Thursday May 24, 2018

0 and 1: The undercurrent of computing, mathematics and life

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Yin and Yang in the Daoist philosophy

By Gaurav Sharma

Throughout the annals of history, a wide array of inquisitive people–from dreaming children to logical mathematicians and explorative scientists–have been captivated by 0 and 1 as symbols of existence.

The utility and vitality of the magical numbers encompass variegated fields of workings, ranging from binary code in computer languages to theology and metaphysical precepts of existence or reality.

Intriguingly though, the binary numbers combine a mystical yet practical personage, thereby presenting a paradoxical conundrum permeating the diverse gamut of life.

 Historical Evolution

The binary system (modern) which comprises the binary digits 0 and 1, is believed to have been devised by Gottfried Wilhelm Leibniz, a German polymath and philosopher in 1679. However, the binary system finds a mention in ancient civilizations such as India, China and Egypt as well.

In Egypt, two different systems were used for fractions; the Egyptian fractions (not related to binary system) and the Horus eye fractions. The latter system enabled the expression of fractions into a sum of binary numbers which in turn helped to translate fractional quantities of food-grains and liquids into binary digits. (1200-2500 BCE)

In the 9th Century BC, the I Ching which was a divination text based on the dual forces of yin and yang delineated a binary system comprising of eight trigrams and sixty-four hexagrams. In the lexicographical order, yin represents 0 whereas yan refers to 1.

It would be pertinent to point out that Leibniz was himself deeply inspired by the text when he came in touch with it through his friend Joachim Bouvet.

Around 200 BC, Pingala– an Indian scholar devised a binary system involving the use of short and long syllables–which is strikingly reminiscent of the Morse Code. (Morse Code involves transmission of textual information into a string of lights, clicks and on-off tones, thereby helping differently-abled with an assistive technology in communication)

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Morse Code

Pingala revolutionized the mathematical field of permutations and combinations known as Combinatorics. He answered the fundamental question of how many patterns can be formed from a given number of syllables by enumerating a plausible poetic meter of the syllables. ( Something which we now popularly know as the Pascal Triangle).

Pingala’s work included Fibonacci series ( a series in which each subsequent number is the sum of the previous two, such as  0,1,2,3,5, 8, 13,21….) and his discussion of combinatorics defined what is now the binomial theorem.

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Fibonacci in spiral form

In the 19th Century, Boolean algebra, an algebraic system of logic was introduced by George Boole. The Boolean system also consisted of a binary operation involving a yes-no or an on-off approach. The system was however never put to use.

Highlighting that objects were capable of a twofold difference only, in 1906, Francis Bacon discussed a system of binary coding whereby the letter of the alphabet were reduced to subtle variations in font in the text.

In 1937( almost 100 years since Boolean was introduced), Claude E. Shannon brought to light the use of Boolean algebra in simplifying arrangement of relays, the basic constituents of the electromagnetic automatic telephone exchanges in those days. Shannon was instrumental in proving the efficacy of the binary code in practical applications such as computers, circuits among many others.

To put it succinctly, binary properties of electric switches is the underlying factor for development of electronic digital computer designs. (Telecommunication and computing use binary codes for encoding data)

Spiritual Significance

The concept of 0 and 1 as the unchanging and underlying reality behind the dynamic life process can best be understood through the Chinese philosophy of Yin and Yang.

As per the Daoist way of thinking, Yin and Yang are contrary or dualistic forces which are actually interconnected, complementary and interdependent. This essentially means the lightness and darkness, fire and water, birth and death are complementary phenomena which work in unison to produce a dynamic system in which the whole is greater than the constituent parts.

This can be best understood through the analogy of the seed which grows from the earth towards the sky (yang) and after reaching its pinnacle falls (yin). This illustrates the concept of dependent origination, a penetrating insight which Buddha lucidly described through emptiness or shunyata.

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Shunyata as depicted in Zen buddhism

Dependent origination essentially means that existence is neither real nor unreal but merely a reflection of moon in water or the self in the mirror. A reflection cannot be real because if it were real, transformation could not take place. But since it manifests in the real world, it cannot be outrightly rubbished as unreal also.

Existence, therefore, is not a void or a nothingness but a middle way between eternalism and nihilism.

Buddha’s peerless insight is shared by the Kashmiri Shaivites in the theory of nondual monism, as per which shunya is said to ashunya. In line with the Buddhist thought, the Kashmiri Shaivites do not view shunya as a void but as inherently possessing multiplicity within. ( Zero in Kashmiri Shaivism refers to Shiva or supreme consciousness)

0 and 1 (like the Yin and Yang), can be visualized as a polarity without poles, wherein activity and stillness alternate and are basis of each other. To distinguish and elaborate between the movement of life, dualistic words such as yin and yang, 0 and 1 have been framed but they are essentially part of complete whole which cannot be segregated, just as one cannot point where the neck ends and the head begins.

Yet, the combination of the two forces is the building block of the eclectic forms that we see through the naked eye. This principle of ‘bipolarity without polarity’ is referred to as the cosmic principle or the fundamental order principle.

