Space is the machineBill Hillier

SinceThe social logic of spacewaspublishedin1984,BillHillierandhiscolleaguesatUniversityCollegeLondonhavebeenconductingresearchonhowspacefeaturesintheformandfunctioningofbuildingsandcities.Akeyoutcomeistheconceptof‘spatialconfiguration’—meaningrelationswhichtakeaccountofotherrelationsinacomplex.Newtechniqueshavebeendevelopedandappliedtoawiderangeofarchitecturalandurbanproblems.Theaimofthisbookistoassemblesomeofthisworkandshowhowitleadsthewaytoanewtypeoftheoryofarchitecture:an‘analytic’theoryinwhichunderstandinganddesignadvancetogether.Thesuccessofconfigurationalideasinbringingtolightthespatiallogicofbuildingsandcitiessuggeststhatitmightbepossibletoextendtheseideastootherareasofthehumanscienceswhereproblemsofconfigurationandpatternarecritical.

Space is the machineBill Hillier

A configurational theory of architecture

Hardback and paperback editions first published in the United Kingdom in 1996 and 1999, respectively, by the Press Syndicate of the University of Cambridge.

This electronic edition published in 2007 by:

Space Syntax4 Huguenot Place, Heneage StreetLondon E1 5LNUnited Kingdom

www.spacesyntax.com

Copyright © Bill Hillier 2004, 2007

ISBN 978-0-9556224-0-3

Layout and designby Christian AltmannSet in Haas Unica

‘Ahouseisamachineforlivingin…’Le Corbusier (1923)‘ButIthoughtthatallthatfunctionalstuffhadbeenrefuted.Buildingsaren’tmachines.’ Student

‘Youhaven’tunderstood.Thebuildingisn’tthemachine.Spaceisthemachine.’Nick Dalton, Computer Programmer at University College London (1994)

Contents Spaceisthemachine|BillHillier SpaceSyntax

Prefacetothee-edition v Acknowlegdements xii Introduction 1

Part one Theoretical preliminariesChapterone Whatarchitectureaddstobuilding 10Chaptertwo Theneedforananalytictheoryofarchitecture 39Chapterthree Non-discursivetechnique 65

Part two Non-discursive regularitiesChapterfour Citiesasmovmenteconomies 111Chapterfive Canarchitecturecausesocialmalaise? 138Chaptersix Timeasanaspectofspace 171Chapterseven Visiblecolleges 190

Part three The laws of the fieldChaptereight Isarchitectureanarscombinatoria? 216Chapternine Thefundamentalcity 262

Part four Theoretical synthesesChapterten Spaceisthemachine 288Chaptereleven Thereasoningart 314

Index 344

Contents

Preface to the e-edition Spaceisthemachine|BillHillier SpaceSyntax

Space is the Machine wasfirstpublishedin1996byCambridgeUniversityPress.ThebookbuiltonthetheoryofsocietyandspacesetoutinThe Social Logic of Space (CambridgeUniversityPress1984),tooutlineaconfigurationaltheoryofarchitectureandurbanism.Unfortunately,althoughThe Social Logic of Space isstillinprintafter23years,whentheinitialprint-runofSpace is the Machine wasexhausted,thenumberofcolourplatesforbadtheuseofthecheapreprintingtechnologythatwouldhavemadeasuccessionofreprintseconomicallyviable.So,althoughthebookwassellingwellatthetime,itfelloutofprint.Asdemandforthebookhascontinued,forseveralyearscopiesofthebookhaveeitherbeenimpossibletofindorprohibitivelyexpensive. IamnowimmenselypleasedthatSpaceSyntaxLimited,withsupportfromUniversityCollegeLondon(UCL),havedecidedtorectifythissituationbycreatinganewe-editionofthebookandmakingitavailableforfreeontheweb.IamparticularlygratefultoTimStonorfortheinitialdecisiontofundtheproject,toTim,ChrisStutzandShinichiIidafororganizingandmanagingtheprojectandactingaseffectiveeditorsofthenewedition,andtoLauraVaughanandSuzanneTonkinofUCLfortheirencouragementthroughouttheprocess.ThanksandappreciationarealsoduetoChristianAltmannforthenewdesignofthepublication;toRodrigoMoraforpreparingelectronicimagesfromtheoriginalartworks;toMarcoGandini,JosephLaycock,SachaTan,andSaussanKhalilforproofreading;toMollyHallforcreatinganewindex;andtoChristianBerosforimagemanipulationandcreationofthewebdistributionpagesforthee-edition. LookingbackonSpace is the Machine,asonThe Social Logic of Space,Ifindmyselfpleasantlysurprisedthatthefoundationssetoutthereforthe‘spacesyntax’approachtohumanspatialphenomenastillseemrobust.Atthesametime,thedevelopmentsinthesubjectsince1996havebeensubstantial,notleastthroughtheinaugurationofthebi-annualspacesyntaxsymposiain1997(originallythebrainchildofMarkDavidMajor).Thesehavecreatedaresourceofseveralhundredpapersondevelopingthetheory,methodologyandapplicationsofthespacesyntaxapproachandnowconstituteoneofitsmostimportantresources.Tomepersonally,itismostgratifyingthatasetofideascreatedbyasmallgroupofpeopleworkingtogetheratUCLinthenineteenseventieshasnowfloweredintoalargeandcoherentbodyofworkbelongingtoaworld-wideresearchcommunity. Attheriskofbeingunfairtoothers,however,itdoesseemtomethatcertaincontributionstothetheoryandmethodofspacesyntaxhavebeensosignificantastodeservereviewinthisprefacetowhatisnowaneleven-year-oldtext.Forexample,onthetheoreticalfoundationsofspacesyntax,thethreepaperspublishedbyJohnPeponisandhiscolleaguesoftheGeorgiaInstituteofTechnologyinAtlantainEnvironment and Planning B in1997and1998(Peponisetal1997,Peponisetal1998a,b)onthegeometricalfoundationsseemsofpermanentsignificance,asdothetwopapersofMikeBattyofCASAatUCL(Batty2004a,b)onthegraphtheoretic

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foundations.Iwouldalsohopethatmyownattemptstoshowthattheeffectsonambientspaceoftheplacingandshapingofphysicalobjectsaresystematicandcanbemathematicallyexpressedwillprovesimilarlyrobust.Theimportanceoftheseeffectsbothfortheunderstandingofurbanform(Hillier2002),andhumanspatialcognition(Hillier2007)will,Ihope,leadtoamoreunifiedunderstandingofthelinkbetweenthesetworealms. Onthemethodologicalside,therehasbeenaremarkableflourishingofnewsyntacticmethodsfrommanysourcesandlocations.FromUCL,themostsignificantofthesehavebeenthe‘syntacticising’ofvisibilitygraphanalysisbyAlasdairTurnerinhisDepthmapsoftware(Turner&Penn1999,Turneretal2001)andthedevelopmentofsegmentbasedaxialanalysiswithangular,metricandtopologicalweightings,initiallythroughthepioneeringworkofShinichiIidaandhisSegmensoftwarewithsubsequentimplementationinDepthmap.Itwasthesemorecomplexanddisaggregatedformsoflineanalysisthatallowedustoshownotonlythathumanmovementwasspatiallyguidedbygeometricalandtopologicalratherthanmetricfactorsbutalsotoclarifywhyapowerfulimpactofspacestructureonmovementwastobemathematicallyexpected(Hillier&Iida2005).OtherkeymethodologicaldevelopmentsincludethepioneeringworkofDaltononangularanalysis(Dalton2001),nowavailableintheWebMapandWebMapatHomesoftware;theworkofFigueiredoandAmorimoftheUniversityofPernambucoinBrazilon‘continuitylines’intheMindwalksoftware(Figueiredo&Amorim2005),whichextendlinesbydiscountingangularchangesbelowacertainthreshold;andtheSpatialistsoftwaredevelopmentbyPeponisandhiscolleaguesinconnectionwiththethreepapersreferredtoabove.Othersignificantsoftwaredevelopmentsfocusonlinkingspacetootherurbanfactorssuchaslandusepatternsanddensities,notablythePlaceSyntaxsoftwarefromMarcusandhiscolleaguesattheRoyalCollegeofTechnologyinStockholm,SequencesoftwaredevelopedbyStegenatARSISinBrussels,andtheConfeegosoftwarepioneeredbyStutz,Gil,FriedrichandKlaasmeyerforSpaceSyntaxLimited. Inthemoresubstantiveareasoftheory,myownresearchhasexploredtheinter-relationsofspace,movementatdifferentscalesandlandusepatterns,anditcannowarguablybeseentobepointinginthedirectionofadesign-level(meaningpreciseenoughfortheideastobeusableindesign)theoryofcitiesasself-organisingsystems.Thetheoryisintwoparts:ontheonehand,atheoryofhowthespatialformofcitiesisshapedbyspatiallawslinkingtheemergenceofcharacteristicallyurbanspacepatternstocognitiveaswellastosocialandeconomicfactors;ontheother,atheoryofhowtheemergentpatternsofspaceshapemovement,andthroughthisshapelandusepatterns,leadingthroughfeedbackandmultipliereffects,tothegenericformofthecityasaforegroundnetworkoflinkedcentresatallscalessetintoabackgroundnetworkoflargelyresidentialspace.Criticaltotheemergenceofthistheorywasthepaper“Centrality

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asaprocess”(Hillier1999)whichshowedhowlocalprocesseswithanessentiallymetricnaturecombinedwiththelargerscalegeometricandtopologicalpropertiesofthespatialnetworktocreatetheprocessesbywhichcentresandsub-centresemergeinthenetworkthroughthelogicofthenetworkitself-thougheachisofcoursealsoaffectedbyitsrelationtoothers. Takentogetherthesedevelopmentsinspacesyntaxsuggestthatitoffersapowerfulcomplementtotraditionalmethodsformodellingcities,notleasttransportmodellingmethods.Thesehaveconceptualfoundationsquitedifferentfromsyntacticmodelsandseektoexplaindifferentthings,buttheycouldbebroughtintoasymbioticrelationwithsyntacticmodelstothebenefitofboth.Akeyresearchpriorityintheimmediatefuturewillbetoexploretheirinter-relations.Infact,followingthepioneeringworkofPennontheconfigurationalanalysisofvehicularmovement(Pennetall1998)workbyChiaradia,RafordandothersinSpaceSyntaxLimitedhasalreadysuggestedthatconfiguationalfactorscancontributeinsightsintootherkindsofmovementnetworks,includingcycles,buses,andovergroundandundergroundrailnetworks. Oneaspectofthedeepeningrelationbetweenspacesyntaxandthewiderspatialresearchcommunityhasbeenthedebateastohowfarspacesyntax’sbasictenets,suchastherepresentationofcitiesaslinenetworksandthesettingasideofEuclideanmetricfactorsatthelargerspatialscaleinfavouroftopologicaland/orgeometricones,aretheoreticallyvalidandmethodologicallyviable.Fromthesyntacticpoint,certainpointsofcriticism,suchasthataxialmapsare‘subjective’andmeasuresshouldbemetricised,seemtohavebeenanswered.Turneretal(2005)haveshowedthatleastlinegraphs(allowingrandomselectionamongsyntacticallyequivalentlines)arerigorouslydefinedandindeedareobjectsofgreattheoreticalinterestinthemselves,asisshownbyrecentworksuggestingtheyhavefractalproperties(Carvalho&Penn2004).Likewisethecriticismthatsyntaxdisregardsmetricinformationhasbeenansweredbyshowingclearlythatintermsoffunctionalitythisisascaleissue.Asshownin(Hillier1999)referredtoabove,atasufficientlylocalisedscalespaceworksinametricway,perhapsreflectingthescaleuptowhichpeoplecanmakereasonablyaccuratejudgementaboutdistanceincomplexspaces,soanaccountofthemetricpropertiesofspaceisnecessarytoafunctionallysensitiveandpredictiveanalysisofspaceatthislevel.Butatthenon-locallevel,itseemsthatthefunctionalityofspacereflectspeople’suseofageometricalpictureofthenetworkconnectivityratherthanametricpictureinnavigatingtheurbangrid,andatthisscaleintroducingmetricweightingintothemeasuresispositivelymisleading(Hillieretal2007). Thestudyofspacewithinbuildingsusingspacesyntaxmethodshasalsomuchadvancedsince1996,notleastofcoursethroughthepublicationofJulienneHanson’sDecoding Homes and Houses (1999),thethirdofthesyntaxbooksfromCambridgeUniversityPress.AlsonotablehasbeentheworkofPenn

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andhiscolleaguesonspatialformandfunctionincomplexbuildings,inparticulartheinfluentialworkonspatialdesignandinnovationinworkenvironments.Althoughnotstrictlywithinthesyntaxcontext,thehighlyoriginalworkofSteadman(Steadman1998,2001)ontheenumerationofbuiltformsthroughaclarificationofgeometric,constructionalandenvironmentalconstraintsbothanswersquestionsaboutenumerabilityraisedinSpace is the Machine,andoffersaplatformforanewapproachtospatialenumerabilitywhichcouldandshouldbetakenupwithinthesyntaxcommunity. Againstthebackgroundofthesetheoreticalandmethodologicaldevelopments,andcross-disciplinaryexchanges,spacesyntaxresearchisnowbecomingmuchmoreinterdisciplinary.FollowingaspecialissueofEnvironment and Behaviourin2003editedbyRuthConroyDaltonandCraigZimringbringingtogetherpapersonspacesyntaxandcognitionfromthe2001AtlantaSymposium,the2006conferenceonSpatialCognitionattheUniversityofBremenorganisedawell-attendedalldayworkshoponspacesyntax.Thelinkbetweenspacesyntaxandcognitivestudiesisnowbecomingawell-establishedbranchofsyntaxresearch.AtthesametimethepioneeringworkofLauraVaughanandhercolleaguesistakingsyntaxinthedirectionofagreaterengagementwithsocialstudies,andaspecialissueofProgress in Planningwillshortlyappearontheuseofspacesyntaxinthestudyofspaceasadimensionofsocialsegregationandexclusion(Vaughan(ed.)2007). Overall,spacesyntaxisbecomingaflourishingparadigmforspatialstudies,increasinglywellintegratedwithotherapproachesandincreasinglyexpandingitsscopeandscaleofinvestigation.Buttherealtestoftheoryandmethodisapplicationintherealworldofprojectsanddevelopment.HerethecontributionofSpaceSyntaxLimitedcannotbeoverestimated.SinceitsfoundationasanactivecompanyofferingspatialdesignandspatialplanningconsultancyundertheleadershipofTimStonor,ithastestedthetheoryandtechnologyonawiderangeofprojects,manyofthemhighprofile.TherearenowasignificantnumberofprojectsinwhichSpaceSyntaxhasexertedakeyspatialdesigninfluence,includingofcourseintheredesignofTrafalgarSquare(withNormanFoster)andNottingham’sOldMarketSquare(withGustafsonPorter),arguablythetwomostfamoussquaresintheUK,bothnowfunctioninginanewandhighlysuccessfulwayfollowingtheirrespectivere-designs.OtherupandrunningprojectsincludetheBrindleyPlacedevelopmentinBirmingham,ExchangeSquareandFleetPlaceinLondon,andofcoursetheMillenniumBridge,whereSpaceSyntaxshowednotonlyhowwellthebridgewouldbeusedbutalsohowstrongandbeneficialitslongtermeffectswouldbeontheareasonbothsidesoftheriver.Equallyinterestingtospacesyntaxarecaseswhereaspectsofspacesyntaxadvicewasnotfollowed,sinceineachcaseproblemshaveappearedthatwereclearlyforeseenbysyntaxatthedesignstage.

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Carefullyandresponsiblyused,itisclearthatsyntaxworksasadesignandplanningtool.Oneconsequenceofitssuccessinrelativelysmall-scaledesignandplanningproblemsisthatsyntaxisnowincreasinglybeingusedasthefoundationforthespace-basedmaster-planningofwholepartsofcitiesorevenofwholecities,andsoineffectasanewwayofmodellingcities.Itisincreasinglywellunderstoodthatasyntacticmodelofacityhastwogreatadvantagesasacomplementtoanorthodoxmodel.First,asyntacticmodelallowsthedesignerorplannertoworkacrossallurbanscalesusingthesamemodel,sothatoneformofanalysiswillidentifythelargescalemovementnetworksanditslanduseeffects,whileanotherwillsimilarlyidentifymicro-scalefeaturesandlandusepotentialsofthelocalurbangrid.Second,exactlythesamemodelthatisusedinresearchmodetoinvestigateandunderstandhowthecityisworkingnowcanbeusedindesignandplanningmodetosimulatethelikelyeffectsofdifferentdesignandplanningstrategiesandschemes,allowingtherapidexplorationofthelongtermconsequencesofdifferentstrategies. SpaceSyntaxLimitedalsoconstitutesanexperimentinhowtherelationsbetweenauniversityandaspin-outcompanycanbeorganised.AlthoughSpaceSyntaxLimitedcarriesoutitsownresearch,itmaintainsaverycloserelationtotheuniversityresearchdepartment,feedingproblemsintoitandtestingnewideasandnewtechnologies.Collaborationisbothatthestrategicresearchlevel,butalsoreachesdowntothelevelofindividualprojectswherenecessary.Theexperienceofaworkingcollaborationbetweentheuniversityandthecompanyhasconvincedusallthatinthisfieldeventhemostbasicresearchcannotbeseparatedfromthedemandsandquestionsraisedbypractice.Manytheoreticaldevelopmentshavebeensparkedbyquestionsraisedbyprojects,andatthesametimeprojectshaveprovidedasuperbearlytestinggroundforturningresearchideasintoworkableandproventechnologies.ThefactthatitisSpaceSyntaxLimitedwhichisnowre-publishingoneofthebasictheoreticaltextsofspacesyntaxisanemblemoftheclosenesswithwhichtheoryandpractice,andtheuniversityandthecommercialworld,havedevelopedcollaborativelyoverthepastdecade.

bhJune6th2007

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References

Batty,M.(2004)ANewTheoryofSpaceSyntax,WorkingPaper75,CentreforAdvancedSpatialAnalysis,UCL,London:availablefromWWWathttp://www.casa.ucl.ac.uk/working_papers/paper75.pdfBatty,M.(2004)DistanceinSpaceSyntax,WorkingPaper80,CentreforAdvancedSpatialAnalysis,UCL,London:availablefromWWWathttp://www.casa.ucl.ac.uk/working_papers/paper80.pdf Carvalho,R.,Penn,A.(2004)“Scalinganduniversalityinthemicro-structureofurbanspace.”PhysicaA332539-547.Dalton,N.(2001)“FractionalconfigurationanalysisandasolutiontotheManhattanProblem.”Proceedingsofthe3rdInternationalSpaceSyntaxSymposium,GeorgiaInstituteofTechnology,Atlanta,GA,7-11May2001.Figueiredo,L.,Amorim,L.(2005)“Continuitylinesintheaxialsystem.”Proceedingsofthe5thInternationalSpaceSyntaxSymposium,TechnischeUniversiteitDelft,theNetherlands,13-17June2005.HansonJ(1999)Decoding Homes and HousesCambridgeUniversityPress,Cambridge.Hillier,B.(1999)“Centralityasaprocess:accountingforattractioninequalitiesindeformedgrids.”Urban Design International 4107-127.Hillier,B.(2002)“Atheoryofthecityasobject.”Urban Design International 7153-179.Hillier,B.,Iida,S.(2005)“Networkandpsychologicaleffectsinurbanmovement.”InCohn,A.G.,Mark,D.M.(eds)Spatial Information Theory: COSIT 2005,LectureNotesinComputerSciencenumber3693,475-490,Springer-Verlag,Berlin.Hillier,B.(2007)“Studyingcitiestolearnaboutminds:howgeometricintuitionsshapeurbanspaceandmakeitwork.”Environment and Planning B: Planning and Design (forthcoming).Hillier,B.,Turner,A.,Yang,T.,Park,H.T.(2007)“Metricandtopo-geometricpropertiesofurbanstreetnetworks:someconvergences,divergencesandnewresults”Proceedingsofthe6thInternationalSpaceSyntaxSymposium,ITU,Istanbul,Turkey,12-15June2007.

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Penn,A.,Hillier,B.,Banister,D.,Xu,J.(1998)“Configurationalmodellingofurbanmovementnetworks”Environment and Planning B: Planning and Design 2559-84.Penn,A.andDesyllas,J.andVaughan,L.(1999)“Thespaceofinnovation:interactionandcommunicationintheworkenvironment”Environment and Planning B: Planning and Design,26(2)193-218Peponis,J.,Wineman,J.,Rashid,M.,Kim,S.H.,Bafna,S.(1997)“Onthedescriptionofshapeandspatialconfigurationinsidebuildings:convexpartitionsandtheirlocalproperties.”Environment and Planning B: Planning and Design 24(5)761-781.

Peponis,J.,Wineman,J.,Bafna,S.,Rashid,M.,Kim,S.H.(1998)“Onthegenerationoflinearrepresentationsofspatialconfiguration.”EnvironmentandPlanningB:PlanningandDesign25(4)559-576.

Peponis,J.,Wineman,J.,Rashid,M.,Bafna,S.,Kim,S.H.(1998)“Describingplanconfigurationaccordingtothecovisibilityofsurfaces.”Environment and Planning B: Planning and Design 25(5)693-708.

Steadman,J.P.(2001)“Everybuiltformhasanumber.”Proceedingsofthe3rd

InternationalSpaceSyntaxSymposium,GeorgiaInstituteofTechnology,Atlanta,GA,7-11May2001.

Steadman,J.P.(1998)“Sketchforanarchetypalbuilding.”Environment and Planning B: Planning and Design, 25th Anniversary Issue,92-105.

Turner,A.,Penn,A.(1999)“Makingisovistssyntactic:isovistintegrationanalysis.”Proceedingsofthe2ndInternationalSpaceSyntaxSymposium,UniversidadedeBrasília,Brasilia,Brazil,29March–2April1999.

Turner,A.,Doxa,M.,O’Sullivan,D.,Penn,A.(2001)“Fromisoviststovisibilitygraphs:amethodologyfortheanalysisofarchitecturalspace.”Environment and Planning B: Planning and Design 28(1)103-121.

Turner,A.,Penn,A.,Hillier,B.(2005)“Analgorithmicdefinitionoftheaxialmap.”Environment and Planning B: Planning and Design 32(3)425-444.Vaughan,L.(ed.)(2007)ProgressinPlanning(TheSpatialSyntaxofUrbanSegregation)67(4)(inpress).

Acknowlegdements Spaceisthemachine|BillHillier SpaceSyntax

Acknowledgementsandthanksareduefirsttothemanyfriendsandcolleagueswhohave,overtheyears,madeanenormouscontributiontotheideasandresearchsetoutinthisbook,mostnotablyDr.JulienneHanson,AlanPennandDr.JohnPeponis,eachofwhosecontributionshasbeentoolargeanddiversetoacknowledgeindetail;toNick‘Sheep’Daltonforthetitleofthebook,andalsoforthebrilliantsoftwareonwhichmuchoftheresearchisfounded,theoutwardandvisiblesignofwhichisinthePlatesinthebook;toMarkDavidMajorformastermindingthegradualandpainfulevolutionofthetextandillustrations;toMyrto-Gabriella(Petunia)Exacoustouforreading,criticisingandhelpingmesubstantiallyimprovethefinaldraft;toProfessorPatO’Sullivan,HeadoftheBartlett,forasixmonthssabbaticalin1992,whenIsaidIwouldfinishbutheknewIwouldn’t;totheEngineeringandPhysicalSciencesResearchCouncilforcontinuedresearchfunding;tothemanycontributorstotheresearch,andespeciallyTimStonor,KayvanKarimi,BeatrizdeCampos,XuJianming,GordonBrown,JohnMiller,TadGrajewski,LenaTsoskounoglou,LauraVaughan,MartinedeMaesseneer,GuidoStegenandChangHuaYoo(whodrewthefirstversionofthemapofLondon);totheMScanddoctoralstudentsoftheBartlettSchoolofGraduateStudieswhocontinuetogivesomuchintellectualbuzztothedepartment;toProfessorsPhilipSteadman,TomMarkusandMikeBattyforsustainedintellectualsupportovertheyears;toStuartLiptonandhisteamatStanhopePropertiesPlcforprovidinguswithsomanyopportunitiestoapplyourresearchonrealdevelopmentanddesignprojects,andtolearnsomuchfromthem,andalsotoGordonGrahamoftheLondonRegenerationConsortium,theSouthBankEmployersGroup,ChesterfieldPropertiesPlc,OveArupandPartners,andPeterPalumbo;tothemanypublicbodieswhohaveinvitedustocontributetotheirworkthroughappliedresearch,includingNationalHealthServiceEstates,BritishRailways,BritishAirways,Powergen,theDepartmentofEducationandScience,TechnicalAidforNottinghamCommunities,theLondonBoroughsofCroydonandCamden,andtheTateGallery;tothemanyarchitecturalpracticeswhohaveinvitedustoworkwiththemontheirprojects,butmostespeciallySirNormanFosterandPartners,theRichardRogersPartnership,TerryFarrellandCompany,Skidmore,OwingsandMerrill,NicholasGrimshawandPartners,BennettsAssociates,SWArchitects,andAvantiArchitects;toProfessorSheilaHillierandMarthaHillierfortoleratinganobsessivelap-topperinthehouseforlongerthanwasreasonable;toKate,CharlotteandBenHillierforcontinuingtobethegoodfriendsandsupportersofapreoccupiedandinconsideratefather;tothethiefwhotookallcopiesofthedraftofthefirstfourchaptersfrommyhomewhenstealingmycomputer,thussavingmefromprematurepublication;toRoseShawe-Taylor,KarlHowe,EmmaSmith,SusanBeerandJosieDixonofCambridgeUniversityPress;andfinallytoUCLforcontinuingtobethemosttolerantandsupportiveofUniversities.

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Introduction

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Introduction�

In1984,inThe Social Logic of Space,writtenincollaborationwithJulienneHansonandpublishedbyCambridgeUniversityPress,Isetoutanewtheoryofspaceasanaspectofsociallife.Sincethenthetheoryhasdevelopedintoanextensiveresearchprogrammeintothespatialnatureandfunctioningofbuildingsandcities,intocomputersoftwarelinking‘spacesyntax’analytictoolswithgraphicalrepresentationandoutputforresearchersanddesigners,andintoanexpandingrangeofapplicationsinarchitecturalandurbandesign.Duringthistime,alargenumberofarticles,reportsandfeatureshaveappeared,theseshavebeenwritteninmanyuniversitiesusingthetheoryandmethodsof‘spacesyntax’,andresearchhasbeeninitiatedinmanypartsoftheworldintoareasasdiverseastheanalysisofarchaeologicalremainsandthedesignofhospitals. Duringthistime,manytheoreticaladvanceshavealsobeenmade,ofteninsymbiosiswiththedevelopmentofnewtechniquesforthecomputerrepresentationandanalysisofspace.Onekeyoutcomeoftheseadvancesisthattheconceptof‘configuration’hasmovedtocentrestage.Configurationmeans,putsimply,relationstakingintoaccountotherrelations.Thetechniquesof‘configurationalanalysis’-ofwhichthevarious‘spacesyntax’techniquesareexemplars-thathavebeenbuiltfromthisideahavemadeitpossibletobringtheelusive‘patternaspect’ofthingsinarchitectureandurbandesignintothelightofday,andtogivequantitativeexpressiontotheage-oldideathatitis‘howthingsareputtogether’thatmatters. Thishasinturnledtoacleararticulationofaphilosophyofdesign.Architecturalandurbandesign,bothintheirformalandspatialaspects,areseenasfundamentallyconfigurationalinthatthewaythepartsareputtogethertoformthewholeismoreimportantthananyofthepartstakeninisolation.Theconfigurationaltechniquesdevelopedforresearchcan,infact,justaseasilybeturnedroundandusedtosupportexperimentationandsimulationindesign.Inlinkingtheoreticalresearchtodesigninthisway,wearefollowingahistoricaltraditioninarchitecturaltheorywhichhasbothattemptedtosubjectthepatternaspectofthingsinarchitecturetorationalanalysis,andtotesttheseanalysesbyembodyingtheminrealdesigns.Thedifferencenowisonlythattheadventofcomputersallowsustobringamuchgreatdegreeofrigourandtestingtotheoreticalideas. Theaimofthisbookistobringtogethersomeoftheserecentdevelopmentsinapplyingconfigurationalanalysistoissuesofarchitecturalandurbantheoryintoasinglevolume.Thesurprisingsuccessofconfigurationalideasincapturingtheinnerlogicofatleastsomeaspectsoftheformandfunctioningofbuiltenvironments,suggeststhatitmightinduecoursebeusefultoextendtheseideastootherareaswheresimilarproblemsofdescribingandquantifyingconfigurationseemtobecentral,includingsomeaspectsofcognitivepsychology,butalsoperhapssociologyitself.Atpresentweareencouragedbythecurrentinterestintheseideasacrossarangeofdisciplinesand,justasthelastdecadehasbeendevotedtothedevelopmentandtestingoftechniquesofconfigurational

�

Introduction

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Introduction2

analysiswithinarchitectureandurbandesign,sowehopethatthecomingdecadewillseecollaborationsamongstdisciplineswhereconfigurationisidentifiedasasignificantproblem,andwheresomedevelopmentoftheconfigurationalmethodologycouldconceivablyplayausefulrole. Theimmediatecontextofthebookisthechangingtheoreticaldebatewithinandaroundarchitecture.Lookingback,itiseasytoseethatinspiteoftheattentionpaidtotheoryinarchitectureinthetwentiethcentury,andinspiteofthegreatinfluencethattheorieshavehadonourbuiltenvironment,architecturaltheoriesinthelastdecadeshaveingeneralsufferedfromtwodebilitatingweaknesses.First,mosthavebeenstronglynormative,andweaklyanalytic,inthattheyhavebeentoomuchconcernedtotelldesignershowbuildingsandenvironmentsshouldbe,andtoolittleconcernedwithhowtheyactuallyare.Asaresult,theoriesofarchitecturehaveinfluencedourbuiltenvironmentenormously,sometimesforgood,sometimesforill,buttheyhavedonelittletoadvanceourunderstandingofarchitecture. Second,therehasbeenanexplosionofthehistorictendencytoformarchitecturaltheoriesoutofideasandconceptsborrowedfromotherdisciplines.Asaresult,architecturaldiscoursehasbeendominatedbyaseriesofborrowings,firstfromengineeringandbiology,thenfrompsychologyandthesocialsciences,thenfromlinguisticsandsemiology,andmostrecentlyofallfromliterarytheory.Eachofthesehashadthemeritthatitallowedarchitecturetobecomepartofwiderintellectualdebate.Buttherehasbeenaprice,inthatverylittleattentionhasbeengiventotheinternaldevelopmentofarchitectureasadiscipline.Throughthisturningaway,architecturehasincreasinglyignoredthelessonswaitingtobelearnedfromtheintensivestudyofexperimentaltwentieth-centuryarchitecture,andacquiredwhatnowamountstoahiddenhistoryinwhichkeyaspectsofrecentarchitecturalrealityhavebeensuppressedasthoughtheyweretoopainfultotalkabout. Theaimofthisbookistobegintheprocessofremedyingthisbiastowardsoverlynormativetheoriesbasedonconceptborrowingfromotherdisciplines,byinitiatingthesearchforagenuinelyanalyticandinternaltheoryofarchitecture,thatis,onebasedonthedirectstudyofbuildingsandbuiltenvironments,andguidedbyconceptsformedoutofthenecessitiesofthisstudy.Theguidingbeliefisthatwhatweneedattheendofthetwentiethcenturyisabetteranddeeperunderstandingofthephenomenonofarchitectureandhowitaffectspeople’slives,andhowthisrelatestoinnovativepossibilityinarchitecture,andthecentralroleofthearchitecturalimagination. Thisbookisthereforeconcernedwithwhatbuildingsandcitiesarelike,whytheyareastheyare,howtheywork,howtheycomeaboutthroughdesign,andhowtheymightbedifferent.Theword‘theory’isusednotinthecommonarchitecturalsenseofseekingsomesetofruleswhich,iffollowed,willguaranteearchitecturalsuccess,butinthephilosophicalandscientificsensethattheoriesaretheabstractionsthroughwhichweunderstandtheworld.Anarchitecturaltheory,asweseeit,shoulddeepenourgraspofarchitecturalphenomena,andonlysubsequentlyandwithgreatmodesty,suggestpossibleprinciplesonwhich

Introduction

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Introduction3

tobasespeculationandinnovationindesign.Suchatheoryisanalyticbeforeitisnormative.Itsprimaryroleistoenquireintothepuzzlethatweseeandexperiencearchitecture,butwedonotunderstandwhatweseeandexperience.Howeverstronglywemayfeelthatarchitecturemaybewrongorright,werarelyunderstandthearchitecturalgroundsonwhichsuchjudgmentsaremade.Thisbookthereforeseeksanunderstandingofthetheoreticalcontentofarchitecture. Thebookisinfourparts.Thefirst,‘Theoretical Preliminaries’,dealswiththemostbasicofallquestionswhicharchitecturaltheorytriestoanswer:whatisarchitecture,andwhataretheories,thattheycanbeneededinarchitecture?Inthefirstchapter,‘Whatarchitectureaddstobuilding’,thekeyconceptsofthebookaresetoutonthewaytoadefinitionofarchitecture.Theargumentisthatinadditiontofunctioningasbodilyprotection,buildingsoperatesociallyintwoways:theyconstitutethesocialorganisationofeverydaylifeasthespatialconfigurationsofspaceinwhichweliveandmove,andrepresentsocialorganisationasphysicalconfigurationsofformsandelementsthatwesee.Bothsocialdimensionsofbuildingarethereforeconfigurationalinnature,anditisthehabitofthehumanmindtohandleconfigurationunconsciouslyandintuitively,inmuchthesamewayaswehandlethegrammaticalandsemanticstructuresofalanguageintuitively.Ourmindsareveryeffectiveinhandlingconfigurationinthisway,butbecausewedoworkthisway,wefinditverydifficulttoanalyseandtalkrationallyabouttheconfigurationalaspectsofthings.Configurationisingeneral‘non-discursive’,meaningthatwedonotknowhowtotalkaboutitanddonotingeneraltalkaboutitevenwhenwearemostactivelyusingit.Invernacularbuildings,theconfigurational,ornon-discursive,aspectsofspaceandformarehandledexactlylikethegrammaroflanguage,thatis,asanimplicationofthemanipulationofthesurfaceelements,orwordsandgroupsofwordsinthelanguagecase,buildingelementsandgeometricalcoordinationsinbuilding.Inthevernaculartheactofbuildingreproducesculturalgivenspatialandformalpatterns.Thisiswhyitseldomseems‘wrong’.Architecture,incontrast,isthetakingintoconscious,reflectivethoughtofthesenon-discursiveandconfigurationalaspectsofspaceandform,leadingtotheexerciseofchoicewithinawidefieldofpossibility,ratherthanthereduplicationofthepatternsspecifictoaculture.Architectureis,inessence,theapplicationofspeculativeandabstractthoughttothenon-discursiveaspectsofbuilding,andbecauseitisso,itisalsoitsapplicationtothesocialandculturalcontentsofbuilding. Chapter2,‘Theneedforananalytictheoryofarchitecture’,thentakesthisargumentintoarchitecturaltheory.Architecturaltheoriesareessentiallyattemptstosubjectthenon-discursiveaspectsofspaceandformtorationalanalysis,andtoestablishprinciplestoguidedesigninthefieldofchoice,principleswhicharenowneededasculturalguidanceisnolongerautomaticasitisinavernaculartradition.Architecturaltheoriesarebothanalyticinthattheyalwaysdependonconjecturesaboutwhathumanbeingsarelike,buttheyarealsonormative,andsayhowtheworldshouldberathermorestronglythantheysayhowitis.Thismeansthatarchitecturecanbeinnovativeandexperimentalthroughtheagencyoftheories,but

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itcanalsobewrong.Becausetheoriescanbewrong,architectsneedtobeabletoevaluatehowgoodtheirtheoriesareinpractice,sincetherepetitionoftheoreticalerror-asinmuchofthemodernisthousingprogramme-willinevitablyleadtothecurtailmentofarchitecturalfreedom.Theconsequenceofthisistheneedforatrulyanalytictheoryofarchitecture,thatis,onewhichpermitstheinvestigationofthenon-discursivewithoutbiastowardsoneorotherspecificnon-discursivestyle. Chapter3,‘Non-discursivetechnique’,outlinestheprimerequirementforpermittingarchitectstobeginthistheoreticallearning:theneedforneutraltechniquesforthedescriptionandanalysisofthenon-discursiveaspectsofspaceandform,thatis,techniquesthatarenotsimplyexpressionsofpartisanshipforaparticulartypeofconfiguration,asmostarchitecturaltheorieshavebeeninthepast.Thechapternotesacriticaldifferencebetweenregularitiesandtheories.Regularitiesarerepeatedphenomena,eitherintheformofapparenttypingorapparentconsistenciesinthetimeorderinwhicheventsoccur.Regularitiesarepatternsinsurfacephenomena.Theoriesareattemptstomodeltheunderlyingprocessesthatproduceregularities.Everysciencetheorisesonthebasisofitsregularities.Socialsciencestendtobeweaknotbecausetheylacktheoriesbutbecausetheylackregularitieswhichtheoriescanseektoexplainandwhichthereforeoffertheprimetestoftheories.Thefirsttaskinthequestforananalytictheoryofarchitectureisthereforetoseekregularities.Thefirstpurposeof‘non-discursivetechnique’istopursuethistask. PartIIofthebook,‘Non-discursive Regularities’,thensetsoutanumberofstudiesinwhichregularitiesintherelationbetweenspatialconfigurationandtheobservedfunctioningofbuiltenvironmentshavebeenestablishedusing‘non-discursivetechniques’ofanalysistocontrolthearchitecturalvariables.Chapter4,‘Citiesasmovementeconomies’reportsafundamentalresearchfinding:thatmovementintheurbangridis,otherthingsbeingequal,generatedbytheconfigurationofthegriditself.Thisfindingallowscompletelynewinsightsintothestructureofurbangrids,andthewaythesestructuresrelatetourbanfunctioning.Therelationbetweengridandmovementinfactunderliesmanyotheraspectsofurbanform:thedistributionoflanduses,suchasretailandresidence,thespatialpatterningofcrime,theevolutionofdifferentdensitiesandeventhepart-wholestructureofcities.Theinfluenceofthefundamentalgrid-movementrelationissopervasivethatcitiesareconceptualisedinthechapteras‘movementeconomies’,inwhichthestructuringofmovementbythegridleads,throughmultipliereffects,todensepatternsofmixeduseencounterthatcharacterisethespatiallysuccessfulcity. Chapter5,‘Canarchitecturecausesocialmalaise?’thendiscusseshowthiscangowrong.Focussingonspecificstudiesofhousingestatesusingconfigurationalanalysiscoupledtointensiveobservationaswellassocialdataitisshownhowtheoverlycomplexandpoorlystructuredinternalspaceofmanyhousingestates,includinglow-riseestates,leadstoimpoverishmentofthe‘virtualcommunity’—thatis,thesystemofnaturalco-presenceandco-awarenesscreatedbyspatialdesignandrealisedthroughmovement-andthisinturnleadstoanti-

