The Australian Ugliness (30 page)

The ‘Golden Mean', ‘Golden Section', ‘Golden Cut', or ‘Divine Proportion', which were revived from near oblivion by
Le Modulor
, are artist's quasi-mathematical terms for one of the geometrical propositions which has fascinated many men who have gone in stumbling search of a rhythm of creation. The Pythagorean mathematicians, who sought a rational explanation for the phenomenon of beauty in the sixth century BC and decided that the circle was the most beautiful figure and the sphere the most beautiful form, first solved the problem of devising a mathematical basis for the perfect visual proportioning of parts. They discovered how to divide a line into two parts, the ratio of the smaller to the greater being the same as the ratio of the greater to the whole line (roughly .618 to 1). As the Pythagoreans discovered, this proposition leads to absorbingly interesting mathematical consequences. For instance, if the length of the smaller section of the divided line is marked on the larger section, again an extreme and mean ratio is created, for the offcut that remains bears the same ratio to the original small section as the small does to the large, and as the large to the whole. This process may be repeated again and again, but the end of the line—zero—will never be reached, for the parts of the golden proportion are incommensurable, which adds to their fascination and to the aura of mysticism surrounding them for twenty-six centuries. Artists saw in the phenomenon a golden rule of proportions for building, sculpture and painting. Plato saw in it a clue to the secrets of creation, and Aristotle saw in the balanced tension of the long and short parts an analogy for a code of ethics. Developing from the divided line, the aesthetic theory of the Golden Section goes on to state that a rectangle formed of the two parts of the linear division is a plane shape of absolute beauty, a solid rectilinear body based on the proportion is one of the forms of absolute beauty, and a building subdivided in accordance with it will be a building of perfection.

The rule may in fact be traced through the proportions of many famous paintings and buildings, and its ‘objective beauty' is occasionally ‘proved' by art instructors in simple experiments. If a group of people is asked to select the most pleasing shapes from a range of different lines and rectangles, one is fairly safe in calculating on the majority selecting the figures which approximate to the Golden Section. An experiment even so simple as this supplies substantial evidence supporting the idea of a mathematical formula for beauty. Here, clearly, is the basis of a system of scientific determination of the most popular, satisfying shapes and subdivisions, and eventually an architect might be able to apply this to all the openings and appurtenances of his building.

At the highest pitch of enthusiasm the Golden Section suggests the possibility that the eye can recognize here a microcosm of universal harmony, that the human being somehow senses the progression from zero to infinity of further ratios implicit in the single given ratio, and that somewhere beyond the reach of our present knowledge an understanding of the all-pervading pattern of creation flickers in the soul.

At a lower pitch of excitement the psycho-analyst interprets the mystique of it as a comparatively simple psychological trick. Even when conscientiously applied to the parts of a building, the mathematical simplicity of the proportions of the Golden Section are never obvious. The conscious eye finds nothing offensive yet can find in the lines no apparent mathematical law, but meanwhile the subconscious has perceived the precision hidden in the form relationships, and its secret goading of the surface mind is the seat of the fascination.

At the most prosaic level the ‘universal beauty' of the Golden Section may be explained flatly as a matter of compromise. Any pure mathematical form of simple mathematical system is approved by the eye because it is a decisive statement. A line cut in the middle satisfies because there is nothing woolly about the even balance of the halves. In a line cut in the golden proportion of .618 to 1 the ratio of the parts is more subtle but the statement is still clear, for if the cut is moved close to one end of the line, it reduces the shorter section to an inconsequential tag. And if it is not moved far enough from the centre the indecision is disturbing; perhaps the draftsman's hand slipped as he was about to make a central cut. A position in which the cut is far enough from the centre to be clearly no slip of the pen and far enough from the end to give the short section sufficient strength of its own, is the point at which the eye finds a satisfyingly definite statement; this is approximately the point of the Golden Cut. It may not always agree exactly with the mathematician's calculation, but then in practice the eye cannot judge with any accuracy the parts of a building seen in perspective. The golden arithmetical progression may be converted for everyday use from decimals to round figures, say 3, 5, 8, 13, etc., and a board-room may be cut to this pattern with every confidence in its ultimate pleasingness. It will seem neither constrictingly narrow nor oppressively low, and a building on the same pattern will be neither too thin nor too squat. The Golden Mean means neither too much nor too little, but moderation, the comforting average; everything to rest the eye and nothing to concern the mind.

