Tools for Thought

Citation preview

PRATT aC

HURT

PALADIN

C. H.W.addington.

ToolsforThought

Paladin

GranadaPublishing Limited Publishedin 1977byPaladin Frogmore,St Albans,HertsAL22NF FirstpublishedbyJonathanCapeLtd 1977 Copyright © TheEstateofthelateC. H. Waddington,

andYolanda Sonnabend

Filmsetin ‘Monophoto’ Ehrhardt andprintedin GreatBritainby RichardClay(TheChaucerPress)Ltd Bungay,Suffolk Thisbookis soldsubjectto theconditionthatit shallnot,bywayoftradeor otherwise, belent, re-sold,hiredoutor otherwise circulated withoutthepublisher’s priorconsentin any formofbindingor coverotherthanthatin whichit is publishedandwithouta similar

condition including thiscondition beingimposed onthesubsequent purchaser. Thisbookis publishedat a netpriceandis suppliedsubjectto thePublishers Association StandardConditions ofSaleregistered underthe Restrictive TradePracticesAct,1956.

ProfessorConradHalWaddington, M.A.,Sc.D.,Hon.D.Sc.,wasborn

on8November 1905. HewasBuchanan Professor ofAnimal Genetics at

theUniversity ofEdinburghsince1947,theHonoraryDirectorofthe Agricultural ResearchCouncil’s UnitofAnimalGeneticsandthe MedicalResearchCouncil’s ResearchGrouponEpigenetics; andthe PresidentoftheInternational UnionofBiological Sciences. Hismany| publications include/ntroduction toModernGenetics (1939),Organisers andGenes(1940),TheScientific Attitude(1941),Science andEthics(Ed.) (1942),Epigenetics ofBirds(1952),Principles ofEmbryology (1956),The StrategyofGenes(1957),TheEthicalAnimal(1960),TheNatureofLife (1961)and,NewPatternsinGenetics andDevelopment, aswellasmany articlesinscientific journals.In 1947hebecamea FellowoftheRoyal Societyandin 1958hewasawardeda C.B.E.

Contents

X1

Introduction

1 Philosophies 15 A NaturalPhilosophy 17] ThingsandProcesses B MoralPhilosophy 25 Values;Thinkingand Feeling;Christianityand, Environment

2 Complexity

A TheNatureofComplexity Relations,InstructionsandtheMind B Complexity of Information in theModernWorld

30 30

32

3 ComplexShapes A Symmetry andOrderedShapes B_ Shapes,neitherSymmetrical norOrdered 4 TheStructureofComplexSystems A Hierarchies B OtherTypesofOrder 5 Processes in ComplexSystems A OpenandClosedSystems B Growth ExponentialGrowth; CompoundInterest and Discountingthe Future;Accelerated Exponential Growth;Limitsto Growth;Differential Growth

64 64 65

80 6 Feed-backin Systems 80 A Sequences PositiveFeed-back;Chain Reactions;Negative Feed-back B_ Networks 87 Modelling Networks;SoftSpots Q2 C_ Lock-In,Schismogenesis andDouble-bind

Stablization in ComplexSystems

A Terminating Systems andStableStates

97

B_ Progressive SystemsandStableFlows 103 Chreodsand EpigeneticLandscapes; Exploringa Landscape 114 C_ TheEpigenetic LandscapeofHumanSociety 117 Analysing Systems 117 A The Classical Scientific Method Verification, Refutationor Gettinga Likeness?; Strong Inference;Hard Work and Skill; The LimitsofScience B Statistics 130 Populations; Samples;Correlations 140 Communication in Systems 140 A Information Theory B InstructionsandPrograms 145 The SameRulesand DifferentStarts;Different RulesandtheSameStart Io

HandlingSystems A TheTheoryofGames Zero-SumGames;Non-Zero-SumGames;Real Games TimeBudgeting ‘omc: MeetingConflicting Requirements Theory;Democratic Practice DealingWithanUnpredictable Future

tO Operational Research

161 161

173 177 185

189

11 ‘Technological Forecasting 198 198 A Exploratory Forecasting Brainstorming; DelphiTechnique;Cross-Impact Matrices;ScenarioWriting;Models—Operational, Mathematical,=Physical; Gaming-Simulation; TrendExtrapolation 215 B- Normative Relevance ‘Trees; Pattern; Levels in the Relevance Tree 223 C Technology Assessment 12 SystemModelling TheWorldasa System

225 226

Epilogue

231 236 241

References andSuggested Reading Index

Vii

Publisher’sNote

C.H. Waddington diedon26September1975shortlyaftercompleting hisrevisionto Toolsfor Thought but beforehe wasableto seeproofs. His originalplanwasto writetwobooksto coverthe ideasthat had concerned himsincethelate1960s.Tools for Thought wasintendedasa popularguideto the newwaysof perceivingand thinkingaboutthe worldanditsintendedsuccessor, Man-Made Futures,wasa workingout ofthoseideasin relationto whathecalledtheworldproblematique, the

keyecological andpolitical problems facing Earth.Thesecond bookwas finished indraftandhewascompleting revisions whenhedied.Alas,it

hasnotbeenpossiblesofartobringthesecondbooktoa sufficient state wherepublication wouldbe easy. Thepresenttextof Tools for Thought hasbeenleftuntouchedexcept forthedeletionofminorreferences to thesecondbook.

P.M.S. 1977

1X

Introduction

I doubtiftherehaseverbeena periodinhistorywhena greaterproportionof peoplehavefoundthemselves franklypuzzledby the waythe worldreactsto theirbesteffortsto changeit, if possibleforthebetter. Weknockdownsomedilapidated slumsandput up reasonably smart newbuildingsin theirplace,onlyto finda fewyearslaterthat the

inhabitants oftheareaarejustasbadlyoffandlivinginasgreatsqualor

asbefore.Welendconsiderable sumsofmoneytoa tropicalcountryand showit howtoorganizepublichealth,andevenprovideit withmedical stafffor someyears,andthe resultis that the levelof nutritionfalls alarmingly andthebabiesaredyingof starvation,insteadof theinfectiousdiseasesthatkilledthembefore.If thingsgounexpectedly wrong onceor twice,that is, onemightsayratherparadoxically, onlyto be expected; butrecentlytheyseemtohavebeengoingwrongsooftenand in so manydifferentcontexts,that manypeoplearebeginningto feel that theymustbe thinkingin somewrongwayabouthowthe world works.I believethat this suspicionis probablycorrect.The waysof

looking at thingsthatwehaveinthepastaccepted ascommon sense reallydonotworkunderallcircumstances, anditisverylikelythatwe

havereacheda periodof historywhentheydo not matchthe typeof processeswhichare goingon in the worldat large.

Wehavebeentrainedto think,or haveacceptedas commonsense, thatwhatgoeson aroundus canusuallybe understoodas somesetof

simplecausalsequences inwhich,forinstance, a causes) andbthen

causesc, thenc causesd andsoon.Thisis onlygoodenoughwhena causes5 but hasverylittleothereffecton anythingelse,andsimilarly theoverwhelmingly mostimportanteffectof}istocausec.Manyofour ownindividualactionsstillhavethischaracter.That is reallybecause theyarein somewaysrelativelyfeeblecomparedto the wholemassof thingsandprocessesof whichtheyarea part.The changewhichhas occurred,or is occurringnow,is thattheeffectsofhumansocietieson theirsurroundings arenowsopowerfulthatit is nolongeradequateto x1

concentrate ontheprimaryeffectsandneglectallsecondary influences. Whenmodernhealthcareis appliedto a primitivesociety,it is so powerfulthat it is no longera questiononlyof curinga fewcasesof illness;it drasticallylowersthe deathrate,particularly of youngchildren,so that the numbersof the populationincreaserapidlyand,of course,demandmorefood.This effecton agricultureand imports, whichis quitesecondary,and indeednegligiblewhenmedicinewas fairlyinefficient andappliedonlyona smallscale,becomesofrealand possiblydecisiveimportancewhenthe medicalworkis massiveand effective. Wecannolongerconsiderthefieldofmedicineasisolated;we haveto see it as linkedup in a complexwiththe numbersof the population, the demandforfoodstuffs, the sourcesof payingforfoodstuffs,anda wholelotofotherfactors. The scaleof verymanyof the impactsof mankindon the world surrounding himisnowsogreatthattheygorightbelowthesurfaceof things.At the deeperlevel,wefindthat mostaspectsof lifeand its interactions: withits surroundings are interconnected intocomplexes. No powerfulactioncan be expectedto haveonlyone consequence, confinedto thethingit wasprimarilydirectedat. It is almostboundto affectlotsofotherthingsaswell.Ourold-fashioned commonsensehas nothadto facesuchsituationsbefore,andis notwelladaptedto doing so. We need nowadaysto be able to think not just aboutsimple processesbut aboutcomplexsystems.Manysuggestionshavebeen made,particularlyin the lastyearswhenthe problemshavebecome morepressing,of differentwaysof tryingto do this.This bookis an attemptto bringtogethermostoftheseproposed“ToolsforThought’. Manyof themwereoriginallyput forwardaccompanied by a lavish decorationof technicaljargon.Partof thismayhavebeendueto the genuinedifficultyof findingwaysof formulating newideas;partperhapsforthelessexcusable reasonthatit mightmaketheideaslookmore profoundand novelthantheyreallywere.However,anyideathat is goingto be reallyusefulin thisconnection can,afteradequatetimeto digestit,beputintoreasonably simplelanguage. Thisbookisoneofthe firstthathastriedto dothiswiththewholerangeofpresent-day ideas on thinkingaboutcomplexsystems.It demandsabsolutelyno mathematicsfromits readers,and | thinkthere are not morethan two examples ofmathematical symbolsusedin thewholebook;andanyone couldunderstandtheideasinvolvedevenif he skippedthose. The ideasarein factexplainedas faras possiblein straightforward Englishwords.However,manypeople,includingmyself,findthatit is Xil

oftenusefulandenlightening tohavevisualillustrations ofideas.This

bookisthereforeprovidedwitha largenumberofdiagrams. Theseare not intendedto expressfactsaboutquantitiesof things,likethe usual graphsoneseesin scientificbooks.Theyare strictlyillustrations of ideas,andtheirpurposeistostimulateyourimagination toseizethegist ofwhatanideaisabout.Theyarethereforenotdrawnin thewaythat has becomeconventional for illustrations in technicalor mostother intellectualbooks,but havebeenexecutedby someonewhosemain interestsarein paintinganddesign.YolandaSonneband is a painter— andthereareratherfewsuch,thoughmorethansuggested bytheold jibe,‘bétecommeun peintre’—whocombinestheintellectual capacity

tograsptheideaswiththevisualimagination tofindawayofsymboliz-

ing them in drawingswhichare alwayspleasant,and sometimes beautiful. AttheendI haveprovided alist ofbooksandarticlesaboutparticular methods,whichI hopewillbe usefulbothto thosewhowouldlikea littleadditionalexplanation anddiscussion, andto thosewhowantan indicationof howto enterconsiderably moredeeplyinto particular thingswhichhavecaughttheirattention.SectionAandpartofSection B of Chapter11arebasedon a reportwrittenformeby RobinRoy, whois nowwiththeOpenUniversity, whilehe wasonmystaffat the StateUniversityof NewYorkat Buffalo.I am gratefulto himfor allowing meto usethis. Thecomplexities revealed bythemorepowerful effectswhichhuman societies arenowexertingarenowonlywithincertainareas,suchasfood, populationandso on.Wefinallyfindourselvesdrivento realizethat eachofthesemajorcomplex areasisinitsturnrelatedtotheothers.We havefoundourselves facedbya seriesofproblems —atomicwarfare,the populationexploion,thefoodproblem,energy,naturalresources, pollutionandsoon—eachcomplexenoughin itself,butthenit turnsout thateachoftheseisonlyoneaspectof,asit were,a TotalProblem,in whichallaspectsoftheworld’sworkings areinter-related. Onewayof beginning to approachit isbrieflydescribed in Chapter12ofthisbook. ThisTotalProblemissometimes calledtheWorldProblematique. Edinburgh, Scotland

C. H. Waddington

X1ll

1 Philosophies

‘ForHeaven’s sake,’you’llsay,‘justhowsystematic doyouhaveto try to be?Let’sskipthisandgetonto something thatmatters.’Okay,we could,but you’dcomebackto it. Philosophy doesmatter.It matters particularly to those—the greatmajorityof mankind—whoselifeis

devoted tobringing aboutchanges ofsomekindorotherintheworld surrounding them;evenif theseeffectsareof nomoreimportthan sellingmoreof MessrsX’srefrigerators than MessrsY succeedsin unloadingon to the market.The onlypeoplewho,to someextent, escapefromthe domination ofa philosophy whichtheyconsciously or unconsciously believein are thosefew who devotethemselvesso wholeheartedly to researching intonewunderstandings of humanor

inanimate naturethatthesheerbrutefactstheycomeacrossimpose systemwithwhichtheywere themselves regardless ofthe philosophical approached (seep. 17). Andthereareveryfew,evenamongtheminority whotry to do research,whoareluckyenoughto strikea bonanza whichsweepsthemofftheirfeetto thatextent.Fortherestofus,it is

justaswelltoknowsomething ofthemainalternative philosophies, if onlytoseewhytheotherchapistalkingsuchnonsense, andwhyhe simplydoesnot seemableto get the drift of whatyouare saying yourself.It islikelytobenothisintelligence, buthisphilosophy, which is responsible. Philosophy usedtobeconsidered thequeenofthesciences, themost

genuine expression ofthehumanness ofman.Butrecently it hasfallen onbaddays.Atpresent theconventional wisdom ofthedominant group tofifty-eights) usestwokindsofbrush-off.Thescien(thethirty-eights Allyouneediscomispurelyspeculative. tistssay:‘Allthistheorizing andthe monsense.Get downto the benchandmeasuresomething’, or rococo Arts peoplesay:‘Allthis theorizingis aridlogic-chopping

linguistic elaboration: Allyouneedis common sense.Gooutto the arenasoflifeandfeelsomething!’ Of courseboththesestatementsare highlyphilosophical. Whatis

15

F1G.1a.1

commonsenseexceptthephilosophy whichyourparentsor yourpeers

havesoaked youinwhenyouweren’t realizing whatyouwereabsorb-

ing?Philosophy ofonekindor anothercannotbeavoidedor evadedor givenuplikesininLent.Perhapsthemostconvincing proofofthisisto lookatthesadfateofpeoplewhohavetriedtoprogramme computers to see,or to uselanguage, or eveneventually to thinkin wayswhichthey hopewouldbegintoresemblethoseofthehumanspecies.Theystarted

offtheirtaskwiththeusualConventional Wisdom oftheDominant Group * —thatwedon’thavetofussaboutphilosophy. Attheendoften or fifteenyears,and a scoreor so millionAmericandollars(mostly

* If youwouldliketo contractthislengthyphrasetoa setofinitials,in thefashionable way,COWDUNGis memorizable, appropriateandaccurateenough.

16

drawnfromthe US Departmentof Defense,whichmighteasilyhave usedthemforworsepurposes),thisis justwhattheyarefindingthey havetofussabout.Theonlywaytomakea robotanythingmorethanan addingmachineistoprovidehimwitha philosophy. Hecannotevensee to anypurpose,let aloneuse language,unlessthereis builtinto his

system somesortofmodelofthekindsofthingsorprocesses thathe

mayexpectto encounter. It’sonlywhensomeoneendowshimwitha philosophy thata robot beginsto getwithinsightof eventhesimplesthumancapabilities. It’s nogoodsaying‘Okay,but I’vegotbeyondthatstage.I candowithout

one.’Youcan’t,anymorethanyoucandowithout yourDNAgenes, - although mankind hasin important ways‘gonebeyondthem’.Some sortof philosophyis a prerequisitefor humanity.Whereyoucando betterthanthe robotis to haveeithera betterphilosophy or moreof them. Philosophies donotneedtobedetailed.In factiftheyaretoodetailed

theybecome counter-productive. Theessential function ofaphilosophy is to providea mentalmachineryfor dealingwitha largevarietyof things—electro-magnetic vibrations(light),oscillations of air density (sound),chemicalsubstances(smells),pressures(tactilesensations) — andinterpretingthemintosomethingwhichhas‘meaning’, i.e.somethingtowhichwerespondorreact(ofthelightrayspassingthroughthe lensofoureyeat anymomentwemayrespondto something betweeno and5 percent,but notmuchmore).Butthereis no reasonwhywe— andI supposeeventually ourrobots—shouldnothaveat ourdisposal severalalternativephilosophies, whichprovidedifferentwaysof interpretingchaosinto sense.Accordingto COWDUNG,if we deignto

noticephilosophy atallweoughttochoose oneorotherofanumber of

conflicting schemes. Wewillnowdiscussthemainvarieties,butit isnot quitefrivolous tosuggestthatthebestthingtodoistoadoptallofthem—a bit —so as to havea nicerangeof toolsamongstwhichyoumayfind something suitableforwhichever situationyoufindyourselfdealingwith.

A.NaturalPhilosophy Let us start by consideringthe two greatphilosophical alternatives whichareconcerned withthekindofintellectual picturewehaveofthe worldof nature—at the momentleavingon one sidequestionsof emotions,morals,etc.,whichwewilldiscussin thenextsection. 17

ThingsandProcesses Oneviewis that the worldessentially consistsof things,andthat any changeswe noticeare reallysecondary,arisingfromthe waythings interactwithoneanother.The alternativeis thatthe worldconsistsof processes, andthat the thingswediscernareonlystillsout of whatis essentially a movie.Thesealternativesgo backto the earliestGreek philosophers wholivedbeforeSocrates(about600—500 BC).The‘thing’

viewisusually associated withthenameofDemocritus, whoactually usedtheword‘atom’ asthenameforthebasicthings—invisibly small

unchangeable andunchanging littlelumpsofsomething whichcouldbe calledmatter,thoughtheywerenotquitethe sameas whata modern chemistor physicistwouldcallanatom. The classicalspokesmanfor the other viewwasHeraclitus,who

argued thatitisanessential feature ofthingsthattheyarealways inthe

processofchange,likea flameintowhichburnablesubstances pass,are burnt,andhotgasescomeout.Youcanneverstepintothesameriver twice,saidHeraclitus, forthewaterisflowing, andwhenyoustepintoit againtomorrowit willnotbethesamewaterasit waswhenyoustepped in today.

