References are to the pages of
- [C] Jean-Louis Cohen, Le Corbusier's Modulor and the Debate on Proportion in France, Architectural Histories 2(1) (2014), Article 23, pp. 1-14. [Contains also the original French texts of our English quotations.] (here)
- [M] Matila Ghyka, The geometry of art and life, Dover 1977 (original 1946). (here)
- [Z] Frank Zöllner, Anthropomorphism: From Vitruvius to Neufert, from Human Measurement to the Module of Fascism, In: K. Wagner and J. Cepl (editors): Images of the body in architecture. Anthropology and built space. Tübingen, Berlin 2014, pp. 47-75. (here)
Adolf Zeising (1810-1876) — Matila Ghyka (1881-1965) — Le Corbusier (1887-1965)
As explained here, Zeising invented Golden Numberism in 1854. Among those responsible for spreading this weird belief, two names must be mentioned expressly: the Romanian diplomat Matila Ghyka and the influential Swiss painter and architect who operated under the pseudonym Le Corbusier.
Among Ghyka's many publications, we mention two that Le Corbusier owned:
- Esthétique des proportions dans la nature et dans les arts (Aesthetics of Proportions in Nature and the Arts, a title which could have been Zeising's), 1927
- Le nombre d'or — rites et rythmes pythagoriciens dans le développement de la civilisation occidentale (The golden section — Pythagorean rites and rhythms in the development of western civilization), 1931
Ghyka recombined much of his writings into different forms, and The geometry of art and life (1946) offers a good English synthesis.
It is very clear that Ghyka believed everything Zeising had put forward. He mentions
the dominant role of the golden section in the proportions of the human body, rediscovered [after the Greeks, that is] by Zeysing [sic], who also recognized its importance in the morphology of the animal world in general, in botany, in Greek architecture (Parthenon) and in music. [G16]
As for the Parthenon, he writes that
Zeysing already had observed the obvious presence of the Golden Section in the frontal view of the Parthenon [G124].
Actually, far from being obvious, the Golden Section is not present at all in the Parthenon and Zeising simply doesn't know how to deal with measurements. But for Ghyka, it's a simple fact that
Zeysing had already noticed that Φ was the fundamental ratio for this façade [G136].
Also, he summarizes Fechner's biased experiment by stating that the golden rectangle obtained the great majority of votes [G10]. Actually, as explained here, an overwhelming 2/3 majority did not choose it.
The influence of Ghyka would have remained restricted had he not raised the interest of Le Corbusier. The latter became an internationally acclaimed architect, therefore seen by the general public as a solid scientific mind. Alas, if only this were true! He knew and admired Ghyka's writings, and described them as some esoteric revelation, in these very words:
a book of the revelations of the laws of our being and our world [C3]of a nature so noble and so inaccessible that it requires much work and a certain intellectual persistence on behalf of those who seek the truth [C3]deep enough to give you the key of the world [C11].
The laws of our being, the key of the world, no less! And yes, here comes the classic humbug with some esoteric flavour added:
He also wroteThe 'divina proportione' appears in mathematical relationships that are one and all, in whole and in part, in the facts and in the hypotheses, in the calculation, in geometry, in natural objects and in the paintings and architecture of major epochs (the Egyptians, Greeks, the Gothic, the Renaissance, French classicism etc.) [C11]
It has been proved—particularly during the Renaissance— that the human body follows the golden rule. [Modulor 1, Chapter 2, p.56 (French original here)]No doubt, Le Corbusier had completely wrong convictions about the golden ratio and the human body. Before Zeising (1854) no one ever saw any golden proportions in any body! Clearly, an architect guided by such wrong convictions must feel challenged to invent some golden standard worthy of such a supposedly great tradition. It was eventually born in 1948, and called the Modulor. The name is composed of the French words Module and Or ("gold", after "golden section"). Le Corbusier himself provides some insight into its genesis.
The ridiculous reference to good-looking policemen in detective novels convincingly proves the completely arbitrary nature of the "universal" norm invented by Le Corbusier. François Le Lionnais, mathematician and personal friend of Le Corbusier's, seemed to have been among the few men brave enough to challenge the invention. Le Corbusier was fair enough to include the criticism in the sequel Modulor 2 (1955).Ill luck so had it that almost all these metric values were practically untranslatable into feet and inches. Yet the 'Modulor' would, one day, claim to be the means of unification for manufactured articles in all countries. It was therefore necessary to find whole values in feet and inches.I had never anticipated having to round off certain figures of our two series, the red and the blue. One day when we were working together, absorbed in the search for a solution, one of us—Py— [Marcel Py] said: 'The values of the "Modulor" in its present form are determined by the body of a man 1·75 m. in height. But isn't that rather a French height? Have you never noticed that in English detective novels, the good-looking men, such as the policemen, are always six feet tall?'We tried to apply this standard: six feet=6 x 30·48=182·88 cm. To our delight, the graduations of a new 'Modulor', based on a man six feet tall, translated themselves before our eyes into round figures in feet and inches! [Modulor 1, Chapter 2, p.56 (French original here)]
In order to remain within the modesty of our search, let us quote the following letter from Le Lionnais, mathematician and man of high culture:
Paris, 12th February, 1951". . . As you know, I reproach certain authors—of whom, let me hasten to say, you are not one—with using the Golden Mean in a way which presupposes and encourages a point of view more or less akin to occultism. Every time the Golden Mean is mentioned, I feel it is necessary to define one's personal attitude on this point. But I need not pursue the matter further, for in this matter our points of view are the same.So far as the technical aspect is concerned, I believe that the Golden Mean does not represent a particularly exceptional or privileged concept; but it may represent a useful convention and, as often happens, the adoption of a convention—however arbitrary it may be—can lead to substantial progress, provided one remains faithful to it, because it becomes a principle of selection and order. Alphabetical order, which does not rest on any natural foundation, is extremely useful and it would be foolish to criticize it. I have, of course, indulged in the mathematician's vice of "going to the extreme" in giving you an example which exaggerates my thought in order to make it more readily understandable. It is obvious that, whilst the Modulor has not the unique nature which would authorize it to impose a sort of dictatorship in the plastic arts, it nonetheless possesses certain natural characteristics which recommend it, with other numbers, to the attention of the artist and the technician."
Such is the mathematician's warning. [Modulor 2, Chapter 1, p.18-19 (French original here)]
Perhaps Le Lionnais was unaware of the esoteric ideas which Le Corbusier had copied from Ghyka. But, if he said they agreed on rejecting these, he may also have done so for friendship's sake. But he's very outspoken in calling the Modulor an arbitrary convention and the Golden Mean a concept without particular merits. (In 1983 Le Lionnais, in his book Les Nombres Remarquables, would himself make several wrong claims about the golden number, e.g., that the Greeks had made it the cornerstone of their aesthetic system. Relevant page here.)
It's is a very famous icon though, and we feel obliged to include it here. We do so reluctantly because it is not only based on wrong and arbitrary assumptions, it is at the same time very ugly. Remembering da Vinci's masterly composition of the Vitruvian Man, one feels embarrassed by Le Corbusier's clumsy drawing of a beefy man (apparently in a football pauldron, seen his shoulders) with a thin head and an oversized hand, standing in a vulgar position with one arm ambiguously stretched in a crooked fashion. The only body element unambiguously marked is the Zeisingian navel, the axiom on which the whole shaky construction rests.
Famous icon of a wrong cause, yes, but there is also good news.
As is well known, the golden section leads to irrational number relationships, which are hardly suited to architectural practice. Hence, the golden section was rarely used in architecture. [Z59]
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