Milieu, spirit, flesh and fusion in Le Corbusier’s life and work

How can a study of Le Corbusier’s post-war work – the Poème de l’angle droit and Modulor 1 and 2 – throw light on his earlier preoccupations. These works are retrospective and confessional. They are obsessed with the question ‘By what right may I create?’ The former work looks for answers in experience and the latter in the ‘divine’ world of mathematics. From at least 1906, when he bought and devoured Edouard Schoré’s Les grands initiés, Le Corbusier had a strong sense of predestination and a conviction that suffering was a necessary part of the voyage to enlightenment. His dualism, the belief in the separation of the spiritual and material worlds, encouraged him to view mathematics as part of the ‘hidden world’ of the spirit. His problem, in the research leading up to Modulor 1, was how to reconcile divine proportion and human experience. He invariably described the passage from the material to the spiritual worlds in terms of physical processes – smoking, simmering, brewing, giving birth. This idea, clearly described in one of his lectures in 1929, and his frequent discussion of ‘cosmic’ forces and symbolism during the 1930s, indicates that these ideas were well entrenched before the war.

Two reasons permit me to venture down this perilous path of 'reading in'. I remember vividly Josep Quetglas explaining to me that many ideas can lie dormant in the mind, active and influential, without finding overt expression in word or image until much later. This proposition gained traction with me during my research on Le Corbusier's photographs of the 1930s, when I discovered a taste and talent for the New Photography of the 1920s that had left no visible trace in his work until he began taking photographs with his 16mm movie camera in 1936 and turned to Lucien Hervé as his preferred photographer in 1950. 6 My other excuse is that, after drawing out some themes from these confessional works of the 1940s and 1950s, I will revert to an inductive method, 'reading out' propositions from textual or iconographic evidence. A comparison could be made with the investigative procedure of 'profiling' employed by some police departments which cannot provide proof of guilt but may narrow down the field of enquiry. This is not the place to offer any new insights into the Poème. The most balanced analysis is that of Juan Calatrava, to set aside the accounts of Richard A. Moore and Mogens Krustrup. 7 Where Moore reads in alchemical symbolism and hermetic mysticism, Krustrup looks for insights into Le Corbusier's personal life by trying to interpret his personal iconography. When discussing a document, it is normally best to begin with the text, which Calatrava does well.
In some ways the Poème might be discounted as a scrap book of experience: imagery and parables collected over a thirty-year period. It does not read like a theoretical text or a well-structured programme. Much of the text of the Poème, as well as much of Modulor II, is personal. Most of the illustrations reference his wife Yvonne, vacations on the Bassin d'Arcachon, his collection of seashells, bones and pine-cones and his dog Pinceau. Le Corbusier did, however, take the trouble to organise the pages into an 'iconostase' arranged as 5-3-5-1-3-1-1, which indicates a system of thought. As already mentioned, this structure hinges on the fourth level, given the alchemical label 'Fusion', that separates the physical from the metaphysical worlds. It is notable that this programme is 'top heavy', that is, focusing most closely on lived experience before passing over into the world of the spiritual.
The master set great store by the Poème, as he did for that other troubled work, La Ville Radieuse (1935). In the Avertissement of his book Quand les cathédrales étaient blanches, published in 1937, Le Corbusier described La Ville Radieuse, published two years earlier: Ce livre est le fruit de quinze années de travaux; il est touffu; il est comme un collier garni de nourritures. On me l'a rapproché. Je ne puis pas aujourd'hui encore, aménager un beau salon, où l'étiquette soit reine. 8 He clearly did not worry greatly about consistency. Experience is messy, troubled and confusing. Insights and creativity require failure, struggle and incomprehension on the part of the public.
My strategy now will be to consider Le Corbusier's image of himself as the sacrificial prophet of Modernism. Then I will consider five instances of Le Corbusier's dualist approach before trying to understand how Le Corbusier envisaged the 'harmonising' of the opposites that defined his world.
The path of the initiate I interpret the Poème and the introduction to Modulor II as the via crucis of the initiate, an answer to the question 'By what right can I create?' Le Corbusier had a fixed idea of himself as a predestined prophet or poet, condemned to seek enlightenment and transcend tribulations, sacrifice and calumny. In the Poème he lets slip a phrase evocative of Nietzsche's Superman or the life of Christ: 'Je vis au milieu des hommes en plein dans leur écheveau embrouillé '. 9 This separation of 'Je' from 'hommes' demonstrates Le Corbusier's sense of predestination, perhaps inherited from the Calvinist milieu of his 6 Tim Benton, Lc Foto : Le Corbusier : Secret Photographer (Baden, London: Lars Müller, Springer distributor, 2013). 7 Le Corbusier and Juan Calatrava, Poème de l'angle droit ; Lithographies originales, [Reproduction en fac-similé] ed. (Milano: Electa, 2007). Mogens Krustrup, «Persona,» in Le Corbusier Maler Og Arkitekt;Painter and Architect (Fonden tiludgivelse af arkitekturtidsskrift, 1995), 118-57. I have not been able to consult the dissertations by Nancy Monroe Stephenson (1981), Daphne Becket-Chary (1990) or James M. Splawn (1991). home town. It also reveals Le Corbusier's assumption that he was working for humanity rather than for individuals. Each house design was also a solution to a general problem.
