Pattern, Geometry, and Abstract Christian Art

"Geometric pattern is the abstract art of Christianity."

We tend to think of abstract as something that has come about only within the last one hundred years. But liturgical artists have had their own form of abstract art for nearly two thousand years. Geometric pattern is the abstract art of Christianity.

God made all of creation, visible and invisible, to teach us about Himself. When we perceive the order and pattern that is inherent in creation, the numbers that underlie all of creation, we see the thumbprint of God.

Geometrical forms, built up from mathematical (numerical) forms, are a symbolic expression of Christian Truth. They represent the thoughts of God.

In the Christian world, numbers have both a quantitative meaning and a qualitative meaning. They tell us the amount of some thing (quantity) but they also tell us about the thing itself. (qualitative.)

A carton of a dozen eggs, for example, holds a quantity of 12 eggs. But the number 12 also has a symbolic meaning. it may represent the 12 tribes of Israel, the 12 apostles, 12 signs of the zodiac, or 12 months of the year. Which of these symbols the number represents will depend on the context in which it is used.

In the context of a work of sacred art, depending on the other elements of the work, 12 eggs could represent the New Covenant, a new Church emerging from the "sealed tomb" of the old Law, resting on the foundation of the twelve apostles.

But this qualitative and quantitative language of numbers can also be used to construct abstract, i.e. non-representational, patterns that can lead us to contemplate heavenly things. Medieval manuscript paintings often have a geometric pattern serving as the background as a symbol of the order of heaven.

The work above is a design for a church floor, completed as part of the Masters of Sacred arts program at Pontifex University. It incorporates a specific type of scrolling pattern known as a guilloche. This is a meditation on Christ in the form of a geometric pattern.

Down the middle axis of the design are three shapes. The first shape at the top contains the symbol for "alpha," the first letter of the Greek Alphabet, The bottom shape holds the symbol for "omega," the last letter. Alpha and omega, the first and the last, the beginning and the end, come together in the middle in a "Christogram" a symbol representing Christ. Jesus Christ is the alpha and the omega, the first and the last, the beginning and the end. Christ is the mediator between man and God. In the ancient world, the number "2" was a mediator between the numbers 1 and 3. The number "2" then, represented a mediation between two extremes, heaven and earth, divine and human, God and man. We might also say then that Jesus, the second person of the Holy Trinity, mediates between God the Father and God the Holy Spirit.

Flowing around these central shapes is a bough of laurel leaves in a guilloche pattern. Laurel leaves are a symbol of victory, Christ is victorious over sin and death. The laurel bough weaves around eight medallions which contain another type of Christogram, in this case a cross and the letters INRI. They serve to remind us that Christ obtained His victory through death on a cross, a death at which He was proclaimed Jesus of Nazareth, King of the Jews.

And "eight" medallions also have a hidden meaning. Eight is the number of the victorious resurrected Christ and a redeemed world. Eight is the sum of "7" the number of totality and completion, and the number "1," representing the singularity of God. The number "8" is used in baptismal fonts as a symbol of a new life brought from darkness  into light.

The victorious Christ is the eight day, heralding a new birth and a new creation. He brings the world from darkness into light.

There is no reason we cannot imbue the design of our churches with such geometric patterns and symbols that hold a rich symbolic language revealing the truths of the invisible world that are hidden within the visible. All it takes is the knowledge, and the will.

this article originally appeared at www.DeaconLawrence.org

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Pontifex University is an online university offering a Master’s Degree in Sacred Arts. For more information visit the website at www.pontifex.university

Lawrence Klimecki is a deacon in the Diocese of Sacramento. He is a public speaker, writer, and artist, reflecting on the intersection of art and faith and the spiritual “hero’s journey” that is part of every person’s life. He maintains a blog at www.DeaconLawrence.org 

Rose Windows and Sacred Geometry - the Ancient Mystical Path to God

I have just been creating a new online course on the mathematics of beauty and as part of this, I wanted to show how to represent the symbolic meaning of number in the context of the liturgy in such a way that it might deepen participation. The obvious way to do this is to have a pattern with the symmetry of the number. This will require also some catechesis of the congregations so that they are reminded of what it is pointing to every time they see it. It can be part of the decoration of the church, incidental, as it were, to the structure:

