THE MODULOR IN THE MIRRCJR

A Thesis Submitted to the Faculty of Graduate Studies and Rasearch in Parüal Fuffilment of the Requirements for the Degm of Master of Architecture.

TANIA MARA GUERRA DE OLIVEIRA

School of Architecture McGill University

Montréal August, t 999.

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AESTRACT

This essay discusses Le Corbusiets Modulor through its appearance

in the Podme de l'angle droit. The Poéme reveals the aichitect's later

thinking in a synthetic and prease way, offenng precious help for its

comprehension. A study of the Modulor in such wntext demonstrates

that it was more than an attempt to develop a modular methaâology.

Embodied in the Poème, the Modulor disdoses Le Corbusiet's

struggle to create a framework for his praûice, providing invaluable

insights into our present condition.

Cette essai discute le Modulor 4 travers son insertion dans le Poème

de L'angle Droit. Le Poème indique la pensée postérieure de

I'architede d'une voie synthétique et précise, ofkant raide précieuse

pour sa compréhension. Une étude du Modulor dans une tel contexte

démontre qu'il Mit plus qu'une tentative de développer une

méthodologie modulaire. Inserée dans le Poème, le Modulor &v&k la

lutte de Le Corbusier pour rendre ça pratique significatif, fournissant

de perspicacitth de valeur inestimable dans Tétat actuel de

l'architecture.

A few persons have contributecl to maâe this wark possible and 1 would

Iike to express my sincere gratitude to them.

t am thanldul to Dr. Alberto PBrez-Gdmer, my thesis advisor, for his

patience and guidance in the earty steps of this research, and also for

his insights and invaluable comments during the course of the w o k

Swal thanks tb rny colleagues Dion Wilson, Jose Thevercad and

Khaldmn Ahmad for some very helpful comrnenis, and to Claudia

Migaire, for proof-reading the final version of the present work.

My thanks also goes ta Susie Spurdens for being a h y s available for

help or simply for a nice talk, and to Marcia King, Helen Dyer and

Kattileen Innes-Prevost for their help with administrative matters.

My special gratitude goes to my mother, Cleusa Guerra, for the love

and care she dedicated to both me and my liile baby, so that I could

have the peaœ of mind to finish this work, and to my father, Antonio

Guerra, for his love and support

Finally, I thank my husband, Ma& Oliveira for his unresenred love

and friendship, as well as feir his unfailing support and encouragement,

and my son, Alewndre, for gMng me his support in the forrn of

beautiful srniles. Ta them I ded'kate mis work.

CONTENTS

a THE MODULOR AND ICON 82: THE MIUD 1 0

FINAL REMARUS:

THE MODULOR IN THE MIRRQR

(Unless indfcated. all fiqurse and drrnnings by Le Carbusisr)

Fig.1 - Chape1 of Ronchamp. wuîh fac..de, 'showing the shadaw profile of a bulrs head which occurs in the evening', and painting Taumaux Xlll (Pentecorte '56 and Naissance du Minotaure), from Jaime Coll. 'Stntdurs and Play in Le Corbusier's Art Works.'

Fig.2 - Regulaiing lines from a painting and facade of the skyscraper at Algien. from Le Corbusier, Modulor 1 and Pmubions on th Pmsant State d Amhitectum end CXy Planning, rwpedively.

Fig.3 - Wooden sadpture Ozon, 1947, by Le Carbusier and Joseph Savinas, f m Christopher Pearson. 'Le Corbusier and the Acoratical Trope.'

Fig.4 - Cover page, fmrn Le Corbusier. M m cb i'angie cimit, 1955.

Fig.5 - Iconostase, from Le Corbusier, Podm de l'angle droit, 1955.

Fig.6 - Painting and sketches showing the genesir of the Taumaux series, fmm Jaime Coll, 'Strudure and Play in Le Corbusiefs Art works:

Fig.7 - lcan 82: The Mind and nspedive poam. fmm Le Corbusier, Padnnr db i'angk dmit, 11955.

Fig.8 - lcon A3: Milieu and respecüve poem. h m Le Corbusier, P d m ds l'angle dmit, 1955.

Fig.9 - lcon G3: Tool and feqwcüwe p m , from Le Corbusier, Pdme ds lbngk dm& 1955.

Fig.10 - lcon 02: The Mind, fmm Le Carbusier, Podm ds l'angle droit, 1955.

Fig.11 - Drawing of the Modulor qsiem, from Le Corbusier, Modulor 1,1943.

Fig.12 - Sketch of a tres, ftom Le Corbusier, Piacisons on the Pissent State of Atchihctuta and City Planning.

Fig.13 - Photograph of the Grssk Parthenon, from Le Corbusier, Vers une architsctuIbIb

Fig.14 - Photograph of the Gmek Parnenon, fmm Le Corbusier, Vers une atchitocturn.

Fig.15 - Man-withamupraised, fmm Le Corbusier. ~ l l con t r ss a- Le Cotbuyi,r.

Fig.16 - The Modulor man in diiemnt pasitiom, from Le Corbusier, Malulor 1. Fig.17 - Diagmm of the Modulor with the manwith-amupraised

inwrted, from Le Corbusier, Madulor 1.

Fig.18 - Hanning's proposal for the consirudian of the diagram of the Modulor, from Le Corbusier, Madulof 1.

Fig.19 - Le Corbusier and Mlle. Elisa MaillaMs prnposal for the constniction of the diagram of the Modulor, h m Le Corbusier, Modulor 1.

Fig.20 - Diagram and the series of Golden Sections it originated, from Le Corbusier, Modulor 1.

Fig.21 - Slylued watercolour of a pine tme, fmm Le Corbusier, Renconlres avec Le Cohuskr:

Fig.22 - MichelangeIo's Capitol in Rome with rsgulaüng I i drawn by Le Corbusier, h m Le Corbusier, Modulor 1.

Fig.23 - Drawing sent by Hanning to Le Corbusier demonsaating the only possible solution for the insertion of a right angk into the diagram of the Modulor, from Le Corbusier, Modulor 1.

Fig.24 - Three paintings by Le Corbusier with their respedivs mgulaüng lines, from Le Corbusier, Modulor 1.

Fig.25 - Orawing demonstnting the lineanty of the Fibonacci senes, frum Le Corbusier, Modulor 1.

Fig.26 - Le Corbusier and the measunng tape made by Soltan, from Ivan faknic, Mise au Point.

Fig.27 - Working dnwing of the Modulor Jystem, from Le Corbusier, Modulor 1.

Fig.28 - Sea-shell WIUI b respective goometrical structure, from Le Corbusier, P&ons on the Pissent Stete of A~hi'tsdum and City Plenning.

Fig.29 - Detail of ison 82: The Mind. showing a sea-shet si-. from Le Corbusier. W m e ûe i'angkt dmit, 1955.

FÎg.30 - Sketch of the Greek Parthenon, from Le Corbusier. Joumy io the East, 1911-

Fig.31 - Sketch of the Greek Parthenon. ftom Le Corbusier, Rumey to Uie East, 1911.

Fig.32 - lcon A3: Milieu, fmm Le Corbusier. Podme de i'angk dm?, 1955.

Fig.33 - Iconostase, from Le Corbusier. M m e bs I'angbe dmit 1955.

Fig.34 - Assembly Hall at Chandigarh, frorn Le Corbusier, Remn2iss evsc Le Cdmusk?~

Fig.35 - Sketch of the Palace of Justice at Chandigarh shWng the duplication of the facade in îhe water pad, from Le Corbusier. Rsnconbas avwc Le Cotûuskc Fig.38 - lcan G3: Taal. fFam Le Corbusier. Wme ds i'angk d M 11955.

Fig.37 - Oaail of icon 82: The Mind. from Le Corbusier, Wm ûa l'a* chi', 1955.

Fig.58 - tan A5: Miliau. frcm Le Corbusier, Wms ûe I'angls M, 1955.

Fig.39 - lcon F3: ORsr [The Op4n Hand), Imm Ls Corbusier, P o d m de I'anpls dtuit, 1955.

Fig.46 - Last page of the liihograph Entre-Dsw. from Jaime Coll. 'Shdunt and Play into Le Corbusieh Afl Woth.'

Fig.41 - lcan G3: Tool and b reverse sids, from Le Corbusier, Wms d8 /SI@ d a 1955.

Fig.42 - Mai l of b n G3: Tool. b m Le Corbusier, Mm de hngle dror% 1955.

Fig.43 - Gouache on wlluioid Taumaux senes, 1983. h m Jaime Coll, 'Slructura and Plsy into La Corbusier's AI¶ Works.'

Fig.44 - Painting Taumaux II, from William J. R Curiis, Le Ca~usier: Idsas and Fonns, London: Phidon P w Ud.. 1987.

Fig.45 - Painiings Neluis Morta au Vmion, 1951, and Mtamorphose du Vioion, 1952, ffim Jaime Coll, "Shdure and Play into Le Corbusiefs Ar! Works.'

Fig.46 - Sketch of a codwu, from Alexander Godin, The Ghost in the Machine: Surrealism in Ihs work of Le Corbusier.'

Fig.47 - Çkntch Tor 7M Opan Mnd Monument at Chandigarh, 1952, frorn Le Corbusier, Modulor 1.

Fig.4 - Imns 82: The Mind and Reveme side of G3: Tool, fmm Le Corbusier. M m e de i'angk dM, 1965.

Fig.49 - Modulor man cast in the wall at the Unith &Habitation al Maneilles, h m William J. R Curtis, Ls CO&S&I: Mess and Fam. London: Phaidon Press Ud.. 1987.

Fig.50 - lwn A4: Milieu. fmrn Le Corbusier. P d m de hm dm& 1955.

Fig.51 - Ubu Roi, ùy M d Jarry, 1900, h m AIberto Pdnz-G6mar and Louise PeNetier, A~~htTuctural Fasplssbntation and ?ho htspecbim MW, CamiWge: MIT Pros, 1997.

Fi. 1

Passing down the line, you end up by knitting something together. I Say 'knitting',ôecause îhat means that al1 thinge are one in andher, me implying anoiher.

Le Corbusier's oeuvre is a nedwork of relationships. His themes and

ideas often find ernbodiment in more than one media, creaüng

interesting connections among the different aspects of his wrk- One

can easily recognize in his built work elernents of his paintings or

sculptures. Such is the case of the chape1 of Notre-Dame du Haut at

Ronchamp with its explicit references to his work in sculpture and

painting [fig.l], or the project for his Algiers' skysctaper which he

recounts originated from 'regulating lines' he found on the back of one

of his painüngs: (fig.21

Suddenly I saw the whole thing clearly in my mind: here was the framework of proportions which wodd fit into the landscape of Ngieo 9 sky-scraper of which I had been thinking since 1930, ihat is, for eight yean.

Fi. 2

' Le Corbusier, exttacted ffom Maurice Besset, Who was Le Corbusier? (Geneva: d'Art Albert Skira. 1968). p.194.

Le Corbusier, M u f o r 1, tr. by Peter de Francia and Anna Bostock (London: Faber and F aber Lirnited, 1954), p.216.

It is also the case of his sculptures, which were Iiterally transfated from

his paintings [fig.3]. Around 1944, Le Corbusier started a partnership

wiîh Josef Savinas, a Breton cabinet-maker who found in his paintings

sculptable foms. From this partnership the famous 'awustic8

sculptures were bom, sharing their themes and foms with Le

Corbusier's paintings and drawings. This intemingling of ideas,

themes, foms and figures is the basis of Le Corbusier's work, and had

influenced not only his plastic wrk, but also his understanding of

architecture and the wortd.

Le Corbusier &en pointed out the importance of painting in the

development of his work. He started painting in 1918, under the Purist

influence of Amedée Ozenfant. At the beginning, this was a paraltel

acüvity and he used to paint only on Sundays. At the end of the

twenties thaugh, his attitude had changed and he staited taking his

painting adivities more senously. From 1927 on, he began to paint

every moming, and changed the signature of his paintings from

Jeanneret, his family name. to Le Corbusier, the pseudonym he

adopted in his architectural pmcüce. This suggests not only that his

painting pracüce grew in importance. but alsa that it had started to

build up some connedion wiîh his architecture.

The Modulorin me h@mf

The 'secret' of his architecture, Le Corbusier affined, was in his

painting? Painting for him was an exercise, a 'mental gymnastics',

which he practised unintemptedly every rnoming. It was this exercise

that gave him his 'freedom of spirit', k ing also the source of the

'integrity' of his inventions? He considered his painting a research and

used to cal1 his studio at rue Nungesser-et-Coli 'l'atelier de la

recherche ~atiente'.~ From this studio came out not only the foms and

shapes of his architecture, but also hi 'intellectual produdion'8

There is a close connection between Le Corbusiets painting acüvities

and his thinking about architecture and the arts, speeially dunng his

later pend. Hii principles of the 'acoustique plasfique' and d the 'right

angle' are good examples of such cannedion. Both of them originated

in his painting practice, and later developed into philosaphical

statements about his work and the world. The principle of the

'acousîique plastique' was responsible not only for the musical analogy

that dominated Le Corbusiets work, but also for his 'polychrome'

sculptures and the exuberant foms of the Chapel of Ronchamp.

Moreover, the 'acousb'que pladque' was the basis for the research

and invention of the Modulor, and fias played, along with it, an

important role in the development of his theory of the 'right angle'.

Le Corbusier expressed his theory of the 'nght angle' in the Poéme de

/'angle droit, his most wrnprehensive theoreücal wrk [fig.4]. The

P m is a moment of synthesis, of maturation and crystallization of

his thoughts and ideas. There, Le Corbusier stated in paetic and

graphic fom, his most intimate beliefs about art, architecture and their

relationship with the world, praising the very act of making, and

transfoming the Podm de l'angle droit into a debraüon of artistic

creativity.