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socialusesofspace,whicharethefirststageindeclinetowardsthe‘sinkestate’.Becausetheroleofspaceinthisprocessistocreateadisorderlyandunsafepatternofspaceuse,andthisisthenperceivedandexperienced,itispossibletoconceptualisehowarchitectureworksalongsidesocialprocessestocreatesocialdecline.Inasense,thecreationofdisorderlyspaceusethroughmaladroitspacedesigncreatesthefirstsymptomsofdecline,evenbeforeanyrealdeclinehasoccurred.Inasensethen,itisargued,wefindthatthesymptomshelptobringaboutthedisease. Chapter6,‘Timeasanaspectofspace’thenconsidersanotherfundamentaldifferencebetweenurbanforms:thatbetweencitieswhichservetheneedsofproduction,distributionandtrade,andthosewhichservetheneedsofsocialreproduction,thatisofgovernment,majorsocialinstitutionsandbureaucracies.Aseriesof‘strangetowns’areexamined,anditisshownhowintheirspatialproperties,theyareinmanysensestheoppositetothe‘normal’townsconsideredinChapter5.Thedetailedspatialmechanismsofthesetownsareexamined,anda‘genotype’proposed.Anexplanationisthensuggestedastowhy‘citiesofsocialreproduction’tendtoconstructthesedistinctivetypesofspatialpatterns. Chapter7,‘VisibleColleges’,thenturnstotheinteriorsofbuildings.Itbeginsbysettingoutageneraltheoryofspaceinbuildings,takingintoaccounttheresultsofsettlementanalysis,andthenhighlightsaseriesofstudiesofbuildings.Akeydistinctionismadebetween‘longandshortmodels’,thatis,betweencaseswherespaceisstronglygovernedbyrules,andthereforeactstoconservegivensocialstatusesandrelationshipsandcaseswherespaceactstogeneraterelationsoverandabovethosegivenbythesocialsituation.Theconceptoflongandshortmodelspermitssocialrelationsandspatialconfigurationtobeconceptualisedinananalogousway.Aritualisalongmodelsocialevent,sinceallthathappensisgovernedbyrules,andaritualtypicallygeneratesaprecisesystemofspatialrelationshipsandmovementsthroughtime,thatis,aspatial‘longmodel’.Apartyisashortmodelevent,sinceitsobjectistogeneratenewrelationshipsbyshufflingtheminspace,andthismeansthatrulesmustbeminimisedbyusingaspatial‘shortmodel’.Inalongmodelsituationspaceisadaptedtosupporttherules,andbehaviouralrulesmustalsosupportit.Inashortmodelsituation,spaceevolvestostructure,andoftentomaximise,encounterdensity. PartIIIofthebook,‘The Laws of the Field’,thenusesthesenotedregularitiestoreconsiderthemostfundamentalquestionofallinarchitecturaltheory:howisthevastfieldofpossiblespatialcomplexesconstrainedtocreatethosethatareactuallyfoundasbuildings?First,inChapterEight,‘Isarchitectureanarscombinatoria?’,ageneraltheoryof‘partitioning’isproposed,inwhichitisshownthatlocalphysicalchangesinaspatialsystemalwayshavemoreorlessglobalconfigurationaleffects.Itisthelawsgoverningthispassageformlocalphysicalmovestoglobalspatialeffectsthatarethespatiallawsthatunderliebuilding.Theselocal-to-globalspatiallawsarelinkedtotheevolutionofrealbuildingsthroughwhatwillbecalled‘genericfunction’,bywhichismeantthe

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spatialimplicationsofthemostfundamentalaspectsofhumanuseofspace,thatis,thefactofoccupationandthefactofmovement.Atthisgenericlevel,functionimposesrestraintsonwhatisspatiallyviable,andthisisresponsibleforwhatallbuildingshaveincommonasspatialdesigns.Genericfunctionisthe‘firstfilter’betweenthefieldofpossibilityandarchitecturalactuality.Thesecondfilteristhentheculturalorprogrammaticrequirementofthattypeofbuilding.Thethirdfilteristheidiosyncrasiesofstructureandexpressionthatthendistinguishthatbuildingfromallothers.Thepassagefromthepossibletotherealpassesthroughthesethreefilters,andwithoutanunderstandingofeachwecannotdeciphertheform-functionrelation.Mostofall,withoutaknowledgeofgenericfunctionanditsspatialimplicationswecannotunderstandthatwhatallbuildingshaveincommonintheirspatialstructuresisalreadyprofoundlyinfluencedbyhumanfunctioninginspace. InChapter9,‘Thefundamentalcity’,thetheoryofgenericfunctionandthethreefiltersisappliedtocitiestoshowhowmuchofthegrowthofsettlementsisgovernedbythesebasiclaws.Anewcomputermodellingtechniqueof‘alllineanalysis’,whichbeginsbyconceptualisingvacantspaceasaninfinitelydensematrixoflines,containingallpossiblestructures,isusedtoshowhowtheobservableregularitiesinurbanformsfromthemostlocaltothemostglobalcanbeseentobeproductsofthesameunderlyingprocesses.Afundamentalsettlementprocessisproposed,ofwhichparticularculturaltypesareparameterisations.Finally,itisshownhowthefundamentalsettlementprocessisessentiallyrealisedthroughasmallnumberofspatialideaswhichhaveanessentiallygeometricalnature. PartIVofthebook,‘Theoretical Syntheses’,thenbeginstodrawtogethersomeofthequestionsraisedinPartI,theregularitiesshowninPartIIandthelawsproposedinPartIII,tosuggesthowthetwocentralproblemsinarchitecturaltheory,namelytheform-functionproblemandtheform-meaningproblem,canbereconceptualised.Chapter10,‘Spaceisthemachine’,reviewstheform-functiontheoryinarchitectureandattemptstoestablishapathologyofitsformulation:howitcametobesetupinsuchawaythatitcouldnotbesolved.Itthenproposeshowtheconfigurationparadigmpermitsareformulation,throughwhichwecannotonlymakesenseoftherelationbetweenformandfunctioninbuildings,butalsowecanmakesenseofhowandwhybuildings,inapowerfulsenseare‘socialobjects’andinfactplayapowerfulroleintherealisationandsustainingofhumansociety.Finally,inChapter11,‘Thereasoningart’,thenotionofconfigurationisappliedtothestudyofwhatarchitectsdo,thatis,design.Previousmodelsofthedesignprocessarereviewed,anditisshownthatwithoutknowledgeofconfigurationandtheconceptofthenon-discursive,wecannotunderstandtheinternalitiesofthedesignprocess.Anewknowledge-basedmodelofdesignisproposed,withconfigurationatitscentre.Itisarguedfromthisthatbecausedesignisaconfigurationalprocess,andbecauseitisthecharacteristicofconfigurationthatlocalchangesmakeglobaldifferences,designisnecessarilyatopdownprocess.Thisdoesnotmeanthatitcannotbeanalysed,orsupportedbyresearch.Itshowshoweverthatonlyconfigurationallybiasedknowledgecanreallysupportthedesign

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process,andthis,essentially,istheoreticalknowledge.Itfollowsfromthisthatattemptstosupportdesignersbybuildingmethodsandsystemsforbottomupconstructionofdesignsmusteventuallyfailasexplanatorysystems.Theycanservetocreatespecificarchitecturalidentities,butnottoadvancegeneralarchitecturalunderstanding. Inpursuingananalyticratherthananormativetheoryofarchitecture,thebookmightbethoughtbysometohavepretensionstomaketheartofarchitectureintoascience.Thisisnotwhatisintended.Oneeffectofabetterscientificunderstandingofarchitectureistoshowthatalthougharchitectureasaphenomenoniscapableofconsiderablescientificunderstanding,thisdoesnotmeanthatasapracticearchitectureisnotanart.Onthecontrary,itshowsquiteclearlywhyitisanartandwhatthenatureandlimitsofthatartare.Architectureisanartbecause,althoughinkeyrespectsitsformscanbeanalysedandunderstoodbyscientificmeans,itsformscanonlybeprescribedbyscientificmeansinaveryrestrictedsense.Architectureislawgovernedbutitisnotdeterminate.Whatisgovernedbythelawsisnottheformofindividualbuildingsbutthefieldofpossibilitywithinwhichthechoiceofformismade.Thismeansthattheimpactoftheselawsonthepassagefromproblemstatementtosolutionisnotdirectbutindirect.Itliesdeepinthespatialandphysicalformsofbuildings,intheirgenotypes,nottheirphenotypes. Architectureisthereforenotpartart,andpartscience,inthesensethatithasbothtechnicalandaestheticaspects,butisbothartandscienceinthesensethatitrequiresboththeprocessesofabstractionbywhichweknowscienceandtheprocessesofconcretionbywhichweknowart.Thearchitectasscientistandastheoristseekstoestablishthelawsofthespatialandformalmaterialswithwhichthearchitectasartistthencomposes.Thegreaterscientificcontentofarchitectureoverartissimplyafunctionofthefargreatercomplexityoftherawmaterialsofspaceandform,andtheirfargreaterreverberationsforotheraspectsoflife,thananymaterialsthatanartistuses.Itisthefactthatthearchitectdesignswiththespatialstuffoflivingthatbuildsthescienceofarchitectureintotheartofarchitecture. Itmayseemcurioustoarguethatthequestforascientificunderstandingofarchitecturedoesnotleadtotheconclusionthatarchitectureisascience,butneverthelessitisthecase.Inthelastanalysis,architecturaltheoryisamatterofunderstandingarchitectureasasystemofpossibilities,andhowthesearerestrictedbylawswhichlinkthissystemofpossibilitiestothespatialpotentialitiesofhumanlife.Atthislevel,andperhapsonlyatthislevel,architectureisanalogoustolanguage.Languageisoftennaïvelyconceptualisedasasetofwordsandmeanings,setoutinadictionary,andsyntacticrulesbywhichtheymaybecombinedintomeaningfulsentences,setoutingrammars.Thisisnotwhatlanguageis,andthelawsthatgovernlanguagearenotofthiskind.Thiscanbeseenfromthesimplefactthatifwetakethewordsofthedictionaryandcombinethemingrammaticallycorrectsentences,virtuallyallareutterlymeaninglessanddonotcountaslegitimatesentences.Thestructuresoflanguagearethelaws

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whichrestrictthecombinatorialpossibilitiesofwords,andthroughtheserestrictionsconstructthesayableandthemeaningful.Thelawsoflanguagedonotthereforetelluswhattosay,butprescribethestructureandlimitsofthesayable.Itiswithintheselimitsthatweuselanguageastheprimemeanstoourindividualityandcreativity. Inthissensearchitecturedoesresemblelanguage.Thelawsofthefieldofarchitecturedonottelldesignerswhattodo.Byrestrictingandstructuringthefieldofcombinatorialpossibility,theyprescribethelimitswithinwhicharchitectureispossible.Aswithlanguage,whatisleftfromthisrestrictivestructuringisrichbeyondimagination.Evenso,withouttheselawsbuildingswouldnotbehumanproducts,anymorethanmeaninglessbutsyntacticallycorrectconcatenationsofwordsarehumansentences. Thecaseforatheoreticalunderstandingofarchitecturethenrestseventuallynotonaspirationtophilosophicalorscientificstatus,butonthenatureofarchitectureitself.Thefoundationalpropositionofthebookisthatarchitectureisaninherentlytheoreticalsubject.Theveryactofbuildingraisesissuesabouttherelationsoftheformofthematerialworldandthewayinwhichweliveinitwhich(asanyarchaeologistknowswhohastriedtopuzzleoutaculturefrommaterialremains)areunavoidablybothphilosophicalandscientific.Architectureisthemosteveryday,themostenveloping,thelargestandthemostculturallydeterminedhumanartefact.Theactofbuildingimpliesthetransmissionofculturalconventionsansweringthesequestionsthroughcustomandhabit.Architectureistheirrenderingexplicit,andtheirtransmutationintoarealmofinnovationand,atitsbest,ofart.Inasense,architectureisabstractthoughtappliedtobuilding,eventhereforeinasensetheoryappliedtobuilding.Thisiswhy,intheend,architecturemusthaveanalytictheories.

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Part oneTheoretical preliminaries

Defining architectureWhatisarchitecture?Onethingisclear:ifthewordistoserveausefulpurposewemustbeabletodistinguisharchitecturefrombuilding.Sincebuildingisthemorebasicterm,itfollowsthatwemustsayinwhatsensearchitectureismorethanbuilding.Theessenceofourdefinitionmustsaywhatarchitectureaddstobuilding. Thecommonest‘additive’theoryisthatarchitectureaddsarttobuilding.Inthisanalysis,buildingisanessentiallypracticalandfunctionalactivityontowhicharchitecturesuperimposesanartisticpreoccupationwhich,whilerespectingthepracticalandfunctional,isrestrictedbyneither.Theextremeversionofthisviewisthatarchitectureistheadditiontobuildingofthepracticallyuselessandfunctionallyunnecessary.1Themorecommonisthatbuildersmakebuildingswhilearchitectsaddstyle. Fromthepointofviewoffindingwhatpeople‘reallymean’whentheysay‘architecture’,thereareseriousproblemswiththeseviews.Themostobviousisthatitdefinesarchitectureintermsofwhatisnormallythoughtofasitsdegeneration,thatis,thatarchitectureisnomorethantheadditionofasurfaceappearancetobuilding.Evenifwetaketheviewthatthisiswhatarchitecturehasbecome,itissurelyunacceptableasadefinitionofwhatitshouldbe.Architectsbelieve,andclientsonthewholebuy,theideathatarchitectureisawayofbeingconcernedwiththewholebuilding,andameansofengagingthedeepestaspectsofwhatabuildingis.Ifarchitectureisdefinedasanadd-onwhichignoresthemainsubstanceofbuilding,thenarchitecturewouldbeanadditiontobuilding,butwouldnotbemorethanbuilding.Onthecontrary,itwouldbeconsiderablyless.Ifweaccusearchitectureofbeingnomorethanthis,weimplythatarchitectureoughttobemuchmore.Wearethereforebacktothebeginninginourpursuitofadefinition. Anequallydifficultproblemwiththisviewisthatitisveryhardtofindexamplesofbuildingwithapurelypracticalandfunctionalaim.Whereverwefindbuilding,wetendtofindapreoccupationwithstyleandexpression,howevermodest.Someofthemoststrikinginstancesofthishavecomefromourgrowingawarenessofbuildingbytechnologicallysimplesocieties,wherewedonotfindthatsimplicityoftechniqueisassociatedwithsimplicityofculturalintentortheeliminationofthepreoccupationwithstyle.Onthecontrary,wefindthatthroughtheidiosyncrasiesofstyle,buildingandsettlementformbecomesoneoftheprimary—thoughmostpuzzlingandvariable—expressionsofculture.2Thetermthatexpressesthisdiscovery.‘architecturewithoutarchitects’confirmstheexistenceofarchitectureassomethingoverandabovebuilding,eventhoughatthesametimeitaffirmstheabsenceofarchitects.3

ItistheawarenessoftheculturalrichnessofeverydaybuildingthatleadRogerScruton,inhisThe Aesthetics of Architecturetotrytosolvethedefinitionproblemforarchitecturebyarguingthatsinceallbuildingsharesapreoccupationwiththeaestheticandthemeaningful,allbuildingshouldbeseenasarchitecture.4Scrutonseekstoreintegratearchitecturewiththewholeofbuilding.Inhisview,allthatweeverfindinarchitectureisfound,atleastinembryonicform,intheeveryday

The visual impression, the image produced by differences of light and colour, is primary in our perception of a building. We empirically reinterpret this image into a conception of corporeality, and this defines the form of the space within…Once we have reinterpreted the optical image into a conception of space enclosed by mass, we read its purpose from its spatial form. We thus grasp…its content, its meaning. Paul Frankl

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vernacularinwhichmostofusparticipatethroughoureverydaylives.Thus:‘Evenwhenarchitectshaveadefinite“aesthetic”purpose,itmaynotbemorethanthedesirethattheirworkshould“lookright”injustthewaythattablesandchairs,thelayofplacesatatable,thefoldsinanapkin,anarrangementofbooks,may“lookright”toacasualobserver.’Thisleadshimtoadefinition:‘Architectureisprimarilyavernacularart:itexistsfirstandforemostasaprocessofarrangementinwhicheverynormalman[sic]mayparticipate.’5

Thedifficultywiththisdefinitionisthatitleadstoexactlythewrongkindofdistinctionbetween,forexample,thecarefulformalandspatialrulesthatgovernedtheEnglishsuburbanhouseasbuiltendlesslyandrepetitiouslybetweenthewarsbyspeculativebuilders,andtheworksof,say,PalladioorLeCorbusier.TheworkofbothofthesearchitectsischaracterisedbyradicalinnovationinexactlythoseareasofformalandspatialorganisationwhereaccordingtoScruton’sdefinition,thereshouldbeapreoccupationwithculturalcontinuityandreduplication.ItwouldseemtofollowthatScruton’sdefinitionofarchitecturewouldcoverthefamiliarEnglishspecbuilders’vernacularmoreeasilythanitwouldtheworksofmajorarchitecturalinnovators. Whileitmaybereasonable,then,toprefertheEnglishinter-warvernaculartotheworksofPalladioandLeCorbusier,itdoesnotseemlikelythatadefinitionoftheordinaryuseofthewordarchitectureliesinthisdirection.Onthecontrary,Scruton’sdefinitionseemstoleadusexactlythewrongway.Architectureseemstobeexactlynotthispreoccupationwithculturalcontinuity,butapreferenceforinnovation.FarfromusingthisasabasisforadefinitionthenScruton’spreoccupationwiththevernacularseemstoaccomplishtheopposite.Ittellsusmorehowtodistinguisheverydaybuildingfromthemoreambitiousaspirationsofwhatwecallarchitecture.

Is architecture a thing or an activity?Inwhatdirectionshouldwelookthenforadefinitionofarchitectureasmorethanbuilding?Reflectingonthecommonmeaningsoftheword,wefindlittlehelpandmoredifficulties.Theword‘architecture’seemstomeanbothathingandanactivity.Ontheonehanditseemstoimplybuildingswithcertain‘architectural’attributesimposedonthem.Ontheother,itseemstodescribewhatarchitectsdo,acertainwayofgoingabouttheprocessofmakingbuildings.Thisdoublemeaningraisesseriousproblemsforadefinitionofarchitecture.If‘architecture’meansbothattributesofthingsandattributesofactivities,thenwhich‘reallyis’architecture’?Thedefinitionsurelycannotencompassboth.Propertiesofthingsseemtoexistregardlessoftheactivitythatcreatesthem,andactivitiesarewhattheyareregardlessoftheirproduct.Isarchitecture,then,‘essentially’athingoranactivity?Itmust,itseems,beoneortheother. However,whenwetryeachdefinitioninisolationwequicklyrunintoparadoxes.Letusexperimentfirstwiththeideathatarchitectureisessentiallyathing;thatis,certainattributesfoundinsome,butnotall,buildings.Ifthatiswhatarchitecture‘essentially’is,thenitwouldfollowthatacopyofabuildingwhich

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possessesthearchitecturalattributeswillalsobearchitecture,toexactlythesamedegreeandinthesamewayastheoriginalbuilding.Butwebaulkatthisidea.Copiesofarchitecturalbuildingsseemnotthemselvestobearchitecture,butwhatwehavenamedthemas,thatis,copiesofarchitecture.Certainlywewouldnotnormallyexpecttowinanarchitecturalprizewithadeliberatecopy.Onthecontrary,wewouldexpecttobedisqualified,oratleastridiculed. Whatthenismissinginthecopy?Bydefinition,itcannotbepropertiesofthebuildingsincetheseareidenticalinbothcases.Thedisqualifyingfactormustlieintheactofcopying.Theactofcopyingsomehowmakesabuildingwitharchitecturalattributesnolonger,initself,architecture.Thismeansthatwhatismissinginthecopyisnottodowiththebuildingbuttodowiththeprocessthatcreatedthebuilding.Copyingisthereforeinsomecrucialsensenot‘architectural’.Evenifwestartfromthepropositionthatarchitectureisattributesofbuilding,andthereforeinsomesense,‘intheobject’,theproblemofthecopyshowsthatafterallarchitectureimpliesacertainkindofactivity,onewhichismissingintheactofcopying. Whatthenismissingintheactofcopying?Itcanonlybethatwhichcopyingdenies,thatis,theintentiontocreate,ratherthansimplytoreproduce,architecture.Withoutthisintention,itseems,abuildingcannotbearchitecture.Soletuscallthisthe‘creativeintention’andtrytomakeitthefocusofadefinitionofarchitecture.Wemayexperimentwiththeideaasbefore.Thistime,lettherebeanambitiousbuttalentlessarchitectwhointendsashardaspossibletomakearchitecture.Istheproductofthisintentionautomaticallyarchitecture?Whetheritisornotdependsonwhetheritispossibletoapprovetheintentionasarchitecturalbutdisqualifytheresult.Infactthisisaverycommonformforarchitecturaljudgmentstotake.Theproductsofaspiringarchitectsareoftenjudgedbytheirpeerstohavefailedinexactlythisway.Ajurymaylegitimatelysay:‘Weunderstandyourintentionbutdonotthinkyouhavesucceeded.’Howaresuchjudgmentsmade?Clearlythereisonlyoneanswer:byreferencetotheobjectiveattributesoftheproposedbuildingsthatourwould-bearchitecthasdesigned. Itseemsthenthenormaluseofwordsandcommonpracticehasledusinacircle.Creativeintentionfailsasadefinitionofarchitecturebyreferencetopositiveattributesofthings,justaspositiveattributesofthingspreviouslyfailedbyreferencetointentions.Yetarchitectureseemsatthesametimetomeanboth.Itseemsitcanonlybethattheideaofarchitectureisatonceathingandanactivity,certainattributesofbuildingsandacertainwayofarrivingatthem.Productandprocessarenot,itseems,independent.Injudgingarchitecturewenoteboththeattributesofthethingandtheintellectualprocessbywhichthethingisarrivedat. Thismayseematfirstsightratherodd.Itviolatesthecommonconceptionthatattributesofthingsareindependentoftheprocessesthatputthemthere.Butitdoesreflecthowpeopletalkaboutarchitecture.Architecturaltalk,whetherbylaypeopleorbycritics,typicallymixescommentonproductwithcommentonprocess.Forexample,wehear:‘Thisisaningenioussolutiontotheproblemof…’,or‘Thisisacleverdetail’,or‘Thisspatialorganisationisboldlyconceived’,‘Ilikethewaythe

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architecthas…’,andsoon.Eachoftheseisatoneandthesametimeacommentontheobjectiveattributesofthebuildingandacommentonthecreativeintellectualprocessthatgaverisetoit.Inspiteoftheunlikelihoodofproductandprocesssomehowbeinginterdependentintheideaofarchitecture,thisdoesseemtobeexactlythecase.Indescribingourexperienceofarchitecturewedescribenotonlytheattributesofthings,butalsotheintellectualprocessesofwhichthethingisamanifestation.Onlywiththesimultaneouspresenceofbothdoweacknowledgearchitecture. Thereis,itseems,someinconsistencybetweenournormalwayofreasoningaboutthingsandthewaywetalk,reasonablyandreasoningly,aboutarchitecture.Wemightevensaythattheideaofarchitectureexhibitssomeconfusionbetweensubjectsandobjects,sincethejudgmentthatabuildingisarchitectureseemsatoneandthesametimetodependontheattributesofthe‘objective’thingandonattributesofthe‘subjective’processthatgivesrisetothething.Itmightbereasonabletoexpect,then,thatfurtheranalysiswouldshowthatthisstrangenessintheideaofarchitecturewaspathologicalandthat,withamorecarefuldefinition,productandprocess,andobjectandsubject,couldandshouldbeseparated. Infact,wewillfindthecontrary.Asweproceedwithourexplorationofwhatarchitectureisandwhatitaddstobuildingwewillfindthattheinseparabilityofproductsandprocessesandofsubjectandobjectsistheessenceofwhatarchitectureis.Itisourintellectualexpectationsthatitshouldbeotherwisewhichareatfault.Architectureisatonceproductandprocess,atonceattributeofthingsandattributeofactivity,sothatweactuallysee,orthinkwesee,bothwhenweseeandnamearchitecture. Howdoesthisapparentinterdependenceofproductandprocessthenariseasarchitecturefromtheactofmakingabuilding?Tounderstandthiswemustfirstknowwhatbuilding,theallegedlylesseractivity,is,andwemustunderstanditbothasproductandasprocess.Onlythiswillallowustoseewhatisdistinctiveaboutarchitecture,andhowthisdistinctivenessinvolvesbothproductandprocess.Toallowthistobecomefullyclear,theargumentthatfollowswillbetakenintwostages.firstwewilllookatbuildingasaproduct,inordertoaskwhatitisaboutthebuildingasproductthatarchitecturetakesholdofandaddssomethingto.Thenwewilllookatbuildingasaprocess,inordertoaskhowtheprocessofarchitecture,asaddingsomethingtobuilding,isdifferent.

So what is a building?Thequestion‘whatisabuilding?’tendstoprovoketwokindsofsimplification.Thefirstisthatbecausebuildingsarepurposefulobjectswecansaywhattheyarebysayingwhattheirpurposeis.Thesecondisthattheremustbesomesimpleprimordialpurposewhichwastheoriginalreasonforbuildingsandthereforeconstitutesakindofcontinuingessenceofbuilding.Thefirstsimplificationisalogicalerror,thesecondahistoricalone.Bothfindtheircommonest,butnotonly,expressioninsuchideasasthatbuildingsareessentially‘shelter’.

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Bothsimplificationsarisebecausepurposesareseentobeanteriortoobjectsandthereforeinsomesenseexplanatoryofthem.Butlogically,functionaldefinitionsareabsurd.Indefiningbuildingintermsofafunction,ratherthananobject,nodistinctionismadebetweenbuildingsasobjectsandotherentitieswhichalsocanordoprovidethatfunction,asforexampletrees,tents,cavesandparasolsalsoprovideshelter.Functionaldefinitionsarealsodishonest.Onewhodefinesabuildingasashelterhasapictureofabuildinginmind,butonewhichisimplicitratherthanexplicit,sothattheimprecisionofthedefinitionisneverrevealedtothedefiner.Ifwesay‘abuildingisashelter’wementallyseeabuildingandconceiveofitfunctioningasashelter,sothatthefunctionseemsto‘explain’theobject.Functionaldefinitionsonlyappeartoworkbecausetheyconcealanimplicitideaoftheobject.Thispreventstheimprecisionofthedefinitionfrombeingapparenttothedefiner.Evenifthefunctionwerethoughttobeuniquetotheobject,thedefinitionofanobjectthroughitsfunctionwouldneverbesatisfactorysincewecouldneverbesureeitherthatthisfunctionisnecessarilyuniquetothisobject,orthatthisistheonly‘essential’functionofthisobject. Historicallyinfactalltheevidenceisthatneitheristhecase.Ifweconsiderthephenomenonofbuildingevenintheearliestandsimplestsocieties,oneofthemoststrikingthingsthatwefindisthatbuildingsarenormallymultifunctional:theyprovideshelterfromtheelements,theyprovidesomekindofspatialschemefororderingsocialrelationsandactivities,theyprovideaframeworkforthearrangementofobjects,theyprovideadiversityofinternalandexternalopportunitiesforaestheticandculturalexpression,andsoon.Ontheevidencewehave,itisdifficulttofindhistoricaloranthropologicalgroundsforbelievingthatbuildingsarenotintheirverynaturemultifunctional. Noristhereanyreasonwhyweshouldexpectthemtobe.Inspiteofthepersistenceoftheabsurdbeliefthathumankindlivedincavesuntilneolithictimes(beginningabout10–12,000yearsago),andthenusedthecaveasthemodelforthebuilding,6thereisevidencethathumanbeingshavecreatedrecognisablebuildingsforaverylongtime,perhapsaslongasatleastthreehundredthousandyears.7Wedonotknowhowtheantiquityofbuildingcompareswiththatoflanguage,butitisclearthattheevolutionaryhistoryofeachisverylong,andthatconjecturalhistoricalontologiesareequallyirrelevanttobothintryingtounderstandthecomplexnatureofeitherassocialandculturalphenomenon.Thespeculationthatbuildingsaresomehow‘explained’bybeingdefinedasshelters,becauseweimaginethattheremusthavebeenatimewhenthiswasallthatbuildingwas,isaboutasusefulinunderstandingthesocialandculturalcomplexitiesofbuildingastheideathatlanguagebeganwithpointingandgruntingistotheoriesofthestructureandfunctioningoflanguage. Butitisnotonlytimethathasgivenbuildingstheirvarietyofculturalexpression.Thenatureofthebuildingasanobjectitselfhascomplexitieswhichinthemselvesnaturallytendtomultifunctionalityanddiversityofculturalexpression.Itisonlybyunderstandingthecomplexnatureofthebuildingasobjectthatwe

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canbegintounderstanditsnaturaltendencytomultifunctionality.Atthemostelementarylevel,abuildingisaconstructionofphysicalelementsormaterialsintoamoreorlessstableform,asaresultofwhichaspaceiscreatedwhichisdistinctfromtheambientspace.Attheveryleastthen,abuildingisbothaphysicalandaspatialtransformationofthesituationthatexistedbeforethebuildingwasbuilt.Eachaspectofthistransformation,thephysicalandthespatial,alreadyhas,asweshallsee,asocialvalue,andprovidesopportunityforthefurtherelaborationofthisvalue,inthatthephysicalformofthebuildingmaybegivenfurtherculturalsignificancebytheshapinganddecorationofelements,andthespatialformmaybemademorecomplex,byconceptualorphysicaldistinctions,toprovideaspatialpatterningofactivitiesandrelationships. However,eveninthemostprimitive,unelaboratedstate,theeffectofthiselementarytransformationofmaterialandspaceonhumanbeings—thatis,its‘functional’effect—iscomplex.Part,butonlypart,ofthiscomplexityisthefunctionaleffectthatthe‘shelter’theoristshavenoted,namelythephysicaleffectthatbodiesareprotectedfromambientelementsthatintheabsenceofthebuildingmightbeexperiencedashostile.Theseelementsincludeinclementweatherconditions,hostilespeciesorunwelcomeconspecifics.Whenwesaythatabuildingisa‘shelter’,wemeanthatitisakindofprotectionforthebody.Tobeaprotectiveshelterabuildingmustcreateaprotectedspacethroughastableconstruction.Whatisprotectiveisthephysicalformofthebuilding.Whatisprotectedisthespace.Buildingshaveabodilyfunction,broadandnon-specific,butclassifiableasbodily,asaresultofwhichthebuildinghasspaceabletocontainbodies,andcertainphysicalpropertiesthroughwhichbodiesareprotected. However,eventhesimplestbodilyactofmakingashelterismorecomplexthanmightappearatfirstsight.Toencloseaspacebyaconstructioncreatesnotonlyaphysicaldistinctiononthesurfaceoftheearth,butalsoalogical,orcategoricdistinction.Weacknowledgethisthroughtermslike‘inside’and‘outside’.Thesearerelationalnotionswithanessentiallylogicalnature,notsimplephysicalfacts.Theyariseasakindof‘logicalemergence’fromthemoreelementaryphysicalfactofmakingaboundary.Therelationalityofthese‘logicalemergents’canbedemonstratedbysimplypointingtotheinterdependenceof‘inside’and‘outside’.Oneimpliestheother,andwecannotcreateaspaceinsidewithoutalsomakingaspaceoutside.Logicalitycanbedemonstratedbydirectanalogy.Thephysicalprocessofdrawingaboundaryisanalogoustonamingacategory,sincewhenwedosowealsobyimplicationnameallthatisnotthatcategory,thatis,weimplythecomplementofthatcategory,inthesamesensethatwhenwenamethespaceinsidewealsoimplyallthespacethatisoutside.Inthatsensethespaceoutsideisthecomplementofthespaceinside.LogiciansconfirmthisanalogybydrawingVenndiagrams,thatrepresentconceptsasallthatfallswithinthespaceofacircle,anexactlyanalogouslogicalgesturetothecreationofaboundaryinrealspace. AsRussellhaspointedout,8relations,especiallyspatialrelations,areverypuzzlingentities.Theyseemtoexist‘objectively’,inthesense(tousetheexample

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givenbyRussell)that‘EdinburghistothenorthofLondon’,butwecannotpointdirectlytotherelationinthewaythatwecantootherentitieswhichseemto‘reallyexist’.Wemustaccept,Russellargues,that‘therelation,likethetermsitrelates,isnotdependentonthought,butbelongstotheindependentworldwhichthoughtapprehends,butdoesnotcreate’.Wemustthenaccept,hecontinues,thatarelation‘isneitherinspacenorintime,neithermaterialnormental,yetitissomething’. The‘objectivity’ofrelations,andofthemorecomplexrelationalschemeswecall‘configurations’,willbeacontinuingthemeinthisbook.However,evenatthesimplestlevelofthecreationofaboundarybythesimplestactofbuilding,mattersareyetmorecomplex.Thelogicaldistinctionsmadebydrawingboundariesarealsosociologicaldistinctions,inthatthedistinctionbetweeninsideandoutsideismadebyasocialbeing,whosepowertomakethisdistinctionbecomesrecognisednotonlyinthephysicalmakingoftheboundaryandthecreationoftheprotectedspacebutalsointhelogicalconsequencesthatarisefromthatdistinction.Thisisbestexpressedasaright.Thedrawingofaboundaryestablishesnotonlyaphysicalseparateness,butalsothesocialseparatenessofadomain—theprotectedspace—identifiedwithanindividualorcollectivity,whichcreatesandclaimsspecialrightsinthatdomain.Thelogicaldistinctionandthesociologicaldistinctioninthatsenseemergefromtheactofmakingasheltereveniftheyarenotintended.Theprimaryactofbuilding,wemightsay,isalreadycomplexinthatminds,andevensocialrelations,areengagedbybodilytransformations. Asisthecasewiththelogicalcomplexity,thesociologicalcomplexityimpliedbytheboundaryisinitsverynaturerelational.Indeed,itisthelogicoftherelationalcomplexthatgivesrisetothesociologicaldistinctionsthroughwhichbuildingfirstbeginstoreflectandinterveneinsocialrelations.Itisthisessentialrelationalityofformandofspacewhichisappropriatedintheprocessesbywhichbuildingsaretransformedfrombodilyobjectstosocialandculturalobjects.Thefundamentalrelationalcomplexofformandspacecreatedbytheactofmakingthesimplestbuiltobjectistheseedofallfuturerelationalpropertiesofspacesthroughwhichbuildingsbecomefullysocialobjects. Abuildingthenbecomessociallysignificantoverandaboveitsbodilyfunctionsintwoways:firstbyelaboratingspacesintosociallyworkablepatternstogenerateandconstrainsomesociallysanctioned—andthereforenormative—patternofencounterandavoidance;andsecondbyelaboratingphysicalformsandsurfacesintopatternsthroughwhichculturallyoraestheticallysanctionedidentitiesareexpressed.Thefundamentaldualityofformandspacethatwenotedinthemostelementaryformsofthebuildingthuscontinuesintoitscomplexforms.Bytheelaborationofspace,asocialdomainisconstitutedasalivedmilieu.Bytheelaborationofformasocialdomainisrepresentedassignificantidentitiesandencounters.Inbothsenses,buildingscreatemorecomplexpatternsfromthebasicbodilystuffofformandspace.Itisthroughthesepatternsthatbuildingsacquiretheirpotentialatoncetoconstituteandrepresent—andthusintimetoappearastheveryfoundationof—oursocialandculturalexistence.

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Wemaysummarisewhatwehavesaidaboutthenatureofbuildingsasobjectsinadiagramwhichwewillusefromnowonasakindoffundamentaldiagramofthebuildingasobject,(seefig.1.1).Theessenceofthediagramisthatabuildingevenatthemostbasiclevelembodiestwodualities,onebetweenphysicalformandspatialformandtheotherbetweenbodilyfunctionandsocio-culturalfunction.Thelinkbetweenthetwoisthatthesocio-culturalfunctionarisesfromthewaysinwhichformsandspacesareelaboratedintopatterns,or,aswewillinduecoursedescribethem,intoconfigurations.Wemustnowlookmorecarefullyatwhatwemeanbytheelaborationofformandspaceintoconfiguration,sincethiswillbethekeytoourargumentnotonlyaboutthenatureofbuildings,butalso,induecourse,tohowarchitecturearisesfrombuilding. Letusbeginwithasimpleandfamiliarcaseoftheelaborationofthephysicalformofthebuilding:thedoriccolumn.Whenwelookatadoriccolumn,weseeaplinth,apedestal,ashaft,acapital,andsoon,thatis,weseeaconstruction.Theelementsrestoneupontheother,andtheirrelationtoeachothertakesadvantageofanddependsonthenaturallawofgravity.Butthisisnotallthatwesee.Therelationsoftheelementsofacolumngovernedbythelawofgravitywouldholdregardlessofthe‘doricness’oftheelements.If,forexample,weweretoreplacethedoriccapitalwithanioniancapital,theeffectontheconstructionwouldbenegligible,buttheeffectonthe‘doricness’oftheensemblewouldbedevastating. Sowhatisdoricness?Clearlyitisnotatypeofconstruction,sincewemaysubstitutenon-doricelementsintheensemblewithoutconstructionalpenalty.Wemustacknowledgethatdoricnessisnottheninitselfasetofphysicalrelations,althoughitdependsonthem.Doricnessisaschemeinwhichelementswithcertainkindsofelaborationare‘above’and‘below’othersinacertainrelationalsequencewhichemergesfromconstructionbutisnotgivenbyconstruction.Onthecontrary,thenotionof‘above’andbelow’aswefindthemindoricnessseemtobe‘logicalemergents’fromtheactofconstructioninexactlythesamesensethat‘inside’and‘outside’werelogicalemergentsfromthephysicalconstructionofaboundary.Doricnessisthenalogicalconstruction,onebuiltonthebackofaphysicalconstructionbutalogicalconstructionnonetheless.Throughthelogical

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doricnessoftheensemble,wemaysaythatwemovefromthesimplevisualityofthephysicallyinterdependentsystem,toentertherealmoftheintelligible.Doricnessisaconfigurationofpropertiesthatweunderstand,overandabovewhatweseeasphysicalinterdependencies,aformofrelationalelaborationtosomethingwhichexistsinphysicalform,butwhichthroughthiselaborationstandsclearofitsphysicality.Thisprocessofmovingfromthevisibletotheintelligibleis,wewillseeinduecourse,verybasictoourexperiencebothofbuildingandofarchitecture,and,evenmoreso,tothedifferencebetweenoneandtheother. Spatialpatternsinbuildingsalsoariseaselaborationsonprimitivelogicalemergentsfromthephysicalactofbuilding.Aswithdoricness,theydependonbutcannotbeexplainedbynaturallaw(asmanyhavetriedtodobyappealtobiological‘imperatives’suchas‘territoriality’).Theoriginsofrelationalschemesofspaceliesomewherebetweentheorderingcapacitiesofthemindandthespatialorderinginherentinthewaysinwhichsocialrelationshipsarerealisedinspace.Withspace,aswithform,wethereforefindasplitinbuildingbetweenabodilynature,albeitwitharudimentaryrelationalnature,andamoreelaboratedconfigurationalnaturewhichrelatestomindsandsocialexperienceratherthantobodiesandindividualexperience.Thepassagefromthesimplespacetoaconfigurationofspaceisalsothepassagefromthevisibletotheintelligible. Spaceis,however,amoreinherentlydifficulttopicthanphysicalform,fortworeasons.First,spaceisvacancyratherthanthing,soevenitsbodilynatureisnotobvious,andcannotbetakenforgrantedinthewaythatwethinkwecantakeobjectsforgranted.(SeeChapter10forafurtherdiscussionofthisassumption.)Second,relatedspaces,almostbydefinition,cannotbeseenallatonce,butrequiremovementfromonetoothertoexperiencethewhole.Thisistosaythatrelationalityinspaceisrarelyaccessibletousasasingleexperience.Wemustthereforedigressforamomenttotalkaboutspaceasaphenomenon,andhowwecanovercomethedifficultiesthatexistintalkingaboutit.Wewilltakethisintwostages.First,wewilltalkabouttheproblemofhowfarspacecanbeseenasanobjective,independent‘thing-in-itself’.Wemustdothisbecausethereisgreatconfusionaboutthestatusofspaceandhowfaritcanberegardedasanindependententityratherthansimplyasaby-productof,say,thearrangementofphysicalthings.Second,wewilltalkaboutspaceasconfiguration,sinceitisasconfigurationthatithasitsmostpowerfulandindependenteffectsonthewaybuildingsandbuiltenvironmentsareformedandhowtheyfunctionfortheirpurposes.