Or it can be more intimately and obviously bound with the form of the church, as it is in the medieval rose window. Here is a window dating from about 1500 in the cathedral at Amiens in France:

It is important to awaken our innate sense of the symbolism of the natural world and all that is created as this stimulates also our natural sense of the divine. The awe and wonder that we feel when we contemplate the world around us is, for all that it seems profound, little better than a shallow emotion generated artificially by a drug if we stop there and do not allow it to draw us closer to its source - God. This is its true consummation, we are made to see the glory of God in his creation and it will be to his greater glory and our greater joy if we allow the beauty of the world to take us to what it points to.

We can consider this to be a form of relation. Creation is in relation to its Creator. By virtue of its existence, it is relational, for it is connected to its Creator by the mark of divine beauty He has impressed upon it. This interconnectivity of all that exists, therefore, is not a mental construct thrust upon the cosmos artificially by mankind. Rather it is a property of the object that we see. All being is relational by nature and is patterned lattice that has the Creator at its heart.

As created beings ourselves, we participate in this dynamic too, seeing a natural connection between ourselves and the rest of the cosmos. All of mankind is endowed by the Creator with an intellect and the capacity to observe the world around us in such as way that it can derive from it an understanding of our place within it, and ultimately this points to and sheds light on our relationship with the Creator.

Part of our task as people seeking to evangelize the world is to re-awaken the final link in the chain of connection between creation and Creator by re-establishing a culture that is rooted in this principle of interconnectivity through its beauty. This process of evangelization of the culture begins in the church in which all that we perceive and all that we do participates in this language of symbol and is there to connect us to God.

Coming back to the symbolism of number, it is widely accepted, even in the secular culture, that the natural world is connected to mathematics. The connection is so strong that few, if any, doubt, for example, the power of mathematics to help the natural scientist to describe the processes of the natural world. However, I think we should stop for a moment and think about this - it need not automatically be the case. Once I realised this it became a source of great wonder to me that the abstract world of mathematics is so intimately bound in its structure with the behaviour of the natural world.

This had to be noticed before the connection could be made, and it is why figures such as Boethius commented, in his De Institutione Arithmetica, (Bk1, Ch.2) that 'number was the principal exemplar in the in the mind of the Creator' and from this is derived the pattern of its existence that the scientist observes.

The natural scientist of today is generally less aware of the symbolism that runs through both nature and mathematics. The medieval thinker would not have rejected method of today's natural scientists I suggest but would have added to his description of the natural world the symbolic language of number, which is largely forgotten today. If scientists were to do this today, I suggest that it would inform his work in such as way that technology would both enhance his work as a conventional scientist and allow its applications to become more in harmony with the flourishing of man. Rather than being in conflict with today's scientist, the proponent of sacred number has something that can help him to be a better scientist.

Geometry is a way in which number can be expressed in space through matter, and so this is why geometric patterned art ought to be right at the heart of the evangelization of the culture and any sacred art. It is also why the study of the symbolic meaning of number in conjunction with the study of geometry is so important in a Catholic education today. What I propose is a study of geometry that is so much deeper, and more exciting than the dull task of memorizing Euclidian proofs (which sadly seems to be the way it is taught in Great Books schools today). This is about connecting the pattern of the universe to the creative impulse of man so that the beauty of the culture can direct us to God even more powerfully than the most beautiful sunset you have ever seen.

And so this is why I would like to see the rebirth of the Rose Window, in our new churches. This is more than simple decoration, if done well it has the power to stimulate in us a profound sense of our place in the world and in relation to God. Always assuming that even if we got as far as seeing them in churches, the catechesis available would be minimal or poor (we're Catholics!) these would need to be designed in such a way that the symbolism was obvious. There is nothing stopping words and scriptural quotes being added, just as we must in figurative art, in order to clarify, for example.

Here I give some examples of such windows with, three, four, five and sevenfold symmetry. I have obtained these photographs from a great resource that I discovered online called therosewindow.com, run by Painton Cowen, who kindly gave us permission to reproduce his photographs here. This site has photos of windows based upon numbers that you don't normally associate with Christian symbolism - 11 and 13 for example. I would want to consider carefully the basis of these before replicating them today. We must learn from the past, but we must be aware also that not everything that it tells us is true!