Guillemette Morel Journel has tellingly described his literary style as 'polygénérique'. 10 By this she means that Le Corbusier weaves a web of overlaid arguments, anecdotes and parables to persuade his readers. As part of the introduction to Sur les quatre routes, written in 1939, Le Corbusier recounted in gory detail the terrible accident he had suffered in August 1938, when swimming in the port of Saint-Tropez. 11 A motorboat split open his skull and slashed his thigh, creating a wound as long as La Ville Radieuse (as he explained to his mother). 12 He claimed that there had been nine means of being killed or maimed for life and described his survival as 'the miracle of St-Tropez'. He underwent a painful operation without anaesthetic and spent several weeks in hospital.
When this manuscript was presented to the publisher Gallimard, the redoubtable Jean Paulhan could not see the point of this personal anecdote in an introduction to a book on urban theory. It was cut from the edition published in 1941, but Le Corbusier was unhappy and tried to have the story reintroduced when the book was proposed for republication between 1951 and 1953. 13 In my view, Le Corbusier considered his near-death experience as evidence both of divine intervention and of his maturity achieved through suffering, providing unique insights and solutions for modern society. In the original introduction, he explains that this anecdote was not meant to 'évoquer une situation pittoresque' but to 'expliquer cetaines choses utiles à ce livre.' 14 He explains: La plus forte, c'est la preuve acquise de l'expérience accomplie…Le mal fait, l'accident révolu, l'homme a changé. The experience of facing death is described as a passage to 'the other side -another side of life'. One is reminded of the second temptation of Christ, prompted by the devil to jump from a great height. 16 It lies alongside the many references, in this and other books, to his defeats at the hands of bureaucrats and politicians (League of Nations 1926-7, 1937Paris exhibition, United Nations 1946. Le Corbusier characterised his defeat in 1927 in terms of life and death (figure 1). 17 He sketches the failure of his project for the League of Nations as a fall of Icarus, spiralling to his death. All his efforts over ten years had been crushed ('écrasés par la concussion'). I have interpreted these notes as an exercise in the rhetorical figure of pathos, but they also bear witness to a deeper belief in his tragic status as sacrificial prophet or Messiah. 18 Not only do his failures at the hands of the establishment guarantee his modern credentials, they also reflect his fundamental view of the life of suffering as the true path of the initiate, leading to wisdom. This is exactly the program of Édouard Schuré's Les grands initiés. Schuré explains in his introduction that the great initiates, from Krishna to Jesus, progressed from a perfect understanding of the world and a life of action and sacrifice to arrive at a higher level: only some initiates achieve access through personal sacrifice and pain. 24 The initiate has to spend time in the desert or high mountains, rejected by people and face to face with his thoughts. Jeanneret cited with approval a note from Eugène Grasset stressing the importance of predestination: Vous voilà encore errant à la recherche de la beauté. Elle viendra vous trouver un jour si vous êtes prédestiné. Et alors ressortiront autrement les chocs sensibles que vous aurez reçus ; parce que la beauté ne se donne ni à la volonté ni à la violence -ses entrepreneurs de travaux. 25 This idea of a predestined ascent to wisdom through sacrifice would have been reinforced by his reading of Provensal's Art de demain, where the plight of the modern world is described as an inability to combine art and science, faith and knowledge. The real architect/artist should climb to the highest point and reflect on '…l'endroit où il va, ce que son moi agrandi par la connaissance peut reporter dans l'univers…'. 26 Provensal expresses the anxiety of the artist face to face with creation: Au seuil des portes d'or où l'Initiation groupe les génies aux paroles pleines de mystères, il s'arrête haletant. Cette lumière splendide l'éblouit. L'énigme l'épouvante. 27 Le Corbusier uses similar imagery in Modulor II to describe the experience of entering into the divine world of numbers: 'Le choc de cette lumière est difficile à supporter'. 28

Le Corbusier's dualism
The second theme is Le Corbusier's dualism. In part, this was a habit of thought, tending to separate any condition into opposites. We will turn to five practical examples of this tendency (in engineering, mathematics, the Modulor, dimensions and nature). But first, we will focus on its epistemological form, which insists on the separation of the physical and spiritual worlds. This is stated clearly in the Poème.