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About spaceItisfarfromobviousthatspaceis,insomeimportantsense,anobjectivepropertyofbuildings,describableindependentlyofthebuildingasaphysicalthing.Mostofourcommonnotionsofspacedonotdealwithspaceasanentityinitselfbuttieitinsomewaytoentitiesthatarenotspace.Forexample,evenamongstthosewithainterestinthefield,theideaof‘space’willusuallybetranscribedasthe‘useofspace’,the‘perceptionofspace’,the‘productionofspace’oras‘conceptsofspace’.Inallthesecommonexpressions,theideaofspaceisgivensignificancebylinkingitdirectlytohumanbehaviourorintentionality.Commonspatialconceptsfromthesocialsciencessuchas‘personalspace’and‘humanterritoriality’alsotiespacetothehumanagent,anddonotacknowledgeitsexistenceindependentlyofthehumanagent.Inarchitecture,whereconceptsofspacearesometimesunlinkedfromdirecthumanagency,throughnotionssuchas‘spatialhierarchy’and‘spatialscale’westillfindthatspaceisrarelydescribedinafullyindependentway.Theconceptof‘spatialenclosure’forexample,whichdescribesspacebyreferencetothephysicalformsthatdefineitratherthanasathinginitself,isthecommonestarchitecturalwayofdescribingspace. Alltheseconceptsconfirmthedifficultyofconceptualisingspaceasathinginitself.Onoccasion,thisdifficultyfindsanextremeexpression.Forexample,RogerScrutonbelievesthattheideaofspaceisacategorymistakemadebypretentiousarchitects,whohavefailedtounderstandthatspaceisnotathinginitself,butmerelytheobversesideofthephysicalobject,thevacancyleftoverbythebuilding.ForScruton,itisself-evidentthatspaceinafieldandinacathedralarethesamethingexceptinsofarastheinteriorbuiltsurfacesofthecathedralmakeitappearthattheinteriorspacehasdistinctivepropertiesofitsown.Alltalkaboutspaceiserror,heargues,becauseitcanbereducedtotalkaboutbuildingsasphysicalthings.9

Infact,evenatapracticallevel,thisisabizarreview.Spaceis,quitesimply,whatweuseinbuildings.Itisalsowhatwesell.Nodeveloperofferstorentwalls.Wallsmakethespace,andcostthemoney,butspaceistherentablecommodity.WhythenisScrutonembarrassedbytheconceptofspace?LetmesuggestthatScrutonismakinganeducatederror,onethathewouldnothavemadeifhehadnotbeensodeeplyimbuedwiththewesternphilosophicaltraditioninwhichhehasearnedhisliving—andtowhich,incidentally,hehaswrittenanoutstandingintroduction.10

Thedominantviewofspaceinwesternculturehasbeenonewemightlooselycallthe‘Galilean-Cartesian’.ThisviewarisesfromaschemeofreasoningfirstsetoutinfullclaritybyDescartes.11Theprimarypropertiesofphysicalobjectsare,heargued,their‘extension’,thatis,theirmeasurablepropertieslikelength,breadthandwidth.Becauseextensioncanbequantifiedbymeasuringdeviceswhichdonotdependonhumanagency,extensionscanbeseenastheindubitablyobjectivepropertiesofthings,unlike‘secondary’propertieslike‘green’or‘nice’whichseemtodependinsomewayoninteractionwithobservers. Nowifextensionistheprimarypropertyofobjects,thenitisashortstep

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toseeitalsoastheprimarypropertyofthespacewithinwhichobjectssit.AsDescartessays:‘Afterexaminationweshallfindthatthereisnothingremainingintheideaofbodyexceptingthatitisextendedinlength,breadthanddepth;andthisiscomprisedinourideaofspace,notonlyofthatwhichisfullofbody,butalsothatwhichiscalledavacuum.’12Inotherwords,whenwetaketheobjectawayfromitsspaceitsextensionisstillpresentasanattributeofspace.Spaceisthereforegeneralisedextension,orextensionwithoutobjects.Descartesagain:‘Inspace…weattributetoextensionagenericunity,sothatafterhavingremovedfromacertainspacethebodywhichoccupiedit,wedonotsupposewehavealsoremovedtheextensionofthatspace.’13

Followingthisreasoning,spacecomestobeseenasthegeneralabstractframeworkofextensionagainstwhichthepropertiesofobjectsaredefined,ametricbackgroundtothematerialobjectsthatoccupyspace.Thisviewofspaceseemstomostofusquitenatural,nomorethananextrapolationofcommonsense.Unfortunately,onceweseespaceinthisway,wearedoomednottounderstandhowitplaysaroleinhumanaffairs.Culturallyandsocially,spaceisneversimplytheinertbackgroundofourmaterialexistence.Itisakeyaspectofhowsocietiesandculturesareconstitutedintherealworld,and,throughthisconstitution,structuredforusas‘objective’realities.Spaceismorethananeutralframeworkforsocialandculturalforms.Itisbuiltintothoseveryforms.Humanbehaviourdoesnotsimplyhappeninspace.Ithasitsownspatialforms.Encountering,congregating,avoiding,interacting,dwelling,teaching,eating,conferringarenotjustactivitiesthathappeninspace.Inthemselvestheyconstitutespatialpatterns. Itisbecausethisissothatspatialorganisationthroughbuildingsandbuiltenvironmentsbecomesoneoftheprinciplewaysinwhichcultureismaderealforusinthematerialworld,anditisbecausethisissothatbuildingscan,andnormallydo,carrysocialideaswithintheirspatialforms.Tosaythisdoesnotimplydeterminismbetweenspacetosociety,simplythatspaceisalwayslikelytobestructuredinthespatialimageofasocialprocessofsomekind.Thequestionis:howexactlydoesthishappen,andwhatarethesestructureslike?

Space as configurationOnethingisclear.Encountering,congregating,avoiding,interacting,dwelling,conferringarenotattributesofindividuals,butpatterns,orconfigurations,formedbygroupsorcollectionsofpeople.Theydependonanengineeredpatternofco-presence,andindeedco-absence.Veryfewofthepurposesforwhichwebuildbuildingsandenvironmentsarenot‘peopleconfigurations’inthissense.Weshouldthereforeinprincipleexpectthattherelationbetweenpeopleandspace,ifthereisone,willbefoundattheleveloftheconfigurationofspaceratherthantheindividualspace.Thisisconfirmedbycommonsense.Individualspacesplacelittlelimitonhumanactivity,exceptforthoseofsizeandperhapsshape.Inmostreasonablespaces,mosthumanactivitiescanbecarriedout.Buttherelationbetweenspaceandsocialexistencedoesnotlieattheleveloftheindividualspace,orindividualactivity.

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Figure1.2

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Itliesintherelationsbetweenconfigurationsofpeopleandconfigurationsofspace. Totakethefirststepstowardsunderstandinghowthishappens,wemustunderstandhow,inprinciple,aconfigurationofspacecanbeinfluencedby,orinfluence,aconfigurationofpeople.Letusthereforeconsidersomesimplehypotheticalexamples.Thetwonotional‘courtyard’buildingsoffigure1.2aandbshowinthefirstcolumninblack,inthenormalway,thepatternofphysicalelementsofthebuildings.Thecorrespondingfiguresinthesecondcolumnthenshowinblackthecorrespondingpatternofspatialelements.Thebasicphysicalstructuresandcelldivisionsofthetwo‘buildings’arethesame,andeachhasthesamepatternofadjacenciesbetweencellsandthesamenumberofinternalandexternalopenings.Allthatdiffersisthelocationofcellentrances.Butthisisenoughtoensurethatfromthepointofviewofhowacollectionofindividualscouldusethespace,thespatialpatterns,or‘configurations’,areaboutasdifferentastheycouldbe.Thepatternofpermeabilitycreatedbythedispositionofentrancesisthecriticalthing.Seenthisway,onelayoutisanearperfectsinglesequence,withaminimalbranchattheend.Theotherisbranchedeverywhereaboutthestrongcentralspaces. Nowthepatternofpermeabilitywouldmakerelativelylittledifferencetothebuildingstructurallyorclimatically,thatis,tothebodilyaspectofbuildings,especiallyifweassumesimilarpatternsofexternalfenestration,andinsertwindowswherevertheotherhadentrancesontothecourtyard.Butitwouldmakeadramaticdifferencetohowthelayoutwouldworkas,say,adomesticinterior.Forexample,itisverydifficultformorethanonepersontouseasinglesequenceofspaces.Itofferslittleinthewayofcommunityorprivacy,butmuchinthewayofpotentialintrusion.Thebranchedpattern,ontheotherhand,offersadefinitesetofpotentialrelationsbetweencommunityandprivacy,andmanymoreresourcesagainstintrusion. Thesedifferencesareinherentinthespacepatterns,andwouldapplytowholeclassesofhumanactivitypatterns.Inthemselvesthespatiallayoutsofferarangeoflimitationsandpotentialities.Theysuggestthepossibilitythatarchitecturalspacemightbesubjecttolimitinglaws,notofadeterministickind,butsuchastosetmorphologicalboundswithinwhichtherelationsbetweenformandfunctioninbuildingsareworkedout. WewillseefromChapter3onwardsthatitisbyexpressingthesepatternpropertiesinanumericalwaythatwecanfindclearrelationsbetweenspacepatternsandhowcollectionsofpeopleusethem.However,beforeweembarkonnumbers,thereisavisuallyusefulwayofcapturingsomeofthekeydifferencesbetweenthetwospatialpatterns.Thisisadevicewecallajustifiedgraph,orj-graph.Inthisweimaginethatweareinaspacewhichwecalltherootorbaseofthegraph,andrepresentthisasacirclewithacrossinscribed.Then,representingspacesascircles,andrelationsofaccessaslinesconnectingthem,wealignimmediatelyabovetherootallspaceswhicharedirectlyconnectedtotheroot,anddrawintheconnections.Thesearethespacesat‘depthone’fromtheroot.Thenanequaldistanceabovethe‘depthone’rowwealignthespacesthatconnectdirectlytofirstrowspaces,formingthelineof‘depthtwo’spaces,and

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connectthesetothedepthonespaces,andsoon.Sometimeswewillhavetodrawratherlongandcircuitouslinestolinkspacesatdifferentlevels,butthisdoesnotmatter.Itisthefactofconnectionthatmatters.Thelawsofgraphsguaranteethatifthelayoutisallatonelevelthenwecanmakealltherequiredconnectionsbydrawinglinesconnectingthespaceswithoutcrossingotherlines.14

Theresultingj-graphisapictureofthe‘depth’ofallspacesinapatternfromaparticularpointinit.Thethirdcolumninfigure1.2aandbshowsj-graphsforthecorrespondingspatialstructures,drawnusingtheexteriorspaceasroot.Wecanimmediatelyseethatthefirstisa‘deeptree’form,andtheseconda‘shallowtree’form.By‘tree’wemeanthatthereisonelinklessthanthenumberofcellslinked,andthattherearethereforenoringsofcirculationinthegraph.Alltrees,eventwoasdifferentasinthetwointhefigures,sharethecharacteristicthatthereisonlyoneroutefromeachspacetoeachotherspace—apropertythatishighlyrelevanttohowbuildinglayoutsfunction.However,where‘rings’arefound,thejustifiedgraphmakesthemasclearasthe‘depth’properties,showingtheminaverysimpleandclearwayaswhattheyare,thatis,alternativeroutechoicesfromonepartofthepatterntoanother.Theseriesoffiguresinfigure1.2cshowsahypotheticalcase,basedonthesamebasic‘building’asthepreviousfigures. Wedonothavetojustifythegraphusingtheoutsidespaceasroot.Thisisonlyoneway—thoughasingularlyusefulway—oflookingatabuilding.Wecanofcoursejustifythegraphfromanyspacewithinit,andthiswilltelluswhatlayoutislikefromthepointofviewofthatspace,takingintoaccountbothdepthandringproperties.Whenwedothiswediscoverafactaboutthespatiallayoutsofbuildingsandsettlementsthatissofundamentalthatitisprobablyinitselfthekeytomostaspectsofhumanspatialorganisation.Thisisthesimplefactthatapatternofspacenotonlylooksdifferentbutactuallyisdifferentwhenjustifiedfromthepointofviewofitsdifferentconstituentelements.Thethreenotionalj-graphsshowninfigure1.2dappearverydifferentfromeachother,butallthreeareinfactthesamegraphjustifiedfromthepointofviewofdifferentconstituentspaces.Thedepthandringpropertiescouldhardlyappearmoredifferentiftheyweredifferentconfigurations.Itisthroughthecreationanddistributionofsuchdifferencesthatspacebecomessuchapowerfulrawmaterialforthetransmissionofculturethroughbuildingsandsettlementforms,andalsoapotentmeansofarchitecturaldiscoveryandcreation.Letusseehow.

Formally defining configurationFirstweneedtobringalittlemoreformalityintothedefinitionof‘configuration’.Liketheword‘pattern’(whichwedonotusebecauseitimpliesmoreregularitythanwewillfindinmostspatialarrangements),configurationseemstobeaconceptaddressedtothewholeofacomplexratherthantoitsparts.Intuitively,itseemstomeanasetofrelationshipsamongthingsallofwhichinterdependinanoverallstructureofsomekind.Thereisawayofformalisingthisideathatisassimpleasitisnecessary.Ifwedefinespatialrelationsasexistingwhenthereisanytypeoflink—sayadjacencyorpermeability—betweentwospaces,then

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configurationexistswhenrelationsbetweentwospacesarechangedaccordingtohowwerelateoneorother,orboth,toatleastoneotherspace. Thisratheroddsoundingdefinitioncanbeexplainedthroughasimplegraphicexample.Figure1.3ashowsacelldividedbyapartitionintotwo,sub-cellaandsub-cellb,withadoorcreatingarelationofpermeabilitybetweenthetwo.Itisclearthattherelationisformally‘symmetrical’inthesensethatcellaistocellbasbistoa.Thesamewouldbetrueoftwocellswhichwereadjacentandthereforeintherelationofneighbourtoeachother.Ifaisb’sneighbour,thenbmustalsobea’sneighbour.This‘symmetry’,whichfollowsthealgebraicratherthanthegeometricaldefinition,isclearlyanobjectivepropertyoftherelationofaandbanddoesnotdependonhowwechoosetoseetherelation. Nowconsiderfigures1.3bandcinwhichwehaveaddedrelationstoathirdspace,c(whichisinfacttheoutsidespace),butinadifferentwaysothatin1.3bbothaandbaredirectlypermeabletoc,whereasin1.3c,onlyaisdirectlypermeabletoc.Thismeansthatin1.3cwemustpassthroughatogettobfromc,whereasin1.3bwecangoeitherway.In1.3ctherefore,aandbaredifferentwithrespecttoc.Wemustpassthroughatogettobfromc,butwedonotneedtopassthroughbtogettoafromc.Withrespecttoc,therelationhasbecomeasymmetrical.Inotherwords,therelationbetweenaandbhasbeenredefinedbytherelationeachhastoathirdspace.Thisisaconfigurationaldifference.Configurationisasetofinterdependentrelationsinwhicheachisdeterminedbyitsrelationtoalltheothers. Wecanshowsuchconfigurationaldifferencesratherneatly,andclarifytheirnature,byusingthej-graph,asinfigure1.3dande,correspondingto1.3band1.3crespectively.Comparedto1.3a,spacesbandcin1.3ehaveacquired‘depth’with

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respecttoeachother,inthattheirrelationisnowindirectandonlyexistsbyvirtueofa.Thenumbersadjacenttoeachspaceinthej-graphindexthisbyshowingthetotaldepthofeachspacefromtheothertwo.Incontrast,1.3dhasacquireda‘ring’thatlinksallthreespaces,meaningthateachhasachoiceofroutetoeachoftheothers.Thegraphof1.3disidenticalwhenseenfromeachofitsspaces,whilein1.3e,bandcareidentical,butaisdifferent.

Society in the form of the objectNowletususethisconceptofconfiguration,anditskeyspatialdimensionsofdepthandrings,totrytodetectthepresenceofculturalandsocialideasinthespatialformsofbuildings.Figures1.4a,bandcshow,ontheleft,theground-floorplansofthreeFrenchhouses,andtotheirimmediateright,theirj-graphsdrawninitiallyfromtheoutside,treatingitasasinglespace,thentotherightagainthreefurtherj-graphsjustifiedfromthreedifferentinternalspaces.15Lookingatthej-graphsdrawnfromtheoutside,wecanseethatinspiteofthegeometricaldifferencesinthehousestherearestrongsimilaritiesintheconfigurations.Thiscanbeseenmosteasilybyconcentratingonthespacemarkedsc,orsallecommune,whichisthemaineverydaylivingspace,inwhichcookingalsooccursandeverydayvisitorsarereceived.Ineachcase,wecanseethatthesallecommuneliesonallnon-trivialrings(atrivialringisonewhichlinksthesamepairofspacestwice),linksdirectlytoanexteriorspace—thatis,itisatdepthoneinthecomplex—andactsasalinkbetweenthelivingspacesandvariousspacesassociatedwithdomesticworkcarriedoutbywomen. Thesallecommunealsohasamorefundamentalproperty,onewhicharisesfromitsrelationtothespatialconfigurationofthehouseasawhole.Ifwecountthenumberofspaceswemustpassthroughtogofromthesallecommunetoallotherspaces,wefindthatitcomestoatotalwhichislessthanforanyotherspace—thatis,ithaslessdepththananyotherspaceinthecomplex.Thegeneralformofthismeasure16iscalledintegration,andcanbeappliedtoanyspaceinanyconfiguration:thelessdepthfromthecomplexasawhole,themoreintegratingthespace,andviceversa.Thismeansthateveryspaceinthethreecomplexescanbeassignedan‘integrationvalue’.17

Nowoncewehavedonethiswecanaskquestionsabouthowthedifferentfunctionsinthehouseare‘spatialised’,thatis,howtheyareembeddedintheoverallspatialconfiguration.Whenwedothis,wefindthatitisverycommonthatdifferentfunctionsarespatialisedindifferentways,andthatthiscanoftenbeexpressedclearlythrough‘integration’analysis.InthethreeFrenchhouses,forexample,wefindthatthereisacertainorderofintegrationamongthespaceswheredifferentfunctionsarecarriedout,alwayswiththesallecommuneasthemostintegrated,ascanbeseeninthej-graphsbesideeachplan.Ifallthefunctionsofthethreehousesaresetoutinorderoftheintegrationvaluesofthespacesinwhichtheyoccur,beginningwiththemostintegratedspace,wecanreadthis,fromlefttoright,as:thesallecommuneismoreintegrated(i.e.haslessdepthtoallotherspaces)than

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Figure 1.4

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thecorridor,whichismoreintegratedthantheexterior,andsoon.Totheextentthattherearecommonalitiesinthesequenceofinequalities,thenwecansaythatthereisacommonpatterntothewayinwhichdifferentfunctionsarespatialisedinthehouse.Wecallsuchcommonpatterns‘inequalitygenotypes’,becausetheyrefernottothesurfaceappearancesofformsbuttodeepstructuresunderlyingspatialconfigurationsandtheirrelationtolivingpatterns.18

Theseresultsflowfromananalysisofspace-to-spacepermeability.Butwhatabouttherelationofvisibility,whichpassesthroughspaces?Thethreerowsoffiguresontherightinfigure1.4(lowerpanel)showallthespacethatcanbeseenwiththedoorsopenfromadiamond-shapedspacewithineachsallecommuneandoneotherspace,drawnbyjoiningthecentrepointsofeachwallofaroom,andthuscoveringhalfofthespaceintheroom.Theideaofthediamondshapeisthatspaceuse(inmostwesterncultures)isnormallyconcentratedwithinthisdiamondshape,thecornerscommonlybeingreservedforobjects.Thediagramsshowthatineachcasethesallecommunehasafarmorepowerfulvisualfieldthanthesalle.Inotherwords,thespatialandfunctionaldifferencesbetweenspacesthatwefindthroughtheanalysisofpermeabilityinthehousesalsoappearintheanalysisofvisibility.Thesevisibilitydifferencescanalsoformthebasisforquantitativeandstatisticalanalysis. Thistypeofmethodallowsustoretrievefromhouseplansconfigurationalpropertiesthatrelatedirectlytothesocialandculturalfunctioningofthehouse.Inotherwords,throughspatialconfigurationculturallydeterminedpatternsareembeddedinthematerialandspatial‘objectivity’ofbuildings.Bytheanalysisofspacesandfunctionsintermsoftheirconfigurationalrelationswithinthehouse,andthesearchforcommonpatternsacrosssamples,wecanseehowbuildingscantransmitcommonculturaltendenciesthroughspatialform.Wemustnowaskhowandwhythisisthecase,andwhatfollowsfromit?

The non-discursivity of configuration: ideas we think of and ideas we think withTheanswerwilltakeustothecentreofourargument:thenon-discursivityofconfiguration.Non-discursivitymeansthatwedonotknowhowtotalkaboutit.Thedifficultyoftalkingaboutspatialorformalconfigurationsinarchitecturehasalwaysseemedaratherperipheralproblemtoarchitecturaltheory.Isuggestitisthecentralproblem,andpartofamuchmoregeneralprobleminhumanaffairs. Letusbegintoexploretheintuitiveaspectsoftheideaofconfigurationalittlefurther.Considerthefourgroupsofelementsinfigure1.5.Eachgroupisadifferentsetof‘things’,butplacedinmoreorlessthesameoverall‘configuration’.Thehumanmindhasnodifficultyinseeingthattheconfigurationsarethesame,inspiteofthedifferencesintheconstituent‘things’,andthisshowsthatweeasilyrecogniseaconfiguration,evenwherewehavenowayofgivingitanameandthusassigningittoacategory—althoughwemighttrytodosobymakinganalogieswithconfigurationsforwhichnamesarealreadyathand,suchas‘L-shaped’,or‘star-shaped’.However,thefactthatourmindsrecognisedconfigurationsasbeingthesameevenwhenthereisnonameathandtolinkthemshowsthatourability

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torecogniseandunderstandconfigurationispriortotheassignmentofnames. Configurationseemsinfacttobewhatthehumanmindisgoodatintuitively,butbadatanalytically.Weeasilyrecogniseconfigurationwithoutconsciousthought,andjustaseasilyuseconfigurationsineverydaylifewithoutthinkingofthem,butwedonotknowwhatitiswerecogniseandwearenotconsciousofwhatitisweuseandhowweuseit.Wehavenolanguagefordescribingconfigurations,thatis,wehavenomeansofsayingwhatitisweknow.Thisproblemisparticularlysalientinbuildingsandarchitecture,becausebothhavetheeffectofimposingspatialandformalconfigurationontheworldinwhichwelive.Buttheproblemisnotconfinedtoarchitecture.Onthecontraryitappearstobepresenttosomedegreeinmostculturalandsocialbehaviours.Inusinglanguage,forexample,weareawareofwordsandbelievethatinspeakingandhearingwearehandlingwords.However,languageonlyworksbecauseweareabletousetheconfigurationalaspectsoflanguage,thatis,thesyntacticandsemanticruleswhichgovernhowwordsaretobeassembledintomeaningfulcomplexes,inawaywhichmakestheiroperationautomaticandunconscious.Inlanguagewecanthereforedistinguishideaswethinkof,thatis,thewordsandwhattheyrepresent,andideaswethinkwith,thatis,syntacticandsemanticruleswhichgovernhowwedeploywordstocreatemeaning.Thewordswethinkofseemtouslikethings,andareatthelevelofconsciousthought.Thehiddenstructureswethinkwithhavethenatureofconfigurationalrules,inthattheytellushowthingsaretobeassembled,andworkbelowthelevelofconsciousness.This‘unconsciousconfigurationality’seemstoprevailinallareaswhereweuserulesystemstobehaveinwayswhicharerecognisableassocial.Behaviourattable,ortheplayingofgames,appeartousasspatio-temporalevents,buttheyaregivenorderandpurposebytheunderlying

Figure 1.5

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configurational‘ideas-to-think-with’throughwhichtheseeventsaregenerated.Weacknowledgetheimportanceofthisunseenconfigurationalitylabellingitasaformofknowledge.Wetalkabout‘knowinghowtobehave’,or‘knowingalanguage’. Wecancallthiskindofknowledge‘socialknowledge’,andnotethatitspurposeistocreate,orderandmakeintelligiblethespatio-temporaleventsthroughwhichwerecognisethepresenceofcultureineverydaylife.Wemustofcoursetakecaretodistinguishsocialknowledgefromformsofknowledgewhichwelearninschoolsanduniversitieswhosepurposeistounderstandtheworldratherthantobehaveinit,andwhichwemightthereforecallanalytic,orscientificknowledge.Initself(thoughnotnecessarilyinitsconsequences)analyticknowledgeleavestheworldasitis,sinceitspurposeistounderstand.Analyticknowledgeisknowledgewherewelearntheabstractprinciplesthroughwhichspatio-temporalphenomenaarerelated—wemightsaythe‘configurationality’—consciously.Weareawareoftheprinciplesbothwhenweacquireandwhenweusetheknowledge.Asaresult,throughtheintermediaryoftheabstract,wegrasptheconcrete.Insocialknowledge,incontrast,knowledgeofabstractconfigurationalityisacquiredthroughtheprocessofcreatingandexperiencingspatio-temporalevents.Socialknowledgeworkspreciselybecausetheabstractprinciplesthroughwhichspatio-temporalphenomenaarebroughttogetherintomeaningfulpatternsareburiedbeneathhabitsofdoing,andneverneedbebroughttoconsciousattention.19

Inspiteofthesefunctionaldifferences,socialknowledgeandanalyticknowledgearemadeupofthesameelements:ontheonehand,thereisknowledgeofspatio-temporalphenomena,ontheother,thereareabstract‘configurational’structuresthatlinkthemtogether.Butwhereasinsocialknowledgetheabstractideasareheldsteadyasideastothinkwithinordertocreatespatio-temporaleventsintherealworld,sothattheabstractideasbecomethenormativebasesofbehaviour,inscientificknowledge,anattemptismadetoholdspatio-temporalphenomenasteadyinordertobringtheabstractstructuresthroughwhichweinterpretthemtothesurfaceinordertoexaminethemcriticallyand,ifnecessary,toreconstitutethem. Thiscanbeusefullyclarifiedbyadiagram,seefigure1.6.Thedifferencebetweenthetwoformsofknowledgeliesessentiallyinthedegreetowhichabstractideasareatthelevelofconsciousthoughtandthereforeatrisk.Thewholepurposeofscienceistoputtheabstract‘ideaswethinkwith’inmakingsenseofspatio-temporaleventsatrisk.Insocialknowledge,thewholepurposeofthe‘knowledge’wouldbeputatriskbybringingthemtoconsciousthoughtsincetheirfunctionistobeusednormativelytocreatesociety.However,itisclearlyapossibilitythattheabstractstructuresofsocialknowledgecould,aswithscience,themselvesbecometheobjectofconsciousthought.This,inanutshell,istheprogrammeof‘structuralism’.Theessenceofthestructuralistmethodistoask:canwebuildamodeloftheabstractprinciplesofasystem(e.g.language)that‘generates’allandonlythespatio-temporaleventsthatcanlegitimatelyhappen?Suchamodelwouldbeatheoryofthesystem.Itwould,forexample,‘explain’ourintuitivesense

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thatsomestringsofwordsaremeaningfulsentencesandothers—most—arenot.Structuralismisratherliketakingtheoutputofacomputerasthephenomenatobeexplained,andtryingtofindoutwhatprogrammecouldgenerateallandonlythesephenomena.Structuralismisanenquiryintotheunconsciousconfigurationalbasesofsocialknowledge,thatis,itisaninquiryintothenon-discursivedimensionsofsocialandculturalbehaviour.

Building as the transmission of culture through artefactsThespatialandformalpatternsthatarecreatedthroughbuildingsandsettlementsareclassicinstancesoftheproblemofnon-discursivity,bothinthesenseoftheconfigurationalnatureofideaswethinkwithincreatingandusingspace,andinthesenseoftheroletheseplayinsocialknowledge.Ashasalreadybeenindicated,oneofthemostpervasiveexamplesofthisisthedwelling.Domesticspacevariesinthedegreetowhichitissubjecttosocialknowledge,butitisnotuncommonforittobepatternedaccordingtocodesofconsiderableintricacywhichgovernwhatspacesthereare,howtheyarelabelled,howboundedtheyare,howtheyareconnectedandsequenced,whichactivitiesgotogetherinthemandwhichareseparated,whatindividualsorcategoriesofpersonshavewhatkindsofrightsinthem,howtheyaredecorated,whatkindsofobjectsshouldbedisplayedinthemandhow,andsoon.Thesepatternsvaryfromoneculturalgrouptoanother,butinvariablywehandledomesticspacepatternswithoutthinkingofthemandevenwithoutbeingawareofthemuntiltheyarechallenged.Ingeneral,weonlybecomeawareofthedegreeofpatterninginourownculturewhenweencounteranotherformofpatterninginanotherculture. Butdomesticspaceisonlythemostintensiveandcomplexinstanceofamoregeneralisedphenomenon.Buildingsandsettlementsofallkinds,andatalllevels,aresignificantlyunderpinnedbyconfigurationalnon-discursivity.Itisthroughthisthatbuildings—andindeedbuiltenvironmentsofallkinds—becomepartofwhatMargaretMeadcalled‘thetransmissionofculturethroughartefacts’.20Thistransmissionoccurslargelythroughtheconfigurationalaspectsofspaceandforminthoseenvironments.Forexample,wethinkconsciouslyofbuildingsasphysicalorspatialobjectsandwethinkoftheirpartsasphysicalorspatialparts,likecolumnsorrooms.Butwethinkof‘buildings’aswholeentitiesthroughtheunconsciousintermediaryofconfiguration,inthatwhenwethinkofaparticular

abstractprinciples spacial-temporalevents socialknowledge codes,rules speech,socialbehaviour, ideastothink spaces,ideastothink analyticknowledge theories,hypotheses ‘facts’,phenomena paradigms

Figure 1.6

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kindofbuilding,weareconsciousnotonlyofanimageofanobject,butatthesametimeofthecomplexofspatialrelationsthatsuchabuildingentails.Asspace—andalsoasmeaningfulforms—buildingsareconfigurational,andbecausetheyareconfigurationaltheirmostimportantsocialandculturalpropertiesarenon-discursive.Itisthroughnon-discursivitythatthesocialnatureofbuildingsistransmitted,becauseitisthroughconfigurationthattherawmaterialsofspaceandformaregivensocialmeaning.Thesocialstuffofbuildings,wemaysay,istheconfigurationalstuff,bothinthesensethatbuildingsareconfigurationsofspacedesignedtoorderinspaceatleastsomeaspectsofsocialrelationships,andinthesensethatitisthroughthecreationofsomekindofconfigurationintheformofthebuildingthatsomethinglikeacultural‘meaning’istransmitted.

Building as processHowthencanthishelpusmakethedistinctionbetweenarchitectureandbuilding?Wenoteofcoursethatwenowbeginnotfromthenotionthatbuildingspriortoarchitectureareonlypracticalandfunctionalobjects,butfromthepropositionthatpriortoarchitecturebuildingsarealreadycomplexinstancesofthetransmissionofculturethroughartefacts.Thisdoesnotmeanofcoursethatbuildingsofthesametypeandculturewillbeidenticalwitheachother.Onthecontrary,itiscommonforvernaculararchitecturestoexhibitprodigiousvarietyatthelevelofindividualcases,somuchsothatthegroundsforbelievingthatthecasesconstituteinstancesofacommonvernacularstyle,eitherinformorspace,canbequitehardtopindown. Thecrucialstepinarrivingatourdefinitionofarchitectureistounderstandfirsthowthevernacularbuildersucceedsinmakingabuildingasacomplexrelationalstructurethroughwhichcultureistransmitted,whileatthesametimecreatingwhatwilloftenbeauniqueindividualbuilding.Wedonothavetolookfarfortheanswer.Thiscombinationofcommonstructureandsurfacevarietyisexactlywhatwefindwheresocialknowledgeisinoperationintheforminwhichwehavejustdescribedit:complexconfigurationalideasatthenon-discursivelevelguidethewaysinwhichwehandlespatio-temporalthingsatthesurfacelevel,andasaresultconfigurationalideasarerealisedintherealworld.Inbuildingterms,themanipulationofthespatialandformalelementswhichmakeupthebuildingwill,ifcarriedoutwithinthescopeofnon-discursiveconfigurationalideastothinkwith,whichgovernkeyaspectsoftheirformalandspatialarrangement,leadtoexactlythecombinationofunderlyingcommonstructureandsurfacevarietythatcharacterisesvernaculararchitecturesingeneral. Tounderstandhowthishappensinparticularcases,wecandrawontheremarkableworkofHenryGlassie.21GlassieproposesthatweadaptfromNoamChomsky’sstudiesoflanguageaconceptwhichhecalls‘architecturalcompetence.’‘Architecturalcompetence’isasetoftechnological,geometricalandmanipulativeskillsrelatingformtouse,whichconstitute‘anaccountnotofhowahouseismade,butofhowahouseisthought…setoutlikeaprogramme…aschemeanalogoustoagrammar,thatwillconsistofanoutlineofrulesetsinterruptedbyprosyexegesis’.

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Theanalogywithlanguageisapposite.Itsuggeststhattherulesetsthevernaculardesignerusesaretacitandtakenforgrantedinthesamewayastherulesetsthatgoverntheuseoflanguage.Theyareideasthedesignerthinkswithratherthanof.Theythereforehaveacertaindegreeofabstractionfromthematerialrealitytheyhelptocreate.Theyspecifynotthespecificbutthegeneric,sothatthevernaculardesignermayusetherulesasthebasisofacertainrestrainedcreativityininterpretingtherulesinnovelways. NowtheimplicationofGlassie’sideaisthat‘architecturalcompetence’providesasetofnormativerulesabouthowbuildingshouldbedone,sothatavernacularbuildingreproducesaknownandsociallyacceptedpattern.Thehousebuiltbyabuildersharingthecultureofacommunitycomesoutrightbecauseitdrawsonthenormativerulesthatdefinethearchitecturalcompetenceofthecommunity.Inthiswaybuildingsbecomeanaturalpartof‘thetransmissionofculturebyartefacts’.Throughdistinctivewaysofbuilding,aspectsofthesocialknowledgedistinctiveofacommunityarereproduced.Thusthephysicalactofbuilding,throughasystemofwelldefinedinstrumentalities,becomesthemeansbywhichthenon-discursivepatternswecallculturearetransmittedintoandthroughthematerialandspatialformsofbuildings.Thenon-discursiveaspectsofbuildingaretransmittedexactlyaswewouldexpectthemtobe:asunconsciouspatternimplicationsofthemanipulationofthings.

So what is architecture?Tounderstandbuilding,then,wemustunderstanditbothasaproductandasaprocess.Havingdonethis,wecanreturntoouroriginalquestion:whatisitthatarchitectureaddstobuilding?Byunpackingtheculturalandcognitivecomplexityofbuilding,itwillturnoutthatweareatlastinsightofananswer.Whateverarchitectureis,itmustinsomesensegobeyondtheprocessbywhichtheculturallysanctionednon-discursivitiesareembeddedinthespatialandphysicalformsofbuildings.Inwhatsense,then,isitpossibleto‘gobeyond’suchaprocess? Theanswerisnowvirtuallyimpliedintheformofthequestion.Architecturebeginswhentheconfigurationalaspectsofformandspace,throughwhichbuildingsbecomeculturalandsocialobjects,aretreatednotasunconsciousrulestobefollowed,butareraisedtothelevelofconscious,comparativethought,andinthiswaymadepartoftheobjectofcreativeattention.Architecturecomesintoexistence,wemaysay,asaresultofakindofintellectualprise de conscience:webuild,butnotasculturalautomata,reproducingthespatialandphysicalformsofourculture,butasconscioushumanbeingscriticallyawareoftheculturalrelativityofbuiltformsandspatialforms.Webuild,thatis,awareofintellectualchoice,andwethereforebuildwithreason,givingreasonsforthesechoices.Whereasinthevernacularthenon-discursiveaspectsofarchitecturearenormativeandhandledautonomically,inarchitecturethesecontentsbecometheobjectofreflectiveandcreativethought.Thedesignerisineffectaconfigurationalthinker.Theobjectofarchitecturalattentionispreciselytheconfigurationalideastothinkwiththatinthevernaculargovern

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configurationaloutcomes.Thisdoesnotmeanthatthedesignerdoesnotthinkofobjects.Itmeansthatatthesametimethedesignerthinksofconfiguration. Theessenceofarchitectureliesthereforeinbuildingnotbyreferencetoculturallyboundcompetences,andthewayinwhichtheyguidethenon-discursivecontentsofbuildingsthroughprogrammesofsocialknowledgespecifictooneculture,butbyreferencetoawould-beuniversalisticcompetencearrivedatthroughthegeneralcomparativestudyofformsaimedatprincipleratherthanculturalidiosyncrasy,and,throughthis,atinnovationratherthanculturalreduplication.Itiswhenweseeinthenon-discursivecontentsofbuildingsevidenceofthisconcernfortheabstractcomparabilityofformsandfunctionsthatbuildingistranscendedandarchitectureisnamed.Thisiswhythenotionofarchitectureseemstocontainwithinitselfaspectsofboththeproductwhichiscreatedandoftheintellectualprocessthroughwhichthiscreationoccurs. Architectureexists,wemightsay,wherewenoteasapropertyofthingsevidencenotonlyofacertainkindofsystematicintent—toborrowanexcellentphraseproposedbyacolleagueinreviewingthearchaeologicalrecordforthebeginningofarchitecture22—inthedomainofnon-discursivity,butofsomethingliketheoreticalintentinthatdomain.Inakeysensearchitecturetranscendsbuildinginthesamewaythatsciencetranscendsthepracticalcraftsofmakinganddoing.Itintroducesintothecreationofbuildingsanabstractconcernforarchitecturalpossibilitythroughtheprincipledunderstandingofformandfunction.Theinnovativeimperativeinarchitectureisthereforeinthenatureofthesubject.Weshouldnomorecriticisearchitectsfortheirpenchanttowardsinnovationthanweshouldscientists.Inbothcasesitfollowsfromthesociallegitimationswhichgiveeachitsnameandidentity.Botharchitectureandscienceusethegroundoftheoreticalunderstandingtomovefrompastsolutionstofuturepossibility,thelatterinthedirectionofnewtheoreticalconstructs,theformerinthedirectionofnewrealities.Thejudgmentwemakethatabuildingisarchitectureariseswhentheevidenceofsystematicintentisevidenceofintellectualchoiceanddecisionexercisedinafieldofknowledgeofpossibilitythatgoesbeyondcultureintoprinciple.Inthissense,architectureisaformofpracticerecognisableinitsproduct.Thejudgmentwemakethatabuildingisarchitecturecomeswhenweseeevidenceinthebuildingbothofsystematicintentwhichrequirestheabstractandcomparativemanipulationofformwithinthegeneralrealmofarchitecturalpossibility,andthatthisexplorationandthisexerciseofintellectualchoicehasbeensuccessfullyaccomplished. Architectureisthusbothathingandanactivity.Intheformofthethingwedetectevidenceofasystematicintentofthearchitecturalkind.Fromthebuiltevidencewecanjudgeboththatabuildingisintendedtobearchitectureand,ifwearesoinclined,thatitisarchitecture.Weseenowwhythedefinitionofarchitectureissodifficult.Becauseitisthetakingholdofthenon-discursivecontentsofbuildingbyabstract,universalisticthought,itisatonceanintentionalmentalactandapropertyweseeinthings.Itisbecauseweseeinthingstheobjectivisedrecordofsuchthoughtthatwenametheresultarchitecture.