'Je pense que si i'on accorde quelque signification à mon oeuvre d'architecte, c'est à ce labeur secret qu'il faut en attribuer la valeur profonde.' Le Corbusier, My Wdr (London: The Architedural Press, 1960). p.197. ' Jean Petit, Le Cm& - Lui Même (Geneva, 1970). p.112

See Le Corbusier, My Work,

The Modiùorin ihe Minu

Fi. 4

The Podme is part of a special collection organized by the Verve

publishing company to celebrate one of its anniversaries, They invited

a few artists and gave them total liberty in creating a book. Matisse's

J a n is part of that collection. Being one of the invited artists, Le

Corbusier t w k the opportunity to state his artistic beliefs, editing the

work of a lifetime. He created a loose-feaf book, where he manifested

a very personal set of ideas, using calligraphied poeûy and

corresponding icons. These were organized in a structure composed

of seven secüons named from A to G, as a reference to the musical

scale, to which Le Corbusier gave the name Iconostase. Fg.51 Each of

these icons is dedi ïed to an idea, and athough Le Corbusier oifered his own reading of the PNme in the Iconostase, hii chaice to l ave

the book unbound suggests the possibilii of changing the order of the

images, combining them in different arrangements and re-inte~reting

them.

It is particularly significant that Le Corbusier chose to express his

mature thought through liiographs and poetic prose, for it wnfirmed

the importance his arîistic adivities had in the formation and

development of his thinking. Le Corbusier used to say that his

Jean Petit, Le Corbusier - Lui Mme, p.112.

nie Moduiorin ihe Minw

reasoning was mainly visual,' wmething that allowed him more

freedom to manipulate and transfomi his ideas. In the P W m de

/'angle droit these manipulations am brwght to the kre, disdosing

intercannedons until then ignored. Such is the case of the Modulor.

Through its insertion in the Pobme, ii is possible to understand not only

its real meaning for Le Corbusier but also its reMionship with his later

thin king.

The Poéme reveals the importanœ of the Modulor as a researeh. The

reading diers fram eadier ones because it deals with the experiences

that led Le Corbusier to 'discover' the Modulor, M e a d of viem'ng it as

a simple tool. It also demonstrates the importance the graphic

appearance of the Modulor had in its definition and also in its

understanding by Le Corbusier.

The Modulor originated fmm the ttieory of the 'acous@ue piastii'que'',

an interesting way of work that allowed Le Corbusier ta 'discover' and

"Being a cubisf he had a bent for plastic phenornenon, and his reasoning was visual.' Le Musier, IliikxluIar 1, p.29.

The Modulor in the M m 5

develop ideas thmugh graphic manipulation. An important feature of

the 'acous(Hiue plasb;que8 was the continuous working of a theme.

Using painting and drawing as a means of exploration, Le Corbusier

would pick up found objeds, which he named 'objets B reawn

poètique', and draw them over and over again until a new fonn or a

new idea had emerged. In the Poeme de /'angle droit he exemplified

this operation by demibing how he transfomed a pebble and a mot

into a bull, by drawing and re-drawing them during one of his stays in

Ozon.

Les éldments d'une vision se rassemblent. La clef est une souche & bois mort et un galet ramassés tous les deux dans un chemin creux des Pyrenées. Des boeufs de labour passaient tout le pur devant ma fenêtre. A hm dttre dessiné et redemnd le boeuf - de gallet et ch racine dewbnt taureau.

Another way of achieving sirnilar results was to redraw old drawings

and paintings, some ofthem daüng fmm thirty yean back. That is how

Le Corbusier 'accidentally' found a bull while lwking at a photograph

of one of his Pun'st paintings sideways lfig.61. This process of tuming

pictures or drawings upside d w n or sideways sine then became an

important pmperty of his piclorial wrk, particulariy the 'acoustic' ones.

Fi. 6

Chance and the unetxpedd wre fundamental to the discovery of new

foms. These were fater d m and re-drawn until Le Corbusier fek that

the idea was ready to be painted. As he rernarked, an idea takes a

' Le Corbusier, Poéme de l'angle drpit (Pans: &Mons Verve, 1955), C l : Flesh.

long time to be developed. After painted, the idea wuld then be

brought into other media, becoming a compositional eletnent or a

theme for elher his sculpture, architecture, or other graphic media.g

This way of working allowed Le Corbusier to link the diierent artistic media he used establishing a dialogue between them.

lntuitively over the past twenty years my figures have evolveü in the diredon of animal foms, vehicies of charader, by means of the sign. the algebraic means to enter into a relation$ip between themselves and thereby praduàng a single ptic phenomenon.

The Modulor, as a development of the 'acoustic' phenomenon, also

played an important role in this unification. With the help of the

dimensions of the Modulor, each element and each piece of work

became related, as if 'tuned' together in one 'single family', as André

Wogensky, one of Le Corbusiets collaborators remarked."

This way of working has also contnbuted to the maturation of his

pnnciple of the 'right angle'. From a simple rule, discovered by chance,

the 'place of the nght angle' made its way through Le Corbusier's work,

coming to stand for a comprehensive philosophy of architecture and

reality. The 'right angle' offered Le Corbusier the possibility of

synthesmng his ideas through metaphor, through putüng together

diierent elements, which would relate to each other in unexpeded

ways pmducing new meanings and relationships. Moreover, the 'right

angle' allowed for the diverse and sometimes opposing themes and

ideas of Le Corbusier's oeuvre to be united in a more dialedical. more

intuitive and poetic way. In this context, the Modulor was also an

important step, for it strengthened Le Corbusiets beliefs in his

intuitions and in his own pfocess of discavery. - - - - -

For an examination of Le Corbusieh working process, see Jaime Colt, 'Le Corbusier: lauream an Analysis of the Thinking Pracess in the Last Series of Le Corbusier's Plastic WoW in AR Hijtdry Vol. 18, No. 4 (Dec. 1 995),

.537-567, p.30. "Jaime Coli, *Le Corùusier. Taureaux an Anslysis of the Thinking Pmeau in the Last Series of Le Carbusier's Plastic W W p.31.

The Modulor ln the M m

It is in the Poème de /'angle droit that the full signifince of the 'right

angle' is fleshed out. There, the relationship between the Modulor and

the 'right angle' also becornes more evident. 60th of them started as a

search for mathematical nlationships that would help organize the

propoiüons of a building or a painting, and both of them were Mer

developed into comprehensive theones that revealed a lot about Le

Corbusiets relationship to architecture and the world. Their

relationship is important because it allows for a better understanding of

Le Corbusier's ideas as a &le, hile also fumishing some important

insights into out present condition.

lcon 82: The Mind (fig.7 in the Po- de i'angle droit is dedi ied to

the Modulor. While presenting this icon in his book on the Modulor, Le

Corbusier placed two other icons of the Poème beside it, namely icons

A3: Milieu and 63: Tooi [fig.8 & 91. He made no refennœ ta these

images, which leads one to condude that they were intended simply

as illustrations of the Podme, sine they both refer to the principle of

the 'nght angle'. Oespite that, the present work wiil examine these

three images and discuss their relationship, for together they are of

invaluable help for the wmprehension of the connedion between the

Modulor and the prin~iple of the 'right angle'. As Le Corbusier's own working process suggests, when hvo or more ideas are put together,

they begin to interad, opening up the possibility of new meanings,

" Andr6 Wogensky, The Unité d'Habitation at Marseille," in Le Ca&usier The Garland E ~ y s (New York: Garland Publishing, Inc.. l987), pp. 1 17-1 25,

The ModWorm me M i 8

... assembling everything within a banal wherence and presenting al1 the facts to be taken into accourt So there are many things at the bottom of this poem. Then he detacheci himsetf. then rose abave it all; he burned his bridges. Fmm then on, it is up to the reader to read the paem.''

125. Le Corbusier Oeuvre Complete V. p.M, emgted ftm Jaime Coll,

'Structure and Play in Le Corbusier's Art Works,' in AA Fïfes 31 (Summer

The Modulor in the MIIW

THE MODULOR AND ICON 62: THE MIND

The 'Modulor' is a measure based on mathematics and the human sale: it is constiîuted af a double series of numbers, the red and the blw. But, if that is ail it is, wuldn't a numerical taMe do the tri& just as welt? -No. That is where 1 have to explain again and again the set of ideas which 1 place at the very mot of the invention.'

Defming the Modukr is not an easy task. Le Corbusier refend to i! as

a system of proportions, but refused to accept the two series of

applicable rneasures as its definition, insisting that in order to

comprehend the Modulor one had to know the 'set of ideas' that came

to fomi 1.

Most of these ideas have been with Le Corbusier for a long period of

time, having each one of them a particular signifiince in the

architeas thinking and work.

The history of the Modubr accounts for each of these ideas. and for

this reason its examination is essential. This examinaüon also revaals

the importance of the drawing of the Modulor. [fig.liI This dtawing

holds the definition of the Modutor and also furnishes important

1 Le Corbusier, W u l o r 1, p.60.

information conceming its creafion, because there one finds

represented the ideas that Le Corbusier considered to be at 'the raat of

the invention'. It was only Mer defining this drawing that Le Corbusier

wnsidered his invention ready and was finally able to explain it.

When Le Corbusier started his research on the

Modulor he did not have a dear idea of what he

was doing. He was after a module to be used in

the standardikation of industrial goods. But, as he

pointed out to his young collaborator Hanning,

this module could not be the product of an

arbitrary decision, but rather the result of a

search into the worlds of art, nature and

mathemaücs:

Here you are, the AFNOR proposes to standardize ail the objects imrolved in the construction of buildings. The method they are proposing to employ is somewhat over-simplified: simple anthmetic, getting a simple cross-sedion of the methods and customs used by architeds, engineen and manufacturers. This method seems to me an arbitrary and a poor one. Take trees: if I look at their trunks and branches, their baves and veins, I know that the laws of growih and interchangeability can and should be something subtler and richer. There must be some mathematical link in these things.

The year was 1942, and Pans had been taken over by the Nazis. Le

Corbusier's office was closed due to the new regulations in the

pradice of architecture, leaving him without work. To make things

worse, he, who had since the First World War been talking about the

necessty of mass-producing the elements of const~ction,~ had not

been invited to participate in the discussions on standard'kation held

by the AFNOR4 group. His complaints were many, and the whole

Ibid., pp.3637. These were the insîrucüons Le Corûusier gave to his collaborator Hanning canceming the research on the Modulor men the latter had to cross the demarcation line the Gemans imposed on the French during the Second World War, and asked Le Cotôusier for something to oaaipy his mind. See Le Corbusier. Vers une arCnI'tedure (Pans: Flammarion, 1995).

4 AFNOR: Association Française pour la Nomaliîon. an association aeated to detïne noms for the French industry.

The ModuIar in Che M i m 11

situation d m him inwards. forcing him to engage into mat he called

'intensive theoretical research wor lc '~m~rche docfn'nalel?

Thus he decidexi to create a parallei research group, the ASCORAL!

and started working upon the theme of reconstruction. tike the

AFNOR, Le Corbusier and the ASCORAL group saw on

standardkation a big aIly for helping dealing with the destruction and

hmelessness caused by the wat. A rapid solution was needed and Le

Corbusier believed this to be his chance to iinaliy d i t e his dreams of

mass-produang the elemnts of constmcîion. He saw on

standardion flot only an opportunity to attend the increasing

housing demand, but alsa a great way of bringing unity and hannony

into the realm of visual pmdudion.

Let's not los0 sight of our a h : to harmanize the flow of îhe WWfds P r ~ d ~ ~ . 7

'Hamiony' and 'unity' are essential words in the Corbusian vocabulary,

as weil as cornplex ones. For the moment, it is enough to say that he

was searchirig for a consonance among the diverse produc& of the

industrialized worid. He believed them to be in a &te of total

dishanony, and saw on standardkation the possibiiity of bringing

them into harmony, jdning them in un@. This is the first inconsistency

in Le Corbusier's standadkation program. Standardkation means reducing things to a mmmon denominator. hornqmiu'ng production

in order ta make it simple, fast, cheap and efficient. Obviously, Le

Corbusier was not thinking about that. He cnticized the AFNOR

module precisely for its Iack of flexibitity. He believed standardkation

to be a-ated with un*, but not with homogenization. In his

' Le Corbusier, Modubr l, p.36. ASCORAL, an association apparentiy created by Le Corbusier to develop

researches parailel to those of the AFNOR Ta these lwo associations, ASCORAL and AFNOR, Le Corbusier refers to only by aieir abbreviation, not krrnishing any additional infwmatÎon on them.

Le Corùusier, Modubr l, p. 107.

opinion, unity never exduded diiersity. On the contrary, it was based

on diiersity and on crehvity and on imagination.

1 am, in principle, against 'modules' &en üiey curtail the imagination, claiming absdute rights over the objeet and leading to the petrification of invention. But I befieve in oie absolute nature of a (poetic) relationship. And relationships are, by definition, variable, diverse and innumerable. My mind cannot adopt the modules of AFNOR and Vignola in building. I a- no cannons. l daim Vie presence of hannony between the objects involved.

That is precisely why Le Corbusier refused to accept the solution

proposed by the AFNOR, because it would jeopardke his freedom and

his creaüvity. He believed the solution proposed by the AFNOR was an

arbirary one, the resuk of a simple rule of thumb operaüon, and he

could not admit such a simplidc formula interfering in his creative

work. He believed in technological ideals, as long as they did not take

away his liberty to create, the 'free ffow of the imagination.'