L'indicible en fin de compte, soustrait au contrôle de la raison, porté hors des réalités diurnes, admis au coeur d'une illumination. Dieu incarné dans l'illusion. La perception de la vérité peut être bien. 29 Reduced to its simplest form, we find it in some notes for a lecture in 1942: A confirmation of the separation of material and spiritual worlds would have come from an article published in L'Esprit Nouveau No 7 (7 April 1921) by the Chilean Surrealist poet Vicente Huidobro. 31 In an article entitled 'La création pure', he proposed a strange genealogy of art that progressed from intelligence to sensibility. Representational art was a matter of understanding the physical world (intelligence). As art evolved, it moved into the realm of pure creation. As he put it: 'L'Art n'est autre chose que l'histoire de l'évolution de l'Homme-Miroir vers l'Homme-Dieu…'. 32 Citing Schleiermacher, Huidobro insisted : 'La poésie ne cherche pas la vérité, ou plutôt elle cherche une vérité qui n'a rien de commun avec la vérité objective.' 33 '[l'artiste] ne cherche plus à l'imiter [la nature] dans ses apparences, mais à faire comme elle en l'imitant dans le fond de ses lois constructives.' This is the work of poetic and divine sensibility building on intelligence. It is also an explanation for Le Corbusier's illustration of botanical sketches in the opening pages of La This is effectively the basis for Le Corbusier's aesthetic for the rest of his life although Ozenfant and Jeanneret did not express themselves in these terms in the period of Purism. In Après le Cubisme, the emphasis was on searching for order, the unchanging laws of Nature and form, usually understood in terms of geometry. Le Corbusier assumed that art (but also the sphere of number) belongs to a higher level and to access it is to transcend the physical realm into a spiritual one. Mystics, philosophers and mathematicians might aspire to gain access to the metaphysical sphere but, for Le Corbusier, the artist and poet have to find their inspiration in the real world. How to pass from the material to the spiritual is the subject of the last section of this essay.
Le Corbusier's dualism was clearly expressed in the opening drawing of his lecture 'Les techniques sont l'assiette même du lyrisme' in Buenos Aires on 5 October 1929 ( Figure 2). Le Corbusier begins by drawing the line that separates the domain of material things from the world of the spirit: "Sous la ligne: ce qui est; au dessus: ce qu'on ressent". 35 It is notable how many pages of the Poème are divided in two by a horizontal line, sometimes separating the physical and spiritual worlds, sometimes sky and earth, sun and moon. The lecture drawing is extremely important because it explains both Le Corbusier's theory of creativity and his attitude to the material changes that had revolutionized the world. To take the second first, Le Corbusier explains that you have to understand the full reality of the modern world -economic, sociological and technological -before you can create. These realities have to be physically consumed like the three dishes of a French meal. This immediately sets the architect apart from the world of the academy and makes him 'modern'. But this is not enough. To create there has to take place a mysterious process of digestion and reflection -symbolized in the drawing by a smoking pipe -before the little bird of inspiration will take flight, leading to the spiritual and ethereal sphere of lyricism, individual creation and eternal values. To be modern is necessary but insufficient. Work of eternal value -like the Parthenon -will always retain its eternal value. This is his response to the functionalists who asserted that solving practical problems was enough. It was also his answer to the question: 'If new tools replace old tools, why does new art not make old art redundant?' Le Corbusier's dualism is essential to this formula. Le Corbusier's theory of creativity always involves a mysterious but physical transition from matter to spirit: digestion, brewing, simmering or giving birth, often stimulated by smoking and drinking. We will return to this theme.

Engineers and architects
The allegory of the 'trois assiettes' also informs Le Corbusier's attitudes to engineers. As he says in Précisions, he had glorified the engineers in Vers une architecture. 36 Constrained by economy, engineers are forced to base their designs on geometry, thus achieving the pure forms that Le Corbusier celebrated in Vers une architecture. But, as he explains in Urbanisme, the engineers do not understand what they have created. When Le Corbusier and his friend Paul Budry visited the Barberine dam high in the French Alps, they enthused to the engineers about the possibilities of using such methods in Paris. The engineers were appalled: 'Nous leur disons : « Que c'est beau ! ». Ils nous prennent pour des imbéciles. Des poètes ! On est horriblement déçu'. 37 Engineers mastered the physical world but not the spiritual one.
It is interesting how Le Corbusier's symbolic union of hands -originally those of the engineer and architect -become transposed into a symbol of general conciliation of opposites (spiritual and material) in the Poème (figure 3). Opposition of black and white, sun and moon are given powerful graphic expression. With the logo for ASCORAL, the symbol had already been transposed into a cosmic diagram with the sun and moon symbolising spiritual and economic man ( figure 4). This reflects a general progression in Le Corbusier's thinking, towards an attempt to synthesize all the opposites that framed his world into a general system.

