12th century Christian geometric art

Some readers will already be aware of the Christian tradition of geometric and patterned art (see longer articles in the section Liturgy, Number, Proportion on the archive site). This was an adaptation of the patterned geometric art that we see in the pre-Christian classical period. TMC is, in a small way. The Way of Beauty class, students reproduce some of the patterns seen at the Romanesque Cappella Palatina in Sicily.The principles behind this geometric design echo the patterns and harmonies that are the basis of proportion and compositional design in traditional architecture and art (and they are surprisingly simple to learn – you do not need special artistic ability). Although all artists would benefit from this knowledge, this is not simply an artistic pursuit. It relates to the study of the traditional education called the ‘quadrivium’.

The quadrivium, four of the seven liberal arts (geometry, music, number and cosmology), is concerned with the study of cosmic order as a principle of beauty, and which is expressed mathematically. The patterns and rhythms of the liturgy of the Church reflect this order too. Christian geometric art is an abstract (in the sense of non-figurative visual representation) manifestation of Christian number symbolism. This aspect of traditional education came from the ancients too. Pope Benedict XVI, again in one of his weekly papal addresses, described how St Boethius worked to bring this aspect of Greco-Roman culture into a Christian form of education, by writing manuals on each of these disciplines. In the medieval university, he seven liberal arts were the basis of qualification of the Bachelor of Arts (the Trivium), the Master of Arts (for the Quadrivium) and these then were the preparation for further study in the higher subjects of Theology or Philosophy, for which one could receive a Doctorate.

Geometry is not now, to my knowledge, a living tradition as a Christian art form. By the time of the Enlightenment the acceptance of number symbolism had fallen away and it died out.

I recently taught an undergraduate class about Islamic geometric patterned art at Thomas More College. This tradition, an example from a tile at the the Alhambra in Granada is shown right, is derived from the Byzantine patterned art of the lands they conquered (and of course the classical mosaics and other patterned art that preceded them). Because Islam was forbidden completely, in its strictest interpretation, from any figurative art, their focus on abstract art forms was intensified. Islamic craftsmen took what they had taken from the Byzantine craftsmen and developed it into something more complex than had previously existed.

The question I asked that first class was: can we safely take it back?  That is, in order to reestablish this as a Christian form, can we look to the Islamic art form and re-form it into Christian tradition again?

I was pleased that in response my class said, yes. (Teachers are always pleased when their class agrees with them!) They understood further that while we can adopt some of the forms, we don’t have to adopt the Islamic numerical symbolism as well. Islamic number symbolism is similar, but crucially different from the Christian symbolism. (The number three and the Trinity come to mind immediately.) That is, it is always important to make sure that due proportion is used – that the number symbolism contained within the symmetry of the pattern is appropriate to the place where it is used, when understood in Christian terms.

For the final project of the semester I suggested to them that they consider how to incorporate some of the patterns they are learning to draw one that could be used in the floor of the sanctuary of a church. (The class in the Way of Beauty summer program will be doing something similar.)

The day after introducing the topic to the TMC students, I stumbled across this website, which is a great resource of images of mosaics and opus sectile work. Its gallery ranges from the floors in the offices of a Victorian architect in Norwich to Roman villas and the great churches of the world. The section on Sicilian mosaics has 80 photographs of the Palatine Chapel in Palermo. This revealed that precisely what my class was proposing had been done by the Norman king, Roger II of Sicily when he built his private chapel in the 12th century. He employed not only Christian mosaicists and Cosmati pavement specialists who produced geometric art in the Christian tradition, but also Islamic craftsmen.  He instructed them to produce patterns obviously derived from those that can be seen in mosques and adapted for Christian use.  This a model that would be well worth further study and I hope any architects reading this might consider commissioning something like this. I have included some photographs below of the chapel, and one pattern from a mosque for comparison; and you can see more at

Below are examples of opus sectile (cut work) from the Palatina)

Geometric Tile Patterns in Andalusia

  Here are some photographs of decorative tiles that I took on my trip to Andalusia. These designs are commonplace in Spanish towns here and will be seen on both old and new buildings. They are obviously derived from those of the Islamic Moors who ruled this part of southern Spain for nearly 800 years. The last Moors were defeated and surrendered the Alhambra - the palace in Granada - in 1492.  These were taken in two villages Alcaucin and Canillas de Aceituno about 20 miles inland from Velez-Malaga on the Costa del Sol.

The photo above is of the public drinking fountain in Alcaucin. What I found delightful about these villages is the effort made to decorate details of the exterior. For example, you will see here some steps, small interior parts of doorways. I have included some street scenes of the villages to give you a sense of the villages, and not all of them have geometric patterns.





Islamic Tile Patterns Point the Way to Modern Nobel Winning Mathematicians and Chemists

I have written before, here, how the study of sacred geometry and harmony and proportion can point the way to scientists, when describing the discovery of quarks in the early 1960s. Here is another example and the end of the story is this year's Nobel Prize for Chemistry. Anyone who has studied geometry will know that only threefold and fourfold symettrical patterns are preferred when covering large areas because patterns based on this symmetry will fit together exactly without creating gaps. The Islamic craftsmen of, for example, 13th century Turkey, overcame this difficulty by developing a system of longer range order and using irregular shapes filling the gaps, but creating the sense of a regular order. This way they could create geometric patterns based upon, for example, fivefold symmetry.

Move forward to the 1970s and Cambridge mathematician Roger Penfold developed the same idea (independently and unaware of his Islamic predecessors). He called his irregularly shaped insertions 'darts'. About 20 years later the similarity of Penfold's darts to the Islamic tiled patterns was noticed.

These abstract patterns could be extended into three dimensional structures and in the early 1990s microstructure of materials were observed by an Isreali chemist that included, in essence, three-dimensional darts. Here were real materials whose microstructures had been anticipated by the Islamic artists of the 13th century. The discovery of  Daniel Schechtman went against the established ideas of what a crystal was his work was not accepted initially. The lab that he was working for asked him to leave. Finally, his work has been recognised now, 20 years later, as ground breaking and he has been awarded the Nobel prize.

The study of traditional proportion and harmony is the study of the natural patterns and rhythms of the cosmos. For the ancients the starting point was those aspects for which there was a consensus of beauty, for example, in enumerating musical harmony. What is so interesting to me is that the patterns seen in a macro scale are observed in atomic and even sub-atomic scale by scientist.

It reinforces the point I made in my first article. That a traditional education in beauty will enhance the creative process. Even in scientific research, ideas are not generated by reason. The process of scientific discovery comes through the observation of nature and then 'seeing' solutions to problems. These solutions just occur as ideas or hunches. The scientist sees the symmetry and order in the situation and can intuit what is missing or what completes the picture, so to speak. Reason is used to test these hypotheses and to confirm or reject them. Of course, this also means that any discipline in which creativity is an asset would benefit from such and education...which is just about every situation in life.

There is another interesting aspect to this tale. It emphasises how the scientist, the mathematician and the artist are all seeking to represent the natural order in different ways, but in their different approaches arriving at the same solution.  The scientist is describing mathematically the order that he observes in nature; the mathematician seeks to portray perfect pattern and order in the abstract world of mathematics that conforms to logic and reason; and the geometer seeks to reveal the beauty of the idealised natural order. They are all approaching the same underlying truth and revealing it in different ways.