GEOMETRY AS THE GRAMMAR OF HARMONY

1   Excerpt from a paper entitled "Re-approaching Islamic Visual Tradition Through The Language of Physics - Geometry and the Grammar of Harmony 

“Geometry is a mathematical expression and description of the physical space. One way to describe space is through geometry. It’s a mathematical tool.” (Prof. Dato’ Mazlan Othman, phone interview, 12 December 2017)

7.1 Symmetry

One of the central themes of quantum physics is geometry, especially the symmetry principles.

“Many of the symmetry principles of quantum mechanics are about the features of fundamental particles.”(Stewart: 2017, p55)

           

Recent developments in physics reveals what many physicists argue as the law of nature, called supersymmetry.

                       

“Every known fundamental particle is thought to posses a supersymmetric partner, known as sparticle.”(Ibid, p 55)

In particle physics (a branch of quantum physics), symmetry takes a central position, especially if one interprets the universe as obeying a given symmetry and that the laws of physics are the same for everything in it with respect to the symmetry (Whyntie & Pugh: 2013, p141). One example of such symmetry can be observed in what is referred to as ‘the Eightfold Way’, used by Gell-Mann in 1962 to predict the existence of a strange Omega particle.

Figure 1. The Eightfold Way

(Whyntie and Pugh: 2013, p108)

Figure 2. Top view of a part of Taj Mahal, Agra (1631-1648)

The design of built-environment in Islamic visual tradition emphasizes on symmetry, echoing similar symmetry of the sub-atomic scale to the galactic scale.

(Image from al-Faruqi: 1992, p 457)

Symmetry is also embedded within the conservation laws of nature, as explicated through special and general relativity, quantum mechanics, electro-magnetism and gravity.

“It was Albert Einstein, above all others, who realizes the importance of symmetry in the law of physics. Earlier mathematicians had discovered a link between symmetry and ‘conservation laws’, which tell us that certain physical quantities such as energy or momentum can either be created nor destroyed. Einstein however, went further and made symmetry the foundation of all deep laws of nature.” (Stewart: 2017, p55)

This ‘foundation of all deep laws of nature’ is also visualized through the language of Islamic visual tradition. The visualization can be identified from the use of symmetry principle in various patterns. One example is the art of weaving, used in the making of a wall for a traditional Malay house. 

Figure 3. The wall of Rumah Tok Cu made of weaved bertam, by Abang Mustaffa Kamal bin Mat Awang (2018)

One key feature in the pattern of the wall is symmetry. Similar feature is further replicated on the floor as the sunlight penetrates the small holes in the wall. The wall and eventually the house, echo the ‘foundation of all deep laws of nature’. They also emulate the symmetry feature of fundamental particles. The echoing of such laws of nature can be read as a form of visual zikir or invocation in Islamic context. The wall, the floor, the house, the objects in the house and the surrounding natural habitat, invite the human occupants to harmonize and be in synchrony with the deep laws of nature. Symmetry in this regards, provide a pathway for a deeper and closer connection with nature and most importantly, God..

 “Einstein had a particularly deep understanding of nature’s underlying simplicities….,he founded his view of physics on a symmetry principle. The symmetry transformation of space-time must leave the laws of nature unchanged.”(Stewart: 2017, p196)

Figure 4. Research notes and drawings by Hasnul J Saidon (2019)

These notes and drawings explore the correlation between Islamic visual tradition with the language of physics. In this case, the notes and drawings explore the notion of symmetry from the perspectives of both tradition and physics. One of the key findings is that the symmetry principle commonly found in many forms of Islamic visual tradition may not anymore be interpreted as a mere decoration for aesthetic purpose, but a visualization of the symmetry transformation of space-time within the laws of nature. This initial exploration can be further pursued in future research, especially in regards to symmetry in the thematic structure of the Quran.

The terms ‘Fundamental Spacetime Geometry’ or ‘Quantum Geometry’ in quantum physics are indicative of how geometry, harmony and order are central in our understanding of both micro and macro domains of the phenomenal world.

Harmony and order, as visualized by the geometrical and arabesque language of Islamic visual tradition, are also parts of a larger ‘shared insight’ known as the ‘sacred geometry’ or ‘the grammar of harmony’ that can be observed in Nature as well as many forms of traditional visualizations around the world. It is a quantum language that visualizes the “models of the universe, both its outer aspect and its inner one” (TPW, Juniper & Skelly: 2010, p118).