Mathematics and proportion
Le Corbusier also interpreted the distinction between geometry and number in metaphysical terms. He expressed this in different and sometimes contradictory ways

Milieu, spirit, flesh and fusion in Le Corbusier's life and work
Un grand mathématicien déclare : « Faire appel simultanément à la géométrie et aux nombres, c'est là le vrai but de notre vie ». 38 The 'grand mathématicien' was his friend Dr Andreas Speiser, professor of mathematics at the University of Zürich. Speiser distinguished between number, which was the sphere of 'order, harmony, beauty etc… in short, everything spiritual' and space, which was the sphere of physical objects and extension. He explained, 'Dans le monde spatial sont projetés des images du monde numérique', a clear transposition of Plato's allegory, which describes the physical world as being like a cave, on the walls of which are projected the shadows of the 'forms' belonging to the higher existence outside the cave, this existence being that of science and geometry, illuminated by the sun of pure reason. For Speiser, number and geometry belong to the world of pure reason whereas space belongs to the real world.
Le Corbusier did not share this Platonic idealism in this form. Le Corbusier explicitly rejects the approach of pure theory -the approach of the mathematician or philosopher -to insist on his own route to 'illumination'.
Quand cinquante années d'une passion accumulent les observations de chaque minute d'une vie active, il est pardonnable, explicite, possible, qu'en certains virages, une illumination se produise : un homme voit clair, il découvre. 39 Le Corbusier meant by this an insight that passes beyond reasonable deduction into the realm of immutable truth. The word 'illumination' is important here, since Le Corbusier constantly defines happiness and wisdom in terms of sunlight.
Employing a different sense of the word 'number', Le Corbusier contrasted his approach to that of the mathematician Le Lionnais: Le mathématicien joue avec les nombres, il est messager des « dieux ». L'homme n'est pas un dieu, par définition. Et le poète que je suis déclare : pour prendre contact avec l'univers, l'homme regarde, employant ses yeux qui se trouvent « à 1m. 60 » environ du sol. 40 The artist cannot 'play with numbers' but must search for truth through his senses. For Le Corbusier, the poet is similar to the visionary and prophet, figures of enlightenment who see beyond the physical world.
[…] Le poète est celui qui montre la vérité nouvelle. 41 The difference between a poet and a prophet is that the former is inspired by experience and the latter by faith, a faith nourished by his belief in himself as predestined initiate.

The Modulor : golden section and dimensions
Le Corbusier conceived of another way of contrasting number and space. In Modulor II he contrasted proportional systems, which are based on geometry and number, and therefore 'divine', and dimensions, which relate to the real world and the bodies of men and women. He expressed this in a comment about an architect Guettard who visited him and enthused about the 'key number 113' and no doubt about the mathematical and esoteric significance of numbers in general. Le Corbusier noted: The proposition was to begin with human dimensions and then look for an intersection with geometric proportions. Important for Le Corbusier was that the construction should be inscribed in two squares. The incoherence of this instruction was demonstrated by the first solution of Le Corbusier's assistant Gerard Hanning, which was to extend one square by the diagonal of half the square on one side ((√5-1)/2) and by the diagonal of the square (√2-1) on the other. This creates a rectangle with a combined length of the extended square equal to ca. 2.032, nearly forming a double square. If this rectangle had been a double square, the right angle inserted into it would necessarily have constructed an isosceles triangle symmetrically disposed around the centre point.  Hanning and Maillard diagrams in his sketches over the next five years demonstrates both that they were significant and that he had trouble understanding them.
Although Le Corbusier first presents this in Modulor I in purely geometric terms, he must have been thinking in more anthropocentric terms ( Figure 6). Here the square '1' reflects the width of a man with arm stretched sideways (1.10m in this scheme). This was also the height of a man's navel and half the height of a man with arm raised. 45 The problem was then how to turn this square into a proportional series. All it took was to take 1.10m and 2.20m (or 1.13 and 2.26 in the final version) and insert them into Fibonacci series to arrive at the Modulor. But Le Corbusier wanted the 'proof' of a geometric and visual solution. On the Vernon S. Hood freighter, on which he crossed the Atlantic in the winter of 1945-1946 in considerable discomfort, he made a number of sketches in which he tried to make sense of the complicated mathematics of the Modulor in visual terms (Figure 7). He constructed three blocks, starting with the square (108cm in this version of the Modulor), a second block based on the golden rectangle and a third based on doubled squares. This is much simpler to understand than the   (1918)(1919)(1920)(1921)(1922)(1923)(1924)(1925). But, here again, they distinguished between geometry as an aid and the judgment of the artist as final arbiter. They frequently marked up their canvases with a pre-existing geometric structure consisting of two golden section rectangles. This was facilitated by the French system of dimensioning canvases in three sequences: 'F: figure (portrait)', 'P: paysage (landscape)' and M: marine. The proportions of these are, respectively, based on the double golden rectangle (2/(√5+1)/2), 2:3 and the golden section ((√5+1)/2    178-180). A gnomon is a shape that when added to a given form reproduces its proportions in a new shape. The gnomon of a golden rectangle is a square. On the diagram on page 214 (Figure 10), Le Corbusier begins with a golden rectangle ABCD and adds a square to the right CEDF. This does not create a new golden rectangle. Le Corbusier correctly constructs a set of golden rectangles and gnomons in his diagram 2 on page 213. What he should have done, in order to create a sequence of golden rectangles and their gnomon squares, is shown in Figure 11. Starting with the square ABCD, the golden rectangle EBCF is formed. The square FCHG is its gnomon, creating a new golden rectangle EBHG, and the process is repeated to the left and then above. The lengths a,b,c,d are in a golden sequence. 