TheDemocritean ‘things’ viewisthemostusualinpresent-day com-

monsense.A greatmanyof the thingswehaveto dealwithdo not changetheirnaturemuchoverthe periodof timewithwhichweare concerned withthem.Thesun,themoon,theearthanditsrocks,do,of course,undergochanges, andwhenpressedeveryone willadmitit.Butthe changesaresoslowthatformostpurposesit is alrightto forgetthem.

Again, attheotherendofthescaleofsize,thechemical atomsofiron,

carbon,oxygen,sodiumandtherest,withwhichthechemistdeals,will not changein theiressentialnaturewithinanyperiodof timeweare normallyconcernedwith.It seemsmuchsimplerto regardthemnotas processesbut as things,and to get downto the practicalproblemof

finding outhowthesethingsinteract withoneanother, tobringabout theessentially secondary processes of chemical reaction. Thereare, therefore,manycontextsin whichthe‘thing’viewisthesensibleoneto adopt. It isjustinanintermediate rangeofsubjects,betweenastronomy and geologyontheonehand,andchemistryandphysicsontheother,that the weaknesses of the ‘thing’viewbecomeapparent;and frommany pointsof viewit is justthisintermediate rangethatis the mostinteresting.If oneconsidersa livingcreature,for instance,onecantakea 18

‘thing’ view,andregarditasasetofchemical andphysical interactions

goingon betweenessentially unchanging things,namelythe chemical substances outofwhichit isbuilt.Butthisattitudeseemslesssatisfying whenappliedtoa livingsystemthanit doeswhenused,forinstance,in connection withan industrialplant.Althoughit mayindeedleadus to discovera reasonably goodaccountofhowthebodyworksasa machine fromminuteto minute,takingin food,digesting it, excreting thewaste, usingthe energyof substancesit absorbsto carryout variousother processesand so on, this doesnot seemquiteenough.In fact,the activities whichthebodydoesareusuallymoreinteresting inthemselves thanon accountof the natureof the chemicalsubstancesusedto do them.Wearemoreinterestedin the factthatmusclescancontractto

bringaboutbodily movement thanweareinthechemistry bywhich the

contraction is produced.Again,to takeanotherexample,notthistime froma livingsystem,it is muchmoreinterestingto findout whata computercandothantoknowwhatit ismadeof—whetherit iscopper, silver,glass,plastic,funnycompounds ofsiliconorwhathaveyou.The ‘thing’viewmaybeusefulto thepracticalengineer,butdoesnotseem to leadat alldirectlyto thesubjectswhichareofmostgeneralinterest. Again,concentrating onthe‘thing’aspectsofa livingsystemtendsto leadoneto forgetthatanimalsdevelop;theystartasfertilizedeggs,go throughan elaborateprocessof developing intoan adultform,which usuallylastsa reasonably longtime,butwhichisallthewhileundergoing slowchanges,whichwillleadeventuallyto old age and death. Further,thereis a stillslowerkindof change,that involvedin the evolution ofthespeciesfrommoreprimitiveancestors, uptothepresent form,and presumablybeyondthis into somethingelse.The wholeheartedadoptionofthe‘thing’viewisa temptation to forgettheseother sortsof change,and to concentrate mainlyon findingout howadult bodieswork,asthoughtheywerenomoreinvolved indevelopmental or evolutionary changesthanare automobiles. Its enemiesclaimthat it leadsto a garage-mechanic mentality. Duringmostofthiscentury,theconventional wisdomofthedominantgroupaboutthenatureoflivingorganisms hasbeena ratherexaggeratedformofthe‘thing’view;andwhenthisisappliedtomanandhis socialaffairs,it seems,to meat least,to fallquiteappropriately under theheadingCOWDUNG. It arguesthattheworldandeverything in it is constitutedfromarrangements of essentiallyunchangingmaterial particles,whosenature has alreadybeen largely,if not entirely, discovered bytheresearches ofphysicsandchemistry. Thesephysico19

chemicalentitiesare supposedto constitutethe wholeof objective reality. In the earlyyearsof the century,thisview,whenappliedto living things,wasknownas‘mechanism’. Thehumanbeingwasregardedasa verycomplicated machine,builtup ofthesephysico-chemical parts.A fewrathereccentricbiologists pointedoutthattherearemanypropertiesof livingthings,suchas theirdevelopment, theirevolution,their apparentorganization and particularly theirconsciousness, whenone canbecertainthatthatoccurs,asit doesinourselves, whicharedifficult

orimpossible toexplain intermsofarrangements ofmaterial particles as thoseareusually defined byphysics andchemistry. It wassometimes claimedthatlivingthingsmustinvolvesomeothertypeofprinciple,a ‘vitalforce’of somekind. The adherentsof this view,knownas ‘vitalism’, werehowevernotableto explainthenatureof thisforcein any termsin whichit couldbe reconciledwiththe rest of human knowledge. It remainedno morethan an inexplicable joke.Actually fewscientists wereevertemptedto believein it wholeheartedly; butthe fiercerbelieversin mechanism areoftentemptedto believethatthere wasa vitalisthidingunderthebedofmanyoftheirquiterespectable, butlessdoctrinaire, colleagues. Thegreatadvances in ourunderstanding oflivingthingsduringthe

firsthalfof thiscenturyis evidence of howeffectively the‘thing’, mechanistic, viewcanworkas a practicalrecipefor investigating biological processes. It hasledto anenormousincreasein understandinghowthebodyworksasa physiological machine,withalltherepercussionsofthatknowledge onmedicine, andfinallyto thediscovery of the materialbasisof heredity,and its basisin DNAand the genetic code.Butstill,powerful thoughthisapproachis,it hassofarreallyonly beensuccessful inconnection withsomeofthequestions wewanttoask aboutlivingthings,notallofthem.It hasgivenuslittleunderstanding of embryonicdevelopment; littleexceptsomeratheremptytheories aboutevolution; andhardlyanythingat allaboutthemind. In searchof a pointof viewwhichwillbe successful in thesefields also,veryfewscientists,if any,aretodaytemptedto go backto the vitalistviewwhichwasin termsofsomespecial‘lifeforce’.Insteadone of the earliestgroupswhotriedto thinkout a newpointof view— mainlyBritishbiologists inthethirties(e.g.Needham, Woodger) argued that oneshouldthinkof livingsystemsas madeup of the physicochemicalentities,p/uswhattheycalled‘organizing relations’between them. These organizingrelationswerethoughtof as complicated 20

a

a

networksofinteractions, comparable to whatwouldnowadays becalled cybernetic relations(seeChapters6 and7),althoughthatwordhadnot beeninventedat the time.In the lastthirtyor fortyyears,therehas indeedbeenprogressin understanding the natureof the networksof interaction whichareinvolvedin theprocesses bywhich a collection of cellsbecomesorganized intoanorganwitha unitarycharacter,orintoa neuralsystemcapableof functioning in a coherentway.Asa developmentofthisapproach,somebiologists spokeofa processof‘emergence’ of newpropertiesat certain‘levelsof complexity’. Bythistheymeant that whena mechanism,madeup out of materialphysico-chemical parts,becomescomplicated enough,it mightexhibita typeofbehaviour whichdidnotandcouldnotoccurat allin theisolatedparts.To givea crudeexample: whentheengine,propeller,wings,fuselage, landinggear and so on are put togetherin the rightway,the complicated set-up becomesan aircraftwhichcanfly;but noneof the partscanflywhen isolated.It washopedin thiswayto accountforthefactthatalthough man,at least,hasself-consciousness, hisultimateconstituents —if one takesthemto be physico-chemical atomsandmolecules —donothave anythingofthatkindat all. Theideas,oftheimportance oforganizing relationsbetweenthebasic entities,andof the possibility of the emergence of novelpropertiesin systemswhicharecomplicated enough,arenowadays probablythemain rivalto the‘nothingbutmaterialthingsCOWDUNG’. However,there is anotherview,stilla minorityone,whichmakesanevenmoreradical attackontheorthodoxy.It questionsthebasicassumption oftheother views,that the foundationfor our understanding of the worldis a knowledge ofmaterialentitiessuchasphysico-chemical atoms,andis a returninmodernform,totheHeraclitan ‘process’ philosophy asopposed to theDemocritean ‘thing’view.Perhapsthefirstinfluential exponents ofan approachof thiskindwereMarxandEngels,in theirattemptto substitutea dutalectical materialismfor the current mechanical materialism. Theywere,of course,concernedmostlywiththe social— economic—political arena;but Engelsin particularwrotefairlyextensivelyaboutthe worldof naturalscience.Perhapsbecauseof their overwhelming interestin politicalstrugglesand confrontations, they arguedthat all the interactionsinvolvedin naturalprocessescan be thoughtof in termsof the confrontation of antagonists —a thesisopposedbyanantithesis, leadingtoa synthesis. Anotherauthorwho,later, andwithlittlereferenceto MarxandEngels,developed a similarlineof thoughtmorethoroughly,and muchmorein relationto the natural 2I

worldasa wholeandour knowledge ofit, wasA.N. Whitehead. Thebasisofhisviewcanberegardedasa returnto whatpeoplehad thoughtaboutscience,asa meansof understanding nature,in its very earliestdays,wellbeforethe triumphsof Newtonianphysicsand its laterdevelopments inchemistry.It arguesthatthefoundation ofknowledgeisnottheatom,aschemistsdescribeit, or whateverfundamental particlesthemostrecentphysicists arewillingto admit.Insteadscience is based on observations,which, made in a controlledand organized way,amountto experiments.Nowan observation,or an experiment,has

to be observedby someone.It is ‘an occasionof experience’; and

involves theexperiencing personaswellaswhatisexperienced. Thus

phenomena likemind,orconscious perception, areincludedin thevery foundationof knowledge.COWDUNG,of both the minorityand majoritykind,leavesmindoutofwhatit callsobjective reality,andthen has to try to smuggleit backthroughsomedoctrineof organizing relations,emergence andthelike. Foranyviewwhichemphasizes theprocesscharacterof things,and the importanceof the relationsbetweenthem,the boundariesof each thingmustappearsomewhatindefinite,sincenothingcanexisttotally for itself,withno involvement withanythingelse.However,classical logic,andmostofthemathematics whichisderivedfromit, isbasedon consideration ofclearlydefinedentitieswith,asonemightput it, defi-

nitehardedges.Recently, withtheattention beingpaidtoHeraclitan processideasas againstthe Democriteanatomisticones,peopleare tryingtodevelopa mathematics of‘fuzzy’entities;a logic,and,perhaps moredowntoearth,a computer-programming system,whichdealswith notionswhichcannotbeprecisely defined.Anothersimilardevelopment is to saythat the stateof a system,whichconventionally wouldbe representedby a pointon a graph,shouldbe representedby a point surroundedby a ‘tolerance’ region,and canlie anywherewithinthat region;thenonedealsnotwitha clear-cutgeometrical space,butwitha ‘tolerance space’.Ofcourse,manyofoureverydaystatements, andthe mostimportantonesat that,do alreadydealwithsuchconcepts.Who woulddareto offerprecisedefinitionsof any of the mainwordsin statements like‘Lovethyneighbourasthyself’,oreven‘applesarenicer thanpears’?Thesenewdevelopments inmathematics aregenuinely new Toolsfor Thoughtwhich,whendeveloped,willmakeit possibleto handlesuchmattersmoreprecisely. Thereisnospaceherefora fulldiscussion ofthealternative thingor processpointsof view.However,thereare twopointswhichit seems 22

usefultomake.Thefirstisrelatively minorinimportance, butisnecessaryinformationin relationto whatone is likelyto comeacrossin readingrecentmaterial.Thecontroversy betweenvitalismandmechan-

ism,andthedevelopment oftheminority viewoftheimportance of organizing relations andemergence, waslargelya European phenomenonduringthethirtiesandforties.TheAmericans playedlittlepart in it, andonthewholeevennowdonotunderstandwhatyoumeanif youspeakof vitalismandmechanism. Theybecameinterestedin the subjectconsiderably later,indeedmostlynotuntilthesixties,andthey

tendtouseinthisconnection theword‘reductionism’. Onemightthink at firstsightthatthiswouldindicatetheviewthatoneshouldstartfrom theobservation or experiment, andattemptto reduceitscomplexity to termsof the simplerentitieswhichone has alreadycomeacrossin physicsand chemistry;whichis just what the most radicalantiCOWDUNG viewwouldmaintain.However, inAmerican practice,the

wordisusedinexactly theopposite sensetothis.‘Reductionism’ 1m-

pliestworatherdifferentthings.As a philosophyit meansthat the objectiveworldconsistsof physico-chemical entitiesandexplicitly describable interactions betweenthem.Thisistheviewthatwehaveabove designated asmajorityCOWDUNG. Secondly, reductionism isa recipe foraction:thenit isthebeliefthatifyouareconfronted witha complex

situation, forinstance a livingsystem, yourbestbettogetsomesortof

pay-offorotheristolookforthephysicalorchemical factorswhichcan influence thephenomenon in question. Treatsexassomething in thefieldofchemistry, andyoumaycome up withthe Pill —a pretty definiteagentwhichproducesa pretty

definite result.If, ontheotherhand,yourefuseeverto treatit as

anythinglesscomplex thanthefullcontentofoccasions ofsexualexperience,youmayfindthat it is evenmorecomplexthan youthought (owingto the unconscious factorsin it) andfinishup feelingyourself boggeddownin a bottomless morassofFreud,Jung,Reich,Laingand therest.It is a difficultchoice.Undoubtedly, the‘thing’view‘works’, upto a point;the‘reductionist’ approachto sexuality canfixit sothata girldoesn’tproduce a fertilizable ovumjust whenits presenceis not wanted.Butthepresenceor absenceofa fertilizable eggisnottheonly thingofimportance ina sexualexperience. Theexperience doesinclude factorswhich,onecanrecognize, Freudet a/. aretryingto talkabout, howeverdifficulttheyfindit to dosoin anymeaningful way. Asanexpression ofpersonalopinion,I wouldsaythatreductionism is lousyphilosophy (becausescienceis basedon experiments, not on 23

atoms),but is a goodrecipefor makinga quick(scientific) buckby discovering someusefulpracticalinformation; but is bad againas a methodformakingmajoradvancesin humancomprehension, suchas thoseofDarwin,Freud,Einsteinor thequantumphysicists. TherearetwopointsworthaddingaboutWhitehead. In hislaterlife he developed hisphilosophy intosomewhat esotericcomplexities. Few peopleexceptprofessional philosophers willwishtogointoit.However, in the earlierstagesof histhought,he coinedtwophraseswhichit is worthanyone’s whileto beacquainted withandto consider. The firstis the ‘Bifurcation of Nature’;by whichhe meantthe (to himmistaken)ideathatit is possibleto splitnatureintotwoseparate parts,mindonthe onehand,andmatteron the other.Thisthesisis particularly associated withthenameofDescartes, andisalsoknownas theCartesian dualism.Whitehead maintained, inopposition tothis,that primitively wegettoknowabouttheworldbya processwhichinvolves minds,whichoperatebymeansofourbodilymaterialstructures,interactingwithexternalevents.Heclaimedthatanattempttomakeacleancut break,betweenthe subjectivementalobserverand the objective materialobserved,is a basicerror. They are initiallyparts of a

whole,andifonewantsforsomepurposes toseparate them,thatcan

only be a matterof convenience that shouldbe indulgedin with greatcaution. The secondof his phrasesworth rememberingis ‘Fallacyof Misplaced Concreteness’. Mostconventional thought,heargues,recognizescertainderived,andessentially abstract,notions,that havebeen

invented bymantotrytomakesenseofthesituations hecomes across.

Examples arephysicalatoms,orfeelingssuchasanger,orsocialnotions suchas justice.Mantendsto acceptthesenotionsas beingconcrete things,whichcould,asit were,bepickedupandplacedsomewhere else. Whiteheadarguedthat suchnotionsare in factalwaysderivedfrom

actualoccasions of humanexperience. Theexperiences arethereal things;thenotionsaresecondary andderivative. It is dangerous to

forgetthis,andtotakethesesecondary thingsasmoreconcreteandreal thantheyactuallyare.Thisis,ofcourse,justanother,butanilluminatingway,ofputtingtheargumentagainstreductionism asa philosophy. If weacceptthattheuniversecontainsthingswhichareindependent of our personalselves—thenit is a fallacyto supposethat our present descriptions of theseindependentfactorssumup the wholeof their concretereality,leavingnothingout.‘Atomsarereal.”Okay,but what sortofatoms?Allweknowaboutthemiswhatwehavesofarsucceeded

24

in findingout, by analysingour experiences, and arrangingto have experiences(experiments) whichlook like beinginformative.The FallacyofMisplaced Concreteness, initssimplestform(therearemany moresubtleforms),istosupposethatwhatwehavesofardiscovered is thewholeofwhatiscontainedin therealityindependent ofourselves.

B.MoralPhilosophy Values Discussion ofthephilosophical natureofthe worldwelivein—things or processes? —hasbeenunfashionable bothforacademic philosophers and for ordinarypeople.Discussingthe other main questionsin philosophy, aboutvaluesandethics,hasbeenin somewaysevenmore pushedintothebackground inthelastthirtyorfortyyears.Formostof Europeanhistory,andof the historyof mostotherpartsof the world too,thecharacteroftheGoodandtheRighthavebeencentralissuesfor civilizedthought,fallingoutofpublicdiscussion onlyin periodswhen there was such generalagreementabout them that argumentation seemedunnecessary. Rathersuddenly,in the lasthalf-century, people havebegunactingasthoughsuchconceptseitherhadnomeaningatall, or, if theyhadany,thiscouldbe leftin the handsof a fewspecialist theologians ora dwindling bandofmoralphilosophers nearthebottom ofthescaleofesteemandprestigein theacademic world.Manyofthe youngergeneration todaydonotagreewiththisnegligentdismissal of suchmatters,and I do not myself.The branchof philosophy which dealswithmoralsandvaluesrequiresdiscussion, evenin a bookwitha methodological slantlikethis one;not becauseit providesToolsfor Thought,butratherbecauseit suggestswhatkindoftoolsaregoingto berequired. Thereare,ofcourse,a largevarietyofopinions, andallwehavespace forhereisto listthemwithoutattempting tocomparetheirmerits.The mainvarietiescanbe describedas arisingby combining itemschosen fromthreepairsofalternatives: a Natureconsistsofthings; b Natureconsistsofprocesses; p Valuesareinsidenature; q Valuesareoutsidenature; x ValuesstemfromGod; y Godstemsfromvalues.

