Geometry And Symbolism

Laying out anything by geometry is a symbolic re-creation of the world. Because of this, ancient traditions portray the creator as the supreme geometer of the universe. In the fourth century bce, Plato stated that Zeus is the supreme geometer, and the Greek legend of how Apollo determined the location of the omphalos at Delphi employs a form of landscape geometry. Medieval illustrations of the creation show God the Father as the grand geometrician of the universe, compasses in hand, measuring out the sacred geometry of the cosmos. This transcendent image was expressed beautifully by John Milton in his Paradise Lost, written in the mid-seventeenth century:

Then stayed the fervid wheels, and in his hand He took the golden compasses, prepared In God's eternal store, to circumscribe This Universe, and all created things. One foot he centred, and the other turned Round through the vast profundity obscure, And said, 'Thus far extend, thus far thy bounds, Be this thy just circumference, O world!'

This image was popularized by the druidic mystic William Blake in his engraving The Ancient of Days.

In ancient Europe, the divine order of the cosmos was represented geometrically by the pattern of the rectilinear grid. The grid is a powerful symbol of the underlying structure of existence, and of divine or human dominion over it. Signifying the works of the great architect of the universe, in the shape of law and order, authority and justice, the rectilinear grid is present in Celtic art. It served to depict holy figures in both the Pagan and Christian traditions. The back of an image of the horned god Cernunnos from Roqueperteuse in southern France has a grid in the form of four squares within another square. Repeating cross-patterns based on the grid were being carved on Celtic stones 600 years before the Christian religion came into being. Tesselations of T-shapes with crosses can be seen in Germany on Celtic memorials dating from the La Tene period. The lower piece of a stone image in human form, found at Steinenbronn in Baden-Württemberg and now kept in the Württembergisches Landesmuseum in Stuttgart, is carved with designs that were used again on Christian artefacts in the British Isles. A thousand years later, an evangelist in the Book of Durrow wears a cloak with a grid pattern upon it.

Celtic Scene

The crucifixion scene at the centre of the high cross of Muiredach at Monasterboice, Ireland. (Nigel Pennick)

Flayed on a gridded board, the Celtic game known as Tawlbwrdd in Wales, and Fidclieall or Bramiuinh in Ireland, was more than just a pastime, for it symbolized the land and the royal order necessary for its proper functioning according to divine laws. Because of this, one of the official emblems of the judge in ancient Wales was a Tawlbwrdd board. As the ruling principle, the rectilinear grid underlies Celtic artwork on stone crosses and manuscripts. Just as good laws and just administration of a land should be apparent only through the proper functioning of society, so the guiding grid of Celtic art is usually just an underlying principle invisible in the finished artwork.

The men who made the Celtic high crosses were the best stonemasons of their day. Their craft is evident both in the actual construction of the high crosses from several pieces of stone, fitted together in a masterly manner; and in the use of geometry in their design. Their Celtic understanding of geometry was masterful, evident in the interlace and spiral designs not only of stone crosses but also of illuminated manuscripts, metalwork and stonecarving. Here, the Christian tradition did not extirpate the earlier Pagan vision, but continued and developed it. The geometric grid that underlies a considerable amount of surviving ornament on Celtic Crosses is of one or other of two basic forms, the square or diamond. The construction of both patterns was one of the fundamental mysteries of ancient geometry. The construction of the square grid is self-evident, but the diamond pattern is more esoteric. This pattern, which has what the Celtic art researcher George Bain (The Methods of Construction, McLellan, 1951) called the 'Pictish Proportion' of is better known in the craft of masonry as the Egyptian Diamond. It is a lozenge-shaped figure composed of four 3-4-5 triangles, so that it measures eight units in length and six units wide, with a perimeter of 20 units and an area of 24 square units. Thus, the Egyptian mystery of the three holy rods of Isis, Osiris and Horus is embodied in Celtic art.

