Denis Mr. Villeneuve
Since non-linear language is rather central in your movie, allow me to share my reflection on it. I will do so in relation to the idea of non-linear geometry as the 'grammar of harmony'.
The following reflection is sourced from my current research and writing.
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).
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 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).
Unity of Geometry – Root Power
by Jonathan Quintin Art
in The Resonance Project facebook site at
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 (and the low ebb of the West then) between 8th. to 13th. century. (1)
"Penrose Tiling (Rhombi)" (https://commons.wikimedia.org/wiki/File:Penrose_Tiling_(Rhombi).svg#/media/File:Penrose_Tiling_(Rhombi).svg)
Geometrical patterns at the Darb-e Imam shrine
located in Isfahan, Iran. The first structures were built by Jalal al-Din Safarshah in 1453.
Such grammar of harmony is also 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.
Fibonacci sequence, proportion and curve
Fibonacci in a spiralled nautilus shell
The grammar of harmony in the Malay traditional visualization
A Fibonacci curve composited on an artwork by
Hasnul J Saidon
“Rhythm and Movement Series” (1987)
Oil on canvas
This Is another example of a seemingly non-geometrical painting that contains an underlying grammar of harmony (Fibonacci curve) as the basis of its composition.
Abdul Muthalib Musa,
"Centrifugal 10 degree" (2005),
120cm x 120cm x 8cm, lasercut mild steel with clear 2K coat.
Aliya & Farouk Khan Collection.
Muthalib deploys mathematical equations converted into geometrical forms as the basis of his
creative visualization. Here, one can discern a spiralling Fibonacci curve formed by a sequence of
The spiralling movements of planets along the trajectory of the sun (in the middle). Video still from www.djsadhu.com
The grammar of harmony between heaven and earth
A composite of the spiraling movement of planets with the S curve (two Fibonacci curves) tracing of a snail’s movement on a pavement, captured by the author.
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).
“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
Radiant pattern made by animal
An extraordinary sand sculpture with radiant geometric pattern created by a pufferfish to attract and win a mate.
Geometrical and arabesque language of Islamic visual tradition
((TPW, Juniper & Skelly: 2010, p109)
Similar 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 zikr 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.
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. (Buzan: 2001)
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'.
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).
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).
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.’
“…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: 2001, p38).
Dear Mr. Villeneuve,
I hope that your movie will help us return and arrive back to 'the point of unity'.
Kebun Jiwa Halus
7 Tingkat Permai
11700 Gelugor Penang
1. Pepin van Roojen (2004, p11) lists several early Western researchers of geometrical design from the Islamic visual tradition. Amongst them include Thomas Daniels (1749-1840) and William Daniels (1769-1837) who published representations of Islamic and Hindu architecture of India in 1808, Pablo Lozano who published surviving Arab remains in Spain in 1780, James Cavanah Murphy (1760-1814) who published “The Arabian Antiquities of Spain” in 1813, Owen James (1809-1874) and James Goury (1800-1834) who published “Alhambra” in two volumes.
1. Whyntie, Tom & Pugh, Oliver (2013), Introducing Particle Physics, London: Icon Books Ltd.
2. TPW, Juniper, Tony & Skelly, Ian (2010), Harmony – A New Way of Looking At Our World, New York: HarperCollins Publishers
3. Yau, S.T & Nadis (2010), The Shape of Inner Space, New York: Basic Books
4. Drago De Silver, ‘Cymatics, Sound And Consciousnes’ in In5D May 4, 2015.
5. Christina Sarich, ‘Why Sound Heals’, in Upliftconnect.com, Saturday October 10th.
6. Niranjan Rajah, ‘The Art of Sulaiman Esa’ in Insyirah – The Art of Sulaiman Esa From 1980 to 2000, exhibition catalogue, Petronas Art Gallery, 2001.