If these are the qualities desired of all buildings irrespective of their site, environment, function and meaning to society, then the Golden Mean should dictate the proportions of everything man makes and
Le Modulor
should be on every drawing-board. But Le Corbusier cannot believe that these qualities are desirable in all buildings, for his own have the expressive range to be expected from a master who can control tons of concrete as few men control a tube of paint. The golden proportions can be discovered in most of his buildings only if they and credulity are stretched to breaking point, and they will relate to almost anything when thus extended. On the other hand they may be sensed like a grid of invisible wires between one's eyes and most of Le Corbusier's paintings, contributing to the singular monotony of his work along this sideline.

Contradicting nearly everything that has gone before, Le Corbusier concluded his first book on
Le Modulor
with a caution: ‘Any door that offers an escape is dangerous,' and by quoting Kahnweiler's comment on the Cubist movement—including Le Corbusier's architecture: ‘Every one of these artists has attempted to create works of art which have as strong an autonomous existence as possible, to produce objects whose unity is ensured by the force of their rhythm and in which the parts are subordinated to the whole. To each of these objects, fruits of their emotion, they intend by its uniqueness to guarantee complete autonomy.' Could Le Corbusier have discovered a more devastating condemnation of
Le Modulor
's pretensions to universal proportioning? How can a work of art have an autonomous existence while it is pulling its forelock to some inviolable rule of proportion? Le Corbusier makes this apparent contradiction because he sees the dimensions on his measuring stick not as an architectural scale like a footrule, but more as a musical scale on which the designer may play freely. But surely language is working some mischief here. Le Corbusier's interpretation of playing freely on
Le Modulor
is to ignore it altogether, to change the key, whenever it offers no dimension applicable to a practical task in hand—for instance, in the height of an ordinary doorway. This is the traditional way with systems of architectural proportions. ‘The artist is always present beside the geometrician,' said Viollet-le-Duc, ‘and will be able, when necessary, to bend the formulas.' [
Dictionnaire raisonne de l'architecture
francaise du XIe au XVIe siecle: ‘Proportion'; ‘L'architecture n'est pas l'esclave d'un systeme hieratique de proportione, mais au contraire peut se modifier sans cesse et trouver des applications toujour nouvelles.'
(p. 534)
‘…l'artiste est toujours present a cote du geometre, et sait, au besoin, faire flechir les formules.'
(p. 549)] Now just what—one may ask in Heaven's name—is bent geometry? It is certainly not geometry, probably it is not the best art, and it can hardly be the way to the stars.

While scientists are being led into deeper and deeper mysteries, while the basic theoretical concepts of existence are ever more in doubt, while scientific writers continually warn against over-simplification, while ‘all highroads of the intellect, all byways of theory and conjecture lead ultimately to an abyss that human ingenuity can never span' (Lincoln Barnett), it is preposterous for artists to play with a simple formula or two from the mathematician's primers. Many an artist-architect is a Flash Gordon at heart, but he should not worry about the cosmic value of his work. Everything he builds must be as much a part of the universal harmony as he is. The greatest architect and the meanest speculative builder involuntarily wade, alongside the vulture and leaf mould, under the ultimate law of the expanding universe. Some artists receive blinding glimpses of what they believe to be eternity. If you are not by nature the type given to receiving these messages, mathematics will not increase your capacity. If you are, translation of the message will not be strengthened but weakened by dressing it in numbers, by confusing your medium with the elementary mechanics of scientific theory.

But perhaps there is an eternal quality of beauty not discoverable by numbers or geometry and not mystical, but a self-sufficient object existing independently of the eyes of the beholder, as C. E. M. Joad proposed in
Matter, Life and Value
. ‘It is a real and unique factor in the universe,' he wrote. ‘When I say that a picture or a piece of music is beautiful, I am not making a statement about any feeling that I or any other person or body of persons may have or have had…I am making an assertion about a quality or property possessed…' This property, he explained later, is ‘the awareness of value'. At a moment of perception the artist, attended by a thrill of excitement, apprehends albeit obscurely the patterns and arrangement of the real world. Recalling their outlines as he works, he reproduces them in his medium.