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Itisclearfromthisanalysisthatarchitecturedoesnotdependonarchitects,butcanexistwithinthecontextofwhatwewouldnormallycallthevernacular.Totheextentthatthevernacularshowsevidenceofreflectivethoughtandinnovationatthelevelofthegenotype,thenthatisevidenceofthekindofthoughtwecallarchitecturalwithinthevernacular.Thisdoesnotmeanthattheinnovativeproductionofbuildingswhicharephenotypicallyindividualwithinavernacularshouldbethoughtofasarchitecture.Suchphenotypicalvarietyisnormalastheproductofculturallyconstrainednon-discursivecodes.Itisonlywhentheinnovation,andthereforethereflectivethought,changesthecodethatunderliestheproductionofphenotypesthatwedetectthepresenceofabstractandcomparative—andthereforearchitectural—thoughtwithintheconfinesofvernaculartradition.Itisthereforeperhapsattimesofthegreatestchangethatwebecomeawareofthistypeofthoughtinvernaculartraditions,thatis,whenanewvernaculariscomingintoexistence.Thisiswhythedemarcationbetweenthevernacularandarchitectureconstantlyshifts.Thereproductionofexistingforms,vernacularorotherwise,isnotarchitecturebecausethatrequiresnoexerciseofabstractcomparativethought,buttheexploitationofvernacularformsinthecreationofnewformscanbearchitecture. Architectureexiststhentothedegreethatthereisgenotypicalinventioninthenon-discursive,thatis,inventionwiththerulesthatgovernthevariabilitythatispossiblewithinastyle.Thepreconditionforsuchinventionisanawarenessofpossibilitieswhicharenotcontainedincontemporaryculturalknowingbutwhichareatthesametimewithinthelawsofwhatisarchitecturallypossible.Architectureischaracterisedthereforebyapreoccupationwithnon-discursivemeansratherthannon-discursiveends.Thisisnottheoutcomeofaperverserefusaltounderstandtheculturalnatureofbuilding,butatakingholdofthisveryfactasapotentialitytoexploretheinterfacebetweenhumanlifeanditsspatialandphysicalmilieu.Intheactofarchitecturalcreation,theconfigurationalpotentialitiesofspaceandformaretherawmaterialswithwhichthecreatorworks. Likeanycreativeartist,therefore,thearchitectmustseektolearn,throughintellectualinquiry,thelimitsandpotentialitiesoftheserawmaterials.Intheabsenceofsuchinquiry,therearemanifestandimmediatedangers.Inthevernacularthepatternofformandthepatternofspacewhichgivethebuildingitssocialcharacterarerecreatedthroughthemanipulationandassemblingofobjects.Wecansaythenthattheform,thespatialpatternandthefunctionalpattern—theform-functionrelation,inshort—areknowninadvanceandneedonlyberecreated.Becausearchitectureofitsnatureunlinksthepatternaspectsofthebuildingfromtheirdependenceonsocialknowledge,theseaspectsofthebuilding—andabovealltheirrelationtosocialoutcomes—becomeuncertain. Inarchitecturethen,becausethesecrucialrelationsbetweennon-discursiveformsandoutcomesarenotknowninadvance,architecturehastorecreateinanew,moregeneralisedform,theknowledgeconditionsthatprevailinthevernacular.Becausearchitectureisacreativeact,theremustbesomethingintheplaceofthesocialknowledgestructureasideastothinkwith.Sincearchitectureisbased

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onthegeneralcomparabilityofpossibleforms,thisknowledgecannotsimplyencompassparticularcases.Itmustencompasstherangeofpossiblecasesandifpossiblecasesingeneral.Thereisonlyonetermforsuchknowledge.Itistheoreticalknowledge.Wewillseeinthenextchapterthatallarchitecturaltheoriesareattemptstosupplyprincipledknowledgeofthenon-discursive,thatis,torenderthenon-discursivediscursiveinawaythatmakesitaccessibletoreason.Intheabsenceofsuchknowledge,architecturecanbe,asthetwentiethcenturyhasseen,adangerousart. Thepassagefrombuildingtoarchitectureissummarisedinfigure1.7.Theimplicationofthisisthat,althoughweknowthedifferencebetweenarchitectureandbuilding,thereisnohardandfastlinetobedrawn.Eithercanbecometheotheratanymoment.Takingabroaderviewwhichencompassesboth,wecansaythatintheevolutionofbuildingwenotetwowaysinwhichthingsaredone:inobediencetoatradition,orinpursuitofinnovation.Buildingcontainsarchitecturetothedegreethatthereisnon-discursiveinvention,andarchitecturebecomesbuildingtothedegreethatthereisnot.Vernacularinnovationisthereforeincludedwithinarchitecture,butthereduplicationofvernacularformsisnot.Architectureisthereforenotsimplywhatisdonebuthowitisdone. Thebringingofthenon-discursive,configurationdimensionofbuiltformfromculturalreproductiontoreflectiveawarenessandabstractexplorationofpossibilityisatonceapassagefromthenormativetotheanalyticandfromtheculture-boundtotheuniversal,thelattermeaningthatallpossibilitiesareopenratherthansimplythepermutationsandphenotypicalinnovationsthataresanctionedbythevernacular.Thepassageisalsoonewhichtransformstheideaofknowledgefromculturalprincipletotheoreticalabstraction. Inastrongsense,then,architecturerequirestheory.Ifitdoesnothavetheoreticalknowledge,thenitwillcontinuetodependonsocialknowledge.Worse,thereiseverypossibilitythatarchitecturecancometobebasedonsocialknowledgemasqueradingastheoreticalknowledge,whichwillbeallthemoredangerousbecausearchitectureoperatesintherealmsofthenon-discursivethroughwhichsocietyistransmittedthroughbuilding.23Architectureisthereforepermanentlyenjoinedtotheoreticaldebate.Itisinitsnaturethatitshouldbeso.Inthatitistheapplicationofreflectiveabstractthoughttothenon-discursivedimensionsofbuilding,andinthatitisthroughthesedimensionsthatoursocialandculturalnaturesareinevitablyengaged,architectureistheoryappliedtobuilding.Inthenextchapterwewillthereforeconsiderwhatwemeanbytheoryinarchitecture.

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NotesJ.Ruskin:Seven Lamps of Architecture,London1849,chap.1.Theliteratureonvernaculararchitectureascultureisnowextensive,andgrowingrapidly.AmongtheseminaltextsofferingwidecoverageareRudovsky’sArchitecture Without Architects,1964;PaulOliver’sShelter and Society,Barrie&Rockliff,TheCressetPress,1969anditsfollow-upShelter in Africa,Barrie&Jenkins,London,1971;AmosRapoport’sHouse Form and Culture,PrenticeHall,1969;LabellePrussin’sclassicreviewofthecontrastingvernacularswithinaregion,Architecture in Northern Ghana,UniversityofCaliforniaPress,1969;SusanDenyer’sAfricanTraditionalArchitecture,Heineman,1978;andKajAndersen’sAfricanTraditionalArchitecture,OxfordUniversityPress,1977;inadditiontoearlieranthropologicalclassicssuchasC.DaryllForde’sHabitat, Economy and Society,Methuen,1934.Studiesofspecificculturesarenowtoonumeroustomention,asarethemuchlarge-numberoftextswhichhavenowdealtwiththearchitectureofparticularculturesandregions,butwhicharenotyetavailableinEnglish.Amongrecentstudiesofthevernacular,themostimportanttomymind—andbyfarthemostinfluentialinthistext—hasbeentheworkofHenryGlassie,andinparticularhisFolk Housing in Middle Virginia,UniversityofTennesseePress,1975,referencestowhich,explicitandimplicit,recurthroughoutthistext.Thesamehasoftenbeensaidof‘industrial’architecture.J.M.Richards,forexample,inhisAn Introduction to Modern Architecture,Penguin,1940,describes

Figure 1.7

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ThomasTelford’sStKatharine’sDockas‘Typicalofthesimplebutnobleengineer’sarchitectureofhistime’.RogerScruton,The Aesthetics of Architecture,.Methuen,1977.Ibid.,p.16.ForarecentrestatementofthisbeliefseeS.Gardiner,The Evolution of the House,Paladin,1976.Seeforexampleprehistoricalsectionsofthemostrecent(nineteenth)editionofSirBanisterfletcher’sA History of Architecture (editedbyProfessorJohnMusgrove)writtenbymycolleagueDrJulienneHanson.Itisacommentonarchitecturalhistorythatitisonlyveryrecentlythatthetrueantiquityofbuildinghasbeenreflectedinthehistoriesofworldarchitecture.SomeofDrHanson’ssourcesareinthemselvesremarkabletextswhichifbetterknownwouldentirelychangepopularconceptionofthehistorynotonlyofbuildingbutalsoofhumansociety.ThekeytextsaregiveninDrHanson’sbibliography,butIwouldsuggesttheremarkableR.G.Klein,Ice Age Hunters of the Ukraine,ChicagoandLondon,1973asagoodstartingpoint.B.Russell,The Problems of Philosophy,HomeUniversityLibrary,1912,OxfordUniversityPresspaperback,1959;Chapter9‘Theworldofuniversals’.R.A.Scruton,The Aesthetics of Architecture,p.43etseq.R.A.Scruton,A Short History of Modern Philosophy: from Descartes to Wittgenstein,ARKPaperbacks,1984.R.Descartes,The Principles of Philosophy,Part2,PrincipleXinThe Philosophical Works of Descartes,CambridgeUniversityPress,vol.1,p.259.Descartes,PrincipleXI,p.259.Descartes,PrincipleX,p.259.Graphswhichhavethispropertyarecalled‘planar’graphs.Anyspatiallayoutononelevel,consideredasagraphofthepermeabilityrelations,isboundtobeplanar.TheseexamplesaretakenfromastudyofseventeenhousesinNormandycarriedoutfortheCentreNationaledeRechercheScientifique,andpublishedas‘Ideasareinthings’inEnvironment and Planning B, Planning and Design 1987,vol.14,pp.363–85.ThisarticlethenformedoneofthebasicsourcesforamuchmoreextendedtreatmentinJ.Cuisenier,La Maison Rustique: logique social et composition architecturale,PressesUniversitairesdeFrance,1991.The‘normalisation’formulafortakingtheeffectofthenumberelementsinthegraphoutofthetotaldepthcalculationfromanelementis2(md–1)/k–2,wheremdisthemeandepthofotherelementsfromtherootelement,andkisthenumberofelements.ThereisadiscussionofthismeasureinP.Steadman,Architectural Morphology,Pion,1983,p.217.ThemeasurewasfirstpublishedinHillieretal.,‘SpaceSyntax:anewurbanperspective’intheArchitect’s Journal,no48,vol.178,30.11.83.ThereisanextensivediscussionofitstheoreticalfoundationsandwhyitissoimportantinspaceinHillierandHanson,The Social Logic of Space,CambridgeUniversityPress,1984.Themeasuretheoreticallyeliminatestheeffectofthenumbersofelementsinthesystem.However,inarchitecturalandurbanrealitythereisanadditionalproblem:bothbuildingsandsettlements,forpracticalandempirical

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reasons(aswillbefullydiscussedinChapter9)tendtobecomerelativelylessdeepastheygrow.Asecond,‘empirical’normalisationformulaisthereforerequiredtotakeaccountofthis.SuchaformulaissetoutinThe Social Logic of Space,whichhasprovedrobustinuse,buthasbeenextensivelydiscussed,forexampleinJ.Teklenberg,H.Timmermans&A.vanWagenberg,‘Spacesyntax:standardisedintegrationmeasuresandsomesimulations’,Environment & Planning B: Planning & Design,vol.20,1993,pp.347–57.SeealsoM.Kruger,‘Onnodeandaxialgridmaps:distancemeasuresandrelatedtopics’,paperfortheEuropeanConferenceontheRepresentationandManagementofUrbanChange,Cambridge,September1989,UnitforArchitecturalStudies,UniversityCollegeLondon.Thereisafurthermeasurecalled‘differencefactor’,whichexpresseshowstrongthesedifferencesare,setoutin‘Ideasareinthings’,citedinnote15above.Itshouldbenotedthattheargumentinthepaperfromwhichtheseexamplesaretaken,‘Ideasareinthings’isagreatdealmorecomplexthanthatpresentedheretoillustratethetechnique.Infact,itwasproposedthattwofundamentaltypologicaltendencieswouldbeidentifiedwithinthesample,whichweremoretodowithdiffer-encesintherelationsofthesexesthananythingelse.AnewversionofthispaperwillbepublishedinJ.Hanson,The Social Logic of Houses,forthcomingfromCambridgeUniversityPress.TheseissuesaredealtwithatgreaterlengthandforaslightlydifferentpurposeinChapter7.MargaretMead,Continuities in Cultural Evolution,YaleUniversityPress,1964,Chapter5.Forexample,HenryGlassie,Folk Housing in Middle Virginia.J.Hanson,writtenfortheintendedEncyclopaedia of Architecture,McGraw-Hill,NewYork,butnotyetpublished.Wewillseeinlaterchapters,andparticularlyinChapters6and11,exactlyhowthiscanoccurandwhatitsconsequencesare.

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Do architects need theories?Inthepreviouschapter,architecturewasdefinedasthetakingintoreflectivethoughtofthenon-discursive,orconfigurational,aspectsofspaceandforminbuildings.Invernaculartraditions,theseaspectsaregovernedbythetakenforgrantedideas to thinkwithofaculture.Inarchitecture,ideas to think withbecomeideas to think of.Spatialandformalconfigurationinbuildingsceasestobeamatterofculturalreproductionandbecomesamatterofspeculativeandimaginativeenquiry. Itfollowsfromthisdefinitionthatarchitectureisanaspiration,notagiven.Tobringtoconsciousthoughttheprinciplesthatunderliethespatialandformalpatternsthattransmitculturethroughbuildings,andtoformulatepossiblealternativesthatworkasthough they were culture—sincearchitecturemustbeanadditiontoculturenotsimplyaremovalofit—isanintellectualaswellasacreativetask.Itrequiresnotonlytheconceptualisationofpatternandconfiguration invacuo,butalsocomparativeknowledgeandreflectivethought.Thisiswhyarchitectureisareflectiveaswellasanimaginativeproject,onewhichseekstoreplace—oratleasttoaddto—thesocialknowledgecontentofbuildingwithanenquiryintoprincipleandpossibility. Architecturaltheoryistheultimateaimofthisreflection.Anarchitecturaltheoryisanattempttorenderoneorotherofthenon-discursivedimensionsofarchitecturediscursive,bydescribinginconcepts,wordsornumberswhattheconfigurationalaspectsofformorspaceinbuildingsarelike,andhowtheycontributetothepurposesofbuilding.Inasense,theorybeginsatthemomentarchitecturebegins,thatis,whenspatialandformalconfigurationinbuildings,andtheirexperientialandfunctionalimplications,arenolongergiventhroughatraditionofsocialknowledgetransmittedthroughtheactofbuildingitself.Assoonasbuildingmovesfreefromthesafeconfinesofculturalprogramming,somethinglikeatheoryofarchitectureisneededtosupportthecreativeactbyproposingamoregeneralunderstandingofthespatialandformalorganisationofbuildingsthanisavailablewithinthelimitsofasingleculture. Thisisnottosaythatcreativearchitecturedependsontheory.Itdoesnot.Butinthatarchitectureistheapplicationofspeculativeabstractthoughttothematerialworldinwhichwelive,thereflectiveaspectsofarchitecturalenquiryleadtotheformulationifnotoftheorythenatleastoftheory-likeideas.Theneedfortheorybecomesgreaterasarchitectureadvances.Theoryismostrequiredwhenarchitecturebecomestrulyitself,thatis,whenitbecomesthefreeexplorationofformalandspatialpossibilityinthesatisfactionofthehumanneedforbuildings. However,thefactthattheoryisaninevitableaspectofarchitecturedoesnotmeanthatalltheorieswillhaveapositiveeffectonarchitecture.Onthecontrary,thedependenceofarchitectureontheoreticalideascreatesanewtypeofrisk:thattheoriesmaybewrong,maybedisastrouslywrong.Themuchdiscussed‘failure’ofmodernisminarchitectureisseenasatleastthefailureofatheory—themostambitiousandcomprehensiveeverproposed—andevenbysomeasthefailureoftheveryideaofatheoryofarchitecture.

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Asaresult,inthelatetwentiethcenturyanumberofnewquestionsareposedabouttheoriesofarchitecturewhicharealsoquestionsaboutarchitectureitself.Doesarchitecturereallyneedtheories,oraretheyjustapretentiousadjuncttoanessentiallypracticalactivity?Ifarchitecturedoesneedtheories,thenwhataretheylike?Aretheylikescientifictheories?Oraretheyaspecialkindoftheoryadaptedforarchitecturalpurposes?Ifarchitecturaltheoriescanbewrong,andhaveapparentlyadverseconsequences,thencantheyalsoberight?Howcanwesetaboutmakingarchitecturaltheoriesbetter?Andmostdifficultofall:howcanarchitectureasacreativeartbereconciledtothedisciplinesoftheory?Arethetwonotopposedtoeachother,inthatbettertheoriesmustleadinevitablytotheeliminationofarchitecturalfreedom. Theanswerproposedinthischapteristhatonceweacceptthattheobjectofarchitecturaltheoryisthenon-discursive—thatis,theconfigurational—contentofspaceandforminbuildingsandbuiltenvironments,thentheoriescanonlybedevelopedbylearningtostudybuildingsandbuiltenvironmentsasnon-discursive objects.Tohaveatheoryofnon-discursivityinarchitectureingeneralwemustfirstbuildacorpusofknowledgeaboutthenon-discursivecontentsofarchitectureasaphenomenon.Thisofcourserunscountertomostcurrenteffortsinarchitecturaltheory,whichseektobuildtheoryeitherthroughtheborrowingofconceptsfromotherfields,orthroughintrospectionandspeculation. However,theproductofthefirst-handstudyofnon-discursivityinbuildingsandbuiltenvironmentswillleadtoanewkindoftheory:ananalytictheoryofarchitecture,thatis,onewhichseekstounderstandarchitectureasaphenomenon,beforeitseekstoguidethedesigner.Ananalytictheoryofarchitectureis,itwillbeargued,thenecessarycorollaryofarchitecturalautonomy.Withouttheprotectionofananalytictheory,architectureisinevitablysubjecttomoreandmoreexternallyimposedrestrictionsthatsubstitutesocialideologyforarchitecturalcreativity.Analytictheoryisnecessaryinordertoretaintheautonomyofcreativeinnovationonwhichtheadvanceofarchitecturedepends.

Are architectural theories just precepts for builders?Beforewecanembarkonthetaskofbuildingananalytictheoryofarchitecture,however,wemustfirstexploretheideaoftheoryinarchitecturealittletopreventourenquirybeingobscuredbysomeofthemorecommonmisconceptions.Architecturaltheoriesdotakeaverydistinctiveform,butallisnotasitseemsatfirstsight,anditisimportantthatwedonotallowappearancestodisguisetheirtruenatureandpurposes. Wemayusefullybeginbyexaminingtheviewsofawell-knowncriticofarchitecturaltheories.Inhis1977polemicagainstarchitecturalmodernismanditsintellectualfashions,The Aesthetics of Architecture1RogerScrutonisdismissiveoftheveryideaofatheoryofarchitecture:‘Architecturaltheory’,hesaysinafootnote,is‘usuallythegestureofapracticalman,unusedtowords’.Elsewherehegoesfurther.Thereisnotandcannotbeatheoryofarchitecture.Whathasbeencalled

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architecturaltheoryaremerely‘…precepts…which…guidethebuilder’.Whilesuchpreceptscanbeusefulcanons,theycanneveramounttoarealtheory,becausetheycannotbeuniversal,anditisonlywiththeclaimtouniversalitythattheoryarises.2

Atfirstsight,Scrutonseemstoberight.Forthemostpart—modernismisoneofthefewexceptions—weassociatetheoriesofarchitecturewithindividualarchitects.WhenwethinkofPalladio’sorLeCorbusier’stheoryofarchitecturewetakeittomeansomethingliketheintellectualgroundofastyle,thegenericprinciplesunderlyinganapproachtodesign.Itseemsselfevidentthatnosuchprinciplescouldeverbeuniversal.Theideaevenleadstoparadox.Auniversalformulaforarchitecturewould,iffollowed,renderarchitecturethesameandunchanging,andthereforeultimatelydull. Butdoestheoryinarchitecturereallyonlymeanaformulaforarchitecturalsuccess?Ascientistwouldfindthisastrangeuseoftheword‘theory’.Forascientistatheoryisarationalconstructintendedtocapturethelawfulnessofhowtheworldis,notasetofguidelinesastohowitshould be.Scientifictheorieshelpusactontheworld,butonlybecausetheyhavefirstdescribedtheworldindependentlyofanyviewofhowitshouldbe.Theessenceofscienceisthatitstheoriesareanalytic,notnormativeinintent.Theydescribehowtheworldis,notprescribehowitoughttobe. Mightwethensuggestthatthisisexactlythedifferencebetweenarchitecturalandscientifictheories,namelythatscientifictheoriesareanalytic,andaboutunderstandinghowthingsare,whereasarchitecturaltheoriesarenormative,andabouttellinguswhattodo?Thereseemstobesometruthinthis.Itisreasonabletosaythatarchitectureisabouthowtheworldshouldberatherthanhowitis,andthatitstheoriesshouldthereforetendtoexpressaspirationsratherthanrealities.Infact,oncloserexamination,itturnsoutthatthisisnotandcanneverbethecase.Admittedly,architecturaltheoriesarenormallypresentedinnormativeform,butatadeeperleveltheyarenolessanalyticthanscientifictheories. Takeforexample,twotheorieswhichareaboutasfarapartastheycouldbeinfocusandcontent,Alberti’stheoryofproportion,3andOscarNewman’stheoryof‘defensiblespace’.4Botharepresentedaspreceptsforsuccessfuldesign,inthatbothauthors’booksareaimedprimarilyatguidingthearchitecturalpractitionerindesign,ratherthanexplainingthenatureofarchitecturalexperienceasexperienced,asScruton’sbookis.Butifwereadthetextscarefully,wefindthatthisisnotalltheyare.Ineachcase,thenormativecontentoftheworkrestsonclear,ifbroad,analyticfoundations.Alberti’stheoryofproportionrestsonthePythagoreannotionofmathematicalforminnature,5andthecoincidenceitassertsbetweentheprinciplesofnaturalformandthepowersofthemind,asevidencedbytherelationshipbetweenoursenseofharmonyinmusicandthesimplenumericalratiosonwhichthoseharmoniesarebased.Ifarchitecturefollowsthemathematicalprinciplesfoundinnature,Albertiargues,thenitcannothelpreproducingtheintelligibilityandharmonythatwefindinnaturalforms.Similarly,Newman’s‘defensiblespace’theoryrestsonthetheoryof‘humanterritoriality’,bywhichgenetictendenciesincertainspeciestodefendterritoryagainstothersofthespecies,aregeneralisedtohumanbeings,both

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asindividualsand—mistakenlyinmyview—asgroups.If,Newmanargues,architectsdesignspaceinconformitywith‘territorial’principles,thenitwillbefollowingbiologicaldrivesbuiltintousbynature.6

Itisnotablethatinbothofthesetheories,theprinciplesfordesignaresaidtobebasedonprinciplestobefoundinnature.Inaverystrongsense,then,inbothcasesthenormativecontentofthetheorydependsontheanalytic.Onreflection,itmustbesotosomedegreeinallcases.Anytheoryabouthowweshouldacttoproduceacertainoutcomeintheworldmustlogicallydependonsomepriorconceptionofhowtheworldisandhowitwillrespondtoourmanipulations.Carefulexaminationwillshowthatthisisalwaysthecasewitharchitecturaltheories.Weinvariablyfindthatthepreceptsaboutwhatdesignersshoulddoaresetinapriorframeworkwhichdescribeshowtheworldis.Sometimesthisframeworkisexplicitlysetout,andrestsonaspecificscientificorquasi-scientificfoundation,asinthetwocaseswehaveinstanced.Sometimesitismuchmoreimplicit,reflectingnomorethanacurrentlyfashionablewayoflookingattheworld,asforexamplemanyrecenttheorieshaverestedonthefashionableassumptionthat‘everythingisalanguage’sothatdesignerscanandshoulddesignfollowingtheprinciplesoflinguistictheoriesinmakingtheirbuildings‘meaningful’. Althoughpresentednormatively,then,architecturaltheoriesmusthaveagreatdealofanalyticcontent,whetherthisisexplicitorimplicit.Inpointoffact,facedwithanarchitecturaltheory,ourfirstreactionwouldusuallybetotreatitexactlyaswewouldascientifictheory.Offeredageneralpropositiononwhichtobasearchitecturalpreceptsfordesign—sayapropositionaboutthepsychologicalimpactofacertainproportionalsystemsorthebehaviouraleffectsofacertainkindofspatialorganisation—ourfirstreactionwouldbetoquestionthegeneralproposition,oratleasttosubjectittotestbyareviewofcases.Weusuallyfindquitequicklythatwould-begeneralpropositionsrunfoulofcasesknowntous,whichwetheninstanceascounter-examplestothetheory.Inotherwords,wetreatanarchitecturaltheoryverymuchinthesamewayaswewouldtreatascientifictheory:thatis,wetreatitasananalytictheorybytryingtofindcounter-exampleswhichwouldrefuteitsgenerality.Evenwhenitsurvives,wewouldbeinclinedtotreatitwithcontinuingscepticismasatbestaprovisionalgeneralisation,whichwecanmakeuseofuntilabetteronecomesalong. Itisamistake,then,totreatarchitecturaltheoriessimplyasnormativeprecepts,asScrutondoes.Architecturaltheoriesarenotandcannotbesimplynormative,butareatleastanalytic-normativecomplexes,inwhichthenormativeisconstructedonthebasisoftheanalytic.Itfollowsthatproperlytheoreticalcontentofarchitecturaltheoriesisspecifiedbytheanalytic.Iftheanalytictheoryiswrong,thenthelikelihoodisthatthebuildingwillnotrealiseitsintention.Architecturaltheories,wemightsay,areabouthowtheworldshouldbe,butonlyinthelightofhowitisbelievedtobe.

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Theories in designWhyshouldarchitecturaltheoriestakethisdistinctiveformofcombiningpropositionsabouthowtheworldshouldbewithpropositionsabouthowitisbelievedtobe?Theansweristobefoundinthenatureofwhatarchitectsdo,thatis,design.Throughitsnatureasanactivity,designraisesissuestowhicharchitecturaltheoristsproposesolutionsintheformofanalytic-normativecomplexesoftheoreticalideas.Tounderstandwhythisisso,wemustunderstandalittleaboutdesign. Designisofcourseonlyapartoftheprotractedprocessesbywhichbuildingscomeintoexistence.The‘buildingprocess’involvesformulatinganeedforapossiblebuilding,conceptualisingwhatitmightbelike,initiatingaprocessofresourcing,negotiatingandorganising,creatingsomekindofrepresentation,orseriesofrepresentationsofincreasingrefinement,ofwhatthebuildingwillbelike,thenconstructing,fitting,operationalising,andfinallyoccupyingthecompletedbuilding.Vernacularbuildingisofcoursealesscomplexprocess.Butifthecircumstancesexistinwhich‘design’isafunction,thenthecorollaryisthatthismorecomplexbuildingprocess,orsomethingapproximatingtoit,alsoexists.Designdoesnotexistasafunctionindependentofthislargerprocess.Onthecontrary,itimpliesit. Howthendowedefinedesignwithinthisprocess?First,wenotethatitisonlyattheendoftheprocessthattheobjectoftheprocess—anoccupiedbuilding—exists.Formostofitsduration,theprocessisorganisedaroundasurrogateforthebuildingintheformofanabstractideaorrepresentationwhichcontinuallychangesitsform.Itbeginsasanideaforthebuilding,thenbecomesanideaofthebuilding,thenamoreformalisedconcept,thenaseriesofmoreandmorerefinedrepresentations,thenasetofinstructionsandfinallyabuilding.Forthemostpart,thecomplexprocessofbuildingtakesplacearoundthisshifting,clarifying,graduallymaterialisingidea. Theprocessofseeking,fixing,andrepresentingarealisableconceptofabuildingfromanideaforabuildingisdesign.Designiswhatarchitectsdo,thoughitisnotalltheydo,andnotonlyarchitectsdoit.Butitisdesignthatkeepswhatarchitectsdo—whetherornotitisarchitectsthatdoit—fixedintheprocessofcreatingbuildings.Therehastobeacontroloftheprocessofsearchingout,conceptualising,andrepresentingthesurrogatebuildingthroughtheprocess.Letuscallthisthe‘designfunction’,sothatwecanseethatitisindependentofwhoactuallycarriesitout. Thedesignfunctionexistswithinthebuildingprocessforonefundamentalreason:becauseatallstagesoftheprocess—thoughwithdifferingdegreesofaccuracy—thepropertiesandperformanceofthebuildingasitwillbewhenbuiltmustbeforeseeninadvance,thatis,theymustbeknowablefromthesurrogate.Withoutthisforesight,thecommitmentsofresourcesnecessaryateachstageoftheprocesscannotbemadewithconfidence.Thedesignfunctionisessentiallyamatterofstage-managingaconstantlychangingrepresentationofwhatwilleventuallybeabuilding,sothatatallstagesoftheprocessthereisinviewaproposalforanobject

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thatdoesnotyetexist,andwhichisprobablyunique—sinceifitwereacopytherewouldbenoneedfordesign—butwhosetechnical,spatial,functionalandaestheticpropertiesifandwhenbuiltare,asfaraspossible,predictableinadvance. Thedesignfunctioninthebuildingprocessthereforeinvolvesontheonehandsearchingoutandcreatingarepresentationofapossiblesolutionforthedesignprobleminhand,andontheotherthepredictionoftheperformanceofthebuildingwhenbuiltfromtherepresentation.Theactivitiesthatmakeupthedesignprocessreflectthisduality.Designessentiallyisacyclicprocessofgeneratingpossibledesignproposals,thenselectingandrefiningthembytestingthemagainsttheobjectivesthebuildingmustsatisfy—tobebeautiful,tobecheap,tobeostentatious,torepresentanidea,torepayinvestment,tofunctionforanorganisationbyprovidingadequateandwell-orderedaccommodation,andsoon.7Thesetwobasicaspectstothedesignprocesscanbecalledthecreativephasesandthepredictivephases.Inthecreativephasestheobjectistocreatepossibledesignproposals.Inthepredictivephases,theobjectistoforeseehowproposalswillworktosatisfytheobjectives. Onceweunderstandthecreative-predictivenatureofthedesignprocess,thenitiseasytoseehowthenormativeandanalyticaspectsoftheoriescanusefullycontributetotheprocess.Theoriescanbeused,andoftenareused,tacitlyorexplicitly,intwoquitedistinctmodesinthedesignprocess:asaidstothecreativeprocessofarrivingatadesign;andasaidstotheanalyticprocessofpredictinghowaparticulardesignwillworkandbeexperienced.Oftenofcoursethesetwoaspectswillbeconflatedinaundifferentiatedthoughtprocess.Thenormativeaspectsofatheorytellsthedesignerwheretosearchforcandidatesolutionsinthecreativephases,theanalyticaspectshowthesolutionwillwork.Forexample,ifyouareaPalladian,theninthecreativephasesofdesignyousearchforaformalandspatialsolutionwithPalladianproperties—acertainrangeofenvelopegeometries,certainsymmetriesofplanandfaçade,certainkindsofdetailing,andsoon—confidentthatifyouproceedinaPalladianmannerthenyoucanpredictaPalladianoutcome.IfyouareaNewmanite,thenyousearchforformalandspatialsolutionswithacertainlayeringofspatialhierarchies,certainpossibilitiesofsurveillance,theavoidanceofcertainformalthemesandsoon,againconfidentthatbyproceedingthiswayasafeenvironmentwillresult.Theorythusstructuresthesearchforapossibledesigninasolutionspacethatmightotherwisebebothvastandunstructured,anditdoessoinawaythatgivesthedesignerconfidence—whichmayofcoursebequitemisplaced—thatthenatureandpropertiesoftheeventualbuildingcanbeknownfromthetheory. Theuseoftheoryisofcourseonlyonewayofstructuringthedesignprocess.Infactfewdesignersclaimtocreatedesignsfromtheory,andmanywouldgooutoftheirwaytodenyit.Butthisdoesnotmeanthattheydonotdesignundertheinfluenceoftheory.Muchuseoftheoreticalideasinarchitectureistacitratherthanexplicit.Thisisnotduetomalignintentonthepartofdesigners,butmuchmoretodowiththeneedfortheoryindesign,howeverlittlethisisrecognised.

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Consider,forexample,theproblemofprediction.Havingcreatedacandidatedesign,thedesignernowhasthetaskofforeseeinghowthe‘unknownnon-discursivities’offormandspacethatwillbecreatedbythedesignwillworkandbeexperiencedwhenbuilt.Logicallythereareonlytwopossiblebasesforsuchprediction:knownprecedentandtheoreticalprinciple.Predictionbyprecedentmeanspredictionbyreferencetoknowncasesthatalreadyexist.Predictionbyprinciplemeanspredictionbyreferencetothegeneralityofknowncases.Bothareessentiallyclaimsbasedonexperience,buttheformerisspecific,andthelattergeneral. Predictionfromprecedentraisestwoproblems.Theideaofarchitectureincludestheideathatthebuildingtobecreatedwillnotsimplybeacopyofonewhichexists.Thismeansthatprecedentcannotbeusedlockstockandbarrelforthewholebuilding.Precedentcanthereforeonlybeusedpiecemealforaspectsorpartsofthebuilding.Sinceformallyandspatiallybuildingsarecomplexconfigurations,andnotsimplyassemblagesofparts,itcanneverbeclearthatthenewembeddingofaprecedentattributeorpartwillnotworkdifferentlyinthecontextofthenewwhole.Theuseofprecedentindesignisnecessary,sinceitbringsinconcreteevidenceinsupportofprediction,butitisneversufficient,becauseeachnewsynthesisrecontextualiseseachaspectofprecedent.Theuseofprecedentthereforenecessarilyinvolvesinterpretation. Thepressureondesignerstoworkatleastinpartfromknowledgeoftheoreticalprincipleisthereforeintense.Theapparentadvantagetothearchitectofworkingwithinaparticulartheorybecomesthesolutiontothepredictionproblemappearsalreadytobecontainedwithinthetheory.Thenormativetheoreticalconceptsthatguidethegenerationofacandidatedesignalsotaketheformofanalyticconceptswhichindicatethatifthedesignerfollowsthepreceptsofthetheory,thenitistobeexpectedthatthedesignwillworkinthewaythearchitectintends.Theanalyticfoundationsofthenormativetheoryreturnatthepredictivestagestoappeartoguaranteearchitecturalsuccess.Thisiswhyarchitecturaltheoriestaketheformofnormative-analyticcomplexes.Theyfulfilthetwoprimaryneedsofthedesignprocesswithasinglesetofpropositions. However,itisclearthattheseadvantageswillonlyexisttotheextentthatthetheory’sanalyticfoundationsarenotillusory.Iftheydonotofferarealisticpictureofhowtheworldworks,thenitislikelythatthedesigner’spredictionswillreferonlytoanillusoryreality.Apoorlyfoundedanalytictheorywillnotinhibitthedesignerinthecreativephasesofdesign,butitwouldleadhimorhertolookinthewrongplace.Itwouldalsomeanthatthedesigner’spredictionswouldbeunlikelytobesupportedbyeventswhenthebuildingisbuilt.Thisiswhybadtheoriesaresodangerousinarchitecture.8Theymakedesignappeartobemucheasier,whileatthesametimemakingitmuchlesslikelytobesuccessful.This,inthelastanalysis,iswhyarchitectsneedanalyticallywellfoundedtheories. However,thisisnotthesameastosaythatarchitectssimplyneedscientifictheoriestoguidethemindesign.Thedualuseoftheoryinarchitecturebothtogeneratedesignsandtopredicttheirperformancepermitsustointroduceavery

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importantcomparison:betweentheoriesinartandtheoriesinscience,andtoarguethatarchitectureneedstheoriesbothinthesensethatthewordisusedinartandinthesensethatthewordisusedinscience. Theoriesinartarenotanalytic-normativecomplexesofthekindwetypicallyfindinarchitecture.Theyareprimarilyaboutsupportingthecreativeprocess,thatis,theyareinessenceaboutpossibility.Theoriesinartexpandtherealmofthepossible,bydefininganewwaytoartorevenbydefininganewformofart.Thereneedinprinciplebenoconstraintsonwhattypeoftheoriesareused.Theroleofatheoryinartisnottoclaimauniversalart,ortosetuponeformofartassuperiortoanother,buttoopenuponemorepossiblekindofart.Theoryinartisthenessentiallygenerative.Itdoesnothavetotakemuchaccountoffunctionalorexperientialconsequences.Itusesabstractthoughtonlytogeneratenewpossibilitiesinartthathadnotbeenseenbefore. Ifarchitectureweresimplyanart,itwouldneedtheoriesonlyinthesensethatpaintersorsculptorshavetheories:thatis,asspeculativeextensionsoftherealmoftheartisticallypossible.Itisclearthatarchitectureasarthasandneedsthiskindoftheory.Butthisisnotallithasandneeds.Thedifferencebetweenarchitectureandartisthatwhenanartistworks,heorsheworksdirectlywiththematerialthatwilleventuallyformtheartobject—thestone,thepaintandsoon.Whattheartistmakesistheworkofart.Architectureisdifferent.Anarchitectdoesnotworkonabuilding,butarepresentationofabuildingwecalladesign.Adesignisnotsimplyapictureofabuilding,butapictureofapotentialobjectandofapotentialsocialobject—thatis,anobjectthatistobeexperienced,understoodandusedbypeople.Adesignisthereforenotonlyapredictionofanobject,ratherthananobjectitself,but,howeverfunctionallynon-specificitclaimstobe,apredictionofpeopleinrelationtobuilding.Thisiswhereanalytictheoriesareneeded,andanalytictheoriesareanalogoustoscientifictheories.Theoriesinsciencearesetsofgeneral,abstractideasthroughwhichweunderstandandinterpretthematerialphenomenatheworldofferstoourexperience.Theydealwithhowtheworldis,nothowitmightbe.Becausearchitectureiscreativeitrequirestheoriesofpossibilityinthesensethattheyexistinart.Butbecausearchitectureisalsopredictive,itneedsanalytictheoriesofactualityaswellastheoriesofpossibility. Itisthisdoublenaturethatmakesarchitecturaltheoriesunique.Theyrequireatoncetohavethegenerativepoweroftheoriesinartandatthesametimetheanalyticpoweroftheoriesinscience.Thefirstdealswiththeworldasitmightbe,thesecondwiththeworldasitis.Thequestionthenis:howmaytherebetheoriesofarchitecturewhichareatoncecreativeandanalytic.Oneaspectoftheanswerturnsouttobesimple:goodanalytictheoriesarealreadylikelytobealsogoodtheoriesofpossibility.Theentireusefulnessofscientifictheoriesintheirapplicationsinscienceandtechnologyisinfactfoundedonthesimplebutunobviousfact:thatanalytictheoriesdonotsimplydescribetheworldasitis,butalsodescribethelimitsofhowitcanbe.Scientifictheoriesarearrivedatthroughtheexaminationoftheworldasitis.Butitisexactlythetheoreticalunderstandingoftheworldasitisthatopensup

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wholerealmsofnewpossibilitythatdonotyetexist. Itisthisfundamentallinkbetweenactualityandpossibilitythatopensthewaytoananalytictheoryofarchitecture.Butbeforeweexploreit,wemustfirstlookalittlemorecarefullyatarchitecturaltheoriestoseehowtheyarestructured,andwhy,andhowtheymighteventuallymoveinthedirectionofbecomingmoreanalytic.