25

For instance,onemightbelievethat natureconsistsof things,and thatthethingsarethemselves valuablebecauseGodcreatedthem;this wouldbe thecombination of a—p—x. Or onemightbelievethatnature consistsof things,whichhavenovaluein themselves, but valuesexist andfromthisfactonecandeducetheexistence ofGod;thiswouldbe a—q—y. Andsoon.Thereareeightpossiblecombinations, andnearlyall ofthemhavebeenbelievedbysomepeoplesomewhere sometime. Therecanalsobeviewswhichrejectbothofoneormoreofthepairs ofalternatives. Forinstance,themostextremevarietyofthe‘reduction-

ist’philosophy, whichsomepeoplewouldhaveusbelieve isthebasic philosophy ofscience,tellsusthattheworld,includingman,isnothing buta machine; everything ismolecules andnothingbutmolecules. This is acceptinga, but it is rejectingthat therereallyare suchthingsas values,andis thusturningdownbothp andgq,andx andy. A milder

formof this,whichis theformoriginally presented by theearlier

philosophers ofscience,suchasDescartes,didat leastofficially accept theexistence ofGod,andthatvaluesarederivedfromHim;thatistosay it wastheviewa—q-x. Perhaps,as a wordof guidance(or warning)aboutthe restof this book,I shouldsaythatmyownpersonalviewfallsundertheheadingb—

p—y; natureismadeupofprocesses, andtheprocesses involve values, and God—if one wishesto usethat term— arises fromthe values inherentin theprocesses. Thinking andFeeling In thelastfewyearstherehasbeena considerable revivalofinterestin

themodeofdealing witha worldwhichrejectsthewholeideaofan

intellectual analysis.Theonlytypeofintellectit valuesis whatRoszak calls‘Rhapsodic Intellect’. In effectit doesnotwanttohaveanythingto dowithanyofthealternatives listedabove.It presentsthefeelingthat intellectual thoughtcanneverbemorethananexploration ofrelations betweenabstractconcepts; andanabstractconceptisbyitsverydefini-

tiononlya partialandincomplete reflection of reality.Oneof the

greatestspokesmen forthispointofviewin classical Englishliterature wasWilliamBlake(‘togeneralise istobeanidiot’).Wordsworth andthe otherpoetsoftheRomanticmovement oftheearlynineteenthcentury _put thesamepointofviewin a slightlylessextremeform;then,more recently,D. H. Lawrence.Todayit is mostforcefully expressedby a groupofyoungAmerican writers,suchasCharlesReich,PhilipSlater andTheodoreRoszak.Theserecentwritersareexplicitly writingagainst 26

something whichtheytaketobecharacteristic ofthedominantculture— theCOWDUNGofthepresenttime.Theyarguethattheaffairsofthe worldareat presentrun solelyunderthe influenceof the head,whose modeofbehaviour isintermsofconceptual thought;whiletheycallfor dealingwiththe worldthroughthe body,whosemodeof behaviouris throughspontaneous feelingandaction.Theyusuallyalsoidentifythe headanditsconceptual thinkingwithscience,andtheythereforeappear asanti-scientists. Thishasbeenaninfluential setofvaluesin recentyears,particularly amongstyoungpeople.In manywaysquiterightlyso,at leastin asfar

asit stresses theimportance ofotherfaculties to thatofconceptual

thoughtalone.But it is actuallyquitewrongin its identification of sciencewithconceptual thought,asI shallpointoutlaterwhendiscussingthe scientificmethods(p. 117).Scienceinvolvesthinkingbut does notarisefromit; the groundwork ofscienceis observation andexperiment.The generalexploration of oursurroundings involvedin asking ‘whatsort of thingsare we comingacross?’bringsthe scientistup againstjusttherawmaterialofexperience whichtheanti-rationalists are emphasizing. Of course,sciencethen goeson to utilizeconceptual analysis,to clarifyexperiences andtryto makesenseofthem.Butit is basicallywrongto supposethat sciencedoesnot includethismodeof behaviour —althoughit mustbeadmittedthatsomescientistshavetried to givethatimpression. Again,I wouldarguethat it is incorrectof the anti-scientists to attributethe presentillsof the worldto scienceas such.Theyarise muchmorefromthemisapplication ofscienceundertheinfluence ofa basicallyinadequatesocialphilosophy, whichputs too muchstress— bothincapitalistandinCommunist countries—onmaterialgoods.This lastpoint,ofcourse,goeswellbeyondthefieldofmethodologies which arebeingdiscussedin thisbook. Christianity andEnvironment Anothertopicaldiscussion abouttheimportance ofmoralphilosophy in the worldtodaycentresroundthe argumentthat it is becauseof the valuesenshrinedin Westernman’sreligionofChristianity, thathe has allowedhimselftoravagethenaturalresources oftheplanetandpollute hisenvironment withhiswasteproducts.It isclaimedthatthesanction forthesemalpractices is foundin theBookofGenesis,wherethestory oftheCreationtellsthatGodgavetheearthandtheplantsandanimals 27

init tothedominionofAdamforhimtouseashesawfit.Exponents of thisargumentusuallydonotgoonto pointoutthatwhatwasgivento Adamat the timeof the creationwasthe Gardenof Eden,in which man,althoughthe mostimportantof livingcreatures,livedat peace withalltheothers.It wasonlyaftertheFallofmanandtheexpulsion fromtheearthlyparadisethatanyquestionofexploitation oftheworld bymanarose. In any case,it seemsverydifficultto sustainthe argumentthat Christianmanhas alwaysalteredthe naturalecosystems moredrasticallythanthoseof otherreligions,or that the alterationsthathe has producedhavealwaysbeendeleterious.All greatcivilizations, at all timesandwithallmannerofreligions,havemadeprofoundchangesin naturalecology. TheMesopotamian, EgyptianandChinesecivilizations alldependedon drainingswampylandandcontrolling the waterwith elaboratecanals.Prettyvigorousremodellings of the landscapewere necessary to supportthemountaincivilizations ofthe IncasofPeru,or thericecultivators inthehillcountriesofSouth-EastAsia,oragainthe greatcivilizations whichconqueredthe rainlessplainsof Ceylonby controllingthe waterfromthe mountains.Noneof these,of course, were Christian.Their justificationfor imposingtheir will on the naturallandscapecannotbe lookedforin theBookof Genesis.Moreover,someofthemproducedin thelongrun effectsevenmoredevastatingthan anythingbroughtaboutso far by WesternChristianity. Mesopotamian civilizations eventually ruinedthe fertilityof theirland andreducedthecountryto desert,byagricultural practiceswhichledto

thefertilesoilbeingsweptintorivers. Thepre-Christian Mediterranean civilizations of GreeceandRome,combinedwiththe Muslimcivilizationsin the earlycenturiesof our era, succeededin devastatingthe southernshoresof the Mediterranean, whichhadbeenthe granaryof Rome.Moreover, ontheothersideofthepicture,Christiancivilizations cannotbe accusedof alwayswreckingtheir ecosystems.Christian Europenotonlyconvertedthe ill-drainedtangledforestsnorthof the Alpsintofertileagriculturalland,but foundwaysof cultivatingthis whichhavekeptit in goodshapeforabouta thousandyears. The real blame for the harmfuleffectswhich man is now undoubtedlyproducingin industrialized ChristianWesternEurope andNorthAmerica,can,I think,beblamedmuchmoreontheindus-

trialcomponents inhisculturethanontheChristian. Reallyharmful

pollution—otherthanthatcausedbytheage-oldproblemofgettingrid of humanexcretafromlargecities,whichhasbeenmoresatisfactorily 28

solvedin the industrialcountriesthan in anypreviouscivilization — beganto arisewiththedevelopment ofheavyindustryinBritainduring theearlyphasesoftheIndustrialRevolution. It wasduealmostentirely

toa mixture ofignorance andlackofforesight. Peoplesimplydidnot

knowhowharmfulsomeproducts,suchas sulphurdioxide,or heavy metalslikemercury,leadandsoon,couldbe.Andtheydidnotforesee theenormousexpansion ofindustrywhichwouldconverta fewisolated squaremilesofpollutedregionaroundparticularindustrialtownsintoa conditionblanketing a largeproportionofthecountry. Theselessonswerenot learntuntilthe damagehad becomequite considerable.However,anti-pollutionlawscameinto operationin Britainat a relativelyearlystage.It wasin America(followed bynonChristianJapan)thatpollutionrosetoreallyspectacular levelsincertain places,andit is in Americathattheanti-pollution outcryhastherefore beenmostviolent.TheintensityofpollutioninAmericaandthefeeble-

nessofanyattempttocontrolit untilthelastfewyearsisnot,I think,

fairlyattributableto thePuritanethic.In the earlytimesin American history,whenthe Puritanethicwasan importantforcein theirsocial behaviour, theNewEnglanders, guidedbythismorality,werenotparticularlybad polluters;nor werethe Southerncotton-growing slaveowners.Reallyirresponsible exploitation and pollutionof naturegot underwaywiththegreatinfluxofimmigrants fromthemid-nineteenth centuryonwards.Their behaviourwas very little influencedby a Christianmorality,Puritanor otherwise.It wasdominatedmuchmore by the worshipof the greatgodMolock—the dollar.Therewasoil, gold,copperand whoknowswhatelseto be foundjust beyondthe westernhorizon.The manwhogottherefirstcouldtakethemout as fastas possible,andgoon to the nextpieceof treasuretrove,leaving behindhimwhatmesshepleased,to beclearedup byanyoneunenterprisingenoughto be contentto try to geta second,poorercrop.It is onlyto shirkthe realissueto attributeresponsibility to thesemalpracticeseitherto Christianity, or forthatmatterto science.Theyarethe responsibility ofunmitigated materialism —andyoudon’tseemto make it allthatmuchbetter,in thisconnection, bybeingdialectical aboutit.

—

2 Complexity

A. The Natureof Complexity Relations,Instructionsand the Mind

This bookis aboutthe problemsinvolvedin tryingto geta graspon complexity. The following chapterswilldescribea numberofdifferent wayswhichmakeit nottoodifficultto beginto getsomesortofunderstandingof complexsystems.Butsomepeoplemayfeelthatoneought to startby definingwhatweshallbe discussing. However,no onehas

yetsucceeded ingiving a definition of‘complexity’ whichismeaningful

enoughtoenableonetomeasureexactlyhowcomplexa givensystemis. Obviously it issomething to dowiththenumberofelementswhichcan beseparately identifiedin thesystem,andwiththenumberofwaysin whichtheyare related;but it is oftena matterof choicehowmany elementsonewishesto distinguish, andhowfaronewantsto followup theramifications oftheirrelationships andinterconnections. It isworthpointingout,though,thathoweveronemighttrytodefine complexity, it tendsto increasefasterthan the numberof elements involved. Considera verysimplecase:a numberofpeople,allofwhom getto knoweachotherin pairs—andwewillnot pursuetheirinterrelationsbeyondthe pairwise.If thereare twopeople,thereare two pairwiserelations—a’srelationwithb, andb’srelationwitha, which maynotbe quitethesame.If therearetenpeopleeachindividualhas nineotherstoknow,sothereare10x g = gorelations;iftherearefifty people,thereare50 x 49= 2,450relationsandsoon(Fig.2a.1). Roughlyspeaking, therelationsofthissortgoupasthesquareofthe numberof elementsin a system.This means,for instance,that the difficultyof runningsomethinglikea telephoneexchangeincreases not in proportionto the numberof subscribers,but morenearlyin proportionto the squareof the number—hencethe installationof electronicswitchingapparatusin placeof the villagepostmistress. 30

FIG.24.1

Somethingof the samesorthappenswiththe interference withyour drivingby othercarson the roads,or evenmoregenerally,withthe advantages and disadvantages of livingin a placeof highpopulation

density. Two’scompany, three’s acrowdandfiveorsixisgetting tobe

a shambles. Theincreasein thecomplexity ofrelationswhenthereis anincrease in thenumberofthingsto berelatedmayseemalarmingenough,butit is slightin comparison withwhathappenswhenweconsider,notrelationsbetweenthings,butcombinations ofinstructions. Thereareonlya verysmallnumberofrulesformoveswhichcanbemadein chess,but thenumberofdifferentpositionsofthepiecesontheboardwhichcan resultwhenthesefewrulesareimplemented alternately bytwoplayers istrulyimmense. Evenwhenthereisonlyone‘player’, anda setofrules whichitselfspecifies whichruleisto beoperatedat thenextmove,the resultswhicharegeneratedmaybe ofincalculable complexity (though sometimestheycan alsobe verysimple);someexamplesof this are describedinChapter9,whichdealswithinstructions (seepp. 145-160). In suchcircumstances thereseemsto be no generaldefinitionofcomplexitywhichwouldbemeaningful. It makesmoresenseto givespecial definitions of whatonemeansin anyparticularcontext,to makeclear whatoneis talkingaboutat thetime. Thereis,however, onegeneralpointtobearinmind.Man’sattempts to dealwithcomplexsituationshaveto becarriedoutwithinthelimitationsset by the capacitiesof his brain.Theselimitationsare rather severe.Evenin well-trainedpeople,the humannervoussystemcan processinformation onlyat therateof250—1,000 wordsperminute(in

comparison, electronicequipment,usingsuchmethodsas microfilm, canstoreandretrieveup to 700,000wordsperminute;andthisrateis

beingrapidly increased). Ifoneconsiders man’scapacity ofconsidering itemssimultaneously, thenumberhecandealwithistiny.Forinstance, if he is subjectedto a numberofincomingstimulito hisvarioussense organs,ingeneralhecandiscriminate andrecognize onlyaboutsevenor eightat once.Again,thisis aboutthenumberof itemsthata mancan simultaneously bringtomind,outofallthosestoredinhismemory,and takeintoconsideration at oneand the sametimewhencomingto a

decision aboutsomething. Thisisaremarkably small‘channel capacity’,

to usetheelectricalengineers’ term. The sevenor eightideasthat canbe broughtintoimmediateconsciousness neednotbe itemsof specificdetailedinformation. Someof themmaybe complexideasor theoriessynthesizing intoa singlecon-

cepta massofminutedetails.Theprocess offormulating theoretical concepts (suchasatom,gene,Oedipus complex, Hamlet andthelike)is the onlydevicethatmanhasat hisdisposalto helphimdealwiththe highlycomplexworld.Thisis theessentialjustification forthepursuit ofpurescience,high-browliteratureandart.Withouttheassistance of thesymbolicconceptsformulated bytheseapparentlyluxuryactivities,

manwouldbereducedeithertotakingdecisions in thelightonlyof

sevenor eightparticularfacts,or to turningthe wholethingoverto a computer(which,ofcourse,he wouldhavehadto programme without theaidofappropriate generalconcepts).

B.Complexity ofInformation intheModern World It is impossible to giveanythinglikea completeor accuratepictureof the complexity of the modernworld,whichmanhasto try to handle withthesesomewhat imperfectinstruments. However, onecangetsome

ideaofatleastpartoftheproblem byconsidering studieswhichhave beenmadeofthegrowthofscientific information inthelasttwocen-

turies.Eventhiscanbeestimatedonlyindirectly,byfigureswhichgive indicationsof trendsratherthan anythingmoreprecise.One such indicationis the numberof scientific journalspublished.The firsttwo journalsdevotedwhollyto science—ThePhilosophical Transactions of theRoyalSocietyofLondon, andtheFrenchJournaldesScavants—were bothstartedin 1665.A numbermorewerebegunat regularintervals duringthe nextcentury.The processreallygotunderwayin earnest 32

around1760;andsincethenthenumberofnewjournalsestablished has doubledeveryfifteenyears(orincreased ten-foldeveryfiftyyears).By nowwellover100,000scientificjournalshavebeenfounded.Not all havepersisted,andnobodyknowsquitehowmanyjournalsarebeing publishedatthepresenttime.Aslongagoas1938,Bernalestimated that thereweresome33,000currentscientific publications. Anotherestimate in thelate1960sputthenumberat 50,000,containing about1 million separatescientific papersperyear. Oneattemptto handlethismassofmaterialhasbeenthefoundation ofsecondary journals,whosefunctionis to summarize andabstractthe paperspublishedintheprimaryjournals.Thefirstoftheseappearedas longagoas1714inGermany. Bythetimetherewereenoughofthemto forma representative sample,theyalsostartedto multiply,at thesame exponential rate as the primaryjournals,doublingin numberevery fifteenyears,andreachinga totalof1,900bythemid1960s.Bythistime therehad beendevelopeda tertiarylevelof periodicalpublications, givinginformation abouttheabstracting journals.Atpresentthereis a planfora WorldScienceInformation System,undertheauspicesofthe UnitedNations(UNISIST),whichcontemplates centralcomputer storageof allscientificinformation, witha suitablyelaborateretrieval system. It is veryobviousthatnosinglemancan‘know’allofthisinformation,orevenhaveveryreadyaccesstoit;buthemaybeabletofindany particularitem,if he searcheshardenoughforit. The consequence of thismaybethatit becomes easiertorediscover a factratherthantofind outwhethersomebody elsehasalreadydiscovered anddescribed it.One getsthe impression thatin somebranchesof science,suchas partsof biologywhichare stillfloundering aboutin searchof firmtheoretical framework, a gooddealof currentresearchis alreadyof thiskind:an earnestyoungworkercomingup withwhatseemsto him a novel discovery, whichin factwaswellknownaboutfiftyyearspreviously, althoughforgottenorneglected intheinterim.This‘rediscovery phenomenon’maywellbecomeoneof themajorfactorslimitingthe rateof advanceofscience. Anothereffectofthemassofscientific information is thatit encouragesspecialization. Thereis no evidence that the manof todaycan remember, andhaveat hisfingertips, manymoreitemsthancouldhis predecessor twocenturiesago,when1,000fewerjournalswerebeing published. Hehasperforcetonarrowtherangeoftopicsonwhichheis wellinformed,thoughnotnecessarily bya factorof 1,000,since,aswe 33

sawbefore,thedevelopment oftheoretical insightmakesit possibleto sumup largemassesofinformation undertheheadingofa singleconcept.Nevertheless, thenarrowing ofrangemustbequiteconsiderable. Attemptsto overcome thisdifficultyby inter-disciplinary or transdisciplinary teachingcanonlybesuccessful uptoa point.If,asseemsto be necessary, oneassumesthatroughlyspeakingthe amountthatany onepersoncanknowis approximately fixed,thereis no usethinking thatbyteachinga studenttwoorthreesubjectsonecangethimtoknow as muchaboutthesesubjectsas do specialists whostudyonlyoneof them.The purposeof inter-disciplinary teachingis bestconsidered as

theproduction ofa different mixofinterests whichseemsparticularly relevantto importantproblemsofthetime,ratherthantheimpossible taskofaddingoneexistingspecialism to another. Oneofthemostimportanteffectsoftherapidincreaseinthevolume of information is thatinformation is veryrapidlyrenderedobsoleteby thediscovery ofnewfacts.DeSollaPricehasdiscussed thisintermsof ‘acoefficient ofimmediacy’. Thisistheratiooftheincreaseina variable (suchasinformation) overaperiod,toitsvalueattheendofthatperiod. For instance,if the amountof information doublesin fifteenyears,it wouldbeAat thebeginning ofthatperiodand2Aat theendofit.The

increasein A andthe coefficient of immediacy is a 4, That is to 2 say,that at the endof the fifteenyears,50per centof the available information willhavebeendiscovered duringthatperioditself. Thereisanother,perhapslessflattering, wayoflookingat thissituation,whichis veryrelevantto peoplewhoareundergoing coursesof formaleducation.Supposesomebody’s schoolingfinishedin the year the fifteen-year periodmentionedabovebegan,thenfifteenyearslater 50percentof the availableinformation wouldnot havebeenin existencewhenhe ceasedhis coursesof study.Unlesshe had goneon learningin themeantime,hecouldberegardedas50percentobsolescent.Overa workinglifeof forty-five years,a personin thissituation wouldbecome87:5percentobsolescent. In someveryrapidlyadvancingfields,suchascomputerscience,thedoubling periodis notfifteen years,butmorelikefouryears,andin suchcircumstances obsolescence reaches98percentin onlytwenty-four years. Thesearetheoretical figures,butthereissomeactualevidence about therateat whichuniversity instruction goesoutofdateincertainfields. AstudyhasbeenmadebyZelikoff(1968)ofsome7,000undergraduate and graduatecoursesin engineeringsciencesgivenat five major 34

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Americanuniversities. He tookthe numberof coursesofferedat the start of a givenperiodas representingthe ‘amount’of information availableat that time.The quantityof ‘newknowledge’ accumulated duringthe periodwasestimatedby thenumberofnewcourseswhich wereoffered.

