Klaus-Peter Gast, Le Corbusier: Paris -- Chandigarh. Birkhäuser, Basel, 2000. To order this book from Amazon.com, click here.
Reviewed by Steven Fleming and Michael J. Ostwald
Le Corbusier's designs have always provided fertile grounds for the study of geometry and mathematics in architecture. Le Corbusier is a rare twentieth-century architect who has outlined a detailed theory of proportions and has provided descriptions of how he applied this theory in his buildings. As a result, many hundreds of books and papers have been written on the topic of Le Corbusier and the application of geometry to design. Some of these books and papers have been ground-breaking and original, while others have been shallow and derivative. The key to determining the success of most of these scholarly investigations lies in the analytical method being employed. If the method is applied with the right combination of critical rigour and sensitivity (to the designer's era and intent) then the result can be highly informative. If the method is applied inconsistently, and with little regard for the designer or for history then the result will be no better than an interesting anomaly. Despite the vast quantity, and variable quality, of research already existing on the topic of Le Corbusier and geometry, works continue to be published which purport to provide a new or original interpretation. The success of these new works, like the old, ultimately rests on the methods they employ to support their aims.
Klaus-Peter Gast's latest book, Le Corbusier: Paris-Chandigarh, attempts to assert a lasting place for itself in a body of scholarship dealing, seemingly, with every conceivable aspect of Le Corbusier's theory, practice and personal life. Superficially at least, Gast achieves a clear point of difference through the extensive use of well-chosen photographs. Like his previous offering, Louis I. Kahn: The Idea of Order , Gast's new book is supported by a variety of photographs which present Le Corbusier's architecture as it has rarely been seen. Whereas most published photographs of Le Corbusier's architecture have been taken specifically to assert a building's rightful place in the canon of great architecture, Gast provides a range of new, or unusual views of these famous buildings. For example, his photographs of Chandigarh display the dramatic ruin that many of the buildings have become today and the Villa Shodan is pictured ringed by bamboo fencing. Gast has also captured those elements of Le Corbusier's architecture which intrigue the visitor to these structures but which are never published. The "mini-Savoye" gatehouse and the view of the lawn from the central bedroom window of the Villa Savoye are both rarely, if ever, seen in published photographs. Aside from his careful cropping of fellow pilgrims, Gast has captured much of the atmosphere of these buildings as they exist today.
However, the thoroughness Gast displays with his lens does not extend to his central thesis. For observant readers the sense of unease about this book commences with the cover design. The cover features a close-up of the brise-soliel façade of Le Corbusier's Parliament Building in Chandigarh. Overlaid on top of the photograph of the brise-soliel is a crisp, white, Fibonacci rectangle. Ironically the rectangle simply does not match the geometry of the brise-soliel. As an illustration of the kinds of proofs presented within the book, Gast could not have designed a less fortunate cover. The rectangle on the cover of Gast's book is produced by a consecutive spiral of squares emanating from a double square figure at the centre of the spiral. It has a proportion of 55:34, which, to three decimal places, produces a ratio identical to that of the golden section, that is, 1:1.618. Therefore, neither the Fibonacci rectangle which Gast has overlaid, nor the golden section, fit the underlying photograph exactly, as indeed they should for Gast's thesis to stand. Le Corbusier's brise-soliel is relatively close to the geometry of the golden section but it is also relatively close to several other geometric constructions which bear no relationship to the golden section. The book also commences with a foreword by Arthur Rüegg which contains a number of veiled references to Gast's method which raise further concerns for the serious scholar. Rüegg clearly states that Gast's method does not rely on Le Corbusier's own stated theories of design and geometry "but uses a method developed from historical buildings of a different context". Rüegg also argues that it is a characteristic of Le Corbusier's "buildings that they can be read in different ways"  and thus, he finds Gast's interpretations "highly stimulating"  alternative readings. While these are legitimate comments they clearly suggest that Gast's thesis is unconventional and they provide little support for it other than the simplistic argument that buildings can be interpreted in different ways and that we should embrace such interpretations. Such an argument has the aura of an apology rather than of unconditional support.
Gast's central thesis, which is described in the pages that follow Rüegg's foreword, is that certain geometrical patterns, which he has unearthed in the plans of a number of Le Corbusier's buildings, prove that Le Corbusier was at once rational and irrational. Gast defines those sections of a building which conform to his geometric patterns (usually derived from the golden section or from the Fibonacci set) as "rational", and those sections which do not conform as "irrational" . Significantly, the geometrical patterns in question are not ones for which records exist in the form of sketches, drawings or statements left by Le Corbusier himself, or for which anecdotal evidence exists, in the form of recollections by Le Corbusier's associates. Instead these are patterns uncovered by Gast, in isolation, using a method of analysis developed for historic, seventeenth-century, buildings. The details of this particular method, known as "plan analysis", are not outlined by Gast. Instead, Gast refers the reader to what appears to be an unpublished German Doctoral thesis by Harmen Thies who Gast acknowledges as the inventor of this analytical tool.
