclineovertime.

• Weibulldistributionfit:riskgrowingas𝑡"#$ overtime.

• PDF𝑓 𝑡; 𝑘, 𝜆 = "+

,+

"#$𝑒#

./

0

• Survivalcurve:morerectangular(𝑘 >1,“ageing”)orsteeperearlydecline(𝑘 < 1,“childhoodmortality”)

• (Needtoconsidercensoringissues)

Empires

• Civilizationsarebadlydefined(andprobablytoofewtobestatisticallysignificant).Whatwecareforislargetransgenerationalsocialorganisations

• Solution:useempiresandstatesinstead

ThomasCole:TheArchitect’sDream(1840)

Taagepera empiredata

• ReinTaagepera:• Empire:“anyrelativelylargesovereignpoliticalentitywhosecomponentsarenotsovereign”.

• 5,000yearsofempires.

• SamuelArbesman(2011):exponentialsurvivalcurvewithhalf-life220years.

Taagepera empiredata

• Fromstarttofinish:• 𝜆 = 348.3815and𝑘 = 0.9205with95%confidenceinterval[0.7869,1.0768].• Hence,cannotrejectnullhypothesisofnoageing!

• From“adulthood”(80%ofmaxsize)tofinaldate:• 𝜆 = 188.1137 yearsand𝑘 = 1.0217.Noageing!

• Notrendovertime(!)

Otherempiresets

• Wikipedia'slistofempires:𝜆 = 270.9173 yearsand𝑘 =0.9986with95%CI[0.8951,1.1141].Noageing.

• EstimatesbyLarryFreemanonhisblogofthedurationsofancientcivilizations/empires:𝜆 = 381.8091yearsand𝑘 = 1.2500witha95%CI[1.0294,1.5177].Mildageing,nearlynonsignificant.

StatesEurope1000-1850

• DatacourtesyofSchönholzerandWeese,basedonBairoch.• 𝜆 = 136.6277 yearsand𝑘 = 0.8604with95%CI[0.7950,0.9312]:abitofchildhoodmortality!

Worldsystems

• Worldsystemstheory/perspective(Wallerstein,Chase-Dunn)• 9pastcivilizations/worldsystemslistedbyWilkinson.• 𝜆 = 1080.7years(theypersistfarlongerthantheirindividualcomponentempires)and𝑘 = 0.8083,CI[0.4611,1.4169].• Noclearageing,butlittledata.

Humanbigsocialorganisations

• Atleastinthisdata,noclearsignofsenescence:riskisconstantovertime.

• Caveat:thishasbeenlifespans ratherthantimetocollapse.

• Maybecollapseshavedifferentdistribution.

• ButIwouldneedadefinitionofwhichcaseisacollapsetotest.

Complexadaptivesystems

• States,societies,civilizationsareallCAS.

• Backgroundassumption:maybetherearejointrulesforlargeclassesofCAS.• (Backgroundworry:maybeeverythingisjustindividualcasesbecauseof“wild”properties.)

• WhatkindsofCASshowlimitedlifespans?

Firms

• Exponentialsurvivalcurve• Independentofbusinesssector• Sizeatbirthhaspositivecorrelationlongevity

• Liabilityofnewnessandadolescence• 𝜆 ≈ 10 yearsforcurrentcorporations,𝜆 ≈ 170 yearsforextremetail

• Liabilitiesatbankruptcypower-laws,butlongevityexponential(Fujiwara2004)

• Salesandcostscloselybalanced?(West2017)

Daepp,M.I.,Hamilton,M.J.,West,G.B.,&Bettencourt,L.M.(2015).Themortalityofcompanies.JournalofTheRoyalSocietyInterface,12(106),20150120.

Species

• VanValen’s lawofconstantextinction• Appearstrueinmanybutnotallcases• Complicationsduetofossilrecord,clades• ExplainedbyoneofthevariantRedQueenHypotheses?

• Žliobaitė,Fortelius&Stenseth:extinctionduetoabioticfactors,bioticcompetitionforspatialspread.

Pearson,P.N.(1995).Investigatingage-dependencyofspeciesextinctionratesusingdynamicsurvivorshipanalysis.HistoricalBiology,10(2),119-136.

Jaeger,J.J.(1994).TheevolutionofbiodiversityamongtheSouthwestEuropeanNeogenerodent(Mammalia,Rodentia)communities:patternandprocessofdiversificationandextinction.Palaeogeography,Palaeoclimatology,Palaeoecology,111(3-4),305-336.