Fromthesefigures, hecouldcalculate therateatwhicha personwho

graduatedin a givenyearwouldbecomeobsolescent if heceasedlearningintheyearheleftcollege.Thefiguresareprettyalarmingtoanyone

osSS oonKnow

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1945 1950 1955

1960

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35

whothinksallyouhaveto do is to learna certainnumberof factsat universityandtheywilllastyoutherestofyourlife.Evenpeoplewho graduatedin 1955(thelastyearin whichtherewasanythinglikesufficientfactualevidence)wouldbe about30 per cent obsolescent five yearsaftergraduation,andnearly60per centafterfifteen.If oneextrapolatesthefiguresto thepresenttime,engineers whoceasedlearning anythingin 1970wouldbegetting50percentoutofdatein aslittleas fiveyears. nom a

graduation after Year

19501960 1970 19801990 2000 Yearof graduation

FIG.2b.3 Thismethodis,ofcourse,onlya veryroughtwayof estimating the rateat whichnewknowledge is beingaddedto the oldstock,andthe figuresofratesofobsolescence shouldclearlynotbetakenasaccurate. Theyare theoreticaland indicativeonly;but theyare probablyright

enough asordersofmagnitude, andinsuggesting thatitonlytakesa few

yearsfora considerable fractionofmostpeople’sstoreofknowledge to getoutofdate.Perhapsthisis especially soin science,in whichinformationis veryactivelysought,andis recordedforotherpeopleto use.

Buteveninlessformalized intellectual fields, suchastheunderstanding ofpeoples,societies andpoliticalsystems,thesamesortofobsolescence ofpointsofview,opinionsandunderstanding alsooccurs,thoughpossiblyat a slowerrate. It wouldbeoptimisticto thinkthatanyonereallyknowshowto deal withthe situation.The solutionliespresumablyin somemixof (a) teachinggeneralprinciples whichwillgooutofdateonlyslowly,and(b) teachingmethodsforfindingoutrapidlyandfairlycomprehensively the

up-to-date factual information whichwillputfleshonthesebarebones

atanytimewhenit becomes necessary toapplythe(c)teachingmethods ofclassifying information intoa hierarchy ofcategories, sothattheitems 36

relevantto a particularcontextcan be rapidlyfilteredout, and (d) instillingmotivationfor continuingself-education afterthe periodof formaleducationhasceased.Butexactlywhatthismixshouldbe and howtoachievetheseendsstillremainstobeworkedout(andshouldbe thesubjectofmuchmorevigorousdebatethanit usuallyis).

37

3 Complex Shapes

Perhapsthe simplestexamplesof complexthingswhichone comes acrossarecomplexshapes;in them,nothingischanging,andnothingis engagedinactiveinteraction withanythingelse.Evenso,theyarequite difficultto graspor describe.

A.Symmetry andOrderedShapes Oneofthefirststepswecommonly taketotryto makesenseofa shape is to lookforsymmetryin it. The derivationof the wordsymmetry— fromtwoGreekwordsmeaning‘with,or accompanying’ and‘measure’

—givesit theverygeneral meaning ofreferring topartswithsimilar geometrical properties;and, of course,manyof the thingswe come acrossdohavepartswithsimilarproperties.Humanbeingshavea right sidewhichisverysimilartotheirleftside;catsanddogshavefourvery similarlegs,insectshavesix,spiderseightandcentipedes many;andthe

legsarenotonlyverysimilar butarearranged inanorderly way.Itisan orderliness inthearrangement ofsimilar partswhichisusually meant by the wordsymmetry.Thereis no doubtthata shapewhichwecan describeasanorderlysymmetrical arrangement ofsimilarpartsismuch morecomprehensible andgraspablebythemindthanit wouldbe if it doesnotcontainanysimilarsub-parts,or if thosepartswerejustscat-

teredhiggledy-piggledy, without anyrational principles ofarrangement. However,thedegreeto whichonecanunderstanda complexsystem byfindinganddescribing a symmetry ofitsshapesisreallyverylimited. It turnsoutthatthereareonlya fewwaysin whichsymmetrycanbe produced,and this meansthereare relativelyfewpossibletypesof symmetry. Considerfirsthowonecouldproducesymmetry. Startwitha singleasymmetrical shape,suchas a hookdrawnona sheetof paper, whichbends,say,to theright.Therearebasically threewaysin which wecanarrangeotherhooksin somesortof symmetrical relationto it. 38

~tetation FIG.3a.1

Oneis to produceits mirrorimage;if the hookis reflectedin a mirror set at right anglesto the planeof the paper,a new hookwillbe produced,this time bendingto the left. Anotherwayof producing symmetry isto imaginethatthereisa lineperpendicular totheplaneof the paper,and that the hookis rotatedaroundthisas an axis.If the revolutiongoesthe wholewayround,360°,it of coursereturnsto whereit wasbefore,butifthewholeturniscompleted intwosteps,the firsthalf-turnof 180°wouldproduceanotherhook.Andonecouldalso producesymmetrical arrangements bymakingthe wholeturnin three, four,fiveor sixsteps.Allthe hooksproducedwill,of coursebe righthandhooksliketheoriginalone;butonecancombinetheserotational symmetries withmirrorsymmetries, andso obtainarrangements containingbothright-andleft-handhooks.Thereisa thirdwayofproducingsymmetry, simplybydisplacing theoriginalhook,througha certain distance,withouteitherrotatingor mirroringit. Thesethreetypesof changedeterminethe onlythreebasictypesof symmetrythereare— reflectional, rotationalandtranslational. Therearealsoonlya relatively smallnumberofwaysin whichthese symmetries canbecombinedwithoneanother.If oneisconcerned with flatpatterns,whichcanbe drawnonaplain sheetof paper,thereare onlyseventeen possiblearrangements ofcombinedsymmetries thatwill producea patternthat doesnot haveemptygapsin it. For instance, 39

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vera

BED

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ee

-

e. Re 3

©

Diagramof17symmetrygroups

iA

ee mt

at

of ag Se

& ce

& &

Com,

FIG.3a.3

pentagonsproducedby five-steprotationscannotbe packedtogether withoutgaps,thoughhexagons can.Theproofthatthereareonlyseventeenpossiblearrangements is quitedifficultandwillnotbegivenhere, butthedrawing3a.2showsthemall. Themostperfectexamples of symmetry onecomesacrossin thereal worldare the arrangements of atomsandmolecules in crystals.These cannot,of course,be seenwiththenakedeyeor evenwithanordinary microscope; but the positionsand arrangements of the atomscan be discovered bythe useofX-rays.Sincetheyarearrangedin solidthreedimensional structuresthereare morepossibilities of symmetrythan thereareinthetwodimensions ofa plane.Thereareinfactexactly230, but thereis little pointin anyonebut a chemistor crystallographer workinghiswaythroughthewholelist. In mostof the moreordinary 41

FIG.3a.4

affairsof lifeoneismuchmorelikelytocomeacrossthingswhichshow completely ratherthanfollowing onlysomepartialdegreeofsymmetry, anyof the preciselyspecifiedpatterns.In manyculturesartistshave usedpatternsymmetryas a methodfor introducinga certaindefinite senseoforderintotheirproductions. but not overwhelming in thestrictsensein whichwehavebeenusing However,symmetry, the wordhere,is certainlynot the onlypropertywhichcanimparta in degreeof visualunityto a shape.Thereare otherarrangements, ways,which whichthe partsarerelatedin somespecificmathematical the mind can acceptas orderly,evenwhen it cannotimmediately theorder.For instance,a underlining expressthe precisearrangement of twoarrangerecentartist,Max Bill,hasmademanyexplorations mentswhichmostpeoplefindto havea strongapparentorder.Oneis

42

basedon the arithmetical fact that 1 +24+3+4+5+6+ 7+8 adduptothirty-six.Billtakesa squarewitheachsidesixunitsinlength

anddivides it intothirty-six smallsquares; inthesehearranges different

tonesorcolours,eachcharacterizing oneofthe seriesof 1, 2, 4; 4, 55°, 7, 8.Eachgroupis symmetrically arranged,butthe wholearrangement of themwithinthe thirty-sixsquaresis not symmetrical in any strict formofsense,andyetisveryorderly.

B. Shapes,neitherSymmetrical norOrdered Many,probablymost,naturalcomplexshapesexhibitlittlesymmetry. Howcantheybedealtwith?Theconventional procedureis to thinkof them in terms of their outline(let us confineourselvesto two-

dimensional flatshapes, forthesakeofsimplicity). Butthisisnotvery

satisfactory. Theoutlineisprobablyverydifficulttodescribe; moreover, ifwearedealingwitha livingthingsuchasa fish,wormortadpole,the outlinewillchangedrastically as theanimalwriggles, yet clearlyin the samesensethe shaperemainsthesameor almostthesame.Finally,if onethinksonlyof theoutline,canweevensayjustwheretheshapeis

located?

Anotherwayoftreatingcomplexshapes,developed byHarryBlum, considerstheshapeasmadeup ofa numberofoverlapping circles,the largestthatcanbefittedintotheshape.Thecentresofthesecircleswill lieona lineora setoflines.Sucha lineisknownasthe‘medialaxis’or ‘symmetry axis’,sinceit expresses a propertyof the shaperelatedto a verygeneralized conceptof symmetry.This is illustratedbelowwith respectto a shapetakenfroma paintedreliefbyArp(3b.1).

Fic. 3b.1

43

Nowwecansaythatthelocationoftheshapeisgivenbytheposition ofthecentreofthelargestinscribedcircle.Andwecanaltertheshape slightly,whileretainingits basicform,by flexingthe symmetryaxis whileretainingthesamesetofcirculardisks(3b.2).

FIG.3b.2

To describea shapein theseterms,onehasto knownot onlythe symmetry axis,butalsothesizeofthecircleswhicharetobecentredon it (3b.3).

Fic. 3b.3

Oneofthesimplestwaysto providethisinformation isto regardthe circlesasbasesofconeswithsomestandardangleofslope(3b.4).Then theapicesoftheseconeswilllieona lineinthethree-dimensional space

abovetheshape,andtheheightofanyparticular apexwillbeprecisely

Fic.3b.4

44

relatedto theradiusofthecirclefromwhichit arises.Thewholeshape is thendescribedbythisone‘ridgeline’in three-dimensional space. The symmetry-axis descriptioncan be used veryconveniently in connection withsomesortsofgrowthprocesses. Allweneedto doisto giverulesfor the waythe sizesof the variouscircles,or the timesat whichtheyareinitiated,changeastimepasses.Forinstance,in 3b.5we haveassumeda branchedsymmetry axis,withcirclesbeinginitiatedata constantratefromthetopdownwards, and,wheninitiated,growingout at a constantspeed;the‘contourlines’givetheoutlineoftheresulting shapeatsuccessive intervalsoftime.Thiswayofrepresenting theresult is sometimes spokenofasa ‘grass-fire’: it is whatwouldhappenif one starteda firein a fieldof dry grass,whichspreadfasteralongthe symmetry axisandmoreslowlyoutwardsuntilit metsomeotheralready burntarea.

Fic. 3b.5

Thedrawings in3b.6showsuccessive stagesofa systeminwhichthe circlesareallinitiatedat thesametime,butgrowfasternearthelower

endoftheaxis,whiletheaxisitselfbecomes curved morerapidly atthe other,slow-growing end.Clearlytherearea greatmanychangingand growingshapeswhichcanbe describedin thismanner.

FIG.3.b.6

45

The strengthsandweaknesses of methodslikethiscanonlybe appreciatedwhenonetriesto usethem.Hereis an examplein which Blum’smethodhasbeenfounduseful.Peoplewhotrytoreconstruct the evolutionof manfromhis ape-likeancestorshaveto workfromthe comparatively fewrarefossilsoftheintermediate forms—the ‘missing links’—thathavesofarbeenturnedup.Someofthesebones,including someof the mostimportantof them,havecomplexshapeswhichare difficulttograsp.Thereis,forinstance,a famousbonewhichwasfound at Sterkfontein in SouthAfrica,andisclearlypartofthepelvisofsome creaturewhichbearsresemblances bothto the greatapesand to the humanspecies.It is a puzzlingsortof shapeto geta holdof. In fact althoughmanybonesin the bodyhavebeengiventechnicalnames, basedonrecognizable formswhichtheysuggest,thisboneistechnically knownas ‘theinnominate’, that is to saythe unnamed,presumably becauseit doesnotreallysuggestanythingin particular.However,it is oneof the partsof the skeletonthat has to get modifiedduringthe evolutionfromrunningonallfoursto walkingupright,anditschanges in shapearethereforeveryimportantin connection withtheevolution oftheuprightpositionofman. Therehasalwaysbeenconsiderable controversy amongstudentsof thesematters,whetherit reallyshowsmoreresemblance to thesimilar bonein the apesor in the humas.One can see their difficulties by lookingat thedrawingsin3b.7and3b.8whichshow,fromtwodifferent pointsofview,theinnominate bonesofthechimpanzee, modernman,a modernpygmyofsmallstatureandtheSterkfontein fossil.Mostcomparisonsthathavebeenmadehaveinvolvedextremely elaboratemeasurementsoftheoutlines,andcomplicated statisticalanalyses,resulting in tablesoffigureswhicharenotveryeasyto grasp.However,Charles OxnardhasappliedtheBlumtechniqueof‘medialaxistransformation’, bywhichtheshapeofthecomplexoutlineistransformed intosomewhat simplershapesof internalmediallines.Thismakesit easyto seethat fromsomepointsofview,forinstancethatfromwhichit wasdrawnin 3b.7,the fossilhas strongresemblances to the human;whilefrom anotherpointofview,suchasthatusedin 3b.8,it is muchlesslikethe humanandmorelikethechimpanzee. Thusthemethodmakesit fairly easyto visualizethebroadoutlinesoftheresemblances anddifferences betweentheseforms.It doesnot;however, easilyresultin numerical or quantitativeestimatesof resemblance. Moreover,it is undoubtedly a weakness thattheanalysis hastobemadeona seriesoftwo-dimensional outlines,whereasreally,of course,one is tryingto comparethree46

dimensional solidstructures.However, it isalwaysdifficult,exceptfora fewexceptional people,to visualizesolidstructuresveryclearly,and mostpeoplehaveto be contentwithseeingwhatthree-dimensional

shapes looklikeintwo-dimensional projections, aswehavedonehere. Chimpanzee i

Modernmarr

|

Sterkfortcir Pygmy

Fic.3b.7

Chimpanzee

ie Ag

Sterkfontein Pygmy

Fic.3b.8 47

4 TheStructureofComplex Systems

Ashape,howevercomplex,canonlybea description ofanappearance; but to beginto understanda thingor a system,wehaveto findout aboutitsstructure.Thiswillbethesubjectofthischapter;in laterones weshallgoonto discussthechangesandoperations ofstructures. Perhapsthesimplestkindofstructurea complexsystemcanhaveisa hierarchical chainof command,suchas onefindsin an armywithits generalat the top, its battalioncommanders, companycommanders, platooncommanders and so on downto the commonsoldier.If one makesa diagramwith a dot for eachindividual,then they can be arrangedin a tree-likeorder,corresponding to the chainof command

andresponsibility.

