The Dia­gram as an Abstract Map

Whether graph or chart, the archi­tec­tur­al dia­gram is today an ubiq­ui­tous pres­ence. As graph­ic inscrip­tion of abstrac­tion in space, since the 1990s, the notion of dia­gram has been so much extend­ed that now it near­ly encom­pass­es every aspect of design. To think of the dia­gram as an archi­tec­ture of ideas, (or, more clas­si­cal­ly, the idea of archi­tec­ture), means to be still ensconced in some sort of pla­ton­ic con­cep­tions.1 To avoid this trap, a first step would be to turn to Gilles Deleuze’s notion of the dia­gram as an abstract map, and to show how the mod­el acquires its mean­ing, specif­i­cal­ly when con­front­ed with bio­log­i­cal par­a­digms. Such under­stand­ing may lead to a bet­ter com­pre­hen­sion of the present algo­rith­mic nature of dia­grams. These script­ed pro­ce­dures refer to form, or, more pre­cise­ly, to process­es of mor­pho­gen­e­sis. Their aim is to enhance a mod­u­la­tion between nat­ur­al com­po­nents, phys­i­cal ele­ments, and archi­tec­tur­al design. A range of prac­tices (or pro­to­cols), based on adapt­able (cus­tom­able) soft­ware, capa­ble of pro­duc­ing chang­ing modal­i­ties of a struc­tur­al topol­o­gy dri­ven by per­for­mance, are cur­rent­ly avail­able.2 For instance, address­ing the issue of the use of genet­ic algo­rithm in design, Manuel De Lan­da, inspired by Deleuze’s work, has pro­posed to intro­duce three the­o­ret­i­cal lev­els of com­plex­i­ty: to think in terms of pop­u­la­tion (not the indi­vid­ual); to think in terms of dif­fer­ences of inten­si­ty (ther­mo­dy­nam­ic and entrop­ic); last­ly, to think in terms of topol­o­gy.3 The ques­tion addressed here will be there­fore to know if (and how) the dia­gram is able to topol­o­gise the var­i­ous fields of design.4

Morphogenesis

As Deleuze writes in Dif­fer­ence and Rep­e­ti­tion (1968), we live in a world dom­i­nat­ed, by ​“a com­plete­ly oth­er dis­tri­b­u­tion which must be called nomadic, a nomad nomos, with­out prop­er­ty, enclo­sure or mea­sure.” 5 The prob­lem today is no longer the dis­tri­b­u­tion of things and divi­sion of per­sons in seden­tary spaces, ​“but rather a divi­sion among those who dis­trib­ute them­selves in an open space – a space which is unlim­it­ed, or at least with­out pre­cise lim­its. … To fill a space, to be dis­trib­uted with­in it, is very dif­fer­ent from dis­trib­ut­ing the space.”6 The leap from seden­tary struc­tures of rep­re­sen­ta­tion to nomadic dis­tri­b­u­tion, brings unset­tling dif­fi­cul­ties, tran­scend­ing all lim­its, and deploy­ing ​“an errant and even ​‘deliri­ous’ dis­tri­b­u­tion”.7 Seden­tary dis­tri­b­u­tions, good sense, and com­mon sense, are all based upon a syn­the­sis of time, which has been deter­mined as that of habit.8 On the oth­er hand, nomadic struc­tures lead to ​“mad repar­ti­tions …, mad dis­tri­b­u­tion – instan­ta­neous, nomadic dis­tri­b­u­tion, crowned anar­chy or dif­fer­ence.”9 Such is the state that physics described in ther­mo­dy­nam­ics, from Sadi Carnot to Rudolf Clau­sius and Lud­wig Boltz­mann (whose equa­tion described the dif­fu­sion of gas par­ti­cles on a sta­tis­ti­cal method): that is, entropy.10