Unclearcases

• Institutions?• Multi-centuryuniversities.• Multi-millenniareligiousorders.• Toolittledataforthelong-livedones.

• Cities?• Jericho9,000BC,fortificationsfrom6,800BC.• GeoffreyWest:renewingeconomiesofscale?

Biologicalageing

• Senecense commoninmulticellularorganisms.• Butexceptionsinsomespecies:Perennialangiosperms,Blanding'sturtle,Olm,easternboxturtle,redseaurchin,rougheye rockfish,oceanquahogclam,bristleconepine...

Software

• Japanesecorporatesystems𝜆 ≈ 11.4 years,𝑘 ≈ 1.7• MeirLehman'slawsofsoftwareevolution:unlessworkhardtocounterit,maintainabilitywillgodownduetogrowingentropy/complexity.• “Lawofcontinuingchange.Asystemthatisusedundergoescontinuingchangeuntilitisjudgedmorecosteffectivetofreezeandrecreateit.“

• “Lawofincreasingentropy.Theentropyofasystem(itsunstructuredness)increaseswithtime,unlessspecificworkisexecutedtomaintainorreduceit.“

Belady,L.A.,&Lehman,M.M.(1976).Amodeloflargeprogramdevelopment.IBMSystemsjournal,15(3),225-252.

CASageing

• Causes:• Evolutioncanproduceageingbecauseofgeneticdrift

• Growthandunmitigatedcomplexity

• Notatalluniversal:manynon-ageingCAS• Competitiondoesnotcauseageing

• Butwhyshouldlack ofageingbecommon,either?

Asimplemodelofconstantrisk• Randomchallengeshappensatrate𝜆 withseverityX ∼ 𝑓 𝑥 .• Xhascomplementarycumulativedistributionfunction𝐹D 𝑥 = Pr[𝑋 > 𝑥].

• Systemhasresistancelevel𝜃, willsurviveif𝑋 < 𝜃.• Systemsurvivesageometricallydistributednumberofchallengeswithparameter𝐹D 𝜃 .

• Expectedtimeofsurvival:𝜏 = $+LD M

.

• Markovinequality𝐹D 𝑥 ≤ 𝐸[𝑋]/𝑥 givesthebound𝜏 ≥ M+R S

if𝐸[𝑋]exists.

• One-sidedChebyshevinequality𝐹D 𝑥 − 𝐸 𝑋 ≤ UV

UVWXVgivesthe

bound𝜏 ≥ $

+1 + MWR S V

UV∝ 𝜃[ ifvariance𝜎[ exists.

• If𝑓 𝑥 isheavy-tailedallbetsareoff.Weakdependenceon𝜃!

Heavytaildistributedrisksarecommon

• Naturaldisasterfatalities(earthquakes,volcanos,floods,tsunamis…)• Richardsonlawofwarfatalities.• Pandemicoutbreaksizes?• Ifcombiningseveral,mostextremetaildominates.

• ForextremeParetodistribution,survivaltimeindependent of𝜃

102 104 106 10810-3

10-2

10-1

100

Pr(X

³ x

)

x

War dead

100 101 102 103 104 10510-3

10-2

10-1

100

Pr(X

³ x

)

x

Flood dead

Synthesis:collapseascombined badluck

• Thedisastersaremixturesofveryextremeeventsorcombinationsoffactors.

• Hardtoavoid(unprecedentedorrareconfluences,“blackswans”)

• Competitivepressures(cost,alternativecosts,competition)leadtofinite𝜃.Butevenlarge𝜃 insufficientagainsttailrisks.

Centralsystemidea• Wilkinson:a“centralsystem”ofmergingpolitical-militarynetworkshasgrownbymergersandexpansionover7,500years

• Shklovskii &Sagan:“ThepresenttechnicalcivilizationoftheplanetEarthcanbetracedfromMesopotamiatoSoutheasternEurope,toWesternandCentralEurope,andthentoEasternEuropeandNorthAmerica.”

Whatdoesthistellusaboutourfragility?

• Maybelessthanwewouldwish:wearethefirstglobal,high-techcivilization.Wehavegoodreasonstobeconcerned.

• Butthereisapparentlynounavoidablelawforcingdecline onus.

• TheCentralSystemhasbeenaroundfor7,500years.Wehaverebuilteverhigher.Buthavingbackupssoundslikeagoodidea. RobertMcCall,ThePrologueandthePromise(1983)