This is, of course,a verysimpletypeof organizedstructure,and ofhumanrelationships based whenwearedealingwithan organization on thisprincipleit is usuallyquiteeasyto discoverwhichlevelof the hierarchyanypersonbelongsto.Buthemaybelongtodifferentlevelsin

different hierarchies. Someone whoisa private soldier inanarmymay atthesametimebeamember ofParliament, orapriestinanorganized church,andthereforeoccupymuchhigherlevelsin thosehierarchies. A. Hierarchies

Theconcept ofa hierarchy isaverybasiconeinconsidering theorganizationof a complexentity.Weare so usedto it that whenwefind ourselvesin a socialset-upwhichwedon’tunderstandour firsttendencyisto ask‘whoisbossaroundhere?’Andwhenwetrytoorganize a socialsystemofsomeotherkind,perhapsmoredemocratic andmore

pluralistic, thereisoftena greattendency forit gradually toturnitself

intoa hierarchical systemofthetraditionalkindin whicha fewpeople bosstherest. It isaprincipleoforganization whichhasbeenfoundveryconvenient

48

General

Colonels

Captains

A SimpleHierarchy FIG.4a.1

in dealingwithmanyorganizedsystemsapartfromthoseinvolvedin man’ssociallife. For instancein biologyit is convenient,in fact probablyessential,to distinguish betweendifferentlevelsof operation whichcanbeconsidered aslevelsina hierarchical system;forinstance, theecological level,whichincludesallthelivingthingsandthenatural resources available ina certainregion;theleveloftheindividual animal, e.g.a rabbit;the levelof its organs,its liver,kidneysand so on;the cellularlevel;andthenseveraldifferentsub-cellular levels. The stillonlypartiallysolvedproblemis: whenis onetempted,or whenis it justified,to analysea complicated systemintoa hierarchical structureinvolvingdifferentlevels?The bestanswerthatseemsto be availableis thatwedo thiswhen,havinganalysedthecomplexintoa numberofmoreelementary units,welookat therelationships ofthese unitsandfindthattheinter-relations fallintoa fewseparateclasseswith fewintermediates. Forinstance,theremaybea numberofquitestrong interactions anda numberof weakerones,but fewin between;or the activities goingoninthesystemmaybeclassified intoveryfastonesand veryslowones,againwithfewintermediates. If youfoundyourself confronted withanarmywitha strangeuniform,whoseinsigniaofrank youdidnotunderstand, youwouldfind,ifyouwereallowedto observe 49

things,thattherewassomeindividualwhowouldspendfiveminutes decidingthatB companywouldadvancealongthatroad,accompanied byX batteryofartillery;andBcompany andX batterywouldspendthe nextcoupleofhourstryingto doso;whilethispersonhadgoneonin the nextfiveminutesto saythata squadronoffighterbomberswould carryouta raidlastingforfourhourson someothertargetand,long beforetheyhaddonethat,wouldorderthetanksto dosomething else. Hewouldbeactingona timescalemuchfasterthanthatofthepeople hewasinteracting with.Thiswouldbegoodgroundsforsayingthathe washigherup on the hierarchy,at a levelabove,capableof andempoweredto giveordersto anddelegateresponsibilities to,thepeopleat thelevelsbelow. The differentclassesof interactions neednot alwaysbe connected withtimescale.If youlookat allthecellsinthebodyofananimal,you findthattheyfallintogroupswithstronginteractions betweenthosein thesamegroup(forinstanceallthekidneycellsinthekidney,orallthe livercellsin the liver),and muchlessinteraction,thoughstillsome,

between thekidney andthelivercells.Youcouldthensaythatthecells

werearrangedina hierarchical organization, withorganssuchaskidney and liverforminga higherlevel,and the cellsgroupedunderthese variousorgansmakingup the levelbelow.If one wantsto ask,for instance,isa citya hierarchical organization?, onewouldhavetolookto seeif onecoulddetectimportantactivitiesandinteractions whichfall

intocontrasting groupsofintensity ortimeconstants (I doubtif one

wouldfindmany;I donotthinkthatcitiesarehierarchically organized in theiractivities,thoughtheymayoftenbe in theiradministrative apparatus). It is essentialto rememberthathierarchies, in the sensetheyhave beendiscussedhere,are onlydescriptions of structure;theydo not

implythat‘lower levels’ inthehierarchy are‘lower’ inallthepossible

sensesofthatword.Forinstance,it isclearthatsomespecialfunctions maybedelegated to membersofa fairlylowlevelin thehierarchy(e.g. toa colonelora captaininanarmy),andhemaythenhavefullresponsibilityfor that particulartask.Again,membersof a lowlevel(e.g. dustmenorworkersinasewageplant)maycarryoutfunctions onwhich allthe higherlevelsarequitedependent.The wholesubjectof howa hierarchically organized humanassociation works—whatisitsstrategy, whatitstactics,andwhogivesordersaboutwhat?—isoneofthemajor preoccupations oftheimportantsubjectofManagement Science. Simonhasbroughtout oneof the reasonswhyorganization intoa 50

hierarchyis bothsousefulandso usual;he putsit in a parableabout twowatch-makers, Horaand Tempus,bothof whomproducedvery fine,accuratewatches.But Horahad designedhis on a hierarchical scheme;he couldput togetherten componentsinto a stablesubassembly,whichhe couldleaveasidefor a time;then he couldput togetherten differentsub-assemblies intoa majorpart;andfinallyten majorpartsintothe wholewatch.Tempushadn’tplannedit thatway. Hiswatchhada thousandparts,justas Hora’sdid.Buthe hadto get themassembledall at onetime;if he had gotonlyhalfof themput together,butthenhadtostopworkfora bit,theyrapidlyfellapart.And, of course,producingsuchgoodwatches,they wereboth veryoften calledon by customers,and hadto stopwhattheyweredoingat the moment,to servethemor takeorders.SoHorafoundtheinterruptions a bit of a nuisance,but theyneversethimbackmorethana ten-stage operation;butpoorTempusfoundit practically impossible to complete a watchat all;hemighthavegotit to stage950,whenthetelephoneor — thedoorbellrang,andbythetimehecouldgetthecustomeroutofhis hairwithoutlosinghiscustom,thewatchmighthavefallenapartdown to stage250or evenworse. Thisis,ofcourse,nomorethantherationaleonwhichHenryFordI madehis fortune,and saddledthe modernworldwiththe materially enrichingbut humanlybrutalizinghierarchically organizedassembly linesofmassproduction.It isa methodthatworks;butitspriceisa bit stifferthanyoumightguessat firstsight.Buthierarchical organization has,in fact,beenadoptedby an extraordinarily widerangeof natural systems.

B.OtherTypesofOrder Therearemanytypesoforganization in whichthecomponent elementaryunitsarenotrelatedto oneanotherinastrictly hierarchical order, but in some more complicatedway. The structurecannot be representedby a simplehierarchical tree diagramas in the drawing 4a.1;but,asweshallsee,onecanoftenshowit asa somewhat modified tree.Therearealsootherwaysof makingdiagramsofthesestructures whichlookratherodd at firstsightto olderpeople,althoughyoung childrenarenowoftentaughtaboutthemin elementary schoolswhich teachthe‘NewMaths’. It willbewelltobeginbyconsidering anorganized structurewhichis 51

notchanging; neitherthestructureasa whole,noritscomponent parts, alterastimepasses;buttheunitshavecertainrelationswitheachother, and wewantto expressthesein a waywhichmakesit easyto get a generalgraspof howthe wholething is put together.Take as an exampleanorganized complexmadeupoffiveelementary units,a, ), c, d ande, whichmaybe anythingfrom,say,individualpeoplewhoare relatedbybondsoffriendshipat variousdegreesofintimacy,or towns at variousdistancesfrom each other, all the way up to such complex

factorsas population,food,pollution,naturalresources,capitalinvestment,etc.,whoserelationswitheachotherconstitutethe‘organization’ oftheWorldProblem. | Obviously wecannotsaymuchaboutthe structureof the organizationunlessweknowsomething aboutthestrengthoftherelationsorthe interactionsbetweenthe units.Obviouslyalso,we shallneverknow enoughaboutthesestrengths.Weshallalways,oratleastshouldalways, betryingto discovermore.Whatweareconcerned withhere,however, is the mostconvenient wayof expressing whateverwedo knowat the presenttime. The mostcompletewayof expressing thisinformation is to listthe fivecomponents a, 5, c, d ande alonga horizontallineand alsovertically,andat eachsquarewheresaythe4columninterceptsthec row, writedownsomefigureindicatingthe strengthof the interactionbetween/ andc(wherethe4columnmeetsthe/ row,wecaninsertsome signindicating identity).Thiswillgivea tableor‘matrix’, madeupofa lot of figures,likethe chartsof distancesbetweentowns,e.g.in the Automobile Association handbook. a b c d e 2°0 08 4°1 2°9 SS 2°0 x 4°I 2°9 a) I‘O 0-8 41 x 31 QS 471 2°9 31 v 3°9 2°9 1-9 IO 3°9 x »

Fic. 4b.1

It isdifficultforanyonewhoisnotanarithmetical geniustogetmuch senseoutof it merelyby inspection. Onefirststepto makingit more comprehensible isto forgetaboutbeingreallyaccurateandtogroupthe figuresintoa fewclasses.Sometimes it isgoodenoughtosimplifyreally drastically, andsimplysaythata givenpaireitherdoesinteractenough to countor doesnotintereactenoughto count.Or onemightbea bit 52

moreinformative,and say that it interactsstrongly,or it interacts weakly,or doesnot interact;or one can haveastill moredetailed classification includingidentity(5),strong(4),moderate(3),weak(2) andveryfeeble(1)interactions. Thenthetableaboveturnsinto: a

a

b c d

Fic. 4b.2

e

b

c

Se

= ee

d

eS

Poe ee eS a. a er 3

2

e

I

4

5

It isclearthatalthoughthesesimplifications maymakethesystemsa

biteasiertocomprehend, it willinvolve making thepicturelessaccur-

ate.Wearelosinginformation in orderto gaincomprehensibility. Thenextsteptomakingthepicturemoreeasytograspistorearrange thingsto bringout anynaturalgroupstheremaybe in the system. Thereareseveralwaysofdoingthis,eachwithitsownadvantages and disadvantages, andsomewithmorevisualimpactthanothers. Onevisuallyappealingwayis to representthe strengthsof interactionsbytones,orsizesofdots,insteadofnumbers.Thusonecouldturn the tableabove(whichclassifies relationsin fiveways)to a patternof tonesorspotslikethefigures4b.3or4b.4.Thisin itselfdoesnotseem to makethepicturemuchmoreeasyto understand. However,wecouldthentry to rearrangethe rowsandcolumnsin sucha wayasto producea morecomprehensible pattern.Forinstance,

the rearrangement in 4b.5or 4b.6producesa darkareaat thetop left occupiedby the threemembers,A, E, D, and anotherat the bottom rightwherethereis stronginteractionbetweenthemembers B andC. Forinstance,if A,B,C,D andE werepeopleallacquaintedwitheach otherA,E andD wouldbeonegroupofspecially closefriends,andB andC another.Thetroubleaboutthisprocedureisthatit isnotalways obvioushowto rearrangethe rowsandcolumnsto producethe most clear-cutpatterns.

A E

Fic. 4b.5

D B C

RSL

A. Ee

fo Se

Bd

oe

eg

4s Be 3 ee ee ee I a. Fee A

B

C

D

e

Anotherwayto exhibittherelationsin a visualformis to turnthem intoa ‘treediagram’ or‘dendrogram’. Thishastheeffectofshowingthe structureas a modifiedhierarchy,withsomegapsand jumps.To do this,the fivecomponents are writtenin a lineat the bottomandthe appropriateonesare connectedtogetherat successively higherlevels, indicatinginteractions, of strengths4, 3, 2 and 1. Againthe diagram wouldbesimplerifonecouldfinda suitablearrangement intowhichto placethe elementsin the lowestline. It is usuallybest to start by groupingtogetherthosewhichinteractmoststrongly(4b.7).In this example,a and d, d and e, and b and ¢, all interactat strength4. Furthermore wemaynoticethatd interactsmorestronglywithb andc 54

Level |

Level 2

Level3

Level4

a

Fic.4b.7 thana ande do.It isfairlysimple,therefore,in thiscaseto seethatthe bestarrangement willbeputto a, e andd in onegroupandb andc in another,andtohaved nextto b andc.Thusa goodordertotrywillbe a,e,d,b,c.Nowinthelineabove,representing Level4,wecanconnect a andd, e andd, andb andc. AtthenextLevel,3, wehaveto makea channelof communication betweena ande (thisin the diagramalso makesanotherroundabout connection betweene andd, butasthereis alreadya shorterconnection betweenthemat Level4, this doesnot signify).AtthisLevelwealsohaveto connectb andc withd. Atthe nextLevel,2, the onlynewconnections to makearebetweenb anda ande.Finallyat Level1wewillhaveto establisha connection between c anda ande. Thewaytousesucha diagramisasfollows: ifwewanttoknowwhat istherelationbetweenb andsayd,wehavetodiscover towhatLevelin thetreewehavetogobeforewefinda bridgeto getacrossfromoneto 55

theother.In thiscaseit isat Level3. If wewanttogetfromb toa ore wehaveto goup to Level2. Anotherwayofdrawingexactlythesameinformation asthereisina treediagramisto makewhatiscalleda Venndiagram.In thiscomponentsarewrittendownnotina line,butinsomesuitablearrangement on the page.Thenoutlinesare drawnenclosingthe oneswhichinteract together,the heavinessof the line correspondingto the strength of the interaction.So we shalldraw heavylines around the pairs A and D, E

andB, andB andC. Nextwedrawa thinnerlineroundthe groups whichinteractwithstrength3 or more.Thisgivesthe twogroups,A, D,E andB,C,D.ThenwithastillthinnerlinewesurroundA,B,D,E, whichinteractwithstrength2 or more.Andfinallywitha thinnerline stillwebringin C whichincludesinteractions at strength1(4b.8).

Fic.4b.8 56

Thesemethodsofmakingdiagramsof therelationships areusefulin sofarastheystimulatetheimagination, andhelponeto geta ‘feeling’ forthesituationwhichwillallowoneto seehowto gofurtherintoit. The diagramsarestillobviously verycomplicated. The onlywayto

prevent thisistoleaveoutsomemoreoftheinformation intheoriginal table.For instance,insteadof usingfour categoriesto measurethe strengthof interaction(strong,moderate,weakand veryweak),we mightuseonlythree,lumpingtheveryweakalongwiththeweak.We shouldthensimplifyourtreediagramandVenndiagramto 4b.9and 4b.10.

If wewentdowntoonlytwoclasses(strongandweak),nowlumping themoderateoneswiththestrongones,weshouldgetthefigures4b.11 or4b.12.Thesearegettingquiteeasyto understand,butunfortunately theydonottellus verymuchaboutthesystemin detail. Level |

Level2

Level3

Fic.4b.11 ~~Fic.4b.12

57

Anotherwayof forminga mentalimageof the system,whichis

stimulating to theimagination of peoplewholiketo thinkof solid

structures,istoregardthelinesintheVenndiagramascontourlineson a map,andusethemto buildupa ‘mountain’, whosethree-dimensional shapewouldthen incorporatethe informationin the.Venndiagram. This can be donequitestraightforwardly if we haveuseda lot of simplification to geta treediagramlike4b.11,anda Venndiagramon whichtheloopsat anyoneleveldonotintercept.

a

d

2

b

C

FIG.4b.13 If wehaveusedlesssimplification, andVennloopsof a givenlevel interceptone another,we haveto be contentwithlessprecisionin makingthemountain.With a bitoffiddlingit is oftenpossibletomodel a three-dimensional structure,whichgivesquitea goodoverallpicture

ofrelationships (4b.14isanattempttovisualize 4b.10asa mountain). There is still anotherdifferentwayof givingvisualformto the relationships suchasthosesetoutinthetablewestartedwith.Thisisto

writedownthefiveelements,a, b, c, d ande onthepageratherasone did for the Venndiagram,then drawlinesbetweenthosewhichare relatedtooneanother.If weareusingseveralgradesofrelationship, we canusethickerlinesforstrongrelationships andthinnerlinesforweaker ones. We then get what is calledan associationgraph,4b.15,a

methodological toolwhichhasbeenmuchusedbythoseplanning buildingsor cities.

Fic. 4b.15

It wouldbe particularlyusefulif onecould‘scale’suchdiagrams. Thatistosay,arrangethefivepointssothatthedistances betweenthem areinverselyproportional to thestrengthsoftheirrelationships, sothat

theclosely relatedonesareneartogether andtheweakly relatedones fartherapart.Thisis justwhatan architect wouldliketo dowhen

planninga groupofbuildings.Anothergroupofworkerswhowouldbe veryinterestedto developsuchmethodsarepeoplestudyingthenatural grouping(species,genera,etc.)of animalsand plantsbasedon the characteristicsof the organisms,rather than on their supposed

evolutionary history.

Unfortunately it is notalwayspossibleto carryoutan accuratescaling.Forinstanceifyouhaveonlythreeelements, a,b andc,it mightbe thattherelationship betweena andb willbesay2,andbetweena andc, 3, butbetweenb andc, perhaps20.Thismightbeso,forinstance,if a wasa centralcity,b andc suburbsandyouweremeasuring thetimeof 59

travelbetweenthem.Clearlyonecannotplacethreepointsona planeso

thatthedistances between themare2, 3 and30.Youcannothavea

triangleunlessthelengthofthelongestsideis lessthanthesumofthe lengthsof the othertwo sides.Sometimesone can get out of such difficulties bychangingthecharacteroneis measuring. In thiscasethe interestingrelationbetweenthe city and the two suburbsmightbe broughtoutsufficiently if wemeasurenotlengthsoftimeoftravel,but the numberof tripspeopleactuallymadebetweenthe threepairsof points.Youwouldpresumably finda lotbetweena andb, andbetween a andc, andquitefewbetweenb andc, andit mightbepossiblethat thesefigurescouldbeplottedonto a properlyscaleddiagram. Procedures forscaling,ortryingtoscale,setsofrelationsmaybecome rathercomplicated. I willdiscussthem a littlemore,but I wouldadvise

thosewhohavenosenseofmathematics thattheywillnotlosemuchif theyskiptherestofthissection.

It isnotpossibleto scale,accurately, theassociation graphoftheset ofinteractions wehavebeenusingasanexample.If thepointsa,b,c,d, e, wereto besetapartbythereciprocal ofthecloseness ofinteractions, thedistanceshouldbe asin 4b.16. a

e

4/3

b c

2 4

d Fic. 4b.16

e

d

b

I

=. 43 4 4/3 I

It is quiteeasyto arrangea, d ande at therightdistances apart

(4b.17).Thenb andc shouldbe oneunitapart,somewhere alongthe circlebed,whichisdefinedbytheirdistancefromd; butthenb should alsobeoncircleabtogettherightdistancefroma,andalsooncircleeb to berightwithregardto e; andit cannotbe both.Onewouldhaveto acceptsomecompromise, puttingb perhapsat B’,a bittooneara anda bittoofarfrome.Thereareevenworsedifficulties aboutc. It shouldbe fourunitsawayfrombotha ande, andthiswouldtakeit rightoffthe diagram.Thebestonecandoistoputit asfaraspossiblebeyondtheab andebcircles,withoutlettingit gettoofarawayfromd. In general,however, onesimplyhastoacceptthatinanycomplicated

situation completely accurate scaling islikelytobeimpossible. Various methodshavebeenworkedout forestimatingthe degreeof distortion whichanygivenscaleddiagramimposeson theactualdata.Thereare

60

Fic.4b.17

alsomethodsforusinga computertocalculatethebestpossiblescaling thatcanbemadefrom a givensetofdataonto,say,a flatsheetofpaper, or possiblyas a three-dimensional model.However,this is onlyfor reallyprofessional purposeswherea highdegreeofquantitative accuracy is required.Fairlyroughand readyscaledassociationgraphs preparedwithnothingmoreelaboratethancommonsenseanda bit of trialand erroroftengiveonequitea goodmentalpictureof a complicatedsetofrelationships. To givean exampleI'll quoteone givenby PhilipTabor.This showedthe relationships betweentwenty-onedepartmentsin a fairly largetownhall,therelationships beingmeasured bythenumberoftrips andmessages thatpassedbetweenthem.Theactualfiguresaregivenin 4b.18.Fromtheseyoucanmakea scaledassociation graphwhichisnot toobadlydistortedandwhichcomesoutlookinglike4b.19. 61

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Thisshowsclearlytheparticularly closerelationship between1and8 and 1 and2; whilebetween2 and8 it wasratherless,but stillquite strong(1 wasthe TownClerk,2 wasthe Treasurerand8 the Estate

Surveyor).