No human progress and no human rule b s the nght to proscribe, or even to inhibit, the imagination.'*

The inwmpatibiiii hem is obvious: joining mass-production and

standardkation, means of technologid domination, with creatiirty and

imagination, symbois of human freedom, is against their ver' essence.

This, along with other examples throughout Le Corbusiets description

of the Modulor, demonstrate that he wnfounded technology with

technique.'' He saw technology and its products not as ends in

themselves, but as means, as vehides to achieve something else,

particularly hamony.

This creative confusion of technology and technique in Le Corbusiets

understanding of technology is made dear by an examination of his

intentionalii in the research of the Modulor. Even thought the ends

were the mechanical produdion of both 'containers and extensions of

Ibid., p.90. ' Le Corbusier, Modulor il, tr. by Peter de Francia and Anna Bostock (London: Faber and Faber Limiteci, 1954), p251. 'O Ibid., p.102.

The Moâularin üte Mina 13

man1, a dear instance of an instrument of technological domination, Le

Corbusier wouid not saüsfy himsdf with a simple solution. He did not

want to simply invent a nile, but to dkmver one. 'Standardization: to

obtain the status of a nile; to uncover the principie capable of serving

as a nile'f2 For him, a nile could not be imposed, it had to be the

produd of an intuitive searcfi in order to guarantee a harmonious

m u t . And what could serve m e r than the universal and

unchangeable principles af nature to assure the achievernent of such a

goal?

Le Cnrbusiets instructions to Hanning were dear

Take trees'. mat is, take nature as the ideal madel.

In Corbusian iconography, the tree is one of the

symbols for the ideal of proportional growth. [fig 12)

Unity within dienity. Complexity coming from

simpliaty. What he did not realize though, was how

far his aims were from the reality of standardization

and mas-production.

Le Corbusier aIways had an ambiguous relationship with technology.

He envisaged in mas-production the opportunw of bringing harmony

and unity to the world's production. He believed modem society to be

living in a dishamtonious worid mainly due to its inability to cope with

technology, and its incapacity to cuntrol it. A simple shift at the root of

the matter, in his opinion, wouid change everything. Organiration could

make technokgy work 'in the senrice of men'.

The second period of ihe machine ti$kaüon has begun. the pend of harmony, machines in the seMœ of men.

Technology and human values for him were not neœssarily in

contradidion. On the conûary, machines could be used in favour of

11 Le Corbusier, Modulor 1, p.112. l2 Ibid.. p.109. " Le Corûusier, M e n aie Caaredrals Were White (Cornwall, 1948), p.2W.

humanity. Harmony between men and machines was not only

possible, but desirable. In this context, his grid of proportions would

work as a 'tool of reconciliation', sefving as a bridge bdueen men and

machines.

Concord between men and machines, sensitivity and mathematics, a harvest of prodigious harmonies reapad from numberç: the grid of pr~~ortions.'~

Hence the solution was to humanize technology. In order to

açcomplish that, Le Corbusier decided he would start his research

from man. If what he wanted were measures to be used in the

manufacturing of adcles for men, hoth contairiers and extensr'ons of

men, why not siart with human dimensions? Again, what he wanted

was 'to uncover the principte' behind human measures.

sa valeur @si en ceci: ie curps Ifmain choisi comme support admissible des nombres . . . VoiM la proportion!

One wuld say that Le Corbusiets architecture had only one theme - man. As Maurice Be& temarked, Le Corbusier never thought 'of

architecture in ternis of anything kyond man, anything pureiy political,

social, or even re~igious."~ Le Corûusier believed architedure had only

one aim - to contain man, to relate physicaliy and psychologically to

this man, and to help him h e in hannony with himself and his

environment. In his opinion, only architecture could achieve such a

goal." Le Corbusier considered his concem about man a search, to

which he dedicated most of his He. This search began in his youth,

when he decided to take a trip around Europe in order to 'see' and

'disçovef, and it remained with him until the end of his life. In his last

written text, a kind of 'final testament' - Mise au Poinee- he was still

- --

l4 Le Corbusier, Ahdufor i, p. 1 12 " Le Corbusier. Le Pbeme de l'angle droit, 82: Esprit '' Maurice Bsssef Who was Le C&w&r?, p.189. '' 'Only the arehitect cm strîke the balance between man an his envimnmem' Le Corbusier, W u b r l, p. 1 1 1. " Ivan Zaknic, Le Corbusër - The Final Testament of Père Corbu, a translation and interptetafion of ' M i au Point' (New Haven, 1997).

The Mcmblor in the M m 15

prodaiming the necessity of rediscoveririg man: 'Il faut n W e r

homme'.'^

Le Corùusier studied architecture mainly through persona1

observations. After finishing his studies at the AR School of La-Chaux-

des-fond, where he was being trained to become a watch engraver,

Le Corbusier decided to take a study trip around Europe. He &en

referred to this trip as one of discovery, because it was then that he

began to open his eye.sa Through observing and drawing, Le

Corbusier was able to grasp invaluabk lessons. One of these lessons

was architecture's relationship with man and his sunounding reali, or

what he called the 'human scaie'.

In one of the most remarkable accounts of this trip,n Le Corbusier

described his encounter wiîh the Athenian Acropolis. He spent a week

there and later dedared that this experience had changed the course

of his Iife:

How painful was the ecstasy that sized us in those temples of the East! How withdrawn I feit, overcome by shame. Yet the hours spent in those siient sanduaries inspired in me a youmful wurage andJhe bue desire M become an honorable builder.

One of the things that had impressed Le Corbusier the most was the

Parthenon's reWonship with man. The G m k temple [figs.13 8 141,

despite its monumentality and grandeur, seemed to speak directly ta

the hurnan body. Its measurements looked as if made to resound with

the body's own, making Le Corbusier understand that architecture

could not be thought of without man.

lS Ibid., p.155. See Maurice Besset, Who was Le Codusier?, p.4 1. " Le Corbusier, Joumey to the EastI Ir. by lvan Zaknic in collaboration wdh

Nicole Pertuiset (Cambridge: MiT Press, 1994). Le Corbusier, extraeted from lvan Zaknic's prefaœ to the English

translation of Joumey to aie East, p.XM

The Mobulor in the M m

... an awareness of dimensions struck me swn after. From that time came what I alleci 'We man with upraised amis," the key to al1 archite~ture.~

Neverthdess, it was not only in iis measures that Le Corbusier saw the

Parthenon's relationship with man. He was also able to obsenre a uniiy

of intention, of thought, capable of speaking about the men who buiit

and i n h a b i the place. The Greek temples were buiit not only

according to the measures of the Greek men, but also to their way of

Me, to the way they perceived and related to the world sumunding

Hence the 'human scale', more than

a reference to the dimensions of

man, was used to describe the way

certain pieces of architecture

related to man, how they were able

to embody culture, locaüon, thinking

and human aspirations. The 'human

scale' represented a hamonious

and dialedical way of relating to the

environment.

This same harmony Le Corbusier

perceived in what he called the 'folk

house,' the house of the common

man, the vemacular architecture he

was able to experience during his

study trip. Besides Greek and Gothic architecture, what Le Corbusier

admired most was folk aR and architecture. He saw on these houses

austerity and tnRMulness, an authenticity that most contemporary

architecture lacked. They were designed for the men who Iived there.

They related to these men both physically and cuiturally, incorporaüng

their measures and values. When compared to Beaux Arts

architedure, which Le Corbusier believed was dimensioned for 'fleas

Le Corbusier, Joumey to the East, p.232.

The Modulor in the Mitmr -1 7

or for giraffes, one is not quite sure which'?' these houses seemed so

'dose to men', so fit to their bodies and souls, îhat Le Corbusier Men

mirrored himseif on them.

Je techerche avec une véritable awïdité œs masns qui sont ûes 'maisons d'hommes' et nun pas des maisons d'architectesS

5 On these 'rnaison#hommes1, Le Corbusier found a perfect agreement

nat oniy among its parts, but also among the houses, the men who

inhab i i them and the whole surrounding environment, induding the

landscape, the culture and the artefacts produceci and used by these

men. White visiting these houses, Le Corbusier twk their measures.

He believed these measures had a hrndamental significanœ in the

achievement of such consonant state, and began to observe them,

trying to understand their relationship with man and architecture.

Falk art, both in handcrafts and in anonymous architecture, has in the course of centuries worked out standards perfectly suited to the needs and rneasures of man, standards whid for that very reason are in mmpIgte hmony arnong themselves and with the natural setting in wtiich they rise.

Also, he noüced a certain -rrence in the distance between flwr and

ceiling in what he called 'hamnious architecture', which included bath

vernacular and historical pieces of architecture, or 'primitive' and

'highly intelledual' architectures. This distance corresponded to the

heigM of a man with his a m upraised, 2.20m. a measure that he found

'very much to the human scale'. He adopted this measure in his eariy constructions, and was proud to say that despite the fad that the

Parisian regulaüons did not permit such short distance between flmr

and œiling, tie had been entitled to do SQ by one of the town

councillon, because he knew Le Corbusier was working for the 'gaod

of rnan'n Henœ. the 'man-withamupraised' [fig.lS] became a

foundation for his thinking in architedure, not only a support of

24 Le Corûusier, W u f o r ll, p.262, 25 Le Corbusier, Pm&ns sur un état présent de I'archMtufe et de l'urbanisme (Park Les kMions G Cr& e Cie., 19301, p.9. amunce Besset, W ~ I O was ~a Cohusier?, p.10.

ïhe Modulorin the M m

measurements, but a symbol of an architecture that accounted for

man's relaüanship with his environment.

The 'man-with-am-upraiseb is a man occupying

space. It has &en been described as a dynamic

man? for instead of the outstretched man of the

Renaissance, caught in an immobile, static position, Le Corbusier picked a man engaged in

dismering his environment. Le Corbusier

contemplated himself a 'man of space,' and

remarlced that his 'entire intelledual adivrty was

directed towards the manifestation of ~pace. '~~ He

considered man's occupation of space, his act of

'taking possession' of space, 'the first gesture of

living things, of men and animals, of plants and

clouds, a fundamental manifestation of

equiiibrium and d~ration.'~'

Le Corbusier also described the 'man-with-ami-upraised' as a man

upright on his feet: 'it has a top and a bottom, not a left and a right.g'

This position allowed him to occupy space and influenced ail his

sensations, for man 'appreciates al1 things, including the horizon ta^,'^^ by virtue of such poslion. Le Corbusier considered this a 'fundamental

postulate of ar~hiiecture,~ and stated that whoever did not understand

such principle would 'never be able ta organite a symphony of foms

and space meant for men?

f7 Le Corbusier, Modulor l. p.28. Sw Rudolf Wntk~r , "Le Corbusier's Modulor," in Peter Serenyi ed., Le

Corbusierin Perspective (New Jersey: Prentice Hall, Inc., 1975), pp.84-89. 28 Le Corbusier, Modulor Il, p.27. " Le Corbusier, New Worfd of Spaœ (New York: Reynal and Hitchkock, 1948), p.7. '' Le Corùusier, ~odo~or i l , p.79. " Ibid., p.80. " lbid., p.BO. j4 Ibid., p.80.

Fig. tu

From 1925 until 1933 Le Corbusier began to intensify his research on

the 'human scale'. He drew a meiric seale on the wall of his studio to

which he would confront himseif in different positions, 'those of resüng,

sitting, walking and so forth' [fig.16]. The experiment drove him to

condude that the rnetre was nothing but an abstract number,

'incapable, in architecture, of quaiiiing an interval (a masure in

space).* Le Corbusiets cnticism to the metric system was vehernent.

Due to its total alienaüon to the dimensions of man, he believed it was

the main cause of the crisis of architecture. He wnsideted Rs adoption

by 'the savants of the Conventionm an arbitrary decision, creâiiing it

for the 'dislocation' and 'penrersion' of architedure.

'Dislocation' is qu~te a ggxl word for it: it ir disilocated in relation to its abjecf, which is to contain men.

The Modulor sough to repair the situation by giving eorporalite to the

dimensions used in architecture, that is, in the Modulor these

measures were made fie*, 'the living expression of our universe,

ours, the universe of men, the only one concenfable to our

intelligencea This was achieved by Le Corbusier's adoption of the

measures of the 'man-with-am-upraiM as the starting point of his

research. He believed that starting fmm sudi a concrete measures, he

36 Ibid. pp-32-33. Ibid., p.20. - si Ibid., p.20. Ibid., p.160.

ïhe Modulor in the M m

would achieve his goal: to 'obtain a series of masures reçanuling

human stature and mathematics.a Thus he created a 'containet,

composeci of two supen'mposed squares, intersectecl by a hird one,

and inserted his 'man-witti-atm-upraiscd' within it [fig.lq.

Take a man-witharm-upraised, 2.20m in heighî; put him inside two squares, 1.10 by 1.10 metres each, superimposed on each other; put a third square astride these first hnro squares. This third square shauld give you a soluüan. The place of the right angle should help you to decide when to put this third square. "

Fm. 17

The insertion of the third square was the fruit of a long discussion and

the product of two independent researches. One of these marches

was held by Hanning. Gien the problem of inserting the third square

into the grid 'at the 'place of the right angle',' Hanning, worlcing alone a i

Savoy, sent Le Corbusier the following proposa?': [fig.18]

Fm. 18

" Le Corûusier, Madulor 1, p.37. " Ibid., p.41. " It is important to note at this point that the graphic presentation of these mathematical constnictions was Le Corbusier's own way of descfibing the making of the diagrams, as he did for the whole research an the Modulor, and hey am here reproduced as qwtations.