The problem of architectural theoryThemostcommonproblemwitharchitecturaltheoriesisthattheyhavetoooftenbeenstronglynormativeandweaklyanalytic,thatis,ithasbeentooeasytousethemtogeneratedesigns,buttheyaretooweakinpredictingwhatthesedesignswillbelikewhenbuilt.Thetheoriesofmodernismwere,forexample,quiteeasytofollowingeneratingdesignstosatisfynormativelystatedobjectives.Theproblemwasthatthearchitecturalmeansproposedwerenotthemeansrequiredtoachievethoseobjectives.Thetheorieswereweaklyanalytic.Theydidnotdealwiththeworldasitactuallyis.Thenormativedominatedtheanalytic. Exactlyhownormativelystrongbutanalyticallyweakarchitecturaltheoriesareheldinplacecanbeseenbytakingonemorestepindisaggregatingwhatarchitecturaltheoriesarelikeandhowtheywork.Forexample,lookingalittlemorecloselyatourtwoexemplarsofarchitecturaltheories—theAlbertianandtheNewmanite—wefindbothhavetwoquitedistinctcomponents:oneintherealmofbroadintention,tellingarchitectswhattheyshouldaimtoachievethrougharchitecture,andoneintherealmofwhatwemightcallarchitecturaltechnique,tellingarchitectshowtorealisethatintention.Alberti’stheory,forexample,tellsarchitectsthatinordertodesignbuildingsthatpeoplewillexperienceasharmonious,theyshouldaimtoreflectintheirbuildingsthemathematicalorderfoundinnature.Hethengoesontoofferamethodforcalculatingproportionstoserveasatechniqueforrealisingthisaiminarchitecturalterms.9Newmantellsarchitectstheyshouldaimtodesignspacesbeyondthedwellingsothatinhabitantsmayidentifywiththemandcontrolthem,thenspecifieshierarchicaltechniquesofspaceorganisationinordertorealisethis.Wemightcallthesethebroadandnarrowpropositionsaboutarchitecturecontainedinatypicalarchitecturaltheory.Thebroadproposition,orintention,setsagoalwhilethenarrowproposition,orarchitecturaltechnique,proposesawayofdesigningthroughwhichtheintendedeffectwillberealised. Onedifferencebetweenthebroadandnarrowpropositionsliesinwhattheyengage.Thebroadpropositionengagesaworldofideaswhichmaybeverylargeinitsscopeandmaycontainmuchthatispoorlydefinedandlittleunderstood.Thenarrowproposition,ontheotherhand,engagestherealitiesofarchitecturaldesignandexperience.Ifingeneraltheoriesareabstractpropositionswhichengagetherealworldofexperience,thenthebroadandnarrowpropositionsofarchitecturaltheoriesoccupyoppositeendsofthespectrumcoveredbytheories.Thebroadpropositionsareintherealmofphilosophicalabstraction,wherethetheoryengagesthevastworldofideasandpresuppositions,implicitandexplicit,whicheventuallyrestsnowherebutintheevolutionofhumanminds.Thenarrowpropositionsarein

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therealmofdirectexperienceoftheworldwheretheoriesengagetheminutiaeofeverydayexperience. Broadpropositionandnarrowpropositionalsodifferintheirintendeduniversality.Broadpropositionsareintendedtobeuniversalisticinthattheyattempttosaythingsaboutarchitecturewhichareheldtobegenerallytrue,andtosayitinsuchabroadwayastoallowittobetrueinquitedifferentarchitecturalcircumstances.Butitisclearthatweshouldnotregardthenarrowpropositionsasuniversalistic.10Forthemostpartthenarrowpropositionsareofferedaspossibletechniquesforrealisinganabstractlystatedaim,nottheonlysuchtechniques.Onreflection,againthismustbeso.Thenarrowpropositionsofanarchitecturaltheoryaretechniquesforbridgingbetweentheabstractandtheconcrete.Onlyanabstractioncanbegeneral.Weshouldnotmistakeatechniqueforrealisingananalyticabstractionfortheabstractionitself. Nowconsiderthesebroadandnarrowpropositionsinrelationtowhatisrequiredoftheoryinthetwophasesofdesign,thatis,inthefirstphase,ideasaboutpossibleformsand,inthesecondphase,ideasabouttherelationsbetweenformsandperformanceoutcomes.Bothofthetheorieswehavebeenconsideringappeartosupplybothneeds.Ideasofpossibleformsarecontainedinthenarrowpropositions,thatis,theconstructivetechniquesthroughwhichthetheoristadvisesthedesignertogoaboutdesigntoensuresuccess.InthecaseofAlberti’stheory,thismeansthesystemsofworkedoutproportionswhichguidethedesignerinsettingupthebuildingasaphysicalform.InNewman’scase,thismeansthediagramsofspatialhierarchywhichthedesignercanfollowinsettingupthespatialdesign.Ideasoftherelationbetweenformandfunctionaloutcomearethenexpressedatthemorephilosophicallevelofthebroadpropositions.InAlberti’scase,thismeansthebroadpropositions,basedontheanalogywithmusic,aboutthehumanexperienceofvisualharmony.11InNewman’scase,itmeansthebroadpropositionsabout‘humanterritoriality’anditsspatialimplications.12Inotherwords,inbothcases,itisthehighlyspecificnarrowpropositionswhichguidethecreativeprocessofdesign,andtheverygeneralisedbroadpropositionswhichguidethedesignerinpredictingfunctionaleffectfromformalconfiguration. Nowtheproblemwithmostarchitecturaltheoriesisthatthisisexactlytheoppositeofwhatisrequiredforarchitecturewhichiscreativelyinnovativeandfunctionallysuccessful.Inthegenerativephaseofdesign,whatisneededifarchitecturalcreativityistobemaximisedisideasaboutformalandspatialconfigurationwhichareasunspecificaspossibleaboutspecificsolutions,inordertoleavethesolutionspaceasopenaspossibletocreativeinvention.Inthepredictivephases,whatisneededisprecisionaboutspecificformssincewhatisatissueisthepredictionofthefunctionaloutcomeofthisorthatrealdesign.Inthegenerativephases,wherewhatisrequiredareabstractorgenotypicalideaswhichopenuprealmsofpossibilityjustastheoriesdoinart,architecturaltheoriesofthistypeofferarathernarrowrangeofsolutiontypeswhichareessentiallynomorethanasetofabstractexemplarstofollow—particularsystemsofnumerical

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proportionsinonecase,particulardiagramsofhierarchicalspatialrelationsintheother.Thenwheninthepredictivephasesofdesignthedesignerneedsamuchgreaterdegreeofanalyticprecisioninordertoforeseehowthisorthatinnovativeformwillworkfunctionallyorexperientially,allthatthetheoriesofferisthevagueanalyticgeneralisationsofthebroadpropositions. Inotherwords,architecturaltheoriesofthistypeareover-specificwheretheyshouldbepermissiveandvaguewheretheyshouldbeprecise.Thedesignerisgivenconcretemodelstofollowwhenheorsheneedsconstructivecreativeideastosearchthesolutionspace,andvacuousabstractionswhenheorsheoughttobegiventechniquestopredicttheperformanceofparticulardesigns.Thisis,inanutshell,theproblemwithmostarchitecturaltheories,andthisishow,inrealdesign,thenormativeaspectsoftheorycometodominatetheanalytic.Whatisneededaretheorieswiththereverseproperties,thatis,theoriesthatareasnon-specificaspossibletoparticularsolutionsinthegenerativephasesofdesigninordertoleavethesolutionfieldaslargeanddenseaspossible,andasspecificandrigorousaspossibleinthepredictivephasesinordertobeabletodealpredictivelywithunknownformswheretheneedforeffectivepredictionisgreatest.Theimplicationofthisisthatweneedafullyfledgedanalytictheorywhichwouldofferabstractunderstandingratherthanspecificmodelsinthecreativephasesofdesign,andphenotypicalprecisionratherthanvaguegeneralisationsatthetestingstages.

What exactly, are theories?Howshouldwegoaboutsettingupsuchatheory?Thefirststepmustbetomakesureweunderstandexactlywhatananalytictheoryis.Thisturnsouttobenotaseasyaslookingthewordupinadictionary.Fewwordsareinfactmoreambiguousintheiroriginsthan‘theory’.InitsancientGreekorigins,theverbtheoreeinmeanstobeaspectator,andtheproductsofthisspeculativeactivity,theoremata,were,notsurprisingly,speculations.ForBacontheoriesweresimplyerrors,the‘receivedsystemsofphilosophyanddoctrine’,tobereplacedinduecoursebysomethingaltogetherbetter.13Thismeaningisstillreflectedineverydayuse.Incommonusage,theoriesarespeculations,oflesserstatusthanfacts,atbestatemporaryfixuntilthefactsareknown.Afictionaldetectivewithapremature‘theory’aboutacasewillalmostcertainlybeshowntobewrong.Theexpression‘onlyatheory’clearlyexpectstheorynottobeeventuallysupportedby‘facts’,buttobereplacedbyfacts.Inthesesenses,theoriesembodyirremediableuncertainties,andappeartoconstituteaformofthoughtwhoseobjectistoreplaceitselfwitha-theoretical,andthereforesecure,knowledge.Incompletecontrast,inmodernsciencetheword‘theory’todaystandsforthedeepestlevelofunderstandingofphenomena.Successfultheoriesinareaswherenonehadpreviouslyprevailed,likeevolutiontheory,arethemostepochmakingofintellectualevents.Conflictsbetweenrivaltheoriesof,say,theoriginsoftheuniverseorthenatureofmatter,conductedontheobscurebattlefieldsofmacroandmicrophenomena,areamongtheepicsofthelatetwentieth-centurythought. Sowhatthenis‘theory’,thatitcanbesubjecttosucharangeofinterpretationsandambiguities?Thesourceofthisambiguityliesofcoursenot

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inthevagariesofetymologicalhistorybutinthenatureoftheoriesthemselves.Theoriesarefoundintherealmofspeculativethought,becausetheyareatroot,speculations.Theyarenotinthemselves,forexample,statementsaboutobservablephenomena,norevenstatementsabouttheregularitiesthataretobefoundinobservablephenomena.Theyarepropositionsabouthypotheticalprocesseswhichmightberesponsiblefortheregularitiesweseeinphenomena.Assuchtheyhaveanecessarilyabstractnature,andarepurelyconceptualentities.Youcannotseeatheory,onlyitsconsequences,soyoucannotverifyatheory,onlyphenomenathatareconsistentwithit.Whenwetestatheorywedonotsimplylookatthetheorytoseeifallthepartsareinworkingorderandproperlyrelated,thoughwedoalsodothis.Wecheckthetheorybyseeinghowfarthephenomenaavailableintherealworldareconsistentwiththetheory,andpreferablywithnoother.Tocheckatheory,ineffect,welookawayfromthetheory.Theoriesareinthemselvesunobservableandunexperiencable,andthisiswhyintheendeventhebestandthemostdurableremaininsomesensespeculative. Butevenwhenweaccepttheabstractandspeculativenatureoftheories,wehavenotyetexhaustedtheapparentindeterminacyoftheidea.Nosetofconceptswhichbecomepartofatheorycanexistinisolation.Onthecontrary,conceptscanonlyexistaspartofconceptualschemesthroughwhichweinterpretourexperienceoftheworldandturninformationintoknowledge.Noconceptorsetofconceptscanexistinavacuum.Eachmustbeembeddedinabroaderrangeofpropositionsorassumptionsaboutwhattheworldislikeandhowitworks.ThesebroaderframeworkshavebeenknownasparadigmssinceThomasKuhnfirstdrewattentiontotheirexistence.14

Withallthisindeterminacyinwhatwemeanbytheory,howisitthattheycanbesoimportantandsouseful.Toanswerthiswemustunderstandthecircumstancesinwhichtheoriesariseandwhatpurposestheyserve.Theorisationbeginswhenwenoteacertaintypeofphenomenonandmakeacertaintypeofpresupposition.Thephenomenonwenoteisthatofsurfaceregularityintheworldasweexperienceit.Thepresuppositionwemakeisthatsurface regularityimpliesunderlying invarianceintheprocessesthatgiverisetothephenomenawesee. Thefirstofthese—thenotingofregularities—theorisationshareswithlanguage.Thefactthatlanguagehaswordsforclassesofthingsratherthansimplyforindividualthingsassumesthatweknowthedifferencebetweenorderandchaos,thatis,thatwecandiscernintheobjectiveworld‘structuralstabilities’15whicharesufficientlywelldefinedandrepetitioustosupporttheassignmentofnames.Thesenamesare,asphilosophershaveendlesslynoted,abstracttermsforclassesintheguiseofnamesforthings,withtheconsequencethatevensuchasimpleapparentlyconcreteactofpointingatathingandnamingitdependsonthepriorexistencenotonlyoftheabstractuniversalconstitutedbythatclassname,butalsooftheschemeofsuchabstractionsofwhichthatparticularabstractionformsapart.Theseschemes,aswehaveknownsincedeSaussure,16differfromonelanguagetoanothersothatwearecompelledtoacknowledgethatnamesarenot

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neutral,simplehandlesonthings,butconceptualinstrumentsbywhichwecreateanorganisedpictureoftheworld.Namescreateunderstanding,anditisagainstthebackgroundoftheorganisedpictureoftheworldalreadygiventousbylanguageandculturethattheorisationbegins. Theorybeginsinthesameplaceaslanguagewherewenote,inthefluxofexperience,regularities,butaddsafurtherpresupposition:thatsinceregularityisunlikelytobetheproductofchance,theremustbesomekindofordernotonlyintheregularphenomenathatweobservebutalsointheprocessesthatgiverisetothephenomena.Whyweshouldmakethispresuppositionisnotclear.Butitseemsplausiblethatjustaslanguageseemsintimatelyboundupwithhowwecognisetheworldsotheorisationisboundupwithhowweactintheworld.When,forexample,westrikestonestomakesparksandthenfire,thesequenceofeventsfromonetotheotherisnotinscribedonthesurfaceofthingsbutimpliessomeinteriorprocesswhichissetinmotionbyouractions.Justastheworldrespondstoouractionsonitbyproducingregularities,sowepresupposethattheexistenceofregularitieswhichdonotresultfromouractionsmustbetheresultofinvariantprocessesanalogoustoouractions.Ifthenlanguagearisesfromourbeingintheworldandneedingtoknowitsobjectivepersistences,sotheorisationseemstoarisefromouractingintheworldandontheworldandneedingtoknowtheinteriorprocessesbywhichoutcomereliablyfollowsfromaction. Wethusseethatregularitiesarethestartingpointoftheory,buttheyarenotthetheoryitself.Regularitiesinitiatetheprocessoftheorisationsinceweinferfromtheexistenceofregularitiesthattheremustbesomeinvariantstructureinwhateverprocessitisthatproducesthesesurfaceregularities.Theoriesareconcernedwiththenatureofthatprocess,morepreciselytheyareattemptstomodeltheinvariantstructureofprocesseswhicharethoughttoexistfortheretobesurfaceregularities.Atheory,then,isnotalistofregularities.Regularitiesarewhattheoryseekstoexplain,butarenotinthemselvestheory.Theyinitiatethesearchfortheorybutarenotandcannotbeitsendpoint.Atheorywhichseeksto‘explain’regularitiesisanentityofanaltogetherdifferentkindfromalistofregularities. Moreover,althoughtheorisationmovesonfromlanguagebyseekingtoidentifythehiddenprocessesthatgiverisetosurfaceregularities,itdoesnotbegininaconceptualorlinguisticvoid.Itbeginsintheonlyplaceitcan,intheevolutionofthoughtandlanguage,andtheirrelationtothespace-timephenomenathatweexperience‘withouttrying’.Becausethoughtandlanguagealreadygiveusapictureoftheworldwhich,atsomelevelatleast,seemstoreflectitsorderandthereforetoexplainit,wearecompelledtoacknowledgethatwhenwebegintheprocessoftheorisationwearealreadyinpossessionofaviewoftheworldwhichinmanywaysisverylikeatheory,inthatitmakestheworldseemamoreorlesscoherentandorganisedplace.Thedifferenceisthatthetheory-likeunderstandingweacquirefromcultureandlanguagereflectsnotaninteriororderwhichgivesrisetothesurfaceregularitiesbutanorderinthosesurfaceregularitiesthemselves.Whenforexamplelanguagetellsusthat‘thesunrises’,itreflectstheregularities

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thatwenoteonthesurfaceofthings,notahiddenprocesswhichgivesrisetothissurfaceregularity.Wemightusefullythenthinkofsucheverydayconstructionsas‘theoryintheweaksense’.Analytic,orscientifictheories,are‘theoriesinthestrongsense’.Theyaimatagreatertruthbecausetheyseeknottobringordertosurfaceregularitiesbuttoshowhowthosesurfaceregularitiesarisefrominvariantnecessitiesburieddeepinthenatureofthings.

Formally defining simple regularitiesBecausesurfaceregularitiesaretheobjectoftheory,thefirststepintheorisationistoformalisetheidea.Infact,thereisabeautifullysimplewaytoextracttheideaofregularityfromphenomenaandrepresentitaspureregularity,independentoftheoverallqualitativenatureofthings.Theideaisthatoftranslatingthepropertiesofobjectsintheworldasweseetheminrealspaceintoanabstractspacewhichallowsustobequiteclearaboutwhatthesepropertiesare.Thisisdonebythefamiliartechniqueofreplacingthespacewithinwhichtheobjectexistswithanabstractco-ordinatesysteminwhichtheaxesrepresentthosepropertiesoftheobjectthatseemtobeofinterestasregularities.Thusoneco-ordinatemightrepresenttheheightoftheobject,anotherthelengthandanotherthebreadth.Wemaythenrepresentanyobjectwhichhasthesepropertiesasasinglepointinthe‘propertyspace’. Oncewecanrepresentthepropertiesofanobjectasapointinapropertyspaceratherthanasthatsetofactualpropertiesinrealspace,wecaneasilyrepresentexactlywhatwemeanbyaregularityasfarasthesepropertiesareconcerned.Forexample,totheextentthatthingsarecomparabletoeachotherinmorethatonepropertyinthepropertyspace,thepointsrepresentingtheminthepropertyspacewillclusterinaparticularregionofthespace.Clustersinthepropertyspacegiveaformalmeaningtotheideaofatypeorclassofthings,insofarasthosepropertiesareconcerned.Ifthingswhenrepresentedaspointsinthepropertyspacearerandomlydistributedthroughoutthespace,thatis,iftherearenoclusters,thenwewouldsayeitherthattherewerenotypes,butonlyindividuals,orthatwehadselectedthewrongpropertiesforanalysis.Ifontheotherhandweseeclusters,weinferthatthingstendtofallintotypes,bywhichwemeanthatvariationononepropertytendstobeassociatedwithvariationonatleastoneother,orperhapsmanyothers.Thisisshowngraphicallyinthetoptwodiagramsoffigure2.1.Wemayequallyusethepropertyspacetoformalisetheideathattheregularityweseeliesnotinapparentclassesortypesofthingsbutsequencesofstatesofthings.Inthiscaseweask:whenanentitychangesononedimension,doesitchangeinanyother?Ititdoes,thentheregularitywillshowitselfasaregularpatterninthedistributionofentitiesinthepropertyspace.Thisisshowninthebottomtwodiagramsinfigure2.1.Whenweseesuchapattern,wewouldinferthatsomeprocessifnotofcauseandeffectthenatleastofregularco-variationwasinoperation,sinceeachtimeonevariablewaschangedachangeinanothervariableregularlyappeared.

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Figure 2.1

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Wemightthenreasonablysaythatquestionsabouttypes,thatis,aboutsimilaritiesanddifferences,arequestionsoftheform:doentitiesclusterinparticularregionsofthepropertyspace?;whilequestionsaboutcauseandeffectareoftheform:whenentitiesmoveinonedimensionofthepropertyspacedotheymoveinanother?17Bothofthesedescribetheapparentregularitiesofsurfacephenomena,thatis,theappearanceoftypesandtheappearanceofcauseandeffect,inanabstractway.Thepropertyspaceisameansofcontrollingtheattributesthataretobeaccountedforinthepatternofsimilaritiesanddifferences.Wheretherealobjectispresent,allitspropertiesaremanifest.Inthepropertyspace,onlyselectedpropertiesarepresent.Ofcourse,everythingdependsonourselectingtherightpropertiesforthepropertyspaceinthefirstplace.Forthisreasonwecanneverbesurefromtheabsenceofaregularitythatnoregularitiesarepresentinthesephenomena. Butevenifwegothroughalongprocessofexperimentingwithdifferentpropertiesuntilweeventuallyfindtheclustersorcovariationsthatindicatethepresenceofregularities,itwillalwaysstillbethesurfacephenomenathatarerepresentedregardlessofthedegreeofabstraction.Wearestillseeingthesurfaceofthings,thatis,apparentregularitiesofthingsaspresentedtoourexperience.Wearenotseeingthetheorythatpurportstoaccountforthoseregularities,thatis,wearenotseeingthemodelofthestructuresoftheprocesswhichmightaccountfortheseregularities.Whatwearedoingisrecordingphenomenainsuchawayastobeabletoseeclearlywhatwemeanbyregularities,bytranslatingpropertiesintothedimensionsofacoordinatespaceandlocatingobjectsaspointswithinthisspacesothatonlytheregularpropertiesarerepresentedinwhatwesee.Thisbothseemstobeandisafundamentalway—maybethefundamentalway—ofrigorouslyrecordingsimilaritiesanddifferences,andconstantassociationsbetweenthings,withinanobjectiveandindependentframework. Themeaningofthewordtheorycanthenbemadeprecise.Aswehavesaid,justasthe a priori givenforthenotingofregularitiesisthatweknowthedifferencebetweenorderandrandomness,the a priori givenfortakingthisintotheorisationisthatregularityonthesurfaceimpliessomesystemicprocessbelowthesurface,suchthatthestructureofthatsystemisinsomesenseinvariant.Atheoryisanattempttomodeltheseinvariantsinasystemofinterdependentconcepts.Atheoryisamodelbecauseitdealswiththewayinwhichthingsmustbeinterrelatedinordertoproducethesurfacephenomena,andabstractbecauseitrepresentsthesystembysomemeansotherthanthatofthesystemitself.Atheoryisamodel,butnotinthesensethataphysicalmodelisamodel,thatis,asmallcopyofthethingitself,butinthecontrarysenseofamodeltakingasabstractaformaspossible,uncommittedtoanyparticularkindofrepresentationorembodiment.Initspurestform,atheoryisakindofabstractmachine,sinceitisanattempttocreateanabstractrepresentationoftheworkingofprocesseswhichgiverisetowhatwesee. Nowtheenormouspoweroftheoriesarisesfromoneveryspecificpropertyofsuch‘abstractmachines’,apropertywehavealreadytouchedupon.Becausetheoriesareabstractworkingmodelsofprocesseswhichgiverisetotheactual,

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theyalsogiveabasisforconjecturingaboutthepossible.Theoriesineffectallowustogobeyondtheaccumulatedexperienceofrealityandconjecturepossiblestatesofrealitythatarecompatiblewiththemodel.Itisthislinkbetweentheactualandthepossiblethatmakestheoriessousefulforprediction.To‘apply’atheoryisessentiallytoposethequestion:iswhatisproposedapossiblecase? Itistoolimitingthentocalltheories‘explanations’ofhowtheworldis.Atheorydefinestheinvariantsthatunderliemanydifferentstatesofreality.Itisinprincipleunlikelythatallpossiblestatesofaparticularsetofphenomenaalreadyexistorarealreadyknown.Itislikelythenthatthetheorywillalsopredictpossiblestatesthatdonotexistbutcouldaccordingtothemodel.Itisthispropertyaboveallothersthatimpartstotheoryitsimmensepowerasatoolofthoughtandasanagentofhumancreativity,andalsoitspracticalusefulness.However,itisclearthatthesevirtueswillariseonlytothedegreethatthetheorycapturesinvariantsthatreallyare‘outthere’.Buthowcanthisbe?Howcananabstractioncapturewhatisreally‘outthere’.Totakethisnextstep,wemustknowalittlemoreabouthowtheoriesareputtogether,howtheywork,andwhattheyaremadeof.

What are theories made of?Thefirstthingwemustnoteisthattheoriesaremadeofconcepts,usuallyintheformofasystemofinterdependentconceptswithtwoformsofexpression:words,andformalexpression,usuallymathematical.Sinceeverydaylifeandlanguageisalsorunonconceptswemustknowthedifferencebetweenascientificconceptandanunscientificone.Whatthenisthedifference?Wecandonobetterthantodiscusstheconceptsonwhichbothlanguageandscienceseemtobefounded,thatis,thedifferencebetweenorderandrandomness. Orderandrandomnessarebothconceptswhichhaveapowerfulintuitivemeaning.Bothareverybroadindeedintheirapplication,somuchsothatitisveryhardtopindownwhatthetwotermsmeanwithanyrealclarity.Bothterms,andevenmorethewaytheyarerelated,expresscomplexintuitionsaboutthewaytheworldis.Eachtermcanbeusedinawiderangeofsituations,andthemeaningonlybecomesclearenoughtofeelunderstoodinthespokenorwrittencontext.Thisiscommonenough.Theintuitiveconceptsthatpervadeandgivesensetoourlanguageshavethisrichnessandimprecision,sotheycanbeusedinagreatvarietyofsituations,andindeeditisonlyinthecontextinwhichaconceptisusedthatitsmeaningbecomesunambiguous. Inscience,itisexactlythisrichnessandimprecisionthatisrestricted.Scientificconcepts,althoughexpressedinlanguage,aremuchnarrowerintheirpotentialapplicationthannormallinguisticconcepts.Buttheyarealsomoresystemic,inthattheycompressandexpressmoreinterrelationshipsbetweenconcepts.Theyexpressmoreconnectionbetweenthings,butatthecostofanarrowingoftherangeofapplication.Theconceptof‘entropy’isagoodexampleofthisbecauseitrelatesbothorderandchaosinasystemicway,andindoingsorestrictstherangeofapplicationofthenewsyntheticconcepttothosesituations

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wherepreciselythesesystemicrelationshold.Thedegreeofentropyinasystemdescribesthatsystem’spositioninacontinuumfromordertochaos.Likemanyscientificconceptsofgreatprofundityandgeneralityitcanbeexplainedsimply,thoughnotthroughwordsbutthroughasimplemodel.18Imaginetwojars,aandb,withacontaining100ballsnumbered1–100,andbempty,andsomesystemforselectingarandomnumberbetween1and100—say,apointeronaspindlewhichcanbespunsothatitlandswithequallikelihoodonthenumberssetoutinacircle.Spinthepointerandwhenthepointrestsonanumber,findtheballwiththatnumberandtransferitfromwhicheverjaritisintotheotherone.Thenrepeatthisoperationasmanytimesasnecessary.Whathappens?Intuitively—andcorrectly—wesaythattheprocesswillsettledowntoabouthalftheballsineachjar.Why?Theanswertellsuswhatentropyisandhowitcanbemeasured.Thefirsttimethepointerselectsanumber,theprobabilitythattheballselectedwillgofromatobis1,thatis,itiscertain,becausealltheballsareina.Thesecondtime,thereisonechancein100thatthesingleballinbwillreturntoa,but99chancesoutof100,thatis,aprobabilityof.99,thatanotherballwillgofromatob.Thenexttimethereisonechancein50thatoneoftheballsinbwillreturntoa,but98chancesoutof100thatanotherballwillgofromatob.Clearly,astheprocessgoeson,thechancesofballsgoingbackfrombtoagraduallyincreaseandthechancesofballsgoingfromatobdiminishcorrespondingly. Whenabouthalftheballsareineachjar,theprobabilitiesareaboutequal,sothesystemtendstosettledowntosmallvariationsaboutthisstate.Toseewhythishappensletusdefineamicrostateofthesystemasaparticulardistributionofindividualballsinjarsandamacrostateasaparticularnumberofballsineachjar.Thereare,clearly,only200possiblemicrostatesofthesystemforthemacrostateinwhichoneballisinonejarandtherestareintheother,thatis,oneforeachofthehundredballsineachjar.Forthemacrostatewithtwoballsinonejarand98intheotherthereareallpossiblecombinationoftwoballsforeachjar,thatis,200×200.Forthemacrostatewiththreeinoneand97intheotherthereareallcombinationsofthreeballs.Inotherwords,thenumberofmicrostatesforthemacrostateismaximisedwhenthelargestpossiblenumberareintheleastfulljar—thatis,whenhalftheballsareineach—becausebeyondthatpointtherewillbefewerballsintheotherjarandeverythinghappensinreverse. Thisiswhythesystemtendstothehalfandhalfstate.Therearefarmoremicrostatescorrespondingtothehalfandhalf(ornearhalfandhalf)macrostatesthanforthoseinwhichafewballsareinonejarandmanyintheother.Inotherwordsallthesystemdoesistotendtoitsmostprobablestate.Thisisalsothedefinitionofthestateofmaximumentropy.Entropyismaximalinasystemwhenthesystemisinoneofthemacrostatesforwhichtherearethelargestnumberofmicrostates.Anexampleofthis,iswheretwogasesareeachrandomlydistributedinacontainer,withoutregionswhereoneorothergaspredominates.Therearefarmoremicrostateswithrandomdistributionthanmicrostateswithconcentrationsofoneorothergasinacertainregion.Ourmodelofjarsandballsisthenastatistical

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representationofthemixingoftwogasesinaclosedcompartment—orforthegradualheatdeathoftheuniverseastheuniversetendsfromitscurrentimprobablestatetoitsmostprobablestate,thatis,oneinwhichheatismoreorlessevenlydispersedthroughouttheuniverse.19

Inotherwords,entropyrelatesthenotionsoforderandchaosintoasingleconcept,butatthesametimegivesitamuchmorepreciseandlimitedreferencetotheworld.However,italsodoessomethingelseofnolessimportance.Itpermitstheconcepttobecapturedinaformalmathematicalexpressionaswellasthroughwords.Itisthroughthisformalexpressionthatthelinkbetweentheconceptandtheobservableworldismade.Thistwo-wayemancipationofconcepts,ontheonehandreorganisingconceptsintomoreprecisesystemsofinterdependenceandontheotherrelatingthemtotherealworldbyassociatingthemwithformalexpressionsistheessenceofwhattheoriesare. Theoriesarethereforemadeoftwothings:wordsandformalexpressions.Butbothrepresentconcepts.Atheoryisasystemofconceptswithonetypeofexpression,theverbal,whichlinkstheconceptsbackintoourunderstanding,necessarilywithsomeimprecision;andanother,mathematicalformwhichlinkstheconceptsforwardintophenomena,necessarilywithgreatexactness.Theoriesthuslinkourunderstandingtotheworld,connectedtoourunderstandingbylinguisticconceptsandconnectedtophenomenabyformalexpressionscorrespondingtotheconcepts. Thistwo-wayrelationusinglanguageandformalismtolinkconceptstoourunderstandingontheonehandandtotherealworldontheotheristheheartofwhattheoriesare.Wemayclarifyallthesecomplexrelationsinadiagram,seefigure2.2.Thisfigureshowsnotonlyhowtheoriesintervenebetweenlanguageandtheworld,butalsohowsciencerelatestophilosophy,whichoverlapswithscienceinpartofthisoverallscheme.Theoverallformofthediagramsetstheevolutionoflanguageandideasontheleftandthephenomenaofspace-timeontheright.Theoriesareinthecentre,definedasarelationbetweenasystemofconceptsandasystemofformalexpressionswhichlookstwoways:throughtheconceptsitlooks

Figure 2.2

Figure 2.2

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backfirstintothebroaderconceptualschemeswecallparadigms,thenintotheevolvingstructureoflanguageandideaswhicharebothaninevitablecontextandaninevitableconstraintontheorisation;andthroughtheformalismitlooksforwardtowardstheregularitiesinspace-timephenomenawhichtheoriesseektoaccountfor,andthenonwardsintothegeneralforegroundofspace-timephenomenawhichdonotformpartoftheregularitiesbutwhichmayatanystagearbitrarilyengagethetheorybyofferingphenomenawhichareinconsistentwiththe‘abstractmachine’forgeneratingphenomenaproposedbythetheory. Theearliestancestorsofwhatwewouldrecogniseas‘scientific’theories,suchasthoseofthePythagoreanswhoaresaidtohavefirstnotedtherelationbetweennumericalratiosandformsoccurringinnature,areprobablybestseenasparadigmsratherthanasfullyfledgedtheories,althoughintheirpreoccupationwiththerelationbetweenspace-timeregularitiesandformalexpressiontheycertainlyprefiguretheoriesinthemodernsense.20Pythagoreanism(asweearliernotedasinfluencingAlberti)isageneralisationofasingleconceptwhichgeneratedawayoflookingattheworldonthebasisofafewresults.Thisislegitimatelyaprecursortotheorybutnotinitselfwhatweoughttobecallingatheory.Howevertheattractionofsuchover-generalisationremains,asisseenintheprevalenceofvariantsonPythagoreanisminthemysticalsubstitutesfortheorywhichhavecontinuedtooccupythefringesofarchitecturalthoughtthroughoutthetwentiethcentury.21

Theoriesinthescientificsenseareonestepinfrombothparadigmsontheonesideandregularitiesontheotherinthattheyarecomposedofconceptswhicharefocusedandrelatedtoeachothertoformasystem,withpreciserelationsbetweeneachconceptandformaltechniquesorexpressionswhichareusedtocheckhowfartheregularitiesimpliedbythesystemofconceptsaredetectableinspacetimephenomena.Scientifictheoriesthusrequirethreerelationstobeparticularlystrong:therelationsamongconceptswhichformtheconceptualsystem;therelationsbetweenconceptsandformaltechniquesofmeasurement;andtherelationsbetweentheseformaltechniquesandspace-timephenomena.Intermsofthediagram,wemaysaythenthatscienceneedstobestrongfromthe‘conceptsystem’inthedirectionofphenomena. Scienceis,andmustexpecttobe,weakerintheotherdirection,thatis,inthepassagebackthroughparadigmsintothemoregeneralevolutionofideas.Thistendstobegroundoccupiedbyphilosophy.Philosophyoverlapswithscienceinbeinginterestedintheories,andrelatingthembacktobroaderfamiliesofconcepts22rightthroughtothosethatprevailineverydaylifeandsocialpractices,23butdoesnotnormallypreoccupyitselfwiththerigoroustestingoftheoriesagainstrealspace-timephenomena.Scienceandphilosophyarerivalsintherealmoftheory,butonlybecausetheirpreoccupationsreachoutfromtheoryincontrarydirectionswiththeeffectthatbetweenthemscienceandphilosophycoverthegroundthatneedstobeoccupiedbytheoreticalthought.However,itisbecausesciencemovesfromconceptstophenomenathatitstheorieseventuallycometohaveapuzzlingstatus,becausetheintuitivesensethatthey‘explain’thingscomes

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fromtherelationbetweentheconceptsthatmakeupthetheoryandthesensewehavefromeverydaylanguagethatourideas‘explain’theworld.Scientifictheoriesareinthissensepsychologicallystrongestwheretheyareinfactweakest,thatis,wheretheconceptsthatformthetheoryrelatebackintothebroaderconceptualsystemswhichinformeverydaylife.24

Towards an analytic theory of architectureGiventhesedefinitions,howthencantherebeananalytictheoryofarchitecture?first,letusbecompletelyclearaboutonething.Iftherearenoobjectiveregularitiesintherealworldofarchitecturalformandspace,linkingtheconfigurationalaspectsofformandspacewithbehaviouralandexperientialoutcomes,thentherearenogroundswhatsoeverforseekingtobuildananalytictheory.Theneedforandthepossibilityofananalytictheorybothstandorfallwiththeexistenceofsuch‘non-discursiveregularities’. Thismeansthattobuildananalytictheory,non-discursiveregularitiesmustfirstbeinvestigatedand,iftheyexist,broughttolight.Howcanthisbedone?Wemayfirstrecallthatanarchitecturaltheoryisanattempttorenderoneorotherofthenon-discursiveaspectsofarchitecturediscursive,bydescribingnon-discursivityinconcepts,wordsandnumbers.Wemaysaythatanarchitecturaltheoryseekstocreatea‘non-discursivetechnique’,thatis,atechniqueforhandlingthosemattersofpatternandconfigurationofformandspacethatwefindithardtotalkabout.Inresearchtermswecouldsaythatanarchitecturaltheory,atleastinthe‘narrow’aspectsthroughwhichitdescribesandprescribesdesigndecisions,isanattempttocontrolthearchitecturalvariable. Now,aswehaveseen,architecturaltheoriesinthepasthavetendedtobestronglynormativeandweaklyanalytic,becausethenon-discursivetechniquesproposedareonlyabletodescribecertainkindsofconfiguration.Thisiswhyinapplicationtheyarepartisanforthatkindofconfiguration.Forexample,ifanon-discursivetechniquedescribessystemsofproportionintermsofnumericalorgeometricratios,itisunlikelytobeabletodealwithconfigurationswhichlacksuchproportionality.Itwillonlydescribethosecaseswheretheseproportionshold.Inanyattempttoapplysuchpartisantechniquesgenerally,theyaremorelikelythereforetoactasdistortingmirrorsthanadiscoveryofnewregularities.Likewise,ifournon-discursivetechniqueisasystemofdiagramsexpressingspatialhierarchy,itisunlikelythatthosetechniquescanbeusefullyappliedtothevastrangeofcaseswheresuchclearhierarchisationisnotfound.Itfollowsagainthatsuchatechniquewillbeuselessforinvestigatingspatialpatternsingeneral. Wecansaythenthatanon-discursivetechniquewhichispartisanfor—usuallybecauseitisaproductofapreferencefor—oneparticularkindofnon-discursivity,willnotbeusableasananalytictool,andcannotthereforebeusedforthediscoveryofnon-discursiveregularities.Thisdeficiency,however,doespointusinthedirectionofwhatisneeded.Tobringtolightnon-discursiveregularities,weneednon-discursivetechniquesforthedescriptionofeitherspatialpatterns

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orformalpatterns(orconceivablyboth)whichareuncommittedtoanyparticulartypeofspatialorformalconfigurationorpattern,andwhicharecapableofgeneralapplicationtodescribeallpossibletypesofpattern.Forexample,itoughttobeabletohandlespatialpatternsorbuiltformpatternswhichlackgeometricregularityaswellasthosewhichhaveit.Unlessthiscanbedonewithrigourtherethereislittlehopethattheoreticalpropositionsinarchitecturecaneverbeanalyticinthesensethatwerequirethemtobe. Thenextchapterofthisbookwillintroducesuchasetofnon-discursivetechniquesfortheanalysisofconfiguration,firstdevelopedinspatialformas‘spacesyntax’,butnowbeingbroadenedtocoverotheraspectsofconfiguration.Thesetechniqueshavebeenusedoverseveralyearsfortwoprinciplepurposes,firsttodiscoverhowfaritwaspossibletobringtolightandsubjecttorigorouscomparativeanalysestheconfigurationalaspectsofspaceandforminbuildingthroughwhichcultureistransmitted,andsecond,throughthesecomparativestudiestodevelopacorpusofmaterialwhichwouldpermitthegradualdevelopmentofageneraltheoryofarchitecturalpossibility.Theremainderofthisbookisessentiallyanaccountoftheprogressthathassofarbeenmadeinthisproject. Aswewillsee,whatwediscoverthroughapplyingthesetechniquestotheanalysisofspatialandformalpatternsinarchitecture,wherevertheyarefoundandwhatevertheirembodimentineitherbuildingsorurbansystems,areinvariantsinpatternswhichlienotonthesurfaceofthingsbutwhichareburiedinthenatureofconfigurationsthemselves.Theseinvariantswecanthinkofasdeepstructuresorgenotypes.Eachculturalmanifestationthroughbuilding,whetherasabuilding‘type’foraparticularpurpose,oraparticulararchitecturalethosorimprintingofcultureonbuilding,doessothroughsuchgenotypes.Forexample,seenassystemsoforganisedspace,itturnsoutthattownsandcitieshavedeepstructureswhichvarywithculture.Likewise,seenasorganisedspaces,buildingsfordifferentfunctionpurposesalsohavedeepstructuresorgenotypes.Thesegenotypesare—orembody—culturalortypologicalinvariants.Thesearenotofcoursegenerallaws.Theyareatbestthe‘coveringlaws’ofcultures.Therearethegenotypicalinvariantsbywhicheachsocietyandeachfunctioninsocietyseekstoexpressitselfthrougharchitecture. However,aswebuildourcorpusofgenotypeswegraduallybegintoseethatthereisanotherlevelofinvariance:therearegenotypesofthegenotypes.Belowthelevelofculturalvariationinarchitecturethereexistinvariantsacrossculturesandtypes.These‘genotypesofgenotypes’arenotthecoveringlawsofculturesbuttheinvariantlawsthatbindhumankindingeneraltoitsartificialmaterialworld.Theyaretheabstractrawmaterialoutofwhichallconfigurationalpossibilityinspaceandforminthebuiltworldareconstructed.Itisatthislevelofinvariance—andonlyatthislevel—thatwecanbuildagenuineanalytictheory.ThesepossibilitieswillbedealtwithinChapters8and9.

