Proportion

Science, Philosophy, Architecture

Richard Padovan

• Publisher: Taylor & Francis
• Year: 2002
• ISBN:
  9781135811105
• Edition: 1
• Topic: Architecture
• Subtopic: Architecture General

This handbook provides readers with a well-illustrated and readable comparative guide to proportion systems in architecture, setting out the mathematical principles that underlie the main systems and illustrating these with examples of their use in historical and modern buildings. The main body of the text traces the interplay of abstraction and empathy through the history of science, philosophy and architecture from the early Greeks through to the two early twentieth-century architects who made proportion the focus of their work: Le Corbusier and Van der Laan. The book ends with a reflection on the present and future role of proportion in architecture.

Chapter one
THE HARMONY OF THE WORLD MADE MANIFEST IN FORM AND NUMBER

Language analysts believe that there are no genuine philosophical problems, or that the problems of philosophy, if any, are problems of linguistic usage, or of the meaning of words. I, however, believe that there is at least one philosophical problem in which all thinking men are interested. It is the problem of cosmology: the problem of understanding the world—including ourselves, and our knowledge, as part of the world.¹

1.1 NOT WITH A BANG, BUT A WHIMPER

On 18 June 1957 the motion ‘that Systems of Proportion make good design easier and bad design more difficult’ was defeated, by 60 votes to 48, in a debate at the Royal Institute of British Architects in London. The debate is remarkable less for the arguments put forward than for its timing: just ten years after the appearance in 1947 of Colin Rowe’s The Mathematics of the Ideal Villa.² Rowe’s essay coincided with the start of a period during which the theory of proportion and the application of mathematical systems to design became a burning issue in architecture. It was followed, a few years later, by a trio of more substantial publications: Architectural Principles in the Age of Humanism, in which Rowe’s tutor Rudolf Wittkower presented Renaissance architecture in a new light, as an abstract art of mathematical harmonies;³ Le Modulor, Le Corbusier’s exposition of a new system of proportions derived from the golden section and the human body;⁴ and Symmetry,⁵ an account by the eminent mathematician Hermann Weyl of the laws governing symmetry and proportional harmony in art and nature. The summit of this wave of enthusiasm, but also the first signs of its decline, can be identified with the holding, in 1951, of the First International Congress on Proportion in the Arts at the Ninth Triennale in Milan.

According to Rudolf Wittkower the Milan congress fizzled out ‘without making an appreciable impact on the younger generation’.⁶ By 1957, the year of the RIBA debate, the focus of architectural thought was already shifting in other directions —to the question of space,⁷ and about a decade later to semiotics.⁸ One of the opposers of the motion, Peter Smithson, declared that

Proportion was important to architects, as a matter of tooth and claw debate, in 1948 and 1949. Then one could have had a debate in which people’s actual beliefs were tested against other people’s strident disbeliefs, rather than this somewhat polite exchange of qualified attitudes…If one went to look at the Palladian buildings in 1948, one could not step an inch without tripping over an architect, and what were they all there for? They were looking for something to believe in.⁹

Ten years later, that quest for a faith was ending with half-hearted apologies and lame excuses.

The motion itself betrayed the narrowing of vision since the heady days of the 1940s. As Misha Black, leading the opposition, put it: ‘The conviction is diluted to something which makes good design easier (as though design were a safe which could be cracked with the help of a system of numbers)…’¹⁰ The wording of the motion was borrowed from Albert Einstein’s comment on the modulor, when Le Corbusier presented it to him at Princeton in 1946, that it ‘makes the bad difficult and the good easy.’¹¹ Note that Einstein did not say ‘bad design’ and ‘good design’: simply ‘the bad’ and ‘the good’. He had in mind something wider and more all-embracing than aesthetics: a moral goodness, or even a cosmological one, of which the visual appearance of a work of art was no more than the outward sign. In contrast, by 1957, at least for the proposers of the motion (E.Maxwell Fry and W.E.Tatton Brown), proportion had come to be regarded as entirely an aesthetic matter, and proportion systems simply as devices or prescriptions for avoiding shapes that were ugly and for making shapes that were pleasing.

The difficulty with the aesthetic argument for proportion is that it quickly becomes entangled in a mesh of contradictions. Are certain shapes or relations inherently more pleasing than others? If so, how can one explain the fact that the buildings of both Palladio and Le Corbusier are regarded as beautifully proportioned, although they are based on quite different mathematical principles?¹² In any case, is not the aesthetic impact of a work more or less instantaneous, whereas to appreciate the underlying mathematical relations—leaving aside the problem of their distortion by perspective — requires patient study, measurement and calculation? And again: do the rules constitute fundamental principles to be followed at the start of the design process, or are they to be applied only as correctives at the end? If the former, and if the recipes are effective, do taste and talent become superfluous? But if the latter, must not the adjustment of forms conceived in the white heat of creativity, to fit a rigid set of mathematical formulae, lead inevitably to a watering down or a deadening of the original inspiration?