Here are some images.

Three, 15th century, Barrien, France:

Four and three in a quincunx arrangement of five objects, 15th century, Agen, France

Five, Exeter, England, 13/14th century:

Seven, Beaulieu en Rouergue, France, possibly 14th century:

If you want to know more about the symbolism of number and the philosophy behind it, I suggest that you either read The Way of Beauty or take the course, the Mathematics of Beauty which will soon be offered at www.Pontifex.University, Master's in Sacred Arts program.

In the meantime...believe it or not, lucky thirteen! Larino Duomo, Italy,

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, www.thejoyofshards.co.uk 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 12^th 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 joyofshards.co.uk.

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

Astonishing Geometric Patterned Art by Russian Icon Painters

Recently I featured carved icons by Russian Rashid and Inessa Azbuhanov. Also on their website, here, there is a section entitled Avante Garde 21st Century Art (I am assuming that the Google translator is accurate here). I imagine that the artists describe them in this way because they do not think of them as works of sacred art at all. I think that these are worth looking at in the context of sacred art. What I find on their site are some geometric patterns that I would happily see as the basis for tiled floors, for example, in churches. The artists have given each one a title which assigns an allegorical meaning to them. I don't understand the basis of these and without wishing to undermine any significance that they see in them, we are entitled to see them in the light of traditional numerical symbolism and use them in the light of this. So any shapes with octagonal symmetry, for example, could be used in a sanctuary floor given the symbolism of Christ as the 'eighth day' of Creation. In some ways they remind me of traditional Romanesque, western patterns, but there are also elements that I have not seen elsewhere before.

Christian Geometric Art in an Arabic Gospel

Last week I featured the first work produced by my students at Thomas More College of Liberal Arts in their sacred geometry class. They did eight sided figures based upon an Islamic design. Just in case anyone has been wondering if this is an over adventurous pushing back the envelope of what appropriate in the context of sacred illumination, I thought that it would be interesting to show these images that I discovered on the British Library website (which is wonderful resource for images of ancient manuscripts). These are from a 14th century Palestinian gospel of St Luke. I have no additional information as to why this particular design was chosen. All I can say is that I would have been very happy to see this in my bible because of the four-fold and eight-fold symmetry that exists in this. Four symbolises the world and four gospels were chosen by the Church so that the Word was carried to the four corners of the world by the four evangelists, each evangelists is symbolised by the four figures described as sitting around the throne of Christ in the book of the Apocalypse.

Regular readers will be familiar also with the symbolism of eight: it corresponds to the eighth day of Creation that ushers in the new covenant: the incarnation, death, resurrection of Christ. Sunday is the eighth day of the week. In the basic repeat unit, which is repeated like floor tiles, we have, geometrically portrayed, four versions of the Word in the gospels (four small octagons) spinning out of one large one, the Creator himself, enthroned and in glory. Pictorially, this would be Christ in Majesty surrounded by the Angel, the Lion, the Ox, and the Eagle. When you have four of the repeat units combined, there is long-range order which has a fourfold symmetry in which four large octagons surround the central, which is the broad design of this 'carpet page'. There is a beautiful harmony to this, and it seems to me to reinforce the superabundant truth of Eucharist: that through the propagation of his gospel in a literary description of his life, Christ in Majesty is really made present in the world in the liturgy of His Holy Church.

I repeat, this is my personal reaction to this design, a meditation upon what I am seeing, so I could be reading more into this than the artist intended. However, as an artist, I would happily reproduce this design with the intention of incorporating this symbolism into my work. There is such a beautiful harmony to it, it seems.

Images: below the images of the 14th century gospel, I have given the Thomas More College, Christ in Majesty to illustrate the point, painted by myself.