For Deleuze, it is nec­es­sary to rec­og­nize the pri­ma­cy of mul­ti­ple forces upon the form. In Dif­fer­ence and Rep­e­ti­tion, he iden­ti­fies this link between forces and forms as the two vec­tors of dif­fer­ence, using Hen­ri Berg­son and Gilbert Simon­don as sources.11 For Simon­don, the indi­vid­u­a­tion of the crys­tal is the phys­i­cal for­ma­tion obtained by a dif­fer­ence in poten­tial. This dif­fer­ence is the entrop­ic arrow between ten­sion and mat­ter (as in a crys­tal).12 Deleuze trans­lates this dif­fer­en­ti­a­tion in terms of oscil­la­tion, a simul­ta­ne­ous vibra­tion between the actu­al and the vir­tu­al, which are coex­is­tent. Over­com­ing Bergson’s oppo­si­tion between mat­ter and dura­tion, he trans­pos­es the arrow of inten­si­ty into a mod­el of the coex­is­tence of the vir­tu­al and the actu­al.13 Both states are real, but the actu­al char­ac­ter­izes the com­plet­ed indi­vid­ual, such as the mate­ri­al­ized crys­tal, while the vir­tu­al refers to the prob­lem­at­ic field of the pre-indi­vid­ual, when the inten­sive dif­fer­en­ti­a­tion is not yet actu­al­ized. To illus­trate this, Deleuze, fol­low­ing Simon­don, uses the mod­el of an egg, the par­a­digm of an inten­sive body, lit­er­al­ly a body with­out organs, because it is a body going through phas­es of dif­fer­en­ti­a­tion.14

Actu­al­iza­tion occurs in things through a process of dif­fer­en­ti­a­tion. Embry­ol­o­gy shows that the divi­sion of an egg into parts is sec­ondary in rela­tion to more sig­nif­i­cant mor­pho­genet­ic move­ments. Deleuze describes the kine­mat­ics of an egg, going through its var­i­ous process­es.15 The dif­fer­en­ti­a­tion of species and parts pre­sup­pos­es a whole set of spa­tio-tem­po­ral dynam­ics: ​“The entire world is an egg.”16 How­ev­er, if the world is an egg, then the egg itself is a the­ater: a stage with actors, spaces, and ideas, and where a spa­tial dra­ma is played. To sub­stan­ti­ate this con­clu­sion, Deleuze employs mul­ti­ple sources, includ­ing Éti­enne Geof­froy Saint-Hilaire’s the­sis on the kinet­ics of the fold; and Karl von Baër’s hypoth­e­sis on mor­pho­genet­ic move­ments, includ­ing the stretch­ing of cel­lu­lar lay­ers, invagi­na­tion by fold­ing, and the ori­en­ta­tion and axis of move­ment, all to be found in the kine­mat­ics of the egg.17 In addi­tion, Deleuze men­tions Charles Man­ning Child’s gra­di­ent the­o­ry, which offered a frame­work for think­ing about for­mal arrange­ment, and Paul Weiss’s par­a­digm of amphib­ian gas­tru­la­tion, pre­sent­ed in his 1939 book Prin­ci­ples of Devel­op­ment, which elu­ci­dates how mor­pho­genet­ic process­es were capa­ble of shap­ing form.18

In phi­los­o­phy, the main source was the work of Ray­mond Ruy­er, who, inspired by Jakob von Uexküll’s eti­ol­o­gy,19 had elab­o­rat­ed a phi­los­o­phy of dif­fer­en­ti­a­tion already in 1939. For Ruy­er, in every domain, form is endowed with a prop­er rhythm.20 In his 1958 book, The Gen­e­sis of Liv­ing Forms, Ruy­er dis­cuss­es the spa­tio-tem­po­ral dynamism in cel­lu­lar migra­tion and makes a dis­tinc­tion between mor­phol­o­gy and mor­pho­gen­e­sis: ​“Mor­phol­o­gy, the study of forms and their arrange­ments, … does not present any fun­da­men­tal dif­fi­cul­ty”, because it relies on vision and descrip­tion, while mor­pho­gen­e­sis, ​“presents … the max­i­mum of dif­fi­cul­ty and mys­tery.”21 If Deleuze acquired ideas about spa­tial drama­ti­za­tion and the mys­tery of dif­fer­en­ti­a­tion from Ruyer’s opus, it is not clear whether the two philoso­phers agreed that the vir­tu­al did not dis­ap­pear once indi­vid­u­a­tion (and dif­fer­en­ti­a­tion) were com­plet­ed.22 For Deleuze, form is not what remains of a phys­i­cal action, nor is it the result of a deplet­ed force: it is the out­come of a pro­vi­sion­al state of equi­lib­ri­um between forces.23

