Harmony and Geometry  

This paper offers an introduction to the ethos and methodology of The Prince's Foundation School of Traditional Arts in terms of a holistic understanding of the universal principles that underlie the traditional arts of the civilisations which define humanity. Director of the School, Khaled Azzam explores the concept of tradition and the integration of the awareness of harmony as the means for contemporary artists and designers to seek timeless inspiration for their creative journey and work.

How does one understand Harmony and how does one seek it? Sharing some perspectives on these two questions is my hopeful purpose here. But if I may, as an architect and as Director of The Prince’s Foundation School of Traditional Arts, I also feel bound to address a third question in relation to our search for harmony – what is the role of the artist in this search?  Or to pose this question in another way, how can the artist, through a holistic engagement with the discipline of geometry, open channels for a better understanding of the harmonious order of nature of which we are an integral part?

In essence, the purpose of our lives is a simple one – it is to seek an existence that is in harmony with our true nature.  As human beings we have free will – the will to define ourselves and the will to decide whether we base that on the belief in the existence of a Divine being as the source of our lives or not.  No matter how we decide however, one thing is clear – we cannot deny the reality of our existence here on this earth, nor can we can escape from the order which defines every aspect of its existence in a harmonious whole.  This is the Natural Order of Being which touches every aspect of our lives – physical, mental and spiritual.  Every day we all witness the majesty of the rising and setting sun; we are all moved by the gentle waxing and waning of the moon and from time immemorial we have all structured our lives according to the cycle of the four seasons.  That a harmony and an order exists, one which binds all creation together we cannot deny, since as human beings our instinct is to seek harmony – harmony in our relationships with others, harmony with our environments, and above all a harmony in ourselves which translates into the melting of the individual ego with the collective consciousness of a higher reality – a unity which holds all existence in a harmonious whole.

To seek harmony means to journey inwards and outwards.  To connect harmoniously with other people, to transcend historical and geographical differences, to live in respectful harmony with our environment – these are aspects of the outward journey on which the health and survival of humanity and our planet depend.  Yet the outward journey is an extension of an inner one, which allows us to live well within ourselves and to achieve a balanced fulfilment in the mental and spiritual aspects of our lives.

Traditional arts represent physical and spiritual bridges between these inner and outer dimensions of our lives; between the material manifestation of our lives in this world and the archetypal realm of the Divine.  Traditional arts engage us on every level of our existence – the heavenly, the earthly and the realm of human consciousness, bringing them together in our hearts.  The language of the traditional arts is the language of symbolism that speaks directly to the heart.  Of this symbolic language the expression through geometry is the most direct in linking the sacred essence of our being and its physical manifestation.

The Teaching of Geometry at the Prince’s Foundation School of Traditional Arts

In Plato’s Academy, geometry was one of the Seven Liberal Arts considered vital to the education of a student. Even after Plato, the educational importance of geometry continued to be upheld by other traditions as seen in the Rasail of Ikhwan elSafa, a group of philosophers who were instrumental in transferring Platonic thought to the Islamic world and from there to eleventh century Europe:

Know that the study of physical geometry leads to skill in all practical arts while the study of intelligible geometry leads to skill in the intellectual arts because this science is one of the gates through which we move to the knowledge of the essence of the soul and that is the root of knowledge.[1]

Today, The Prince’s Foundation School of Traditional Arts carries on this tradition and teaches geometry not simply as an objective language which informs the traditional arts but also and essentially, as a sacred language which addresses the many levels of our common origin and core being.

It is through practical application and contemplative insight that students learn and see for themselves how the patterns and forms of the traditional arts are inspired by and reflect the order of the natural world around us.  They also discover that it is geometry that provides the essential link between the traditional arts and the underlying universal creative principles of this natural order; a harmonious order which has inspired artists throughout time to express Truth through the language of Beauty.

At the School of Traditional Arts, Geometry is not just, as many would have it, an artistic style, or a way of making harmonious patterns (although of course it is that too).  It is a discipline that exposes and unfolds the relationship between unity and multiplicity, between the heavenly, the earthly and human consciousness, between our inner nature and Divine creation.  Geometry is taught and learned both as an objective tool of measure but also as “Measure,” the ordering of time and space, manifested in the order of nature that reflects the supreme creative principle.