“This is all pretty remarkable evidence that there is a mysterious unity about the patterns found throughout the whole of creation. From the smallest of molecules to the biggest of the planetary ‘particles’ revolving around the Sun, everything depends for its stability upon an incredibly simple, very elegant geometric patterning – the grammar of harmony” (Ibid, p118).

  

  

Figure 5. Unity of Geometry – Root Power

by Jonathan Quintin Art

in The Resonance Project facebook site at

http://www.facebook.com/video.php?=1050073191692442

The unity of geometry, especially its underlying mathematical algorithm, can be traced in many spiritual traditions around the world, including in the geometrical and arabesque language of Islamic visual tradition. It cuts across many boundaries : geographical, historical, disciplines of knowledge and many more.

In Islamic context, the geometrical language is not merely a response to the Quranic objection to representation of living creatures as popularly claimed by many writers, but more importantly is a reflection of a deeper understanding of the underlying fabric of the universe – the fundamental quantum space-time geometry. It is a ‘shared insight’ originally acquired from the Greeks by Muslims during the high ebb of Islamic Civilization between 8^th. to 13^th. century.

Figure 6. "Penrose Tiling (Rhombi)" (https://commons.wikimedia.org/wiki/File:Penrose_Tiling_(Rhombi).svg#/media/File:Penrose_Tiling_(Rhombi).svg).

Penrose’s tiling bears some resemblance to the geometrical and arabesque language

of Islamic visual tradition, including for example the geometrical patterns at the Darb-e Imam shrine in

Isfahan, Iran. Here we may find another example of how a contemporary physicist-mathematician speaks in a similar visual language with artisans of the past from the vast regions of Islamic visual tradition.

Figure 7. Geometrical patterns at the Darb-e Imam shrine

located in Isfahan, Iran. The first structures were built by Jalal al-Din Safarshah in 1453.   

(https://commons.wikimedia.org/wiki/File:Darb-i_Imam_shrine_spandrel.JPG#/media/File:Darb-i_Imam_shrine_spandrel.JPG)

7.2 Fibonacci

The grammar of harmony is embodied by Fibonacci sequence, proportion, curve and spiralling vortex that can be observed in both microscopic and macroscopic domains of the phenomenal world. The sequence starts with 1, 1, 2 to 3 to 5 to 8 to 13 to 21 and so on with each number a product of adding the preceding two. Dividing any of these numbers by one that precedes it yields 1.618, also known as phi or the ‘Golden Ratio’ in the field of mathematics (1:1.618). Fibonacci sequence, proportion, curve and spiralling vortex can also be observed in the geometrical and arabesque language of Islamic visual tradition, including in the traditional Malay carvings.

Figure 8. Fibonacci sequence, proportion and curve

(i)

(ii)

(iii)

Figure 9. The grammar of harmony in the Malay traditional visualization

(i)

A composite of two curved lines with an image of the head of a traditional Malay dagger known as hulu keris. A keris is traditionally-used as a part of silat or a form of Malay traditional martial art, during a one-to-one combat and a cultural ritual or performance. The two curved lines trace the movements of two points in space during one solat (Islamic prayer) movement by a single human subject. The movements were traced and captured by motion-capture cameras. One point was placed on the forehead of the subject while another point was placed on the tip of the subject’s middle finger. The resulting curved lines were then separated from their original positions and composited with the curvature of the keris head. They fit nicely, implying the close correlation between a body movement (in this case, a movement during a prayer) with the design of a keris. There is an underlying geometrical language that coheres or resonates harmoniously between the two, despite the seemingly distinct body movement in comparison to the organic design of the keris. As a traditional object, keris is also used during a traditional healing ceremony.

(ii)

A Fibonacci curve is composited on top of image (i), again it fits nicely. It shows that the human body movement and the hulu keris speak with similar grammar of harmony that can also be traced across both the micro and macro domains of phenomenal world.

(iii)

This image shows a composite of a Fibonacci curve with a sample of Malay traditional carving motif. Again, they fit nicely.

The presence of Fibonacci sequence, proportion, curve and spiral in many forms of Islamic visual tradition further affirms the harmonious relation between such tradition with nature. In such tradition, nature is not only understood and interpreted from a material or physical point of view, but more importantly, from an abstract or conceptual perspective that experience nature as a quantum event. Nature in this case is experienced as an inner awareness in which the observer or witness is a part of, in contrast to just an external physical phenomena separated from the observer. The boundary between the observer and the observed is dissolved into the awareness of the presence of God.    