As pre­vi­ous­ly indi­cat­ed, in Dif­fer­ence and Rep­e­ti­tion, Deleuze attempt­ed there­fore to draw a the­o­ry of dif­fer­ence, in part based on bio­log­i­cal dif­fer­en­ti­a­tion, giv­ing a new mean­ing to the ancient mytholo­gies of the world egg, begin­ning with Anaximander’s cos­mic egg, while he also pro­vid­ed a renewed inter­pre­ta­tion of William Harvey’s 1651 bio­log­i­cal dic­tum ex ovo omnia (“every­thing comes from the egg”): ​“In order to plumb the inten­sive depths or the spatium of an egg, … the poten­tials and poten­tial­i­ties must be mul­ti­plied. The world is an egg. … We think that dif­fer­ence of inten­si­ty, as this is impli­cat­ed in the egg, express­es first the dif­fer­en­tial rela­tions or vir­tu­al mat­ter to be orga­nized.”24 More­over, span­ning a bridge between their the­o­ries, Deleuze relied also on Bel­gian biol­o­gist Albert Dalcq’s mor­pho­genet­ic embry­ol­o­gy,25 in addi­tion to Simondon’s the­o­ry of indi­vid­u­a­tion. Dalcq’s epi­ge­n­e­sis offered a mod­el for the dif­fer­en­ti­a­tion modus operan­di, which was at the heart of Deleuze’s the­sis. The pop­u­lar­i­ty of Dalcq’s work, in the 1950s among artists and archi­tects, was equal to that of D’Arcy W. Thompson’s On Growth and Form (1917). More a treaty on mor­phol­o­gy than a mor­pho­genet­ic the­o­ry, D’Arcy Thompson’s vol­ume argued that evo­lu­tion had been overem­pha­sized as the fun­da­men­tal deter­mi­nant of the forms of liv­ing beings, and pro­posed mechan­i­cal process­es of trans­for­ma­tion as equal­ly impor­tant in the shap­ing of life.26

It is note­wor­thy that Albert Dalcq’s book on embry­ol­o­gy was the pri­ma­ry source on epi­ge­n­e­sis, as much for the design­ers behind the exhi­bi­tion, ​“On Growth and Form,” held at the Insti­tute of Con­tem­po­rary Arts in Lon­don in 1951, the title of which was inspired by the new edi­tion of D’Arcy Thomp­son, On Growth and Form (1944), as for Gilles Deleuze.27 Read through the glass­es of the philoso­phies of Spin­oza, Leib­niz and Berg­son, Simondon’s the­o­ry of indi­vid­u­a­tion helped to iden­ti­fy the egg as a vast metaphor of the world. If Deleuze’s phi­los­o­phy of nature could antic­i­pate the sci­ence of his time, it is because he suc­ceed­ed in iden­ti­fy­ing the con­tem­po­rary metaphors that but­tressed his con­cep­tu­al­iza­tions, the par­a­dig­mat­ic shifts that were enact­ed, togeth­er with the sig­nif­i­cant epis­temic break­throughs. Posi­tioned (as he was) in oppo­si­tion to the over­cod­ed trends of Struc­tural­ism, and, at the same time, implic­it­ly con­trast­ing hard-nosed geneti­cists that read only in codes, Deleuze intro­duced the egg’s metaphor that helped reartic­u­late the con­nec­tion between the sym­bol­i­cal and the vital. With­out enter­ing the con­tem­po­rary debate on biol­o­gy and genet­ics, it seems that Deleuze the­o­ry was not far from the posi­tion sus­tained by the Amer­i­can Stephen Jay Gould’s 1977 Ontoge­ny and Phy­loge­ny.28

Deleuze will often use the embryo’s mod­el to expose the inor­gan­ic vital­i­ty of tis­sues, not yet sta­bi­lized in the shape of an organ, capa­ble of mul­ti­ple trans­for­ma­tions: “… the body with­out organs does not lack of organs, it sim­ply lacks the organ­ism, that is, the par­tic­u­lar orga­ni­za­tion of organs. The body with­out organs is thus defined by an inde­ter­mi­nate organ, where­as the organ­ism is defined by deter­mi­nate organs.” 29 In Deleuze’s The Log­ic of Sense (1969), every­thing will col­lapse around the par­a­digm of Antonin Artaud, whose poet­i­cal, schizoid delir­i­um called for a body beyond its organ­ic deter­mi­na­tion.30 For Artaud, the com­plet­ed organ­ism felt like a form that impris­ons the body.31 Dur­ing the 1970s, Deleuze and Guat­tari will nev­er ask any­body to deprive him­self of its organs, but to replace the notion of a full-grown organ by the meta­mor­phic and poly­mor­phic con­cep­tion of an imma­ture organ while it dif­fer­en­ti­ates. Deleuze’s bio-phi­los­o­phy illus­trates the vir­tu­al­i­ty of inten­sive forces, while they oper­ate before the organ­ic form is achieved and con­sti­tut­ed. What Deleuze and Guat­tari pro­posed was to con­sid­er the vir­tu­al axes of infor­mal forces.32

