MILTON: "In his handhe took the golden compasses prepared In God's eternal stone to circmscribe This niverse and all created things One foot he centered and the other trned Rond throgh the vast profndity obscre And said Ths far extend ths far thy bonds
This be thy just circumference, O World!"
The earth has existed for more than 4,000 million years.
Through all this time it has been shaped and changed by two kinds of action.
The hidden forces within the earth have buckled the strata
and lifted and shifted the land masses.
And on the surface, the erosion of snow and rain and storm,
of stream and ocean,
of sun and wind,
have carved out a natural architecture.
~ MESSIAEN: Et Expecto Resurrectionem Mortuorum
Man has also become an architect of his environment,
but he does not command forces as powerful as those of nature.
His method has been selective and probing,
an intellectual approach in which action depends on understanding.
I've come to trace its history and the cultures of the New World,
which are younger than Europe and Asia.
This is the Canyon de Chelly in Arizona.
This breathless, secret valley has been inhabited by one Indian tribe after another,
almost without a break, for 2,000 years since the birth of Christ,
longer than any other place in North America.
Sir Thomas Browne has a springing sentence -
"The huntsmen are up in America and they're already past their first sleep in Persia."
At the birth of Christ, the huntsmen were settling to agriculture here in the Canyon de Chelly
and starting along the same steps in the ascent of man
that had first been taken in the Middle East.
Why did civilisation begin so much later in the New World than in the Old?
Evidently because man was a latecomer to the New World.
He came before boats were invented,
which implies that he came dry shod over the Bering Straits
when they formed a broad land bridge during the last ice age.
That means that man came from Asia to America not later than 10,000 years ago
and not earlier than about 30,000 years ago.
And he didn 't come all at once.
There is subtle, but persuasive, biological evidence...
...that I can only interpret to mean that he came in two small successive migrations.
The evidence is that there is no blood group B anywhere in America
as there is in most other parts of the world.
In Central and South America,
all the original Indian population is blood group O.
In North America, it is the blood groups O and A.
I can see no sensible way of interpreting that...
...but to believe that a first migration of a small related kinship group,
all of blood group O,
came into America, multiplied and spread right down to the south.
And then a second migration, again of small groups,
this time containing both A and O,
followed them only so far as North America.
The American Indians, then, certainly contained some of this later migration
and are, comparatively speaking, latecomers.
Agriculture in the Canyon de Chelly reflects this lateness.
Although maize had long been cultivated in Central and South America,
here it comes in only about the time of Christ.
People are very simple. They have no houses, they live in caves.
Pottery is introduced.
Pit houses are dug in the caves themselves and covered with clay or adobe.
And at that stage the canyon is really fixed until about the year 1000,
when the great Pueblo civilisation comes in with stonemasonry.
That seems a very simple distinction -
the mud house, the stonemasonry.
But, in fact, it represents a fundamental intellectual difference, not just a technical one.
And I believe it to be one of the most important steps that man has taken...
...wherever and whenever he did so.
The distinction between the moulding action of the hand
and the splitting or analytic action of the hand.
...it seems the most natural thing in the world to take some clay
and mould it into a ball, a little clay figure, a cup, a pit house.
At first, we feel that the shape of nature's been given us by this.
But, of course, it's not.
This is the man -made shape.
What the pot does is to reflect the cupped hand.
What the pit house does is to reflect the shaping action of man.
And nothing has been discovered about nature herself...
...when man imposes these warm, rounded, feminine, artistic shapes on her.
The only thing that you reflect is the shape of your own hand.
There is a great intellectual step forward...
...when man splits a piece of wood, or a piece of stone...
...and lays bare in that the print that nature had put before he split it.
From an early time, man made tools by working the stone.
Sometimes the stone had a natural grain.
Sometimes the tool-maker created the lines of cleavage by learning how to strike the stone.
It may be that the idea comes in the first place from splitting wood
because wood is a material with a visible structure which opens easily along the grain,
but which is hard to shear across the grain.
The notion of discovering an underlying order in matter
is man 's basic concept for exploring nature.
The architecture of things reveals a structure below the surface,
a hidden grain which, when it's laid bare,
makes it possible to take natural formations apart
and assemble them in new arrangements.
For me, this is the step in the ascent of man with which theoretical science begins
and it's as native to the way man conceives his own communities as well as nature.