56 Instead, Le Corbusier seems to have begun with a rectangle in the proportion of 1:3 enclosing the box of matches on the lower left of the painting. If we give the short side of this rectangle the dimension 1, it creates a square below it (3x3), a square to the right (4x4) and a square above (7x7), thus creating a rectangle in the proportion of 7:11 or 1:1.57, which approximates to the figure 1:1.5669 inscribed by Le Corbusier on the painting (Figure 12). The centre points of the diagonals of these three squares have been explicitly picked out on the painting. The progression 3,4,7 corresponds approximately to the geometric progression 3, 3(4/3), 4(4/3) 2 which does not justify le Corbusier referring to it as a 'harmonic progression'. Le Corbusier's chose this strange construction for a reason that has noting to do with proportion and more to do with symbolic association. On page 266 of his Esthétique des proportions dans la nature et dans les arts, Matila Ghyka uses exactly this diagram, complete with the proportion 1.5669, to explain the proportions of the skull of the Harvard skeleton. Ghyka explains this number as representing 2x (3ᶲ+1)/(4ᶲ+1), which is one of the least convincing claims for proportionality in his 55 If the square CEDF has a side 1, DW=Ɵ/2 (0.707), BX=Ɵ/2x ᶲ 2 (1.851), AY= Ɵ/2x ( ᶲ 2 +1) (2.558) and ZE= Ɵ/4x(4ᶲ 2 +2) (4.4095). I can identify no geometric progression in this sequence.
56 The spiral has to be drawn by hand, since there are no indications for the multiple centres required.  This demonstration shows, once again, that Le Corbusier's grasp of the mathematics of the golden section was very approximate. I have found no logical explanation for the mysterious ratio '1:1.5669' that Le Corbusier gives as the proportion of the rectangle KLHI ( Figure 10)

The place of the right angle and dimensions
It is important to understand the properties of the place of the right angle, which Le Corbusier set such store by ( Figure 13). I will show that the actual geometric properties of the right angle triangle have very little to do with Le Corbusier's use of it and very rarely involve the golden section. The apex of a triangle whose base coincides with the diameter of a circle will always lie on the circumference of the circle if the height does not exceed the radius of the circle. The vertical line indicating the height of this triangle ('h') will always be the geometric mean of the portions of the width to left ('m') and right ('n') of this vertical line. The ratio of the geometric progression 'm':'h':'n' will be different in each case and bear no fixed relation to the ratio of width to height of the triangle. Only if the ratio of width to height of the triangle is √5 will the progression 'm':'h':'n' follow the golden mean. The right triangle inscribed in a circle has the useful property, however, of identifying similar triangles (and therefore the rectangles defined by them). 57 This is the property of the geometric progression: m:h = h:n. The two right triangles imposed on the photograph of the Petit Trianon demonstrate this simple property. 58 It should be clear, however, that we are dealing with a practical rule of thumb quite different from the divine proportion or pure geometry.

Milieu, spirit, flesh and fusion in Le Corbusier's life and work
To take the example frequently cited by Le Corbusier, the Palazzo dei Senatori on the Campidoglio in Rome (Figure 14). Le Corbusier claimed that Michelangelo ordered the dimensions of the façade 'par la force des nombres.' In Modulor I he candidly explains that his method was simply to lay a postcard over the photograph in order to find the place of the right angle. According to Le Corbusier's triangle AAA, the ratio of the width of the right hand bay to the height of the building is equal to the ratio of the height of the building to its width minus the right hand bay. Similarly, triangle BBB asserts that the ratio of the height of the lower storey to the width of the left hand bay is equal to the ratio of the width of the bay to the height of the upper storey. Furthermore, triangle CCC claims that the ratio of the width of the left hand bay to the height of the upper storey is equal to the height of the upper story to half the width of the building minus the width of the left bay. Stated in these terms, it is difficult to see the significance of these diagrams, but graphically they look persuasive. 59 Unfortunately, the photograph is severely distorted: the left wing is shown considerably wider than the right. Applying the three right triangles to a measured drawing shows that, apart from the triangle AAA, they do not 'fix' either the height of the base of the piano nobile, nor confirm the width of the left-hand bay ( Figure 15). The triangles AAA, BBB and CCC are interrelated. Curiously the three triangles only work in the unique case that the ratio of the height of the building to its width is as 39.31:100. 