Rie Madubr in ihe M m 21

At the same üme, in Paris, Le Corbusier and Mlle. Elisa ail lard^ w r e

working on anather sctreme, which offered a similar solution tfig.191.

What both these sdutions had in m m o n was the use of the Golden

Section to dupiicate the initial square. For a long time Le Corbusier

had been looking for a way of incoqmathg Golden Sedion ratios into

his wrk and this seemed ta be a good opportunity to do it.@ What he

did not know though, was mat the use of su& mathematical device would change the course of his search.

M e n Le Corbusier first introduced the Gdden Section, he was looking

for a 'grid of proportions', a module Mering flexible measures which

could be used both in the manutaduring of industrialized goods and in

the making of arcfiiteciun. H m e r , as he was basing his research

mostiy on intuition and on second hand mathematicsu, once he found

his gtid, he could not define or explain what he had done.

This is what twk him and Mlle. Maillard to the Dean of the Facuky of

Sciences at the Sorbonne, M. Montel, in order to show him the 'design

of the grid'. After analysing the diagram. M. Montel expiaineci that by

insertirtg the rigM angle in the construction, they had introduced the

mathematical fundion of root of 5, 'thus pioducing an efflorescence of

4 Author of a bodr on regufating Iines, Du nombre d'w, puMished by Andrd Toumn et Cie. who was helping Le Corbusier in the researeh of me Modulor. a André Wogensky, "The Unit6 d'Habitation at Marseille*, pp.117-125. 44 As mentioned Mm, his knowiedge of the discipline was poar, and he had to rely mainiy on second hand infmation to consîruct hi$ grÏd.

The Mdubr in the lc(riw 22

golden sedionsl.& [fig.20] Until then, they had no idea what they had

stumbled upon. Nevertheless, even k i n g mare of the fact that his

construction had originated a senes of Golden Sedions, which he

found out were called the Fibanacci ~ e r i e s , ~ it took Le Corbusier

almost a year to get to the final design of the ~adulor." During this

time he kept improving the use of his invention, yet a full

wmprehension of it, as well as a definition, were still lacking.

An interesting incident demonstrates Le Corbusier's inabiti to

understand his invention. Afier defining the diagram, still composeci

only by the 'man-with-am-upraised' and by the geometrical

construction based on the three squares, Le Corbusier went to patent

his 'invention'. At the brevè office, he was unable to explain ta the

agent what his invention was. He told him the history of the invention,

which is how his personal experience led him to iîs diswvery, but was

unable to explain what the Modulor was. This strange incident is typical of Le Corbusier and reveals a lot about his way of working.

which was always very intuitive.

- -~

" Le Corbusier, Modulor 1, p.43. 4a 'In the early îhirteenth œntury Leonardo de Pisa. calied Fibonacà, diswvered that on a ladder of numbers with each number on the rigM k ing the sum of the pair on the preceding m g , the arithmetid ratio ktween the two numbers on the same ning rapidly approaches the Golden Section. Thus, for practjcal purposes, the Golden Section may be appmâmated to such ratios as 5:8,8:13, l3:21 .' Rudolf WWowert "Le Corbusier's Modulor," p.14. " He went to the Sorbonne on the 7m of February, 1945, and it wasn't until December, on his way to New York that he got 10 the final design and definition of the Modulor. See Le Corbusier, Modulor i, p.43 and p.#.

The Modulor in oie Mirm 23

t found it very dficult to give a succina simpb and qui& explanaüon of the Proportioning Grid. ... How to rnake him understand that, following a long personai experience of matten connedeci with architedue - fumiîure, tDwn planning, building, ecwiomics, thé plastic phenomenon and so forth - you have stnick out on a road which seems to have brougM p u to a Erst result? That you are standing at a door on the M e r side of which something is taking place, but you have not yet got the key mat wilt let you understand what it is?

The history of the Modulor is full of such instances, indicating that the

investigation, besides being intuitive, was a difficult one for Le

Corbusier. Because he had very little knowledge of mathematics, Le

Corbusier used to say that his reasoning was mainly visual," which

was eanfimed by his use of geometry. Geornetry was ttie basis of his

mathematical reasoning, a sort of graphic mathematics, more

concrete, more tacti'le and more visible. He believed geometry was

visually manifesteci in nature and the arts, and was aiways seeking to

understand and emulate it. Even the Gdden Section, an apparently

more abstract, less visible phenomenon, was grasped with the hetp of

graphic means.

Le Corbusiets main source on the subject of the Golden Section was Matila ~ h y k a ~ , aulhor d a book on the use of regulating lines and the

Gdden Seetion in art and their dationship to natures' Le Corbusier

found the explanations given by her on the subjeet of the Golden

Section hard to fotlow, saying that he 'was not equipped to fdlow the

mathematical argument of these books, but he was able to grasp at

once the meaning of the figures wtiich are, in point of fact, the chief

abject considered in them?

Despte his limited grasp of mathematics, Le Corbusier constantly

neferred ta it and tried to understand it. He believed mathematics to be

Le Corbusier, Modulor 1, pp.444. " Ibid., p.29. André Wogensky, "The Unité d'Habitation at Marseille.' p.124.

'' Matila Ghyka, The Geamefs. of Art and U& (New York Sheed and Ward, 1946).

Le Corbusier, MaduIor I. p.29.

The #&brin the h k w 24

part of the unchangeable world of Being, holding the key to the

inherent order of the universe.

Le Corbusier's interest on mathematics started under the influence of

his drawing master L'Eplattenier, from the Art School at La-Chauxde-

Fonds, who taught him to see and obseive nature in order to

understand the principles and the 'imvocable organization' behind its

visual appearanœ. L'EpWenier would a h y s tell his students that

only nature was inspiring and capaMe of serving as the basis for works

of art, but he vvould also warn them not to copy it 'like landscapers

painters do', but tathet to 'ponder its cause, its fom, its vital

development', synthesking it in the creation of orna ment^.^^ He

believed the world's imrnutable pdnciples and laws, its order and

organkation were manifested in a geometric, visual way in nature.

Therefore, through a study of nature one wuld get to the

unchangeable laws niling the universe. L'Eplattenier taught Le

Corbusier not only to see and observe things, but to atways try to get

to their essence and inner structure, making use of their visual

appearance. He also made Le Corbusier believe that the world was a

geometrical phenomenon, ready to be grasped by the attentive eye.

The fundamental principle is 'Wom the inside out'' (cantrary 10 appearances). ... Frorn the inside out.. Nothing is seen, admired or loved exœpt what is sa fine and beautiful that ftom the outside one penetrates into the very heart of the thhg by stu% reseadi and exploration. By deviws ways. we therefwe reach the centre.

Le Corbusiets drawings from this pend are gaod examples of h w he

scrutinized naîure, trying to grasp the essence behind its visible

expression. They are also a good instance of how he tried to translate

nature into a geomeûic language [fig.21]. Le Corbusier believed

53 Le Corbusier, extradeci from Paul Turner Le CofBusierin Pefspectnle (New Jersey: Prentiœ Hall, Inc., 1975).

Le Corbusier. extracted from Geaffray H. Baker, Le M u s h r - The Creative Search, The Formatnre Years of Charles-Edouard Jeanmet (London: E & FN Spon, 1996.). p.73.

The Modubrin the M m 25

geometry to be inherent and visiMe in nature.% Thus the artist or the

architect would only have to perceive this

geometric structure and try to adapt it to his

work. He stated mat architecture was a

'purely human mation', and should be a

kind of 'logarithm of nature', since man

himself was a produd of nature.=

In this context, mathematics worked as a

link, a way of achieving hamony and uniiy.

However, as architecture was a 'thing of the

body', a ancrete mari, Le Corbusier did not believe that the abstract

mathemaücs of the schools, which he referred to as 'high

mathernatics', auld be used to produce architecture. On the contrary,

he was searching for a mathematics that he could see in the worid, a

concrete mathematics that spoke to him and to his embodied seff, like

the one he was able to observe in nature.

At the time Le Corbusier left the Art School at La-Chaux-de-Fonds, he

started a series of travels throughout Europe, which were then

wmplemented by some pradical work at the oflices of Auguste Perret

in France and Peter Berhens in Germany. These trips supplemented

what he leamed from CEplattenier, intensifying his beliefs in

observaiion as a way of leaming. Through observation Le Corbusier

was able to perceive that rnathemaücs mled not only the realm of

nature, but also the world sf human creation. The great architecture of

the past, which he Iater considered as his mal mastep, wnfirmed his

format bdiefs and made Le Corbusier embark on a search for

mathematical principles that coufd be used in the creation of both his

art and his architecture,

" 'Everything is geometrical to our eyes.' Le Corbusier, Pmsicions, p.134. Le Corbusier, When the CaaiedraIs Were White, p.ll6. " 'Je vais vous confesser que ie n'ai jamais eu qu'un maître: ie passé; qu'une

formation: I'Btude du passé.' Le Corbusier, PréQsions. p.34.

The Mœiulor in the MBmr 26

This is what led him, back in the early twenties, to expriment with

'regulating fines' [tracés mgutafeurs), which he discoveied were used

in most of the great architecture he saw on his trip, as w-eil as in the

books on architectural history he read at the Bibliothéque ~ationale.~

These regulating lines inciuded the use of the Golden SectionIs and

his intuitiveiy discovered 'place of the right angle'.

Le Corbusier related the 'discovery' of the 'place of the rigM angle'

back to when he was about to build his first house. A 'striking question1

came to his mind, which set him on what he later defineci as a 'que&

for harmony': 'What is the rule that orders, that conneds al1 thingsp

In Modulor 1 he describes h m one day in Paris, under the oil lamp of

his linle mom, he spread some post cafds on a table:

His eye lingered on a pidure of Michelangelo's Capitol in Rome. He tumed over anotfter card, face downward, and intuitively projecied one of its angles (a right angle) on 10 the f a d e of the Capitol. Suddenly he was stnick afresh by a familiar truth: the right angle govems Vie composition; the lieux (Iku de l'angle dm& place of the right angle) command the entig composition. This was 10 him a revelation.

Despite the fad that he later confimec! his intuitions in Auguste

Choisy's book on the History of Architecture, Le Cohusier accepteci fi

as a rule only after he was able to expriment with it in practice, for he

only believed what his eyes could see and what his hands could touch.

Le Corbusier's notion of mathematical relaüonships must be weil

understood. He vehernently cnticized Vignola and his legacy, for he

Paul Turner "The Beginnings of Le Corbusiets Education, lgO2-Or' in Serenyi, Peter ed., Le CorbuWin Perspecfnle, p.24. 98 For an account of Le Corbusier's use of the Golden Section in the eafiy twenties, see Roger Herz-Fistieler, 'The Eatiy Relashionship of Le Corûusier to the 'Golden Numbef," in Environment and Planning 6 (1979), pp.SfO3. 'JO Le Corbusier, Modulorl, p.27. '' Ibid, p.26-

The Moduiorin the Mhw 27

believed their laws to be nothing but a set of meaningless niles, fruit of

abstract mathemath, which he called 'hdl on earth'. For the same

reason, he Cnüazed Renaissance aichitedure, aüributing the crisis of

architecture to their indisuiminate use of abstrad mathematics. As he

used to Say, their intelledual manipulations ofFered 'precision without

flavout, taking away the 'fiesh' and 'blood' of architecture by their

indim'minate use of the compasses. Wth the help of compasses, they

devised, 'on papef, 'star-shaped icosahedrons and dodecahedrons,

forcing the mind to a philosophaing interpretation, worlds removed. in

so far as building is cuncemed, from the basic premise of the problem:

the eye's vision.'@ Mathematics could only make sense if related to

man's embodied seiF. It had ta speak first to his body, and through it,

mach the mind. Le Corbusier exemplified the operation by calling the

eye a 'master of ceremonies', and the mind the 'master of the h o u ~ e ' . ~

According to him, the 'master of the house' was able to appWate only

that which the 'master of ceremonies' had the pfivilege of grasping

first.

A tnie measure is an appreciation, a judgement, an acceptance arising from argument and examination, acfiieved by the play af refiexes or by reasoning; it is held between the hands, between the outstretched ans, appreciated by the eye in order îhat its power might be transmitted to al1 things within direct reach. ... lt is appfe&ted. Rie tension of the mind plays its part, the play hardens, relationships are established, intense, intelligent, having an infinitely more powwlul andashaltering and on ouf senses than the trite acmuntancy of the compasses.

Similady, he never a-ated mathematical relationships with

creativity. They were simply a way of bringing unity and harmony to the

work, a way of organizing his ideas into a hamonious wtide. They

would corne only after the idea, never before 1. Its use was

instrumental, a tool for ordering forms and relationships. reducing them

to one sole denominator.

lbid., p.72. Ibid., p.76.

a4 Ibid., pp.222-3.

The Moûuiorm the M m

The regulating lines are not, in prinaple, a preconceived pian; they a n chosen in a particular fomi depending on the demands of the mposiiion itself, already fomiulated, already well and tnily in existence. The lines do no more than establish order and darity on the level of geometrieal equilibrium, achieving or claiming !O achieve a ventable purification. The regulating Iines do not bring in any poetic or lyrical ideas; üiey do rmt inspire the theme of the work; they are nat creati2 they merely establish a balance. A matter of plasticity, pure and simple.

This was also how Le Corbusiet's understood the Modulor. As André

Wogensky remarked, the Modulor was a twl, not 'a machine for the

manufaduring of bea~ty. '~ He recalls h m Le Corbusier himself

rejected its indiscriminate use. When some of Le Corbusiet's

collaborators from the studio at 35, rue des Sèvres showed him

miserable works done with the help of the Modukr, Le Corbusier

would reply them saying: 'To hell with the Modulor! When it doesn't

work, you shouldn't use it.@

For Le Corbusier, the 'regulating lines' were a more intuitive than

scientific device. They were like a tuned keyboard, ready to be played.