We human beings are joined in families,
the families are joined in kinship groups,
the kinship groups in clans, the clans in tribes, the tribes in nations.
And that sense of hierarchy, of a pyramid, in which layer is imposed on layer,
runs through all the ways that we look at nature.
The fundamental particles make nuclei,
the nuclei join in atoms,
the atoms join in molecules, the molecules join in bases,
the bases join in amino acids.
We find again in nature something which seems profoundly to correspond
to the way in which our own social relations join us.
The Canyon de Chelly is a kind of microcosm of the cultures.
But its high point was reached when the Pueblo people built these great structures
just after 1000 AD.
They represent not only an understanding of nature in the stonework, but of human relations,
because the Pueblo people formed here and elsewhere a kind of miniature city.
Stones make a wall, walls make a house, houses make streets and streets make a city.
A city is stones and a city is people.
But it's not a heap of stones and it's not just a jostle of people.
In the step from the village to the city, a new community organisation is built,
based on the division of labour and on chains of command.
The way to recapture that is to walk into the streets of a city that none of us has seen
in a culture that has vanished.
This is Machu Picchu in the high Andes, 8,000ft up, in South America.
It was built by the Incas at the height of their empire,
round about 1500 AD, or a little earlier,
when the planning of a city was their greatest achievement.
When the Spaniards conquered and plundered Peru in 1532,
they somehow overlooked Machu Picchu and its sister cities.
After that, it was forgotten for 400 years
until, one winter's day in 1911, Hiram Bingham of Yale stumbled on it.
By then it had been abandoned for centuries and was picked bare as a bone.
But in that skeleton of a city lies the structure of every city civilisation,
in every age, everywhere in the world.
A city must live on a base, a hinterland, of a rich agricultural surplus.
And the visible base for the Inca civilisation was the cultivation of terraces.
Of course, now the bare terraces grow nothing but grass.
But once the potato was cultivated here -
it's the native product of Peru.
Maize, which was long native and had come from the north.
And since this was a ceremonial city of some kind,
when the Inca came to visit, no doubt there were grown for him tropical luxuries of this climate,
like the coca, which is an intoxicating herb that only the Inca aristocracy was allowed to chew.
At the heart of the terrace culture is the system of irrigation.
This is what the pre-lnca empire and the Inca empire made.
It runs through these terraces through canals and aqueducts, through the great ravines,
down into the desert towards the Pacific,
and makes it flower.
Exactly as in the Fertile Crescent, it's the control of the water,
and so here in Peru, the Inca civilisation was built on the control of irrigation.
A large system of irrigation, extending over an empire,
requires a strong central authority.
It was so in Mesopotamia, it was so in Egypt,
it was so in the empire of the Incas.
And that means that this city, and all the cities here,
rested on an invisible base of communication -
the bridges in a wild country like this,
They came here, they went out of here.
They are the three links by which every city is held to every other,
and which, we suddenly realise, are different in this city.
Roads, bridges, messages.
Yet on the roads there were no wheels.
Under the bridges there were no arches.
The messages were not in writing.
The culture of the Incas had not made these inventions by the year 1500 AD.
That's because civilisation in America started several thousand years late
and was conquered before it had time to make all the inventions of the Old World.
It was a remarkably tight social structure.
Everyone had a place, everyone was provided for...
...and everyone - peasant, craftsman, soldier - worked for one man, the supreme Inca.
The artisans who lovingly carved this stone to represent the symbol of the link
between the sun and its god and king, the Inca, worked for the Inca.
So, of course, it was an extraordinarily brittle empire.
In less than a hundred years, from 1438 onwards,
the Incas had conquered 3,000 miles of coastline.
Almost everything between the Andes and the Pacific.
And yet, and yet...
In 1532, a Spanish adventurer, almost illiterate, Francisco Pizarro,
rode into Peru with no more than 62 terrible horses and 106 foot soldiers.
And overnight he conquered the great empire.
How? By cutting the top of the pyramid. By capturing the Inca.
And from that moment, the empire sagged...
...and the cities, the beautiful cities, laid bare for the gold plunderer and the vultures.
But, of course, a city is more than a central authority.
A city is people, a city is alive.
What is a city?
It is a community which lives on a base of agriculture so much richer than the 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 this city -
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 mason.
The beautiful craftsmanship of the men who made this city.
Not the Incas, but the craftsmen.
But, of course, if you work for an Inca, if you work for 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 had reached 2,000 years earlier
and at which they also stopped.
