Ever since I visited some of the historic marvels in 2018 – the Candi Borobudur (9th century CE) in Java Indonesia, the Mahabodhi Temple (3rd century BCE – 6th century CE) in Bodhgaya Bihar India and the Taj Mahal (17th century CE) in Agra India – I became interested to write a piece on symmetry. The interest to write was also exacerbated by the tourist guides mentioning the symmetry of these structures again and again. As I went deep into writing, it became obvious that symmetry is indeed the symbol of beauty, peace, stability and harmony. No wonder ancient religious and burial monuments from the Egyptian Pyramids (3rd millennia BCE) and Mayan Temples (3rd millennia BCE) to modern places of worship – all show amazing styles and diversity of symmetry. In these monuments, symmetry was seen in human aspirational context – as abodes of peace in heaven or paradise. Let us attempt to understand all these wonderful aspects of symmetry – but realizing the fact that asymmetry is also the reality of life, Nature and society. I have included an image of Borobudur I shot while there.
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What is symmetry? It is simply the exact replication of things about an axis – a mirror image, and the simplest example is ourselves – the humans. We are axi-symmetric about our vertical spinal axis that runs through our nose – with the left balancing the right. Similar is the case with all the vertebrates – and the balance or stability is ensured by symmetry. This symmetry is also known as reflectional; others include rotational (like a circle, a wheel, a sphere, a flower, a square, an equilateral triangle, etc.) and translational (like brick layers). Invertebrates can be both symmetric and asymmetric – indicating some of Nature’s wonder and mystery. Fractal analysis reveals another type of replicating self-similar shapes – e.g. the large shape being the composite mosaic of smaller but similar shapes – and Nature is abound with Fractals.
Symmetry can also be viewed from another angle – as the balance between the disturbing and the restoration forces. We have discussed this in the Linear Waves piece on the NATURE page – that a linear or symmetric wave represents the perfect balance between the disturbing force caused by a moving wind or water pressure system and the restoring gravitational force. And that the symmetry of a sinusoidal wave or its equivalent a circle – both in phase and amplitude – is a manifestation of balance and stability. And while that balance is maintained, the wave celerity transports the gained energy forward. Engineers view symmetry as an inter-active balanced system of imposed and resisting forces for the stability of a structure. All these examples of Nature and technical applications suggest that a balanced system is the best way for an entity to function, work and propagate energy in tranquility.
But as also discussed in the Ocean Waves and other pieces in WIDECANVAS, the survival of a linear or symmetric wave is only momentary, if any. Because any moving fluid – displaying the most vivid sign of dynamic balance and equilibrium – immediately comes under various interaction and transformation processes of reflection, transmission, absorption and resistance with the result that it becomes quickly asymmetric – nonlinear and spectromatic. These processes are not so vivid in other elements of Nature, such as the solid – but they are there in various scales of magnitude and frequency – defining the fluidity of Nature. This fact leads us to realize that the processes of Nature, life and society are essentially asymmetric – in multiplicity and impermanence – but all heading to the aspiration to attain equilibrium or symmetry. In other words: asymmetry of processes --> symmetry and stability of entities – or that the Natural asymmetrical processes – that are not broken or collapsed – constantly aim to attain symmetry or equilibrium as an aspirational goal.
No wonder – as an indication of human aspiration – most religious architecture and monuments of every creed are depictions of heavenly peace in the tranquility of symmetry. In Buddhism this started with depicting the statue of the meditating Buddha (Gautama Buddha, 624 – 544 BCE) - The Tathagata sitting on the petals of an axi-symmetric open lotus throne. As an indication of reality and aspiration, Tibetan Sand Mandala is a show of both impermanence and axi-symmetry. Similarly, some Japanese artifacts and paintings have depictions of imperfection or impermanence together with the beauty of symmetry – saying that imperfection must strive toward the perfection in the tranquility of symmetry. Candi Borobudur located on a hill top surrounded by plains, has exact proportional symmetry both in horizontal and vertical directions – with the tapering layers from the bottom 6 square levels rising to 3 circular heights adorned with Stupas.
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The axi-symmetric Lion Capital of Mauryan Emperor Ashoka (304 – 232 BCE) shows four back-to-back lion heads – representing the Buddha standing on an inverted lotus flower with the Dharma Chakra (the Wheel of Law) on top. The inverted lotus flower took the shape of hemispherical stupas, domes, and pagodas in Buddhist architecture. The dome shape inspired many architectural shapes around the world including the door and window arches, and arched recesses. The bell-shaped Buddhist pagoda such as the spectacular Shwedagon Pagoda (6th century CE) in Yangon, Myanmar is a beautiful architectural metamorphosis of the inverted lotus flower. The inverted lotus flower on top of hemispherical domes can also be found in Moghul monuments such as the Taj Mahal, and in Indian Palaces and Hindu temples.