Finally,onecanusesucha scaledassociation graphas a basisfora Venndiagramifonemakesa simpleonewithnon-overlapping contours. It comesoutlookinglike4b.20,andthatcanbeturnedintothemountain4b.21.

5 Processes in Complex Systems

We haveso far beenconsidering the structureof systemsin which, althoughthingsaregoingon,thesystemitselfremainsthesameastime passes.Wenowhaveto considersystemswhichalterwiththelapseof time. Timeisoffundamental importance intwoways.Foronething,itisan essentialpart of reality.Everythingreal lastssomelengthof time, changingmore,lessor inappreciably, astimepasses.Aninstantaneous momentis an abstractnotion,sometimesusefulbut neverreal.As Whiteheadremarked,thepresentis reallythefringeofmemorytinged withanticipation. Then,again,anyattempttoinfluence theworldhasto

actontheprocesses whicharegoingon.Temporal change isthebasic

mediumof allactivity,includingourown.For boththesereasons,an understandingmerelyof the structureof a complexsystemis not enough;wemusttryto understandit asaninter-related setofprocesses.

A.OpenandClosedSystems A firstimportantdistinctionis betweenclosedand opensystems.A closedsystem,as the nameimplies,is one that is entirelycontained withinsomeenvelopethroughwhichnothingpasseseitherinwardsor outwards.Allchangesgoonwithinthebagwhichinsulatesthesystem fromtherestofthe world.In an opensystem,in contrast,thingspass intothe systemfromthe outside,areprocessed, andsomethingelseis extrudedoutwardsagain. The conventional mechanical dynamicswhichareusuallytaughtin school—ballsrollingdowninclinedplanes,levers,cog-wheels, bodies collidingwitheachother,orbilliardballsbouncingoffcushions,andall the rest of ‘Newtonian mechanics’ —reallyappliesto closedsystems only.Thegreatlaws,oftheImpossibility ofPerpetualMotion,andthe SecondLawof Thermodynamics, that thingsalwaystendto become

64

lesswellordered,arelawsofclosedsystems.Butnearlyallthesystems onehastodealwithintherealworldareopensystems,becausetheyare reallypart-systems. Theonlycompletely closedsystemis the universe asa whole,andit isonlya fewastronomers whohavetothinkseriously

aboutthat.

It is quitedifficultto thinkof naturalexamplesof smallerclosed systems,butperhapsa barrelofwinewhichisgradually maturing,ora cheesewhichis ripeninginsidean airproofcontainer,wouldbe examples.Sinceanysortof changerequiressomeenergy,the closed systemcanonlyundergochangeifit includesa stockofenergy-yielding materialwhichcanbe graduallyutilized.It is the sugarin the grape juicewhichsuppliesenergyforthefermentation processes inthematuringwine.Even‘Space-Ship Earth’,whichweareoftenadvisedtothink ofasa bodycompletely isolatedinspace,dependent onlyonitsstoresof enclosedenergy,is actuallyall the timereceivinga veryconsiderable supplyofenergyfromtheradiationofthesun.Animals, plants,human society,ecosystems andso on are obviously opensystems,sincethey alwaysreceiveinputsoffoodorothersourcesofenergy,andrawmaterialsofvariouskinds;andproducevariouskindsofwastesandartefacts.

B. Growth Theword‘growth’ is oftenappliedto almostanythingwhichincreases in sizewiththepassageof time;andwehaveonlyto admitthepossibilityofde-growthornegativegrowthtoapplyit alsoto systemswhich getsmallerastimepasses.Changeofsizewithtimeis sucha common phenomenon in human,socialoreconomic affairsthatit isnecessary to havesomenotionofthewaysinwhichit canbedescribed. Thesecanbe mostpreciselyandneatlyexpressed in mathematical language; but the basicideasarequitesimple,andcanalsobe expressedwithoutmuch difficultyin ordinaryEnglish;it willbecomeapparentthatthemathematicalsymbols,whichat firstsightscareoffsomepeoplewhohave gotintotheirheadsthefoolishnotionthatmathematics is toodifficult forthem,arereallyquitesimpleto understand. Growingthingsmaybe of twokinds.Theymaybe populations, whosesizecanbe estimatedbycountingthenumberof individuals in them;for instance,peoplein a nation,or bacteriaor othercellsin a culture.What increases,then, is the total numberof countable individuals.Alternatively the growingsystemmaybe a continuous

65

mass,whosesizehasto beestimatedbyweighing it or measuring it;in thiscasethe thingthatincreasesis the numberof unitsof weightor unitsofmeasurement. In discussing thebasicideasaboutgrowththere is usuallynoneedto makethisdistinctionexplicitly. Weshallreferto boththesemeasuresofthegrowingsystemasmeasuresofitssize. Thesimplestformofgrowthisonein whichthesystemincreases by acertainamountineachunitintime.Thatistosay,therateofgrowthis constant.If,forinstance,atthebeginning oftheprocesswetakethesize ofthesystemasXp,thenafteratimef,itssizewillbex. + &t,wherekisthe amountaddedin eachunittime.Thisiswhathappenswhen aseries of equal-sized dropsofwaterfallfromaleakytapintoabucketplacedbelowit. In livingsystemsgrowthof this sort is ratherrare. Instead,the amountofnewgrowthis usuallyverymuchdependentontheamount of thegrowingsystemwhichis alreadyin existence. For instance,the numberof childrenbornin a populationdependsin someway(not alwaysa verysimpleway)on the numberof existingindividuals who canactas parents.The simplestsituationof thiskindis onein which therateofgrowth(i.e.theamountaddedinunittime)dependsdirectly onthesizeofthesystemalreadythere.Thiswouldbesoif in a human

population everyone gotmarried,andeachpairof parentsalways

produceda certainnumberofchildren(sayfour),allofwhomlivedto maturityto becomeparentsin theirturn.Anotherexamplewouldbea fatteningcalfwhichalwaysputona givenfractionofitsexistingbody weightduringthecourseof thenexttwenty-four hours. Exponential Growth Thissortof growthis knownas exponential growth.Anotherwayof expressing it istosaythattheabsolutesizeincreases exponentially. This nameis derivedfromthe mathematical expression of the situation.If the sizeof the systemis.calledx, and the rateof increasein sizeis writteneitheraso (i.e.the difference in x whichoccursovera very t

shorttimedt) or somethingevenmoreshortlyas x. If this rate of es proportional increaseisdirectly tothesizeweshallhavetheequationeae t

= kx,where&istheconstantofproportionality. Fromthisequationit

follows mathematically (though wedonotneedheretogointowhythis

isso)thatat anygiventime,¢,thesizex = xye*’wherexyistheinitial sizefromwhichthesystembegan.Thewordexponential referstothefact

66

thatin thisformulatime,¢,comesin asa powerofthenumber,e,as2 comesinasa powerwrittenabovethelineintheexpression .”. This typeof growthhassomeratherremarkable properties,which canmosteasilybeseenbydrawinga graphoftherelationbetweensize andtime.

Ade

Fic. 5b.1

% LAL *@ é PYLE

Drawing5b.1showsthe growthof a simpleexponential system.It startswithoneunitat timet,; at timet, it addssomething ofthesame sizeitself,i.e.it adds1,or doublesitself.Bytimet, it addsonanother pieceat the samesizeas it is, i.e.doublesitselfagain.Thusit grows from1to 2 to 4 to 8, 16,32.The amountsaddedin eachintervalget largeras the systemitselfgetslarger.It willbe seenthatthe absolute sizeseemsto begettinglargerat a fasterandfasterrate.Thisisnecessarilysosincethe rateat whichit increasesis proportional to thesize itself,sothatifthatgetsbiggertherateofincreasemustalsogetbigger. Onepeculiarconsequence of thisis that,oncetheprocesshasbeen goingonforsometime,therateofincreases becomes sofastthatit only takesa shortperiodfor the systemto add on to itselfas muchas everything it hadcontainedin thepast.Considerforinstancea populationof an annualplantin whichat the endof eachseasoneachplant producestwo seedswhichgivetwo plantsin the followingseason. Startingfromoneplantthenumbersin thepopulation go1,2,4,8, 16,

67

32,64,128... If youcareto addupto thetotalnumberofplantsthat hadeverbeenin existenceup to andincludinganyparticulargeneration,saythatinwhichtherewere128individuals, youwillfindthatthe totalofthepreviousgenerations amountto 127.Thusin sucha system youcouldalwayssaythatofalltheplantstherehaveeverbeen,more thanhalfarealiveat the presenttime.Thissortof argumentis often used,eitherto spreadalarmand despondency, or alternatively in a boastfulway, about situationsin human populations(of all the scien-

tists,or artists,or houses,or automobiles, or crimesof violence,etc., etc.,thattherehaveeverbeen,morethanhalfhappenedinourlifetime).

Thisis a simpleconsequence ofexponential growth—if exponential growthreallyoccursforverylong,whichweshallseeis verydoubtful.

Compound InterestandDiscounting theFuture Oneofthemostwidelyknownexamples ofexponential growthismoney

putoutatcompound interest. Youlend{100at6percentinterest, and

attheendofthefirstyearyouhavegot£106;attheendofthenextyear youget6percentnotonthe£100buton£106,andsoon.Areasonably accurateformulaforwhatwilleventually happenisthe‘Seventy Law’.If therateofinterestis X percent,thesumyouhaveinvestedwillhave doubledin70/Xyears.At10percentitwillhavedoubledinsevenyears;at6

percentitwillhavedoubled insomewhat undertwelve years; anditwillgo

ondoublingagaineverysevenortwelveyearsasthecasemaybe. Thisisfineifit isyourownmoney.Ifyoucanlaydown£100andget a steady6 percentonit, in 100yearsthiswillhavedoubleda bitover eighttimesandwillbegettingonfor£26,000.Anicelittlenest-eggfor yourgreat-grandchildren. It isprobablymoreimportanttoappreciate howthesystemworksin reverse,as it were.Somebody startsbuildinga factory,or undertakes someotherlong-termexercise, whichin,say,thirtyyearsisgoingto be causingpollutiontowhichsocietyhasbythattimewokenup,andwhich it willwantto control.Sayit wouldcost£100,000to installtheextra mechanisms requiredto dealwiththe dangerof pollution.If thefirm

building thefactory isnotgoingtobeobliged legally, orbysomeother

socialpressure,to providethispurification plantuntilsometime about thirtyyearsin the future,it can’tpossiblyafford(in straightfinancial terms)tobuildit intotheplantfromthebeginning. Thirtyyearshence, £100,000willrepresentonlyabout£20,000now,at say6 per cent compoundinterest;andthatis clearlynot nearlyenoughto buildthe

68

requiredmachinery.If, insteadof spendingthe £100,000on building the purification plantintothe factory,whereit won’tbe demandedof youforthirtyyears,youinvestedit in something elseat 6 percent,it wouldhavedoubledmorethantwiceand be worthnearly£500,000 beforeyouwerecalleduponto providetheanti-pollution facility.The

financial systemis suchthatpeoplearecompelled to discount (i.e.

neglect)the future,at a rate whichis an inverseof an exponential growthrate.It forcesoneveryone a veryshort-termpointofview.This hasbeenoneofthemainreasonswhyourtechnological advanceshave landedussofarinthesoup;andit presentsoneofthemajordifficulties in seeinghowwecanplanmoresensiblyfor a reasonablylong-term future. Accelerated Exponential Growth Thisissimpleexponential growth;buttherecanbe,andoftenare,even moreacceleratedtypesof growth,whichone mightcall second-or

third-order types.Onesortofsecond-order growthwouldbeif the

fractionof the existingsystemaddedon after each intervalitself increased, asforinstancein a humanpopulation in whichhealthconditionswereimprovingsothatmoreof thebabiesbornsurvived.In the exampledrawnin 5b.2,it hasbeenassumedthatthefactorofincrease aftereachintervalincreases by$ateachstep,sothattheygo2,23,3,34 ... Thisresultsinthenumbersin thesystembeing1,2, 5, 15,525.. insteadof 1,2, 4, 8, 16... as theywouldbe withsimpleexponential growth.

Fic. 5b.2

69

Anothertypeofsecond-order acceleration isproducedif eachunitin thesystemisgrowinglargeratthesametimeasthesystemisgrowingin numbers;forinstance,eachpersonin a populationis demanding more and moreof something,suchas steel,as timepasses.In 5b.3,the numbersin thepopulationgrowin a standardexponential way,1,2,4, 8, 16... but eachindividual’s sizeis enlargedby 50percentat each step,goingI, 1°5,2°25,3°375...

Fic. 5b.3

Ofcourse,ifoneputstwosecond-order exponential growthstogether, togeta third-ordersystem,it growswithenormous acceleration —thisis whatishappening, forinstance,indemandsonresources, inmanyparts ofthe worldtoday. Limitsto Growth

Anotherverydramaticresultof exponentialgrowthoccurswhenit 7O

happensin somesystemwhichhasnaturallimitsthat willeventually bringit toa stop.Thereisa well-known storyofa farmerwhonoticeda water-lily onhispond,whichdoubleditssizeeveryday.To startwith,

ofcourse, itcovered onlyaverysmallareaofthepond,andthefarmer saidto hellwithit. Eventuallyit gotquitebig,and covereda fairly sizeablearea,butthefarmersaid,‘Ohwell,I won’tdoanythingaboutit untilit covershalfthepond.’Butwhenit didcoverhalfthepond,how longhadhegottocopewithit?—exactlyoneday,ofcourse.Thecrunch comesveryfastundersuchcircumstances. It comesevenfasterin the stillmorerealisticsituationinwhichthegrowingsystemremovessomethingnecessary foritsgrowthfromtheenvironment, sothattheenvironmentiseffectively gettingsmallerasthesystemisgrowing. Thenthe crunchbetweentherisingsizeofthesystemandthedecreasing sizeof itscontainercomesevenfaster.Thisisthekindofsituationwhichsome peoplehavesupposedtoapplytoman’suseofthelimitedrawmaterials

ofhisSpace-Ship Earth.

Drawing5b.4showsa situationin whicha populationis growing exponentially, and usingup naturalresourcesfroma fixedstockat a constantrateperperson.Obviously, eventually theywillhaveusedup all the resourcesthereare;the onlysurprisingpointto noteis how rapidlythesituationdeteriorates towardstheend.

Fic. 5b.4 71

Clearlyifresources aregivenonceandforall,theymusteventually be usedup, howeverslowlythey are consumed.It is onlypossibleto achievea stablesystemwhichcancarryonindefinitely ifnewresources canbeproducedandaddedcontinuously to theinitialstock.Thenthe systemcanbecomestablewhenresourcesareusedat thesamerateas theyareproduced.Drawing5b.5showsanexampleofwhatwillhappen if a populationusesup its initialstockof resourcesmuchfasterthan theycanbe replaced.Therewillbe an upsurgeof numberswhilethe

Pi waehepato pee

¥Ve Ra

initialstockisbeingused,followed byarapidfallbacktothenumbers whichthecontinuous productionofresourcecansupport. Asimpliedbythe lasttwoexamples, exponential growthcangoon indefinitely onlywhenthereareinfinitespaceandrawmaterialsavailableforit. Thisis neverthe casein the realworld.Growthhasbeen mostfullystudiedin biological systemsconsisting ofcellsofanimalsor plants.Thesimplesituationofexponential growthis an idealwhichis reallyverydifficultto achievein practice.It is notonlythatgrowing systemssoonbeginto be limitedbythesizeofthecontainer—thatis, theamountofspaceandrawmaterials available toit —buttherearetwo 72

otherfactors.Thesystemisboundtoproducea certainamountofwaste productswhichit cannotitselfutilize,andwhichin factarelikelyto be harmfultoit.Thenagain,themechanisms ofgrowth,bywhichthenew

materials arebroughtintobeing,tendto wearoutandbecome less

efficientastimegoeson. If welookat the actualgrowththat oneis likelyto findin a real biological system,whatweseeisa curvemuchmorelike56.6.Thereis oftena shortperiodat thebeginning, knownasthelagphase,in which

FIG.5b.6

Time

thesystemis adaptingitselfto itsnewsurroundings. Thenit maygrow for a timeexponentially. This periodis commonlyknownas the log phase,becauseit is a mathematical consequence of the exponential formula,that the logarithmof the size appearsas a straightline whenit is plottedas a graphagainstthe time.Thishasbeendonein 5b.7,andthelogphaseisquiterecognizable asthestraightlinepart,on theleft.Buteventually therateofgrowthbeginstoslacken,thecurveof sizebeginsto riselesssteeply,andthenturnsoverandbecomesflat.If it hadgoneon indefinitely in exponential growththe graphofthesize wouldhavebeenJ-shaped.In practiceit is nearlyalwaysS-shaped, 73

Time FIG.5b.7

because ifthesystem isinanyfinitecontainer it isboundtogenerate forceswhichwillslowup the growthandpreventit fromgoingon to infinity. These forcesmayunder somecircumstancesact, as it were,gently,to

producea smoothtransitionfromtheexponential rateintoa slowerrate andaneventualstationarysituation.Quiteoften,however,theywillact

inawaywhichonemightconsider lesswellbalanced. Asystem mayfor

a timegrowbiggerthanthe environment cancontinueto sustain,and willthenundergo a periodofrathervigorousde-growth (see5b.8);there mayin factbe severaloscillations, of periodsof growthfollowedby periodsof de-growth,beforeit settlesdownto a stablesizewhichthe resourcesofthe environment canmaintainindefinitely. It is thepossibilityofsuchtransientoscillations whichhasbeenoneofthemainsubjectsof studyby Meadows,Meadows,Randers,and Behrewin their bookTheLimitsto Growth for theClubofRome. Therehavebeenmanyattemptsto finda suitablemathematical for74

Fic. 56.8 e ae

mulato expressthe S-shapedcurve;but althoughthe turningoverof thecurveat thetoprightisalwaysproducedbysomesortoflimitation in theenvironment, orbya gradualwearingoutofthegrowthmachinery,iNpracticeit takessomanydifferentformsthatnooneformulais appropriate in allcases.It is perhapsworthmentioning justoneofthe bestknownof theseformulae,whichis derivedfromthe ideathatthe growingsystemdependson a storeof somenaturalresourcewhichit usesup at a rateproportional to itsownsize.Thisis whatiscalledthe ‘logistic’ formofgrowth,whichgivesanS-shapedcurvewiththerather complicated formulaI dx =a —bx. It oftenprovidesquitea good xXat description ofmanybiological systems,butbynomeansallofthem. Differential Growth Wehavesofarspokenasifthegrowingsystemwerehomogeneous, that 75

=

is to say,allofonekind.Butmostgrowingsystemshavea numberof differentparts,andthesepartsmaygrowatdifferentrates.Forinstance, differentsectionsor groupsin a humanpopulation mayhavedifferent reproductive ratesor deathrates.The numbersof peoplein different typesof employment maygrowat differentrates,dependingon the development ofindustryandsoon.Thereis nopointin goingintoall the complexities that mayarise;but there is one relativelysimple system,whichoftenhappensin biological entitiesandmayhavesome application in humanaffairsalso.Thisisonein whichthegrowthrate

ofonepartisamoreorlessconstant multiple ofthegrowth rateofsome otherpart,orofthewhole. Thisproduces whatisknownas‘heterogonic’growth.It occurs,for instance,in an animalwhichpossesses particularorganswhichgrowfasterthantherestofthebody(e.g.5b.9).

