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

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)

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.

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.

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.