The success or failure of a work were never -ated to their use,

but rather to the artist's intentions and creativity.

In the research of the Modulor, Le Corbusier decideci to use the 'piace

of the nght angle' to help detemine the spot where the third square

should be inserted in the diagram. However, the 'place of the nght

angle' did not Mer any mathematical certainty, being only a way of

organking the elements in a composition. Its use in the Modulor raised

a few questions conceming the precision of the construction, the first

of thern from Hanning himself.

Le Corbusier describecl that on the 1 Om of March, 1 944, seven months

after sending his proposai for the construction of the grid, Hanning

m e him from Savoy saying that the Maillard-Le Corbusier diagram

was 'a mathematical impossibiiii. While working on the gnd. Hanning -

Ibid., p.34. André Wogensky, The Unit6 d'Habitation at Marseille', p.125.

The Modulor in the M i m

discovered that 'oniy one tigM angle is possible, namely that formed by

the diagonals of the two squaresa (fig.231. At the time tough, the grid

was already being used in prdœ, and Le Corbusier decideci that this

new information was inconsistent with Hanning's own diagrarn sent on

the 2sm of August 1943 [see fig.16). He opted for the Maillard - t e

Corbusier diagram even though aware of the possibie enor, an emr

he refused to accept because it would dismiss the use of the 'place of

the rigM angle', a solution Le Corbusier would later assert as 'the

starting point for the work on the ~ o d u l o r ' ~

This was not the only question conceming the use of the 'place of the

nght angle' in the construction of the diagram. Le Corbusier also

received sorne letters dernonstrating the impossibili of the presenœ

of a right angle in detemining the insertion of the third square. One of

these letters was from R. Taton, a mathematician who wrote him

anirming that his two initial squares were not squares, but rather

'rectangles of a shape approximating that of a ~quare.'~ He added that

only visually could they be considered as reai squares, for

rnathernatically there was a difference of six thousandths betwetn

them. Sinœ Le Corbusier was basing his research on visual and

intuitive phenomenon and not so much on mathematical precision, his

answer to Taton was not really su~rising:

lbid., p.125. Le Corbusier, Mwulor l, pp.4142

dg Ibid., p.213. 'O Ibid., p.235.

The Modulor in îhe Mmu

In everyday practÏœ, six thousandths of a value are what is called a negligibie quanüîy, a quantity which does not enter into accwnt; if is not seen w i h th eye [my italics]. But in philosophy (and I have no key to that austere science), I suspect that these six thousandths of a value have an infinitely precious importance: the thing is open and not stiut, it is not sealed; there is a chink to let in the air; life is there. awakened by the recurrence of a fateful equaiity which is not exactly, not sîridIy equal. ... And that is what aeates movement."

In another instance, M. Dufiau, another mathematidan, wrote him

saying that 'if the two squares are tmiy squares, the angle is not a right

angle. Lf the angle is a right angle, one of the quadrilaterals is not a

square.'72 Similar to his readion to Hanning and Taton, Le Corbusier,

very politeiy, accepted M. Duffau's opinion but did not change his

rnind. The sdution couid be imprecise, but it was, after all, his first intuitionn, and he believed it to be responsible for his 'discovery'.

Thus the fact remains that even with al1 this criticism, Le Corbusier

insisted in rnaintaining the 'fight angle' in the construction. Affirming he

was no scientist, but rather an arüst, he refused to accept the emr, for

the Modulor was, after ail, a lyrical construction, 'a question of high

-es.'74

In reaiii, the 'place uf the right angle' was a -c premise. Its

exactitude was not irnpartant, but rather the fact that if a solution was

to be fourtâ to the pmblem of proportion, the 'right angle' wuid have to

be responsibie for it. The 'place of the right angle' had long been used

by Le Corbusier in his paintings and architecture, and it represented

for him a first certlude Fi.241. lt was, of course, a certitude based on

vision and intuition, for there was no mathematical proof that the 'place

Ibid.. p.235. " ~e Corbusier, MO~UIOTII, p.47. 73 'M.Duffau8s communication is important, corred, elegant, very simple. But.. that was not the way I had chosen. ..A agree that this drawing was based on an i'drea and did not offer any matennal searrity. The Duffau drawing is rigorais and easy in exeanion. But it is an a pshïori drawing, and the idea for it would never have coma to anywie's rnind as a phenornenon of intention: it is a drawing par 8xceilem of checking and redification.' Le Corbusier, Modulor I l pp.47-48 7i lbid.. p l 0 2

The Mcduiwin lhe MEiror 3 1

of the hght angW wuould in fad contml the resub of a painting or a

piece of architecture.

Its use in determining the finai fonn of the diagram of the Moduior

suggests that the Modukr was a more graphic than sienMc

constnrcîion. The 'place of the right angle' helped Le Corbusier place

the third square inside the first two in the same way it helped him

organite the different elements of a canvas, suggesting mat despite its

geometricai basis, the diagram of the Modulor wss in fad a visual

construction. A reading of Le Corbusier's two books on the Modulor:

Modulor I and Modulor II, confimis such hypothesis, demon~tr~ng

that for Le Corbusier the graphic design of the Modulorwas not a mere

illustration of his invention, but the invention itseif.

It was on(y after producing the drawing of the Modulor that Le

Cofbusier considered his invention ready. This happened in December

1945, while he was on board of the Liberty Ship Vernon S. Hood, on

his way to New York aty. Shortly before this trip, Soiîan, a young

collaborator from his studio at 35, rue des Sèvres, demonstrated that

the Fibon- series Le Corbusier had been manipulating

geomeaically were, in fad, a linear phenomenon: 'Your "Grid" is

merely a fragment of a linear system. a series of golden sedions

moving towards zero on one side and towards infinity on the other,' to

which Le Corbusier repiii: 'AI1 nght, Iet us cal1 it henceforth a ~k of

~ h e ~ o t i u h r in ü~e ildbrw 32

pr~portions.'~~ [fig.25] Upon the accasion Soltan made a graduated

strip with the values obtained from these two Fibonacci series and Le

Corbusier from then on took it with him everywhere he went [fig.26].

It is interesüng to notice that this graduated

strip, containing the measures from the

Fibonacci series were already applicable in

practice, and the Modulor, in mechanical terms

could be considered to be the embodiment of

these measures. Le Corbusier however was

not yet satisfted with the resuits of his

investigation. He did not think that a simple

numencal strip or table were the Modulor or

were able to explain The Golden Section was for him a

confirmation that he had found something important. Nonethdes, his

invention was not yet cornpiete, he was still lwking for its explanation.

On board of the ship though, he resurned working on fi. His work

involved a graphie examination of the elements he had so fat, together

with a re-arrangement of them. These elements consisted of the

graduated strip containhg the Fibonacci values and the diagram with

the 'man-with-am-upraisecf inserted in it [see fig.171. He took this

geometfical construction at one side and the nile at the other, and, by

" Le Carbusier, W o r 1, p.48. " The 'Modulor' is a measure based on mathematics and the human scale: it is constituted of a double series of numben, the red series and the blue. But, if that is ail it is, wouldn't a numerical table do the bick just as well? - No.' Le Corbusier. Modulor 1, p. W.

'inmrporating both condusions in a single drawing I obtaind a very

fine pict~n.'~ rig.2n mis picîwe was thsn the definition he haci imm looking for. ARE# the picture was d y , Le Corbusier could findly

expfïcate the Modulor, 'the drawing itseA suppiying an explanalion of

the invention':"

This time, it was a simple matter to give a description[my italicsj: #a 'Modulor' is a measuring bol based on the human body and on mathematicS. A man-with-amiupraised provides, at the detmining points of his occupation of spaœ - foot, solar plexw, head, tips of fingers of the upraised a m - three intmals which give rise to a series of golden secüons, called the Fiùonacci series. On the other hand. maaiematics offers the simplest and also the most powerful variation of a value: the single unit, the double rit and Ore #me goiden &ons.

A drawing for Le Corbusier was not a mere Pustration of an idea, but

the idea itself. Thus, the drawing of the Modufor held itç definition as

well as some of the histary of the invention, In this dmng each element had a meaning, offerhg precious help in undetstanding both

the invention and the search that kd to its discovery. Their insertion in

the drawing was pMse, transfoming the image into a dear

expression of Le Corbusier's intention. That is where Le Corbusier's

invention lied, in the abiiii to absorb an the information he got

- -

* Ibid, p.52 Ibid., p.55. " Md., p.55.

thmughout his research and combine them into one sale thing using

plastic means.

I had not realized at the time that 1 was, in Fad, -ng something: I placed the man in the centre of the drama, his solar plexus being the key to aie three stages expressing occupation of space by his limbs. These three stages started off a series of golden sections which tumed out to be the Fibonacci series (of which I did not know as much as the name). But in my hands, the hands of a plastic artist, a creative artist, a man absorbed by forms and harmony, the mathematical relationship became embodied - spontaneously - in a hamonious spiral, an ideal shell. That is where my invention cornes in, the invention on the Vemon S. Hood, not scientific in character, but a spontaneous product of a passion for poetry and the plastic arts. All that has followed and is still to foJlow, conceming the Modulor and myself, will not deviate from this single line.

Only after Le Corbusier was able to join his ideas graphically, after he

was able to understand them visually, was he finally in a position to

consider his invention ready, at last invented, created. That is where

rny invention cornes in, the invention on Vemon S. Hood, not saentific

in character, but a spontaneous product of a passion for poetry and

the plastic arts.' ''

Thus. his invention wnsisted in the appropriation of the results of his

research and in the creaüon of the drawing of the Modulor. This

drawing contained information that was crucial to its understanding. It

united his first conclusions and their onginating ideas together in a

single figure. Unity and synthesis were what Le Corbusier had been

looking for. He considerd the Modulor a 'tool of unity'." The Modulor

was a 'mechanical tooi' in the sense that its use propitiated un@ into

the work to which it was appried thmugh a consonance achieved

among the measures used. On the other hand, its making, I s

'discovery' by Le Corbusier also allowed for the unification of his main

ideas on art and architecture. He managed to achieve unity both

mathematically and plastically. Mathemaücally through the discovery

and use of the Fibonacci series in his work, and plasticalty through the

" Le Corbusier, W u l o r Il. p.208. Ibid., p.208, Ibid.. p.296.

The Modulor in the Minw

unification brought about by the transformation of the F ibonacci series,

a linear phenomenon, into a spiral.

This is a fad Men overlooked by scholars of the Modulor. When Le

Corbusier entered the Vernon S. Hood what he had was a stnp of

measures, a rule. His invention consisted basically in joining together

of previous discoveries, but also in the metamorphosis of this rule into

a spiral.

And page SI# gives the drawing which was, pehaps, the maa l moment of the Modulor: an image of hamony, an invention by a piastic artist who, across the gnd of figures (or numbers), draws that which is close to his heart: a harrnonious spiral (or shell), &material phenomenon that can be grasped by the eye, danling in its sape.

The spiral, or shell, relates the Modulor to the architeds earlier

researches on space, numbers and sound. Through its incorporation

into the drawing, Le Corbusier made a dired cannedion between the

Modulor an^ these theones, managing to unite, in a single invention, a

signiftcant part of his thinking in architecture.

The series of Golden Sedions were themsehres important, they

allowed Le Corûusier's initial goal wtiich was to rewncile human

measures with mathematics, while &ring flexibiltty. The spiral,

however, transfomecl these measures as well as the nsearch of the

Modulor into a personal matter. It inserted them in a definitive manner

into the whole of his thinking and work, transfomihg his 'discovery' into

an 'invention'.

From the start we had dedared: 'Behind the wall, the gods play; they play wiih numbers, of which the universe is made up.' We had opened a chink on the door and seen the gods et play; tri& vafiogs hypotheses. and had the gmd fortune to stumble on a favourable number.

Le Corûusier, W u l o r 1, p.51. This is the page where he first shawed the definitive drawinp of the Modulor. the one he did on board d the ship Esee

In icon B2:The Mind [see fig.101, in the Pdkne de l'angle droit, Le Corbusier celebrated his invention by placing the dtawing of the

Modulor in the centre of the figure. He also confirmecl thé condusions

presented hem through the insertion of the image of a seashell in the

referred composlion. The sire of this image is apparently exaggerated

when contrasted with that of the drawing of the Modulor, suggesting iî

should be given proportional importance in the interpretation of this

parücular icon. In realii, the sea-shell had an immense significanœ

not only in the making and understanding of the Modulor, but also in

Le Corbusiefs whole work. The sea-shell represents Le Corbusiefs

admiration for nature, and also a fundamental theory for the architect,

namely that of the 'acoustique plastique'. This principle was one of the

most enduring sources of inspiration for the archited's thinking in both

architecture and art, having also been responsibk for sorne of the

most exuberant fonns in his late architecture, k ing Ronchamp a

dassical example.

It is not hard to understand how the sea-shell must have fascinaled Le

Corbusier. Due to its dear and precise geometric structure, the sea-

shell is one of the best examples of mathematics niling the realm of

nature. Moreover, the sea-shed is a concfete expression of the laws of

proportional growth in nature. In its intricate design, the mathematical

progressions of the Goiden Section make themseives visible, lfig.281

transfoming this natural architecture into a perfect source of

inspiration for Le Corbusiefs research.

The image of the sea-shell should also be understood as the

emboâiment of the principle of the 'plastic acoustics', or 'visual

aeoustics'. As the name suggests, the 'acoustique plas@ue' involves

both vision and sound, a fad reinforced by the symbol #self - sea

shdls are both visually harmonic and produce harmonic sounds.