Fic. 5b.9

Theantlersofdeerareoftencitedasexamples; thebiggerthebodyof the deer,the disproportionately biggerwillbe the antlers.A fewmil-

lennia agotherewas a giantelkinhabiting Ireland. Itsevolution seems to

havebeenin the directionof becominga largerand largeranimal, possiblybecausethemalesfoughtwithoneanotherto capturefemales. Bythetimeit becameextinctanddisappeared fromthescene,thefullygrownanimalshadbecomeverylarge;andthismeantthattheirantlers, whichgrewina heterogonic relationtotherestofthebody,hadbecome reallygigantic.It isoftensuggested thatit wastheoverdevelopment of theseantlers,whosesizerenderedthema genuinehandicap,thatledto 76

the extinctionof thisspecies.Perhapsweareseeingsomethingrather similarin the development of motorwaysand parkingplacesin the centreofcities;theyareincreasing in areasomuchfasterthantherest ofthecitythattheyseemto bein dangerofusurpingthewholespace,

leaving nowhere forthehouses andoffices togo.

Whendifferentpartsofa biological organismgrowat differentrates, thesituationisoftenbetterdescribed,notbydissecting theanimalinto separateorgansand considering the growthrateof eachoneof these separately, butratherbysayingthatthereareoneorseveralgradients of growth.Whena humanbabyisbornitsheadisdisproportionately large anditslegsdisproportionately small,comparedto therelativesizesthey willhavewhenthechildis anadult.Duringchildhood, however,there is a generalgradientof growth,so that the lowerend (the legs)is growingfastest,andthe upperend,the head,is growingslowest,and thereforetheproportions ofthebodygraduallychange(5b.10).

Whenonecomparesthe adultformsof closelyrelatedspecies,one oftenfindsthattheshapeofonecouldbechangedintotheshapeofthe other,if onewereto supposethatdifferentsystemsofgrowthgradients hadbeeninvolvedinthedevelopment oftheanimal.Onewayofexhibitingthisistodrawtheoutlineofoneoftheanimalsina straightforward rectangular grid;then,if thisgridis stretchedor bentasthoughit had beendrawnona sheetofrubber,it canoftenbeconvertedintoanother grid into whichthe shapeof the other specieswouldfit. This is sometimes a usefulwayof comparingcomplexshapes,as in 5b.11,to supplement theothermethodsdiscussedin Chapter3. 77

i

©

78

In thelastfewparagraphs wehaveconsidered growingthingsconsist-

ing of differentparts,whichmaygrowat differentrates.When

biologists havereallytriedto getdownto considering thegrowthofan animalor plantin detail,theyhavehad to realizethat the growing systemis alwaysheterogeneous in a muchfiner-grained waythanthese considerations ofoverallshapeandtotalweightimply.Forinstancethe humanswhoare drawnin 5b.10in outlinereallyconsistof bones, muscle,intestinesanda wholelotofotherparts;andeachoftheseparts ismadeofinnumerable cellsofdifferentkinds.Somecellsmaygrowby actuallyincreasingthe amountof livingsubstance;but othersmay increasein sizebylayingdowndepositsofmineralsubstances, suchas the calciumcarbonateof bones.Or again,theymayswellmerelyby absorbingwater. Anydiscussion onoverallgrowthsimplyobscurestheseactualdetails of whatis happening.If onewantsfor somereasonto talkof overall growth,thenonemustbe contentwithsomemoreor lessarbitrarily chosenindex,in whichthe variousdetailedcomponentsare compoundedin a reasonably satisfyingway.For instance,onemaytalkof the increasein dry weight;in this the complexities due to absorbed waterareavoided,buttheindexwillincludedepositednon-living mineralmateriallikecalciumcarbonatein bonesor shells. A verysimilarproblemariseswhenwetalkof the growthof the economy. Thebestonecando,togiveanoverallindexofit, istoadopt somearbitraryformulainwhichallthecomponents arecompounded in somewaythat seemssensiblefor the purposesin hand.The Gross NationalProductis the formulausuallyadopted,but, likethe dry weightofananimal,it takesintoaccountcertainaspectsofthesituation butleavesoutothers;andthequestionmustalwaysbeaskedwhetherit reflectsadequatelythe factorsin whichwe are mostinterestedin a particularcontext.

79

6 Feed-back in Systems

A.Sequences In mostoftheopensystemsin whichoneis likelyto beinterested,the enteringmaterials(theinputs)areprocessed througha numberofstages beforetheyfinallyemergeagainas productionor waste(theoutputs). Themostimportantideasweneedforthinkingaboutcomplexsystems arenotionsconcernedwithsuchprocesses andtheirinteractions.

Tostartwiththesimplest case:consider a system inwhichthereis

onlyoneinput,andthisisoperatedonina sequenceofstepsfrom,say, AtoB,to C,toD, toE,untilit finallycomesoutofthesystemagainas a productF. Evensucha simplesequenceofprocesses hassomequite interestingproperties.Onecan perhapsmosteasilypicturethemby usingtheanalogyofwaterflowingintothesystemthrough a pipeintoa containerAfromwhichit canflowoutagainthroughanotherpipeinto a containerB,thenonthrough aseries ofpipesintocontainers C,D and E, wherethereis thefinalpipeleadingto F (6a.1). TheamountthatflowsperminutefromcontainerC intocontainerD dependsbothonthediameterofthepipeconnecting C withD,andalso ontheheadofwaterinC.Supposethatwehavea set-upwitha seriesof containersconnectedby pipesof differentdiameters,anda certain inflowintoA to startwith.It is clearthat,providedthecontainersare tallenough,theywilleachfillupto a givenlevelwhichisjustsufficient to pushincomingwateroutagain,throughtheoutletpipe;thesmaller the outletpipe,the higherthe headof waterwillhaveto be.Whena systemhasbeenrunningforsometime(and,assaidbefore,providedthe containersaretallenough),the wholethingwillhavesettleddownat appropriatelevelsin eachcontainerwhichwillnot alter thereafter providedtheinputremainsthesame. If theinputintoAisincreasedordecreased then,ofcourse,levelsin allthecontainerswouldhaveto alterin anappropriate wayto maintain the steadyflow.Whenthe systemhassettleddownto dealwithany 80

Inf€

ic “Se ,2

F€ =

Fic. 6a.1

particularrateof inputintoA, it is saidto havereacheda stationary state.It isnot,ofcourse,stationaryinthesensethatnothingishappening—thewaterisflowing throughit;butit isstationary inthesensethat thelevelin eachofthecontainers remainsthesameaslongastheinput is unchanged. It is interestingto considerwhatwouldhappenif we suddenly throttleddownoneofthepipes,saythatbetweenC andD (6a.2).What willeventually happenisclearenough:thewaterin C willriseuntilit is highenoughto pushtherateofflowthroughthenarrowerpipeintoD sothatit deliversthesameamountperminuteasit didbefore.Thusif the inflowremainsconstant,theoutflowF willagainbethesameasit originally was,andallthatwillhavechangedwillbethelevelofwaterin containerC. Thissituationisa simpleexampleofa phenomenon oftenreferredto as ‘buffering’ (a pieceof technicaljargondrawnfromchemistry).In steady-state conditionsthe rateof outflowfromF is bufferedagainst changesin the diametersof the pipesconnecting the variousvessels— unless,ofcourse,onepipeis sonarrowthattheheadofwaterrequired tomaketheflowgofastenoughthroughit ishigherthanthecontainerit leadsoutof,in whichcasethe systemwilleventually breakdownand thiscontainerwilloverflow unlesstheinitialinputat Aisreduced.This characterof“beingbufferedagainstcertaintypesofchange’isoneofthe 81

Fic. 6a.2

mostinteresting properties ofsystems andprocesses. Fromthepractical pointofview,someofthemostimportantpropertiesofsystems,aswe dealwiththemin reallife,arethekindsandlimitations of stabilityin theirbehaviour. Notethatthebufferingwehaveconsidered sofarconcernsthecondi-

tionreached whenthesystem comesbackagainintoa stationary state aftera disturbance suchasa narrowing ofoneoftheconnecting pipes.A numberofchangesmaygoon,someofthemratherunexpected, before the new stationarystate is reached.These changesare knownas ‘trans-

ients’.In practicalaffairstheyalsomaybe veryimportant,particularly whenoneis dealingwithlong-lifesystems,suchashumanpopulations. PositiveFeed-back The analogy,or model,of waterflowingthrougha systemwhichconsistsoffixedtanksandpipesis,ofcourse,muchtoosimpletorepresent mostreallivingsystems,in thebiological or humanorsocialworlds.In livingthingswhatwehavecomparedto tanksandpipesarethemselves

manufactured withinthesystem. Someoftheinitialinputisusedto

makethetanks,andthecontrolling pipesconnecting them,whichother portionsof the inputflowthrough.Ina livingcell,for instance,part of the nutrients,oxygenand so on, takenin fromits surroundings, 82

FIG.6a.3

isconvertedintoenzymeswhichcontroltheratesat whichanotherpart of the inputis convertedintosubstanceA, thenB, C, D and so on. These enzymesthereforecorrespondto the pipesin our previous analogy(6a.3). Sincethese‘pipes’aremadewithinthe system,the cellis perfectly abletobringaboutforitselfa changeina particularrateofflow,sothat an alterationcorresponding to whatwespokeof as ‘throttlingdowna particularpipe’can be producedinternally,and doesnot haveto be imposedfromoutside.It is a verygeneralobservation, in all systems fromcellsthroughindividuals tosocieties, thatsuchinternally produced changesoftenoccur. Theydosoin twodifferentwayswhichhaveoppositeeffects.In one way,themorethereisofa particularcomponent, sayD, thefasterD is produced;D affectstheearlierstagesinthesequence toincreasetherate offlowthroughthem.Thisisknownaspositive feed-back (6a.4),andisa reinforcingtype of action.It is clearlycloselyrelatedto the selfstimulating typeof processwhichresultsin exponential, or accelerated exponential, growth(p.66),suchas the situationin whichthe more youngadultsthereareina population, themorebabiesgetaddedto it.

Buthereweareconsidering theratherdifferent case,in whichthe amountofsomeconstituent ina sequence affectssomeearlierstepinthe

83

FIG.6a.4

sequence,whichmayinvolvethingsof quite a differentkind.For instance,afterthe numberof peoplein a regionof the earth’ssurface growsbeyonda certainpoint,therecanbesomewhoaresurplusto the requirementforagricultural workto producefood;andtheycanstart buildingcities,anddiggingirrigationsystems,andsettingupwindmills, anda wholelot of thingswhichwilleventually, througha numberof steps,leadtoanincreaseintherateofgrowthofthehumanpopulation. Wherepositivefeed-back differsfromexponential growthisthatin the formerwearedealingwithsequences ofdifferentsteps,andinthelatter withonlya singlestep. ChainReactions

Anotherrelatedconceptisthe‘chainreaction’. Theideaisa verysimple one;so simplethat it wouldhavetemptedSherlockHolmesto say ‘Elementary, mydearWatson.’So youmightask,whygiveit special discussion? TheansweristhatI thinkmostpeople,muchtoooften,just tendto forgetit orleaveit outofaccount.It isactuallyoneofthemost dangerous,or, if youplayit right,oneof the mostrewarding,of the processes, dealingwithwhichyouhaveto spendyourlife. Achainreactionis onewhichcanoccurwhenthereis a sequenceof steps;a goestob,andb goestoc,andc tod,anddtoeandsoonandon. Thephrase‘chainreaction’ isusedwhenthereisa sortofmultiplication at eachstep;a slightincreasein a producesa biggerincreasein 5,and thata stillbiggeroneinc,andthata reallyheftyjumpind.Eachstepin the seriescan(perhapsonlyafterit getsabovesomethresholdvalue) opena gate,orturnona valve,whichreallyletsthenextstepgetgoing in a bigway.

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It’snota newidea.Theclassical statementofit, asfarasmyreading goes,wasbyBenjaminFranklin(inthepre-automobile era): For wantof a nailthe shoewaslost, For wantofa shoe,the horsewaslost, For wantofa horse,the battlewaslost, For lossofa battle,thekingdomwaslost.

But,thoughit isbothsimple andold,theideaisofkeyimportance.

And,remember,it worksin bothdirections.Neverneglectto consider that whatyou are goingto do nowmaysparkoff a chainreaction towardsUtopia(I wouldn’tbettooheavilyon actuallyfindingyouget there),or triggerthefirstfusefora succession ofevermoredevastating disasters(buta littlebit of sensealongthe waycanprotectyoubetter

against finishing upinabsolute hellthanitcanguarantee youa smooth progressto absoluteheaven).

NegativeFeed-back Butveryoftenrestraininginfluences alsoarisewithinthe system.It is bynomeansalwaysthecasethatthepresenceofa lotofD encourages theformationofmoreD. Perhapsmoreoftenlivingthingsbehavein a waywhichmaybe called‘satiation’ or ‘enough’s as goodas a feast’. That is to say, after some point is reached, the more D there is, the

slowernewD is formed.This is a negative feed-back(6a.5).It is a \gorerses flow rate

p>

>

FIG.6a.5

restraining typeofaction,andisthebasicprocessthatlivingthingsrely onto seethatnooneoftheirinternalprocesses runsawayandgetsout ofhand.It isalsothekindofprocessincorporated intomanyman-made controlling devices.If thecentralheatingpushesup thetemperature of a roomtoo far, the thermostatcomesinto playand shutsdownthe centralheating,and reducesthe inputof heatintoa roomuntilthe temperature getsbackto theappropriate level.

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Biologistsmakea distinctionbetweentwotypesof negativefeedback;and in socialaffairsthereare analogiesto thesetwokindsof processwhichoriginally describedthelevelofcellsandenzymes(6a.6).

Fic. 6a.6

The first,andin somewaysthemilder,formof feed-backis onein whichthepresenceofonecomponent inachain,suchasD,actsinsome waytoslowupthe flowthroughanearlierstepinthechain,sayfromB to C, by as it werethrottlingdownthat pipeto someextent.This is

known as‘inhibition’ —andsincewecanconsider Dtheendproduct in thesequence wearetalking about,itisoftencalled‘end-product inhibition’. The secondand moredrasticformof negativefeed-backoccursin livingsystemsinwhichthelinkbetweenB andC(the ‘pipe’,or,inmore realterms,the enzymewhichbringsaboutthis chemicalchange)is

actually manufactured withinthesystem outofsomeoftheincoming materials.The secondtypeof feed-backdoesnot merelyreducethe efficiency of the enzymebetweenB and C, but actuallyabolishesits production, at leastuntilthelevelofD dropslowenoughagain.‘Thisis ‘end-product repression’. If a factoryworksveryefficiently and producesa largeoutput(of

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automobiles, say),andtheworkersconcludethatthefirmismakingtoo largea profit,so theygo on strikefor morepayor shorterworking hours,that wouldbeend-product inhibition. Butif,instead,theystaged a revolution,sackedthe management or destroyedthe machine-tools, thatwouldbeend-product repression becausetheywouldbenotmerely slowingtheproduction processbutrepressing themachinery ofproduction.Similarly, ifpupilsina schoolthoughttheywereaskedtolearntoo muchanddecidedto workslowly,that wouldbe inhibition;if they attackedtheteachers,or burnttheirbooks,thatwouldberepression. Inhibitionusuallyproducesits effectsmuchfasterthan repression

does.Forinstance, ifthereisaveryhighconcentration oftraffic usinga certainroad,thetrafficflowwillbeslowed downbyaninhibition which

operatesalmostimmediately. Repression wouldcorrespond toa situationinwhich,bysomesystemofsignalling, thetrafficdensitycontrolled theflowintothatroad,forinstancebydivertingsomealongalternative routes.This mightbe moreefficientin the longrun, but obviously wouldtakelongerto produceits effect. B. Networks Onewayin whichthemodelwehavebeenusingsofaris overlysimplified,to representthe systemswemeetin the realworld,is that we havebeentalkingabouta singleinputwhichis processedthrougha seriesofchangesintoa singleoutput.Ofcourse,in mostsystems,such asourownbodies,inputis ofseveraldifferentkinds—foodconsistsof proteins,fats,carbohydrates, mineralsandwhathaveyou,andtheoutputisalsoofmanykinds—moremuscle,morekidney,moreliver,more nerve,moreexcreta.Thenextstepin makinga morerealisticpictureis to thinkin termsofsomething likea treediagramordendrogram, such as weconsidered onp. 54.Thatis to say,theinputgetsparcelledout intoa numberofdifferentbrancheswhichgooff,dividinganddividing again,intoa largenumberofdifferentendresults(6b.1). But in mostactualsystemsthe inputdoesnot simplyget splitup alonga wholesetofdivergentpathways, likethebranchesandtwigsofa tree.Thesebranchesandtwigsarein generalnot whollyindependent evenaftertheyhavesplitapartfromeachother.Pathways alongwhich thingsareprocessedmayhaveas theirmajorcharacteristic a tree-like character,branchingdownfroma maintrunkto mainlimbs,to main branches,to twigsandsoon;but alongwiththis,andsometimes more

87

Fic. 6b.1

important,are interconnections betweenthe branchesand twigs.The pathwaysforma network,ratherthana simpletree-likepattern(6b.2).

