Tuesday May 22, 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

Know Your India: How Well Do You Know Hindu Wisdom?

Our rich past must remain our greatest inspiration and inform our engagement with the world

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Hindu wisdom and the broader framework of Eastern philosophy talked in the same language as modern physics was beginning to do. Wikimedia Commons
Hindu wisdom and the broader framework of Eastern philosophy talked in the same language as modern physics was beginning to do. Wikimedia Commons

By Bikash Sarmah

No matter how our self-styled secularists vilify ancient Indian or Hindu wisdom, there is an element of eternity and universality about that treasure trove. It is a great work of reason and analysis. And there is no confusion in the discourse. Such is its universality that the intelligent Westerner woke up to it long ago and discovered the wealth therein. Such is its practicality that when Albert Einstein deconstructed the long-held Newtonian worldview in the early part of the 20th century, and when quantum mechanics from the other side revolutionized the whole course of physics and brought about a paradigm shift in our perception of matter and energy, the founding fathers of the evolving field had already taken resort in Hindu wisdom, and to their utter surprise found that Hindu wisdom and the broader framework of Eastern philosophy talked in the same language as modern physics was beginning to do. And it was not restricted to physics or mathematics alone. Even Western writers and philosophers began to appreciate Hindu wisdom, but not without struggling to comprehend the non-Newtonian Hindu worldview — used as they were to a discrete, Newtonian notion of fundamentalism, both in the material and non-material world.

As an acclaimed physicist and thinker Fritjof Capra says in his classic The Tao of Physics, ‘‘The picture of an interconnected cosmic web which emerges from modern atomic physics has been used extensively in the East to convey the mystical experience of nature. For the Hindus, Brahman is the unifying thread in the cosmic web, the ultimate ground of all being… In Buddhism, the image of the cosmic web plays an even greater role. The core of the Avatamsaka Sutra, one of the main scriptures of Mahayana Buddhism, is the description of the world as a perfect network of mutual relations where all things and events interact with each other in an infinitely complicated way.’’

In Buddhism, the image of the cosmic web plays an even greater role. The core of the Avatamsaka Sutra, one of the main scriptures of Mahayana Buddhism, is the description of the world as a perfect network of mutual relations where all things and events interact with each other in an infinitely complicated way.’’ Says Fritjof Capra. Wikimedia Commons
In Buddhism, the image of the cosmic web plays an even greater role. The core of the Avatamsaka Sutra, one of the main scriptures of Mahayana Buddhism, is the description of the world as a perfect network of mutual relations where all things and events interact with each other in an infinitely complicated way.’’ Says Fritjof Capra. Wikimedia Commons

ALSO READ: Future of Hinduism in US: An Analysis

Such worldview brings a lot of discomfort to the typical Western mind brought up in a culture that emphasizes only rigid fundamentals and overlooks the varied possibilities beyond the confinement of fundamentals, unlike in the Hindu system that rejects such fundamentalism and espouses a notion of the world, both material and spiritual, that jells wonderfully with the implications of the theories of modern physics. But how well is this known? It is in this context that a compilation of Western thoughts on India and its ancient wisdom, titled ‘Great minds on India’ compiled by Salil Gewali and published by Academic Publications, Shillong, is pertinent. It captures the best of comments by Western intellectual giants on Hindu wisdom and its timelessness, reflecting also on the parallels between modern physics and Hindu wisdom. Let us hear some of them. Werner Heisenberg, one of the founders of quantum mechanics and celebrated for his epoch-making Uncertainty Principle in quantum mechanics that rejects the Newtonian assertion of predicting the position and momentum of matter simultaneously, glorifies Hindu wisdom thus:

‘‘After the conversations about Indian philosophy, some of the ideas of quantum physics that had seemed so crazy suddenly made much more sense.’’ If Einstein says that ‘‘we owe a lot to Indians who taught us how to count, without which no worthwhile scientific discovery could be made’’, Julius R Oppenheimer, the father of nuclear bomb, goes further: ‘‘What we shall find in modern physics is an exemplification, an encouragement and a refinement of old Hindu wisdom.’’

‘‘Indian philosophers’ subtleties make most of the great European philosophers look like schoolboys.’’ Says TS Eliot. Wikimedia Commons
‘‘Indian philosophers’ subtleties make most of the great European philosophers look like schoolboys.’’ Says TS Eliot. Wikimedia Commons

Coming to TS Eliot, who needs no introduction. He says: ‘‘Indian philosophers’ subtleties make most of the great European philosophers look like schoolboys.’’ What Eliot means, in other words, is that when it comes to subtlety — that is, to the delicate refinement of ideas — most of the great European philosophers should rather be huddled in a classroom with an Indian philosopher teaching and guiding them. That is why Francois M Voltaire, one of the greatest French writers and philosophers, admits thus: ‘‘I am convinced that everything has come down to us from the banks of the Ganga — astronomy, astrology, spiritualism etc. It is very important to note that some 2,500 years ago at the least Pythagoras went from Samos to the Ganga to learn geometry… But he would certainly not have undertaken such a strange journey had the reputation of the Brahmins’ science not been long established in Europe.’’ And that is why Ralph Waldo Emerson, great American author, and essayist, confesses to having been ‘‘haunted’’ by the Vedas. ‘‘In them (the Vedas),’’ Emerson says, ‘‘I have found eternal compensation, unfathomable power, unbroken peace.’’ And hence the candor, again, of Arthur Schopenhauer, one of the greatest German philosophers and writers: ‘‘In the whole world there is no study so beneficial and so elevating as that of the Upanishads. It has been the solace of my life, and it will be the solace of my death. They are the product of the highest wisdom.’’

ALSO READ: Hindu Americans are role models for Hindus in India: Dr. David Frawley

Perhaps the best eulogy for India, as it truly deserves, has come from Frederich von Schlegel, acclaimed German writer, critic, philosopher, and one of the founders of German Romanticism: ‘‘There is no language in the world, even Greek, which has the clarity and the philosophical precision of Sanskrit, and this great India is not only at the origin of everything, she is (also) superior in everything, intellectually, religiously or politically, and even the Greek heritage seems pale in comparison.’’

The booklet, ‘Eat minds on India’, is doubtless a unique venture, and the publishers deserve kudos for having accomplished such an onerous task as to compile comments on India and Hindu wisdom by a galaxy of Western intellectual giants and then to choose the best and the most relevant ones. The tragedy, however, remains: a pseudo-secular dispensation as we are blessed with at the Centre would hardly initiate any move to popularize ancient Indian wisdom, which is essentially Hindu, and call upon the youth of the country to rediscover their past and marvel at the sheer effulgence of Hindu wisdom — stemming not from any dogmatic, fundamentalist and conditioned worldview, but from a holistic way of life and its liberating experience. This is so because the word ‘‘Hindu’’ will invariably echo in any discourse on ancient Indian wisdom and the country’s perverse, self-styled secularists will discover a ‘communal’ agenda there — ‘against our pluralist ethos’. These poor souls do not realize — nor do they want to — that whatever pluralist ethos the country today takes pride in and will sustain for all times is due solely to the Hindu way of life, a preponderant way of life in India. Why, look at how the other by-product of Partition, including Bangladesh, has evolved.

Our rich past must remain our greatest inspiration and inform our engagement with the world. Even quantum mechanics and all of its later avatars recognize that fact of life. Let us all be proud of it all.

(The writer is the former consultant Editor of ‘The Sentinel’, a Guwahati-based
daily. He currently resides in Guwahati)