Resist­ing the Neo-Pla­ton­ism of types and mod­els, Deleuze believed that what exists in the world’s imma­nence is not the copy of a mod­el that would con­sti­tute the ide­al mold of real indi­vid­u­als; that what is real is not the one and unique, or tran­scen­den­tal, but the sin­gu­lar­i­ties and the dif­fer­ences. The ide­al mold is sim­i­lar to the ide­al type in art his­to­ry, art, or design. Simon­don elab­o­rat­ed a pre­cise crit­i­cism of the idea of a mold by intro­duc­ing the con­cept of mod­u­la­tion. In mod­u­la­tion, Simon­don writes ​“there is nev­er time to turn some­thing out, to remove it from the mold.”33 To pro­ceed to such a demold­ing (Fr., démoulage) is unnec­es­sary, ​“because the cir­cu­la­tion of the sup­port of ener­gy is equiv­a­lent to a per­ma­nent turn­ing out; a mod­u­la­tor is a con­tin­u­ous, tem­po­ral mold.” 34 While mold­ing leads to a per­ma­nent state of things, mod­u­la­tion intro­duces the fac­tor of time: ​“To mold is to mod­u­late in a defin­i­tive man­ner, to mod­u­late is to mold in a con­tin­u­ous and per­pet­u­al­ly vari­able man­ner.”35 Through­out his work, Deleuze also rec­om­mends alter­ing the idea of mold­ing by intro­duc­ing that of mod­u­la­tion. In 1978, for exam­ple, he affirmed: ​“Every direc­tion leads us, I believe, to stop think­ing in terms of sub­stance-form.”36 Tak­ing up Simondon’s crit­i­cism of hyle­mor­phism, oppos­ing inert mat­ter to active form, he pro­posed to sub­sti­tute it with a process of mod­u­la­tion, in which the form-giv­ing oper­a­tion would be con­ceived as the cou­pling of forces and mate­ri­als. While this the­o­ry helped Deleuze to escape from resem­blance, oppos­ing the idea that a mod­el needs to be copied, he reached a new def­i­n­i­tion of artis­tic activ­i­ties, as the cap­ture of inten­sive forces by new mate­ri­als: ​“The mate­r­i­al-force cou­ple replaces the mat­ter-form cou­ple.”37 Con­tem­po­rary sci­ence shows that geno­type is not a mold that deter­mines the indi­vid­ual in a uni­vo­cal mode. Between the geno­type and the phe­no­type, a process of devel­op­ment inserts itself, where the tem­po­ral vari­able plays a role as impor­tant as the spa­tial and topo­log­i­cal vari­ables.38 The struc­ture actu­al­izes itself through a process of devel­op­ment, intro­duc­ing fac­tors of sto­chas­tic and tem­po­ral vari­abil­i­ty that sin­gu­lar­ize the indi­vid­ual pro­to­type. As should be clear, Deleuze’s think­ing was not based on vague metaphors or rhetor­i­cal tropes.39 If one can speak of metaphors, it is in the noblest sense, since they were able to grasp the­o­ret­i­cal issues even in domains that had not yet been clear­ly per­ceived by sci­ence itself.