Within suchnetworks therewillbethesametypeoftendencies tode-

stabilizethe behaviour(by positivefeed-back)or to stabilizeit (by negativefeed-back), aswesawin thesimpleunbranchedsequences. If in sucha networkone of the channelsof communications becomes constricted,the flowwilljust go roundit, alongoneor moreof the alternative pathways thenetworkprovides.In a single-channel sequence

thereisacertainbuffering ofthefinalthroughput (p.54);inanetwork this mayworkevenmoreefficiently, and withoutrequiringanyvery largechangesin thelevelofstoragein theearlystoragetanksalongthe way.Again,the levelof somefinaloutputmayactas a negativefeedback,repressingor eveninhibitingsomeotherlink in the network, whichneednotbedirectlyonthesequenceleadingto it. Forinstance,ina citythepresenceoftoomanycarsontheroaddoes not operatedirectlyto inhibitthe productionof newcars,or evento repressautomobile manufacture in general,but ratherto inhibitsome

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otherpartofthenetwork,suchasthetendencyofpeopleto movetheir’ housesout of the centralcitiesinto the suburbs.To giveanother example;in an ecosystem the existenceof toomanyrabbits—abovea certainlimit—tendsto reducetheirrateofreproduction, becausethey getin eachother’swayandthefemalesreadyto bearyoungarealways gettingdisturbedbyaggressive males,andtendtoabortornotlookafter theiryoungadequately. Butina realecosystem, longbeforethesedirect effectsbeginto beimportant,it ismuchmorelikelythatthepresenceof sucha largenumberofrabbitsgivesa fielddayto the foxesandother animalsthatliveontherabbits,sothattheyincreaseenoughinnumber to keepthe rabbitpopulationdownto a reasonable size.The indirect negativefeed-back loop,numberofrabbitsthroughnumberoffoxesto reductionof rabbitpopulation,is likelyto be moreeffectivethanthe directloop,toomanyrabbitsinterfering witheachother’sreproduction.

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Thereis in factwhatmightbe calleda sortof ‘inherentnetworkbuffering’. The morecomplexa networkis and the moreit is interconnected,the moreindifferentit is to the severingof anyparticular link.This is, however,onlya veryroughrule.The generaltheoryof stabilityofnetworksis actuallyverylittleunderstood. Modelling Networks Ideally,one wouldaimat specifyingall the reactionsgoingon in a network,measuring theirrateandthe strengthsof theinteractions betweenthem,and then puttingthesedata togetherinto a systemof equationsfromwhichonecouldcalculatetheresponseofthesystemto anygivendisturbance. Usually,inpractice,it isimpossible tomakesuch a completeanalysis.Thedifficulties arelikelyto bepartlyin measuring the ratesof reactionsandinteractions, andpartlythat the sheercomplexityof thesystemmaymaketheequationsimpossible to handleby normalmathematical methods.The adventof computershas largely overcomethe latterdifficulty,sincewiththeir greatspeedat doing simplearithmetic,they can be programmed to solveeventhe most formidable setofequationsin a reasonably shorttime. Butthedifficulty ofestimating theparameters (ratesofreactionsand interactions) canusuallyonlybe circumvented in ratherunsatisfactory ways.Onecanstartby usingthe bestestimatesandinformedguesses that areavailable,bothaboutthesevaluesandaboutthe structureof linkageswithinthenetwork.Thenonecantry outtheresponseof the

system, ascalculated bythecomputer, against anydataabouttheactual

responsewhichcanbe collected.In the situationsmostfavourable for analysis,it maybepossibleto applyknowndisturbances to thesystem, andto observeandmeasureitsresponses; if theyarenotquitewhatthe computerpredicts,onewouldhaveto changeeitherthestructureofthe model,or someofthevaluesfedintoit, or both,tilltherewasa better agreementbetweenthecomputedandactualbehaviour. Another,usuallylessinformative, wayoftestinga model,is to compareitsresultswiththepasthistoryofthesystem,if onehasgooddata aboutthis. For instance,in a modelof an economicsystem,whose historyhas beenrecordedin goodstatistics,one mightuse the past twentyyearsofhistoryto workout,bygradualapproximations, a model andsetof valueswhichpredictthe actualbehaviouroverthatperiod; and onewouldhavesomedegreeof confidence that the samemodel mightforetellhowthe systemwouldbehavein the nextfewyears. go

However,evenina fieldlikeeconomics, in whichthereareverygood statisticscovering quitelongperiods,it hasprovedverydifficulttomake modelswhichpredictaccurately formorethana veryshorttimeahead. Oneofthemainresultsofsuchstudiessofarhasinfactbeentoshow thatcomplexnetworksystemsbehavein veryunexpected ways.Their behaviourhasbeendescribedas‘counter-intuitive’, in thesensethatif onemakessomechangestothesystemwiththeintentionofproducing a certaineffect,theactualresponseoftenturnsoutto besomething quite unanticipated. Sometimes thesecounter-intuitive resultsoccuronlyin the shortrun; theymaybe causedby somepartsof the systemapproaching a newequilibrium byanoscillatory pathinsteadofa smooth path(seeFig. 6b.2),or by some other transientphenomenon of that

kind.Butsometimes theyareduetoa breakdown insomeapparently unrelatedbut fragilepartofthesystem.To giveanexcessively simple example, a throttlingdownofoneofthetapsinFig.6a.2mightraisethe waterlevelinoneofthetanksearlierinthesystemtothelevelat which it overflowed. It is, perhaps,in the revealingof theseunexpected and stilllittleunderstoodtypesof behaviourof systemsthat the computermodels havebeenmostusefulsofar;butonemayhopethattheywillgradually be improveduntiltheyaremorereliablein predictingactualdetailsof behaviourratherthanmerelyindicatingtypesof responsewhichone mustbeonthelook-outfor.Chapter12is concerned withattemptsto buildup thiskindofmodelofthewholeworldsystem. Meanwhile, oneusuallyhasto becontent,inhandlingmanysystems, withmuchcrudermethodsandideas. SoftSpots In mostnetworks,alterationsat someplacesare likelyto havemore profoundeffectson the systemthanalterationsat others;movingone particularitemfroma houseofcardsmaybringthewholethingtumblingdown,whereasremovingmanyotheritemsmayhavemuchless effect.If oneis tryingto altera systemwhichhassomeinbuiltbuffering,oneoftheimportantfirststepsisto tryto locatethese‘softspots’. Therehasbeena gooddealoftheoretical discussion abouthowtolocate them,or preferablyhowto measurethe sensitivity of eachparticular linkin the network.The mostimportantresultto emergeis that the sensitivityof a particularlinkis not a fixedcharacteristic of it, but dependson the stateofthe restof the network.In somestatesof the gi

system,thesoftspotwillbeinoneplace;andina differentstateit may be somewhere else.For instance,in providinghousingin a cityoneis dealingwithasystemwhichinvolves manycomponents. Insomecircumstancesit maybe that the practicalissueis to providenewsitesfor housingindesiredlocations; inothersit maybetheprovision ofcapital, orsuitablelabourandsoon.Thecontribution ofeachparticularitemto the stabilityor changeablenessof the systemchangesas the systemitself

changes.

C.Lock-in,Schismogenesis andDouble-bind Onemayfindoneselfconfronted withsystemswhichhavenoobvious softspots.Theyseemlikeanironring,ora viciouscircle,fromwhichit is impossible to escape.Therearesomerecentlyintroducedideasand phraseswhichareoftenusefulin thisconnection. Thefirstis‘lock-in’. Alock-inisa situationinwhichinthebeginning component a interactswitha numberofothercomponents, b, c, d, etc., buttheinteraction withoneofthese,sayc, setsoffa reactionwhichin somewaytendsto confinea’sattentionto c; so that as the situation develops,a comesto be reactingonlywithc, all his otherreactions havingpeteredout,a is‘locked in’.(Thelock-inloopneednothaveonly

Lock- in

heck - in

twomembers,a andc;it maybea lock-intothegroupa,c,e (6c.1);the pointis that the interactions becomelimitedto a smallnumberof all those possible.)One often meetssuch a situationin discussions;a gen-

eralpoliticaldiscussion maygetlockedin to a disputeaboutthemerits ofthedoctrinesofLenin,TrotskyandStalin.Asthisexamplesuggests,

lock-ins usually getnowhere; theymayengender alot ofheatbutlittle

light,or theymayfadeoutin a paralysisofboredom. The next notion,whichwas introducedby the anthropologistGregoryBateson,has the ratherdauntingname‘schispsychologist of a chasmor cleft. mogenesis’, a wordwhichmeansthe development

Basically it involves twoparties, a andb,andit isa situation inwhich whatonepartydoesprovokes theothertogofurtherinthebehaviour to

whichthefirstpartyisreacting.Therearetwovarietiesofit. In one,the two partiesare behavingto eachotherin essentiallythe sameway. Competingfor keepingup withthe Joneses,purchasingeverbetter, moresplendidautomobiles or other articlesof competitivedisplay, wouldbea goodexample.Anarmsracebetweentwoopposingnations isanotherinstance.Thisissymmetrical schismogenesis; a takesa stepina certaindirectionandthisprovokesb to takea longerstepin thesame direction,whichprovokesa to gostillfurther,andsoonandon(6c.2).

FIG.6c.2

In theotherkind,thetwocomponents actin oppositeways.A relationofauthorityandsubservience isanexample. Thedominantpartner assumesa somewhat bullyingattitude,andtheotherpersonacceptsit so humblythat this provokesthe dominantone to becomeevenmore masterful, whichagainincreases thesubservience oftheotherandsoon. Thisis complementary schismogenesis (6c:3). 93

A third notion,alsolargelydue to Bateson,is the ‘double-bind’.Here

threecomponents areinvolvedin sucha mannerthatthewayin which

a reactswithb inevitably hastheresultofmaking it moredifficult for himtoreactproperly withc. It iscommon inpsycho-social situations. Ifachildloveshismotherenough,thisistakenbyhisfatherasdisloyalty

to him; so he increaseshis efforts to attract the child’saffection;and

thenthemotherredoubleshers.Or a childmaybetoldhehasto meet twoincompatible goals—beingalwayspoliteandalwayssayingexactly whathethinks;andassoonashedoesone,heisremindedthatheshould bedoingtheother.Ora townsman wantsto getbackto nature,butthe morehe livesin a countrified suburb,themorehe hasto commuteby carandthelesshecanwalk(6c.4).

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The lock-inandschismogenesis situationsarecloselyconnected,in logicalstructure,withsomeofthenon-zero-sum gameswediscusslater, such as ‘Prisoner’sDilemma’(p. 167)and the “Tragedyof the Commons’.An amusingexampleof a locked-insymmetricalschismogenesisin the formof a gameis ‘Auction-A-Dollar’, inventedby MartinShubik(seeJohnPlatt,SocialTraps).Theauctioneer drawsup therules,whicharethatbiddingis to startat fivecents;thebidsmust increasebyat leastfivecentsat a time;and,sinceit seemsat firstsight thatsomeone mightgetthedollarreallycheap,helaysit downthatheis to be giventhetwohighestbids,althoughonlytheonehighestbidder willreceivethedollar.Whatwillhappen?It isallplainsailinguntilthe biddinggetsto forty-five cents,andthento fiftycents.Fromthispoint if it goesanyhigher,to fifty-five cents,the auctioneeris goingto get morethanhisdollarback.Butif it doesnot gohigher,thenthe man whobidforty-five centsisgoingto giveit overandgetnothingback;so heraiseshisbid.Bythetimethebiddinggetsto a dollar,themanwho bidninety-five centsisin anevennastiersituation;if heraisesto $1.05 hewilllosemoneyevenifhegetsthedollaratthatprice;buthewilllose a lotmoreif he letsthe biddingstop;soup he goes.JohnPlattwarns thatit isa dangerous gameto play;thelock-inescalation issotightthat it maywreckfriendships, perhapspermanently. The wayto escape,of course,wouldbe fortheplayersto makesomeside-arrangement, outsidetherulesof the game,suchthattheywouldstopbiddingat some earlystage,belowfiftycents,andwouldagreetosplitthedollarbetween thetwohighestbidders;thenbothwouldhavemadea profit.Weshall seelater,in discussingPrisoner’sDilemma,that communication and agreementbetweenplayersis oneofthe mosteffectivewaysof escape frommanysuchsituations. Thereseemto be onlytwoways,apartfromcollaboration between someof the participants,of dealingwith these vicious-circle-type systems,whichhavenoobvioussoftspots.Onewayisto tryto alterall thelinksinthenetworkofcauseandeffectsimultaneously. Theotheris to lookat the widercontextin whichthe vicious-circle systemis embedded,andtrywithinthattodiscoversomeothersystemwhichcanbe broughtinto such powerfuloperation,that the contributionof the

vicious circleto thewholeset-upbecomes ofreduced importance, so

that it can be forgottenand left to witherawaywithlapseof time. Perhapsthe onlypossiblesolutionto the schismogenic armsracebetweentheUS andtheUSSRwillemergebythe transference, byboth of them,of theirmainintereststo a quitedifferenttopic—the issues 95

of environment,pollution,naturalresourcesand the wholeWorld Problematique.

Thischapterhasdescribed theimportant typesofinteraction be-

tweendifferentcomponents incomplexsystems.Someoftheseinteractions,likepositivefeed-back,or schismogenesis, tend to reinforceor speedupprocesses ofchange,andtheythereforeareliableto‘runaway’ and get out of control.Otherinteractions, likethe differentkindsof negativefeed-back,or networkbuffering,or lock-ins,tend to slow thingsup andthusto controlthem.If weregardcomplexsystemsas

thingswewouldliketo manage, thesecontrolling activities arepar-

ticularlyimportant,especially thosewhichdonotnecessarily involvea narrowingof the fieldof interaction,as lock-insdo.The nextchapter willbedevotedtothevariousformsthecontrolofcomplexsystemsmay take.

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7 Stabilization in Complex Systems

EEEEEEEOEOEOE——_—_ Thelastbutonechapter,abouttheprocesses in complexsystems,may haveleftsomeofthemorefaint-hearted readerswiththefeelingthatall

suchsystems areboundjusttogetintoa mess,andstaythatway.But

actuallyonehasonlyto lookat, say,themovements ofa balletdancer, or evena reasonablyhealthypersonwalkingabout,to realizethat systemswhichwouldappearenormously complicated if examinedin detail,can behavewithconsiderable overallsimplicity.Messagesare goingalongmanydifferentnerves,fromthe brainto the muscles,and

fromthelimbsbacktothebrain;subtleactsofbalance arebeingcarried

outcontinuously; dozensofmusclesin thelegsandarmsarecontracting,andotherdozensrelaxing,at everystep.Butalltheseactionsare balancedoutagainsteachother,sothatthesystemasa wholebehavesin a ‘sensible’,unitaryway,whichwe can call ‘walking’,or even a beautifully coordinated waywecall‘dancing’. Thischapterwilltry to describesomeof the generalprinciplesby whichcomplexsystems becomeorganized sothatthecomplexity doesnotobtrudeandthereis an overallunityof action.The ideasinvolvedare, of course,rather generalones.It is mucheasierto graspparticulardetailsthanto comprehendthewaythosedetailsmergetogether to giveriseto theorganizationof the system.I warnedthat this bookwouldprovidesome challenges totheimagination ofitsreaders;thischapterhasitsfullshare ofthem. Thestudyoftheprocesses discussed hereis oftenreferredto bythe namecybernetics, andtheadjective‘cybernetic’ describesthecharacter of the processes. Thisis a verygeneralterm,andto getmuchunderstandingofthesituationonehasto gointoit in a bit moredetail. Weneedto distinguishfirstbetweensystemswhichcometo some sort of end-statein whichtheyremainconstantor go on repeating themselves indefinitely, and on the otherhandsystemswhichgo on changing aslongasonecarestoobservethem.Theformercanbecalled terminating systems,andthelatterprogressive systems. 97

A.Terminating SystemsandStableStates Wehavealreadymentionedthe possibility thata situationfinallygets

intoasteady state,andpointed outthatthisdoesnotmeanthatnothing

ishappening, butmerelythatsomesortofflowisgoingsteadilythrough the system.Whatremainsstationaryis the patternof this flow.Any end-statewhicha systemattains,or movestowards,is sometimes referredto asa ‘goal’;butthatis a ratheranthropomorphic usage. Thereare,however, severalothertypesofterminalstates.In thefirst place,the systemmaybe onewhichreallyholdsconstantsomeparticularcomponent, asa thermostatholdsconstantthetemperature ofa room.Therearemanycomponents in ananimal’sbodywhichareheld constantin a similarway.Anexampleis thecarbondioxidecontentof one’sblood.Whenyoutakea lotofexercise, thefuelusedupto power

themuscles releases carbondioxide insolution intotheblood.Various partsofthebodymechanism thenchange inrate(heartbeat, breathing,

etc.)insucha wayastocleartheexcesscarbondioxideoutoftheblood andbringits concentration backto thenormallevel.The constancy of theCO,levelintheblood,orthetemperature ina roomcontrolled bya thermostat,areexamplesof steadystates.The technicalwordforthe processofreturningto a steady-state systemafterit hasbeendisturbed is‘homeostasis’ (fromtwoGreekwords,meaning‘thesame’and‘state’). In well-organized systemssuchasthehumanbodytherearehomeostaticmechanisms whichcancontrolseveralvariablesat once.In the blood,it is notonlythe concentration of CO,whichis keptconstant, butalsotheacidity,thelevelofoxygen,thelevelofseveralsaltsandso

on.Thinking about,orvisualizing, thingswhichinvolve manycomponentssimultaneously is,ofcourse,noteasyto do,but thisis oneof the maintaskswhichonehasto attemptwhentryingto comprehend complexsystems.It can be doneaccuratelyin termsof fairlyelaborate mathematics; butonecangetsomesortofa generalimaginative picture ofthesituation,ifoneiswillingtousea littleimagination, anddoesnot

demand toomuchlogical precision.

Everyoneknowsthat one of the standardmathematical waysto expressa relationbetweentwothings,x andy, is to makea graphof them.Agraphofx againsty canbedrawnona flatsheetofpaper,with thevalueofx measuredofffromthepointoforiginfromleftto right, and the valueof y measuredverticallyupwards.If youwereto take

account ofanothervariable, z, youhavetoadda thirdaxisat right-

anglesto the othertwo,and the pointrepresenting the simultaneous 98

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insidea threevaluesof all threecomponentsis locatedsomewhere dimensional space(7a.1). ,(X v XX 4)S

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