In summation, life is not an intricate melodrama where everything has a separate, individual existence but rather it is a play of apparently dualistic forces, a dance of cosmic energy and in computing parlance, a combination of 0 and 1 bits.

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  • Manoj Sethi

    When we observe Nature, we find that the Law of Balance operates very subtly everyday or regularly in our lives. We see the ebb and flow of the tide – high and low, the light and dark as in the availability of sunlight and the change of seasons. The significance of 0 and 1 can therefore be understood if we relate it to Nature and its different cycles.

  • Manoj Sethi

    When we observe Nature, we find that the Law of Balance operates very subtly everyday or regularly in our lives. We see the ebb and flow of the tide – high and low, the light and dark as in the availability of sunlight and the change of seasons. The significance of 0 and 1 can therefore be understood if we relate it to Nature and its different cycles.

Next Story

Buddhist Monk Losang Samten Uses Colors to Spread Message of Peace

Samten was born in Tibet. When he was a young boy, his family escaped to Nepal fleeing Chinese Communist control of his homeland. They lived in a refugee camp for years.

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Samten
Former Buddhist monk and Tibetan scholar Losang Samten uses colored sand to build mandalas, circular images filled with complex iconography, which have great meaning in Hinduism and Buddhism. VOA

According to one estimate, there are a 5 quintillion, 5 hundred quadrillion grains of sand on earth, a number so large it must be approaching infinity. This makes sand an appropriate medium for the construction of spiritual images of the universe.

Former Buddhist monk and Tibetan scholar Losang Samten does just that, using colored sand to build mandalas, circular images filled with complex iconography, which have great meaning in Hinduism and Buddhism.

Tibetan monks have created mandalas over the centuries from a variety of materials. Before sand, they used crushed colored stone. Now Samten travels around the world to find sand in various colors. He also dyes sand in watercolors.

Now Samten travels around the world to find sand in various colors. He also dyes sand in watercolors.
Tibetan monks have created mandalas over the centuries from a variety of materials. Before sand, they used crushed colored stone. VOA

Decades of mandalas

Samten, in his mid-60s, learned the craft at the feet of the Dalai Lama.

“When I was a teenager, age of 17,” he told VOA, “I had a privilege to enter His Holiness Dalai Lama’s monastery … in India. I have been studying sand mandalas ever since then. So it’s a long time.”

VOA found Samten painstakingly layering grains of colored sand at the gallery of the Philadelphia Folklore Project. The particular mandala he was working on was the mandala of compassion, or unconditional love.

Far from random designs, mandalas have been perfected over centuries.

“These are uniquely designed many, many, many, many, many years passing to an artist to another artist to another artist to another artist,” Samten said. “The color has a meaning, the shape has different meanings. Not my design; it didn’t come out of my own idea.”

When Samten created a sand mandala at the American Museum of History in New York in 1988 at the request of the Dalai Lama, it was the first time the 2,600-years-old ancient ritual art was seen outside of monasteries. Since then, Samten has made sand mandalas in museums, galleries and universities across the U.S. and many parts of the world.

“They are used to enhance the spiritual practice through image and meditation, to overcome suffering. Mandalas represent enlightened qualities and methods which explain this path, making them very important for the spiritual journey,” Samten wrote on his web site.

Nothing is permanent

Samten was born in Tibet. When he was a young boy, his family escaped to Nepal fleeing Chinese Communist control of his homeland. They lived in a refugee camp for years.

Now Samten travels around the world to find sand in various colors. He also dyes sand in watercolors.
Samten, in his mid-60s, learned the craft at the feet of the Dalai Lama. VOA

“In the winter of 1959, [we] crossed Mount Everest, it took us two months to cross,” he told VOA. “You cannot travel during the day and so scared and not enough food not enough clothes. I was age of 5. I saw, I mean unbelievable dead bodies, people dying without food. I became a monk at age 11 when I was in school, refugee school.”

Samten left monastic life in 1995 and became the spiritual director at the Tibetan Buddhist Center of Philadelphia. He says the patience of the creative process, can lead observers to find calm determination within themselves.

“When I am doing this mandala at universities and schools, many kids came to me, (saying) ‘when I saw you doing the sand mandala, that help me so much to finish my education, patience …’ I have a lot of stories,” he said.

Monk Samten
Samten was born in Tibet. When he was a young boy, his family escaped to Nepal fleeing Chinese Communist control of his homeland. VOA

Beauty comes and goes

After a sand mandala is completed, it is dismantled ceremoniously.

“Dismantle has many different reasons,” Samten said. “… One thing is, dismantle is a beauty, whatever we see as a beauty on the earth, never be everlasting as a beauty and impermanent, impermanent, comes and goes. It’s like a season.”

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Or like sand, ever changing in the wind.

Samten often invites children to participate in the ceremony.

To gallery visitor Traci Chiodress that was part of the charm of the event.

“I think it’s powerful to see something so beautiful created, and then taken apart, and to be done in a community with a group of people of different ages,” she said. “I just think it’s an important type of practice.” (VOA)