This is Paestum in southern Italy.
A Greek colony, whose temples are older than the Parthenon,
they date from about 500 BC.
Paestum is contemporary with the beginning of Greek mathematics.
Pythagoras taught in exile in another Greek colony not far from here.
Like the mathematics of Peru 2,000 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's 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.
On a computer, we can see the stresses in the beam as we move the columns further 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.
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 in the end, the physical limitations of the material
could not be overcome without a new invention.
Since the Greeks were fascinated by geometry,
it's puzzling that they did not make the beautiful invention of the arch.
But the fact is that the arch is an engineering invention.
This is the aqueduct at Segovia in Spain,
which the Romans built about 100 AD.
The structure seems to us splendid, out of proportion to its function of carrying water.
But that's because we get water by turning a tap
and we lightly forget the universal problems of city civilisation.
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.
The arch is simply a method of spanning space,
which doesn 't 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, too,
when it went into mass production in Arab countries.
This is the great mosque at Cordoba in Spain, built in 785 AD after the Arab conquest.
It's a more spacious structure than the Greek temple at Paestum
and yet it's visibly run into similar difficulties.
It's filled with masonry which can 't be got rid of without a new invention.
The invention is a new form of the arch based not on the circle, but on the oval.
That doesn 't seem a great change
and yet its effect on the articulation of buildings is spectacular.
~ BENJAMIN BRITTEN: A War Requiem
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 here at Reims.
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.
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 about the year 1200.
They 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 in them improvisation becomes invention at every moment.
They 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 12th century, 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
and there is no masonry where there's no stress.
No basic principle in architecture was added to that really
until the invention of steel and concrete buildings.
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 ovals for the pointed 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.
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
and they called themselves freemasons as early as the 14th century.
One has the sense that the men who conceived these 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 and 150ft
at a time when they could not calculate any of the stresses?
Well, the vault of 150ft at Beauvais, less than 100 miles from here, collapsed.
~ VERDl: Requiem - Dies Irae, Part 1
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 125ft here at Reims held.
And from 1250 onwards,
Reims became a centre for the arts of Europe.
You see, here I am, roaming around all these beautiful architectural sites
sitting now on the roof of the cathedral at Reims.
Why? What does it have to do with science?
Particularly, what does it have to do with science
the way we used to understand it at the beginning of this century
when science was all numbers?
The co-efficient of expansion of this, the frequency of that.
The fact of the matter is that our conception of science now,
towards the end of the 20th century,
has changed radically.
We see science as a description and explanation
of the underlying structures in nature.
And words like structure, pattern, plan, arrangement, architecture
constantly occur in every description that we try to make.
I have, of course, lived with this all my life and it gives me a special pleasure.
The kind of mathematics that I have done since childhood is geometrical.
But now that is the everyday language of scientific explanation.
We talk about the way crystals are put together,
the way atoms are made of their parts.
Above all, we talk about the way that living molecules are made of their parts.
The spiral structure of DNA has become the most vivid imagery for science in the last years.
And that imagery lives here. It lives in these arches.
What did the people do who made this building and others like it?
They took a dead heap of stones which is not a cathedral
and they turned it into a cathedral by exploiting the natural forces of gravity,
the way the stone had lain, the brilliant invention of flying buttress and arch and so on.
And they created a structure out of the analysis of nature into this superb synthesis.
The kind of man who is interested in the architecture of nature today...
...is the kind of man who made this architecture nearly 800 years ago.
There is one gift above all others that makes man unique among the animals
and it's the gift displayed everywhere here.
His immense pleasure in exercising and pushing forward his own skill.
~ MACHAUT: Notre Dame Mass
A popular cliche in philosophy says that science is pure analysis or reductionism,
like taking the rainbow to pieces,
and art is pure synthesis - putting the rainbow together.
This is not so.
All imagination begins by analysing nature.
Michelangelo said that: "When that which is divine in s does try to shape a face both brain and hand nite to give from a mere model frail and slight life to the stone by art's free energy"
BRONOWSKl: The material asserts itself through the hand
and thereby prefigures the shape of the work for the brain.
The sculptor, as much as the mason, feels for the form within nature. "The best of artistshath no thoght to show
what the rough stone in its superflous shell doth not terrrible. To break the marble spellis all the hand that serves the brain can do"
BRONOWSKl: By the time Michelangelo carved the head of Brutus,
other men quarried the marble for him.