The understanding of geometry as “Earth measure” was introduced by Prof. Keith Critchlow (founder of the V.I.T.A programme at the School) as the basis of the teaching of Geometry at the Prince’s School through Plato’s definition of geometry.  It is based on the realisation that geometry is the objective expression of the language of creation and that its study leads to the understanding of this order of creation in time and space.  Throughout the history of the School this discipline of geometry has been taught and implemented both as a tool of “measure” but also as an understanding of “Measure” – the understanding of Order in time and space.

The statement of how we perceive and teach geometry as the “Measure” of order in time and space needs to be investigated a bit further to understand it in its fullest sense.  When we draw geometry, we are performing a form of primordial ritual – a process which not only engages every level of our being but which also aligns these different levels to the creative pulse or rhythm of the natural order of being. In a way then, indeed at its profoundest level, we are using the process of drawing geometry to tune in to this natural harmony and find our way to our source and the origin of all creation.  The aim of drawing geometry should therefore be more than the exercise of discovering and constructing geometric patterns; it should extend to engaging with and revealing hidden relationships that explain the order behind our physical world.  When we draw geometry, with true consciousness, we are taking a journey that unveils the layers of physical manifestation and leads us to our metaphysical origin, enabling us to understand it beyond just a physical expression of pattern and symmetries.  We should not be distracted by geometry’s physical patterns, which are so beautiful and engaging in themselves.  Rather, we must aim to perceive this discipline as an expression of a constantly living, moving or breathing order of relationships that harmoniously interact under the surface of all that we see and experience.

The forms that we see on the physical level are simply special moments of “Order in time and space” that manifest the alignment of the multitude layers of grids, networks, symmetries and true forms of this harmonious natural order.  It is the alignment of this order in these special moments that brings through to the surface of our world elements we recognise as beautiful – a flower, a snowflake or a geometric pattern.  This order is the sacred relationship between Truth and Beauty.

It is the Divine order which lies beneath the surface of our physical experience which holds our existence together in a harmonious manner. We see and experience its manifestation on a daily basis but we do not directly experience or are constantly aware of the underlying unity that is at the source of the world of multiplicity and variety in which we live. This is the dilemma of our lives as we also fail to recognise that this unity is also the source of our creation and that we are an inherent part of this order of nature. Thus, geometry should be seen and used as a discipline which explains and reflects the subtle layers of our human nature and how it unfolds from and returns to its source.

Students at The Prince’s School of Traditional Arts are encouraged to practise geometry as a means to understand the Divine creative principle and its manifestation in the order of nature.  They develop patterns of great beauty in many art forms: in ceramics; carved wood, stone or plaster; in stained glass; parquetry; painting and illumination.  Through this process of craftsmanship they realise that practice in the traditional arts is an essential support for the contemplation of a higher state of being.  Our students realise, through activity rather than mere observation, that the subtle patterns and forms they interact with transcend the purely decorative realm; they are earthly manifestations of heavenly archetypes which embody a more profound order of beauty.

The Quantitative and Qualitative Nature of Geometry

In its nature, geometry is both quantitative and qualitative. It encapsulates real, physical manifestation and at the same time symbolises the metaphysical. Its quantitative properties spring from the term’s very roots.  Both the Latin “geometria”and the Greek “geometrein” mean “the measure of the earth.” The ancient Egyptians also used geometry in this literal sense to measure and reset boundaries of agricultural plots once the Nile’s annual flooding had retreated.  This quantitative character also regulates the proportion, form and construction of the arts and architecture. Its qualitative nature extends our consciousness beyond the physical manifestation of things and unfolds the layers that lead back to the origin of physical form into the realm of archetypes. In both its aspects geometry represents an expression of the order of the universe.

Through its qualitative nature, geometry represents symbolic archetypes and expresses these heavenly realms through the three most fundamental shapes of physical form: the circle, the square and the triangle.  At the heart of geometric expression lies the circle; symbol of unity and the infinite whole, mother of all shapes and forms. The circle is the symbol of the heavenly realm. It is the undefined space in which everything is integrated into pure wholeness and from which all proportions and geometric shapes emerge. The circle is the symbol of unity that creates from within itself the realm of multiplicity. It is both beginning and end, and neither. It represents the transcendent heavenly world beyond human comprehension.