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Architecture as art and as scienceIfthistheoreticalprojectiseventuallytosucceed—anditisbeyondthescopeofanysinglebooktodomorethantakeafewfalteringstepstowardssuchatheory—thenitisclearthatsuchatheorywouldliberateratherthanconstraindesign.Atroot,theneedforarchitecturaltheoryarisesfromtheneedtoformulateprinciplesfromtheexperienceofhavingbuilttoinformandguideusonhowwemightbuild.Thisdynamicbetweentheactualandpossibleistheessenceofarchitecturaltheorising.Architecturaltheoryarisesfromthefactthatarchitectscanneitherforgetthearchitecturaltradition,norrepeatit.Inarchitecture,theoryisnotsimplyameanstofixapictureoftheworldinacertainform.Itisalsothemeansbywhichformisdestabilisedandanewfutureisconceived.Architectureprogressesbyincorporatingitsreflectiononthepastintoanabstractframeofpossibility.Thisframeistheory.Withoutit,historicalthoughtissterile,andcanonlyleadtoimitationofthepast.Throughtheintermediaryoftheory,reflectiononthepastbecomespossiblefuture.Historyconstrains,buttheoryliberates,andthemoregeneralthetheory,thegreatertheliberation. Doesthismeanthenthatthelinebetweenarchitectureasscienceandarchitectureasartneedstoberedrawnclosertoscience?Idonotbelieveso.WecancallonthebeautifulideasofErnstCassirerontherelationbetweenartandscience.25‘Languageandscience’,hewrites,‘arethetwomainprocessesbywhichweascertainanddetermineourconceptsoftheexternalworld.Wemustclassifyoursenseperceptionsandbringthemundergeneralnotionsandgeneralrulesinordertogivethemanobjectivemeaning.Suchclassificationistheresultofapersistentefforttowardssimplification.Theworkofartinlikemannerimpliessuchanactofcondensationandconcentration…Butinthetwocasesthereisadifferenceofstress.Languageandscienceareabbreviationsofreality;artisanintensificationofreality.Languageandsciencedependononeandthesameprocessofabstraction;artmaybedescribedasacontinuousprocessofconcretion…artdoesnotadmitof…conceptualsimplificationanddeductivegeneralisation.Itdoesnotinquireintothequalitiesorcausesofthings;itgivestheintuitionoftheformofthings…Theartistisjustasmuchthediscovereroftheformsofnatureasthescientististhediscovereroffactsornaturallaws.’ Thoseofuswhobelievethatscienceisonthewholeagoodthing,acceptthatscienceisinonesenseanimpoverishment—thoughinothersanenhancement—ofourexperienceoftheworldinthatitcannotcopewiththedensityofsituationalexperience.Ithastobeso.Itisnotinthenatureofsciencetoseektoexplaintherichnessofparticularrealities,sincetheseare,aswholes,invariablysodiverseastobebeyondtheusefulgraspoftheoreticalsimplifications.Whatscienceisaboutisthedimensionsofstructureandorderthatunderliecomplexity.Heretheabstractsimplificationsofsciencecanbethemostpowerfulsourceofgreaterinsight.Everymomentofourexperienceisdenseand,assuch,unanalysableasacompleteexperience.Butthisdoesnotmeantosaythatsomeofitsconstituentdimensionsarenotanalysable,andthatdeeperinsightmaynotbegainedfromsuchanalysis.

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Thisdistinctioniscrucialtoourunderstandingofarchitecture.Thatarchitecturalrealitiesaredenseand,aswholes,unanalysabledoesnotmeantosaythattheroleofspatialconfiguration(forexample)inarchitecturalrealitiescannotbeanalysedandevengeneralised.Theideathatscienceistoberejectedbecauseitdoesnotgiveanaccountoftherichnessofexperienceisapersistentbutelementaryerror.Sciencegivesusquiteadifferentkindofexperienceofreality,onethatispartialandanalyticratherthanwholeandintuitive.Assuchitisinitselfthatitisvaluable.Itneedstobeacceptedorrejectedonitsownterms,notintermsofitsfailuretobelikelifeorlikeart. Itisinanycaseclearthatthedependenceofarchitectureontheories,covertorexplicit,doesnotdiminishitsparticipationinCassirer’sdefinitionofart.Thisistruebothinthesensethatarchitectureis,likeart,acontinuousprocessofconcretion,andalsointhesensethat,likeart,‘itsaspectsareinnumerable’.Buttherearealsodifferences.Thething‘whoseaspectsareinnumerable’isnotarepresentationbutareality,andaveryspecialkindofreality,onethroughwhichourformsofsocialbeingaretransformedandputatrisk.Thepervasiveinvolvementoftheoryinarchitecture,andthefactthatarchitecture’s‘continuousconcretion’involvesoursocialexistence,definesthepeculiarstatusandnatureof‘systematicintentofthearchitecturalkind’:architectureistheoreticalconcretion.Architectsareenjoinedbothtocreatethenew,sincethatisthenatureoftheirtask,butalsotorenderthetheoriesthattietheircreationtooursocialexistencebetterandclearer.Itisthisthatmakesarchitecturedistinctandunique.Itisasimpossibletoreducearchitecturetotheoryasitistoeliminatetheoryfromit. Architectureisthusbothartandsciencenotinthatithasbothtechnicalandaestheticaspectsbutinthatitrequiresboththeprocessesofabstractionbywhichweknowscienceandtheprocessesofconcretionbywhichweknowart.Thedifficultyandthegloryofarchitecturelieintherealisationofboth:inthecreationofatheoreticalrealmthroughbuilding,andinthecreationofanexperiencedreality‘whoseaspectsareinnumerable’.Thisisthedifficultyofarchitectureandthisiswhyweacclaimit. NotesRogerScruton,The Aesthetics of Architecture,Methuen,1977.Ibid.,p.4.L.B.Alberti,De Re Aedificatoria,1486;translationreferredto:Rykwertetal.(1988), MITPress,1991.O.Newman,Defensible Space;ArchitecturalPress,1972.Alberti,Chapter9.Newman,pp.3–9.HowthishappensasacognitiveprocessisthesubjectofChapter11:‘Thereasoningart’.Chapter11includesacasestudyinthedangersofbadtheory.Alberti,forexample,Book9.

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Scruton’sfundamentalerroristoconfusethesetwoaspects,andineffectto believethatthenarrowpropositionsofarchitecturaltheoryareintendedto beuniversalistic.SeeScruton,The Aesthetics of Architecture,p.4.Alberti,Book9.Newman,pp.3–9.F.Bacon,The New Organon (1620),BobbsMerrill,1960,AphorismsBook1,Aphorismcxv,p.105.T.Kuhn,The Structure of Scientific Revolutions,UniversityofChicagoPress,1962.TouseReneThom’sadmirableexpressionforwhatweobserve—seeStructural Stability and Morphogenesis,Benjamin,NewYork,1975—originallyinFrench,1972,asStabilite Structurelle et Morphogenese.Seeforexamplep.320.F.DeSaussure,(originallyinFrench1915)versionusedCourse in General Linguistics,McGrawHill,1966,translatedbyC.BallyandA.SechahayewithA.Riedlinger-seeforexamplepp.103–12.Theseexamplesofcoursedealwithlinearvariation,butthebasicargumentsalsoapplytonon-linearvariation.Thismodel,the‘Ehrenfestgame’,istakenfromM.KacandS.Ulam,Mathematics and Logic,PelicanBooks,1971,p.168.OriginallyPraeger,1968.ForafurtherdiscussionseeH.Reichenbach,The Direction of Time,UniversityofCaliforniaPress,1971,particularlyChapter4.SeeK.PopperK,Conjectures and Refutations,RoutledgeandKeganPaul,1963,Chapter5:‘Backtothepresocratics’.SeeforexampleM.GhykaM,Geometrical Composition and Design,Tiranti,London,1956.ForexampleintheworkofAlexanderKoyre,e.g.Metaphysics and Measurement, ChapmanandHall,1968(originallyinFrench)andNewtonian Studies,Chapman andHall,1965orGeorgesCanguilheme.g.La Connaissance de la Vie,Librairie PhilosophiqueJ.Vrin,Paris,1971.AspioneeredintheworkofMichelFoucault.Inthepast,thishasledtoaquiterapidpermeationbynewscientificconceptsoftheconceptualschemesofeverydaylife,bringingchangesinconsciousnesswhichmayseementirelyprogressive,asforexamplewiththetheoriesofNewtonorDarwin.Itmayindeedbethelossofthisillusorystrengththathasboughtaboutmuchofthealienationfromscienceinthelatetwentiethcentury.Assciencehasprogressedfartherintomicroandmacrophenomenaanddiscoveredpatternswhichareutterlyremotefromeverydayintuitiontheconceptsthatmakeupscientifictheoriesbecomesostrangethattheycannotevenbeformulatedsoastointerfaceeffectivelywiththeestablishedconceptualsystemoflinguisticnormality.Thishashappenedwithquantumtheory.Butwhathashappenedwithquantumtheoryconfirmsourmodelassetoutinthediagram:scienceintervenesthroughformalismsbetweenconceptsandphenomena.Itisnopartofitsfunctionoritsmoralitythattheseconceptsshould‘fallwithinthelightedcircleofintuition’(touseHermanWeyl’sadmirablephrase—seehisPhilosophy of Mathematics and Natural

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Science,Atheneum,NewYork,1963,p.66)andsobetranslatableintotheavailableconceptsofeverydaylifeandlanguage.Thereisnogreaterarrogancethanthatweshouldexpectthemtobe,exceptperhapsthebeliefthattheworlditselfinitsdeepestoperationsshouldconformitselftotheapparatusofourintuitions.ErnstCassirer,An Essay on Man,YaleUniversityPress,1944.Editionused:BantamMatrix,1970.Chapter9,‘Onart’,pp.152–88.

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Object artefacts and abstract artefactsOneofthedurableintellectualachievementsofthetwentiethcenturyhasbeentoinitiatethescientificstudyofhumanartefacts.Atfirstsight,suchastudymightseemparadoxical.Mostartefactsarephysicalobjectsthatadaptnaturallawstohumanpurposes.Tomakeanobjectforapurposesurelypresupposesthatweunderstandit.Buttwenty-fiveyearsago,HerbertSimon,inhisThe Sciences of the Artificial,showedthatthiswasfarfromthewholestory.1Eveniftheobjectswemakearenotpuzzlinginthemselves,theyaresowhenseeninthecontextoftheramifyingeffectsoftheirdispersionthroughoutoursocio-technicalecosystem.Hewasthinking,amongstotherthings,ofcomputers.Itwouldbeasenlightening,heargued,tohaveanaturalhistoryofcomputersinourincreasinglyartificialworld,asofanynaturalphenomenon.Empiricalsciencesofartefactswerethereforenotonlyapossibility,butanecessity. Butobjectartefactsareonlythelesseraspectofthepuzzleoftheartificial.Therealsoexistsaclassofartefactswhicharenolessdramaticintheirimpactonhumanlife,butwhicharealsopuzzlinginthemselvespreciselybecausetheyarenotobjects,but,onthecontrary,seemtotakeaprimarilyabstractform.Languageistheparadigmcase.Languageseemstoexistinanobjectivesense,sinceitliesoutsideindividualsandbelongstoacommunity.Butwecannotfindlanguageinanyregionofspace-time.Languageseemsreal,butitlackslocation.Itthusseemsbothrealandabstractatthesametime.Otherartefactswhichsharesomeoftheattributesoflanguage,suchascultures,socialinstitutions,andeven,somewouldargue,societyitself,allseemtoraisethiscentralpuzzleofbeing,itseems,‘abstractartefacts’. Itcannotofcoursebesaidthat‘abstractartefacts’arenotmanifestedinspace-time.Theyappearintheformoflinguisticacts,socialbehaviours,culturalpractices,andsoon.Butthesespace-timeappearancesarenottheartefactitself,onlyitsmomentaryandfragmentaryrealisations.Weapprehendspeech,asdeSaussurewouldsay,butnotlanguage.2Inthesameway,weseesocialbehaviours,butweneverseesocialinstitutions,andweseeculturaleventsbutweneverseecultures.Yetinallthesecases,thespace-timeeventsthatwewitnessseemtobegovernedintheirformbytheabstract,unrealisableartefactsthatwegiveanameto.Thematerialworldprovidesthemilieuwithinwhichtheabstractartefactisrealised,buttheserealisationsaredispersedandincomplete.Theexistenceoflanguages,socialinstitutionsandculturescanbeinferredfromspace-timeeventsbutnotseeninthem. Inspiteofthisstrangemodeofexistence,abstractartefactsseemtobethestuffofwhichsocietyismade.Wecannotconceivewhatasocietywouldbelikeifdeprivedofitslanguages,itscharacteristicsocialbehaviours,itsculturalformsanditsinstitutions.Itisnotclearthatanythingwouldbeleftwhichwecouldreasonablycall‘society’.Wemayconjecture,perhaps,thatabstractartefactsarethewaytheyarepreciselybecausetheirpurposeistogenerateandgoverndispersedevents,andthroughthistoconvertadispersedcollectivityofspeakers,behavioursorsocialactorsintosomesemblanceofasystem.Themultipositionalityofthespace-time

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realisationofabstractartefactsseemstobeanessentialpartofhowtheywork. However,tosaythisistorestatetheproblem,nottosolveit.Infact,inspiteoftheirapparentoddity,abstractartefactsposemanyofthepuzzleswhichscienceseekstoexplainfornaturalsystems.Forexample,theyseemablebothtoreproducethemselvesovertime,andalsotoundergomorphogenesis,thoughwhetherthisisbyaconstantorsuddenprocessisentirelyobscure.Ifabstractartefactshavesuchproperties,thenitwouldseemtofollowthattheymustthereforehavesomekindofinternalprinciplesorlawswhichgiverisetostabilityandchange,asdonaturalsystems.3Yetwhatevertheselawsarelike,theymustalsopassthroughthehumanmind,sinceitisonlythroughhumanmentalactivitythattheselfreproductionandmorphogenesisofthesesystemsoccurs.Itseemsinconceivable,therefore,thatthelawswhichgoverntheformsofabstractartefactsaresimilarto,orevencommensurablewith,thelawsthatgovernnaturalsystems.Atthesametime,suchlawsmustbepartofnature,sincetheycannotbeotherwise.Theymustreflectsomepotentialitieswithinnature. Inviewofalltheseapparentparadoxes,itwasthegreatmeritofLévi-Straussandotherpioneersofthestudyofabstractartefactstohavebothidentifiedthekeyinsightnecessaryfortheirstudy,andtohavepointedtoapossiblemethodologyforresearch.4Theinsightwastohaveseenthedependenceoftheconcreteontheabstractinsystemslikelanguageandculture,asclearlyasPlatooncenoteditforthenaturalworld.5Now,asthen,thisfundamentalinsightprovidesthestartingpointandinitialstanceforthesettingupofsciences.Themethodologywasthat,aswithnaturalsystems,wewouldexpecttofindcluestothenatureoftheseorganisinglawsbystudyingtheregularitiesthatabstractartefactsgenerateinspace-time,thatis,inspeech,behaviour,culturalpracticesandinstitutionalforms.Accordingly,themovementcalledstructuralismaimedtoassignabstractformalmodelswiththestructureandvarietymanifestedinthespace-timeoutputofsuchsystems-observedspeech,socialbehaviour,organisationaldynamicsandsoon-andthroughthistoaccountnotonlyfortheinternalsystemnessofsuchphenomena,butalsotoshowhowthehumanmindwascapableofholdingandcreativelytransformingsuchpowerfullystructuredinformation.Inthissense,structuralismwasnomoreorlessthanorthodoxsciencerewrittenforthestudyofabstractartefacts.6

Thisresearchstrategyreflectsthefundamentalfactthatabstractartefactsmanifestthemselvestousintwoways:throughthespace-timeeventstheygenerate;andthroughtheconfigurationalpatternswhichseemtosupportthemandwhichenableusbothtogenerateandinterpretthem.Thesetwowaysinwhichweexperienceabstractartefactsareboundtogetherbythefactthatinusingconfigurationalstructurestogeneratespace-timeeventswealsoprojecttheseconfigurationalstructuresintospace-timeandindoingsohelptotransmitthemintothefuture.Thisdoubletakebetweentheconsciousmanipulationofspace-timeeventsandthetransmissionofconfigurationalstructureisthedefiningcharacteristicoftheabstractartefactandthereasonitisabletobethestuffof

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society.Bydeployingobjectsandcreatingspace-timeeventswenecessarilytransmitstructures,andthroughthemtheabstractartefactswhichholdsocietytogetherasacommunicativesystem.Theobjectofstructuralismistocapturethedynamicsoftheseprocesses. Formalmethodswerethereforecriticaltostructuralism.However,asHeisenbergonceremarked:‘Ourscientificworkinphysicsconsistsinaskingquestionsaboutnatureinthelanguagethatwepossessandtryingtogetananswerfromexperimentbythemeansthatareatourdisposal.’7Thisissurelytrueofallscientificenquiry.Unfortunately,itseemstopointdirectlytothefailureofstructuralismtodeliveronitspromises.Examiningthespace-timeregularitiesofthephenomenageneratedbyabstractartefacts,wecannotfailtonoteoneoverwhelmingconsistency;thattheyseemtobegovernedbypatternlawsofsomekind.Thewordsthatmakeupspeechandthebehavioursthatseemsocialareallmanifestedinspace-timeassequencesordispositionsofapparentelementswhoseinterdependenciesseemtobemultiplex,andirreducibletosimplerulesofcombination.Forexample,tosay,asChomskydid,8thatsentences,whichappeartobesequencesofwords,cannotbegeneratedbyaleft-rightgrammar,isaconfigurationalproposition.Somedegreeofsyncreticco-presenceofmanyrelationsisinvolvedwhosenaturecannotbereducedtoanadditivelistofpairwiserelations.Thisistosaythatthelawsgoverningabstractartefactsseemtobeconfigurationalinsomethinglikethesensewehavedefineditinthepreviouschapters. Itisinthisrespectthatstructuralismseemstohavelackedmethodology.Itsformaltechniquesdidnottrytodrivestraighttotheproblemofconfiguration,butconfinedthemselvestothemoreelementaryaspectsoflogicandsettheory,thosebranchesofmathematics,thatis,thatsoughttoaxiomatisethethinkingprocessesofminds,ratherthantomodelrealworldcomplexity.9Consequently,justasthe‘languages’availableforPlatoinhistimewereinadequateforhisvisionofnature,10sothetoolspickedupinthemid-twentiethcenturybystructuralismweretoofrailforthevisionofartificialphenomenathathadinitiatedtheirsearch.Thephenomenathatstructuralistanalysissoughttoexplainwereinthemainconfigurational,buttheformaltechniquesthroughwhichinvestigatorssoughttodemonstratethisrarelywere.

Built environments as artefactsThepurposesofthisdigressionintoabstractartefactsaretwofold:first,todrawattentiontocertainpropertiesofbuiltenvironmentsthatmightotherwisebemissed;second,topointtocertainadvantagesofthebuiltenvironmentinprovidingaplatformfortakingontheproblemofconfigurationinanewway.First,however,wemustunderstandtheverypeculiarstatusofbuiltenvironmentsasartefacts. Builtenvironmentsappeartousascollectionsofobjectartefacts,thatis,ofbuildings,andassuchsubjecttoordinaryphysicallaws,anddeservingofSimonianenquiry.Butthatisnotallthattheyare.AswenotedinChapter1,intermsofspatialandformalorganisation,builtenvironmentsarealsoconfigurationalentities,whoseformsarenotgivenbynaturallaws.Ifwewishtoconsiderbuiltenvironmentsasorganisedsystems,thentheirprimarynatureisconfigurational,

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principallybecauseitisthroughspatialconfigurationthatthesocialpurposesforwhichthebuiltenvironmentiscreatedareexpressed.Thecollectionsofobjectartefactsinspace-timethatwesee,arethenameansthroughwhichsociallymeaningfulconfigurationalentitiesarerealised.Inotherwords,inspiteofappearances,builtenvironmentspossessakeypropertyofabstractartefacts.Itsobjectsaremoredurablethan,say,thespokenwordsofalanguage,ortherule-influencedindividualbehavioursthatmakeupasocialevent,buttheyareofthesamekind.Theyarespace-timemanifestationsofconfigurationalideaswhichalsohaveanabstractform.Thebuiltenvironmentisonlythemostdurableofthespace-timemanifestationsofthehumanpredilectionforconfiguration.Thishasanepistemologicalconsequence.Weshouldnotexpectthebuiltenvironmentmerelytobethematerialbackdroptoindividualandsocialbehaviour,asitisoftentakentobe.Itisasocialbehaviour,justastheuseoflanguageisasocialbehaviourandnotjustameanstosocialbehaviour.Wecannotthereforeregardthebuiltenvironmentasmerelyaninertthing,andseektounderstanditwithoutunderstandingthe‘sociallogic’ofitsgeneration. Butjustaswecannottreatabuiltenvironmentasathing,wecannomoretreatitasthoughitwerenomorethanalanguage.Thebuiltenvironmentis,apartfromsocietyitself,thelargestandmostcomplexartefactthathumanbeingsmake.Itscomplexityanditsscaleemergetogether,because,likesociety,abuiltenvironmentisnotsomuchathingasaprocessofspatio-temporalaggregationsubjecttocontinualchangeandcarriedoutbyinnumerableagenciesoveralongperiodoftime.Althoughtheseprocessesofaggregationmaybelocallycharacterisedbythesamekindofautonomicrulefollowingaswefindforindividualactsofbuilding,thereareothernolessfundamentalattributesthatmakethebuiltenvironmentaspecialcase. Themostobvious,andthemostimportant,isthatthespatio-temporaloutputsofbuiltenvironmentprocessesarenotephemerallikethoseoflanguageorsocialbehaviour.Theyarelong-lasting,andtheyaggregatebyoccupyingaparticularregionofspaceforalongtime.Thismeansthatoverandabovethinkingofbuiltenvironmentsastheproductsofabstractrulesystems,wemustalsorecognisethattheyhaveanaggregativedynamicwhichistosomeextentindependentoftheserulesystems,although,aswewillsee,itisrarelyquiteoutoftheircontrol.Theseaggregativeprocesseshavequitedistinctiveproperties.Spatio-temporaladditionstoasystemusuallyoccurlocally,butthedynamicsofthesystemtendtoworkatthemoreglobalaggregativelevels.11Complexityarisesinpartfromtherecursiveapplication,inincreasinglycomplexaggregations,ofruleswhichmayinitiallybesimple,butthemselvesmaybetransformedbytheevolvingcontextinwhichtheyareapplied.Alocallydrivenaggregativeprocessoftenproducesaglobalstatewhichisnotunderstood12butwhichneedstobeunderstoodinorderforthelocallydrivenprocesstobeeffective.Thisistheessentialnatureofthelargeaggregatesofbuildingswhichformmostbuiltenvironments.

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Thiscomplex,processualaetiologyisthemainreasonwhybuiltenvironmentshaveprovedsoresistanttoorthodoxattemptstomodeltheirstructuremathematically.Buildingsandcitiesarenotcrystallineobjects,unfoldingundertheinfluenceonlyoflawsofgrowth.Theelementaryspatialgestuariesofhumankindanditsculturesmayconstructlocalelementalconfigurations,butthesethenoperateaslocalorderingswithingrowthprocessesandactasconstraintsonthe‘natural’evolutionofglobalpatterns.Architecturaland,evenmoreso,urbanformsoccurattheinterfacebetweennaturalprocessesandhumaninterventions.Humanactionsrestrictandstructurethenaturalgrowthprocesses,sothattheycannotbeunderstoodwithoutinsightintobothindividually,andintotherelationsbetweenthetwo.Theinterventionofthemindintheevolvingcomplexitymustbeunderstood,butsomustitslimitations. Thebuiltenvironmentmaythenbethemostobviousofobjects,andtheonethatformsourfamiliarmilieu,butatthesametimeitsinnerlogicandstructureisasinaccessibletousasanythinginnature.However,ithasonegreatadvantageasanobjectofstudy.Itsveryscale,manifestnessandslowrateofchangeofferitupastheparadigmcaseforconfigurationalinvestigation.Theessenceoftheproblemistocapturethelocal-to-globaldynamicsofarchitecturalandurbansystems,thatis,toshowhowtheelementarygenerators,whichexpressthehumanabilitytocogniseandstructureanimmediatespatialreality,unfoldintotheramifiedcomplexitiesoflarge-scalesystems. Inthis,methodologicaldifficultiesarecentral.Theaimofamethodmustbetocapturethelocalorelementalordering,theemergenceofglobalcomplexity,andhowbothrelatetothehumanmind.Foranyofthese,themanifestproblemofconfigurationmustbetackledheadon,andmustbeapproachedfirstandforemostasanempiricalproblem.Ifthespace-timeproductsofabstractartefactsareheldtogetherbyconfiguration,thenconfigurationcanbefoundbyexaminingthem.Thecorpusofconfigurationsthatcanbebuiltthroughthestudyofrealcasesmustbesomeindicatorofwherewemightseekfortheconfigurationalinvariantsofbuiltenvironmentprocesses.Forthistask,theveryscale,relativestabilityandavailabilityofbuiltenvironmentsmakethemtheidealvehicleforanenquiry.Allweneedaretechniquesthatpermittheextractionofconfigurationfromitsspace-timeembodiments-thatis,non-discursivetechnique.

Simplicity as a means to complexityTheconfigurationalformalismsproposedhereasthebasisfornon-discursivetechniqueareinsomewaysmuchsimplerthanothersproposedforthesimilarclassesofphenomenaoverthelasttwentyyears.13Yettheyhaveprovedthemostpowerfulindetectingformalandfunctionalregularitiesinrealsystems.Thereareprobablythreereasonsforthis.First,thequantitativemethodsproposedaredirectedstraightattheproblemofconfiguration,thatis,theproblemofunderstandingthesimultaneouseffectsofawholecomplexofentitiesoneachotherthroughtheirpatternofrelationships.Lackofattentiontothiscentralproblemistheprime

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reasonwhypastformalismoftenseemedtooffermathematicalsophisticationoutofproportiontotheempiricalresultsachieved.Withconfigurationalanalysisitistheotherwayround.Exceedinglysimplequantitativetechniqueshaveledtoadisproportionatesuccessinfindingsignificantformalandform-functionalregularities.Configuration,asdefinedbelow,seemstobeatleastoneofthethingsthatarchitecturalandurbanpatternsareabout. Second,inconfigurationalanalysis,asmuchtheoreticalattentionhasbeengiventotherepresentationofthespatialorformalsystemthatistobeanalysedastothemethodofquantification.Aswewillsee,thisquitenormallygivesrisetoawholefamilyofrepresentationsofthesamespatialsystem,eachonerelevanttosomeaspectofitsfunctioning.Itisalsonormaltocombinerepresentations,literallybylayingonerepresentationontopoftheotherandtreatingtheresultingconnectionsasrealconnectionsinthesystem.Throughthis,wefindthatpairsoreventriplesofrepresentationstakentogetheryieldformallyorfunctionallyinformativeresults.Intermsofresearchstrategy,thismeanstryingtorepresentspaceintermsofthetypeoffunctioninwhichweareinterested.Forexample,simplelinestructuresdrawnthroughspaces,temporarilydiscountingotherproperties,haveprovedsufficient(aswewillseeinthenextchapter)toaccountformanyaspectsofmovementwithinbuildingsandurbanareas. Third,andsynthesisingtheprevioustwo,muchattentionhasbeengiventothegraphicrepresentationoftheresultsofmathematicalanalysis,sothattheformalstructuresidentifiedinspatialorformalcomplexescanbeintuitivelyseenandunderstoodwithouttheintermediaryofmathematicalformalism.Thismeansthatmuchcanbeunderstoodbythosewhosetemperamentsleadthemtopreferagraphicalratherthanamathematicalunderstanding.Byrepresentingmathematicalresultsgraphically,alevelofcommunicationispossiblethatpermitslargenumbersofpeopletobeinterestedandknowledgeablewhowouldotherwisefallatthefirstfenceofmathematicalanalysis.Inparalleltothisgraphicalrepresentationofresults,usuallydrawnbycomputer,thereisaparallelemphasisintheinitialstagesofinvestigationtothedrawingofspatialorformalideasbyinvestigatorsandbystudentsasaconstantadjunctto,andcheckon,formalanalysis. Noapologyisthenofferedforthesimplicityofsomeofthenotionspresentedhere.Othershavediscussedsomeofthesepropertiesbuthavenotbeenmindedtoexploretheirfullempiricalortheoreticalrelevance,orhowtheymightbefittedintotheoverallform-functionpicture.Perhapsonereasonforresearcherstomisskeyrelationswhile‘goingclose’,hasbeenwhatwewouldseeasanoverarchingandinsomewaysprematureconcernwithdesignattheexpenseoftheempiricalinvestigationofbuildings.The‘spacesyntax’researchatUCLhasbeendrivenbyaremarkofLionelMarch’s:‘Theonlythingyoucanapplyisagoodtheory.’14Anotherpossiblereasonwhyformalexplorationhasmissedtheoreticalinsighthasbeenthefrequentlackofacloseenoughrelationbetweenmathematicalandempiricalaspectsoftheproblemsposedbyrealbuildingsandcities.Incontrast,thetechniquesofspatialrepresentationandquantificationproposedhere

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areessentiallysurvivorsofanintensiveprogrammeofempiricalinvestigationspreadoverthebestpartoftwodecadesinwhichformalquestionshavebeenexploredinparalleltotheempiricalpuzzlesposedbyarchitecturalandurbanrealities.WehavealreadydiscussedtheideaofconfigurationatsomelengthinChapter1.Nowweneedtodefineitformally,andtoshowsomeofitspowertosaysimplethingsaboutspaceandform.Itshouldbenotedthatwhatfollowsisnotamethodologicalcookbook,butatheoreticalexplorationoftheideaofconfiguration.Atthisstage,theexamplesgivenareillustrationsofideas,notworkedexamplesofanalysis.Casestudieswillcomeinensuingchapters.Therelationofthischaptertothosethatfollowisthatofaquarry,whichfuturechaptersreturntotopickuponeofthepossibilitiessetouthere,andrefineitforthepurposesofthatchapter.Thischaptershowsthebasesandconnectionofthewholefamilyofmethods.

Defining configurationLetusbeginbydefiningexactlywhatwemeanbyconfiguration,usinganexampledirectlyanalogoustofigure1.3inChapter1,buttakingaslightlydifferentform.WemayrecallthatinChapter1,asimplerelationwasdefinedasarelation-say,adjacencyorpermeability-betweenanypairofelementsinacomplex.Aconfigurationalrelationwasthendefinedasarelationinsofarasitisaffected

bythesimultaneousco-presenceofatleastathirdelement,andpossiblyallotherelements,inacomplex.Infigure3.1i,forexample,aandbaretwocubesstandingonasurface.In3.1ii,thecubesarebroughttogetherfullfacewisetomakeaconjointobject.Therelationofaandbissymmetricalinthatabeing

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the(contiguous)neighbourofbimpliesthatbisthe(contiguous)neighbourofa.Onecouldequallysay,thoughwithlessobviousness,thatin3.1iaandbwerenon-contiguousneighbours,andwerethereforesymmetricalinthissense.Eitherway,therelationofthetworemainssymmetrical,andinfactthisisimplicitinthe‘neighbour’relation.In3.1iii,theconjointobjectformedbyaandbin3.1iiistakenandrestedononeofitsends,withoutchangingtherelationofatob.Butbnowappearstobe‘above’a,andtherelationof‘beingabove’,unlikethatof‘beingtheneighbourof’isnotsymmetricalbutasymmetrical:bbeingaboveaimpliesthataisnotaboveb. Howhasthishappened?Thetemptationistosaythatrelationslike‘above’and‘below’dependonanexogenousframeofreference,like‘east’and‘west’,or‘up’and‘down’.Infact,whathashappenedcanbesaidmoresimply,asshownin3.1iiii.Thesurfaceonwhichthecubesstand-say,thesurfaceoftheearth-wasnotreferredtoindescribingtherelationbetweenaandbin3.1iandii.Itshouldhavebeen,hadwewantedtoforeseetheeffectsofstandingtheconjointobjectonitsend.Letuscallitc.In3.1ii,therelationofbothaandb,takenseparately,tothethirdobject,c,isalsosymmetrical,asistheirrelationtoeachother.So,incidentally,istherelationoftheconjointobjectformedbyaandbtothethirdobject.Theseareallsimplerelations.Butwecanalsosaysomethingmorecomplex:thatin3.1ii,a andbaresymmetricalwithrespecttoc,aswellaswithrespecttoeachother.Thisisaconfigurationalstatement,sinceitdescribesasimplespatialrelationintermsofatleastathird.Whathappensin3.1iiiisnowclear.Althoughaandbremainsymmetricalwithrespecttoeachother,theyarenolongersymmetricalwithrespecttoc.Onthecontrary,theyareasymmetricalwithrespecttoc.Thedifferencebetween3.1iiandiiiisthenaconfigurationaldifference.Therelationofaandbtoeachotherischangedifweaddthe‘withrespectto’clausewhichembedsthetwocubesinalargercomplexwhichincludesc. Thesituationisclarifiedbythejustifiedgraphs(orj-graphs:graphsinwhichnodesarealignedabovearootaccordingtotheir‘depth’fromtheroot—see

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Chapter1)oftheconfigurationsshownin3.1v,viandvii.Ineach,thebottomnodeistheearth,andisinscribedwithacrosstoindicatethatitistheroot.In3.1v,aandbareeachindependentlyconnectedasneighbourstotheearth.In3.1vi,therelationofneighbourbetweenaandbisadded.In3.1vii,therelationbetweenbandc,theearth,isbrokencreatinga‘twodeep’relationbetweenbandc.Onemaynotethatthisset-upalreadyexistsin3.1vbetweenthetwonon-contiguouscubeswithrespecttotheearth.Inthissense,3.1viirecreatesagraphwhichalreadyexistsinv.Thisisalsoshowninthenumbersattachedtoeachofthenodesofthegraph,whichindicatethesumof‘depth’fromthatnodetotheothernodesinthesystem.Thetotaldepthof3.1vandviiistherefore8,whilethatofviis6.Wemightsay,then,thatthedistributionsoftotaldepthsandtheiroverallsumdescribeatleastsomeconfigurationalcharacteristicsofthesecompositeobjects. Nowletusexplorethissimpletechniquealittlefurtherbyexaminingfigure3.2,aseriesofsimplefigurescomposedofsquarecellsjoinedtogetherthroughtheirfaces(butnottheircorners)with‘totaldepths’foreachcelltoallothersinscribedineachcell,andthesumsofthesetotaldepthsforeachfigurebelowthefigure.Thefiguresareallcomposedofsevenidenticallyrelatedcells,plusaneighthwhichisjoinedtotheoriginalblockofseveninitiallyatthetopendintheleftmostfigure,thenprogressivelymorecentrallyfromlefttoright.Therearetwoprincipaleffectsfromchangingthepositionofthissingleelement.First,thetotaldepthvaluesandtheirdistributionsallchange.Second,thesumsoftotaldepthforeachfigurechange,reducingfromlefttorightastheeighthelementmovestoamorecentrallocation.Theeffects,however,arequitecomplex.Thisisnotofcoursesurprising,butitillustratestwokeyprinciplesofconfigurationalanalysis.First,changingoneelementinaconfigurationcanchangetheconfigurationalpropertiesofmanyothers,andperhapsallothersinacomplex.Second,theoverallcharacteristicsofacomplexcanbechangedbychangingasingleelement,thatis,changesdonotsomehowcancelouttheirrelationstodifferentelementsandleavetheoverallpropertiesinvariant.Onthecontrary,virtuallyanychangetoelementsthatisnotsimplyasymmetricalchange,willaltertheoverallpropertiesoftheconfiguration.Wewillseeinduecoursethatconfigurationalchangesofthiskind,evensmallones,playavitalroleintheformandfunctioningofbuildingsandbuiltenvironments.