For Le Corbusier, and apparently also for Einstein, the modulor’s proportions were ‘good’ because they were in harmony with nature’s laws, which however subtle are ultimately consistent and graspable by human reason. Einstein’s comment on the modulor, interpreted in the light of his general attitude to science, accords entirely with the view of architectural proportion held up to and during the Renaissance. ‘God’, as he famously remarked, ‘does not play dice with the world.’ And: ‘Without the belief that it is possible to grasp the reality with our theoretical constructions, without the belief in the inner harmony of our world, there could be no science.’¹³

Mathematical systems of order in art have always been connected, of course, with visual beauty, but beauty in art was formerly regarded not just as an optical phenomenon but as the outward sign of something more profound: an accord with the general harmony of the world. It was from this deeper harmony that it derived its ‘goodness’ or its ‘truth’. Alberti called such order concinnitas (mutual agreement or harmony), and he saw it as the underlying law of nature. In the ninth of his ten books On the Art of Building he writes that ‘Everything that Nature produces is regulated by the law of concinnitas, and her chief concern is that whatever she produces should be absolutely perfect.’ And since ‘It is in our nature to desire the best, and to cling to it with pleasure,’ it follows that

When you make judgements on beauty, you do not follow mere fancy, but the workings of a reasoning faculty that is inborn in the mind…For within the form and figure of a building there resides some natural excellence and perfection that excites the mind and is immediately recognized by it.¹⁴

In the opening pages of his Architectural Principles, Wittkower attributes the practice of mathematical harmony by Alberti and others to an underlying spirituality of aim, contradicting the then customary interpretation of Renaissance architecture as the expression of a new worldliness.¹⁵ The term ‘Humanism’ should not, he implies, be misinterpreted as meaning that the Renaissance valued only, or even chiefly, the human as opposed to the divine, or that the age sought in art only that which was pleasing to the human eye. In the RIBA debate, Smithson quoted with approval Wittkower’s remark that

It is obvious that…mathematical relations between plan and section cannot be correctly perceived when one walks about in a building. Alberti knew that, of course, quite as well as we do. We must therefore conclude that the harmonic perfection of the geometrical scheme represents an absolute value, independent of our subjective and transitory perception. And…for Alberti—as for other Renaissance architects—this man-created harmony was a visible echo of a celestial and universally valid harmony.¹⁶

Le Corbusier, like Einstein, had a breadth of vision that makes him an heir to that Renaissance mentality No other Modern Movement architect has given so central a role to mathematical proportion in architecture. Mathematical law is, for him, not just a prescription for beauty, nor even a means by which human beings are somehow able to comprehend their world, but the axis or ruling principle of the universe itself, and the source of the unity and harmony of nature and of art. Near the start of Le Modulor he quotes his own statement to the Swiss mathematician Andreas Speiser that

Nature is ruled by mathematics, and the masterpieces of art are in consonance with nature; they express the laws of nature and themselves proceed from those laws. Consequently, they too are governed by mathematics, and the scholar’s implacable reasoning and unerring formulae may be applied to art.¹⁷

The argument demands, if not a religious faith, at least a mystical attitude to nature, such as is expressed by the biologist Sir D’Arcy Thompson in the epilogue of his book On Growth and Form, from which I have taken the title of this chapter: ‘For the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.’¹⁸ Underlying Le Corbusier’s approach is the implication that a guiding intelligence or will governs the universe:

This axis leads us to assume a unity of conduct in the universe and to admit a single will behind it…and if we recognize (and love) science and its works, it is because both one and the other force us to admit that they are prescribed by this primal will. If the results of mathematical calculation appear satisfying and harmonious to us, it is because they proceed from the axis. If, through calculation, the airplane takes on the aspect of a fish or some object of nature, it is because it has recovered the axis.¹⁹

Thus (even if only by a side door) God the Geometer enters the scene, armed with a gigantic pair of dividers, much as he was pictured in Medieval manuscripts. Just as the Medieval architect, according to Otto von Simson, felt that by submitting to geometry he was imitating the work of the Creator, who had composed the world according to geometrical laws,²⁰ so Le Corbusier believed that the artist ‘feels and discer...

Table of contents

• COVER PAGE
• TITLE PAGE
• COPYRIGHT PAGE
• LIST OF FIGURES
• PREFACE
• CHAPTER ONE: THE HARMONY OF THE WORLD MADE MANIFEST IN FORM AND NUMBER
• CHAPTER TWO: ABSTRACTION AND EMPATHY
• CHAPTER THREE: UNIT AND MULTIPLIER
• CHAPTER FOUR: THE HOUSE AS MODEL FOR THE UNIVERSE
• CHAPTER FIVE: THE PROPORTIONS OF THE PARTHENON
• CHAPTER SIX: PLATO: ORDER OUT OF CHAOS
• CHAPTER SEVEN: ARISTOTLE: CHANGE, CONTINUITY, AND THE UNIT
• CHAPTER EIGHT: EUCLID: THE GOLDEN SECTION AND THE FIVE REGULAR SOLIDS
• CHAPTER NINE: VITRUVIUS
• CHAPTER TEN: GOTHIC PROPORTIONS
• CHAPTER ELEVEN: HUMANISM AND ARCHITECTURE
• CHAPTER TWELVE: RENAISSANCE COSMOLOGY
• CHAPTER THIRTEEN: THE WORLD AS A MACHINE
• CHAPTER FOURTEEN: FROM THE OUTER TO THE INNER WORLD
• CHAPTER FIFTEEN: THE GOLDEN SECTION AND THE GOLDEN MODULE
• CHAPTER SIXTEEN: THE HOUSE AS A FRAME FOR LIVING AND A DISCIPLINE FOR THOUGHT
• REFERENCES