If this is a correct interpretation, or if there is a single mathematical system behind all creation, and if it is possible for man eventually to discover these secrets and to translate them into buildings; if in an infinitely distant future numbers replace an artist's perception and all buildings repose in sublime harmony, then will architects retire with their logarithms from creative practice? Unless men also are at that time drilled by numbers, the very harmony will be a challenge to some; beauty carried to satiety will goad them into revolt against the codes and numbers and they will find their own satisfaction in some disharmony or, in terms of the canon, ugliness.

But perhaps language is confusing the issue again. Are Professor Joad's ‘patterns and arrangements of the real world' necessarily beautiful? How many of Le Corbusier's Cubist painter colleagues would support his search for ‘the simple harmony that moves us: beauty'? Nothing stood lower in the Cubist's esteem than the beautiful painting with its oily, introverted composition and its eye-resting, soul-soothing centre of interest. They were not aesthetes searching for beauty. They sought a sharper perception to convey a keener experience of form; perhaps this is Joad's ‘awareness of value', and it may be more than beauty. ‘Modern Art' may be beautiful to some and ugly to others, but this is irrelevant. Even those who see a painting as ‘ugly' may find it intensely stimulating; to this extent it gives them pleasure. Provocative fascination is not, however, what modern architecture means by ‘pleasing effect' and ‘beauty' when it perseveres today with these terms. Architects still mean the concept of beauty established by the Greeks and maintained throughout the European classical tradition; and it is the adherence to this meaning of beauty and to beauty as an ideal which distinguishes ‘Modern Architecture' from the revolutionary art movements of the twentieth century. Generally our architecture has sought to re-create the glory of Greece, in different terms perhaps, but essentially the same sort of glory.

There have been exceptions. Some of the early ‘scientific' architects of Central Europe like Hannes Meyer professed no interest in creating beauty, but since they also denied architecture any claim to art and required the architect to suppress any conscious personal expression, their work is not relevant to this discussion. The recent tendency in England towards a revival of early modern architectural morality is more significant. The leaders of this movement hopefully adopted a style-name, ‘The New Brutalism', an expression which the Swedish architect Hans Asplund coined (‘in a mildly sarcastic way', as he recalled later) in January 1950: a new promise perhaps for the second half of the century. The style was still little more than the mildly sarcastic name when Reyner Banham examined it in the
Architectural Review
of December 1955. Its leaders, Alison and Peter Smithson, could then exhibit one completed building: a large school, and drawings of some unsuccessful entries in competitions. The movement also reached across the Atlantic to claim Louis Kahn's Fine Arts Centre at Yale University. The importance of the movement was not to be found in completed works, however, but in the fact that it was the first consistent assault on the classical conception of beauty, and that it was a hot topic in English architectural circles. Banham defined a New Brutalist building as one having: ‘1, Memorability as an Image; 2, clear exhibition of structure; and 3, valuation of materials “as found”.' These qualities exist to a degree in many modern buildings, especially in Mies van der Rohe's work, but the degree makes all the difference, and in the case of the Smithsons it is the
Nth
. A rugged, heavy, over-strong look in exposed concrete and masonry characterizes their work, and a prominent little detail is the exposure of the mechanical sub-contractors' apparatus: pipes on the ceiling and electrical conduits darting up and down the walls to pick up switches. Again, this was hardly an innovation, but the interest lay in their manner of, and reasons for, this exposure. The pipes were not shown simply on the ethical grounds of the scientific school, nor were they rather apologetically aiming to please, as was the ductwork on the ceiling of Markelius's chamber in the United Nations Conference building. And although they looked somewhat like a delinquent youth's pencilled additions to a street poster the pipes were not a destructive but a mildly constructive protest against the reigning concept of beauty. The New Brutalists were reaching back half a century to recapture something of the first excitement of the revolution, and they found a string of devoted disciples falling in behind them.