Intensive Diagram

The body with­out organs con­veys the notion of mat­ter in a not-yet-formed state, of a body not-yet-rep­re­sent­ed, or an unrep­re­sentable body in its schiz­o­phrenic ver­sion. Over­com­ing orga­nized form, one is intro­duced to mat­ter as a recep­ta­cle of forces. Beyond the mat­ter-form oppo­si­tion, beyond orga­nized form, there is mat­ter as a non-for­mal mix of forces and mate­ri­als. More than a metaphor, the body with­out organs refers to the notion of machine and of dia­gram, devel­oped, in par­al­lel, in the work of Michel Fou­cault, of which Deleuze is a keen inter­preter. The dia­gram is a map, which is coex­is­tent with the whole soci­ety, and forms an ​“abstract machine.”40 Deal­ing with flux­es, flu­ids, func­tions, it churns up mat­ter, form, ener­gy, net­works. Every dia­gram is a ​“dif­fer­ent machine.”41 Such a machine is con­cerned with the rep­re­sen­ta­tion of rela­tion of forces, belong­ing to a strat­i­fied for­ma­tion, and it dou­bles the strat­i­fi­ca­tion (for exam­ples, the stra­ta of his­to­ry and of soci­ety). This inten­sive dia­gram should not be con­ceived as a per­ma­nent struc­ture, nor thought as a pre-exist­ing form, but rather as a vir­tu­al prob­lem — that is, a com­plex of forces.42 One could define a Pas­toral dia­gram, a Greek one, a Roman one, or a Feu­dal one.43 Or even a Baroque dia­gram. The dia­gram, how­ev­er, is not his­tor­i­cal, but belongs to a phe­nom­e­non of becom­ing: ​“it dou­bles his­to­ry with a sense of con­tin­u­al becom­ing (devenir).” 44 As Deleuze remarks in near­ly all of his books: ​“There is … a becom­ing of forces which remains dis­tinct from the his­to­ry of forms … It is an out­side which is far­ther away than any exter­nal world and even any form of exte­ri­or­i­ty.”45 Indis­so­cia­ble from its actu­al­iza­tion, the dia­gram is used to inject some becom­ing in every point of the strat­i­fied real­i­ty.46 The con­cept of the dia­gram as an abstract machine helps us to under­stand the bio­log­i­cal and machine-like real­i­ty of so many stra­ta, such as insti­tu­tions, tech­nolo­gies, and appa­ra­tus­es; includ­ing het­ero­topias.47 More­over, it can help char­ac­ter­ize works of art, includ­ing Proust’s In Search of Lost Time, Artaud’s schizo-poet­ics, or Fran­cis Bacon’s exhi­bi­tion of the flesh. The dia­gram offers the tools to map art’s phy­la and genus, its phy­lo­ge­n­e­sis as much as its heterogenesis. 

Sub­se­quent­ly, one reach­es what Deleuze defined as ​“Foucault’s Dia­gram”, a sort of dia­gram of a dia­gram, if not a mas­ter dia­gram, divid­ed by a line between an out­side and an inside, the lat­ter being made of strate­gic zones and con­struct­ed of lay­ers or stra­ta, in which texts and images from the past are archived. In the scheme drawn by Deleuze, there is a gigan­tic fold, which indi­cates the posi­tion of one­self in rela­tion to the task of pro­duc­ing new modes of sub­jec­ti­fi­ca­tion. This way, three agen­cies (or instances) are being held togeth­er by a fold, which acts as topo­log­i­cal oper­a­tor.48 Out­side and inside are invert­ed. Far and near con­verge. Accord­ing to Deleuze, for Fou­cault, Descartes’s, ​“I think, there­fore I am,” should be replaced by the renewed for­mu­la­tion, I think, there­fore I fold: ​“The gen­er­al topol­o­gy of thought … ends up in the fold­ing of the out­side into the inside.” 49 The urgent pre­req­ui­site is to con­struct an inside-space that is com­plete­ly co-present with the out­side-space, ​“on the line of the fold.”50 Inde­pen­dent of dis­tance and with­in the lim­its of any vital, lived space, ​“Every inside-space is topo­log­i­cal­ly in con­tact with the out­side-space … and this car­nal or vital topol­o­gy, far from show­ing up in space, frees a sense of time that fits the past into the inside, brings about the future in the out­side, and brings the two into con­fronta­tion at the lim­it of the liv­ing present.”51 As Deleuze states, this is how Fou­cault grasps the dou­bling, or the fold: ​“If the inside is con­sti­tut­ed by the fold­ing of the out­side, between them there is a topo­log­i­cal rela­tion: the rela­tion to one­self is homol­o­gous to the rela­tion with the out­side and the two are in con­tact, through the inter­me­di­ary of the stra­ta which are rel­a­tive­ly exter­nal envi­ron­ments (and there­fore rel­a­tive­ly inter­nal).”52

It is pos­si­ble to immerse one­self in an archive made of vis­i­ble forms and artic­u­late bod­ies; to cross sur­faces, graphs, charts, and curves; and to fol­low fis­sures in order to reach an inte­ri­or of the world. But at the same time it is also nec­es­sary to climb above the stra­ta in order to reach an out­side, an atmos­pher­ic ele­ment: ​“The infor­mal out­side is a bat­tle, a tur­bu­lent, stormy zone where par­tic­u­lar points and the rela­tions of forces between these points are tossed about. Stra­ta mere­ly col­lect­ed and solid­i­fied the visu­al dust and the son­ic echo of the bat­tle rag­ing above them.” 53 Nev­er­the­less, for Deleuze, ​“up above, the par­tic­u­lar fea­tures have no form and are nei­ther bod­ies nor speak­ing per­sons.” 54 For both Fou­cault and Deleuze, the dia­gram is a ​“micro-physics.”55 How­ev­er, read by Deleuze, Foucault’s dia­gram lives a new life. Ris­ing above the sta­t­ic oppo­si­tion between form and mat­ter, sit­u­at­ing one­self in an ener­getic dimen­sion, it becomes pos­si­ble to think mate­ri­al­i­ty in terms of move­ment and forces, and intro­duce a poten­tial of defor­ma­tion active in the material. 