The square symbolises the expression of order in the earthly, material realm through its regular four, equal-sided form and cardinal axes, resonating in the four elements (Fire, Air,Water and Earth), in the four directions (North, South, East and West) and in the rhythm of the seasons.

The triangle is the symbol of human consciousness mediating between the heavenly and earthly realms.  It represents a proceeding forth, an abiding and a return to the source. Keith Critchlow defined its symbolism beautifully as “consciousness at its most essential, being the Knower, the Known and the act of Knowing. This is the key mystery of our human relation to Creation.”[2]

I have spoken earlier of how geometry expresses the divine creativeprinciple (unity) and its manifestation in the order of nature (multiplicity).  A profoundly tellingexample illustrates this.  The molecular structure of water is based on six-fold symmetry, so all water in all its states is dictated and formed by the principle of this symmetry.  Yet we know of no two identical snowflakes; they all look different, but still express infinite variations of their origin – the order of six-fold geometry. On the level of the macrocosm, the expression of the order behind the relationship of the movement of the planets can also be seen in the precise geometric patterns that their orbits inscribe in the cosmos.

Geometry and the Language of Symbolism

 A further insight into the qualitative and symbolic nature of geometry may be achieved through reflecting on how we perceive its inherent visual language, but also in how we try to express it through our own verbal language.  We understand geometry mainly through the direct visual language of its expression.  However, this language also expresses concepts or principles that engage with us on a philosophical or intellectual level.  We express these concepts in our oral language through such terms as pattern, symmetry and harmony or more abstract concepts such as beauty and the sacred.

Words such as pattern and symmetry are the most commonly used when we discuss geometry.  We assume that these words, as they are used today, are self-explanatory and convey the full meaning of what we are observing.  For instance, we use the word pattern to describe something we instinctively recognise as having a recognisable shape through a certain composition.  However, if we look at how the original meaning of the word was used we might get a better insight into how our ancestors related to this term through a higher level of understanding.  The term pattern derives from “patron” or the model for making something.  Patron is also related to the father and, in a way, a primordial model that was related to in the world of archetypes, and was brought into physical application through the language of geometry.  It is therefore important to see that the word used, and the relation to its origin, that is to patron, relates to that higher primordial archetype and not as we understand pattern today as simply being a series of physical relationships.

This awareness of the deviation in the terminology we use today further explains the common perception of the term pattern – which is simply seen as cosmetic or a superficial surface decoration.  Yet as we have seen, the understanding of the true meaning of the term pattern and how it was applied in the traditional arts was more than just about surface decoration.  The use of the (geometric) language of pattern was a means of expressing the heavenly realm in our worldly existence.  It should be seen as a means of remembrance in our daily lives of what is happening on the cosmic level.  It is cosmetic in the true sense of the word – to make cosmos like.

If we consider the other term we mentioned, symmetry, we find that our understanding of it today is limited to the definition that describes the balance of objects around an axis.  However, we have to extend our understanding beyond that limited analysis and perceive it as relationships that are in balance and harmony with each other – this also includes asymmetrical relationships.  If we extend this understanding into the realm of metaphysics then we perceive that the most fundamental symmetrical relationship is the relationship between the heavenly archetypes and their reflection or physical manifestation in this world. What the language of geometry expresses, on a physical and metaphysical level, is the path and symmetrical reflection between these archetypal ideals and their physical manifestation in our world.  It is the balance of these relationships that gives meaning to what we see in our World, and it is a means to the discovery of its true beauty.

The Geometry of Harmonious Architecture – The Dome as Sphere and Cube

As an architect I am aware that all form has a physical presence and a symbolic relevance.  I am also aware that finding harmony between these two realms is not only the essential responsibility of all architects, but also the biggest challenge they face in the creative experience.  If architecture is the art of ordering space (or of order in time and space), then architects need to aspire to seek their inspiration from the realm of the timeless and universal – the Divine order of creation.  The ordering of physical space then becomes an expression or reflection of a higher metaphysical order, and the focus of the architect is concerned to place the human experience in relationship to and in the presence of the Divine order.  This relationship and positioning is most eloquently represented through geometric symbolism and can be most clearly understood by considering one of the most symbolic elements of any traditional or sacred architecture – the Dome.