Why inverted lotus flower instead of an open one? The inverted lotus flower represents the Mahaparinirvana or passing away of the human Buddha – saying that the opened Buddha lotus does not exist anymore – that instead after his death, the relics are preserved by the inverted lotus in its core. And that the Buddha left his Wheel of Law (represented by tapering concentric wheels on the lotus stem with a parasol on top) to guide humans for their emancipation from the unhappiness of life to peace and tranquility. In addition, that the inverted lotus has the potential to re-open again when time comes (therefore budding lotuses often populate the periphery of the stupas/pagodas).
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Symmetry is often identified with even numbers – for example, number 2 represents 1 on each side around an axis running in-between them. Apart from left and right in all vertebrates – this is most vivid in the duality of things. The visible duality of wave crest and trough containing multiplicity within them drive the engine that heads toward the tranquility of unity and stability.
But an odd number also represents symmetry with the axis running through the middle number. Number 3 is significant in Buddhism and Christianity. Number 5 has been used by many religions. Hindu god Shiva is shown having 5 faces. In Christianity (Jesus Christ, 4 BCE – 33 CE) 5 is a holy number – the Father, Son, Spirit, Creation and Redemption – and many major churches have 5 entry doors (some have 3 doors). Islam (Prophet Muhammad, 570 – 632 CE) has prayer calls 5 times a day. Confucius (551 – 479 BCE) taught 5 virtues required of a good citizen: benevolence, honesty, knowledge, integrity and politeness. The Forbidden City in Beijing has 5 access bridges over the Palace mote.
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In Buddhism, the basic moral code Panchsila has 5 elements. The Mahabodhi Temple having the symmetry of 4 sides and tapering to the Wheel of Law at the apex – is adorned with 5 distinctive bands on each side with the middle band enhanced. I am tempted to spend a little time on this, because the Buddha used the elements of Panchsila to resolve disputes between warring kingdoms – and it inspired the formulation of Panchsheel as an international guideline for peaceful co-existence.
Spearheaded by the Indian independence leader and first Prime Minister J Nehru (1889 – 1964), Panchsheel formed the Sino-India pact (signed in April 1954 by Nehru and the Chinese Premier Z Enlai, 1898 – 1976). The first Non-Aligned Movement conference in April 1955 in Bandung Indonesia adopted Panchsheel as the founding principle. The UN General Assembly adopted Panchsheel in December 1957 as a guiding principle for peaceful co-existence and non-interference among states. Indian capital Delhi bears the name of a park and a road as Panchsheel Park and Panchsheel Marg, respectively.
Beyond scriptural wording, Panchsila meanings can be simply and briefly elaborated as:
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How harmony fits in the paradigm of symmetry and stability? Harmony is integral to both, because it represents concordance or agreement among various components such that the combination is soothing to listen to, or pleasant to look at. A music is in harmony and hears soothing when the melody, rhythm and instrumental notes work in symmetrical unison or synchronicity. In Buddhism, five achievements/accomplishments are identified that are necessary for personal and social harmony:
(1) joy for personal harmony;
(2) mutual respect for harmony in interpersonal relationships;
(3) deference for family life harmony;
(4) cooperation for social harmony; and
(5) peace for world harmony.
For a harmonious conjugal life – the Buddha’s Sigalovada Sutta governs the married couple relationship and deference. The Sutta stands on:
(1) mutuality of love;
(2) mutuality of respect;
(3) mutuality of courtesy;
(4) mutuality of faithfulness;
(5) sharing conjugal authority and responsibility together;
(6) treating relatives and extended family members with hospitality;
(7) taking good care of resources and possessions; and
(8) discharging family duties with skill and industry.
Traditional Buddhist marriage ceremonies are not conducted by monks – instead a respectable elder administers and conducts the ceremony in front of a gathering. The role of Buddhist monks lies only in bestowing blessing to the couple – the chanting of Mahamangala Sutta takes primary position in the blessing processes.
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Symmetry of layouts, arrangements of foliage and flowering plants in proportions and patterns make a garden look beautiful. An architectural piece stands out in beauty and grandeur when symmetry and harmony of proportions in smoothness of flow are integrated – with heeding to the need for aesthetic concordance with the surroundings – Feng Shui – as a new structure is introduced.
In all of these examples, individual components work in a complementary fashion to create the beauty of the whole. Similar can be said of social living – of neighborhoods, of states and countries. If people, families and states are unstable – or are utterly asymmetrical, let us say, in income and wealth distribution – intolerant of one another and mistrustful – such that they cannot complement one another, then harmony is broken dragging everything down to chaos and instability – slowly but definitely. But the processes leading to the achievements of social symmetry and harmony – are far from straight forward. The reason is that – like in waves – when a society becomes corrupt, divisive and mistrustful, the disturbing forces tend to overwhelm the restoring forces – with the enhanced asymmetry having the potential to break social harmony and stability.
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I like to stop at this with a line of wisdom from Tibetan traditional belief (told by Tibetan-Nepalese Buddhist nun, Ani Choying Drolma, 1971 - ): when the stupid speaks, the intelligent learns.
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- by Dr. Dilip K. Barua, 15 January 2019