But Michelangelo had begun as a quarryman in Carrara
and he still felt that the hammer in their hands, and in his,
was groping in the stone for a shape that was already there.
~ ROBERTO GERHARD: Collages
The quarrymen work in Carrara now for the modern sculptors who come here -
Marino Marini, Lipschitz and Henry Moore.
Their descriptions of their work are not as poetic as Michelangelo's,
but they carry the same feeling.
HENRY MOORE: To begin with, as a young sculptor, I couldn 't afford expensive stone...
...and I got my stone by going round the stone yards
and finding what they would call a random block.
Then I had to think in the same way that Michelangelo might have done.
So that one had to wait until an idea came that fitted the shape of the stone
and that was seeing the idea in that block.
~ ELIZABETH LUTYENS: Quincunx
BRONOWSKl: Of course, it can 't be literally true
that what the sculptor imagines and carves out is already there, hidden in the block.
And yet the metaphor tells the truth about the relation of discovery
that exists between man and nature.
In one sense, everything that we discover is already there.
A sculptured figure and the law of nature are both concealed in the raw material.
And in another sense, what a man discovers is discovered by him.
It would not take exactly the same form in the hands of someone else.
Neither the sculptured figure nor the law of nature would come out in identical copies
when produced by two different minds in two different ages.
Discovery is a double relation of analysis and synthesis together.
As an analysis it probes for what is there.
But then, as a synthesis, it puts the parts together in a form
in which the creative mind transcends the bare limits, the bare skeleton that nature provides.
Sculpture is a sensuous art.
The Eskimos make small sculptures that are not even meant to be seen, only handled.
So it must seem strange that I choose as my model for science sculpture and architecture.
And yet it's right.
We have to understand that the world can only be grasped by action, not by contemplation.
The hand is more important than the eye.
We are not one of those contemplative civilisations of the Far East or the Middle Ages
that believed that the world has only to be seen and thought about
and who practised no science.
We are active, and indeed we know in the evolution of man,
that it is the hand that drives the subsequent evolution of the brain.
We find tools made by man before he became man.
Benjamin Franklin called man the "tool-making animal".
And that's right.
And the most exciting thing about that is that even in prehistory,
man already made tools that have an edge finer than they need have.
Henry Moore calls this sculpture "The Knife Edge".
The hand is the cutting edge of the mind.
Civilisation is not a collection of finished artefacts.
It is the elaboration of processes.
In the end, the march of man is the refinement of the hand in action.
~ BEETHOVEN: Ninth Symphony
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 have to look for the limits in the material itself.
It's 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 most powerful drive in the ascent of man is his pleasure in his own skill.
He loves to do what he does well and, having done it well, he loves to do it better.
You see it in his science.
You see it in the magnificence with which he carves and builds.
The loving care, the gaiety, the effrontery.
The monuments are supposed to commemorate kings and religions, heroes, dogmas,
but in the end, the man they commemorate is the builder.
I could not end this essay without taking you to my favourite monument.
Built by a man who had no more scientific equipment than the Gothic mason.
These are the Watts Towers in Los Angeles,
built by an Italian called Simon Rodia.
He came from Italy to the United States at the age of 12
and then at the age of 42, having worked as a tile setter and general repairman,
he suddenly decided, in his back garden, to build these tremendous structures...
...out of chicken wire, bits of railway tie, steel rods, cement, seashells,
bits of broken tile and glass, of course -
anything that he could find or that the neighbourhood children could bring him.
~ GERSHWIN: American Piano Music
It took him 33 years to build them.
He never had anyone to help him because he said, "I never knew what to do next myself."
He finished them in 1954.
He was 75 by then.
He gave the house, the garden and the towers to a neighbour and simply walked out.
"I had in mind to do something big," Simon Rodia had said, "and I did.
You have to be good, good or bad, bad to be remembered."
He'd learnt his engineering skill as he went along, by doing it,
and by taking pleasure in the doing.
Of course, the city building department decided that the towers were unsafe
and in 1959, they ran a test on them.
This is the tower that they tried to pull down.
I'm happy to say that they failed.
The tool that extends the human hand is also an instrument of vision.
It reveals the structure of things
and makes it possible to put them together in new, imaginative combinations.
But, of course, the visible is not the only structure in the world.
There is a fine structure below it and the next step in the ascent of man
is to discover a tool to open up the invisible structure of matter.