In terms of construction and structural stability every dome requires a square base.  This square not only provides physical solidity, but symbolically represents the stability and solidity of the Earth.  Between the square base and the hemisphere of the dome itself, a range of geometric forms (usually based on developments of the octagon or hexagon), act as transitional shapes between the cube and the hemisphere. These shapes are essential structural elements to hold the physical form of the dome; but they also represent planes of existence between the material and spiritual realms.  Finally, arching over all these realms is the hemisphere of the dome itself representing undefined space, the cosmos; the realm of the Spirit.

The sphere is a symbol of primordial form; it represents undefined space.  It is the most universal form, which inherently contains all the other forms within it which will potentially unfold to create the cycle of manifestation.

The cube is the symbol of the earth and represents the other end of the spectrum, the other pole of the cycle of creation that emerged from the undefined and undefinable space of the sphere, the Source.  The cube is defined, solid and stable and is the base or foundation of architectural form.  In the realm of practical geometry, all possible forms derive from the division of the sphere (or the circle in two-dimensional geometry) by inscribed regular figures.  These forms, therefore, all have their root in the symbol of the Source, the sphere, which symbolically contains within itself all the possibilities of creation.

If the sphere and the cube represent opposing and complementary poles in the cycle of creation, then they must correspond perfectly.  At the end of the cycle of manifestation the heavenly sphere “solidifies” or transitions into the worldly cube.  The cube represents the final actualisation of the sphere’s possibilities.  The correspondence of these symbolic forms is usually expressed by the term “squaring the circle;” and it is symbolised in rituals such as the circumambulation of the Kabbah.

The sphere and cube, by extension, can be represented by the circle and the square, which have the same symbolic value in two-dimensional geometry as the sphere and cube do in three-dimensional geometry.  Not only are the forms of the circle and the square related to heaven and earth respectively, but the instruments that are used to draw them, that is the compass and the square edge, have the same significance.  The craftsman, by using his traditional tools, participates in a ritual which is symbolic of heaven and earth coming together.  However, the true squaring of the circle can only be realised at the end of the cycle of manifestation which marks the end of time, when Heaven and Earth meet.

Conclusion

Through these reflections I hope that I have set a context for others to remember or realise that our true nature holds the consciousness of the heavenly and earthly realms and that our actions hold the path between them.  The contemplative nature that practising traditional art induces, inspires the artist’s imagination beyond the constraints of their physical context or the social and psychological pre-occupations of their time. The action we take as artists should be defined through the process of craftsmanship.  It is my belief that the dedicated practice of craftsmanship, until hand, heart and mind find the right harmony – basing our work on the creative principle of unity so that beauty and order lift our consciousness to a higher Plane – are the special roles we are privileged to have as artists.

There is also a more personal engagement to this process of the traditional arts and in particular to the discipline of geometry. This has a subtle impact but leaves a profound residue in our being.  We have to be aware that we present ourselves to this process of drawing geometry as if we are musical instruments that are gradually being tuned to the primordial harmony of our essential existence.  The resonance and revelation that occur go beyond the construction of symmetries or pattern and we carry the transformation that happens within us beyond the classroom into everything we do.

[1]Rasail of Ikhwan elSafa, An introduction to Islamic Cosmological Doctrines by S.H. Nasr

[2]Professor Keith Critchlow,  PFSTA MA teaching hand-outs.

 

Dr Khaled Omar Azzamis is the Director of The Prince’s Foundation School of Traditional Arts in London. He is an architect by training and maintains his practice through offices in Cairo and Jeddah. He has built houses, schools, mosques, offices, commercial buildings and royal residences. Dr Azzam continues to build, not only contemporary architectural projects, but also the basic structures for an integral education programme through a multi-level and multi-cultural approach. Although, the core education programme of The School is maintained in London, its studios and workshops have spread across the globe. Dr Azzam has been involved in the development of the education curriculum of these centers which include primary and secondary schools, graduate and vocational skills training programmes and educational institutions all over the world.

Photographs: The Prince’s Foundation School of Traditional Arts

Leave a Reply

avatar
  Subscribe  
Notify of