“In reference to Malay traditional art, mimicry factor is a common phenomena since it is a part of the natural environment itself. A firm understanding of the natural environment allows traditional artists to produce art that is fine and resonates with nature itself. Such refinement of living experience is manifested through visual utterances, built environment and literature that flow with the rhythm of nature.” (Mohamed Najib Ahmad Dawa: 2003, p23. Translated by the author)

Figure 10. The grammar of harmony in the rattan weaving product by Abang Muhammad bin Mat Awang (2018)

One can clearly discern multiple Fibonacci curves in the pattern. This weaving product epitomizes ‘a firm understanding of the natural environment’ that allows traditional artist such as Abang Muhammad ‘to produce art that is fine and resonates with nature itself’. In this case, the manifestation comes in a form of a table top featuring a pattern that flows ‘with the rhythm of nature’.

It is interesting to note that both Abang Mustaffa’s and Abang Muhammad’s living habitat in Kampung Teluk Mas, Selama, Perak, is surrounded by ‘the rhythm of nature’. Their houses are located at the end of the village’s road, by a hill slope just few meters away from a clean river stream, with a hill and a rainforest as its neighbours.  Even though they didn’t know anything about ‘Fibonacci’, they are living and breathing the Fibonacci sequence, proportion, curve, spiral as well as the rhythm of the universe in their natural living habitat (Site visit and interview with them, 19 July 2018). Such form of tacit knowledge is prevalent amongst the traditional art practitioners, especially those who live and work close to nature. In their case, geometry and the grammar of harmony can be argued as ‘flowing in their blood.’

Abdul Muthalib Musa,

Figure 11.  "Centrifugal 10 degree" (2005),

120cm x 120cm x 8cm, lasercut mild steel with clear 2K coat.

Aliya & Farouk Khan Collection.

In this work, one can discern a spiralling Fibonacci curve formed by a sequence of

circular shapes.

Geometry can also be found in the surrounding environment, including in daily phenomena. All physical phenomena can be seen as a series of movement between points. All the points and movements can be further converted into mathematical formulas. One example is in the working process of Abdul Muthalib Musa.

“My working process does not begin with any mathematical formula or a vision of specific form. Maybe there is a formula, but not mathematical formula. The formula comes from daily phenomena, events and objects from my surrounding, including man-made and nature. The phenomena can be anything, from small scale to big scale like the earth rotating in certain degrees of slant and in elliptical orbit, planetary movement, the structure of a black hole and so on. Of course there are geometry and mathematical formula in my works, but I let the computer to calculate the geometrical structure and provide the mathematical formula. I can focus on the intuitive process of testing out, exploring and experiencing possibilities. Therefore, geometry can be taken as the end result of my working process, not the beginning or preliminary process. But after deploying this system of working for many years, I have to say that now I can see geometry in my surrounding, especially in human and nature.” (Abdul Muthalib Musa, interview,28 December 2017)

(i)

A composite of two palms with the two curved motion-captured lines traced from a solat movement called ruku’.

(ii)

A composite of the two curved motion-captured lines from a solat movement with a cross-section image of a nine month pregnant body,

(iii)

A composite of a Fibonacci curve with spiralling vortex, traced and motion-captured lines from a silat (traditional form of Malay martial art) movement and a cross-section image of a nine month pregnant body. The motion-captured lines from silat movements are sourced from Zaidi Azraai: 2016

(iv)

This is a motion-captured line created by tracing the movement of a point at the tip of a finger during a movement in solat (Islamic prayer) called takbiratulihram. Seen from the right view, the movement creates a curve that resembles a Fibonacci curve.

Figure 12. The grammar of harmony on a human palm, solat and silat movement, and in the profile of a 9 months old pregnant women

Figure 13. The grammar of harmony (Fibonacci) in a ‘mengadap rebab’ movement

The hand movement during a ‘mengadap rebab’ segment in a MakYong performance contains a Fibonacci curve, if traced by using motion capture technology and perceived from a certain angle. The movement corresponds to a lyric of a song that accompanies the performance. The lyric contains a phrase ‘sawa mengorak lingkaran’ (a phyton snake moving spirally’). The small micro gesture embodies the whole essence of tradition, especially in relation to mimicry of nature, as explicated by Dr. Najib Ahmad Dawa. (Norfarizah Mohd Bakhir: 2019, p186).