60 I know of no evidence of the place of the right angle being used before the completion of a project. A partial exception is one of the elevation drawings for the maisons La Roche- Jeanneret. 61 This was the penultimate project corresponding to the wooden model exhibited in the Salon d'Automne in October 1923. There are various tentative diagonals drawn on this elevation but none of them affected the final design. The place of the right angle was invariably applied after the design was finished, to 59 It is sufficient to complete the rectangles defined by the right angle triangles to realise that the similar figures they define are unimportant in the design. More important were the lines themselves as drawn onto elevation drawings or photographs.  The first project of the Villa Savoye, on an unencumbered site, was based on a grid of 5 metres. 68 The dimension of 5 metres corresponds neither to any structural constraints nor to considerations of human proportions. Instead, it seems to have come from some Cartesian notion of the world sectioned in metric units. This reliance on the 'abstract' notion of a unit of measure originally defined as one tenmillionth of the distance from the equator to the North Pole along a great circle, was precisely what Le 62 Ibid.,p. 62. 63 Tim Benton, The Villas of Le Pierre Jeanneret 1920-1930  Corbusier challenged in his research for the Modulor. It was also linked to the idea of standardisation of component parts. For example, Le Corbusier had Henri Frugès order 595 steel windows measuring 2.50x1.05m (doubled up as 5.0m windows), and this was part of his campaign to introduce standard components for the building industry. 69 By contrast, in elevation, Le Corbusier and Pierre never used 'ideal' whole number dimensions. Their room heights, based on subjective judgement, typically varied from 2.60m to 3.15m. For example, the Villa Stein-de-Monzie had ceiling heights (in ascending order) of 2.80, 3.12, 3.12 and 2.60, with the roof parapet measuring 1.12. 70 In his article on the tracés régulateurs published in L'Architecture Vivante in 1929, Le Corbusier made clear that he used the tracés to try to order elements in the façade determined by the plans. 71 He claimed that the external staircase on the garden side of the villa Stein-de Monzie was raised in order to correspond to the diagonal of the façade. Thus we have another opposition between plans notionally based on standard metric modules and elevations based on human dimensions confirmed by the visual test of the place of the right angle or simply parallel diagonal lines. The plan of the Mundaneum project, on the other hand, was designed from the outset around the golden section.

Nature and nature
Jeanneret had been trained at the École d'Art at La Chaux-de-Fonds to study nature closely in all its complexity and then reduce the forms to a geometric order capable of becoming a repeating pattern. 72 Even then, Jeanneret was fascinated by the juxtaposition between natural flora and fauna and the geometric structures of rock. He expressed this most clearly in his watch design of 1906, interpreting the arms of the city of La Chaux-de-Fonds in two fields: the organic with the busy bees on top and the crystalline rock forms below. In the Villa Fallet we find the same contrast on the garden front, with the theme of pine cones and tree branches contrasted with geometric stone features ( Figure 16).
My fifth instance of Le Corbusier's dualism becomes the contrast between Nature and nature. By this I mean the difference between the natural world, in all its richness and complexity ('nature') and the ineluctable laws of nature ('Nature'). He explains this crisply in Urbanisme: Donc: la nature est multiforme, féconde, illimitée, mais l'homme en tire des lois simples et il en fait des équations simples. 73 To begin with, Le Corbusier understood the latter largely in terms of geometry, but later he began to think in terms of the cosmic laws of the twenty-four hour day or the lunar cycle governing the tides.
Le Corbusier expressed himself clearly describing the Villa Savoye: ' Les habitants, venus ici parce que cette campagne agreste était belle avec sa vie de campagne, ils la contempleront, maintenue intacte, du haut de leur jardin-suspendu ou des quatre faces de leurs fenêtres en longueur. Leur vie domestique sera insérée dans un rêve virgilien.' 74 Man had to be kept physically separate from nature which was to be consumed visually. As he noted in OEuvre complète II (1935), 'D'ailleurs, l'herbe est malsaine, humide etc… pour y habiter.' 75 By the time this was published, the pendulum had swung in the direction of nature. The Villa de Mandrot (1930-1931 has load-bearing stone walls and is anchored to the ground with no externally visible pilotis. 76 The two houses built in 1935 -the petite Maison de weekend and the villa Le Sextant -went further, built of stone and wood with brick and plywood detailing. 77 I have argued elsewhere that this return to nature, which transformed his painting and architecture, was influenced by the holidays he spent every year from 1926 to 1936 at Le Piquey on the Bassin d'Arcachon. 78

Fusion
In this section I will review a number of ways that aided the passage from the material to the spiritual worlds. One means of opening the door from the physical to the spiritual world was through 'unity' of dimensions. Le Corbusier's studies for the Modulor follow the line of Abbé Laugier's saying 'tumulte dans l'ensemble; unité dans le détail'. 79 Coordinating dimensions along a proportional system supported by the sacred rules of number and geometry might increase the chances of passing from subjective judgment to objective truth. This was one of the ideas behind developing the Modulor.