As Deleuze wrote, to have some­thing stand up ​“does not mean hav­ing a top and a bot­tom or being upright”.56 One can draw ​“a mon­u­ment, but one that may be con­tained in a few marks or a few lines, like a poem by Emi­ly Dick­in­son”.57 Fol­low­ing this remark, it would be pos­si­ble to attempt to write a brief his­to­ry of the line, say, from William Hogarth’s ​“line of beau­ty” (1753) to Hen­ry van de Velde’s line as a force, to Paul Klee’s inflect­ed lines,58 and up to the topol­o­gy of splines used in 2‑D/3‑D mod­el­ing. Already in the 1950s, while oppos­ing the Pla­ton­ism of Col­in Rowe, Reyn­er Ban­ham advo­cat­ed a topo­log­i­cal archi­tec­ture.59 Sud­den­ly, what formed the basis of the tra­di­tion­al cat­e­gories of space sees its mean­ing trans­formed, by trans­mu­ta­tion, into a topo­log­i­cal con­tact surface. 

Fluid Spaces

Today, a ques­tion remains: how have topo­log­i­cal con­cepts been intro­duced in archi­tec­ture? Per­haps, a par­tic­u­lar­ly refined topol­o­gy is need­ed to describe the for­ma­tion of spi­rals and vor­tices, or nomadic, smooth spaces, which are formed by hap­tic rela­tions. As Deleuze and Guat­tari put for­ward, haec­ceities are to be found along inter­sect­ing lines: ​“Cli­mate, wind, sea­son, hour … Haec­ce­ity, fog, glare. A haec­ce­ity has nei­ther begin­ning nor end, ori­gin nor des­ti­na­tion; it is always in the mid­dle; it is not made of points, only lines. It is a rhi­zome.”60 From there, the well-known dis­tinc­tion between a nomad, ​“smooth” space, as opposed to a seden­tary, ​“stri­at­ed” con­di­tion will be devel­oped by Deleuze and Guat­tari: “… There is an extra­or­di­nary fine topol­o­gy that relies not on points or objects, but on hac­ceities, on sets of rela­tions (winds, undu­la­tions of snow or sand, the song of the sand or the creak­ing of ice, the tac­tile qual­i­ties of both); it is a tac­tile space, or rather ​‘hap­tic’, a sonorous much more than a visu­al space. … The vari­abil­i­ty, the polyvo­cal­i­ty of direc­tions, is an essen­tial fea­ture of smooth spaces of the rhi­zome type … The nomad, nomad space, is local­ized and not delim­it­ed. What is both lim­it­ed and lim­it­ing is stri­at­ed space.” 61 Deleuze, inspired as always by Simon­don, revived the con­cept of haec­ce­ity devel­oped in Duns Scott’s scholas­tic phi­los­o­phy. Haec­ce­ity stems from the Latin haec­ceitas, mean­ing ​“this-ness”, from Haec, ​“this thing.” 

As it were, haec­ce­ity, or indi­vid­u­a­tion, helped to explain the exis­tence of par­tic­u­lar indi­vid­u­als. With Scott, such a con­cep­tion opposed to the Aris­totelian the­o­ry of hyle­mor­phism, which held that any indi­vid­ual being was the cre­ation of dynam­ic form applied on indis­tinct mat­ter, as if nature’s cre­ations were the out­come of a sculp­tor mold­ing clay. Derived from the Greek, hyle­mor­phism (or hylo­mor­phism) referred to the impo­si­tion of an active form (mor­phe) onto pas­sive mat­ter (hyle). Scott refut­ed this the­o­ry, reject­ing the sug­ges­tion that deter­mi­nate, indi­vid­ual beings could be the out­put of inde­ter­mi­nate mat­ter. As pre­vi­ous­ly men­tioned, Simon­don will crit­i­cize hyle­mor­phism for its uni­ver­sal­is­tic, sta­t­ic, and frozen approach, and instead define indi­vid­u­a­tion as an ongo­ing process that con­sists pre­cise­ly of a mod­u­la­tion between form and infor­ma­tion.62 For both Simon­don and Deleuze, one should con­sid­er care­ful­ly the spe­cif­ic process­es of becom­ing-indi­vid­ual, encom­pass­ing the sin­gu­lar­i­ty in each being.63