Some Geometric Art from Thomas More College Students

Here are some examples of geometric art produced by students from Thomas More College of Liberal Arts. They are their first projects for my Way of Beauty class. They were asked to produce an octagonal tile pattern that was based on a traditional Islamic design. I asked them to design the corners and the border and decide on the colour scheme. I encouraged them to use as few colours as possible, using only what was required to give contrast and allow clarity of design. I also insisted on the shape being described by a continuous piece of tape which wove an over under pattern. The colouring was deliberately muted and downplayed as this allows for less clashes of colour. On the whole, I prefer to use natural, earth colours for the same reason. These are difficult to get in the sort of coloured pencil sets that most of our students have, which tend to have very bright, artificial looking colours. If they used these alone then the result would look something like a bad record cover from the 1960s. This might have sold music in 1967, but it won't cut it in traditional design (if only our liturgy musician realised that the same is true for the style of folk music of period)...anyway, back to these design. To try to eliminate the impression of psychedelic kitsch, they carefully built up the colour by overlaying it with lightly shaded layers of earth brown and grey pencil. Students are Isabelle Anderson, Theresa Scott and Katherine Blicharz. In assessing these, remember that this is the very first project that I set them. They are intended as exercise before designing a church floor.

Three Examples of the Geometric Pattern, the Quincunx, in England

Henry III is inspired by Roman patterns to create a two church floors Continuing a theme of traditional floor patterns from a few weeks ago, here are three variations on the quincunx. The quincunx is the name given to an arrangement of five shapes, (usually the same, for example five circles, but not necessarily so) in which four sit around one centrally placed. The first is Roman and is at an ancient site at Hurcott in Somerset. The second and third were both created under the patronage of Henry III during the 13th century. The second is the Westminster Pavement, which is reasonably well known. The third is at Canterbury Cathedral and until I read about it in an article in the Glastonbury Review, here, I was not aware that it existed. This article suggests that Henry, who was patron of two geometric floors, was inspired by seeing Roman patterns. He is shown top left processing with a controversial relic, the precious blood of Christ. All of this is detailed in the Review article.

Those who wish to know more about the quincunx and its place in the Christian tradition of geometric art can read about it here.

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.

Russian Geometric Patterns from the 19th Century

Last year I featured some wall paintings of the Trinity at the Russian Orthodox Cathedral of Christ the Saviour, in Moscow, left. This is a modern reconstruction of a 19^th century church and all the art from that time has been faithfully reproduced too (I hadn’t appreciated this until an NLM reader pointed it out to me!). As well as some striking naturalistic and iconographic art, there is some beautiful geometric and patterned art as well which I show here. This reminds me in some ways of the decoration one might see in an English 19^th century neo-gothic church designed by Pugin. Anyway, I hope that this will inspire those who are responsible for the interior decoration of our churches to consider geometric designs as an option.

Thomas More College Students' Art Work - Geometry

Student work from the Guild of St Luke We have just finished the academic year here at Thomas More College. As part of the graduation ceremonies we had an exhibition of the student art work done by the college's Guild of St Luke. I will show parts of this over the next couple of weeks. Today we see geometric patterned art done by freshmen at the college. In the spring semester the students study Euclidean geometry as part of their introduction to logic. The way that Euclid is taught generally in liberal art schools is that students are expected to memorise and on demand be able to demonstrate proofs to the professor and class in the classroom and then be able to respond to questions and discuss the proof. We do this at Thomas More College too. In addition, however, as a deepening of the learning experience we create some of the Euclidean constructions, using the traditional toools of a pair of compasses and a straight edge. From this foundation the students go on to study geometric patterned art. We look at Islamic patterns and then how Christians have incorporated these designs into churches in the past. For example at the 12th century Capella Palatine in Sicily. The first two examples shown below are exercises where I asked the students to create a simple Islamic tile design. They were required to present it as formed by strips passing over and under each other is a loose weave. I asked them to work out for themselves how a border could be incorporated into what they were doing. Two examples are shown below.

Then I set the students a project to create a design for either the floor of nave or sanctuary in a simple basilica style church. They had to use either the quincunx (four circles coming out of one) or the guilloche - a series of interconnected circles. The infill could be drawn from a series of Romanesque traditional designs that I presented to them. In accordance with the gothic style of pavement design they were encourage to piece it together in orthogonal boxes. The results are very impressive. After one semester they are producing church floor designs that would grace any church in the country and which are more involved than most churches built in the last hundred years at least. The students are Jacqueline Del Curto, Elizabeth Rochon, Devin King, Kristina Landry, Bridget Skidd, and Catherine Mazerella. Well done!