It was important for Le Corbusier that his Modulor was not only supported by Nature (number and geometry) but also by antiquity and the vernacular. In a diagram he sketched the progression, from  India, Egypt, Greece, the arabs, the Italian Renaissance to Paris ( Figure 17). Significantly, this sketch is crowned by a bright yellow sun of enlightenment. He was also interested in antique and traditional units of measure, having his assistants research the Egyptian cubit and the Turkish units of measure ( Figure 18). Having always admired the sense of proportion of Turkish architecture, he sought the explanation in their measurements. Furthermore, his sketchbooks are full of measurements taken of modest vernacular buildings.
As e have seen, the passage from the material to the spiritual worlds was usually described by Le Corbusier in terms of brewing, cooking, digestion or giving birth. At the end of his life, Le Corbusier described the process of creation: Lorsqu'une tâche m'est confiée, j'ai pour habitude de la mettre au-dedans de ma mémoire, c'est-à-dire de ne pas permettre aucun croquis pendant des mois. La tête humaine est ainsi faite qu'elle possède une certaine indépendance ; c'est une boite dans laquelle on peut verser en vrac les éléments d'un problème. On laisse alors « flotter », « mijoter », « fermenter ». Puis, un jour, une initiative spontanée de l'être intérieur, le déclic se produit : on prend un crayon, un fusain, des crayons de couleur [la couleur est la clef de la démarche] et on accouche sur le papier : l'idée sort, l'enfant sort, il est venu au monde, il est né. 80 On page 39 of the Poème, Le Corbusier illustrates the successful outcome of the law of the meander, when life forces its way through the barrage of vicissitudes to run straight, with two sketches: the plan of Chandigarh and a woman and baby with the Himalayas as backdrop. I see the latter sketch as the literal illustration of 'l'idée sort, l'enfant sort' -the act of creation.
In the Poème, he is at his most specific: Faire une architecture c'est faire une créature. Être rempli, se remplir, s'être rempli, éclater, exulter, froid de glace au sein des complexités, devenir un jeune chien content. Devenir l'ordre. 81 To be impregnated, to be filled up, to split open and exult; these are euphemisms for sex and birth, leading to order, which we can assume to be the divine order of l'espace indicible. It is fascinating  that he summarises this by referring to his dog Pinceau ('jeune chien content'), who is often described in his letters in terms of wild, Dyonisiac energy. It is astonishing that Le Corbusier could combine feminine and masculine metaphors of accomplishment.
In the Poème, Le Corbusier describes the 'birth' of 'la maison des hommes' (the Unité d'habitation, Marseilles) as a natural process : Débarrassée d'entraves mieux qu'auparavant, la maison des hommes, maitresse de sa forme, s'installe dans la nature. Entière en soi faisant son affaire de tout sol, ouverte aux quatre horizons, elle prête sa toiture à la fréquentation des nuages ou de l'azur ou des étoiles. Avisée, regardez la chouette venue d'elle-même se poser sans qu'on l'ait appellée. 82 The section of a Unité d'Habitation is juxtaposed with mountain ranges -symbols of the initiate's progress to truth -while the roof plays host to the spiritual world of clouds and stars. This is the miracle of transcendence into the sphere of the Gods, confirmed by the owl of wisdom, messenger of Athena.
Nature itself works the miracles of birth, growth and death. In La Ville Radieuse, Le Corbusier describes the cosmic cycle of the 24 hour day in terms of the continual re-fertilization of male and female, sun 82 Ibid., pp. 58-60.  The photograph of two shells juxtaposed introduce the key chapter 'L'esprit de vérité' in L' Art décoratif d'aujurd'hui. 94 This was the chapter, liberally illustrated with machines and botanical diagrams, where Le Corbusier tries to explain the passage from brutal reality to the inexplicable and the work of art.
Lorsque intervient dans l'oeuvre humaine l'inexplicable, c'est-à-dire lorsque notre esprit est projeté loin du rapport étroit de cause à effet et qu'un sentiment allègre nous soulève et porte nos pensées de l'objet brutal au phénomène cosmique dans le temps, dans l'espace, dans l'insaisissable, dans le seul perceptible de racines qui s'enfoncent tout autour et nous nourrissent du suc du monde, l'inexplicable est alors le miracle de l'art, ce moment où un objet défini, crûment créé, là sus nos yeux, d'une forme semblable pour nous tous, est comme un radium, un potentiel de l'esprit, une puissance concentrée, une oeuvre d'art. 95 Once again, the metaphor is organic, in which the work, with its roots in the material world, sprouts to create the miracle of art. The seashell as illustration of the spirit of truth can only be understood as a representative of nature producing pure geometry and hence divine truth.