The crucifixion scene at the centre of the high cross of Muiredach at Monasterboice, Ireland. (Nigel Pennick)

When the crossmakers used key-patterns or circles and spirals, these, too, were based on underlying grids. These methods were used in mainland Europe before the Celts entered the British Isles, as attested by examples from southern France and Germany, such as the Steinenbronn image. The Egyptian Diamond itself appears on the cross at Moone. The underlying geometry of figures, too, is shown overtly in a few instances, for example on Muiredach's Cross at Monastcrboice in a panel that shows a staff-holding man between two swordsmen. One of them is pulling open the middle figure's garments in the shape of an Egyptian Diamond, to point his sword at the man's navel, while the figure made by the victim's staff and other assailant's sword is the 3-4-5 triangle. Several other martial arts designs on Irish crosses express their underlying sacred geometry through the position of weapons.

According to ancient British Bardic teachings, beneath the outer, visible form of matter lies a subtle matrix upon which all things are based. The old Welsh word manred denotes this invisible matrix of existence; the atoms and molecules, the structures and geometrical relationships that make up physical reality. These patterns are not eternally fixed, but flow through time, expressing its essence through an almost infinite variety of forms. More than any other art form, Celtic art displays these ever-changing dynamic patterns of matired. Like nature, the geometric matrices upon which Celtic tesselations, spirals and knotwork are based are continuous. In their plurality, all of the different pattern-styles are infinitely interchangeable. They can easily fade into one another imperceptibly. The patterns of manred arc infinitely changing, but they are not meaningless. Thus, esoterically, the patterns of Celtic art are the fixed artistic representations of the ever-flowing particles of manred, for all is flux.

Celtic artists use the principle of self-similarity in conjunction with the underlying geometry of Celtic art. This is where a form at one size is included within a similar form on a larger scale. This principle, recognized in Europe over 3,000 years ago by the people of the Hallstatt culture, was re-affirmcd by Benoit Mandelbrot in 1980 when he discovered fractal mathematics. Self-similarity is the innate quality of an integral structure that manifests itself as repeating patterns from the smallest level to the largest. Thus, the smallest part of existence, the

According to ancient British Bardic teachings, beneath the outer, visible form of matter lies a subtle matrix upon which all things are based.

Nevern Cross

Opposite: Varieties of pattern on Celtic Crosses. Top row, left to right: panel from cross at Llantwit Major, South Glamorgan, Wales; Muiredach's Cross, Monasterboice, Louth, Ireland; Littleton Drew, Wiltshire, England. Second row: Llantwit Major; Nevern, Dyfed; Bath Abbey, Bath, Avon, England.

Third row: Monasterboice. Fourth row: Inchbrayock, Tayside, Scotland; St Just-in-Penwith, Cornwall; (above) Maughold, Isle of Man; (below) Mawgan-in-Pyder, Cornwall.

microcosm, is linked to the largest, the macrocosm. This link is not a crude reflection, but a more subtle, ordered repetition through the middle ground that lies between the small and the large. Self-similarity means that a structure that is present at one level is repeated on both higher and lower levels. Thus, the overall pattern of a Celtic artefact may be repeated again in the details of the ornament upon it. Just as there is no place for a void middle ground in nature, so in Celtic art there are no empty spaces, just as there are no blank spaces in the cosmos. Structure is present at every point, with each small part simultaneously reflecting the essential structure of the whole. Thus, all is inseparable. This essential oneness has been the guiding principle of Celtic art from its emergence 2,700 years ago until the present day. It is the leitmotif of the Celtic Cross.

Self-similarity is apparent throughout Celtic art. The magnificent bull-headed tore found at Trichtingen in Germany is a fine example of how the principle of self-similarity operates. Each of the bull-head terminals on the tore wears a tore around its neck, the terminals of which are tores, and so on. In Christian Ireland, the same principle was observed in the construction of shrines which were contained in identical, but larger, sacred containers, which themselves were kept in churches of the same form. In turn, the churches were designed symbolically to be images of the body of Christ and also the form of God's creation, the cosmos.

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  • steffen
    What are the mathematical proportions of the celtic cross?
    2 years ago

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