.
Birkhäuser, Basel, 2000. To
order this book from Amazon.com, click
here.Reviewed by Steven Fleming and Michael J. Ostwald
Klaus-Peter Gast's latest book, 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"[2]. Rüegg also argues that it is a characteristic of Le Corbusier's "buildings that they can be read in different ways" [3] and thus, he finds Gast's interpretations "highly stimulating" [4] 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" [5]. 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.[6] 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.[7] 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 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'," [11] and who describes his own work as one which "attempts to get closer to Le Corbusier by applying concrete analysis," [12] 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 [13] and some of the few references he does provide are incorrect. [14] Ultimately, the striking illustrations, production design and intriguing asides do not make up for the flaws in this otherwise interesting book.
[2]Arthur Rüegg, "Introduction," In Klaus-Peter
Gast, Le Corbusier: Paris-Chandigarh, Birkhäuser, Basel,
2000, 11. [3]Rüegg, "Introduction," 9. [4] Rüegg, "Introduction," 11. [5] Gast, Le Corbusier: Paris-Chandigarh, 12. [6] Although he uses the same method in his previous
book also without substantial critical description. See: Steven
Fleming, " [7] Harmen Thies, Grundrißfiguren Balthasar Neumanns:
Zum Maßstablich geometrischen Rißaufbau der Schonbornkapelle
und der Hofkirche in Wurzburg, Unpublished Dissertation, Florence,
1980. [8] See: Michael J. Ostwald, "Review of [9] Le Corbusier, [10] Le Corbusier, [11] Gast, [12] Gast, [13] Despite Gast's claims on page 96, Plato's [14] 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. Michael
J. Ostwald's review of
Dr
Michael J. Ostwald is Assistant Dean (Research) at the
University of Newcastle in Australia and Reviews Editor of the
Nexus Network Journal. He has written extensively about
the relationship between architecture, geometry and mathematics.
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