From the remainder of Gast's book it can be gleaned that this method relies on a series of geometrical expositions, whereby complex figures, and ultimately architectural plans, are shown to have been derived from the arbitrary diagonal and orthogonal bisecting of simple geometric forms, such as rectangles of golden mean proportion. For example, according to Gast's analysis of the Villa Stein, Le Corbusier used intersections between certain diagonals used to produce a golden section plan shape and a diagonal drawn across the whole plan, to generate regulating lines which, when crossed by other diagonals, generate yet more lines. These latter lines can be found to regulate the positions of such elements as doors and the outer edges of columns. From such examples it must be assumed that "plan analysis" entails the deduction of a designer's intentions based on geometrical relationships found to exist in working drawings. For example, a "plan analyst" might find a plan of square proportions and deduce that its designer was, for some reason, fascinated by the symbolic potential of squares. It would appear that "plan analysts" prefer symbolic explanations to structural, tectonic or otherwise mundane ones. Factors such as the lengths of available materials, modulation related to masonry units, dimensions of site boundaries or structural considerations are not mentioned lest they detract from the overarching assumption that the architect/genius is speaking to us, and that his or her language is geometry. When analysing more complex plan forms, this assumption (about the direct relationship between geometry and intent) is crucial to the implementation of the analytical method. Presumably thousands of combinations of geometric inscriptions must be trialed before a sequence of growth patterns and/or bisections is found to match the plan in question.
While "plan analysis" may be an interesting deductive tool for the investigation of Baroque churches (which is what it appears to have been developed for), the application of this method to the works of architects who have left us detailed descriptions of how they designed seems eccentric to say the least. Gast's central argument, that Le Corbusier was at once rational and irrational in his use of geometry, is exactly what Le Corbusier himself said many times, most notably in The Modulor. In The Modulor Le Corbusier outlines a rational strategy for regulating building proportions, whilst allowing for intuition, or irrationality, by telling his reader that "your eyes are your judges."  Of course Le Corbusier was both calculating and intuitive-he argues strongly in The Modulor that purely rational designs (to use Gast's version of "rational") can be "displeasing"  to the eye. The Modulor provides intrinsic proof that Le Corbusier was at once rational and irrational. The fact that Gast confirms this thesis by extrinsic means-that is, without reference to statements, sketches or recollections, but through "plan analysis"-is potentially interesting for scholars. Indeed, if Gast's inscriptions were highly accurate they would constitute important discoveries, revealing a hitherto unfathomed dimension to Le Corbusier's genius. If a line drawn from the inner corner of the Villa Stein to a geometically determined point along its longer facade, really did touch the outer surface of an internal supporting column, scholars would be forced to accept that Le Corbusier held an unconfessed fascination with imperceptible phenomena.
Unfortunately, readers with a serious interest in Le Corbusier's use of regulating lines will be disappointed by the relative lack of documentary evidence throughout Gast's book. Most significant is the fact that Gast does not provide reference to the specific working drawings on which his plan analyses are based. Presumably he studied these drawings in the course of his research and could simply quote their reference number and place of archival. For an author who accuses others of "throwing together collections of old material and presenting them as 'new and up-to-date documentation',"  and who describes his own work as one which "attempts to get closer to Le Corbusier by applying concrete analysis,"  it remains a mystery that Gast chooses not to disclose the dimensions from the working drawings on which he bases his findings. If Gast's geometrical constructions really do conform to Le Corbusier's working drawings, then what better proof could he provide than a series of simple trigonometric calculations! The scepticism aroused by Gast's method and omissions is exacerbated by a succession of trivial and glaring inaccuracies throughout the book. Gast's history of divine proportions contains several significant errors  and some of the few references he does provide are incorrect.  Ultimately, the striking illustrations, production design and intriguing asides do not make up for the flaws in this otherwise interesting book.
Arthur Rüegg, "Introduction," In Klaus-Peter Gast, Le Corbusier: Paris-Chandigarh, Birkhäuser, Basel, 2000, 11. return to text
Rüegg, "Introduction," 9. return to text
 Rüegg, "Introduction," 11. return to text
 Gast, Le Corbusier: Paris-Chandigarh, 12. return to text
 Although he uses the same method in his previous book also without substantial critical description. See: Steven Fleming, "Louis I. Kahn: The Idea of Order [book review]," in Architectural Theory Review, Vol. 4, No. 2 (1999): 116-117. return to text
 Harmen Thies, Grundrißfiguren Balthasar Neumanns: Zum Maßstablich geometrischen Rißaufbau der Schonbornkapelle und der Hofkirche in Wurzburg, Unpublished Dissertation, Florence, 1980. return to text
 See: Michael J. Ostwald, "Review of The Modulor and Modulor 2 by Le Corbusier (Charles Edouard Jeanneret)", Nexus Network Journal, vol. 3, no. 1 (January 2001). return to text
 Le Corbusier, The Modulor: A Harmonious Measure to the Human Scale Universally Applicable to Architecture and Mechanics, Birkhäuser, Basel, 2000, p. 130. return to text
 Le Corbusier, The Modulor, 130. return to text
 Gast, Le Corbusier: Paris-Chandigarh, 12. return to text
 Gast, Le Corbusier: Paris-Chandigarh, 12. return to text
 Despite Gast's claims on page 96, Plato's Timaeus makes no specific reference to the Golden Section. return to text
 For example, on page 97 Gast incorrectly refers
to Anne Tyng's PhD thesis as "The Energy of Abstraction:
a Theory of Creativity?". Cf: Anne Griswold Tyng, "Simultaneous
randomness and Order: The Fibonacci-Divine Proportion as a Universal
Forming Principle," PhD thesis, Graduate School of Arts
and Sciences, The University of Pennsylvania, 1975. return
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