Other photographs in Wendingen illustrated a shell that entered Le Corbusier's iconography as symbol of eternal truth ( Figure 21). The shell featured on the right side of Le Corbusier's painting Spirales géométriques animées as an allegory of eternal truth (Figure 22). 96 The Dyonisiac figure on the left is based on sketches of women dancing at Le Piquey. 97 Separating this joyful image from the seashell is a wooden barrier, literal evocation of the wall that separates the physical and spiritual worlds.   'Derrière le mur, les dieux jouent ; ce sont les nombres, constituants de l'univers.' 98 It is significant that Le Corbusier seized on the idea of Justin Serralta and André Maisonnier whose foreheads 'had been caressed by the wing of the Muses' and who represented the Modulor dimensions as a kind of Pythagorean spiral (Figure 23). 99 Le Corbusier explored this idea on the Vernon S. Hood, without achieving the clarity of his assistants' model ( Figure 24). Once again, he was not satisfied until he had discovered a visual demonstration of the truths of 'divine geometry'.    plastique' some of the origins of formal sensation are mechanical. 102 The muscles, the 'flux sanguin' and the sense of balance are directly affected by formal combinations. Based on the work of Fechner and Wundt, this was part of an attempt to create a science of aesthetics, although Victor Basch makes clear that physiological sensations are only the first of three stimulations of the aesthetic. 103 For Ozenfant and Jeanneret, therefore, the same plastic elements stimulate the same subjective reactions. The consequence was the policy of Purism to search for the invariable forms underlying all aesthetic sensation: composed of lines and curves and the phileban solids. This was the closest Le Corbusier got to materialism, although he always retained a separate sphere for the spiritual. The reference to 'physiologie' recurs in his teaching, however.
In a lecture at Lausanne in February 1924, Le Corbusier includes a sketch of phileban solids and jagged lines, which he labels 'physiologie' (Figure 25). Further on in this lecture he will claim that the effect of the jagged forms of the French alps, as seen from the Northern Swiss shore of lake

The musical analogy
Perhaps the most potent metaphor for the transition from the physical to spiritual worlds was music. In Modulor 1 Le Corbusier attributed to Pythagoras the resolution of the problem of how to establish the relationships between sounds. 105 He did it by combining the evidence of the human ear with the proofs of mathematics. But whereas the ear can detect precisely harmonious and discordant sequences of notes the eye is less sensitised to proportional relationships. 106 The Modulor was supposed to provide visual guidance similar to the Western system of musical notation, '… how many of us know that in the visual sphere -in the matter of lengths -our civilizations have not yet come to the stage they have reached in music. ' 107 All this makes it surprising that Le Corbusier chose the golden mean rather than a harmonic scale for his system of proportions, There was a great deal of interest in Renaussance theories of harmonic proportion after the war. 108 As Rudolf Wittkower famously argued, Alberti and Palladio favoured proportional systems based on ratios that the human ear can detect, such as the octave (1:1), Fourth (4:3 = 1.333), Fifth (3:2 = 1.5) and Sixth (5:3 = 1.666), as well as the diagonal (1.1414) which has practical utility for nesting rectangles. 109 This was the logical conclusion of taking seriously Plato's Timaeus and the theory of the music of the spheres. When describing the proportions of the Villa Stein-de Monzie, Le Corbusier uses the Fibonacci approximations 3-5-8 as if they corresponded to a sequence of the golden mean. In fact 3:5 (1.666) and 5:8 (1.6) are some way off the golden mean (1.618). But both 3:5 (Major Sixth) and 8:5 (Minor Sixth) do have a correspondence with musical harmony. Le Corbusier seems unaware of this. 110 Despite his love of music, Le Corbusier's sensibility was profoundly visual.
It is no accident that Le Corbusier invariably used the word 'harmoniseur' for the poet who could bridge opposites and reconcile matter and spirit. With a mother and brother who were musicians and who considered music to be the highest form of art, the young Jeanneret had always tried to refine his musical taste. Furthermore, from his early reading he would have absorbed the teachings of Plato in the Timaeus, who considered music to be a record of the harmony of the universe. 111 Le Corbusier cites Leibniz:

Conclusion
Most artists have not written about the sense of wonder they feel when a work of art escapes the materials and processes that constitute it to become extraordinary -I choose the word carefully. Le Corbusier, who wrote about everything, often in embarrassing detail, tried to explain to himself and his readers why he had the gift to create. Part of the answer was his sense of predestination. Another part was his conviction that the life of the prophet and poet must be accompanies by suffering and rejection and that these were both a proof of his vocation as initiate and a constituent part of creation. His dualism allowed him to believe that art belongs to a distinct, spiritual sphere that mortals cannot access directly. He was fascinated by the idea that mathematics and geometry somehow gave direct access to truths behind the wall separating matter and spirit, but he was convinced that only by material means can man break through -looking, listening, touching, feeling. It was human judgment, rather than geometry, that must show the way, but judgment could be confirmed by geometry, just as it could be confirmed by comparison with the great works of the past or the unschooled work of the peasant. He sought explanations for the transformation of matter into spirit in the mysterious miracles of naturebirth, growth, reproduction, brewing and alchemy -and increasingly saw the world as a great machine of cosmic cycles which, if properly understood, could guide the process of creation. The Poème de l'angle droit and the Modulor books give an insight, among many other writings, into this mentality which was established much earlier in his career..