Shapes as configurationsAnotherwayofsayingthis,isthatdifferentarrangementsofthesamenumbersofelementswillhavedifferentconfigurationalproperties.Forexample,figure3.3isasetofrearrangementsofthesameeightsquarecellsthatweconsideredinfigure3.2,againwith‘totaldepths’inscribedineachcell,butalsowithanumberofothersimpleproperties,includingthetotaldepth,setoutclosetothefigure:tdistotaldepth,dbaristheaverageforeachcell,sdisthestandarddeviation, dfisthe‘differencefactor’indicatingthedegreeofdifferencebetweentheminimum,maximumandmeandepthineachcomplex(Hillieretal.1987a),andt/tisthenumberofdifferentdepthvaluesoverthenumberofcells.

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Intreatingshapesasconfigurationsinthissense,thatis,ascompositesmadeupofstandardisedelements,weareineffecttreatingashapeasagraph,thatis,asapurelyrelationalcomplexofsomekindinwhichwetemporarilyignoreotherattributesoftheelementsandtheirrelations.Itisclearthatsuchdescriptionsareverymuchlessthanafulldescriptionoftheshape.Formanyshapeproperties,andformanyofthepurposesforwhichwemightseektounderstandshape,aconfigurationaldescriptionofthiskindwouldbequiteinadequateorinappropriate.Butthereisonesenseinwhichtheconfigurationalstructureoftheshapeisauniquelypowerfulproperty,andgivesinsightsintopropertiesofspatialandformalshapeswhichareincreasinglymanifestingthemselvesasthemostfundamental,especiallyinstudiesofarchitecturalandurbanobjects.Thispropertyisthatgraphsofshapesandspatiallayoutsaresignificantlydifferentwhenseenfromdifferentpointsofviewwithinthegraph.Thiscanbedemonstratedvisuallybyusingthej-graph.Bydrawingj-graphsfromallnodesinashape,then,wecanpicturesomequitedeeppropertiesofshapes. Forexample,ahighlyinterestingpropertyofshapesisthenumberofdifferentj-graphstheyhave,andhowstrongthedifferencesare.Forexample,figure3.4showsalldifferentj-graphsforaselectionoftheshapesinfigure3.3.Thenumbervariesfrom3to6.Thereasonforthisisthatifwefindthatthej-graphsfromtwonodesareidentical,thenthismeansthatfromthesetwopointsofview,theshapehasastructuralidentity,whichweintuitivelycallsymmetry.Thisiswhyintheshapesinfigure3.4,thesmallerthenumberofdifferentj-graphsasaproportionofthetotalnumberofj-graphs(thatis,thenumberofelementsinthegraph)thenthemoretheshapesappearregularbecausetherearemoresymmetriesintheshape.Thisistheratiogivenast/t(typesovertotal)infigure3.3.Thisaspectofthestructureofthegraphthusseemstoreflectoursensethatshapescanberegularorirregulartodifferentdegrees. Thisanalogycanbemademoreprecise.Infact,thesymmetrypropertiesofshapescanbeexactlytranslatedasconfigurationalproperties.Mathematically,symmetryisdefinedintermsofinvarianceundertransformation.IntheirbookFearful Symmetry,IanStewartandMartinGolubitskyillustratesthiswithsingularclarity.‘Toamathematician’theyargue,‘anobjectpossessessymmetryifitretainsitsformaftersometransformation.’15Theyillustratethiswithadiagramshowingthesymmetriesofthesquare,asinfigure3.5,inwhich‘atypicalpointintheplaneismappedintoeightdifferentimagesbythe…eightrigidmotionsthatleavethesquareinvariant’.Thinkingofsymmetriesintermsofpointsinashapeisusefulconfigurationally,sincewemayimmediatelyaskwhatwillbethecharacteristicsofj-graphsdrawnfromeachofthepoints.Itisimmediatelyclearthatthej-graphsdrawnfromeachofStewart’spointswillbeidentical,andthatthiswouldalsobethecaseforanyothercomparablesetofpointswhichStewarthadselected.Itisalsoclearthatonceapointhasbeenselectedtherewillonlybesevenotherpointsintheshapefromwhichj-graphswillbeidentical.Theprincipleisinfactverysimple:inashape,everysymmetrywillcreateexactlyonepointfromwhichthej-graphis

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td=168d=21sd=4.58i=.667df=.937t/t=.5

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isomorphic.Ineffect,j-graphisomorphismisatestforsymmetry.Thej-graphallowsustolookatsymmetryasaninternalproperty,incontrasttothemoreexternalviewpresupposedbythe‘invarianceundermotion’definition.Inasense,theinvarianceundermotionexistsbecausetherearedifferentpointswithintheshapefromwhichtheshapeisidentical.Wemightsaythatinashapewithsymmetrytherearepointswithintheshapewithidentityofpositionalinformationinrelationtotheobjectasawhole,andthisisdemonstratedbyj-graphisomorphism.

Universal distancesThedistributionsofdepthsthatareshownthroughthej-graphs,andwhichunderliebotharchitecturalandgeometricaleffects-areinfactthemostfundamentalideainquantifyingtheconfigurationpropertiesofspatialorformalcomplexes.Theideafirstmadeitsappearanceintheliteratureofappliedgraphtheoryin1959whenHararyappliedittosociometryunderthenameof‘status’.‘Status’isdefinedbyBuckleyandHarary16thus:‘Thestatuss(v)ofanodevin

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G(agraph)isthesumofdistancesfromvtoeachothernodeinG’,distancemeaningthefewestnumberofnodesinterveningbetweenonenodeandanother.Theproblemwithstatusdefinedinthiswayas‘totaldepth’isthatthevaluewillbeverysubstantiallyaffectedbythenumberofnodesinthegraph.Accordingly,asdiscussedinChapter1,anormalisationformulawasproposedinThe Social Logic of Space17whicheliminatesthebiasduetothenumberofnodesinthegraph.Withthisnormalisation,numericalvaluescanbeassignedexpressing‘totaldepth’independentlyofthesizeofthesystem.ThisnormalisationformulawasdiscussedandclarifiedbySteadmaninArchitectural Morphology18Wewillcallthesenormalisedvaluesi-values,toexpresstheideaofthedegreeof‘integration’ofanelementinacomplex,whichwebelievethesevaluesexpress. Theneedforthenormalisationformulaandtheintuitionoftheformitmighttakeinfactcamefromusingthejustifiedrepresentationofthegraph,orj-graph.Simplyasaconsistentlyusedrepresentation,thej-graphmakesthestructureofgraphs,andmoreimportantlythedifferencesintheirstructures,extraordinarilyclear.However,byrepresentingtheminastandardformat,italsomakescleartheneedforcomparativenumericalanalysisandhowitmightbedone.Forexample,itisimmediatelyclearwhatgraphwillbemaximallyandwhatminimallydeep.Itisasimplematterfromtheretofindthenormalisation.Thefactthatnoonefoundthisusefulexpressionbefore,whenitopensupwholenewvistasfortheempiricalanalysisandcomparisonofforms,ispresumablybecausenoonesaweitheritsnecessityorpossibility. However,althoughthei-valueformulaallowsthetheoreticaleliminationoftheeffectsofthesizeofthesystem,itdoesnotdealwiththefactthat,empirically,architecturalandurbanspatialcomplexesuseonlyasmallproportionofthosetheoreticallypossible,andthisproportionshrinksasthesizeofthesystemgrows.TheseeffectsarediscussedinfullinChapter9,andinfactbecomethebasisofafulltheoryofurbanspatialform.Asecond,empiricalnormalisationformulawasthereforeintroducedtocopewiththisempiricalfact.19Thesecondformulaisanempiricalapproximationwithsometheoreticaljustification(thatitapproximatesanormaldistributionofdepthvaluesfromanynodeinagraph)andassuchitlackselegance.Howeveritsrobustnesshasbeendemonstratedinlargenumbersofempiricalstudiesovertheyears,duringwhichtimenoneedhasarisentocallitintoquestion.20Nodoubt,asstudiesadvance,itwillbepossibletoeliminatethissecondnormalisationformulaandreplaceitwithanexpressionwithmoretheoreticalelegance.Inthemeantime,‘integration’willrefertotheoutcomesofbothnormalisations,unless‘total’depth’(status,withnonormalisation)or‘i-value’(statuswiththefirst,theoreticalnormalisationforsize)arespecified.Allthesetermsaredifferentwaysofreferringtothesamequantity. Whyhasthisquantityprovedsofundamentalintheempiricalstudyofspatialandformalconfigurations?Itispossiblethatitssimplicityconcealsaveryfundamentaltheoreticalproperty:thatitisessentiallyageneralisationoftheideaofdistance.Ourcommonconceptofdistanceisthatofaspecificnumberofmetric

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unitsbetweenonepointandanotherwithinsomesystemofspatialreference.Wecancallthisaspecificdistance.Totaldepthsumsallspecificdistancesfromanodetoallothers.Wemaythereforethinkofitasa‘universaldistance’fromthatnode.Ifspecificdistanceisaboutthemetricpropertiesofshapesandcomplexes,universaldistancesseemtobethekeytoconfigurationalproperties.Universaldistanceseemstobeageneralisationoftheideaofdepththatpermitsconfigurationtobecomethecentralfocusofanalysis. Itmaybeobjectedthatsuchaconceptofuniversaldistancehasonlybeenmadepossiblethroughanunacceptablesimplificationoftheideaofashapetothatofagraph,ratherthananinfinitesetofpoints.Thisisadifficulty,butitseemsthatitmightnotbeasgreatasitmightatfirstappear.Ifweconsiderasquareshapemadeupofsquarecells,andthereforerepresentableasagraph,asinfigure3.6,andmeasuredistancesfromandtothecentroidofeachcell,itisclearthatgraphdistanceswillapproximatemetricdistancesonlywhentheyareorthogonallyrelated.Onthediagonal,metricdistanceswillbeeithershorterorlongerthangraphdistances,dependingonwhetherornotweconnectthegraphdiagonallyacrosscellcorners,oronlyallowjoinsthroughthefaces.Ifcornerlinksarenotallowed,thengraphdistanceswillben+m(or‘Manhattan’distances,byanalogywiththeManhattangrid)wheremisthehorizontaldistanceandntheverticaldistance,whilethemetric(or‘asthecrowflies’)distancewillbethesquarerootofmsquared+nsquared.Thiswillbemaximalbetweenoppositetopandbottomcorners.Ifdiagonallinkstoadjacentnodesareallowed,thenthedistancebetweenoppositetopandbottomcornerswillbemorn,whicheveristhegreater,whichequallymisrepresentsthemetricdistance.Ifweplotgraphdistanceagainstmetricspecificdistancesinsuchasystemwewillfindthatnotonlyarethedifferencessubstantial,butalsothattheyvaryindifferentpartsofthesystem.Inotherwords,graphandmetricspecificdistancesarenotlinearlyrelated,sowecannotuseoneasaproxyfortheother.Figure3.7aisaplotofmetricspecificdistanceagainstgraph(Manhattan)specificdistancefor1000randomlyselectedpairofpointsina100×100squarecellarrangementofthetypeshowninthepreviousfigure,andfigure3.7bplotsthedifferencebetweenmetricandgraphspecificdistanceontheverticalaxisforincreasinggraphdistanceonthehorizontalaxis. However,ifwesubstituteuniversalforspecificdistances,andcarryoutthesameanalysis,thisproblemissignificantlydiminished.Figure3.7cshowsgraph(Manhattan)againstmetricuniversaldistancesforallnodesina32×32(i.e.1024cells)squarecellcomplex,andfigure3.7dplotsgraphdistanceagainstthedifferencebetweenmetricandgraphdistances.Althoughthevaluesarestillexactlyasdifferentoverall,theyarenowmoreorlesslinearlyrelated,sothatitismuchmorereasonabletouseoneasaproxyfortheother.Thisfortunatefactpermitsafarmoreflexibleuseofgraphbasedmeasureofconfigurationthanwouldotherwisebethecase.Aswewillsee,suchmattersasshapeandscale,areaanddistancecanallbebrought,asapproximationsatleast,withinthescopeoftheconfigurationalmethod.Allwillbeinsomesensetheoutcomeofseeinga

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complexofrelatedelementsasasetofj-graphs.Thej-graphineffectredefinestheelementofacomplexintermsofitsrelationtoallotherelementsinthecomplex.Summingthepropertiesofj-graphstoexpresspropertiesofthewholecomplexmeanssummingthedifferentpointsofviewfromwhichthecomplexcanbeseeninternally.Theeventualjustificationofthisformalismisthatarchitecturalandurbansystemsareexactlythiskindofcomplex.Theyareglobalsystemswhosestructure,functioningandgrowthdynamicsaremanufacturedoutoftheinnumerabledifferentpointsofviewfromwhichtheycanbeseen.

Regular shapes as configurationsNowletustaketheideaalittlefurther,andclosertoeverydayexperience.Itisclearthatanyshapecanberepresentedasaregularlyconstructedmeshofcellularelements,ortessellation,providedwecanscalethemeshasfinelyasweneed.Thiscanthenbetreatedasagraph,andthusexpressedasapatternofuniversalgraphdistances.Bydescribingsimpleeverydayshapesinthisway,itturnsoutthatwecancaptureimportantaspectsofhowtheyfitintoeverydaylivingpatterns. Suppose,forexample,wecreatean(approximately)circulartessellationofarbitrarilysmallsquarecells,asinfigure3.8a.Wemaycalculatethemeandepthofeachcellfromallothers,andexpresstheresultsinadistributionofdotdensitiesforthesquareelementsinwhichthehigherdensities,ordarkercolours,standforgreaterintegration-thatis,lessdepth—gradedthroughtolightestcoloursfortheleast

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integration,orgreatestdepth.Itisclearthatthecentrehasthehighestintegration,andthatintegrationreducesevenlyinconcentricringsaroundthecentre.Inaperfectcircle,alledgelocationswillhaveanidenticaldegreeofintegration.Ifwethenconsiderthesquaretessellationinfigure3.8cwefindthatthepatternofintegrationnotonlyrunsfromcentretoedge,butalsofromthecentreoftheedgetothecorners.Thesquareformisthusmorecomplexthanthecircularforminasimple,butcriticalway.Wemaysaythatinthesquareform,the‘centralintegration’effectoccurstwice:onceintheglobalstructurefromcentretoedge,andoncemorelocallyoneachsideoftheform.Wecanalsoeasilycalculatethatthesquareformislessintegrated-thatis,hasgreateraverageuniversaldistancespertessellationelement-thanthecircularform. Asweelongatethesquareintoarectangle,asinfigure3.8d,theoverallformisevenlessintegrated,andthepropertiesfirstfoundinthesquarebecomemoreexaggerated.Theglobalstructureoftheformisnowagroupofintegratedcentralsquares,whichincludessomeonorneartheperipheryoftheobject,withthetwo‘ends’substantiallylessintegratedthanotherparts.Eachsidehasacentraldistributionofintegration,butoneinwhichthelongsideshavemuchgreaterdifferentiationthantheshortsides,andcorrespondincreasinglytotheglobalstructureofthetessellationasweelongateit.Inthelimitingrectangulartessellation,thesinglesequenceofsquares,thenthelocalandtheglobalstructuresareallidentical,asinfigure3.8e. Wemaysummarisethisbysayingthatwhilealltheseformsaregloballystructuredfromcentretoedge,inthecircularformthelocalorlateralstructureisuniform,inthesquareformthelateralstructureismaximallydifferentfromtheglobalstructure,whileintherectangularformthelocallateralstructuretendstobecometheglobalstructureasweelongateit,untilthelimitingformofthesinglesequenceisreachedwhenthetwostructuresbecomeidentical.Thecorrespondencebetweenthese‘structures’ofshapesandthewaysinwhichshapeisexploitedforsocialpurposesineverydaylifeisintriguing.Forexample,onsquarediningtablesthecentresideismoreadvantageousthancornerlocations,becauseitisamoreintegratedlocation.Similarly,theEnglishprimeministersitsinthecentreofthelongsideofabroadrectangulartable,maximisingthisadvantageinintegration.Incontrast,wherestatusratherthaninteractionistheissue,caricaturedukesandduchessessitatoppositeendsofalongtable,maximisingproxemicsegregationbutalsosurveillance,whilestudentsandmonksclassicallysitonthesidesofalongthin‘refectory’tablewithnooneattheends,thusmakingallbutlocalisedconversationsdifficult.Thepoliticsoflandholdingknightswithaperipatetickingsittingataroundtableareequallymanifest,asaretheendlesspoliticaldebatesovertheshapesofconferencetablesandparliamentchambers.Thewaysinwhichshapesareexploitedandusedallfollowthepatternofintegrationinsomeway,thoughwithoppositetendenciesdependingonwhetherinteractivestatusorsymbolicstatusismorecritical.

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Plans as shaped spaceNowletusconsiderthemorecomplexcaseofthehouseplan.Inthesequenceofplansinfigure3.9iisaslightlysimplifiedversionoftheplanofoneofthefarmhousesinruralFrancethatwereconsideredinChapter1.Thesallecommuneistheeverydayspacewherecooking,eatingandthereceptionofeverydayvisitorstakeplace.Thegrandesalleisaspaceformoreformalreceptionofguests.Theworkspacestotherightareadairy,washingroomandstorage,allassociatedwiththefemaleroleinthehouse,thebureauistheofficeoftheprincipalmaleoccupant,andthesalleisanindeterminatespace,perhapsfunctionallyassociatedwiththebureau.Whatdoesitmeantoanalysethisplanasashape? Aplanis,first,ashape,whichcanberepresentedasatessellation,see3.9ii.Forconvenienceandspeedofanalysisweusearatherlargeelement,andtreatthresholdsassingleelements.Thisleadstosomeunrealisminwallthickness,butthisdoesnotaffecttheanalysis.Thetessellationmaybeanalysedintoapatternofuniversaldistances.Sincethisreflectsthedistributionofcentralityintheshape,inthiselongatedplantheleastuniversaldistances-showndarkest-arefoundinthefrontcorridorbetweenthelargespacemid-right-thesallecommune-andthemainentrancemid-leftasin3.9iii. Themetricdistributionofuniversaldistancesrepresentsthedegreetowhichphysicaleffortmustbemadetomovefromonepartoftheshapetoanother.Ifwecomparetheplanshapetoasquareshapewiththesamenumberofelementswehaveasimpleindexoftheoverallmetricintegrationoftheshape.Inthiscase,themeanuniversaldistanceofcellsintheshapeis10.3whereasforanequivalentsquareitwouldbe4.9.Dividingtheformerintothelatter,wefindthatourshapehas2.1timestheuniversaldistanceofanequivalentlysizedsquare,indicatingthatabouttwiceasmucheffortmustbemadetomovearoundthisplanasinanequivalentsquare.Wemaythinkofthereciprocalofthisnumberasindexingthedegreetowhichashapegetstowardsbeingasquare.Inthiscasethevalueis.462.Thedegreeanddistributionofuniversaldistancesthusindexessomethinglikethephysicaleconomyoftheshape,thehumancounterparttowhichistheamountofphysiologicaleffortneededtoovercomeuniversaldistances.Wemayperhapsthinkofthiswayoflookingattheplanasitsbodilyorphysiologicalstructure.Itrepresentstheinertiaaparticularshapeofferstothehumanbodyoccupyingit. However,aswesawinChapter1,theplanisalsoanarrangementofconvexelements,thatis,rooms,corridors,halls,andsoon.Wecanrepresentitassuch,again,byusingsingleelementthresholds,asin3.9iiii.Againweanalysethisforitspatternofintegration,thistimetreatingtheconvexelementsaselements,andthereforeignoringactualdistancesandsizes,giving3.9v.Nowofcourse,aswasshowninChapter1,thestrongestintegratoristhesallecommune.Thoughthecolourcodingmakesitlookthesameasthecorridor,theintegrationvalueofthespace(.197,usingthei-valueformula)isalittlestronger(thatis,hasloweruniversaldistance)thanthecorridor(.205).Thismeansthatintermsofconvexasopposedtometricorganisation,thefocusofintegrationhasbeendisplacedfromthegeometric

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Figure 3.9

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centreintooneofthefunctionspaces.Thedistributionsurvivesifweaddfourlinearstripsaroundtheplantorepresenttheoutsideworld(sincetherelationtotheoutsideisoftenacriticalaspectofdomesticspaceorganisation),andreanalyseforintegration(3.9viandvii).Theoffsetsallecommunespaceisstillstrongerthanthecentralcorridorelement.

Wenowoverlaytheconvexelementsonthetessellationshape,connectingeachtoallthetessellationsquaresthatlieimmediatelyunderit,andre-analysethetwolayersasasinglesystem,sothateachconvexelementisaffectedbythenumberoftessellationelementsitisdirectlyconnectedto,andeachtessellationelementisaffectedbythelinksmadetoothertessellationelementsthroughthepatternofconvexelements.Notsurprisingly,wefindthateachlayerhasaffectedthedistributionofuniversaldistancesintheother.Figures3.9viiiandixshoweachlayerofthetwo-layersystemseparately.3.9viii,theconvexlayerofthetwo-levelanalysis,showsthatcomparedto3.9v,thelargespaceontheleft,the‘best’room,hasbecomerelativelymore‘integrated’thantheworkspacesontherightandtheoffice.Thisisaneffectofscale.Thefactthatthemuchlargerconvexareaofthe‘best’roomoverlaysfarmoretessellationsquaresthanthesmallworkroomshastheeffectofdrawingintegrationtowardsthe‘best’roomindirectproportiontoitsmetricscale,andconverselyforthesmallrooms.Ineffect,theconvexlayerofthetwo-levelsystemshowshowthepatternofintegrationoftheconvexelementsisaffectedbytheirarea,asmeasuredbythenumberofuniformtessellationelementseachoverlays.Thiseffectisclarifiedinfigure3.9ixthetessellationlayerofthetwo-layersystem.Comparingthistofigure3.9iii,weseethattheoverlayingofthelargerconvexelementonthetessellationsquareswithinthe‘best’roomhastheeffectofmakingthemmoreintegratedandmoreuniform.Theseresultsshowthatmetricscale,shape,andspatialconfigurationcanallbeexpressedinthecommonlanguageofuniversaldistances,orintegration,inlayeredspatialrepresentationconsideredasunifiedsystems. Wemaytakethisalittlefurther.Anotherpotential‘layer’intheplanisthesystemoflinesofsightlinkingtheconvexelementstogetherthroughthedoorways,assumingforthispurposethattheyareopen.Wecanrepresentthislayerbydrawingaxial‘strips’correspondingtolinesofsightasinfigure3.9xandanalyseitspatternofintegration,figure3.9xi.Wefindthatthefront‘axis’passingthroughthesallecommune,thesalleandthecorridorisnowthemostintegratingelementbutthemainentrancefront-backlinemid-leftandthesallecommunefront-backlinemid-rightarealmostasstrong. Wemaythensuperimposethelinearelementsontheconvexelementsandreanalysetheseasasingletwo-levelsysteminwhichthelineelementsarealldirectlyconnectedtotheconvexelementsthatlieimmediatelyunderthem.Theeffectofthissimultaneousanalysisofthetwolayerswillbetoshowhowintegrationissharedbetweenconvexandlinearelements.Wefindthatthefrontcorridorisstillstrongest,followedbythefront-backlinethroughthesallecommune,followedcloselybyboth

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thefrontbacklinethroughthemainentranceandbytheconvexspaceofthesallecommuneitself.Theseresultscanbeshownbykeepingthelineandconvexsystemtogether,asinfigure3.9xii,butalsobyshowingthemseparatelyforgreaterclarity. Finallywecanassembleallthreelayersintoasinglesysteminwhichbothconvexandlineelementsaredirectlyconnectedtoallthetessellationelementsthatlieimmediatelyunderthem.Wethenanalyseandprintoutthethreelayersseparately,firstthetessellationlayer,figure3.9xiii,thentheconvexlayer,figure3.9xiiii,andfinallythelinelayer,figure3.9xv.Thefinalpatternemergingfromthethree-layeranalysisisthatthe‘frontaxis’linkingthroughallthefrontspaceisthestrongestintegrator,followedbythesallecommune,thegrandesalle,thelinetothebackthroughthesallecommuneandthemainentrancelineandthesecondaryentranceline. ComparedtothepurelyconvexanalysisoutlinedinChapter1,then,anumberofnewsubtletieshavebeenadded.Forexample,ithasbecomeclearthatthepotentiallineofsightlinkingroomsthroughthecorridoratthefrontofthehouseisamorecriticalelementthanappearedintheearlieranalysis,andineffectimpartstothehouseafront-backorganisationthathadnotemergedfromtheearlieranalysis.Also,wecanseethattherelationbetweenwhatwemightcallthe‘energyeconomy’ofthehouseplan,thatis,theamountofeffortneededtogofromonelocationtoanotherasshowninthemetrictessellation,andthehigher-levelorganisationisquitesubtle.Ineffect,convexspaceintegrationforthemajorspacesisdisplacedfromthemetriccentreofgravity,andthedegreeofdisplacementistosomeextentcompensatedbysize.Thusthegrandesalleismoredisplacedthanthesallecommune,butcompensatesforthisgreaterdisplacementbyitsgreatersize.Multi-layeredanalysissuggeststhenthatweshouldnotseeasystemofspaceasonething.Aspatiallayoutisashapewhichcontainsmanyconfigurationalpotentials,eachofwhichseemstorelatetoadifferentaspectoffunction.Thesepotentialsmaybetreatedasindependentsystemsofspacebychoosingtoanalysethelayoutonthebasisofoneparticularrepresentationratherthananother,ortheymaybetreatedinselectivecombinations,orevenaltogether.Italldependsonwhatwearetryingtofindout.

Façades as configurationsIfthedistributionofthevariouslayersofintegrationinashaperelatestothewaysinwhichweuseshapes,thenanintriguingpossibilitymightbethatitcouldalsobeimplicatedinhowweunderstandshapes.Forexample,buildingfaçadesseenasshapesseemcapableofbeing‘understood’ascommunicatorsofinformationinsomesense.Couldconfigurationbeinvolvedinthistypeofapparentcommunication? Considerinaveryelementarywayhowwerecogniseobjects.Thetoprowoffigure3.10showsthreefigureswhichareconstructedbyarrangingthirtysquareelementsindifferentways.Recognisingthesefiguresseemstohappenintwostages.Inthefirststage,weidentifyadistinctshape,differentfromothers.Inthesecondweassignthatshapetoacategorybygivingitaname.Infigure3.10aandb,wesee

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twoshapes.Weeasilyrecognisethedifferencebetweenthetwoshapes,thatis,wereadilymakeapureconfigurationaldistinctionbetweenthetwoobjects.Butwehavenocategorytowhichwecanassigneitherobject.Theprocessofobjectrecognitionisthereforeendedatthefirststage.Infigure3.10cwealsoseeashape,butthistimeweconjectureacategory:theshapelookslikeanover-regularisedhumanoid,soweconjectureitismeanttobeeitherarobot,acaricaturehuman,orperhapsatoy.Ofcourse,thefiguredoesnotreallybearmuchresemblancetoahumanbeingorhumanoid.Theevidenceonwhichourcategoryconjectureisbasedis,tosaytheleast,flimsy.Howeverthenatureoftheevidenceisinteresting.Itseemstobeconfigurational.Figures3.10a,bandcarenomorethanoutlinesproducedbyrearranging30squarecellsintodifferentconfigurations.Wehave,itseems,aclearabilitytodistinguishpureshapesorconfigurationfromeachother,priortoanyintuitionofthecategoryofthingtowhichtheconfigurationmightbelong. Wecancallthefirstthesyntacticstageofobjectrecognition,andthesecondthesemanticstage.Thesecondstagehasbeenextensivelydealtwithbyphilosophersandothers,butwhataboutthefirst,‘syntactic’stage,onlynowbeinginvestigatedbycognitivepsychologists?21Whatdoesitmeantorecogniseaconfiguration?Oneapproachtothisistoreversethequestionandaskwhatpropertiesconfigurationshavethatmightallowthemtoberecognised.Suppose,forexample,weanalysetheconfigurationsasdistributionsoftotaldepthvaluesasinthesecondrowoffigure3.10. Thisgivesusseveralkindsofusefulinformationabouttheconfiguration.First,thereisthedistributionofintegrationineachform,asshownbythedark-to-lightpattern.Thiscanbethoughtofasastructurewithintheshape.Second,therearetheintegrationcharacteristicsoftheformasawhole,asindexedbythemeandepth(md)valuesandtheirstandarddeviation(sd)asshownbeneatheachform.Forcomparison,themeandepthandstandarddeviationforasixbyfiverectangle(thatis,aregularformwiththesamenumberofelementsandapproximatingasquareascloselyaspossible)isalsonoted.Weseethat3.10cismoreintegratedthan3.10a,whichismoreintegratedthan3.10b,andthatallarelessintegratedthanthesixbyfiverectangle.Standarddeviationsfollowasimilarpattern.Thesedepthvaluesseemtocorrespondtocertainintuitionswehaveabouttheforms,asdothestandarddeviations,whichshowsthat3.10bhasgreatervariationinthemeandepthsofindividualelementsthan3.10a,whichhasmorethan3.10c,andallhavemorethanthesixbyfiverectangle. However,thereisanotherintuitionwhichisnotexpressedinthesemeasures.Itisobviousthat3.10cismore‘symmetric’thaneither3.10aor3.10b,sinceithasthepropertyofbilateralsymmetry,oneofthecommonestandmosteasilyrecognisabletypesofsymmetryfoundinartefactsorinnature.However,whilefigures3.10aand3.10bbothlackformalsymmetries,theydonotseemtobeentirelyequivalentfromthispointofview.Insomesense,figure3.10aseemstobeclosertosymmetricorganisationthan3.10b.Thereisapossiblequantificationforthisproperty.Toexplain

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Figure 3.10

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a:si= 21/30 = .7; b:si = 26/30 = .867; c:si =11/30 = .3676x5 rectanglesi = 9/30 = .3

md 5.604 sd 1.389

6x5 rectangle: md 3.554 sd .543

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it,wemustconsiderthewholeideaofsymmetryfromaconfigurationalpointofview.Wehavealreadyseenthatpuresymmetriesinshapescouldbeinterpretedasconfigurationalproperties,namelyj-graphisomorphisms.Fromanarchitecturalpointofview,itisveryusefultoformulatepropertiesofsymmetryinthisway,since,unlikethenormal‘invarianceundermotion’definitionsofsymmetry,itopensthewaytoweakerdefinitionsofsymmetry,andpermitsanaccountofintuitivelyimportantarchitecturalpropertieswhichapproachsymmetrybutcannotbesoformallydefined.Forexample,wecanspecifyidentityofpositionalinformationwithrespectnottothewholeobjectbuttoaregionwithintheobject,thatis,localratherthanglobalj-graphisomorphism,anddiscusstherelationbetweenlocalandglobalj-graphisomorphism.Buildingsarefulloflocalsymmetries—theformofawindow,orofaparticularmasswithinacomplex—whichsometimesareandsometimesarenotreflectedinaglobalsymmetry.Therelationbetweenlocalandglobalsymmetryseemsanaturalwaytoexpressthis. Mostsignificantly,wecanspecifysimilarity,ratherthanidentity,ofpositionalinformation,anddosoinapreciseway.Forexample,j-graphisomorphismmeansthatj-graphssharenotonlythesamenumberofelementsandthesametotaldepth,butalsothesamenumberofelementsateachlevelofthej-graphandthesameconnectionsbetweenelements.Onewayofweakeningthispropertywouldbetomaintainallpropertiesexcepttherequirementthattheconnectionsbeidentical.Anotherwouldbetovarythenumberateachlevel(fromwhichitfollowsthatconnectionswouldbedifferent)buttomaintainthetotaldepththesame.22

Thesecondoftheseseemsparticularlyinteresting,sinceitoffersapossibleformalisationofthepropertyof‘balanced’asymmetryoftendiscussedintheliteratureintheformalpropertiesofarchitecture.23Forexample,infigure3.11weloadasimplelinearshapewithtwosetsoffourbytwocells,onehorizontal,theothervertical,buteachjoinedtoexactlytwocellsinthebasicform.Althoughthetwoendshapescreatedaredifferent,andinthemselveshavedifferentdistributionsoftotaldepthvalues(ori-values),allthevaluesinthebottomtworowsarepairedinthateachcellhasexactlyoneothercellwhichis‘symmetrically’locatedandhasthesamei-value.Thisi-valueequalityseemstogivearatherprecisemeaningtotheideaof‘balancedasymmetry’. Wemayapplythisanalysistothethreeshapesshowninfigure3.10.Thethirdrowshowseachshapewithcellswithequali-valuesmarkedwiththesamenumber,fromthemosttotheleastintegrating.Weseethat3.10ahasfarmoreequali-valuesthan3.10b.Also,in3.10atheequalvaluesreachwellintotheintegrationcoreoftheshape,whereasin3.10btheyaredistinctlyperipheral.Bothoftheseproperties,aswellasthedegreeofintegration,canberepresentedthroughasimplestatisticaldevice:thelinechartshowninthefinalrowof3.10.Hereeachshapeisrepresentedbyaseriesofi-values,plottedfrommosttoleastintegrated(shownasleasttomostdepth),togetherwithaseriesrepresentingthesixbyfiverectangle(shownascircles)toprovideabaselineforcomparison:3.10a

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isrepresentedasdiamonds,3.10bastriangles,and3.10cassquares.Evidently,theoveralldegreeofintegrationisindexedbythelocationoftheseriesontheverticalaxis.Thustherectangleisthemostintegrated,3.10cnext,then3.10aandfinally3.10b.Also,theshapesdivergeastheymovefromintegratedtosegregatedelements,sothatthemostintegratedelementsineachshapearemuchclosertogetherthantheleast.Thelinechartsalsoshowthedegreeof‘balancedasymmetry’intheshapebyaligningelementswiththesamei-valuenexttoeachothertoformahorizontalline.Theratioofthetotalnumberofelementstothenumberofelementsthatformpartofsuchlineswillindexthedegreeofbalancedasymmetryintheshape.Thesimplestindexisthenumberofi-valuesoverthenumberofelements.Identicali-valueswillincludeboththoseresultingfromperfectsymmetryasshownbyisomorphicj-graphs,andthosethatonlysharethesametotaldepth.Thissummaryfiguremaythenbethoughtofasabroad‘symmetryindex’.Sivaluesfor3.10a,bandcarebelowthelinechart. Integrationanalysisofshapes,then,permitsustoretrievesomeusefuldescriptionsofshapepropertiesinaconsistentway,thoughwithoutanypretencethatthisisafullaccountofthoseproperties.Oneareawherethisapproachisuseful,however,isinconsideringbuildingsasshapes.Thekeypointhereisthatbuildingsarenotpureshapes,inthegeometricsenseoffree-standingformsinauniformcontext,butorientedshapes,inthesensethattheyareorientedtoandawayfromthegroundonwhichtheystand.Ifwetakethissimplefactintoaccountinanalysingbuildingfaçadesasshapesthenweeasilyfindsomeverysuggestiveresults.Thiscanbedemonstratedbysimplystandingshapesonaline,whichwewillcallthe‘earthline’.Thethreefiguresoffigure3.12arethesquareandrectangularformsshownearlierwithearthlinesadded.Inthecaseoftherectangularform,theearthlineisaddedtwice,oncetocreateashapehorizontallyalignedtotheearthandoncetocreateashapeverticallyaligned. Thefirsteffectthatmustbenotedisthatinthecaseofthesquare,addingtheearthlinehastheeffectofreducingtheoriginaleightsymmetriesofthesquaretoasimplebilateralsymmetry.Thiscanbeseenvisuallyifwecomparethe

Figure 3.11

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shadingpatternsofthesquarewithanearthlinetotheoriginalsquareform.Theconcentricpatternisstillquitemarked,butnowanadditionalbilaterallysymmetricpatternisdetectable.Thiseffectresults,ofcourse,fromtheearthline,asitwere,drawingintegrationdowntowardsitself.Thisconfirmsintuition.Itisclearthatwedonotregardasquareçashavingthesymmetriesofafree-standinggeometricalsquare.Weseeitasaformanchoredtotheearthandhavingleft-rightsymmetry,butnottop-bottomsymmetry.Indeedthelanguageinwhichwedescribetheform-topandbottom,leftandright,showswhichrelationsweseeassymmetricalandwhichasymmetrical. The‘bilateraleffect’oftheearthlineisfarmoremarkedinasquareformthaninanelongatedform,whetherweelongatetheformhorizontallyorvertically.Intheverticalform,theeffectoftheearthlineistomakeintegrationrunfromthebottomoftheformtosegregationatthetop.Thisobliteratesanysenseofabilateralsymmetriceffectintheshadingpattern,andsubstitutesadifferentiationfrombottomtotop.Addinganearthlinetoahorizontallyelongatedform,weagainfindthebilateraleffectisbarelynoticeableintheshadingpattern,andinsteadthereisatendencytoformbroadlayersintheform,butwithmuchweakerdifferentiationfrombottomtotop. Intermsofintegrationandsymmetryindexthedifferencesbetweenthe

verticalandhorizontalformsarealsostriking.Theverticalform,becauseofthegreaterdistanceofmostelementsfromtheearthlineandthefactthatfarfewerconnectdirectlytoit,isalmostassegregatedastheelongatedformwithouttheearthline.Inthehorizontalform,however,mostelementsarenowclosertotheearthline,withmanyactuallytouchingit,andtheeffectisthattheshapehasnowbecomemuchmoreintegratedthanthesquareform,theoppositeofthecasewithouttheearthline.