Moreover, it is also worth mentioning that its shape resembles the

lobule of the ear and some musical instruments like the hom. In the

case of icon B2:The Mind, the mure of the sea-shell Efig.291 can be

seen bath ways: a visual phenomenan, a naturai structure that appeals

to the eyes and a musical one. By tuming the

picture sideways, it is possible to recognize on

it a musical sign, nameiy a F key. The twisting

of images is a process used by the Le

Corbusier in the production of his plastic work,

king a special feature of the 'acousiique

plastique'.

The semhell is also part of a series of found objects that Le Corbusier

started collecting and which he later named 'objet 8 riseciron poétique'.

The idea appeared in the archited's work by the end of the twenües

and involved the notion that certain abjects were cawble of invoking

p d c emotion, or, to be more pm3se, of 'radiaüng' p 3 ü c emotion. Le

Cohusier would take these abjects and draw therrt over and over

again, until he had finally absorbed them into his own vocabulary. In

the case of the sea-shell, the a r c h i i was able to associate it with his

other researches, including those on space, proportion and his idea of

'radiation' as an architedural phenornenon, and Iater combine them

into one sole phenornenon under the concept of 'acous@ue plasüque".

The notion that architecture is capable of 'radiing' is a rather complex

one, and is undoubtedly related to Le Corûusiefs rnystical experience

at the Athenian ~cropolis.~ wtiere he spent a few weeks obse~ng the

Greek parthenan. Ifig.301 By that time, although œrtainly not

intentionally, he associateci the Ampolis and its power of 'radiaüon'

wiih a sea-shell:

The Ampolis, *se flat summit b a r s the temples, captivates wr attention, like a pari in its shell. One ceiilects the sheil only for the pearl. The temples are the reason for this landscape?

The concept of 'radiation' is samehow expiaineci through the

mlatianship between the shell and the pead. The pearl, as he stàted, is

the reason why one coilects the shell. But even if its beauty and value

exceeds that of the shelt. its existence cannot be completely separateci

from the latter's. If the Pearl exisîs, it is because the shdl existed first.

On the other hand, the shell acquifes special significanœ on aecciunt

of the Pearl. They depend on and support each other. In the same way

a building relates ta its dose environment Its existence depends on

the site, it is influend &y and refteds thé surtoundings. Mile at the

same time it 'radiates' on the landscape, giving it a reason to exist.

This concept, which Le Corbusier also applied to the way works of art

interacteci witt~ their sumundings, was later the basis for the idea of

the 'acoustique plastique', and has been sumrnamed &y Le Corbusier

ACTION OF THE WORK (architecture, statue or picture) on its surroundings: vibrations, aias or çhouts {such as originate from the Patthenon or, the Acropolis in m m ) , a m darting away tike rays, as if springing from an explosion; the near or distant site is shaken by them, touched, wounded, daminated or caresseci. REACTION OF THE SETTING: the walls d the m m , its dimensions, the public square with the various weights of its facaûes, the expanses and stopes of the Iandscape, even to the bare harizons of the plain or the stiarp ouüines of the mauntains - the whale environment brings ib weight to bear on the plaœ where then s a wwk of art, the sign of man's will, and imposes on it iîs % spaces or projections. b hard or soft ciensitier. ii?l violences or its softness.

Le Corbusbr, doumey b the East. Ibid., p.209. Le Corbusier, New W N of Spaœ, p.8.

ne Mcdulorin Ihs Mnw

In a similar way, the -a-shell inwrporated the architect's ideas on

architectural space. Le Corbusier thought of architectural space as a

dynamic sfnidure that had to relate to its inhabitant. He believed the

reason for architecture was man, a man that sses and apprehends it

through his 'embodii seif, as Medeau-Ponty would put it, or through

his 'psycbphysidogy', as Le Corbusier defineci it. A complete being is

both corporeal and spiritual and architecture evokes the spiritual in

man through the mate ria^.^^ The illustration Le Corbusier used to

describe the interadion between architecture and its sumundings also

explains the relationship man has with architecture. It speaks to his

body in order to achieve his spirit, therefore it should f~ his body in the

same way a shell fits I s mollusc, that is, like a second skin. In this

context the word 'radiation' wuld be exchanged by 'resonance'.

Works of art and architedure resound on man. They speak di- to

his body and touctt a mysterious key inside him that vibrates in

response. It is like a dialogue man estaMMes with the environment,

assuming that he is, or was in the beginning of time, one with 1 Thus

the dialogue can only happen wiîh things that relate ta his innermost

essence and are in consonance with him.

Le Corbusier, Wupar l, p.148

The Moduior in the Mhx

On di qu'un visage est beau larsque la p-sion du modelage et la disposition des traits fév&nt des pmportions qu'on sent hamnkuses - parce qu'elles pmvaquent au fond de nous, par de18 nos sens, une dsanance, sotte de table d'hamnie qui se $et B vibmr. Trwe Gabaolu inddfiniissabk pdexistant au fOnd de notre Btre

For Le Corbusier man, nature and the cosmos wefe al1 united. al1 in

consonance. This is what allows man to relate to his surroundings and

to be able to understand it. Man belongs to the same 'axis' [axe] mat

al1 other natural things belong. He is part of the Universe, something

larger than himself, but to which he can relate because he belongs to

it. This presupposes a 'unity of intention in the universe, to adml one

soie will at iis sourceDe meaning that everything is part of a

hamonious whole, everything is in the same 'axis'.

The interesting thing is that manmade objects, that is, the objects of

culture, can also be part of 1, in fact they should be part of ks3 so that

they could produce on man the desirable effects of a universal

harmony, and the example given by Le Corbusier is again the Greek

Parthenon [fig.31]:

Si l'on s*arr&te dzvant le ParthBnon, c?W qu'a sa vue la corde interne sonne; I'axe est touche.

Le Corbusier, 02 Ibid., p.171.

Ibid. p.171. 44 Ibid, p.171.

Vers une architecture, P-1 65-

The reiationship with music is evident, and more than a simple

metaphor, it is the way through which Le Corbusier understood

harmony and man's reiationship with the universe. Everything that is

on mis 'axis', everything harmonious, resounds on man, that is,

produces on him effects similar to the ones provoked by music. Et was

also through music that Le Corbusier was able to understand

mathefnafics.

Mathematics, with its complexes and absûact calculations, had been

out of Le Corbusiets grasp. Music, howevet, had ahmys been part of

his He, for both his mother and his brdher were musicians. To them

Le Corbusier attributed his desire to 'wnquer musid and his

aspirations to find an ' inward essence of music camied beyond sound

to the plane of inner silence: joy - effusion - pknitude - beatitude, if you

wish to cal1 it so.'= Despite k ing unable to read music, Le Corbusier

Men dedared himself able to comprehend and 'pas judgement' upon

it. He also dedared that it was through music that he was able to lay

hold of the mathematical phenomenon.

More than these thirty years past, the sap of matfiematics has R a m i through the veins of my work, both as an architect and painter; for music is akvays pressnt within me. (Let me explain hem that at school 1 was very bad at mathernatics; the subject only filled me with misery and dista~te).~

The W e e n mathemaücs and music is ammonplace

when it cornes to the history of proportions. Music had always been a

source of harmony, and sine Pythagoras found out that there was a

dose relationship between certain numben and the notes in a musical

scate, mathematics have been used to express it. Henœ mathematics,

through this association, became a way to achieve harmony, and the

search for ideal proportions in the visual realm have also, since then,

had mathematics as a means.

95 Le Corbusier, W u h r il, p.144. 9a Le Corbusier. Msduor 1. p. 129.

How many of us know that in the visual sphere our civilization has not yet m e to the stage they have reached in music? Nothing that is built has yet enjoyed the advantage of a measure equivalent to that possessed by music, a working tool in the senrice of musical thougP

Le Corbusiet s admiration for music led him to search for mathematicai

ratios that could bring the beauty found in music into the realrn of

vision. Le Corbusier believed music and architedure to be part of one

same phenomenon, both being a matter of 'time and spacet. 'Music

and architecture alike are a maiier of mea~ure.~ His intention was to

create a scale of visual measures, like the sound scale Pythagoras

had discovered, which would help him organize the malm of visible

things in the same manner a musical scale orders the realm of sounds.

Like Pythagoras, he based himseîf on two certainües: mathematics

and the human body. As he justified, Pythagoras adopted ' two points

of support capable of giving both certainty and diversity: ... the human

ear, ... and Mathematica, herseK the daughter of the ni verse.^

Although a produd of the visual realm, the Modulor had, as a

wunterpart, the audible phenomenon of music. Like in music, this

scale would not interfere in the -on of the work, only in the

orchestration of the ideas already present, already invented. This

interchangeability between music and plastic work, or between vision

and sound is a strong characteristic of Le Corbusier's work. It reveals

his understanding of art as one single phenomenon, based on

intention and intuition, notwithstanding its use of diierent languages,

or its diierent forms of expression, Art is an arüculation of man's

humanity, be it in the from of music, painting, words or stone.

In order to recagnize the presence of an acoustical phenornenon in the realm of fom it is necessary to be, not an initiate of taboo words, but an artist, a being sensitive to the things of the univene. The ear can 'see' proportions. It is possible to 'hear' the music of visual proportion. I belîeve that the arüstic instrument capable of a ~ ~ a t i n g these things is the human animal itself, in equilibnum: it perceives

gT Ibid., pp.16-17- 98 Ibid.. p.29. gg Ibid., p.16. '" Le Corbusier, Modulor II, pp.148-9.

Fig. 32

A3: MILIEU

lcon A3: Milieu [fig.32] belongs to section A, entitM Milieu, wttich is

dedicated to the wrld we INe in and to which architecture should

relate. This world, both natural and manmade, represents the human

environment. the world available to the senses. from which the aRist

draws his inspiration.

Des hommes peuvent tenir un tel propos les bêtes aussi et les plantes peut- &re Et sur cette tene seulement Qui est nbtre.'

In the icon, the world is represented by the straight Iine of the horizon

and by the cide and crossing lines. These latter c m be uncterstood as

a ground plan representation of the situation showed above it, that is,

the man and the horizon line. In this manner, the horizontal line at the

level of the man's navei would gather the four horizons available to

man, that is, it would encircie him, as the arde suggest, gMng him a

home. Le Corbusier used the metaphor of the four horizons to refer to

the natural environment surrounding the Chapel at Ronchamp, the

landscape that would host the churcti and to which the latter would

l Le Corbusier, Poem de rangle dm, A1 : Milieu.

me Modulor in the Minor

address itselt through the phenomenon of the 'acoustique plastique"?

In the Poème de I'angle droit though, these four horizons stand not

only for the natural world, but aisa for the world of culture.

The horizon line has aiways played an important role in Le Corbusier's

Iife. From the vast horizons which open up from the valley region of the

Swiss Jura, where he was bom, to his love for the Mediterranean sea,

where he died becoming one with it, Le Corbusier always stressed the

importance of the horizon. In a very interesting article which examined

the archites penthouse at rue Nungesser-et-Coli, Peter Cari discussed Le Corbusier's relationship with the hori~on.~ As he

remarked, many instances on Le Corbusier's apartment recalled the

horizon line, like the parapet on the bitjardin (itself an artifidal

horizon), the interplay of tables, and his elevated bed, from which the

author suggested Le Corbusier re-enacted every moming his rise to

dmitura. He aiso @nted out the fad that it is rare to find a painting of

Le Corbusier in which a horizontal line is not present. This also applies

to most of the Mhographs in the Paéme de /'angle dmit [fig.33].

This p r e o c ~ u ~ o n with the horizon was also present in the principle of

'radiation', which was the Mec2 that the horizon, or the landscape,

produced in the wark d architecture and the response the latter gave

to the former. This relationship was later used to describe the way a

work of art relates to fis environment, having been transformecl in his

theory of the 'acoustique piastique'.

Furthemore, the horizon establishes with man a very particular

relationship. As far as it depends on vision, the horizon has a diierent

The chape1 at Ronchamp, a pilgrimage chape1 on the last buttress of the Vosges, m'Il be a place of mediiation and prayer. To the west, it commands the Valley of the Saône, to the east the chain of the Vosges; two small valleys to the norVi and south. These landsapes with four horizons are a presence; they are pur hosts. To these four horizons the Chapel addresses itself by the effect 'af an acousüc phenomenon introduced into the realm of foms'l Le Corbusier, lwoduior Il, p.251.

Peter Carl, 'Le Corbusieh PetMouse in Paris, 24 Rue Nungesser-et-Coli," in Daidalos 28 (June 1988). pp.65fS.

The Modulor in fhe M i 45

height for each p e m . Even if the horizon Iine is Mys there. pn-

exMing and fixed, i!s grasping implies a mmpletely individual

experience. Likewise, the worid is one, but each man relates to it in a

personal manner. Each man has his own 'view' of reality.

Nonethefess, !bis expebnce is oniy made possible by man's upnght

position, wttich Le Corbusier referred to as d a m . k is oniy when he

n e Modulor in me MW 46

is on his feet that he is a h to apwate the view th* is offered to

him. Lying down he faœs the sky, an incomprehensible realii for him.

Upright on his feet he sees the wodd, his home, his milhu, to w h i i he

must relate in some way. This position is also a dynamic one, for only

in a standing position is man ready for action. 'Because you are

standing, yw are fit for adion." It is through acting that man engages

the world and becomes reconciled with it. It is also through his uprigM

position, his droiture, which means a msponsible and respectfui

attitude in relation to his surrounding realii, that man can contrad with

the worid a 'right angle', or 'un pacte de sdidanté'.