Figure 14. The grammar of harmony (also known as the ‘golden key’ or ‘golden proportion’) in human body

By Jonathan Quintin Art at

 http://www.facebook.com/Nassim Haramein.official/videos/427590157432248/

"Geometry for me, is human figure. Geometry is a form. Form is built by bits, digits and numbers. Neurons and cells create form. The best reference for geometry and grammar of harmony is human figure, as visualized by Leonardo Da Vinci. In a figure, there is zikir (or invocation), for example in the movement of sujud or prostrating. It means without ego or the need to brag. Instead, just humbling oneself because all creations submit to God, not boasting high in pride. This is the concept of humility that has to be experienced through zikir. Geometry, grammar of harmony and human figure for me, are zikir.” (Nasir Baharuddin, interview,15 Oktober 2017. Translated by the author)

(i)

This is a motion-captured line created by tracing the movement of a point at the tip of a finger during a movement in solat (Islamic prayer) called takbiratulihram. Seen from the front view, the line can be read as forming the Arabic letters Lam & Aliff in an upside-down position. Lam Aliff forms the utterance ‘La’, which means ‘No’. The utterance La is an essential part of the Islamic syahadah. Syahadah is the proclaimation that ‘there is No god but Allah’, the foundational essence of Islamic faith. The utterance La or No is also a form of ‘penafian’ or denial. Denial here refers to the act of detaching oneself from any identification with the illusion of forms. Such detachment is an important pre-requisite before one embarks on the spiritual journey of solat. Solat itself is a form of total submission to God which requires a total detachment from any kind of worldy affairs. Geometry, grammar of harmony and human figure as well as solat movement are zikir as explicated by Nasir in the quotation above. Zikir is an utterance or verbal invocation meant to instil remembrance of God and to experience the presence of God within.

(ii)

Here, the letter Lam Aliff in an upside-down position, can be geometrically seen as a triangular shape. Lam Aliff in an upside-down position can also be read in relation to the side or profile structure of a roof in a Malay traditional house. It also relates to the concept of ‘penafian’ or ‘denial’ in Islam. Essentially, (i) and (ii) above reveal a direct correlation between the movement of solat and the structure of a house within the context of a living habitat. In regards to tradition, this habitat relates to the Malay-Islamic traditional cosmology. It harmonizes the relationship between humans and humans, humans and nature as well as the whole universe, and humans with God. (Visual sourced from Yahya: 1995)

(iii)

Again, the letters Lam Aliff can be seen here in the motion-captured data. In this case, the lines were motion-captured and traced during an opening sequence of a silat movement. Silat is a traditional form of Malay martial art. Lam Aliff, according to Dato Haji Hashim, a sufi tacher and practitioner, can be related Lam Jalallah, in reference to the secret of human’s creation. For him, Lam Jalallah exists within a person who knows oneself and has a connection with the energy of the universe.(Zaidi Azraai: 2016, p309-314)

Figure 15. Lam Aliff in solat and silat

7.3 Unity in Diversity

The inter-connection between the grammar of harmony in geometry as visualized through built environment with the concept of Unity in Diversity is summarized eloquently by the following remark from HRH The Prince of Wales:

“Five times a day the entire world of Islam turns to face Mecca where, in the centre of the central mosque, stands the immovable cube of stone, the Kaabah. The emphasis of this act is unity. It is the single testimony upon which Islam rests: that there is no god but God, who is the God of all, or Allah. In committing to this single testimony, all Muslims are unified and this unity of all things is expressed very visually in Islamic architecture. The intention is to make it perceptible at all levels of the built environment. On every wall of every room, in every building and in while cities, the aim was to create a sense of wholeness, the unity that rests in the heart of every man and woman” (TPW, Juniper & Skelly: 2010, p123).

Since the grammar of harmony can be observed in both micro and macro-domains of life, geometry is epistemologically trans-disciplinary. In this context, trans-disciplinarity is not the result of ideological framework (post-modernism for example), but is the very essence of knowledge and wisdom themselves.

“…geometry has been studied because it has been held to be the most exquisite, perfect, paradigmatic truth available to us outside divine revelation. Studying geometry reveals, in some way, the deepest true essence of the physical world” - Piers Bursill-Hall “Why Do We Study Geometry” (Yau & Nadis: 2010, p17).

Figure 16. Space-time geometry and cell division

“The pattern of cell division in biology matches the fundamental structure of the fabric of the space in which it is dividing. It had better, or else we probably wouldn't be able to coordinate the estimated 100-200 TRILLION chemical reactions that happen per SECOND on a cellular level inside the human body!

