2.1 Containers of space
2.1.1 Pyramids
2.1.2 Henges
2.1.3 Cathedrals
Our conception of science now, towards the end of the t21st century, has changed radically. Now we see science as a description and explanation of the underlying structures of nature; and words like structure, pattern, plan, arrangement, architecture constantly occur in every description that we try to make. 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 image of science in the last years.

Architects 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 is laid naturally in its bedding planes, the brilliant invention of the flying buttress and arch and so on. And they created a structure that grew 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 eight hundred years ago. There is one gift above all others that makes man unique among the animals, and it is the gift displayed everywhere here: his immense pleasure in exercising and pushing forward his own skill.

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 vividly, by implication, in his sculpture (it is particularly clear in the sculptures that he did not finish), and he also said it explicitly in his sonnets on the act of creation.

When that which is divine in us doth try
To shape a face, both brain and hand unite
To give, from a mere model frail and slight,
Life to the stone by Art's free energy.

'Brain and hand unite': 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, and for him it is already laid down there. That principle is constant.

The best of artists hath no thought to show
Which the rough stone in its superfluous shell
Doth not include: to break the marble spell
Is all the hand that serves the brain can do.

A deeper meaning is added by ordinary people to provide the imagery lives in arches and beams.
2.1.1 Pyramids
graphic
Bonapart's Expeditionary Force Survey; 1798
Since the 19th century many archeologists have developed the idea that alignment of the Egyptian pyramids at Giza harks back to one of the first moments in the history of civilization in which astronomy was pressed into the service of the arts, in this case to monumental architecture. In particular, the pyramids of the IV Dynasty Kings Cheops, Khephren and Mycerinus, are orientated with extraordinary accuracy with the four cardinal points of the modern compass.
The British Egyptologist, K. Spence has suggested that the alignment of the pyramids in relation to the cardinal points of the modern compass could have been achieved via observations of simultaneous transits across the local meridian (an imaginary semicircle that divides the sky into its eastern and western halves) of two circumpolar stars, Kochab and Mizar, that were on opposite sides of the north celestial pole at the time when the pyramids were built.  If this is  true, the chronology of the Great Pyramid is shortened by almost 80 years. The article by the IAC's Juan Antonio Belmonte now critically examines Spence's proposal and improves on this with a new hypothesis.
Responding to Spence's ideas, J.A. Belmonte suggests that this orientation, following the local meridian, could have been achieved through meridian transit observations of the stars Phecda and Megrez, belonging to the Leg of the Bull, one of the most imporatant Egyptian constellation (equivalent to our Plough in the constellation Ursa Major). Extending the line joining these two stars leads us to Thuban (the "pole star" at that time) in the same way that the two stars Merak and Dubhe today act as pointers to the present Pole Star, Polaris.
According to this new hypothesis, the greatest accuracy of alignment would have been achieved around the year 2562 BC; consequently, the Great Pyramid could have been orientated close to this date, at a moment falling between the two dates proposed Spence and Belmonte, which would place it at the start of the reign of Cheops (2589 - 2551 BC) and render unnecessary the shortening in the chronology advocated by Spence.
Belmonte's hypothesis has important chronological and historical - even mythological - implications that could help towards a a better understanding of how the Egyptians of the pharaonic era understood the cosmos and made use of it, among other things, to align precisely their most important monuments.

The ancient Egyptians were extremely interested in the night sky, articularly the circumpolar stars.  These stars circle around the North Pole, and as you can always see them, the Egyptians always referred to them as 'The Indestructibles'.  As a result, they became closely associated with eternity and the king's afterlife. So that after death, the king would hope to join the circumpolar stars - and that's why the pyramids were laid out towards them.

The north-finding stars were Kochab, in the bowl of the Little Dipper (Ursa Minor), and Mizar, in the middle of the handle of The Plough or Big Dipper (Ursa Major).

An Egyptian astronomer would have held up a plumb line and waited for the night sky to slowly pivot around the unmarked pole as the Earth rotated.

When the plumb line exactly intersected both stars, one about 10 degrees above the invisible pole and the other 10 degrees below it, the sight line to the horizon would aim directly north.

However, the Earth's axis is unstable and wobbles like a gyroscope over a period of 26,000 years. Modern astronomers now know that the celestial north pole was exactly aligned between Kochab and Mizar only in the year 2,467 BC.

