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In a valley so steep that its gelatinous walls seem never to have been warmed by the sun, a drop of hundreds of feet ends in a furious brown river clotted with stones and brambles. As the train curves around the mountainside, a view opens up along its length, revealing that, several carriages ahead, the burgundy-red locomotive has taken the unexpected decision to cross from one side of the valley to the other, a manoeuvre it proceeds to execute without so much as pausing to confer with higher authorities. It makes its way over the gap, and through a small cloud, with the brisk formality one might associate with the most routine of activities, to which prayer and worship would be at once unnecessary and theatrical supplements. What has rendered this supernatural feat possible is a bridge for which nothing in this setting has prepared us – a perfectly massive yet perfectly delicate concrete bridge, marred by not the slightest stain or impurity, which can only have been dropped from the air by the gods, for we cannot imagine that there would be anywhere in this forsaken spot for humans to rest their tools. The bridge seems unimpressed by the razor-sharp stones around it, by the childish moods of the river and the contorted, ugly grimaces of the rock-face. It stands content to reconcile the two sides of the ravine like an impartial judge, modest and willingly literal-minded about its own achievements, ashamed lest it detain our attention or attract our gratitude.

Yet the bridge testifies to how closely a certain kind of beauty is bound up with our admiration for strength, for man-made objects which can withstand the life-destroying forces of heat, cold, gravity or wind. We see beauty in thick slate roofs that challenge hailstones to do their worst, in sea defences that shrug off the waves which batter them, and in bolts, rivets, cables, beams and buttresses. We feel moved by edifices – cathedrals, skyscrapers, hangars, tunnels, pylons – which compensate for our inadequacies, our inability to cross mountains or carry cables between cities. We respond with emotion to creations which transport us across distances we could never walk, which shelter us during storms we could not weather, which pick up signals we could never hear with our own ears and which hang daintily off cliffs from which we would fall instantly to our deaths.

Bernard Lovell, Charles Husband, Lovell Telescope, Jodrell Bank, Cheshire, 1957

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It follows from this that the impression of beauty we derive from an architectural work may be proportionally related to the intensity of the forces against which it is pitted. The emotional power of a bridge over a swollen river, for example, is concentrated at the point where the piers meet but resist the waters which rise threateningly around them. We shudder to think of sinking our own feet into such turbulent depths and venerate the bridge’s reinforced concrete for the sanguine way it deflects the currents which tyrannise it. Likewise, the heavy stone walls of a lighthouse acquire the character of a forbearing and kindly giant during a spiteful gale which does its best to pant them down, just as in a plane passing through an electrical storm, we can feel something approaching love for the aeronautical engineers who, in quiet offices in Bristol or Toulouse, designed dark grey aluminium wings that could flex through tempests with all the grace of a swan’s feathered ones. We feel as safe as we did when we were children being driven home in the early hours by our parents, lying curled up on the backseat under a blanket in our pyjamas, sensing the darkness and cold of the night through the window against which we rested our cheek. There is beauty in that which is stronger than we are.

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Nevertheless, because beauty is typically the result of a few qualities working in concert, it can take more to guarantee the appeal of a bridge or a house than strength alone. Both Robert Maillart’s Salginatobel and Isambard Brunei’s Clifton Suspension bridges are structures of strength; both attract our veneration for carrying us safely across a fatal drop – and yet Maillart’s bridge is the more beautiful of the pair for the exceptionally nimble, apparently effortless way in which it carries out its duty. With its ponderous masonry and heavy steel chains, Brunei’s construction has something to it of a stocky middle-aged man who hoists his trousers and loudly solicits the attention of others before making a jump between two points, whereas Maillart’s bridge resembles a lithe athlete who leaps without ceremony and bows demurely to his audience before leaving the stage. Both bridges accomplish daring feats, but Maillart’s possesses the added virtue of making its achievement look effortless – and because we sense it isn’t, we wonder at it and admire it all the more. The bridge is endowed with a subcategory of beauty we can refer to as elegance, a quality present whenever a work of architecture succeeds in carrying out an act of resistance – holding, spanning, sheltering – with grace and economy as well as strength; when it has the modesty not to draw attention to the difficulties it has surmounted.

Robert Maillart, Salginatobel Bridge, Schiers, 1930

Isambard Brunei, Clifton Suspension Bridge, Bristol, 1864

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We would not, by this measure, describe a heavy steel beam as elegant if it carried only a tabletop, nor a teacup if its sides were four centimeters thick. Michael Hopkins’s canopy for Bracken House is liable to displease us because of the fuss it makes, through multiple bulky struts, of the task of holding up a few relatively light pieces of glass. There is a disproportion between the modest challenge the canopy is set and the laboured response it offers that violates the principles of elegance – just as Santiago Calatrava awes us through the economy and discreet intelligence with which his sculptures defy the pressures of gravity.

In literature, too, we admire prose in which a small and astutely arranged set of words has been constructed to carry a large consignment of ideas. ‘We all have strength enough to bear the misfortunes of others,’ writes La Rochefoucauld in an aphorism which transports us with an energy and exactitude comparable to that of a Maillart bridge. The Swiss engineer reduces the number of supports just as the French writer compacts into a single line what lesser minds might have taken pages to express. We delight in complexity to which genius has lent an appearance of simplicity.

Michael Hopkins, Bracken House, London, 1991

Santiago Calatrava, Running Torso, 1985

staircase, Shaker House, Pleasant Hill, Kentucky, 1841

Silvia Gmür and Livio Vacchini, house in Beinweil am See, 1999