. 2 volumes. Birkhäuser,
Basel, 2000. [Facsimile of the 1954 Faber and Faber 1st English
Language Edition]. To order this book
from Amazon.co.uk, click
here.Reviewed by Michael J. Ostwald Mathematics is the majestic structure conceived
by man
[1]
to grant him comprehension of the universe LE CORBUSIER
Le Corbusier developed the Modulor between 1943 and 1955 in an era which was already displaying widespread fascination with mathematics as a potential source of universal truths. In the late 1940s Rudolf Wittkower's research into proportional systems in Renaissance architecture began to be widely published and reviewed. In 1951 the Milan Triennale organised the first international meeting on Divine Proportions and appointed Le Corbusier to chair the group. On a more prosaic level, the metric system in Europe was creating a range of communication problems between architects, engineers and craftspeople. At the same time, governments around the industrialised world had identified the lack of dimensional standardisation as a serious impediment to efficiency in the building industry. In this environment, where an almost Platonic veneration of systems of mathematical proportion combined with the practical need for systems of co-ordinated dimensioning, the Modulor was born. For Le Corbusier, what industry needed was a system of proportional measurement which would reconcile the needs of the human body with the beauty inherent in the Golden Section. If such a system could be devised, which could simultaneously render the Golden Section proportional to the height of a human, then this would form an ideal basis for universal standardisation. Using such a system of commensurate measurements Le Corbusier proposed that architects, engineers and designers would find it relatively simple to produce forms that were both commodious and delightful and would find it more difficult to produce displeasing or impractical forms. After listening to Le Corbusier's arguments Albert Einstein summarised his intent as being to create a "scale of proportions which makes the bad difficult and the good easy."[2] A more mundane motive might also partially explain this endeavour. Le Corbusier saw that such a system could be patented and that when it became universally recognised and applied he "would have the right to claim royalties on everything that will be constructed on the basis of [his] measuring system."[3] Like Vitruvius and Alberti before him, Le Corbusier sought to reconcile biology with architecture through the medium of geometry. Just as Vitruvius describes the human body pierced with a pair of compasses and inscribed with Euclidean geometry, as an allegorical connection between humanity and architecture, so too Le Corbusier uses a Euclidean geometric overlay on the body for similar purposes.[4] After much experimentation Le Corbusier settled on a six foot tall (1.828m) English, male, body with one arm upraised. The French male was too short for the geometry to work well [5] and the female body was only belatedly considered and rejected as a source of proportional harmony.[6] According to Le Corbusier, the initial inspiration for the Modulor came from a vision of a hypothetical man inscribed with three overlapping but contiguous squares. Le Corbusier advised his assistant Hanning to take this hypothetical "man-with-arm-upraised, 2.20m. in height; put him inside two squares 1.10 by 1.10 metres each, superimposed on each other; put a third square astride these first two squares. This third square should give you a solution. The place of the right angle should help you to decide where to put this third square." [7] In this way Le Corbusier proposed to reconcile human stature with mathematics. To solve Le Corbusier's conundrum, Hanning started with the central (overlapping) square and then generated a golden section arc (from a diagonal of half the square) in one direction and another arc (from the diagonal of the full square) in the opposite direction. These arcs then generate two new contiguous squares which are also defined by a right angled triangle with its right angle passing through the common boundary between the two newly formed squares. The idea being that the resulting form can be used to create a series of Golden Section rectangles at multiple scales; except that it doesn't work geometrically. The final "squares" generated by the golden section and the arc are rectangles not squares; they are very close to being square (sufficiently close to fool amateur geometers) but are not equal sided as the mathematician Taton pointed out to Le Corbusier in November 1948. [8] A few weeks later, in December 1948, Mlle Elisa Maillard proposed an alternative solution for Le Corbusier's problem. Maillard's solution initially produces a golden section from the starting square to generate the second square and then uses the diagonal of the newly produced golden rectangle (the two overlapping squares) to form one edge of the right angle triangle. The remainder of the triangle generates the second square. Le Corbusier rapidly simplified Maillard's geometric solution (it had too many circles and thus looked too feminine) to the three square problem and replaced the human figure at its centre. He then used the vertical dimensions or heights generated by these three squares (which now overlap creating Golden rectangles) to produce measures which are proportional to the human body and which reflect the Golden Section. Despite now being geometrically valid, Le Corbusier's proportional
system had another problem. Specifically the divisions between
the ideal dimensions were too widely spaced to be useful or practical.
Le Corbusier solved this problem by producing two parallel syncopated
strips of dimensions, one based on the unit 108cm, the
other on double that unit, 216cm. After further development
the first sequence, now called the Le Corbusier's Modulor represents a curious turning point in architectural history. In one sense it represents a final brave attempt to provide a unifying rule for all architecture - in another it records the failure and limits of such an approach. Le Corbusier is quite open when he notes that the Modulor has the capacity to produce designs that are "displeasing, badly put together" or "horrors." [10] Ultimately he advises that "[y]our eyes are your judges" [11] and that the "Modulor does not confer talent, still less genius." [12] He also completely abandons the Modulor when it does not suit and persistently reminds people that since it is based on perception then its application must be limited by practical perception. Large dimensions are impossible to sense with any accuracy and so Le Corbusier does not advocate the use of the Modulor for these scales. Similarly construction techniques render the use of the modular for very small dimensions impractical. This proviso is important to remember and it is in part responsible for the way in which Le Corbusier eventually applied the rule. Having developed the Modulor and used it selectively in a few designs it then became largely invisible (and also immeasurable) in Le Corbusier's later works where it instinctively informed his eye as a designer but did not control it. Ultimately the two books of
Modulor, 58. return to text[3]
Modulor, 46. return to text[4]
See Pollio Marcus Vitruvius, The Ten Books on Architecture.
Trans. Morris Hicky Morgan, Harvard University Press, Cambridge,
Massachusetts, 1914, 73. return to
text[5] Modulor, 56. return
to text[6] See: Robin Evans, The Projective Cast: Architecture
and its Three Geometries, MIT Press Cambridge, Massachusetts,
1995. return to text[7] Modulor, 37.
return to text[8] Modulor, 232.
return to text[9] Modulor, 60.
return to text[10] Modulor, 130.
return to text[11] Modulor, 130.
return to text[12] Modulor, 131.
return to text[13] cf. Modulor 2,
198-200. return to text
- Le Corbusier (Charles Edouard Jeanneret),
*The Modulor*and*Modulor 2.* - Robin Evans,
*The Projective Cast: Architecture and its Three Geometries*(Cambridge, MA: MIT Press, 1995). - Pollio Marcus Vitruvius,
*The Ten Books on Architecture*. Trans. Morris Hicky Morgan, (Cambridge, MA: Harvard University Press, 1914).
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