Either side of this date, the ancient astronomers trying to find true north would lose some accuracy.

Spence shows that the orientation errors of earlier and later pyramids faithfully track the slow drift of Kochab and Mizar with respect to true north.  And because the error in the Kochab-Mizar alignment can be readily calculated for any date, the error in each pyramid's orientation corresponds to a period of several years.
2.1.2 Henges
The term 'henge' is being increasingly used to defined a variety of structures built between 3000-5000 years.  These take the form of banked enclosures, stone chambers and separate stones arranged in avenues and circles.  Some circles have very complex geometry and the local astronomy of the site was often built into the design.
Neolithic farmers appeared first appeared in Britain around 4000BC and by 3000BC the first megalithic (large stone) constructions started. There are several types of stone structures, the simplest being the raising of single, sometimes massive, standing stones called menhirs. Hollow box-like structures made from large stones were used for burials and covered with mounds of soil, these are called dolmens or, in Wales, cromlechs . Cairns are cromlechs covered in stones and barrows are earthen burial mounds. Henges are usually stone or vertical timber circles often surrounded by a ditch and bank.

Most stone circles were constructed in the late Neolithic to early Bronze Age periods. They occur all over the UK except in the southeast where there is no evidence of them, but this does not mean there were none. Many stone circles have been removed and recycled in walls and buildings or cleared for farming. They survive best where there has been little development. Stone circles are also found in parts of Europe.
Early circles, or henges, were made from wood, both Woodhenge and Stonehenge are examples of these. Stone was used for permanence and local materials were generally used but sometimes stones were transported great distances. The proximity of circles to burials suggests they were built with some significance to the dead or to hold ceremonies as well as being "calendars" lined up with astronomical features such as solstice sunrises, moonrise and moonset and specific constellations.
Following detailed surveys of hundreds of sites, Alexander Thom, a professor of engineering at Oxford, concluded that the megalithic builders used a standard unit of measurement.  This unit was 2.72 feet (0.83m), the megalithic yard, about the size of a pace except that over all his surveys he shows there is only a deviation from proportions of this dimension of only 0.003 feet! His findings show the builders used whole or half units of megalithic yards in the radii of stone circles. Many structures include extremely accurate alignments with key solar and lunar risings and settings, often using natural features like mountain peaks, notches in hills or the strategic placement of standing stones as precise sightlines. These astronomical alignments were an integral part of the design of many sites. The geometry of the non circular stone circles was not by accident or inaccuracy but was based on complex ellipse or flattened circle geometric construction.
Solar symbols are common in megalithic tombs, the role of the sun would have been important to Neolithic farmers as crops and cattle depended on it. Stones placed in a circle were sighted to show the occurrence of the summer and winter solstices. In the winter in the northern hemisphere the sun rises in the southeast and stays low in the sky, setting in the southwest. During the spring and summer these positions shift farther north along the horizon and the sun stays in the sky longer. Some tomb passages were aligned so that the rising sun of the winter solstice would shine down them. This would represent the start of the lengthening of the days and the start of the growing season being a cause for celebration.

Stonehenge
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Stonehenge's building and use was longer than that of any great English cathedral; yet we do not know what it was for, and it refuses to give up its secrets. No echoes bounce off its stones when you call out; you are surrounded by the stubborn silence of antiquity, and some power urges you to speak in hushed tones.
George Borrow felt compelled to remove his hat and make obeisance on the ground, and in Tess of the d'Urbervilles Thomas Hardy laid his heroine on the so-called Altar Stone here, in the manner of Greek tragedy, before her sacrifice to the idea of Justice. This building may have been a sanctuary, or it may have been an observatory, but whatever its purpose, it was a place of great importance to the people who began it nearly a thousand years before Tutankhamun was King of Egypt. It must have been the focus of all the most powerful beliefs of the tribes of men, women and children living in southern Britain.
My own strong conviction is that this building was a temple for worship at a period of human history when religion and astronomy were virtually the same thing.
Brian Bailey
2.1.3 Cathedrals
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The interior of the chantry chapel, Worcester Cathedral built to commemorate Prince Arthur the eldest son of Henry VII.  He die in 1502 age 16.
A structural innovation to break the limitation of the Roman builders was 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. 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 organic effect of the Gothic arch with a natural analogy.
"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".
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