When we are 64 cells old, all of our cells are identical and our physical existence matches the geometry of a 3D Flower of Life / 64 tetrahedrons. It is not until after 64 cells that the cells start to bifurcate and differentiate into different types of cells, dividing until we become approximately 100 trillion cells, each made of approximately100 trillion atoms working in perfect synchrony.”

 (Nassim Haramein at https://www.facebook.com/TheResonanceProject/?fref=ts)

Figure 17. The ‘golden key’ extended into infinite fractals

By Jonathan Quintin Art at

http://www.facebook.com/Nassim Haramein.official/videos/427590157432248/

7.4 Cymatics, radiant and the geometry of sound

The grammar of harmony can be observed through cymatics, which is a study and visualization of sound wave phenomena. The word ‘cymatics’ derives from the Greek ‘kyma’ meaning ‘wave’, originally coined by Hans Jenny (1904-1972). In this study, sound is made visible through vibrated thin coat of liquid or crystal particles on the surface of a plate, diaphragm or membrane. The type of mandala-like geometrical sound patterns that emerge on the plate depends on sound frequencies. Cymatics show that forms are basically cohered frequencies of waves (qwiffs or quantum wave functions).

Ancient civilizations and spiritual traditions from various parts of the world have embedded geometry based on sound frequencies or cohered waves inspired by Nature into their visual and built environment. Other than visual, sound takes an important place in many spiritual traditions as a vehicle of higher consciousness, spiritual rejuvenation and healing. One may also relate the vibrational notion of cymatics with the act of zikir that involves verbal invocations of short phrases meant to induce ‘God consciousness’. Cymatics frequencies have an effect on humans, since humans are made of over 70% water. Christina Sarich for example, proposes the following tabulation to suggest the influence of sound frequencies towards human body:

285 Hz - signals cells and tissues to heal, rejuvenating the body

396 Hz - liberates guilt and fear to make way for higher vibrating emotions

417 Hz - undo challenging situations

528 Hz - heals DNA, repair cells and awaken consciousness

639 Hz – induces feeling of love for self and other, oneness, balance

741 Hz - cleans cells and heals them, empower

852 Hz - awakens intuition

963 Hz - activates the pineal gland, and aligns the body to its perfect original state

(Christina Sarich: 2015)

Visual and built environment in ancient civilizations and spiritual traditions echo or resonate in harmony with their human occupants, Nature and the Universe – across both microcosm and macrocosm. Similar to the repeated modular units, radiant and symmetry design found in Islamic visual tradition, cymatics can be taken as a form of quantum visualization that reveal the ‘building blocks of a language based on energy, frequency and form. Sound is behind the manifestation of form and matter’ (Drago De Silver: 2015).

Figure 18. Cymatics

An example of cymatics by Hans Jenny

Cymatics feature shapes that mimic divine geometry. Patterns emerge via waves of energy, displaying the fluctuation of energetic field. Certain sounds frequencies (patterns) can change the brain waves and be used for healing of the body. In this regards, Dr. John Beaulieu explains:

“The fundamental principle of Energy Medicine is that an underlying energy field generates physical, emotional, and mental behaviours or symptoms. If we change the energy field, the physical, emotional, and mental behaviours will also change” (Christina Sarich: 2015).

In compliment, Dr. Robert Friedman posits:

“The deeper I looked, the more deeply I discovered this incredible and ubiquitous Code to be embedded throughout the structure and function of the body…it only followed that the more one could harmonize with this grand principle, the more efficient and effortless life could be” (Ibid. See also Zen Gardner, at ZenGardner.com and  http://www.bibliotecapleyades.net/ciencia/ciencia_cymatics02.htm).

Figure 19. Cross-section of DNA molecule

Souced from a video ‘Unity of Geometry – Root Power’ by Jonathan Quintin Art

in The Resonance Project facebook site at

http://www.facebook.com/video.php?=1050073191692442)

Figure 20. DNA

A top view of a DNA showing ten points on its outer rim which allow

two five-pointed stars to be drawn within

(TPW, Juniper & Skelly: 2010, p117)

Figure 21. Diatomeas-Haeckel

Selections from Ernst Haeckel's 1904 “Kunstformen der Nature” (Art Forms of Nature), showing pennate (left) and centric (right) frustules of a Diatom. Diatom is a form of unicellular phytoplankton.  