For Deleuze, haec­ce­ity is not lim­it­ed to any ques­tion of scale (small or large), but has a pecu­liar con­sis­ten­cy which con­nects it phys­i­cal­ly to phe­nom­e­non, such as vapor, haze, mist or cloud sit­u­a­tions that blur any defined lim­it or bor­der. Haec­ce­ity con­stel­lates, form­ing groups, clus­ters and flocks. Inspired by Pierre Boulez’s the­o­ry of music, Deleuze and Guat­tari write: ​“the mod­el is a vor­ti­cal one; it oper­ates in an open space through­out which things-flows are dis­trib­uted, rather than plot­ting out closed space for lin­ear and sol­id things. It is the dif­fer­ence between a smooth (vec­to­r­i­al, pro­jec­tive or topo­log­i­cal) space and a stri­at­ed (met­ric) space.” 64 In the first case, space is occu­pied with­out being mea­sured, while in the sec­ond space is mea­sured in order to be occu­pied, a dis­tinc­tion tak­en from Boulez. Like a flock, smooth, ​“nomad” art cir­cu­lates in an open and con­nect­ed space, as opposed to a stri­at­ed, geo­met­ri­cal art, cen­tered and self-con­tained. It is actu­al­ly two dif­fer­ent usages of mea­sure: smooth space relies on a ​“num­ber­ing num­ber [which] is rhyth­mic, not har­mon­ic. It is not relat­ed to cadence or [an exter­nal] mea­sure,”65 while stri­at­ed space is based on a homo­ge­neous mea­sure, mark­ing out the sur­face in squares and rear­rang­ing every­thing in order. This obser­va­tion helps tell apart an abstract line, unfold­ing its smooth space from a set of twists and tor­sions — that is, from a stri­at­ed space sub­ject to norms and orthog­o­nal­ly squared by rules.66

Deleuze had read Wil­helm Wor­ringer​’s Abstrac­tion and Empa­thy (1907).67 He was con­vinced that Wor­ringer had giv­en fun­da­men­tal promi­nence to the abstract or prim­i­tivis­tic line ​“see­ing it as the very begin­ning of art or the first expres­sion of artis­tic will. Art as abstract machine.”68 Pur­su­ing the inves­ti­ga­tion, Wor­ringer pub­lished Form in Goth­ic (1911),69 a psy­cho­log­i­cal inves­ti­ga­tion of style, pre­sent­ed by him as a sequel to Abstrac­tion and Empa­thy. Deleuze read also Form in Goth­ic and repeat­ed­ly quot­ed it from the French trans­la­tions:70 ​“From the depths of time there comes to us what Wor­ringer called the abstract and infi­nite north­ern line, the line of the uni­verse that forms rib­bons, strips, wheels, and tur­bines, an entire ​‘vital­ized geom­e­try,’ ris­ing to the intu­ition of mechan­i­cal forces, con­sti­tut­ing a pow­er­ful nonor­gan­ic life.”71 What dif­fer­en­ti­ates the nomadic line from clas­si­cal orna­men­ta­tion are the par­a­digms of speed, of pro­lif­er­a­tion, and of accel­er­at­ed trans­for­ma­tion, which all are char­ac­ter­is­tics of smooth space. In such a space, the line is free from rep­re­sen­ta­tion­al pur­pos­es, as well as untied from the laws of met­rics; as such, it is lib­er­at­ed from clas­si­cal sym­me­try, from the rep­e­ti­tion of the motif, and from the stri­a­tions of ratio­nal coor­di­nates. All these char­ac­ter­is­tics belong to Renais­sance archi­tec­ture, which make it a sta­ble, clas­si­cal and ​“organ­ic” art. 