.178 .477 .124 29/65=.446 .095 20/65=.308

Figure 3.12

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Whenweconsiderthesymmetryindextheeffectsarenolessstriking.Whereasintheoriginalshapes,thesquareformhadmore‘symmetry’thantheelongatedform,theadditionoftheearthlinehasoppositeeffectsontheverticalandhorizontalforms.Theverticalformhaslesssymmetrythanthesquareform,becausefewerelementsareonthesamelevel,whilethehorizontalformhassubstantiallymore,forthecontraryreason.Again,thereisacommon-sensereasonfortheseeffects.Theadditionofanearthlinetoaverticalformconvertsapatternofintegrationthatintheoriginalformwentfromcentretoedgetoonethatalsonowgoesfromtheearthline—which,asitwere,nowanchorstheform—upwardsthroughtheform,frommoreintegrationatthebottom,closesttotheearthline,toleastatthetop,farthestfromtheearthline.Theverticalformineffectnowrunsverticallyfromintegrationtosegregation.Inthehorizontalform,ontheotherhand,insofaraselementsarehorizontallyrelated,theywilltendtobecomemoresimilartoeachother,byvirtueoftheirclosenesstotheearthline.Thiscorrespondstotheintuitionthatthemoreshapesarealignedalongasurface,themoreequaltheybecome.Incontrast,theverticaldimensionstressesdifference,inthattherelationsofaboveandbelowareasymmetrical.Horizontality,wemaysay,equalisesandintegrates,whileverticalitysegregatesanddifferentiates. Theanalysisoffaçadesaslayersisalsosuggestive.Forexample,ifwetakeasimplifiedrepresentationofaclassicalfaçade,wecanrepresentitfirstasashape,thatis,asametrictessellation,then,bydrawingthedominantelementsinthefaçade,asapatternofconvexelements.Byanalysingeachseparately,asinfigure3.13aandb,weseethattheshape,asrepresentedbythetessellationshowsacentralisedpatternofintegrationfocussedabove,andrunningdowninto,thecentralcolumn,givingthedistributionastronglyverticalemphasis.Incontrast,theconvexanalysisfocussesintegrationonthefrieze,creatingahorizontalemphasis.Onemightconjecturethatinlookingatafaçadeweseeashape,andourviewofthatshapeisthenmodifiedbythelarger-scaleorganisationofelementsimposedonthatshape. Thesecentralisedverticalandlinearhorizontalstructureswhicharerevealedbytheanalysisare,takenseparately,amongthecommonest-perhapsthecommonest-formalthemeswhichbuildersanddesignershavecreatedinwholeclassesofbuildingfaçadesacrossmanycultures.Thefactthatanalysis‘discovers’thesestructuresseems,atleast,aremarkableconfirmationofintuition.Theanalysisperhapssuggeststhatonereasonwhytheclassicalfaçadehasoften,fromLaugieronwards24beenarguedtoconstituteafundamentalmodeoffaçadeorganisation,isexactlybecausethroughitsshapeandconvexorganisationitbothexpressesandcreatesatensionbetweenthetwomostfundamentalmodesoffaçadeorganisation.Ifthiswerethecase,thenitwouldsuggestthatwhatthehumanmind‘reads’whenitlooksattheformofabuildingis,oratleastincludes,thepatternofintegrationatmorethanonelevel,andtheinterrelationsbetweenthelevels.

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Urban space as layers: the problem of intelligibilityWhateverthecasewithfaçades,oneareawheresubstantialempiricalresearchhasestablishedtheneedtoconsiderlayersofconfigurationalpotential,andtheirinter-relations,isurbanspace.Consider,forexample,thetwohypotheticalurbanlayoutsinfigure3.14aandb.Thetwolayoutsarecomposedofthesame‘blocks’or‘islands’ofbuildings.Inthefirstcase,theyarearrangedinawaywhichhasacertaindegreeofirregularity,butlooksmoreorless‘urban’,inthatthepatternofspacecreatedbythearrangementoftheblocks—andthisisallthaturbanspaceessentiallyis—seemstohavetherightkindsofspacesintherightkindsofrelations,andasaresultappears‘intelligible’asan‘urban’system.Inthesecondlayout,allthe‘blocks’arethesamebuteachhasbeenmovedslightlywiththeeffectthatthesystemofspaceseemsmuchless‘urban’,andmuchlesseasily‘intelligible’.Itisclearthatanyusefulanalysisofurbanspacemusteithercapturetheseintuitionsorshowwhytheyareillusory.Itwillturnoutthattheyarenotillusoryatall,andthattheyarisefromwell-definedrelationsamongstthedifferentspatialpotentialsthatmakeupthelayout.25

Inonesense,bothlayoutsrepresentthecommonesttypeofurbanspacestructure.Wecancallitthe‘deformedgrid’,becausewhilemadeupofoutwardfacingislandsofbuildingseachsurroundedonallsidesbycontinuousspaceinthemannerofaregulargrid,thestructureofthatspaceisdeformedintwoways:itislinearly,oraxiallydeformed,inthatlinesofsightandaccessdonotcontinuerightthroughthegridfromonesidetotheother,astheywouldinaperfectlyregulargrid,butcontinuallystrikethesurfacesofthebuildingblocksandchangedirectionasaresult;secondlyitisconvexlydeformedinthattwo-dimensionalspacescontinuouslyvaryintheirdimensionsandshape,makingapatternofwiderandnarrowerspaces.Thevisibilityfieldatanypointinthespaceforsomeonemoving

a. b.

Figure 3.13

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inthegridwillbemadeupofbothkindsofelement.Wherevertheobserveris,therewillalwaysbealocalconvexelementofsomekind,inwhicheverypointisvisiblefromeveryotherpoint,plustheshapemadebyalllinesofsightandaccesspassingthroughthepoint.Theeasiestwaytodescribethedifferencesbetweenthetwolayoutsintuitivelyistosaythatamovingobserverineitherlayoutwouldexperiencecontinuouschangesinthevisibilityfield,butthatthekindsofvisibilityfieldexperiencedinthefirstarequitedifferenttothoseinthesecond.Theapparentdifferencesinintelligibilityinthetwolayoutswillturnouttoberelatedtotheseformaldifferencesinthesuccessionofvisibilityfields.Wecanbuildupananalysisofthetwolayoutsbyinvestigatingthesedifferentpotentials.First,wewillconsiderthe‘overlapping’convexelementsthataredefinedbythesurfaceofthisblock.26Hereconvexelementsaredefinedbyreferencetothesurfaceofeachblock,eachofwhichdefinesitsmaximalconvexfield.Thesefieldswillinevitablyoverlap,andwheretheydo,theareaofoverlapwillitselfformasmallerconvexelementfromwhichbothoverlappingconvexspaceswillbefullyvisible,thatis,willbeconvex,althoughthesespacesarenotconvextoeachother.Thesamewillbetruewhenfurtheroverlappingspacesareadded.Certainsmallspaceswillindeedbeconvextoasubstantialnumberofconvexspacesbecauseallthosespacesoverlapinthatarea.Suchareaswillasaresulthavelargevisibilityfields,whereasareaswherethereisnooverlapwilltendtohavemuchsmallervisibilityfields.Overlappingconvexelementsarevirtuallyimpossibletointuit,becausetheoverlappingissodifficulttorepresent.Computeranalysisisthereforerequired. Letuslookfirstatthepatternofoverlappingconvexspacesgeneratedinourtwolayouts.Figures3.14candd,aretheresultoftheanalysisoftheopen-spacestructureofthetwolayouts.Thecomputerhasfirstdrawnalltheoverlappingconvexelementsdefinedbythefacesofeach‘block’andthencarriedoutan‘integration’analysisofthepattern,withintegrationtosegregationshownfromdark-to-light,asbefore.Inthefirst‘urban’layout,thedarkestspacesoftheresulting‘integrationcore’(theshapemadebythedarkestareas)crosseachotherintheinformal‘marketsquare’,anddarkspaceslinkthemarketsquaretowardstheedgeofthe‘town’.Inthesecond,thereisnolongerastrongfocusofintegrationlinkinga‘square’totheedgesofthesystemand,ineffect,theintegrationcorehasbecomediffused.Infact,themostintegratingspacesarenowfoundattheedge,andnolongergettotheheartofthesystem.Onaverage,thelayoutasawholeismuchless‘integrated’thanthefirst,thatis,ithasmuchgreatertotaldepthfromallspacestoallothers. Inotherwords,themarginalrearrangementoftheurbanblocksfromthefirsttothesecondlayoutresultinginaspatialstructurewhichisquitedifferentbothinthedistributionandinthedegreeofintegration.Intuitively,wemightsuspectthattheedge-to-centreintegrationcorestructureofthefirstlayouthasmuchtodowiththeoverallsenseofurbanintelligibility,anditslossinthesecondlayout.Intelligibilityisachallengingpropertyinanurbansystem.Sincebydefinitionurbanspaceatgroundlevelcannotbeseenandexperiencedallatonce,butrequirestheobservertomovearoundthesystembuildingupapictureofitpiecebypiece,wemight

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suspectthatintelligibilityhassomethingtodowiththewayinwhichapictureofthewholeurbansystemcanbebuiltupfromitsparts,andmorespecifically,frommovingaroundfromoneparttoanother. Thereisinfactasimpleandpowerfulwayinwhichwecanrepresentexactlythisproperty.Itisillustratedinthetwo‘scattergrams’infigures3.14eandf,correspondingtothetwolayouts.Eachpointinthescatterrepresentsoneoftheoverlappingconvexspacesinthefigureabove.Thelocationofthepointontheverticalaxisisgivenbythenumberofotherconvexspacesthatspaceoverlapswith,thatis,the‘connectivity’ofthespacewithotherspaces,andonthehorizontalaxisbythe‘integration’valueofthespace,thatis,its‘depth’fromallothers.Now‘connectivity’isclearlyapropertythatcanbeseenfromeachspace,inthatwhereveroneisinthespaceonecanseehowmanyneighbouringspacesitconnectsto.Integration,ontheotherhand,cannotbeseenfromaspace,sinceitsumsupthedepthofthatspacefromallothers,mostofwhichcannotbeseenfromthatspace.Thepropertyof‘intelligibility’inadeformedgridmeansthedegreetowhichwhatwecanseefromthespacesthatmakeupthesystem-thatis,howmanyotherspacesareconnectedto-isagoodguidetowhatwecannotsee,thatis,theintegrationofeachspaceintothesystemasawhole.Anintelligiblesystemisoneinwhichwell-connectedspacesalsotendtobewell-integratedspaces.Anunintelligiblesystemisonewherewell-connectedspacesarenotwellintegrated,sothatwhatwecanseeoftheirconnectionsmisleadsusaboutthestatusofthatspaceinthesystemasawhole. Wecanreadthedegreeofintelligibilitybylookingattheshapeofthescatter.Ifthepoints(representingthespaces)formastraightlinerisingat45percentfrombottomlefttotopright,thenitwouldmeanthateverytimeaspacewasalittlemoreconnected,thenitwouldalsobecomealittlemoreintegrated-thatistosay,therewouldbeaperfect‘correlation’betweenwhatyoucanseeandwhatyoucan’tsee.Thesystemwouldthenbeperfectlyintelligible.Infigure3.14e,thepointsdonotformaperfectline,buttheydoformatightscatteraroundthe‘regressionline’,whichisevidenceofastrongdegreeofcorrelation,andthereforegoodintelligibility.Infigure3.14fwefindthatthepointshavebecomediffusedwellawayfromanyline,andnolongerformatightfitaboutthe‘regressionline’.Thismeansthatconnectivityisnolongeragoodguidetointegrationandthereforeaswemovearoundthesystemwewillgetverypoorinformationaboutthelayoutasawholefromwhatweseelocally.Thisagreesremarkablywellwithourintuitionofwhatitwouldbeliketomovearoundthis‘labyrinthian’layout.27

Nowletusexplorethetwolayoutsinmoredetail.Infigure3.14gandh,wehaveselectedapointinthe‘square’intheanalysisofthefirstlayout,anddrawnalltheoverlappingconvexelementsthatincludethispoint.Thescatterthenselectsthesespacesinthescattergrambymakingthemcolouredandlarger.Wecanseethatthespacesthatoverlapatthispointareamongthebestconnectedandmostintegratedinthelayoutandthatthepointsalsoformareasonablelinearscatterinthemselves,meaningthatforthesespacesmorevisibleconnectivitymeansmore

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Figure 3.14a Figure 3.14b

Figure 3.14c Figure 3.14d

Figure 3.14e Figure 3.14f

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Figure 3.14l Figure 3.14m

Figure 3.14j Figure 3.14k

Figure 3.14g Figure 3.14h

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integration.Boththeshapemadebythesetofspaces,reachingoutfromthesquareinseveraldirectionstowardstheedgeofthesystem,andthescattergrampropertiesconfirmthatthispointinthe‘square’spacehasahigh‘strategic’valueinthelayoutasawhole.Ifwetrytodothesameforpointsinthesecondlayout,asinfigure3.14jandk,wefindthatthepointsareburiedinthescatterandhavenospecialstrategicvalue.Byexperimentallyclickingonaseriesofpoints,andcheckingboththevisualfieldsandthescattergrams,onecanestablishthattherearenocomparablestrategicpointsfromwhichaseriesofkeyspatialelementsinthelayoutcanbeseen. Wemayalsoexperimentwiththeeffectsofchangestothelayout.Suppose,forexample,wedecidethatthecurrent‘marketsquare’,althoughstrategicallyplaced,istoosmallandthatitshouldthereforebemovedelsewhereinordertoenlargeit.Infigure3.14landm,theoldmarketsquarehasbeenbuiltoverandanew,largersquarehasbeencreatedtowardsthetopleftofthelayout.Thelayouthasbeenanalysedandtheconvexelementsoverlappinginthenewsquarepickedout.Inspiteofitssize,thenewsquarehaspoorintegration,anditsoverlapping

Figure 3.14q Figure 3.14r

Figure 3.14n Figure 3.14p

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spacesoccupyapoorpositioninthescatter.Themostintegratedspacesremainthosepointingintotheoldmarketsquare.Inotherwords,thespatialconfigurationasawholecontinuesto‘pointto’theoldsquare.Animportantconclusionfromthis,amplyconfirmedbytheexaminationofrealtownplans,isthatasquareismorethanalocalelement.Howitisembeddedintheconfigurationasawholeisequally,ifnotmore,important.Ifweweretoseektoexploitthisbyexpandingtheoldmarketsquarebyremovingadjacentblocks,wewouldfindthesquarebecomesmuchmoredominant,andthatthelargestspacewithinthesquare(i.e.asopposedtothoseenteringandleavingwhicharenormallymoredominant)isnowitselfthesecondmostintegratedspace.Inotherwords,wewouldbegintoshifttheemphasisofintegrationfromlinearelementstotheopenspaceitself.Again,thiswoulddistorttheessentialnatureoflayout.Thesize,location,andembeddingofmajoropenspacesareallformallyconfirmedasaspectsofwhatweintuitivelyreadastheurbannatureofthelayout. Convexelementsarenot,ofcourse,themost‘global’spatialelementsinalayout,anddonotexhaustallrelationshipsofvisibilityandpermeability.Theselimitsarefoundbylookingnotattwo-dimensionalconvexelements,butatone-dimensionallineelements.Inadeformedgrid,theelementsmostspatiallyextendedlinearlywillbethesetofstraightlinesthataretangenttotheverticesofblocksofbuildings.Relationsbetweenpairsoftheseverticesineffectdefinethelimitsofvisibilityfrompointswithinthesystem.Thiscanbeexploredthrough‘axial’or‘allline’analysis,andinfigure3.14n-rwherethecomputerhasfoundandcarriedoutanintegrationanalysisofallthelineelementstangentialtoblockvertices.Wefindthattheintelligibilityofthesystemseenaxiallyisbetterthanseenconvexly,becauselinesaremore‘global’spatialelementsthanconvexelements,inthattheyexplorethefulllimitsofvisibilityandpermeabilitywithinthelayout.Linesthereforemaketherelationbetweenthelocalspatialelementandtheglobalpatternofspacelookasgoodaspossible.Thedifferencesbetweenthetwolayoutsthatwefoundthroughtheoverlappingconvexanalysisarehowevermoreorlessreproducedintheall-lineanalysis.Thisagreementbetweenthetwokindsofanalysisisitselfasignificantpropertyofthelayouts. Fromthepointofviewofhowlayoutswork,bothtypesofanalysisareimportant.Movement,forexample,canbepredictedfromastrippeddownversionoftheaxialanalysisinwhichonlythelongestandfewestlinesneededtocoverthewholesystemformthelinematrix.Similarly,manyaspectsof‘static’urbanbehaviours,especiallytheinformaluseofopenspaces,exploitthetwo-dimensional‘visibilityfield’propertiesofspace,withthehighestlevelsofusenormallyadjacenttothemoststrategicspaces.

Designing with configurational modelsBecausethesetechniquesallowustodealgraphicallywiththenumericalpropertiesofspatiallayouts,wecanalsousethemcreativelyindesign,bringinginmuchnewknowledgeaboutspaceandfunctionaswedoso.Forexample,extensiveresearchhasshown28thatpatternsofmovementinurbanareasarestronglypredictedbythe

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distributionofintegrationinasimplelinerepresentationofthestreetgrid.Byusingconfigurationalanalysistechniquesinsimulationmode,wecanexploitboththisknowledge,andthepotentialforconfigurationalanalysistogiveinsightintopossibleurbanpatternsthatwillnotbeatallcleartointuition.Thispotentialhasnowbeenexploitedinalargenumberofurbandesignprojects,ofteninvolvingthemodellingofwholecitiesinordertosimulatetheeffectsofnewdesigns.29

Todemonstratetheessentialsofthetechnique,asimplifiedhypotheticalmodelwillsuffice.Thetopleftfigureoffigure3.15isananalysedaxialmap(thelongestandfewestlinesthatcoverthestreetgrid)ofasmallareaaroundahypotheticalredevelopmentsite,withintegrationfromdarktolightasbefore,with,toitsright,thescattergramofitsintelligibility,showingaweaklyintelligiblesystem.Wecanexperimentbyasking,whatwouldhappenif,forexample,weimposedaregulargridonthesitewithouttakingtoomuchaccountofthesurroundingstructure,asthesecond-rowfigureandscatter.Weseethatinspiteofthegeometricregularity,ourlackofconcernfortheglobalpatternhasleftuswitharatheruniformlysegregatedspacepatternwithinthesite,withtoopoorarelationtothesurroundingareas.Asaconsequence,weseefromthescatterthattheareaasawholehasbecomeevenmoreunintelligible. Supposewethengotheotherway,andtrytodesignthesitebyextendingstronglines,andlinkingthemtoothers,asinthethirdrowfigureandscatter.Theresultisanintegratingsite,andgoodintelligibility.Thespatialstructureinthesitealsohasagoodrangeofintegratedandsegregatedspaceincloseproximitytoeachother.Aswewillseeinlaterchaptersthisisanimportanturbanproperty(seeChapters4and5.)Thisisasimpleexample,butitshowstheabilityofconfigurationalanalysisnotonlytoaidthedesigners’intuitioninthinkingaboutpatterns,andinparticularintryingtounderstandthepatternconsequencesofindividualdesignmoves,butalsoitsabilitytopermitthedesignertothinkmoreeffectivelyabouttherelationofnewandexistingpatterns,andingeneralabouttherelationofpartsandwholesincities. Wemayagainillustratethisbyasimplifiedsimulation.Plate1istheaxialmapofahypotheticalurbansystemwithwell-definedsub-areas.Researchhasshownthatthecriticalthingabouturbansub-areasishowtheirinternalstructuresrelatetothelarger-scalesysteminwhichtheyareembedded.Thebestwaytobringthisoutistoanalysethesystemforitsintegrationattwolevels.Firstwedoordinaryintegration,whichcountshowdeeporshalloweachlineinisfromeveryotherline.Secondwecounthowdeeporshalloweachlineinisfromalllinesuptothreestepsaway.Thelatterwecallradius-3integration,sinceitlooksateachlineuptoaradiusof3.Theformerwecancallradius-nintegration.Radius-3integrationpresentsalocalisedpictureofintegration,andwecanthereforethinkofitalsoaslocalintegration,whileradius-nintegrationpresentsapictureofintegrationatthelargestscale,andwecanthereforecallitglobalintegration. Wewillseeinduecoursethatlocalintegrationinurbansystemsisthebestpredictorofsmaller-scalemovement-thatusuallymeanspedestrianmovement

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a

b

c

Figure 3.15

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becausepedestriantripstendtobeshorterandreadthegridinarelativelylocalisedway-whileglobalintegrationisthebestpredictoroflarger-scalemovement,includingsomevehicularmovement,becausepeopleonlongertripswilltendtoreadthegridinamoreglobalisedway.Inhistoricalcities,aswillbeshown,therelationshipbetweenthesetwolevelsofintegrationhasbeenacriticaldeterminantofthepart-wholestructureofcities,becauseitgovernsthedegreeofnaturalinterfacetherewouldnaturallybebetweenmorelocal,andthereforemoreinternalmovement,andmoreglobalandthereforemorein-outmovementandthroughmovement. Someofthedifferenteffectsonthisrelationshipthatdifferenttypesoflocalareadesignwillhavecanbeshownbyhighlightingtheareasinscattergramsofthewholesystemandexaminingthescatteroflocalagainstglobalintegration.Theareashowninthebottomrow,forexample,isaclassicallystructuredareaforaEuropeancity,withstronglinesinalldirectionsfromedgetocentre,withalessintegratedstructureoflinesrelatedbothtothisinternalcoreandtotheoutside.Thisensuresthatthosemovingintheareawillbeconsciousofboththelocalandglobalscalesofspaceastheymovearound,andtherewillbeagoodinterfacebetweenlocalandglobalmovement.Thescatterformedbythesub-areasisshowntotheright.Thepointsoftheareaformagoodlinearscatter,showingthatlocalintegrationisagoodpredictorofglobalintegration,andcrosstheregressionlineforurbanareaasawholeatasteeperangle,showingthatthereisastrongerdegreeoflocalintegrationforthedegreeofglobalintegration.Alineonthecoreofthewholesettlementwill,incontrast,lieatthetopendofthemainregressionline.Thisshowshowsubtlyurbanareascreateasenseoflocalstructurewithoutlosingtouchwiththelarger-scalestructureofthesystem.(SeeChapter4foranexaminationofrealcases). Theareashownimmediatelyabove,inthesecondfrombottomrow,istypicalofthelayoutswetendtofindinhousingestates,withfewconnectionstotheedgeandlittlerelationbetweentheedgetocentrestructureandtheinternalstructureofthelayout.Thistypeoflayoutisinvariablyshownasaseriesoflayersintheredpointscatterwithvirtuallynocorrelationbetweenlocalandglobalintegration.Suchlayoutsinvariablyfreezeallournaturalmovementandbecomestructurallysegregatedlumpsintheurbanfabric.30Theareasinthetoptworowsshowothervariationsonlocalareastructure,oneproducingeffectsrathersimilartothoseintheexperimentalgridinthedesignexperimentoffigure3.16,whiletheotherisarandomscatteroflines,showingthatinspiteoftheapparentinformalityofmuchgoodurbandesign,randomlinessimplydonotworkexceptbychance.

Future urban models: intelligent analogues of citiesInadditiontotheirroleindesign,configurationalmodelsarenowbeingdevelopedasabasisforresearchingintothemultidimensionaldynamicsofcities.Consider,forexample,oneofthebroadestandleasttractableofissuesfacingthebuiltenvironmentindustry:thatoftheeconomic,socialandenvironmental‘sustainability’ofcities.Eventomonitoreffectivelyandcomparecitiesonsustainabilitycriteria,

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whatevertheymightturnouttobe,wemustbringdataonthephysicalandenvironmentalperformanceofcitiestogetherwithdataontheireconomicandsocialperformance,andtorelatebothtosomekindofdescriptionofthecity.Forexample,energyconsumptionandpollutionproductiondepend,amongotherfactors,onsettlementpatterns.Shouldsettlementsbedenseorsparse,nucleatedordispersed,monocentricorpolycentric,oramixofalltypes?Forresearchtogiveananswer,measurementdataonenvironmentalperformance,anddataontheimplicationsofdifferentbehaviouralassumptions(forexampleaboutthedistributionofworkandhome)and‘knock-on’effectssuchastheeconomic,socialandculturalconsequencesofspatialaggregationanddisaggregationpolicies,mustberelatedtodescriptionsofthephysicalandspatialformofcitieswhichreflecttherangeofvariationfoundintherealworld. Toworktowardsatheoreticalmodelofhowthismightbedone,wemaybeginwiththepurely‘configurational’modelswehavepresented,andshowhowotherkeyspatialattributessuchasmetricdistance,area,density,plotratios,shape,politicalboundaries,andsooncanbeexpressedwithintheconfigurationalmodelbyusingtheideaofintegrating‘layered’representationsofspaceintoasinglesystem.Forthepurposesofillustrationwewillagainusenotional,simplifiedexamples.First,werepresentastreetnetworkasaseriesoflinesorstrips,andanalysetheirpatternofintegration,asinfigure3.16aandb.Inthisanalysis,noaccounthasyetbeentakenofmetricdistance.However,insomecircumstancesatleast,thisseemslikelytobeanimportantvariable.Wecansupplythisbyselectinganarbitrarymodule-sayaten-metresquare—andlinkingmodulesintothepatternofthegridandanalysingthisasatessellationshape,asinfigure3.16c.Onitsown,thisisnotofgreatinterest,sinceitinevitablyreflectsthepatternofmetriccentralityinthegrid,asinfigure3.16d,butifwesuperimposethelinenetworkontothemetricmodularsystemandanalysethetwolayersasasinglesystem,thentheeffectistoweighteachlinewithanumberofmodulesdirectlyrelatedtoitslength.Theoutcomeofthis‘lengthweighted’integrationanalysisisshownatbothlevelsofthecombinedanalysis:intermsofthemodularunitsinfigure3.16e,andintermsofthe‘linesuperstructure’ofstripsinfigure3.16f.Thestriplevelismuchthesameaspreviously,butthemodularelementsshowaninteresting-andverylifelike-localisedstructureinwhichgreaterintegrationisconcentratedatthe‘streetintersections’,withlessintegratedmodulesinthecentresoflinksawayfromtheintersections.Thisimmediatelyenablesustocaptureanewandfunctionallysignificantaspectofspaceorganisationinarepresentation. Therelationshipbetweenmetricareaandconfigurationcanbedealtwithinananalogouswaybyunderlayingconvexelementswithatwo-dimensionalmodularlayer,asinfigure3.17a-f.Ina–cweseehowasimplesysteminwhichfourconvexspacesofequalsizeandshapeandtheconnectionsbetweenthemarerepresentedasalayerofmodularelementswithfourconvexelementsandfourstripsfortheconnectionsuperimposed.Thetwo-layersystemisthenanalysed.Whetherwelookattheresultwiththeconvexlayeruppermostorthemodularlayer,theresultswill

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beasymmetricaldistributionofintegrationdominatedbythestrips.Infigure3.17d–fwegivetheconvexelementsdifferentareasandunderlaymodularelementsaccordingly,sothateachisnowweightedbythenumberofmodularelementsitoverlays.Analysisseparatelythentogethershowsthatintegrationisdrawnintotheconvexelementsaccordingtotheirarea.Notehoweverthattheintegrationofthetwosmallerconvexareas(onthetop)areinthe‘wrong’order.Thisisbecausetheoneontheleftisclosertothelargest-scaleconvexarea(bottomleft)andthisaffectsitsownintegrationwithrespecttotherestofthesystem.Thustheresultsshowacombinationofconfigurationaleffectsandmetricareaeffects.Fromthiswecanseethatifwemakealargeandsmallsquareconfigurationallyequivalentinanurbansystemthenthelargesquarewillintegratemore.Metricarea,itturnsoutislikedistance,apropertycapableofexpressionasanaspectofconfiguration.Wemaysimulatetheeffectofplotratiosanddensitiesbyequallysimplemeans.Forexample,ifwewishtoattachabuildingwithagivennumberoffloorstoastreetnetwork,allweneedtodoisattachaconvexspacethesizeofthegroundareaofthebuildingtotheappropriatepositioninthestreetsystem,thenoverlayonthataconvexelementforeachfloor,makingsurethateachelementabovethegroundisdetachedfromthestreetandonlyconnectedthroughthegroundlayerasitwouldbeinreallife.Thiswillnotappearvisuallyasathree-dimensionalstructure,butitwillexactlyrepresenttheadditionofabovegroundfloorspacetotheurbansystem. Wemaynowbuildamodelofanurbansysteminthefollowingway.First,wedividethecityupintoanarbitrarynumberofareasandrepresentthemasnon-contiguouspolygons.Thesemaybeassmalloraslargeasweneed,accordingtothelevelofresolutionrequiredbytheresearchquestion.Thepolygonsmaybebasedonpoliticalboundaries,likewards,administrativeboundarieslikeenumerationdistricts,segmentsdefinedbyanarbitrarilyfinegrid,ortheymaybedefinedbyobjectivemorphologicalpropertiesofthebuiltenvironment.Thesepolygonsrepresentingareasarethefundamentalunitsofanalysisforthetechnique. Figure3.18ashowsourimaginarysimplifiedcaseinwhichthestreetnetworkofthecity(orpart-city)issuperimposedonthepatchworkofpolygonssothateachpolygonislinkedintotheurbansystembyallthestreetsorpart-streetsthatpassthroughitoralongsideit.Thistwo-levelspatialsystemisanalysed‘configurationally’tofindthepatternofintegrationinthewholesystem.Evidently,thestreetpatternwilltendtodominatetheareapolygonssimplybecausethestreetsareconnectors.However,thestreetsystemcanthenbe‘peeledoff’thepolygons,asinfigure3.18b,leavingapatternofpolygonswiththeirspatialcharacteristicsinrelationtothecityareaaroundthem,andtothecitysystemasawhole,recordedasasetofnumbers. Thisbasicprocessoflinkingareastogetherbythestreetnetworkinasingleconfigurationalmodelisthebasisofwhatwecallan‘intelligenturbananalogue’model.Oncethisisestablished,wecanthencomplicatethemodelinallthewayswehavedescribedpreviously.Forexample,wecanunderlaythestreetnetworkwithmetricmodulessothattheanalysisofthestreetsystemtakesdistancesintoaccount.Wecanunderlaythepolygonswithmetricmodulessothatthemetricarea

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ofapolygonistakenintoaccount.Wecanalso,ifwewish,superimposelayersonthepolygonsrepresentingoffthegroundfloorspace. Thereisalsoaneasywayoffurtherdisaggregatinganymodelfromthelevelofresolutionoriginallyselected.Eachoftheoriginalareapolygonscanbeitselfsubdividedintomuchsmallerpolygonsandanalysedasbefore.Thismorelocalisedanalysiswillgiveamuchricheranddenserpictureofthedetailedcharacteristicsofthearea.Thesemaythenbefedintoalarger-scalemodelasmoredetailedenvironmentaldescriptors.Thereisnoreasoninfactwhybothlevelsofthemodelshouldnotbeanalysedasasinglesystem.Theprincipalbarrierwouldbecomputingtime.Inourexperienceaddinganewleveloffinestructuretoanexistingmodelleavesthelarger-scalepicturemoreorlessintactprovidedthatthedisaggregationisdoneuniformlyandisnotconfinedtoparticularregions. Attheotherendofthescale,wemayalsoderivenewmeasuresofthemostmacro-propertiesofthecitysystem,suchasshape,andshapeloadedwithdifferentdensitiesindifferentregions.Thiscanbedonebysimplylinkingtheareapolygonstogetherandanalysingthedistributionofintegrationinthesystemwithoutthesuperimposedstreetsystem.Shapewillbeindexedbythedegreeanddistributionofintegration,andcanbeshownbothbydirectgraphicalrepresentationofthecitysystem,orbystatisticalrepresentationssuchasfrequencydistributions,orsimplybynumbers.Theeffectsofweightingshapesbyloadingdifferentregionswithhigherdensitiescanbeexploredbysimplyoverlayingthespacesrepresentingtheadditionaldensitiesontotherelevantpolygonsofthecontiguouspolygonsystem,thenproceedingasbefore.Byvaryingthepatternanddensityofcentreswecanexploretheireffectsontotaldistancetravelled,otherthingsbeingequal,indifferentkindsofthree-dimensionalurbansystem.Theeffectsofothernearbysettlementscanalsobeinvestigatedbysimplyaddingthemasextensionstothemodel. Thenumericaldataresultingfromtheanalysisoftheurbansystemcanthenbeusedinanumberofways.First,mostobviously,theparametricdescriptorsforthepolygonsresultingfromanalysis,reflectingastheydothepositionandconfigurationofeach‘finiteelement’inthecitysystemasawhole,thenbecometheframeforotherkindsofdatawhichcanbeassignedasdescriptorstothepolygons.Thiscanbedonewithanyfunctionalvariablethatcanbenumericallyindexedforthatareasuchaspopulationdensities,pollutionlevels,trafficmovement,pedestrianmovement,unemploymentrates,crimerates,counciltaxbanding,andsoon.Becausespatialandotherdescriptorsarenowallinnumericalform,simplestatisticalanalysescanbegintorevealpatterns.Second,thedistributionofanypropertymayberepresentedgraphicallyintheurbansystemasavisualdistributionofthatpropertyinthecitysystem.Thismeans,inpractice,thatallthevisualisingandcartographicalpotentialsthathavebeendevelopedinthepastfewyearsthrough‘geographicinformationsystems’canbeinterfacedwith,andpotentiallybroughtwithinthescopeof,ananalyticmodelwithprovenabilitytolinkmorphologicalandfunctionalpropertiesofbuiltenvironmentsystems,hopefullyinamorepredictiveway. Layeredmodelsarethefutureofconfigurationalmodellingofspace.

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Thesenewtechniquesarisefromtheresultsofresearchoverseveralyearsinwhichvarioustypesofconfigurationalmodellinghavebeenusedfirsttoidentifynon-discursiveregularitiesinthewaysinwhicharchitecturalandurbansystemsareputtogetherspatiallyandidentifythe‘genotypes’ofspatialform;secondtocorrelatethesenon-discursiveregularitieswithaspectsofhowhumanbeingscanbeobservedtofunctioninspace;andthird,tobegintobuildfromtheseregularitiesapictureofhighergeneralityofhowspatialsystemsingeneralareputtogetherandfunctioninresponsetothedemandsthathumanbeingsandtheircollectivitiesmakeofthem.Inthenextchapterweintroducethemostfundamentalofallcorrelateswithspatialconfiguration:humanmovement.NotesH.SimonH,The Sciences of the Artificial,MIT,1969.F.DeSaussureF,Course in General Linguistics,McGrawHill,1966translatedbyC.BallyandA.SechahayewithA.RiedlingerSeepp.9–15(originallyinFrench1915).IthasofcoursebecomefashionabletofollowthelaterWittgenstein’sPhilosophical Investigations (BasilBlackwell1953;Editionused1968)anddenyanysystemicpropertiestosuchthingsaslanguages,andseeinthemonlyshiftingcontingencies.Forexample:‘Insteadofproducingsomethingcommontoallthatwecalllanguage,Iamsayingthatthesephenomenahavenoonethingincommonwhichmakesususethesamewordforall,buttheyareallrelatedtoeachotherinmanydifferentways.Anditisbecauseofthisrelationship,ortheserelationships,thatwecallthemall“language”.’—Wittgenstein,para65.Or:‘Languageisalabyrinthofpaths.Youapproachfromonesideandknowyourwayabout;youapproachthesameplacefromanothersideandnolongerknowyourwayabout’—Wittgenstein,para203.Theuseoftheurbananalogyisinteresting.Aswewillseeinlaterchapters,thisistheonetypeofartefactwhereitcanbeshownquiteclearlythatWittgensteinwaswrong.Thecleareststatementisstillprobablythe‘Overture’toClaudeLévi-Strauss’sThe Raw and the Cooked,JonathonCape,London1970,originallyinFrenchasThe Cru et le Cuit,Plon,1964.Plato,The Republic,forexampleVI,509–11,pp.744–7inPlato,The Collected Dialogues,eds.E.HamiltonandH.CairnsH,PrincetonUniversityPress,BollingenSeries,1961.Seealsoed.F.M.Cornford,The Republic of Plato,OxfordUniversityPress,1941,pp.216–21.Fortheclearestformulation,seeR.Thom,‘StructuralismandBiology’,ined.C.H.Waddington,Theoretical Biology 4,EdinburghUniversityPress,1972,pp.68–82.W.Heisenberg,Physics and Philosophy GeorgeAllen&Unwin,1959p.57.N.Chomsky,Syntactic Structures,Mouton,TheHague,1957.Thereareimportantexceptionstothis,forexampleLévi-Strauss’sattempt,incollaborationwithAndreWeil,tomodelcertainmarriagesystemsasAbeliangroups.SeeLévi-Strauss,The Elementary Structures of Kinship,Eyre&Spottiswoode,1969,pp.221–9.OriginallyinFrenchasLesStructuresElementaire de la Parente,Mouton,1949.

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Forexample,hisingeniousattempttomodeltheelementarypropertiesofmatterthroughthefiveregularsolidsintheTimaeus.SeePlato,Timaeus 33etseq.p.1165inThe Collected Dialogues (seenote5above)ThisprocessisthesubjectofChapter9.Asdescribed,forexample,inChapter2ofThe Social Logic of Space.Foralucidsummary,seeP.Steadman,Architectural Morphology,Pion,1983.L.March,Inconversation.I.StewartandM.Golubitsky,Fearful Symmetry,Penguin,1993,p229.F.BuckleyandF.Harary,Distance in Graphs,AddisonWesley,1990,p.42.B.HillierandJ.Hanson,The Social Logic of Space,CambridgeUniversityPress,1984,p108.Seealsonote16inChapter1.Steadman,p.217.Hillier&Hanson,pp.109–13.However,seethereferencesinnote16ofChapter1.Forexample,I.Biederman,‘Higherlevelvision’,ineds.D.Oshersonetal.,Visual Cognition and Action,MITPress,1990.ForadiscussionofsomeofthesevariationsfromthepointofviewofgraphtheoryseeBuckleyandHarary,Distance in Graphs,pp.179–85.Forexample,P.Tabor,‘Fearfulsymmetry’,Architectural Review,May1982.AbbeMarc-AntoineLaugier,Essai sur l’architecture,Paris1755.SeeHillier&Hanson,The Logic of Space,p90.ItshouldbenotedattheoutsetthattheseoverlappingconvexelementsareunliketheconvexelementsdescribedinThe Social Logic of Space,whichwerenotallowedtooverlap.SeeHillier&Hanson,pp.97–8.Itisexactlythispropertythatlabyrinthsexploit.Ateverypointthespaceyouseegivesnoinformation—ormisleadinginformation—aboutthestructureofthelabyrinthasawhole.Ingeneral—thoughnotinvariably—agoodurbanformdoesexactlytheopposite.SeeChapter4.AlsoB.Hillieretal.,‘Naturalmovement:orconfigurationandattractioninurbanpedestrianmovement,Environment & Planning B, Planning & Design,vol.20,1993.As,forexample,inthecaseofthenewShanghaiCentralBusinessDistrictonwhichwecollaboratedwithSirRichardRogersandPartners,ortheoriginalplanfortheKings’CrossRailwaysLands,LondonwithSirNormanFosterandPartners.SeeforexampleB.Hillier,‘SpecificallyArchitecturalTheory’,HarvardArchitecturalReview,vol.9,1993.AlsopublishedasB.Hillier,‘Specificallyarchitecturalknowledge’,Nordic Journal of Architectural Research,2,1993.TheproblemsgeneratedbythistypeoflayoutareexaminedindetailinChapter5.

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