In the Modulor the 'right angle' is seen represented in the figure of the

'man-with-am-upraised' and the Iine joining the two initial squares.

These two squares are brought together by superimposlion. therefore

forming a ho~orrtal line in their junction. Intentionally or not, in icon

B2: The Mind, Le Corbusier stretched this horizontal line, making it

resernble the line of the sea in icon A3: Milieu.

The nlationship between the sea and

the horizontal line of the 'right angle'

is alsa illustrateci in some of Le

Corbusier's buildings at Chandigarh.

Through the use of water pools

supposedly to collect water, Le

Corbusier managed to duplicate the

facades of some of his buildings by

mimring them in the wateafig.341.

The case of the Palace of Justice is

especially signifîcant, for -its side has

the shape of a square which, by refledion, depids the double square

of the Modulor system: tfg.35j

' 'Puisque tu es droit te voil8i propre aw actes.' Le Corbusier, M m e de /'an@ droit, A3: Milieu.

'Montre, par reflet, le double carré-' Le Corbusier, Oeuvre Complehs VI, p. 57. extracted from Jaime Coli, 'Le Cotkisier. Taurwux: an Analysis of the

Like the iefledion of the building on the Wer, the 'riqttt angle' stands

for a dialectical relationship wheré h m elements meet and get

reconciled without overiapping. The same applies to Le Corbusier's

work as an artist. His woh is full of contrastirtg elements, Iike light and

darkness, feâ and blue, old and new, to name anly a few. In this

context, the 'right angle' offen the passibiri of reconciliation and

synthesis, without destroying each elemint's individualii.

Morewer, action Mers to the creativii of the artist, implying both his

engagement wrth the world and his a d of making. It is through his

droitum, that is, through an ethical at!itude, that the artist is able to

perfonn the 'acte kudmyant de cammunibn,' as Le Corbusier wlled

the act of creation on icon 03: Fuskn. What's more, inasmuch as the

relationship ktween man and the horizon ccinstitutes an individual

expedenœ, the 'ade ibudmyant d& communion' is onIy possibie at a

personal level. As Le Corbusier said, 'any architecture which makes an

appeal to the mind is still always the work of one man.' C-on is a

petsonal ad, aniy made possible through the artist's respect to the

m e r and to the reality of the worid.

It was this relationship with the wrld Mat allowed for the creation of

the Modulor. As seen f m the examination of icon B2: The Mind,

each dement of the Modulor came from Le Corbusiet's engagement

Thinking Proaess in the Last Series of Le Musieis Plastic WC#, p.550. Jairne Cal1 refen to these reflected squares as the two squares of the Modulor system. The connecüon is also seen in a graphic fom in the book Remontres avec Le Co&usier, e d i i by Fondation Le Corbusier (Paris: Pierre Mardaga editeur. 1987)

with the reality around him. Le Corbusier, as an upright man, did not

remain unmoved k i n g life and the world. Instead, he threw himseK

'into 1 heart and soui', assuming his droiture and irying to teconcile

himsel with it through this atütude, 'cmting an environment to ffi

himselt'! In this sense, the Modulor becornes a tool of reconciliation

not only in respect to its instrumental use, but also through its

research, that is, through the opportunity it gave Le Corbusier to

engage with the world, recanciling himsetf with it This is confirmeci by

the ?.todulots phce in the Pc&m de i'angie dm. The Modulor does

not belong to section G: Tool, but rather to section 8: The Mind, which

contains the intellectual, abstrad framework with which architecture is

made possible. It is there that the Modulor belongs, amongst the

architeds attempts to create, out of the cosmos, a world for himself,

suggesüng that its real value lies not in its applicabiiii, but in the

research itseff.

The Iine of the horizon appears in icon G3: Taol [fig.36] in a diiferent

fom. lnstead of its usual stretched configuration, it is shown in the

arnbiguous shape of a squared cirde, probably representing both the

world of nature in the shape of a cirde, and that of cuiture in the shape

of a square. These realities, united by the force of the 'dgM angle'.

which bring them together without allowing their dissolution, ernbrace

the archïtect's worid by giving his ideas and his pracke a home.

lnside this circular square or squarsd cirde, the hand of the a r c h i is

seen drawing an inveited cross. This cross is obviiusly a new

metamorphose of the 'right angle', which by the force of being d m

and redrawn. incorporated a new meaning. In the text accompanying

the icon. Le Corbusier desctibed it:

On a avec un charbon tracé lgngle droit le signe II est la dponse et le gui& k f ' ?ne réponse une choix ... Il est la réponse et le guide ma dponse mm chok

' Le Corbusier, W m e de Pangle droit, G3: Twl.

The Moduior in the M i m

Fram a response and a choice, Le Corbusier had taken it as his own

response, his own cltoice. This suggeds a shift in his way of thinking.

Le Corbusier had aiways thought in ternis of universality, and the

Modulor is a classical example. The subtitle of the book on the

Modulor describes 1 as 'a harmonious measure to the human scale

unive~~aIIyfmy italicsl applicable to architecture and me~hanics.'~ Le

Corbusier's aims were to mate a module for the standardkation of

industrial goods and çonstnrction elements. Through this module, he

believed he would be able to bring hamiony and unity into the wodd's

production. 'tet's not lose sight of our aim: to harmonize the tlow of the

world's produds? His dreams of hermony and unity did not wnœm

only his work, but involved the world as a whole. He saw the woild

fragmented by the advent of the machine and the loss of common

ideals and sought to hamnùe it.

From his studies of the architecturai past, Le Corûusier was able to

perceive that most of the great historia1 architecture were brougM

about by people with shared beliefs. As Tim Benton remarked, when

Le Corbusier wrote his book When the Cathedrals Wete White, he

praised gothic architedure not so much for its 'technological daring',

but for the 'international accord with a common ideal," the same

accord he found in the Parthenon and in the 'folk house', a unity of

intention, an embodiment of colleetive values.

Le Corbusier's dilemma was the same faced by contemporary

architects. After the breakdm of traditional cosmologies, there are no

common ideals, no shared Wiefs to which architecture can relate. For

a white, Le Corbusier was driven, Iike so many wrrent practitioners. to

believe in technology as a possible framework for action. His idealism

hawever, âid not allow him to follow that rad. Le Corbusier's belief in

Le Corbusier, lwodulor 1. Ibid, p.107. ' Tim Benton, The Sa#ed and the Search for Myths,' in In the FoUlsteps of

Le Corbusier(New York: R i i International Publications, 1991). pp.238- 245, p.239.

The ModurOrin tncr M m 5 1

what he défined as an 'ideal gfSantesqu8 qui me domine et que je poumis attehdm, '~uld not let him accept such simpüstic modes of

thinking and acting as ideals for his work. Mead , he drove himsell

inwards and tried tu find in c m h t y and in his own work a framework

for adion. In the W m e de f'angle droit the search for universali is

substituted by a more personal relationship with his work and to the

wortd. In the place of a 'universalIy applicable tml, Le Corbusier

asserted his choics fur a more persanal tool, hi's response, his choice.

This is also perceiveci in the metamorphosis of the 'rigM angle' into a

cross. This transformaüon suggests the idea of religiosity.

NeverVieless, since the cross is inverted, the referenœ is not to

institutionalized religion, but rather to a more secolar dodrine. This

doctrine, as seen fmm the text, sîands for a personal set of beliefs,

which the Poéme de l'angle druif is the expression. 'La conscknce en

a faif un s@ne II est la &ponse et le guide."

The Poéme de l'angle droit has been considered by some as an 'act of

faithl."The very fad that its Econs are amnged in a plate which Le

Corbusier gave the name Iconostase helps confinn this hypothesis. ln

an Ortfiodox Churcti, the Icomstase is the screen where the icons am

hung. It serves as a 'barrier between the nave and the sanduary, to

which only the initiated have access." The Pudm can aiso be

interpreted as an initiation pracess, where tnrth (or meaning in the

case) is achieved by foltowing the fitual sequence of the immfase.

Le Corbusier beiieved architedure tu express the spiritual thmugh the

matenal. in a reference ta the Greek Parthenon, he sta!ed that Phiias

'a fait oeuvre de perfectiior?, de haute spiifu8/ii.'a In the same way, he

t e Corbusier, PMWons, p.12. ' Le Corbusier, Poème & Pangie droit, G3: Twl. ' Tim Benton, The Sacred and the Search fw W. p.243.

Jaime Coll, "Sauaure and Play in Le Corbusier's Art Works,' in AA F& 31 purnrner 1996). pp.3-14.,~4

Le Corbusier, eximied from Werner Oechslin, 'lEmmvoir: Boullhe ami Le CMusier,' in Daidebs 30 ( D a 19ûô), pp.42-55, p.51.

used to describe the mathematical phenomenon as 'fiashes of

fundamental truth,' or 'an authentic fact of reiigi~n,''~ accounting for the

divinity he b e i i i numbers expressed. In the Poème de /'angle dm#

this religiosity seems to have been directed, like the already mentioned

seareh for universaii, towards his own work, or more precisely, to his

way of working. As Le Corbusier stated, 'a man who searches for

hamony has a sense of the sacrecl,' a noüon he believed to be

'individual, campletely individual.'"

I am not a diurchgoer myself, but one thing I do know is that every man has the religious consciousness of belonging to a greater mankind, to a greater or lesser degrw, but in the end he is part of it. In my work I bring so much effusion and intense inner life that it becorne something almost re~igious.'~

Desprte Le Corbusier's praising of the 'right angle' as a tool, the icon

conveys an ambiguity. Is the 'right angle' the tool he talks about, or is it

the hand, his own hand drawing, that is, acting, that he considered the

mal tool? In such ambiguity one finds the first reversibiliiy in icon

G3:ToolI namely that between the hands and the 'right angle'. Both

can be msidered as tools, for they both mean the attitude of the artist

in relation to his work, expressing the 'acte fOudroyant de communion'

Fi. 37

that is the act of creaüon, the act of making. The

ambiguity is also illustrated on icon 62: The Mind,

where the hand of the Modulor man is ciyptically rnixed with the shape of a vise grip tool (fig.3a. In fad, the

hand is present in a few lithographs throughout the

Podm, but only in two of them it -pies the heart of

the icon.

Le Corbusier, ~ u I o r l , p.220. I f Le Corbusier, Oeuvre Camplete IV, 17 O. extraded from Tim Benton ''The Sacred and the Search for Myths", p.240. l2 Jean Petit, Le Corbusier- lui même, extradeci from Martin Purdy, "Le Corbusier and the Theological Program," in Russell Walden ed., The Open Hand - Essays on Le CofBusier (Cambridge: MIT Press, 1977). p.289.

In icon AS: Milieu [fig.38], one sees two hands crossed. Acwrding to

Le Corbusier, they repmsent two poles of tension which must be

recclnciled. As happens with the 'right angle', this reconciliation takes

place without the dissolution of the parts. Bath pofes retain their

individuality and their properties, Mile arning together in union.

J'ai pensé que deux mains et leurs ddgfs en-sés expriment mite dmite et cette gauche imprtoyablement solidaims et si neCessairement é ~ona3er-'~

Fig. 38 Fig. 39

Another instance is icon F3:Oner (The Open tland) [fig.39], where the

hand of the architecî becornes a symbol of Le Corbusier's legacy. 'Full

hand I received. Full hand l give.' As Jaime Cal1 suggested, the Open

Hand epitomizes the 'ta& reveaied to humanity, to preserve what has

been acquired and transmitted to p~stenty,"~ which can be understood

as the very act of d o n , which receives from the cuftural legacy and

l3 Le Corbusier, Poém da i'angiè droit, AS: Milieu. l4 Jaime COB, 'Le CoMer . Taureaux: an Analysis of the Thinking Process in the Last Sefies of Le Corûusieds Plastic WblJç. in AH His&ryVol.iB, No. 4 (Dec 1999, p.537567, note 42, p.566.

ThbModraRprin me hamw 54

gives back to it. The Open Hand wzis for Le Corbusier an offer of

reconciiiion, like the Modulor and the 'ngM angle', where past and

present come together, wittiout overiapping, as is suggesied on figure

40.

Yet, the reversibility is reinforceci by anolher reversibility, namely that

of the icon itseif. lcon 63: Tool is the only double icon in the Poème

de l'angle droit- As happened with the squares of the Modulor,

duplicated by mirroring, icon 63: Twl also has been duplicated

[fig.41].

The Modulor in the M m

As it shares the sarne poslion and the sarne ütle in the

Içonostase, the reverse side of icon 03: Tool also

represents the archiied's tad, but in a fnetamo~h~~ed

way. The lithograph is al1 red and has a small sign in its

left bottom corner resembling an artist's signature. This

sign is a double square with a bull and a labyrinth

inscribed on it Lfq.421. Notwithstanding its apparmtiy

dear referenœ to the Cretan myth of the minotaur and the

labyrinth, like the other signs of the Pohe de I'angle droit this one

has a paiticular, personal meaning to Le Corbusier.

The bull was the subject of a series of paintings Le Corbusier started in

the fifties which are known as Taureaux series. On descn'bing the

beginning of the series, Le Corbusier explained how he accidecitally

found the figure of a bull by looking at a photograph of a 1920 painting

sideways:

You will see hw things come about: tom a vertical painting of 1920, the photograph of which has been lookd at horizontally. One thing leads to another, and thirty years later, the mind busy with other îhings and partiarlariy with the potential of human figures in the arrangement of a 'bestiary', a swies of deformations ensued. And one fine day îhe discovery of a bull on rny canvas came to light, quite out of my control. Then, development of the theme itself, its flowering, and finally a change of sensibility with respect to the theme and a new arrangement of the elements of the painting.I5

The 'accidentai' discovery, as wall as its

intuitive development, suggest that the

series was part of Le Corbusier's 'acoustic'

works." By examining some of the

paintings, drawings and lithographs of the

series, one perceives, in the development

of the work, a recurranœ of Le

Corbusier's seFportrait (figs.43,44 & 451. m-a

" Le Corbusier in a letter to Ronald Ailey, 25 June 1958, extraded fmm Jaime Coll, "Stniâure and Play in Le Corûusiets Art Warks", p.6. l6 Confirmed by Jaime Coll, "Structure and Play in Le Corbusi& Art Works".