Fol­low­ing Wor­ringer, Deleuze reveals defin­i­tive­ly an anti­clas­si­cal bend, and shows a pref­er­ence for the north­ern line that swells by indef­i­nite iter­a­tion. Moved by a prin­ci­ple of inter­nal pro­lif­er­a­tion, the line fol­lows the mod­el of flu­ids, not solids: ​“The pic­to­r­i­al line in Goth­ic paint­ing is com­plete­ly dif­fer­ent, as is its geom­e­try and fig­ure. First of all, this line is dec­o­ra­tive; it lies at the sur­face, but it is a mate­r­i­al dec­o­ra­tion that does not out­line a form. It is a geom­e­try … in the ser­vice of ​‘prob­lems’ or ​‘acci­dents,’ abla­tion, adjunc­tion, pro­jec­tion, inter­sec­tion. It is thus a line that nev­er ceas­es to change direc­tion, that is bro­ken, split, divert­ed, turned in on itself, coiled up, or even extend­ed beyond its nat­ur­al lim­its, dying away in a ​‘dis­or­dered con­vul­sion’”72 Potent­ly ​“inor­gan­ic”, the line is set in motion by a mechan­i­cal mobil­i­ty, whose redun­dan­cy and potent vital­i­ty is to be found in bar­bar­ic arts up to the Goth­ic. Worringer’s book described so accu­rate­ly the Goth­ic line of non-organ­ic life that the infi­nite melody of the north­ern line offered a pre­cise basis for Deleuze’s kinet­ic line.73 From A Thou­sand Plateaus and The Log­ic of Sen­sa­tion, to What is phi­los­o­phy?, the bore­al-north­ern line will be used by Deleuze (and Guat­tari) to frame prob­lems, for exam­ple, the organ­ic and the non-organ­ic, and also to map the­o­ret­i­cal issues such as the smooth and the stri­at­ed spaces, the nomad and the seden­tary, and so forth. In Deleuze’s The Fold, mutat­ing itself into a baroque fea­ture, the nomadic line will be defined as the becom­ing-line of the point, which unfolds in a tra­jec­to­ry.74 As an out­come, nomadic lines take on great vor­ti­cal orga­ni­za­tions, prop up smooth topo­log­i­cal spaces, and allow for a speed of pro­lif­er­a­tion that expands beyond the frame. The aim of art is to divert force into mat­ter. What sets apart the nomadic line, whether from the north­ern-goth­ic vari­ety or from the baroque type, is that it embod­ies speed and flu­id­i­ty, while it cap­tures intense forces in new materials.

What are the con­se­quences for today’s archi­tec­ture? At present, through cus­tomized infor­ma­tion­al engines, it seems imper­a­tive to incor­po­rate inten­sive ele­ments into the vir­tu­al build­ing. Such an exper­i­men­tal approach aims at defin­ing design solu­tions in response to a wide range of struc­tur­al and envi­ron­men­tal para­me­ters. Dur­ing the process, ele­ments of struc­tur­al engi­neer­ing, such as dis­tri­b­u­tion of stress­es and the entire load bear­ing data, are tak­en into account, accord­ing to fit­ness cri­te­ria, pri­or to being select­ed by the design­er in terms of their aes­thet­ic apt­ness. Cur­rent spe­cif­ic dig­i­tal tech­nolo­gies, such as topo­log­i­cal opti­miza­tion soft­ware, are based on weight and mate­r­i­al effi­cien­cy mod­el, gen­er­at­ed through an iter­a­tive process.75 Once a base con­di­tion is estab­lished, the soft­ware runs mul­ti­ple iter­a­tions and then ana­lyzes them to deter­mine a best solu­tion. The ini­tial design is based on giv­en para­me­ters, and then is com­put­ed by the appli­ca­tion, allow­ing an opti­mized solu­tion to be deter­mined.76 Such a mode offers the pos­si­bil­i­ty to inte­grate the exper­tise of design­ers and engi­neers on a unique com­pu­ta­tion­al plat­form. Infor­ma­tion, which deter­mines the for­mal con­cretiza­tion of archi­tec­ture, is script­ed to nego­ti­ate between form and mat­ter, or, more pre­cise­ly, between forces and mate­ri­als. Such script­ed pro­ce­dures are akin to Simondon’s ​“mod­u­la­tion”*.77 If evolved archi­tec­tur­al struc­tures are to enjoy the same degree of com­bi­na­to­r­i­al pro­duc­tiv­i­ty as bio­log­i­cal ones, they must be ini­tial­ized by an ade­quate dia­gram, as an ​“abstract” or vir­tu­al build­ing*.78 At this point, the design departs from the con­ven­tion­al prac­tices, engag­ing a com­plex of forces of which one must trace the dia­grams, whether ener­getic, sys­temic, or topological.