(https://commons.wikimedia.org/wiki/File:Diatomeas-Haeckel.jpg#/media/File:Diatomeas-Haeckel.jpg)

Alexey Kljatov

Figure 22. Water Crystal

Originally Published on Nov 9, 2014

 (https://www.youtube.com/watch?v=tAsYtoKktqk)

“To understand water is to understand the cosmos, the marvel of nature and life itself”

Dr. Masaru Emoto, quoted from Jain 108 Mathemagics at https://www.facebook.com/jainmathemagics/?fref=ts

Figure 23. Radiant pattern made by animal

An extraordinary sand sculpture with radiant geometric pattern created by a pufferfish to attract and win a mate.

http://youtu.be/hpdlQae5wP8

Figure 24. Geometrical and arabesque language of Islamic visual tradition

((TPW, Juniper & Skelly: 2010, p109)

“It appears that nothing in nature is so small or seemingly insignificant that it does not merit a pleasing symmetry,…Furthermore, there are numerous other examples - the endlessly embellished hexagons of the snowflake, the lovely geometric spiral of the chambered nautilus, the perfect cubes found in mineral crystals. As for man, himself a remarkably symmetrical creation,..” (Shafie Mehad: 2002, p1).

7.5 Divine Unity and Infinite Wisdom

Geometry as the grammar of harmony and visualization of quantum states, shifts and returns an observer to her or his fitrah or true nature, dissolving the localised frequencies called ‘self’ to be in-synchrony with the non-local symphony of the whole. The folding and unfolding of space-time geometry across dimensions will always depart from and return back to a point of unity, of infinite singularity, the Divine Unity, or in Hagelin’s words, ‘the Single Unified Field of Infinite Wisdom.’

Figure 25. Radiant pattern in Nature

This is an example of the grammar of harmony or quantum mapping in Nature, in this case, radiant pattern of natural architecture, specifically leaf of saw palmetto plant. Nature is perceived in traditional paradigm as a mathematical expression of Divine Unity or in the language of physics, the Single Unified Field of Infinite Wisdom. Eastern forms of traditional visualizations mostly employ such patterns to return observers to fitrah (natural instinct, state and order), to be a part of the Divine Unity. (Image sourced from Buzan: 2001)

Figure 26. Tebar Layar

This is a simplified image of a 'tebar layar' or gable ends of a typical Malay house, inspired by the grammar of harmony in nature, and designed to direct wind into the house to cool the roofing space. Many have beautiful carvings and allow light into the house. The 'tumpal' structure or triangular shape relates to the Islamic cosmology, and can be taken as a form of quantum visualization. The radiant pattern can be related to 'radiant thinking'.

“…geometric expansions provide a metaphor for the law of all phenomena. In as much as space, seen as extension, is created by unfolding through the dimensions – from ‘point’ to ‘line’ then to ‘plane’ and beyond, it can be ‘folded up’ again, leading back to the point of unity (Critchlow: 1976 , p7 in Niranjan Rajah: 2010, p38).

Mohd Fadzil Othman

 Figure 27. "The Element of Surprise" (2008)

, 212cm x 243cm, screws and black threads,

Penang State Gallery Collection.

Fadzil’s work here is an excellent example of quantum visualization, deploying a complex

and tedious manual process of joining threads to create interfering, dynamic and vibrating radiant patterns.

It emulates the underlying grammar of harmony found across both the micro and macro domains

of the phenomenal world.  

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Figure 28. Grammar of Harmony, Point of Unity

a.     Five-pointed star in a flower.

b.    Dance of Venus seen from Earth, charted over its eight year cycle creating the heart-shaped set of five petals.

c.     Relative mean orbits of Mercury and Earth superimposed over each other. The Earth orbit contains a five-pointed star and the circle of Mercury’s fits exactly over the inner pentagon of the star.

d.    View under a chandelier and the main dome of Ubuddiah mosque in Kuala Kangsar

e.     Centre section of floor carpet under the main dome of Ubuddiah mosque

f.     Haji Mohd Daniyalai, Asma Al-Husna (2002), Ink Calligraphy on paper (Collection of Muzium & Galeri Tuanku Fauziah, USM)

(i,ii and iii sourced from TPW, Juniper and Skelly: 2010, pp 108, 116, 117)

Divine Unity and Infinite Wisdom are visually expressed through the underlying principles of Islamic visual tradition such as symmetry, balance, non-linearity, inter-connectivity, modular, repetition and cyclical. The intricate patterns in Islamic visual tradition share such key principles, reflecting the undercurrent of divine ‘law and order’ that bind and unite all natural phenomena.

“Despite the baffling complexity of the events that go on in our universe, there is an undercurrent of law and order into which all the hubbub fits.” (Stewart: 2017, p196)