The Moduiarin the h#mw 56

Metamorphosis is a well known feature of the 'acoustique pias@ue',

responsible for the 'change of sensibiiii with respect to the theme,' as

well as for the 'new arrangement of the eiernents of

the painting.' Thus the sign on icon 03: Tool is

obviously a development of the Taureaux series and

its a-ation with Le Corbusier is reinforced by its -. similarity to the figure of a bird, which Le Corbusier 4 related to himseK by the play of words Coheau and

In such context, the labyrinth becornes Le Corbusiets home. The

labyrinîh symbolizes intuitive knowledge, the battle the atüst has to

fight within himsetf in order to leave the 'depth and darkness in order to

mach light and creation.'" Or, in Le Corbusier's words, the struggle

between Jacob and the angel that takes place M i n the arüst.la

The labyrinth has also been represented

in some of the Taureaux paintings [see

again figs. 43, 44 & 451 by a spiral line

that goes from the stornach to the rie&,

symbolizing 'the transformation of

emotional knawledge, acquired t hrough

work of the hands, to intelledual

know~edge,''~ which is one of the

fundamental features of the 'acoustique

plastique''. In reali, the Taureaux series,

also known as 'the sign of the bull,' is the

no.

" Jaime Coli, 'Le Corbusier. Taureaux: an Analysis of the Thinking Process in the Last Series of Le Corbusier's Plastic WorK. p.550. '' Le Corùusier, The Final Testament, p.142. l9 Jaime Coll, 'Le Corbusier. Taureaux: an Analysis of the Thinking Process in the Last Series of Le Corbusier's Plastic WorK, p.552.

The Maduior in aie M m 57

last of Le Corbusiets 'acousüc' f o n n ~ , ~ which explains the similarity

between the sea-shell, syrnbol of the 'acousEique plastique', and the

labyrinth and its inhabitant, the bull. Like the mollusc that finds a home

in the shell, the artist finds a dwelling in his own work.

Every man can initiate this process which is, in the tnie çense of the word, creation. E v q man can discover in it [...] what I find in this creative power, the secret of truc happiness. Although the dfiwlties increase at every stage reached, I am happy in this joytUl daily activity. And I am sorry that so few realize the existence of this sowce uf jo and penist in seeking an inaccessible or d6cepîive paradise elsewhere. X

ln primordial times, the labyrinth was a ritual, where the communrty

would conneû itself to the order of the cosmos. In the twentieth

century though, as Alberto Pbfez-Gdmez has remarked on his article

on the myth of Oaedalus - the mythological figure of the primordial

architect and the mator of the famous Cretan labyrinth - the act of

making has beccrme the rilual. The a r c h i can no langer wunt an a

valid otder h m which his architecture would withdraw its meaning.

Instead, he has to discover, through personal making, an authentic

referential for his work

- - - -- - -

Ibid., p.537. a Le Corbusier, "Le Corbusier by himseif," in Le Corbusier- The North American Tour (Canada: The WalIingford Prssç Ltd., 196û), p.15.

The Maauforin the IirlVmr 58

Le Corbusier has obviously re-interpreted the myth, for in his version

the bull becomes the creator, a loneiy figure imprisoned into the

labyrinth of his work. Creativity bernes the ultimate referential for the

arctiitect, a solitary being who has to search for order and meaning in

his own making process.

Two drawings suggest that Le Corbusier's association of the bull and

the labyrinth to his Open Hand, one of his symbols for creatnrity. The

first tf1g.471 shows one of the preliminary ideas for the Open Hand

monument at Chandigarh, where the figure of a bull is clearly mixed

with that of the hand. On the other fsee fig.401, Le Corbusier

associateci the Open Hand to his absorption of history using as an

example the Govemots Palace at Chandigarh, which he also

connected to the bull and its labyrinth. Through these associations,

another analogy surfaces, namely that beiween the 'acousüque

plastique' and the hand, both expressions of the artists creativity and

his act of making. Such connedion is confirmed in icon C3: Flesh of

the Icomtase, w h i i makes reference to the correspondenœ

between the hand and the sesshdl:

Tendresse! Coquillage la Mer n'a cesa de nous en jeter les Bpawes de rianfe hamoniè sur ksgn)vss. Main péffif msù, caresse main g f i La main et la coquille s'arment.

Le Corbusier, PoBme de l'angle d M , C3: Flesh.

fne Moduiorin the Minw

Thus the tHn, sides of 03: tool becorne çomplementary,

dernonstrating the reversibility of the pnnciples of the right angle and of

the 'acoustique p1asb;que' and their relaüonship to the hand of the

architect. Like in the case of the duplication of the squares of the

Modulor, one is reflected in the other. Hand, 'right angle' and

'amustique plas@u& in the fonn of a bull and his labyrinth, becorne

refiected in each other, al[ syrnboliing Le Corbusier's creaüvity.

lntuitively over the past twenty years my figures have evolved in the direction of animal forrns, vehides of eharacter, by means of the sign, the algebraic means to enter into a relatiopip behnren themselves and thereby produce a single poetic phenornenon.

Le Corbusier S ~ b o o k s 11,700, extraded h m :Jaime Coll. "Structure and Play in Le Coibusiefs Art Works", p.7.

~ h e ~odulorii me rn 60

FINAL REMARKS:

THE MODULOR IN THE MIRROR

We could go on forever like mis. along the endless path of deledations. An end has to be made. Others, long befon us, have 6caipied themselves with these matters. The inventor of the 'Holy Boffle" made the Lady Noble Lantem Bacbuc ask this question: W I C H OF YOU IS IT WHO WANTS THE VERDICT OF THE LADY BOTTLE? '

There is a striking resernblance between the sign found in ttie reverse

side of icon G3:Tool and the drawing of the Modulor [f~.48]. The fitst

has a sign inserted into a frame wmposed of a square and its double.

lnside this frame the figure of a bird-bull is seen reffected in a spiral,

representing the artist and his refiection in his own work. Likewise, the

Modulor is camposeci of a 'double cane' containing the figure of a man

and that of a spiral. Their simiiarity increases as one compares the

bid-bull from the reverse side of icon G3:Tool to the Modulor man Le

Corbusier cast in his Unité d'habitation at Marseilles [fig.49]. There, the

'man-with-am-opraised' is seen metamorphosed, having the homs of

a bull inscribed on his chest and his face blended with that of a bird.

' Le Corbusier, ~lkxfulorll, p.196.

The Moûuîorin Ihe M m

t e Corbusier adated himself with Wh the buil and the bird. In the

same way, he must have seen hi& in the figure of the Modulor

man. The onginal heigM of the 'man-with-am-upraised' was 1.75m.

the exact heigM of Le Corbusier. Uke the

Modulor man, Le Corbusier was a 'man of

action', a man engaged in the rear'i of the

worid. Moremer, the already rnentioned

analogy between the hand of the 'man-with-

am-upraised' from icon 82: The Mind and

a vise grip twl suggests that this adive

man was also an artist, like Le Corbusier

hirnself.

if Le Corbusier really saw himseif rdected

in both these figures, as the devebpments

of his drawings leads one to imagine, these

figures become a refledion of each other,

meaning that somehw the reverse side of

icon G3: Tool is like a rnirror image of the

Modulor. The fad that both figures are part

of the same 'acoustic' phenornenon helps

expiain their analogy, as well as provides

some insigM into the relationship between

The 'mustique plastique' was part of Le Corbusier's efforts to mate

a framework for his pracüce. In this sense, both figures are

expressions of such Morts, for bath represent Le Corbusiets attempts

to create, out of the cosmos, a wodd for himsdf. However, Mile icon

62: The Mind represents the intelkduat, abstrad ideas that make

architedure possible, the revefse side of ioon 63: Tool suggests that it

is through the work of the hands that architecture finds embodiment.

Nevertheless, the fact that they both belong to the same phenomenon

suggests that they are not successive developments of an idea, but

rather variations of 1, which means that their reiationship does not

necessarily lead to a logical condusion, k ing simply an analogy.

Nelher the intellectual aspect nor the work of the hands prevail,

Instead, they find themsehres refleded on each other, like their icons.

Such condusion invdves the reabtion that truth is not in one of the

sides, but rather in Vie bordedine betweem them, nameiy in the mimr.

Le Corbusier expresseci this understanding in the law of the meander.

L'idée elle aussi tdhnne se cherche bute en tous sens allant aux extdmes poser les bornes de la guache el de la droite. Hle touche I'une des rives et puis l'autre. Ule s'y me? Elfe a dchoué! La ytité n'est préprésente qu'en quelque lieu du murant bu@urs cherchant son lit. [fig.50]

Truth is not found in one of the sides, but rather on bath of them and in

neither. It is in the dialectical relationship expressed by the 'right angle'

that tnnh is found, or in the metaphor praduced by the joining together

of two different realities, Or maybe sn'll, in the force whïch has joined these realiües, namely adan or dmifum.

Le Corûusier, $&me de fangle d e , A 4 Milieu.

The ModMor in lfre Mmw

Panurge was waiting for 'the word that would deliver him from wretthedness'. He demanded a miracle. The Boffle replied 'Drink!' (or 'tnnk'). To assist my own understanding, I interpret: ad, and p u shall see the miracle. Do not seek a gloss! Do not try to escape! The Botüe tdls you: ~ t i n k ! ~

Le Corbusier used an author that was dear to his heart to dose his

remarks on the Modulor and gke a condusion to the book - Rabelais.

He finished the book (or at least tried to since he still m e sotne more

240 pages after that) by quoting the famous episode when Panurge

and his friends amved at the 'island of Our desire' in order to gel from

Lady Noble Lantem Bacbuc's orade the answer for his query. The

answer given by the oracle, which had to be listened to wilh anly one

ear, was: 'TnnM', which made Le Corbusier interpret it as acf.

Le Corbusier was pmud to define hirnself as a 'man of action'. As seen

before, action demanded an ethical attiiude towards the other and the

world, which Le Corbusier expressed by the French word dmifum,

associating it to his principle of the 'right angle'. fhe fad that he

conciuded his book on the Modulor with such remarks should not be

taken for granted, but rather understood as a realization propiliated by

the research he undertook.

Driven by an intuition, Le Corbusier 'discovered' a rule that would bring

his work into unity. He was after a module to be used in setting the

measures of a piece of work into a harmonious relaüonship among

themsdves and the whole. What he discovered was ttiat his never tiring attitude, his ever present curiosity, and most of ail, his intuition as

an artist, could lead him into unexplored regions, to unexpected

resutts. The Modulor gave Le Corbusier not only a 'harmonious

measure to the human scale.' but also the assurance that it was Mer

al1 his attitude, his dmitvm, the sole responsible for the 'discoveries' t'te

came about. It was through his way of working, through his m8lo;ng

that he was able to get to the unity and synthesis the Modulor

propitiated.

Le Corbusier, Modulor Il, p.200.

The Modulor in the M m

Le Corbusier's making and creativii have already been discussed in

the present work. Howeuer, by mirroring icons =The Mind, G3:Twl

and Le Corbusier's own figure one sees reflected AHM Jany's Ubu

Roi [fig.51], confirming the notions of artistii making as the on@

possible framework for action. Through a 'pataphysical' coincidence

between artist and work, Le Corbusier mirrored himself in his creaavity.

In the same way Aifred Jarry became Ubu Roi, Le Corbusier found his

'other haif' in creativm.

In the Podme de i'angle droit Le Corbusier

praised the act of making, saying that 'faim une

atchitectune c'est faine une &alvre* He also

compared it to the experience of love by using

the Platonic notion of completion found on the

'other haif.' Furtherrnore he related it to the

experience of seif-knowledge by using the

metaphor of the mirror to describe 2:

Catégorique angle dmit du charactèm de I'espn? du coeur. Je me suis miré dans ce caracfèm et m'y suis tmuvé b'Ouvd chez moi h ~ v 8 . ~

Creativdy is the subject of the Po&m de i'angle droit as a whole. It is

in creatiin that the artist finds campleiion and it is through the ad of

making that he learns more about himseif and his art.

Against the stnrcturalist and post-struduralist deconstruction of the 'P

and their proclamation of the death of the author, whicfi George

Steiner recails ends up in the anti-ethicai position of the negation of

' Le Corbusier, M m e de l'angle droit, €4 Charader. 'Et la seconde part vient A eux et se soude Et bien ou mal leur en prend B

tous deux Qui se sont rencontrésl' Le Corbusier, Podme de i'angle droit, C4: Flesh.

Ibid., E3: Character.

ïhe Modulor in bhe MNIW 65

the othery Le Corbusier Mers the possible way out. His wrirk

embraces the 'I', the artist-cmtor, while also Mering the hemeneutic

possibiiii of re-interpretation. M is open without being irresponsible.

When the inexplicable appears in human work, that is, when Our spirit is projecteà far from the narrow relation of cause and eiïect [...] to the cosmic phenomenon in time, in spaœ in the intangible [...] then the inexplicable is the miracle of art8

7 George Steiner, Real Presences (Chicago: The University of Chicago Press, 1991), p.101.

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