The Ascent of Man (10 page)

It was a remarkably tight social structure. Everyone
had a place; everyone was provided for; and everyone – peasant, craftsman or soldier – worked for one man, the supreme Inca. He was the civil head of state and he was also the religious incarnation of godhead. The artisans who lovingly carved a stone to represent the symbol of the link between the sun and its god and king, the Inca, worked for the Inca.

So, necessarily, it was an extraordinarily
brittle empire. In less than a hundred years, from 1438 onwards, the Incas had conquered three thousand miles of coastline, almost everything between the Andes and the Pacific. And yet, in 1532 an almost illiterate Spanish adventurer, Francisco Pizarro, rode into Peru with no more than sixty-two terrible horses and a hundred and six foot soldiers; and overnight he conquered the great empire. How?
By cutting the top off the pyramid – by capturing the Inca. And from that moment, the empire sagged, and the cities, the beautiful cities, lay bare for the gold plunderer and the vultures.

But, of course, a city is more than a central authority. What is a city? A city is people. A city is alive. It is a community which lives on a base of agriculture, so much richer than in a village, that it
can afford to sustain every kind of craftsman and make him a specialist for a lifetime.

The specialists are gone, their work has been destroyed. The men who made Machu Picchu – the goldsmith, the coppersmith, the weaver, the potter – their work has been robbed. The woven fabric has decayed, the bronze has perished, the gold has been stolen. All that remains is the work of the masons, the beautiful
craftsmanship of the men who made the city – for the men who make a city are not the Incas but the craftsmen. But naturally, if you work for an Inca (if you work for any one man) his tastes rule you and you make no invention. These men still worked to the end of the empire with the beam; they never invented the arch. Here is a measure of the time lag between the New World and the Old, because
this is exactly the point which the Greeks reached two thousand years earlier, and at which they also stopped.

Paestum in Southern Italy was a Greek colony whose temples are older than the Parthenon: they date from about 500
BC
. Its river has silted up and it is now separated from the sea by dull salt-flats. But its glory is still spectacular. Although it was ransacked by Saracen pirates in the
ninth century, and by Crusaders in the eleventh, Paestum in ruins is one of the marvels of Greek architecture.

Paestum is contemporary with the beginning of Greek mathematics; Pythagoras taught in exile in another Greek colony at Crotone not far from here. Like the mathematics of Peru two thousand years later, the Greek temples were bounded by the straight edge and the set square. The Greeks
did not invent the arch either, and
therefore their temples are crowded avenues of pillars. They seem open when we see them as ruins, but in fact they are monuments without spaces. That is because they had to be spanned by single beams, and the span that can be sustained by a flat beam is limited by the strength of the beam.

If we picture a beam lying across two columns, then a computer analysis
will show the stresses in the beam increase as we move the columns farther apart. The longer the beam, the greater the compression that its weight produces in the top, and the greater the tension it produces in the bottom. And stone is weak in tension; the columns will not fail, because they are compressed, but the beam will fail when the tension becomes too great. It will fail at the bottom unless
the columns are kept close together.

The Greeks could be ingenious in making the structure light, for example by using two tiers of columns. But such devices were only makeshifts; in any fundamental sense, the physical limitations of stone could not be overcome without a new invention. Since the Greeks were fascinated by geometry, it is puzzling that they did not conceive the arch. But the fact
is that the arch is an engineering invention, and very properly is the discovery of a more practical and plebeian culture than either Greece or Peru.

The aqueduct at Segovia in Spain was built by the Romans about
AD
100, in the reign of the emperor Trajan. It carries the waters of the Rio Frio that flows from the high Sierra ten miles away. The aqueduct spans the valley for almost half a mile in more than a hundred double-tiered
round arches made of rough-hewn granite blocks, laid without lime or cement. Its colossal proportions so awed the Spanish and Moorish citizens in later and more superstitious ages that they named it El Puente del Diablo, the devil’s bridge.

The structure seems to us also prodigious and splendid out of proportion to its function of carrying water. But that is because we get water by turning a
tap, and we lightly forget the universal problems of city civilisations. Every advanced culture that concentrates its skilled men in cities depends on the kind of invention and organisation that the Roman aqueduct at Segovia expresses.

The Romans did not invent the arch in the first place in stone, but as a moulded construction made of a kind of concrete. Structurally the arch is simply a method
of spanning space which does not load the centre more than the rest; the stress flows outward fairly equally throughout. But for this reason the arch can be made of parts: of separate blocks of stone which the load compresses. In this sense, the arch is the triumph of the intellectual method which takes nature apart and puts the pieces together in new and more powerful combinations.

The Romans
always made the arch as a semicircle; they had a mathematical form that worked well, and they were not inclined to experiment. The circle remained the basis of the arch still when it went into mass-production in Arab countries. This is plain in the cloistered, religious architecture that the Moors used; for instance, in the great mosque at Cordoba, also in Spain, built in
AD
785 after the Arab
conquest. It is a more spacious structure than the Greek temple at Paestum, and yet it has visibly run into similar difficulties; that is, once again it is filled with masonry, which cannot be got rid of without a new invention.

Theoretical discoveries that have radical consequences can usually be seen at once to be striking and original. But practical discoveries, even when they turn out to
be far-reaching, often have a look that is more modest and less memorable. A structural innovation to break the limitation of the Roman arch did come, probably from outside Europe, and arrived almost by stealth at first. The invention is a new form of the arch based not on the circle, but on the oval. This does not seem a great change, and yet its effect on the articulation of buildings is spectacular.
Of course, a pointed arch is higher, and therefore opens more space and light. But, much more radically, the thrust of the Gothic arch makes it possible to hold the space in a new way, as at Rheims. The load is taken off the walls, which can therefore be pierced with glass, and the total effect is to hang the building like a cage from the arched roof. The inside of the building is open, because
the skeleton is outside.

John Ruskin describes the effect of the Gothic arch admirably.

Egyptian and Greek buildings stand, for the most part, by their own weight and mass, one stone passively incumbent on another; but in the Gothic vaults and traceries there is a stiffness analogous to that of the bones of a limb, or fibres of a tree; an elastic tension and communication of force from part
to part, and also a
studious expression of this throughout every visible line of the building.

Of all the monuments to human effrontery, there is none to match these towers of tracery and glass that burst into the light of Northern Europe before the year 1200. The construction of these huge, defiant monsters is a stunning achievement of human foresight – or rather, I ought to say, since they
were built before any mathematician knew how to compute the forces in them, of human insight. Of course it did not happen without mistakes and some sizeable failures. But what must strike the mathematician most about the Gothic cathedrals is how sound the insight in them was, how smoothly and rationally it progressed from the experience of one structure to the next.

The cathedrals were built
by the common consent of townspeople, and for them by common masons. They bear almost no relation to the everyday, useful architecture of the time, and yet in them improvisation becomes invention at every moment. As a matter of mechanics, the design had turned the semicircular Roman arch into the high, pointed Gothic arch in such a way that the stress flows through the arch to the outside of the building.
And then in the twelfth century also came the sudden revolutionary turning of that into the half arch: the flying buttress. The stress runs in the buttress as it runs in my arm when I raise my hand and push against the building as if to support it – there is no masonry where there is no stress. No basic principle of architecture was added to that realism until the invention of steel and reinforced
concrete buildings.

One has the sense that the men who conceived these high buildings were intoxicated by their new-found command of the force in the stone. How else could they have proposed to build Vaults of 125 feet and 150 feet at a time when they could not calculate any of the stresses? Well, the vault of 150 feet – at Beauvais, less than a hundred miles from Rheims – collapsed. Sooner or
later the builders were bound to run into some disaster: there is a physical limit to size, even in cathedrals. And when the roof of Beauvais collapsed in 1284, some years after it was finished, it sobered the high Gothic adventure: no structure as tall as this was attempted again. (Yet the empirical design may have been sound; probably the ground at Beauvais was simply not solid enough, and shifted
under the building.) But the vault of 125 feet at Rheims held. And from 1250 onwards Rheims became a centre for the arts of Europe.

The arch, the buttress, the dome (which is a sort of arch in rotation) are not the last steps in bending the grain in nature to our own use. But what lies beyond must have a finer grain: we now have to look for the limits in the material itself. It is as if architecture
shifts its focus at the same time as physics does, to the microscopic level of matter. In effect, the modern problem is no longer to design a structure from the materials, but to design the materials for a structure.

The masons carried in their heads a stock, not so much of patterns as of ideas, that grew by experience as they went from one site to the next. They also carried with them a kit
of light tools. They marked out with compasses the oval shapes for the vaults and the circles for the rose windows. They defined their intersections with callipers, to line them up and fit them into repeatable patterns. Vertical and horizontal were related by the T-square, as they had been in Greek mathematics, using the right angle. That is, the vertical was fixed with the plumb-line, and the horizontal
was fixed, not with a spirit-level, but with a plumb-line joined to a right angle.

The wandering builders were an intellectual aristocracy (like the watchmakers five hundred years later) and
could move all over Europe, sure of a job and a welcome; they called themselves freemasons as early as the fourteenth century. The skill that they carried in their hands and their heads seemed to others to
be as much a mystery as a tradition, a secret fund of knowledge that stood outside the dreary formalism of pulpit learning that the universities taught. When the work of the freemasons petered out, by the seventeenth century, they began to admit honorary members, who liked to believe that their craft went back to the pyramids. That was not really a flattering legend, because the pyramids were built
with a much more primitive geometry than the cathedrals.